Sedimentary Structures: v. 2: Their Character and Physical Basis (Developments in Sedimentology)

DEVELOPMENTS IN SEDIMENTOLOGY 30B SEDlMENTARY STRUCTURES THEIR CHARACTER AND PHYSICAL BASIS VOLUME II FURTHER TITLE...

Author: John R.L. Allen

48 downloads 740 Views 42MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!

Report copyright / DMCA form

DEVELOPMENTS IN SEDIMENTOLOGY 30B

SEDlMENTARY STRUCTURES THEIR CHARACTER AND PHYSICAL BASIS

VOLUME II

FURTHER TITLES IN THIS SERIES VOLUMES 1 , 2, 3, 5, 8 and 9 are out of print 4 F.G. T I C K E L L THE TECHNIQUES O F SEDIMENTARY MINERALOGY 6 L. V A N D E R P L A S THE IDENTIFICATION O F DETRITAL FELDSPARS S. D Z U L Y N S K I and E.K. W A L T O N I SEDIMENTARY FEATURES O F FLYSCH AND GREYWACKES 1 0 P.McL.D. DUFF, A. H A L L A M and E.K. W A L T O N CYCLIC SEDIMENTATION 11 C.C. R E E V E S Jr. INTRODUCTION T O PALEOLIMNOLOGY 1 2 R.G.C. B A T H U R S T CARBONATE SEDIMENTS AND THEIR DIAGENESIS 13 A.A. M A N T E N SILURIAN REEFS O F GOTLAND 1 4 K. W. G L E N N I E DESERT SEDIMENTARY ENVIRONMENTS 1 5 C.E. W E A V E R and L.D. P O L L A R D THE CHEMISTRY O F CLAY MINERALS 1 6 H.H. RIEKE 111 and G.V. C H I L I N G A R I A N COMPACTION O F ARGILLACEOUS SEDIMENTS 11 M.D. PICARD and L.R. HIGH Jr. SEDIMENTARY STRUCTURES O F EPHEMERAL STREAMS 18 G.V. C H I L I N G A R I A N and K.H. W O L F COMPACTION O F COARSE-GRAINED SEDIMENTS 19 W. S C H W A R Z A C H E R SEDIMENTATION MODELS AND QUANTITATIVE STRATIGRAPHY M.R. W A L T E R , Editor 20 STROM ATOLITES 21 B. V E L D E CLAYS AND CLAY MINERALS IN NATURAL AND SYNTHETIC SYSTEMS 22 C.E. W E A V E R and K.C. BECK MIOCENE OF THE SOUTHEASTERN UNITED STATES 23 B.C. HEEZEN, Editor INFLUENCE O F ABYSSAL CIRCULATION ON SEDIMENTARY ACCUMULATIONS IN SPACE AND TIME 24 R.E. GRIM and N . G U V E N BENTONITES 25A G. L A R S E N and G.V. C H I L I N G A R I A N , Editors DIAGENESIS IN SEDIMENTS AND SEDIMENTARY ROCKS 26 T. SUDO and S. SHIMODA, Editors CLAYS AND CLAY MINERALS O F JAPAN 21 M.M. M O R T L A N D and V.C. F A R M E R INTERNATIONAL CLAY CONFERENCE 1 9 1 8 28 A. NISSENBAUM, Editor HYPERSALINE BRINES AND EVAPORITIC ENVIRONMENTS 29 P . T U R N E R CONTINENTAL RED BEDS T. SUDO, S. SHIMODA, H . Y O T S U M O T O and S. A I T A 31 ELECTRON MICROGRAPHS O F CLAY MINERALS 32 C.A. N I T T R O U E R . Editor SEDIMENTARY DYNAMICS O F CONTINENTAL SHELVES

DEVELOPMENTS IN SEDIMENTOLOGY 30B

SEDIMENTARY STR UCTUR ES THEIR CHARACTER AND PHYSICAL BASIS VOLUME II

JOHN R m L m ALLEN, F.R.S. Professor o f Geology, University of Reading, England

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Amsterdam - Oxford - New York 1982

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Molenwerf 1, P.O. Box 211,1000AE Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER/NORTH-HOLLAND INC. 52,Vanderbilt Avenue New York, N.Y. 10017

L i b r a r y of Congress Calaloging i n Publiralinn D a l a

Allen, John R. L. Sedimentary structures. (Developments in sedimentology ; 30A-30B) Includes bibliographies and index. 1. Sedimentary structures. 'I. Title. 11. Series. &E472.A44 551.3'05 81-12561 ISBN

ISBN

0-444-41935-7(v. 0-444-41945 -4 ( v .

30A) 30B)

MCR2

ISBN 0-444-41945-4 (Vol. 30B) ISBN 0-444-41238-7 (Series) Elsevier Scientific Publishing Company, 1982 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, P.O. Box 330, 1000 AH Amsterdam, The Netherlands 0

Printed in The Netherlands

V

INTRODUCTION TO VOLUME I1 As the General Preface accompanying Volume I contains an introduction to the work as a whole, it is only necessary for me here to outline the scope of the second volume. Volume I1 is about sedimentary structures found in relatively complex physical settings, where groupings or hierarchies of features are often of most interest, and more emphasis is placed than in the first volume on cohesive as opposed to cohesionless beds. Secondary currents can exist for a number of reasons in boundary-layer flows, giving rise to flow-parallel sedimentary structures on both kinds of bed. A type of secondary flow arises where river or tidal streams occupy curved channels, with the result that definite vertical and horizontal sequences of sedimentary structures are formed. Flow separation is a phenomenon associated with several kinds of sandy bedform and has a significant though not yet completely understood influence on sedimentation to their lee. Closely related physically is the upward-acting two-phase jet, deposition from which gives rise to sand volcanoes. Separated and secondary flows combined in complex and unpredictable ways are called into being by objects placed on the boundary of a flow. The result is local patterns of scour and deposition expressed as current crescents or drifts. Flute marks in mud beds, and Kurren on limestone and other soluble or partly soluble rock surfaces, record a process of mass transfer in which flow separation in certain instances plays a decisive role. An important group of sedimentary structures-soft-sediment deformations -arise shortly after (sometimes during) deposition, and reflected the deformable nature of freshly accumulated sediment, once a liquid-like state has been created through either liquefaction or fluidization. Distinctive combinations of sedimentary structures, representing complex and not yet fully understood phenomena, form when gravity currents transport sediment over the ocean floor or the slopes of a volcano. The littoral zone, where wind-waves interacting with the bottom are the dominant agent, provides another complex and only partly known setting for a Yariety of structures. The possible importance of storm-related currents in forming a species of graded bedding in shallow-marine sediments is attested by the increasing number of claims from workers in the stratigraphic record. However, as the sedimentological aspects of storms have been little studied, as opposed to their engineering implications, an important and potentially fruitful field of enquiry lies open. The final chapter in Volume I1 is essentially a miscellany, in which a variety of unrelated themes are pursued. Here can be found accounts of, for example, tool marks, adhesion ripples, mud waves, shrinkage cracks and ptygmatic folds. Reading, May 1980

J.R.L. ALLEN

This Page Intentionally Left Blank

VII

CONTENTS

INTRODUCTION T O VOLUME I1

....................................

Chupter 1. LONGITUDINAL BEDFORMS A N D SECONDARY FLOWS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General character and effects of secondary flows . . . . . . . . . . . . . . . . . . . . . . . . . . . Causes of secondary flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instability of a fluid in axisymmetric motion . . . .................... Inflectional instability of a rotating fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Asymmetry of flow boundaries (turbulent flow) . . . . . . . . . . . . . . . . . . . . . . . . . Superposed “immiscible” fluids of contrasted density . . . . . . . . . . . ... Thermal convection in a sheared fluid ............................ Langmuir circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... Sand ribbons in aqueous currents . ................................ ..................... O n smooth beds in streams . . . . . . . . . . . . . s ............... On rough beds in streams and beneath ebbing t Sand ribbons in the marine environment . . . . . . . . . . . . . . . . . . . . . . . . . . . ........... Sand ribbons on continuous beds . . . . . . . . . . . . . . . . Fossil record . . ....... ................................ Sand ribbons in aeol ronments ............................... Erosional grooves and ridges . . . . . . . . . . . . . . . . . . . . . . . . . . ............ River and related aqueous environments . . ... ............... Tidal environments . Deep-sea environments . . . . . . . Deserts . . . . . . . . . . . . . . . . . . . Longitudinal desert dunes . . . . . . . . Tidal current ridges . . . . . . ............. Ridge-and- furrow moulds . . . . . . . . Wave-related furrows and ridges . . . . . . . . . . . . . . ............. Wave-related gravel stripes . . . . . . . . . . . . . . Spur-and-groove . . . . . . . . . . . . . . . . . . . . . ................. Glacial flutings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trough banding in layered igneous roc ........... Summary . . . . . . . . . . . . . . . . . . . . . . . .

V

I 2 5 5 7 8

13 17 17

21 23 23 24 25

43 47

52

Chupter 2. FREE MEANDERING CHANNELS A N D LATERAL DEPOSITS

................ Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluvial and tidal meanders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Meander settings . . . . . .... ................... Analysis and description .... ................... Hydromorphological relationships . . . . . . . . . . . . . . . . . . . . . . . . Flow processes in meanders and channel bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . Superelevation of the water surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... ............................ Secondary flow . . ryflow . . . . . . . . . . . . . . . Laboratory and field ns o Theories of meandering ....... ........ .................. Sedimentation processes in meanders and channel bends . . . . . . . . . . . .

53

71 71 72 79

VIII Sediment particle equilibrium on a point bar . . . . . . . . . . . . . . . . . . . . . . . . . . . Transverse shape of point bars and meandering channels . . . . . . . . . . . . . . . . . . . Processes and rates of meander growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evolution of meander loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grain size and bedform on point bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lateral accretion structures and deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80 83 86 88 91 94 100

Chupfer 3. AN OUTLINE O F FLOW SEPARATION 101 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Separation in internal and external flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Streamline mappings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 Rollers and vortices: closed and open separation . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Separation in two dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Externalflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 107 C a v i t y f l o w s . . . . . . . . . . . . . . .. .. .. .. .. ........... .. .. .. .. .. .. . . . . . . . . . . .. .. .. .. .. .. ... 1 0 7 107 S t e p s a n d w a l l s. . . . . .. ..... .. . . .. ..... .. . . . ..... .. . . . .. ..... . . . .. ..... .. . . .. ..... .. . . .. ... . 1109 09 Axisymmetric flows .. ....................................... 114 Separation in three dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 ................... ...................... 114 External flows 107 C a v i t y f l o w s . . . .. .. ......... .. .. .. .. .. .. . . . . . . . . . .. .. .. .. .. ........... .. .. .. .. .. . . . . . . . . 1 0 7 115 Steps and related shapes . . . . . . . . . . . . . . . . . .................... 116 Pressure and stress in low-speed separated flows . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Distribution of temporal mean values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Pressure fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Vortex-production and turbulence in low-speed separated flows . . . . . . . . . . . . . . . . 121 Rolling up of a free shear layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 125 Velocity fluctuations and Reynolds stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow separation at high speeds . . ................................. 127 128 Axisymmetric turbulent jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Chupprer 4. SEDIMENTATION FROM JETS A N D SEPARATED FLOWS ............................................... Introduction . . Particle free falling velocity in the presence of turbulence ..................... Sedimentation from jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sand volcanoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sedimentation from separated flows with normal gravity . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grain size and concentration in the approaching boundary layer . . . . . . . . . . . . . . Grain dispersal beyond the crest of the bed feature . . . . . . . . . . . . . . . . . . . . . . . Avalanching in the lee of ripples. dunes. bars and deltas . . . . . . . . . . . . . . . . . . . Grading in avalanche deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sedimentation in the far lee: shell-pebble lags and ripple fans . . . . . . . . . . . . . . . . . . Geometry and structure of lee-side deposits . . . . . . ............ ..... Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

133 134 135 137 141 141 142 143 148 152 158 168 171

Chuprer 5. FLOW A R O U N D A BLUFF BODY: OBSTACLE MARKS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General features of bluff-body flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-dimensional flow past a bluff body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-dimensional flow past a surface-mounted impermeable bluff body . . . . . . . . .

173 174 174 174

IX Two-dimensional flow past a surface-mounted permeable body . . . . . . . . . . . . . . Surface-mounted bluff bodies in oscillatory and rotary flows . . . . . . . . . . . . . . . . Biuff bodies in planetary boundary layers . . . . . . . . . . . . . . . . . . . . General implications for sedimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Controls on the character of obstacle marks . . . . . . . . . . . . . . . . . . . . . Current crescents in aeolian environments . . . . . . . . . . . . Current crescents in aqueous environments . . . . . . . . ...... River and shallow tidal flows . . . . . . . . . . . . . . . . . . . Sand beaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tidal seas and the deep ocean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current shadows in aeolian environments . . . . . ........................ . Impermeable bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Permeable obstacles . . . . . . . . . . . . . . . . . . . ....................... Current shadows in aqueous environments . . . . . ....................... Scour-remnant ridges . ....................................... ......................... Scour features in comple ts Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

194 194 197 197 197 200 200 203 205

Chuppter 6. HEAT A N D MASS TRANSFER: ICE DUNES. KARREN. A N D RELATED FORMS ........... Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Regimes and mechanisms of heat and mass transfer . . . . . . . . . . . ......... ......... Controls on heat and mass transfer . . . . . . . . . . . . . . . . . . . . . . . . Coefficients and parameters . . ................................. Analogy between momentum, heat and transfer . . . . . . . . . . . . . . . . . . . . . . . . . Laminar boundary layer on a flat surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbulent boundary layer on a flat surface . . . . . . . . . . . . .............. Laminar flow in a conduit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................ Turbulent flow in a conduit . . . . . . . . Free convection . . . . . . . . . . . . . . . . . ............................ Heat and mass transfer in separated low-speed flows . . . . . . . . . . . . . . . . . . . . . . . . .......................... Heat and mass transfer in high-speed flows . . Instabilities accompanying mass or heat-with-mass transfer . . . . . . . . . . . . . . . . . . . ... .................... Classification of Kurren . . . . . . . . . . . . First-order Kurren . . . . . . . . . . . . . . . . .......................... Fhhkurren . . . . . . .... .................................. Kluftkurren . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spitzkurren ................................................ ................. Second-order Kurren . . . . . . . . . . . . . . . Solution basins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trittkurren . . . . . . . . . ...... ..................... Rillenkurren . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rinnenkurren . . . . . . . . . . . . . . . . . .. .. ............. Rundkurren . . . . ........................................ Miiunderkurren and related forms . . . . . . . . . . . . . . . . . . . ......... Roofpendants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cockling . . . . . . . . . . . ..... ................. Transverse Kurren and re1 ............................. Cave flutes and scallops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Iceripples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution ripples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dirt polygons . . . ........ ............................

207 208 210 210 213 214 214 215 215 216 217 218 219 222 224 224 226 228 230 230 233 233 235 235 238 240 241 242 242 245 246 249

i80 181

182 183

191

Structures related to high-speed flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-hatching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ring waves on tektites and meteorites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pits (regmaglypts) on meteorites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

249 249 250 250 251

Chuppter 7. FLUTE MARKS. M U D RIPPLES. S I C H E L W A N N E N AND POTHOLES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flute marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parabolic flute marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spindle-shaped flute marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........... Comet-shaped flute marks . . . . . . . . . . . . . . . . . Asymmetrical flutc marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Patterns of flute marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mud ripples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................... Potholes . . . . . . . . . . . Sichelwunnen . . . . . . . . ................................... Origin of flute marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two pertinent observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An elementary theory of flute marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....................................... Mass-transfer analogy . Flute marks on mud beds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A model for flute marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Origin of mud ripples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Origin of potholes . .. ......................................

253 253 253 255 257 258 259 259 259 261 264 267 267 268 272 277 281 286 288

Origin of Sichelwannen........................................... 289 Summary ....... ............................... 290

.

Chuppter 8. LIQUIDIZATION. LIQUIDIZED SEDIMENT AND T H E SEDIMENTATION O F DENSE PARTICLE DISPERSIONS Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................. Varieties of liquefaction . . . . . . . . . . . . ................. Static liquefaction . . . . . . . . . . . . . . . . Dynamic and cyclic liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General effects of earthquakes and related disturbances . . . . . . . . . . . . . . . . . . . . Laboratory studies of cyclic liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Factors influencing cyclic liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimation of liquefaction potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Varieties of fluidization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stationary fluidization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Regimes of fluidization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minimum fluidization velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bedexpansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .............. ............ Polydisperse systems . . . . . . . . . . . Bulk self-fluidization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................... Grain self- fluidization . . . . . . . . . . ............................... Apparent viscosity of liquidized sedime Controls and means of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Non-fluidized dispersions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................ Fluidized beds . .

293 295 296 298 298 300 302 304 305 306 306 310 312 314 315 317 321 321 321 325

XI Sedimentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monodisperse systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polydisperse systems . . ................................... Graded systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluidization after liquefaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chuppter 9. SOFT-SEDIMENT DEFORMATION STRUCTURES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kinematics and dynamics of soft-sediment deformation . . . . . . . . . . . . . . . . . . . . . . Classification of soft-sediment deformation structures . . . . . . . . . . . . . . . . . . . . . . . Deformation structures related to gravitationally unstable vertical profiles of bulk density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convolute lamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loadcasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pseudo-nodules and ball-and-pillow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heavy mineral sags and drops . . . . . . . . . . . . . . ............ Deformation involving an ephemeral layer: passively deformed beds . . . . . . . . . . . Deformation involving an ephemeral layer: dish structures . . . . . . . . . . . . . . . . . . Deformation structures related to non-uniform confining loads . . . . . . . . . . . . . . . . . Load-casted ripple marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Folds related to the lateral spread of sand mounds . . . . . . . . . . . . . . . . . . . . . . . Deformation structures related to a downslope b force component . . . . . . . . . . . . Sheet slumps formed from multilayers . . . . ......................... Deformed cross-bedding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deformed cross-bedding related to fluid drag . . . . . . . . . . . . . . . . . . . . . . . . Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interpretation of simple deformed cross-bedding . . . . . . . . . . . . . . . . . . . . . . . . Interpretation of more complex forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . ..... ............................... Chupprer f0. STRUCTURES A N D SEQUENCES RELATED T O GRAVITYCURRENT SURGES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... Dissipation of gravity-current surges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Turbidites and the Bouma sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical patterns . . . . ........ .......................... Patterns in the direction .................................... Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pyroclastic flow. ground surge and base surge deposits . . ............. Extent and grading . . . . . . . . . . . . . . . . . . . . . . . . ............. Radial grooves . ............................................ Plane beds and par 1 stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . Sand waves and cross-bedding . . . . . ............................ Other structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . .... ........................ Chuprer If . COASTAL SAND BARS A N D RELATED STRUCTURES Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Morphology of the barred beach and nearby offshore . . . . . . . . . . . . . . . . . . . . . . . Longshore bars and troughs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

327 327 330 334 337 340 341

343 344 348 340 349 354 350 364 366 367 375 375 378 380 380

389 392 393

395 396 401 401 405 412 417 417 419 422 431

433 434 435

XI1

....... Form and behaviour . . . . . . . . . . . . . . . . . . . . . . . . . Controls on longshore bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minor sedimentary structures associated with longshore bars and troughs . . . . . . . . . Intertidal bars and troughs . . . . . . . . . . . . . . . . . . . ......... Submerged bars and troughs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transverse bars . . . . . . . . . . . . . . . . . . . ................... Beachcusps . . . . ........................... Character and d ......................

435 440 446 446 450 452 453 453 C o n t r o l s o n b e a c h c u p s . . . . . . . . . . . . . . . . . . . . . . 455 . 457 Theories of beach cusps . . . . . . . . . . . . . . . . . . . . . . . 460 Internal structure of beach cusps . . . . . . . . . . . . . . . . . . . . . . . . . . 461 Beach lamination . . . . . . . . . . . . . . . . . . . . . . . . . ..... .. 461 Morphological and dynamical background . . . . . . . . . . . . . . . . . . . . 462 Effects on the scale of waves . . . ...... ............ 464 Effects on the tidal scale . . . . . . . . . . . . . . . . . . . . . . . ..... 466 Effects on a storm or seasonal time-scale . . . . . . . . . . . . . . . . . . . . . 468 ........... Beach lamination in the stratigraphic record 469 Summary . .......................................

Chupter 12. STORM SEQUENCES IN SHALLOW WATER Introduction ............................ . Two-dimension wind effects .... .......... Wind set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .... Currents associated with the set-up . . . . . . . . . . . . . . . . . . . . . . . . ... Natural surges and wind-induced currents . .......... Complex models of wind effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dependence of wind stress on wind speed . ............... A model of storm sedimentation in shallow waters . . . . . . . . . . . . . . . Qualitative description . . . . . . . . . . . . . . . . . . . ..... Aspects of a quantitative model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Storm sand-layers in modern sedimentary environments . . . . . . . . . . . Storm sand-layers in the stratigraphic record . . . . . . . . . . . . . . . . . . . . Description of examples . . . . . . . . .... ............ Comparison with the model . . . . . . . . . . . . . . . . . . . . Summary . ............................ Chupprer 13. MISCELLANEOUS SEDIMENTARY STRUCTURES ............................ Introduction Rill marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......... Toolmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General . . . . . . . ... ................. Drag marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roll marks ............................ Prod marks . . . . . . . . . . . . . . . . . . ... Tumble marks ............................ Skim marks . . . . . . . . . . . . . . . . . .................... Marks related to near-approaches . . . . . . . . . . . . . . . . . . . . . . . . . Mechanics of tool marks . . . . . . . . . . . . . . . . . . ......... Scratch circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corrasion beneath the wind . . . . . ................ Swash and foam marks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adhesion and rain-impact ripple marks . . . . . . . . . . . . . . . . . . . . . . .

471 472 472 477 481 483 485 487 487 491 493 496 496 504 505

507 509 509 511 516

525 529

XI11 Cavernous sand. sand holes. and sand domes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mud waves on the deep-ocean floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distribution and character . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Origins of mud waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shrinkage cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Character and distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanics and controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sheet-like sedimentary intrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ptygmatic folds in desiccation-crack infills and sedimentary dykes . . . . . . . . . . . . . .

535 538 538 541 544 544 550 554 556

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

561

...............................

645

SUBJECT INDEX (for Volumes I and 11)

This Page Intentionally Left Blank

1

Chapter 1 LONGITUDINAL BEDFORMS AND SECONDARY FLOWS INTRODUCTION

With the exception of parting lineation and its relatives, the bedforms discussed in Volume I all have a dominant flow-transverse orientation; many of these, for example, dunes and trochoidal wave ripples, are associated with interactive separated flows. There are other bedforms elongated parallel with the mean motion, including longitudinal desert dunes, sand ribbons on sea and river beds, and various linear forms apparently dependent on wave-action at the strand. These longitudinal features all seem explicable in terms of secondary flow, that is, the motion in which a transverse circulation is superimposed on the primary longitudinal flow of the fluid, the streamlines assuming a corkscrew form (Vol. I, Chapter 1). So long as the mean motion remains stable over time, the secondary flow is itself stable and independent of time. Typically, the spiral currents occur in pairs; a longitudinally oriented cell of fluid (roll or vortex) with an internal circulation in one sense is juxtaposed with a parallel cell in which the circulation is oppositely directed. Since we are concerned with explaining a category of bedforms in terms of these vortices, each group of cells must be bordered on at least one side by a stationary boundary. On the bed there must be lines parallel with the mean flow along which streamlines separate from the bed, and other lines, also flow-parallel, along which streamlines reattach themselves. Finally, if the current is divided into more than one pair of cells, the separation and reattachment lines must alternate transversely across the flow. Evidently secondary flows share some kinematic features with the separated flows induced by flow-transverse bedforms. Secondary flows, however, do not invariably require changes of longitudinal bed slope for their formation. Many of the bedforms coupled with secondary flows are merely visualizations of flow structures having an independent origin. The same cannot be said of transverse bedforms, the character of which in large part depends on strong interactions between flow, bed shape, and bed material. That many secondary flows are independent of bed material and shape is further emphasized by the wider range of circumstances under which longitudinal bedforms are found. They appear on beds composed wholly of cohesionless sediment, on surfaces partly cohesive and partly cohesionless, and on boundaries wholly formed of cohesive material such as rock or stiff mud. The transverse features discussed above can only arise where cohesionless sediment is available in large amounts. Secondary flow has many causes, ranging from the effects of channel

2

curvature or side walls, to the combination of horizontal shear with density instability, to complex wave phenomena. The consequent flow patterns are rather similar and, at present, it is rarely possible to infer the fundamental cause from the characteristics of the forms themselves. The context often yields the most useful clues.

GENERAL CHARACTER AND EFFECTS OF SECONDARY FLOWS

Figure 1-1 shows the kinematic structure of a typical secondary flow, as developed above a flat surface in a steady uniform rectilinear boundary-layer flow. Vortices in which the circulation is to the right of an observer looking downstream alternate transversely with those in which the circulation is to the left. Longitudinal separation lines occur where the limiting streamlines converge, and reattachment lines where they diverge. Reattachment and separation lines alternate transversely at a regular spacing, the transverse distance between any two consecutive lines of each type defining the characteristic vortex wavelength, usually about twice the vortex thickness or width. The fluid in each vortex cell follows a spiral path, of a pitch measured at the cell boundaries commonly 50-150 times the cell width or thickness. Hence the deviaton angle S of a limiting streamline from the direction of the mean flow (Fig. 1-1) may be no more than 10-15" at its greatest, and in some cases much less. Vertically above each separation line, where the fluid ascends from the bed, the streamwise velocity component increases relatively gradually away from the boundary. The boundary shear stress along separa-

Fig. 1 - 1 . General character of a boundary layer with secondary flow.

3

tion lines is therefore less than average on the bed. Where the fluid is descending towards reattachment lines, the velocity gradient is relatively steep and the boundary shear stress exceeds the average. At stations between separation and attachment lines, the boundary shear stress T~ tangential to a limiting streamline can be resolved into a downstream component T~ and a transverse component T ~ .Generally r2 is at most a small fraction of T~ and, similarly, the transverse component of velocity within the vortex is seldom comparable with the streamwise value. The ratios of these components mid-way between separation and reattachment lines are measures of the strength of a secondary flow. The sedimentological implications of this motion (Fig. 1-1) may be analysed in terms of at least three idealized cases, distinguished by the amount of cohesionless sediment transportable as bedload available to the flow and the properties of the boundary supporting this load. These cases are: (1) cohesionless sediment small in amount and boundary undeformable, (2) entire boundary underlain by cohesionless sediment, and (3) cohesionless sediment small in amount but boundary deformable as the result of corra-

Fig. 1-2. Implications of secondary flow for sediment transport and transfer. a. Bed material drifted in small quantity 0ver.a rigid surface. b. Effect of secondary flow on a continuous mobile sand bed. c. Effect of secondary flow carrying a,moderate quantity of bed material over a cohesive deformable surface. d. Effect of secondary flow carrying a small amount of bed material over a cohesive deformable surface.

4

sion, fluid stressing, or plastic flow under the action of the flow forces. In the first (Fig. 1-2a), longitudinal bands of sediment should accumulate along separation lines, leaving clear lanes along the reattachment lines between, the band spacing or wavelength equalling the wavelength of the secondary flow. In justification, we can see from Fig. 1-1 that the transverse component T~ of the bed shear stress, where non-zero, is everywhere directed towards the nearest separation line. Hence any bedload particle which strays near a reattachment line will be gradually directed towards the nearest separation line, along which it will subsequently tend to move. Provided that the amount of sediment available is not too small, the bands should be low ridges with either cusped or rounded crests. The ridges may be either smooth or show superimposed transverse bedforms, depending on flow strength, sediment coarseness, and flow scale. Longitudinal ridges and furrows may also be expected in the second case, their transverse spacing again equalling the wavelength of the secondary flow (Fig. 1-2b). A ridge should occur beneath each separation zone, for the reason that the transverse component of the bed shear stress is directed towards such a zone, counteracting the tendency of the downstream-moving debris to roll under gravity into the intervening troughs. But the ridges will grow and steepen only for so long as the transverse fluid force acting upslope on each moving grain exceeds the transverse downslope component of the particle immersed weight. A limiting or equilibrium side-slope will exist only when these forces balance, the grain paths then being parallel with the ridge crests and trough axes. The equilibrium relationship between the local transverse slope-angle p of the ridges and the deviation angle 6 of the limiting streamlines (Fig. 1-2b) may be found from an analysis of particle-equilibrium in river bends (Van Bendegom, 1947; NEDECO, 1959; Allen, 1970b, 1970c), to be studied further in Chapter 2. Equating the fluid and weight forces, we find that: 37, sin 6 sin p = -P

k

in which T, is the bed shear stress tangential to a limiting streamline, D is the sediment particle diameter (assumed spherical), (I and p are the particle and fluid densities respectively, and g is the acceleration due to gravity. The side slope therefore increases with the strength of the mean flow and with the strength (inversely proportional to the pitch) of the secondary flow, but decreases with increasing particle size and relative density. Since the deviation angle is generally small, T~ may be replaced for rough calculations by its streamwise component rx as given by some suitable relationship (Vol. I, Chapter 1). Even with a fully developed sediment transport, the small magnitude of the deviation angle makes it unlikely that sin p will exceed the order of 0.1. The third case is more complex, dividing into at least two. Consider first

5

what happens when the debris supplied is insufficient to cover the whole bed but succeeds in forming longitudinally continuous ridges at separation lines (Fig. 1-2c). The stationary grains in the ridges protect the potentially deformable bed immediately beneath, leaving exposed to erosion only the surface in the zones of reattachment. Hence the bedform should comprise longitudinal furrows corresponding to reattachment, separated by ridges with but a capping of grains. A similar result would be obtained if the flow were sufficiently vigorous that the transported grains remained in suspension, or if the fluid were free from dispersed sediment and the flow was powerful enough to effect a direct erosion or plastic deformation of the bed. Secondly, consider the case when the available sediment is insufficient to afford a continuous grain-cover even along separation lines (Fig. 1-2d). If the mode of erosion is corrasion, the rate must be greatest along the separation zones, because the areal concentration of grains moving at the bed is here a maximum. The furrows now develop where there is separation, with ridges corresponding to reattachment. How might sedentary organisms such as corals and encrusting algae respond to an environment marked by a pattern of secondary flow? Their growth rate could be smaller at reattachment than at separation, because of the greater damage to tissues likely to arise in reattachment zones on account of the larger velocities and stresses there present. If loose debris was available, however, growth could be inhibited most near separation, on account of the increased likelihood of tissue-damage through the action of rolling particles. Alternatively, differential growth could result from the control by the secondary currents of the local food or nutrient supply. If the food originated near the water surface, for example, organisms living on the bottom near reattachment could by feeding impoverish those living further along the path of the circulating fluid. These mechanisms yield different end-products, with ridges either at attachment or separation, but they may help to explain those longitudinal bedforms that involve living algae and corals.

CAUSES OF SECONDARY FLOW

Instability of a fluid in axisymmetric motion A very simple type of instability leading to secondary flow is shown by a fluid rotating about a rectilinear axis, whenever the balance between the centrifugal force and the radial pressure gradient is suitably disturbed. The criterion for stability, established from different standpoints (Lord Rayleigh, 1916a; Synge, 1933, 1938; Von Karman, 1934), is that the square of the circulation K of the fluid should increase monotonically outward from the axis of rotation. We define the circulation as K = Ur, where U is the

6

circulatory speed of a fluid element at a radial distance Y from the axis of rotation. A necessary condition for instability, then, is that the streamline curvature is concave in the direction of increasing flow speed. I t follows that for neutral stability K ( r )= const, whence U ( r ) cannot be too steeply decreasing a function. Von Karman’s explanation of the instability proceeds essentially as follows. If a ring of fluid at Y, is displaced outward to r 2 , the centrifugal force p U ’ / r acting on the ring becomes p( r,U,/ Y ~ ) ~ / Y = ~ p( Y , U , ) ~ /This Y ~ . exceeds the prevailing pressure gradient pU;/r2 if ( r,U,)’ > ( r2U2)’ or, since K = Ur, if K f > K i . Secondary flows due to the above cause, often called Taylor-Gortler vortices, arise in three main circumstances: ( I ) in the fluid between rotating coaxial cylinders, (2) in two-dimensional boundary-layer flows over concave surfaces, and (3) in attaching or reattaching axisymmetric, two-dimensional and three-dimensional flows as a local effect. Several general reviews covering most of these cases are available (Chandrasekhar, 1961; Greenspan, 1968; Joseph, 1976a; Lin, 1955; Yih, 1969b). Secondary flow between rotating coaxial cylinders ( e g Euteneuer and Reimann, 1971) is only of theoretical interest in the context of bedforms. However, the pioneering work by G.I. Taylor (1923) on this problem is a classic, much of the more recent work being reviewed by Coles (1965) and Greenspan (1968). Because U(r ) cannot be too steeply decreasing a function for the retention of stability, it is hardly surprising that Taylor-Gortler vortices should commonly appear in boundary-layer flows over concave surfaces, for viscosity causes U to decrease rapidly towards the flow boundary, that is, with increasing r . Many natural flows occur over concave surfaces, and this cause of secondary flow may be important in the production of bedforms. The occurrence of secondary flow in laminar boundary layers on concave surfaces is well-established theoretically (Gortler, 1940a, 1940b, 1941; Meksyn, 1950; Hammerlin, 1955a; A.M.O. Smith, 1955; Gortler and Witting, 1958; Kahawita and Meroney, 1974; Aihara, 1976), the vortices appearing when, for a given Reynolds number, the radius of flow curvature becomes sufficiently small compared with the boundary layer thickness. Gregory and Walker (1951), Euteneuer (1969, 1972), Wortmann (1969), McCormack et al. (1970), and Bippes and Gortler (1972) studied the vortices experimentally, to find wavelengths between about one-third and two times the boundary-layer thickness. Of greater importance at present are the less well-known TaylorGortler vortices known to arise in turbulent boundary layers on concave surfaces (Tani, 1962; Sandmayr, 1966). A possible natural example is the pattern of dust-filled “streaks” with a wavelength of 25-30 m recorded by Swift et al. (1978) from the Copper River delta, Alaska, where a katabatic wind flowed down a beach and over the sea. Bedforms due to Taylor-Gortler vortices may also occur in that local region of an attaching or reattaching flow where the flow speed increases in

the direction towards which the streamlines are concave, for example, above the troughs of current ripples or dunes (where longitudinal elements are known to be present), and somewhat down-wind from cliffs facing with the wind. There are strong theoretical reasons for expecting the vortices, at least in laminar currents of the above kinds (Gortler, 1955; Hammerlin, 1955b; Kestin and Wood, 1970; Sadeh et a]., 1970a; Persen, 1971; Schlichting, 1971; Tobak, 1971), and there is experimental evidence that they can exist in both attached, attaching and reattached flows (Piercy and Richardson, 1928, 1930; Kuethe, 1958; Hopkins et a]., 1960; Ginoux, 1965, 1967, 1969, 1971; Sutera, 1965; Sadeh et a]., 1970b; Smits et al., 1979; Sadeh and Brauer, 1980). However, the instability may depend only partly on unbalanced pressure and centrifugal forces (Sadeh et al., 1970a; Tobak, 1973). Inflectional instability of a rotating fluid A three-dimensional boundary layer arises when a disc is turned in a still fluid of large extent (Vol. I, Fig. 1-4), or when a mass of fluid rotates in the presence of a stationary rigid boundary about an inclined axis (Schlichting, 1960). Closely related in character is the Ekman boundary layer (Vol. I, Fig. 1-5), developed in the atmosphere and in the upper and lower layers of the oceans as a consequence of flow upon a rotating Earth. These boundary-layer flows all share the property that, of the three velocity components recognizable, the normal profiles of the radial and axial velocities possess an inflection point at a distance from the boundary of the order of the Ekman boundary-layer thickness. Lord Rayleigh ( 1880) showed that motions with such profiles cannot be stable, whence unstable modes of flow may be expected in three-dimensional boundary layers, whether experimental or planetary (e.g. Gregory et al., 1955; Kreith et al., 1959; Wipperman, 1969; Chin and Litt, 1972). Being the larger, the radial component is likely to control these modes. The existence of an unstable mode in the boundary layer (laminar transitional to turbulent) formed on a disc rotating in a still fluid was established experimentally by Gregory et a1.-(1955) and also studied theoretically by them. Because of viscosity, a layer of fluid is dragged round by the disc, the limiting streamlines of this basic motion following in the laminar case a logarithmic spiral of angle 135" (Fig. 1-3). The instability takes the form of a double row of stationary vortices, the axes of which follow a logarithmic spiral with an angle of about 104O, to the right of the spiral made by limiting streamlines in the basic flow. Vortices in the lower row are wall-attached and parallel but isolated, with a common sense of rotation. The vortices of the upper row all rotate in the opposite sense and are removed from the boundary. Although the interior flow structure differs from that of ordinary secondary motions (Fig. 1-1), the patterns of limiting streamlines are similar. A major dynamical contrast is that the bed shear

8

Fig. 1-3. Secondary flow in the three-dimensional boundary layer developed on a disc rotating in a fluid. See also Vol. I, Fig. 1-5.

stresses are distributed asymmetrically under three-dimensional flow. In the motion sketched in Fig. 1-3, the stress is a maximum about one-sixth of a wavelength to the left looking downstream of each separation line, and not where reattachment occurs at one-half the wavelength. Bedforms developed beneath unstable three-dimensional boundary layers should therefore be asymmetrical, with perhaps the steeper slopes facing with the basic radial flow and in the direction towards which the vortices and limiting streamlines are convex. Gregory et a]. (1955) calculated the vortex wavelength at roughly 1.5 times the Ekman boundary-layer thickness, but measured substantially larger values consistent with later findings (Faller, 1963; Faller and Kaylor, 1966; Lilly, 1966; Tatro and Mollo-Christensen, 1967; Brown, 1970; Caldwell and Van Atta, 1970). The pattern of motion predicted theoretically by a number of these workers, however, is more like that in Fig. 1-1 than in.Fig. 1-3. Greenspan (1968) has reviewed the instability of Ekman boundary layers. Asymmetry of flow boundaries (turbulent flow)

It has long been known that secondary currents can form in rectilinear turbulent flows past asymmetrical boundaries (Fig. 1-4), for example, a flat plate with free edges parallel with flow (Elder, 1960; Davies and Young, 1963), a flow-aligned external corner (Nikuradse, 1930), or a conduit with sharp streamwise corners (Nikuradse, 1930; Cruff, 1965; Gessner and Jones, 1965; Liggett et al., 1965; Chiu, 1967; Matthews and Liggett, 1967; Allen, 1968g; Chiu and Lee, 1971; Launder and Ying, 1972; Gessner, 1973;

9

-+

Streamlines

\

_ _ _ _ Irotochs Y

t

Fig. 1-4. Schematic representation of flow (streamlines and isotachs of streamwise velocity) in a boundary layer flowing parallel with an edge or comer. a. Streamwise edge of a plate (based on Elder, 1960). b. Streamwise right-angled comer (after Nikuradse, 1930). c. Channel of rectangular cross-section (after Nikuradse, 1930). d. Channel of triangular cross-section (based on Liggett et al., 1965).

Gerard, 1978). In contrast, no secondary motion develops in two-dimensional or axisymmetric turbulent flow. Secondary currents created through flow-boundary asymmetry could be of practical importance. Natural channels are not axisymmetric and, whether or not curved in plan, should therefore cause a secondary flow. Again, when a river floods or the tide overtops channel banks, secondary currents may be developed along the channel margins, which have become external corners. The first explanation of secondary flows of the kind shown in Fig. 1-4 was advanced by Prandtl (1927a), who suggested that the turbulent velocity fluctuations tangential to an isotach in regions of isotach curvature caused a transverse flow directed from the concave towards the convex side of the isotach. The tangential velocity fluctuations at each point on a curved isotach must therefore be much greater than the normal fluctuations. Alternative theories have subsequently been developed, chiefly from a consideration of the Reynolds stresses or vorticity production (Howarth, 1938; Einstein and Li, 1958; Brundrett and Baines, 1964; Gessner and Jones, 1965; Perkins, 1970; Eichelbrenner and Preston, 1971; Hinze, 1973; Townsend, 1976). Most of these presume, either explicitly oi implicitly, that the anisotropy of the transverse normal Reynolds stresses causes the secondary flow. Gessner (1973) seems to have resolved the issue by showing that it is the gradient of the normal Reynolds shear stress in the vicinity of an edge or corner which actually drives the secondary motion, being such as to mean that energy is continuously fed from the inner flow to regions near an edge or corner where energy is lost. A closely related mechanism appears to explain secondary currents developed during turbulent flow past a surface marked by spanwise-periodic variations of roughness (Townsend, 1976), particularly if those variations are partly related to localized and reasonably intense sediment transport (Bagnold, 1954b).

10

The apparent roughness of a longitudinal strip of sand being transported vigorously over a gravel surface, for example, is paradoxically greater than that of the bare gravel surroundings, because of the added drag arising from the transport. Hence at heights sufficiently near the bed, the flow over the sand strip is retarded relative to that over the gravel. Consequently fluid drifts laterally from above the gravel to above the sand, and a compensatory flow, now directed from the sand to the gravel, is created at a higher level in the current. Profiles of the streamwise component of velocity above the sand strip and above the gravel should resemble those sketched in Fig. 1-5, there being one near-bed height at which the velocity above the sand strip equals that above the gravel. At lower heights, the velocity above the gravel is the larger, while at larger distances the greater value occurs above the sand. At a sufficient height above the general boundary, where its effects can no longer be felt, the profiles should coincide. Hence the profiles define a necessarily symmetrical transverse circulation in the fluid, at the bed from the gravel to the sand. Its spanwise scale would appear to be fixed by the height in the flow at which the two streamwise velocities become equal. This height should depend only on flow strength and sediment characteristics, and could be much smaller than the boundary layer thickness. The effect identified is self-perpetuating and self-adjusting, provided that a vigorous transport is maintained. Once a chance local covering of sand had accumulated, the secondary motion would immediately develop, appearing first as a single pair of rolls and ultimately as a pervasive array of regular longitudinal vortices. The presence of a corner or edge would not be necessary for the

u/

Equal velocities

Fig. 1-5. Probable secondary currents associated with the transport by wind of sand in stripes, usually rippled, over a gravel surface, illustrated by schematic velocity profiles (left) and streamlines in the plane normal to flow (right). A similar difference in roughness may arise in aqueous environments where sand, drifted in small quantities, can be shaped into either current ripples or dunes.

induction of the secondary flow, though such features could trigger or reinforce its development. For the above effect to be displayed, we need only a spanwise change of roughness and not that the bed has everywhere a measurable apparent roughness. Culbertson (1967), for example, describes ribbons of sand deposited on apparently smooth beds. An important difference may be noted between the secondary flow inferred above and that found in, say, Taylor-Gortler vortices. In the latter, the boundary shear stress peaks along the reattachment lines (e.g. Gregory et al., 1955). In the former, the stress along the sand stripes where separation occurs is thought either to equal (Bagnold, 1954b) or be larger than (Fig. 1-5) the value in the adjacent gravel lanes where reattachment seems to happen. Future experimental comparisons may show whether this distinction is correct. Superposed “immiscible” fluids of contrusted density Imagine a rectangular tank filled with two stationary immiscible liquids of contrasted density arranged each in a distinct layer, the one superposed on the other. The lower liquid, of density p I , extends vertically over a thickness h , from y = 0 up t o y =y I ,while the upper, of density p,, fills a thickness h , from y = y I to y = y 2 . Common experience suggests that the arrangement is unstable, tending to invert, if p, > p , and surface tension is negligible. For if some of the denser liquid lying just at the interface is displaced downward, the buoyancy force acting on it is less than the weight, and the downward motion can be continued. If the denser liquid forms the lower stratum, the reverse is true and the arrangement is stable. Alternatively, noting that the local potential energy is pgy, we can calculate the total potential energy for each arrangement when, finding that p h ,h < p2 h h z, the system can be stable only if the total potential energy is a minimum (Rayleigh, 1883). But the arrangement with the denser liquid below becomes unstable if the tank is accelerated downwards with an acceleration greater than g (G.I. Taylor, 1950). The layers again invert, the denser liquid overlying the lighter (the tank is supposed closed and completely filled). This type of instability is the Rayleigh-Taylor instability. It has often been studied (e.g. Lewis, 1950; Bellman and Pennington, 1954; Ingraham, 1954; Melcher and Hurwitz, 1967; Rajappa, 1970; Plesset and Whipple, 1974; Amaranth and Rajappa, 1976; Craik, 1976; Rajappa and Amaranth, 1977) and is reviewed by Chandrasekhar (1961), Yih (1965, 1969b), Dussan (1975) and Joseph (1976a). When instability occurs, the denser liquid flows into the lighter one as a series of regularly spaced pendants symmetrical about axes normal to the initial interface (e.g. Ramberg, 1967). The motion in each pendant resembles that during convection, consisting of circulation in a plane normal to a horizontal ring-shaped axis (Fig. 1-6a). A corresponding

, ,

,

12

flow arises in the inverse pendants formed by the light liquid as it penetrates the denser. A secondary flow similar to that in Fig. 1-1 can be developed from this type of motion if the liquids are sheared parallel with the interface and each is maintained in adequate supply. Important natural examples of gravitationally unstable “immiscible” fluids in shear are afforded by turbidity currents, sea-breeze fronts, and thunderstorm outflows (haboobs). J.E. Simpson (1969, 1972) emphasized that the nose of these surge-like flows is overhanging, with a complex lobe and cleft structure (Vol. I, Figs. 1-27, 1-28). Allen (1971b) showed that some of the medium must be squeezed far under the unstably advancing head, within or behind which it should eventually float up through the main bulk of the current. Figure 1-6b depicts in the xy-plane at a cleft and relative to the head the probable pattern of streamlines in the head and medium. Also shown, but now relative to the ground, are velocity profiles and the generalized

Fig. 1-6. Motions arising from the gravitational instability of superposed liquids. a. Motion in the vertical plane when both liquids are otherwise stationary. b. Motion at the head of a gravity current with lobes and clefts (see also Vol. I, Figs. 1-27 and 1-28). Left-hand portion of figure shows schematically the external appearance of front of head and streamlines in the plane of flow at a cleft. On the right appear suggested patterns of limiting streamlines and velocity profiles (relative to the ground) within the lobes and clefts.

13

pattern of instantaneous limiting streamlines. The base of each lobe contains a pair of spiral vortices, with reattachment occurring beneath the lobe axis and separation where clefts have closed up. Allen suggested that much larger shear stresses are to be expected beneath lobes than in clefts. The secondary flow should decay beyond the station where the entrapped blobs of medium ascend from the bed, since the gravitational instability can no longer operate.

Thermal convection in a sheared fluid A system resembling that in Fig. 1-6 arises in a horizontally sheared fluid heated from below so that it becomes gravitationally unstable. An interface is lacking, however, and the flow may be unstable over all its length. Consider first the simpler stability of a horizontal layer of stationary fluid heated from beneath, the much-studied Benard problem reviewed by Stomme1 (1947), Chandrasekhar (1961), Yih (1969b), J.S. Turner (1973), and Joseph (1976b). The heating causes the density'of the fluid to increase upwards and thus promotes instability, which commonly is expressed as hexagonal convection cells (Fig. 1-7a). But viscosity can stabilize the fluid, even though the density gradient is adverse. Instability may also be reduced in intensity or suppressed by the action of thermal diffusivity, which tends to equalize the temperature of a fluid particle and the surroundings into which it moves. Considering all these factors, Lord Rayleigh (1916b) showed that instability occurred when the parameter:

R a = - - gkTh4 Kv exceeded a certain critical value, where Ra is the Rayleigh number, k is the Cloud Streets

Fig. 1-7. Secondary currents due to thermal convection. a. Polygonal (hexagonal) convection cells arising in a stationary fluid layer either heated from below or cooled from above. b. Longitudinal vortices (roll vortices) associated with cloud streets in the atmospheric boundary layer.

14

coefficient of thermal expansion of the fluid, T is the vertical temperature gradient (negative in a coordinate system in which the upward vertical is positive), h is the layer thickness, and K and v are respectively the fluid thermal diffusivity and kinematic viscosity. Many theoretical studies of the Benard problem have been made, of which those by Jeffreys (1926, 1928), Low (1929), Pellew and Southwell (1940), Fan ( 1959, Hide ( 1959, Chandrasekhar ( 196l), and Wellander ( 1964) are important or representative. The critical Rayleigh number for instability is 1108 when the layer is constrained by a free surface and rigid boundary (the case closest to that of practical interest), the cell diameter (or wavelength) being approximately 2.34 times the layer thickness. Benard convection has also been much studied experimentally. Some of the best work is that by Krishnamurti (1970a, 1970b, 1973, 1975a), who showed that the shape and time-dependent behaviour of convection cells depended strongly on the Rayleigh number. Jeffreys ( 1928) showed theoretically that a sufficiently large shear applied to a convecting layer will stabilize the layer except to disturbances for which the cell boundaries are flow-parallel. Beginning with Ma1 (193 l), many workers proved experimentally that a distinctive sequence of convection patterns is obtained with increasing shear, ending as Jeffreys had predicted with longitudinal spiral vortices (Fig. 1-7b)(Phillips and Walker, 1932; Graham, 1934; Brunt, 1937; Chandra, 1938; Sparrow and Husar, 1969; Lloyd and Sparrow, 1970; Clever and Busse, 1977; Kimura et al., 1971; Krishnamurti, 1975b; Davis and Choi, 1977; Ruth et al., 1980). These vortices have prompted several theoretical studies (Kuettner, 1959, 1971; Kuo, 1963; Gage and Reid, 1968; Asai, 1970a, 1970b; Krishnamurti, 1975a, 1975c; Cheng and Wu, 1976; Wu and Cheng, 1976; Sun, 1978), which reveal amongst other things that the vortex wavelength is approximately three times the thickness of the convecting layer. Jeffreys himself obtained wavelengths of 2.22-3.12 thicknesses. The most important natural examples of longitudinal vortices in thermally unstable shear layers occur in the atmospheric boundary layer, where they have long been associated (Idrac, 1920; Faller, 1965) with the parallel lines of clouds called cloud streets (Malkus and Ronne, 1960; Kuettner and Soules, 1966; Plank, 1966; Kuettner, 1967; Nicks, 1970; Raustein, 1972; Scorer, 1972; Nicholls, 1978; Weston, 1980; Walter, 1981). Cloud streets (Fig. 1-8) form above the sites in the vortex system where longitudinal separation takes place on the ground (Fig. 1-7b), arising under conditions of moderately strong wind and modest thermal instability (Woodcock, 1941; Kuettner, 1959; LeMone, 1973). Hence they are most plentiful in low and intermediate latitudes, where the land or ocean can be readily warmed. According to Kuettner ( 197 1). the transverse spacing of cloud streets ranges between 2 and 8 km and lengths can attain 500 km. The existence of the corresponding atmospheric spiral motions is now well established, both

Fig. 1-8. Oblique aerial view from above of cloud streets over Oxfordshire, England, with wind blowing from upper right to lower left. Photograph courtesy of R.S. Scorer.

visually (Woodcock, 1940, 1941; Woodcock and Wyman, 1947; Gifford, 1953; Hallanger et al., 1962; Angell, 1971, 1972; Angell et al., 1966, 1968, 1972), and by instrumental methods (Plank, 1966; Konrad, 1968; LeMone, 1973; Burt et al., 1974, 1975; Frisch et al., 1975; Markson, 1975). In harmony with the experiments described, atmospheric convection assumes patterns depending on the magnitudes of the shear and thermal instability (e.g. Plank, 1966; Raustein, 1972; Scorer, 1972).-These range from equidimensional (see Fig. 1-6a), as in mammae clouds, to longitudinal as in the vortices, often called roll vortices, linked to cloud streets. Cloud streets and vortices alike lie slightly to the left of the geostrophic wind. Whereas many workers believe that buoyancy combined with shear is sufficient to produce atmospheric longitudinal vortices, others (e.g. Wipperman, 1969; R.A. Brown, 1970) suggest that Ekman-layer inflectional instability is adequate. A combination of mechanisms is possibly operative (R.A. Brown, 1972; LeMone, 1973). Langmuir circulation The surfaces of lakes and oceans affected by a combination of waves and moderate to strong winds frequently show a longitudinal banding, expressed

16

either by transverse variations in wave size and breaking behaviour or, more commonly, by lines or bands of debris and foam indicative of the existence of convergence along zones nearly parallel with the wind. These windrows or wind streaks can be made experimentally (Kraus, 1967a; Faller, 1978; Faller and Caponi, 1978) and in natural environments have often been observed (Langmuir, 1938; Van Straaten, 1950a; Faller and Woodcock, 1964; Roll, 1965; McLeish, 1968; Stewart and Schmitt, 1968; Sutcliffe et al., 1971; Eisenlohr, 1972; Harris and Lott, 1973) or revealed using dyes released into the water (Katz et al., 1965; Ichiye, 1967; Assaf et al., 1971). Their transverse spacing is usually between 10 and 50m in the oceans, depending on wind speed and thermocline depth, but in lakes seldom exceeds 10m and may be as little as 0.5 m. Hunter and Hill (1980) recently described from off the Texas coast what may be Langmuir circulations expressed by a turbidity banding. This banding occurred in water 6-14m deep and took a wavelength, increasing with water depth, between 5 and 25 times the depth. Langmuir (1938) proposed that windrows express a helical circulation in the surface layers of oceans and lakes, the motion (Fig. 1-9) being the mirror-image of that sketched in Fig. 1-1. The longitudinal velocities associated with the circulation are only a few percent of the local wind speed, but the secondary flow itself must be relatively vigorous, to judge from the measurements of Scott et al. (1969). Hence Langmuir circulations could generate longitudinal bedforms if set up by moderate to strong winds. They must also penetrate the full depth of the water body, however, which seems to restrict their action to shallow lakes and seas. Langmuir (1938) himself appreciated that the motion depended on an interaction between the wind-driven surface current and the water waves advancing beneath the wind. The mechanisms possibly involved in this interaction have subsequently been much debated, as may be seen from the reviews by Scott et al., (1969) and Faller (1971), and the theoretical studies Debrls at sonverpence

Fig. 1-9. Schematic streamlines and velocity distribution in Langmuir vortices.

17

by Craik (1970, 1976, 1977), Leibovich and Ulrich (1972), Gammelsrdd ( 1979, Craik and Leibovich ( 1976), Garrett ( 1976), Leibovich ( 1976, 1977), and Leibovich and Radhakrishnan ( 1977). The most acceptable explanation

(Craik, 1977; Leibovich, 1977, 1980) is that of an instability mechanism in which initially weak spanwise-periodic velocity variations in the wind-driven current are amplified by the effect on the vorticity of the mass-transport induced by three-dimensional wind-waves, as substantiated by the recent experiments of Faller (1978) and of Faller and Caponi (1978). Craik calculates that the transverse wavelength of the circulation is X = 0.45U ’ / g , where U is the mean wind speed. This is substantially lower than Leibovich and Ulrich’s (1972) estimate of X = 7rU2/2g, and both relationships yield wavelengths smaller than observed (e.g. Faller and Woodcock, 1964; Scott et al., 1969). Under field conditions, however, circulations of more than one wavelength may be noticeable because a spectrum of waves is inevitably present. There is experimental evidence that, even with a steady wind and waves of a single wavelength, two circulation wavelengths can arise (Faller and Caponi, 1978), in response to an energy-transfer mechanism whereby the vortices tend to fill the water-body to its full depth. SAND RIBBONS IN AQUEOUS CURRENTS

On smooth beds in streams Longitudinal bands of sand-Casey’s ( 1935) Langsstreifen and Vanoni’s (1946) sand ribbons or streaks-are seldom reported from extensive smooth beds. The straight to very gently curved examples described by Culbertson (1967) from the Rio Grande Conveyance Channel have wavelengths in the order of 0.1-0.2m and arose as a little sand was drifted over an apparently smooth bed of clay deposited from suspension not long beforehand. He interpreted them in terms of a secondary flow like that in Fig. 1-1. As the channel walls lie at a distance, a sediment-flow interaction could have been responsible for the secondary circulation. Centrifugal instability cannot be wholly ruled out, however, as some of the ribbons are curved. The rather more closely spaced straight ribbons observed experimentally by Ashida and Narai (1969) occurred on the smooth glass bed of a flume beneath a flow with a depth equal to about one-half of their wavelength. The ribbons probably reflect transverse variations in bed roughness. On rough beds in streams and beneath ebbing tidal flows During transport experiments using mixed grades of sand in a straight flume, Casey (1935) noticed that the finer particles moved over the coarser in the form of longitudinal bands or ribbons which he called Liingsstreifen. These he explained by a pattern of secondary flow having a spanwise wavelength of roughly twice the flow depth. Similar experimental observa-

Fig. 1-10. Sand ribbons developed by the ebbing tide on a gravel surface in (a) general view and (b) close-up, coast near Burnham Overy Staithe, Norfolk, England. Trowel 0.28 m long points in current direction.

tions were made by Vanoni (1946), Allen (1966c), and Ikeda (1981), who also invoked secondary flows to explain the features. Allen found that the ribbons were smooth when the current was powerful enough otherwise to fashion a plane bed but became transversely rippled beneath weaker flows.

19

Vanoni (1946) attributed the secondary flow to the creation of locally unstable sediment concentration (bulk density) gradients, a view challenged by Nemenyi (1946), who urged instead the influence of channel corners. But Vanoni worked at large width-to-depth ratios, and the influence of a corner does not extend far transversely into a flow. The best explanation seems to be that transverse variations of bed roughness gave rise to a secondary motion. Allen (1966~)used flows not much shallower than wide in a short channel, making it plausible in his case that entrance and corner effects determined the secondary flows. Ikeda ( 1981) invoked Reynolds-stress distortion. A field example of sand ribbons formed by the drifting of grains down a shallow channel floored by a level spread of stable gravel appears in Fig. 1-10. Numerous similar bedforms are recorded, largely from shallow flows in which the wavelengths developed are in the order of 0.1-0.3 m (Arnborg, 1957; Hjulstrom, 1957; Karcz, 1966, 1967, 1972, 1974; Slatt and Hoskin, 1968; Bluck, 1971, 1976; Collinson, 1971b; Dalrymple et al., 1975). Karcz noticed that as the amount of sand cover increased, the ribbons merged and became strongly marked transversely by current ripples, longitudinal features being suppressed. Those amongst the “streaming lineations” of Picard and High (1973) not related to obstacles on the bed may also be sand ribbons. The alternative name “harrow marks” was proposed by Karcz (1967) for sand ribbons, but the older name is neither genetic nor likely to mislead. The name “longitudinal rib” was applied by Martini (1977) to apparently solitary streamwise ridges of coarse sand found on bars in a coarse-load stream. Karcz (1966, 1967) and Allen (1966~)in particular urged the interpretation of these sand ribbons in terms of secondary flow. Although Karcz did not observe active currents, his photographs bear out this explanation. They show on the ribbons tiny sand drifts that are oriented relative to the ribbons in the same manner as limiting streamlines near separation (Fig. 1-1).

Sand ribbons in the marine environment Ribbons of sand resting on stable substrates and aligned parallel with the strongest sand-driving tidal currents were first recorded from the marine environment by Stride (1959a, 1961, 1963). Similar structures have since been widely identified in shallow tide-swept seas (Belderson, 1964; Flemming, 1965; Belderson and Stride, 1966; Dobson et al., 1971; N.H. Kenyon, 1970a; Kenyon and Stride, 1970; Belderson et al., 1971, 1972; McKinney et al., 1974; Dalrymple et al., 1975; G.F. Caston, 1976; Pendlebury and Dobson, 1976; Bouma et al., 1977a, 1977b, 1978; Hunt et al., 1977; B.W. Flemming, 1978, 1980; K.B. Lewis, 1979; Karl, 1980), where they are valuable indicators of bedload paths (Stride, 1963, 1973). They occur as well in tidally influenced carbonate environments (Kendall and Skipwith, 1969; G.R. Davies, 1970a; Rigby and Roberts, 1976). Thermohaline marine circu-

20

Fig. 1-1 1. Side-scan sonar record (0.8 by 2.5 km) of sand ribbons composed of trains of low sand waves (light tone), water depth approximately 59 m, English Channel. Photograph courtesy of N.H. Kenyon (see also N.H. Kenyon, 1970a).

lations have also shaped sand ribbons, at great depths (Kenyon and Belderson, 1973; Lonsdale and Malfait, 1974) and in shallows (Werner and Newton, 1975a, 1975b). Marine sand ribbons (Fig. 1-11) typically are found on extensive level surfaces underlain by lag gravels or smoothed rock. They are spaced transversely in the order of 10-200m, and range up to 15 km in length, but seldom rise more than 1 m above their surroundings. The Celtic Sea reveals three varieties of ribbon which N.H. Kenyon (1970a) shows are related to the degree of sand cover and suggests are dependent on the maximum tidal velocities. His type A ribbons (maximum velocity 1.33 m s - I ) comprise longitudinal rows of small, isolated, transversely arranged sand waves or dunes. The largely “smooth” type B ribbons exist in areas of somewhat weaker currents (maximum velocity 1.06ms-I) where the bed is less sandstarved. These ribbons are broad, expanding locally into thin but extensive sand sheets, and often composite, being formed from several ribbons which have merged and are detectable as individuals only near the margins of the sheets. Type C ribbons (maximum velocity 0.93 m s - I ) comprise trains of substantial and locally merging barkhan-like dunes or sand waves. N.H. Kenyon (1970a) distinguished a type D ribbon which he linked genetically to the previous three (see also Auffret et al., 1972; Werner and Newton, 1975a, 1975b; B.W. Flemming, 1980). These ribbons are much more closely spaced than the other varieties in similar water depths, occurring only in the troughs of large partly isolated sand waves and at steep angles to their crests, the two kinds of form making a trellis-like sand spread. The marine sand ribbons belonging to Kenyon’s types A-C are probably attributable to secondary flows created by transverse variations of bed

21

I

/

h

-E

100

--

L

mi

.

A

2: 5 c V

3

40-

20

10

L

L

I

10

/*.

4

O

Allen ( 1 9 6 8 b ) Kenyon (19700) v Kenyon ond Stride 11970) Werner and Newton 11975b) Bouma et a1 (1977a, 1977b, 1978) * s a n d ribbons 0 sand-filled erosional grooves

A

/*

. /-

-

'

m ,

/

1

20

40

60

80 100

200

400

600 8001000

2000

Averoge sand ribbon spocing. L (m)

Fig. 1-12. Average transverse spacing of tidal sand ribbons as a function of water depth, including one case of sand-filled erosional grooves.

roughness, although Karl (1980) prefers to invoke Langmuir circulations. Stride (1959b) compared them to aeolian sand stripes which Bagnold (1954b) had interpreted in these terms. Allen (1966~)explained marine ribbons explicitly in terms of secondary currents and, using Stride's (1963) side-scan sonar records, suggested ( 1968b) that their wavelength scaled on effective flow thickness. A more recent analysis by Werner and Newton (1975b) goes far towards confirming this result (Fig. 1-12) and signifies that ribbon wavelength on the average is 3-5 times the thickness. Some of the scatter may be related to indications that more than one order of longitudinal vortex may coexist in the marine environment (Werner and Newton, 1975b). The type D ribbons found in sand-wave troughs where streamlines are gently concave towards the faster flow are obvious candidates for interpretation in terms of local centrifugal instability, and their affinity as expounded by N.H. Kenyon (1970a) may be questioned. They are best allied to the longitudinal features associated with current ripples and dunes covering continuous sand beds (Allen, 1977b). It is interesting that turbulence patterns suggest the association of longitudinal vortices with active river dunes (J.M. Coleman, 1969).

Sand ribbons on continuous beds Longitudinal ridges and furrows of low relief occasionally arise on continuous level spreads of apparently homogeneous sand. Van Straaten ( 1953a) first described them from sandy intertidal flats, under the title of longitudinal megaripples of deep-water variety. These ridges are 10-60m in wave-

22

length, up to 0.2 m in height, and locally more than 1 km long, lying parallel with the tidal currents that shaped them. During 1966 I saw many similar structures formed by ebbing tides on the flat-topped sand banks of the inner Severn Estuary (Fig. 1-13). When drained the bank tops reveal clusters of usually gently curved ridges and furrows up to 300 m long and from 0.5 to 6 m in wavelength. Ebb-oriented current ripples developed in uniformly textured sand lie transversely across them. The ridges have such little relief that they are visible only because of the deeper water standing in the furrows. Apparently, systems of longitudinal vortices are developed in the ebbing tidal current at the sites of the ridges and furrows. Inspection on calm days revealed curved longitudinal bands of differing reflectivity on the water surface, spaced similarly to the ridges and suggesting streamwise convergence and divergence in the swift flows then in the order of 1-2 m deep. Measurements by Hamilton et al. (1974) at one of these sites (Sheperdine Sands, Lydney) confirm the vigour of the currents. J.M. Coleman (1969) later made similar observations from the Brahmaputra River. On aerial photographs he saw many instances of longitudinal water-surface turbulence patterns consistent with the presence of streamwise vortices (he refers only to rows of turbulence cells), and found on dried

Fig. 1-13. Curving sand ribbons on continuous surface of fine sand, Lydney Sand, R. Severn, Gloucestershire, England. View southwest into cloud-obscured sun. Dark bands, with relatively little water ponded in troughs of current ripples, are elevated above reflective, lower-lying bands. Scale given by Labrador dog. Current curved away and to right of observer.

23

banks examples of longitudinal ridges and furrows more than 1 km long, 8-30 m in wavelength, and up to 1.5 m in height. His echo-sounder records show that, during high stage, similar features are present on nominally plane beds and in association with the vortices. Their wavelengths closely fit the trend for other sand ribbons (Fig. 1-12). Fossil record

Sand ribbons appear to have no known fossil record, unless the pebble trains of Nilsen (1968) are related to them. They perhaps have a better chance of preservation in rivers, where mud blankets can easily form (Culbertson, 1967), than in the marine environment (N.H. Kenyon, 1970a). SAND RIBBONS IN AEOLIAN ENVIRONMENTS

Bagnold (1954b) saw that during storms in the Libyan Desert the sand driven over pebble-covered sand sheets became organized into longitudinal ripple-covered stripes up to 500 m long and 40-60 m in wavelength. Between these stripes coarse-textured ballistic ripples were occasionally to be found.

Fig. 1-14. Sand ribbons with a transverse spacing in the order of 0.5-1.0m composed of bands of medium to coarse sand (large-wavelength ballistic ripples) alternating with very fine to fine sand (small-wavelength ballistic ripples), coast west of Holkham Gap, Norfolk, England. Trowel 0.28 m long points downwind.

24

He interpreted the stripes in terms of a transverse circulation in the wind controlled by the spanwise changes of roughness, Fig. 1-5 presenting this explanation in a more complete form. Similar but more closely spaced structures are often found where ill-sorted grains are supplied to a sand sheet (Fig. 1-14). Simons and Eriksen (1953) give an excellent description from the Peruvian Desert. Here the ribbons are 1.25-3.5 m in wavelength and also comprise longitudinally arranged strips a1ternately of light and dark-coloured grains. The light-coloured ribbons consist of medium-grained sand shaped into relatively small transversely arranged ballistic ripples with crest lines that are concave down-wind. Very coarse sand in substantially larger transverse ripples underlies the dark ribbons. Simons and Erikson follow Bagnold (1954b) in their explanation, a view given some support by the downwind-concavity of ripple crests in the light-coloured sand, suggesting separation along these streams.

EROSIONAL GROOVES AND RIDGES

River and related aqueous environments

Whereas sand ribbons are essentially constructional features, albeit of little relief, there are numerous longitudinal bedforms wholly destructional in origin, as modelled in Fig. 1-2d. These include bold grooves and ridges of many sizes and cross-sectional shapes sculptured in relatively coherent beds by river and related aqueous currents in the course of bedload transport. One of their earliest investigators was P.B. King (1927), who described systems of long, nearly straight, deep, U-shaped grooves and intervening sharper ridges which lay parallel with flow on the limestone bed of a river at a transverse spacing in the order of 1 m. These features he explained by corrasion, mainly because of their smoothness in comparison with the fretted and pitted limestone surfaces which lay nearby out of ordinary reach of the stream. Somewhat smaller but otherwise similar ridges and grooves were later described by Arnborg (1958) from the gneissose bed of the Angermandven. Similar forms occurred where this same river swept cohesive silts deposited when its present valley was a fjord. In each instance, quantities of sand and gravel-the tools of corrasion-were present in the grooves. Arnborg also found smaller and more delicate longitudinal grooves and ridges where the river bed was exposed in the troughs of isolated transverse dunes. Corrasion furrows as deep as 1 m and 3-10m apart were found by Sundborg and Norrman (1963) in depths of about 7 m in the Gota Alv. Gizejewski (1978) has described parallel grooves cut into the floor of a lake at a power-station outfall. Longitudinal ridges and grooves can be rapidly excavated by flows resembling sheet floods. Examples approximately 5 m deep, 80 m in wave-

25

length, and more than a kilometre long were found by V.R. Baker (1974) and Baker and Milton (1974) on the surface of the flat-lying basalt lavas scoured by the Lake Missoula catastrophic floods that swept the Washington Scablands (V.R. Baker, 1973a). These remarkably extensive floods were in the order of 100m deep and flowed at many metres per second. Large-scale secondary flows in which cavitation, corrasion, and rock-plucking acted in combination may have shaped the huge grooves (V.R. Baker, 1974). Laboratory experiments have thus far shed little light on the origin of erosional grooves and ridges. From such work the grooves appear to represent an intermediate stage in the deepening and, under some circumstances, the rounding of an originally wide and uniformly shallow channel (AbdelRahman, 1963; Mosley, 1973; Shepherd and Schumm, 1974), but the nature of the erosion processes, and the role if any of secondary flow in the initiation and growth of the structures, remain undescribed. The fossil record of erosional grooves and ridges in fluviatile sediments is not extensive. Schroder (1965), Nagtegaal (1966, 1969), and Allen ( 1974a) describe examples comparable in size and shape with Arnborg’s (1958) and P.B. King’s ( 1927) larger forms. Smaller round-bottomed erosional grooves are particularly common in the Old Red Sandstone (Allen, 1964; Friend, 1965). Corrasion grooves on the scale described by Sundborg and Norrman (1963) and V.R. Baker (1974) have probably been called channels when preserved in rocks.

Tidal environments Tidal currents have locally cut systems of longitudinal grooves and ridges into cohesive beds. Verger ( 1968) has observed corrasionai furrows approximately 0.1 m in depth and 1 m in wavelength from an intertidal mud flat. Similar features trending parallel with the tidal currents are locally preserved on the mud flats of the R. Severn (Fig. 1-15), where they branch and rejoin to reach 300 m in length, 0.35 m in depth, and 2 m in wavelength. When flushed of loose mud by the more vigorous spring tides, the grooves prove to be steep-sided and of a generally V-shaped cross-section, coarse debris often lying in the bottom. Between the grooves the bed is flat to convex-upward and may bear small rills dipping into the furrows. A metre or more of strongly flowing water can cover these grooves and ridges during the tidal ebb. Of a similar form, but developed on hard sandstone pavements, are the groups of furrows described as striations by Klein (1970) from the intertidal zone of the Bay of Fundy. Like Arnborg (1958), he observed slighter longitudinal grooves developed where bed rock was exposed between isolated transverse dunes. Klein concluded that the rock pavements had been subjected to “tidal current scour and sandblasting”. In all of the examples discussed, it is plausible’ that the differential corrasion necessary for the shaping of the grooves and ridges was initiated by secondary currents furnished with but little coarse debris.

26

Fig. 1-15. Partly sediment-filled longitudinal ridges and furrows on intertidal mud flat southeast of Oldbury Lake, R. Severn, near Aust, Gloucestershire, England. Trowel stuck upright into mud is 0.28 m long. Ebbing tide flows from upper right to lower left. The Institute of Geological Sciences (1981) has recorded similar structures elsewhere in the estuary.

Longitudinal grooves are not uncommon in water-depths of several tens of metres. Those reported by Donovan and Stride (1961) are extremely large but, because they are generally ungrouped and depend closely on outcropping hard and soft strata, are unlikely to be controlled by secondary currents. The latter explanation seems most appropriate to the systems of large grooves and ridges described by Dyer (1970), Stride et al. (1972), Newton et a]. (1973), Bouma et al. (1978), and Reinson (1979), eroded into respectively mud, gravel, fine sand over gravel, bed rock and, possibly, gravel. What may be large erosional grooves are reported by Beiersdorf et al. ( 1980). Bouma’s grooves lie in approximately 45 m of water, are probably many hundreds of metres long, and take a wavelength in the order of 100 m. Like some deep-sea and desert features described below, they are occupied by closely spaced transverse dunes incompletely covering the substrate. The grooves found by Stride showed “tuning-fork” junctures which pointed in the direction of net bed-load transport. Toimil and Reimnitz (1979) also described large apparently flow-parallel structures with such junctures, but their relationship to current direction is uncertain. Dyer loosely associated his grooves with secondary flows, though their spacing relative to flow thickness seems too large to support this idea strongly. A better fit to the trend of Fig. 1- 12 is given by Bouma’s grooves from Cook Inlet. This graph should describe grooves and ridges (other than perhaps those found in dune

27

troughs) equally with sand ribbons, for a groove occupied by transportable coarse debris is arguably a ribbon that has succeeded in embedding itself. Many examples of what could be small tidally scoured grooves and ridges occur as moulds in shallow-marine rocks, going by such names as priel casts (Martinsson, 1965), Rinnen (Hantzschel and Reineck, 1968), sand fingers (Woodrow, 1968), or gutter casts (Whitaker, 1973). The paper by H.S. Williams (1881) is sometimes taken as their first description, but to me his account suggests soft-sediment deformations. When well exposed, gutter casts (Fig. 1-16) are generally seen as arrays of long and stout, occasionally branching, straight to weakly meandrine ribs which project downwards from beneath sandstone or calcarenite beds overlying muddy rocks, or as rows of isolated calcarenite or sandstone ribs in shales (Niehoff, 1958; C.R. Barnes, 1965; Martinsson, 1965; Whitaker, 1965, 1973; Kudrass, 1967; D. Richter, 1967; Hantzschel and Reineck, 1968; Woodrow, 1968; Van Eden, 1970; Gall, 1971; Bridges, 1972; Wincierz, 1973; Allen, 1974a; Aigner and Futterer, 1978; Birkenmajer, 1979; Greensmith et al., 1980). The ribs have steep to overhanging sides, often roughly terraced in conformity with bedding in the adjacent mudstones, which like the bottoms frequently carry swarms of delicate tool marks (e.g. Bridges, 1972). Like their modern counterparts (e.g. Fig. 1-15), the ribs are spaced across relatively flat surfaces at fairly regular intervals averaging from a few decimetres to several metres. Usually the ribs comprise longitudinally transported quartz or bioclastic sandstone often rich toward the base in rolled shells, granules, and small pebbles. Related structures, in possibly lacustrine settings, are described by Berry (1961), P. Allen (1962), Prentice (1962b), and Daley (1968). R.J.Bailey’s (1966) “scour ripples” may also be allied to grooves and ridges. The corrasional origin of gutter casts has long been accepted (Whitaker, 1973), the best evidence being the striated bottoms and sides and the presence of possible tools in the infillings. Berry ( 1961) linked groove-cutting

Fig. 1-16. Schematic view from below of underside of a sandstone bed preserving gutter casts.

28

to secondary currents developed when debris in small quantities is driven across a mud surface. Whitaker (1973) also argued for groove initiation by secondary currents but, with Bridges (1972), thought that single spiral vortices only might affect some deeply excavated examples (meandrine ones particularly). Aigner and Futterer (1978) favour erosion downstream from stationary obstacles such as shells, but this explanation, while applicable to solitary grooves, does not account for the relatively even spacing of many gutter casts.

Deep-sea environments Thermohaline circulation in the oceans creates deep-lying but relatively thin bottom currents in many places vigorous enough to scour huge areas of the sea bed (Hollister et al., 1976). Commonly, the erosion is expressed by the excavation of arrays of grooves and ridges parallel with the direction of the measured currents, though some large grooves on the deep-sea floor are syndepositional (Hollister et al., 1978; Tucholke, 1979)..Under the title of longitudinal ripple marks, Taylor et al. (1975) described shallow, regularly spaced, V-shaped grooves from the muddy flanks of Gilliss Seamount. Small grooves were also reported by Lonsdale (1976) from a chalk surface in the Ecuador Trench, and by Melieres et al. (1970) from a large erosional tract swept by the Mediterranean Undercurrent (Heezen and Johnson, 1969; Kenyon and Belderson, 1973). Infillings of rippled sand or gravel were observed. Groupings of much larger furrows, with wavelengths averaging in the general order of 100 m, seem to be widespread, occurring notably on the Carnegie Ridge and the Bahama Outer Ridge (Lonsdale et al., 1973; Hollister et al., 1974; Lonsdale and Malfait, 1974; Lonsdale and Spiess, 1977). Further examples, with depths up to 10 m and widths reaching 50 m, occur on the Bermuda Rise (Embley et al., 1980). These grooves join in the measured downcurrent direction and are known to have steep terraced sides, with little doubt erosional in character if their form and the magnitude of locally-measured currents is any guide. Trains of isolated dunes (foraminiferal sand) infill the broad, steep-sided grooves found on the Carnegie Ridge, though grooves elsewhere contain no obvious partial infill. Lqnsdale and Spiess (1977) tentatively ascribed the grooves to the action of secondary flows in the benthic boundary layer, an interpretation consistent with their wavelength. The causal instability is probably in most cases related to bed-load transport, but may locally be due to streamline curvature. The location of some irregularly spaced grooves may depend on the distribution of breaches in basin rims through which sand can spill (Lonsdale and Malfait, 1974). Lonsdale and Hollister (1978) report grooves about 20 m apart associated with an abyssal meandering channel.

29

Deserts

Spectacular arrays of longitudinal corrasional forms extending over vast areas occur in several deserts. These features (Fig. 1-17) range morphologically between Mainguet’s ( 1972a) wind ridges-and-furrows and the yurdungs of Blackwelder (1934). In some cases yurdungs alone are present, but in others, notably the surroundings of the Tibesti in the Sahara, the two kinds of structure are closely associated. Wind ridges-and-furrows apparently were first described by Bagnold (1933), who found southeast of the Tibesti an impassable country “scored into grooves 10-50 ft. deep, each running in the south-west direction of the prevailing wind”. Monographic treatments of these structures in the Tibesti area are given by Hagerdorn (1971) and Mainguet (1972a), and there are several shorter reports (Grove, 1960; Peel, 1966; Hagerdorn, 1968; Mainguet, 1968, 1972b; Verstappen and Van Zuidam, 1970; Worrall, 1974; Verstappen, 1977). Similar features occur locally in the South American and Middle Eastern deserts (Rich, 1942; D.B. Krinsley, 1970). Wind ridges-and-furrows (Figs. 1-17a, 1-18) are long and straight to very gently curved hollows and crests carved into some resistant substrate, for example, sandstone, diatomite, or mudstone. Their average wavelength ranges between 10 m and 2 km, and their length is 10-100 times this spacing. Mainguet (1972a) records two main modes of close spatial association of forms of contrasted wavelength: (1) long-wavelength forms grading downwind into those of much smaller wavelength, and (2) small-wavelength ridges occupying the furrows of a more widely spaced system, reminding one of certain marine sand ribbons (Werner and Newton, 1975b). Ridge-and-furrow relief ranges between a few metres and a few tens of metres. Whereas the ridges expose the eroded substrate, the furrows are infilled with stones and blown sand, often arranged as trains of barkhans in the same manner as some marine erosion furrows (Lonsdale and Malfait, 1974; Bouma et al., 1978).

Wlnd

Wind

7

I’

Fig. 1 - 17. Schematic representation of corrasional longitudinal structures in aeolian environments. a. Ridges-and-furrows.b. Yurdungs.

30

Fig. 1-18. Vertical view (approximately 5 by 6.5 km) of wind ridges-and-furrows. Bembkchk, Chad. The ridges (stippled), cut into Palaeozoic sandstones, lie about 2 km apart and have gullied flanks. The intervening furrows (light tone) in some cases are infilled with sand shaped into transverse dunes, and in others have chains of barkhans. After an air photograph of Mainguet (1972a). Wind from lower right to upper left.

The erosional origin of ridges-and-furrows seems clear from their regularity of spacing, strict parallelism with the local dominant wind direction, and the presence on exposed rock surfaces of small flutes, grooves and ridges consistent with corrasion. In the Tibesti area, for example, the features combined with other aeolian forms define a pattern of streamlines clearly showing the wind deflection by the mountain masses (Verstappen and Van Zuidam, 1970; Mainguet, 1972a, 1972b; Roland, 1976). Warrall ( 1974) suggests that secondary currents are involved in the formation of ridges-andfurrows, and Fig. 1-2d amplifies this idea. Instability associated with sand transport is the most likely cause of these currents (Fig. 1-5);except perhaps in the case of the larger ridges-and-furrows. Similar features attributable to wind corrasion are present on Mars (Cutts, 1973; McCauley, 1973; Sharp, 1973). In contrast with ridges-and-furrows, yurdungs (Fig. 1-17b) stand in relative isolation on level debris-covered surfaces generally lacking in drifts or dunes. Yurdungs are widely distributed (McCauley et al., 1977), occurring in the Asian and American deserts (Pumpelly, 1908; Bosworth, 1922; Stein,

31

1920; Blackwelder, 1934; H.T.U. Smith, 1967; McCauley, 1973; Stoertz and Ericksen, 1974) as well as in the Sahara (W.B.K. Shaw, 1936; Capot-Rey, 1957a, 1957b; H.T.U. Smith, 1963; Mainguet, 1968, 1972a; Hagerdorn, 1971; Buckle, 1978) and the Middle East (Gabriel, 1938; Dresch, 1968, 1975; Hallier, 1976). They are best developed in relatively soft materials such as mudstone, diatomite, or friable sandstone. The typical yardang has a streamlined form, the plan approximating to a lemniscate loop, with the blunt steep and in some cases overhanging end facing into the dominant wind. The smallest have dimensions measured in metres, whereas the largest can be up to 1 km in length, 20m in height, and 200m across. It is clear from their characteristics and close association with ridges-andfurrows that yardangs have a corrasional origin, and they may be regarded as recording a more advanced stage of erosion than the ridges. Yardang production is not confined to the wind; the Lake Missoula floods sculptured the loess blanket on the Washington Scablands into large yardang-like forms (V.R. Baker, 1974). There are no known fossilized yardangs or ridges-and-furrows, though these may be expected at unconformities blanketted by aeolian sandstones. In limited exposures the forms might be taken incorrectly for wadis. LONGITUDINAL DESERT DUNES

Active longitudinal or seif dunes (Melton, 1940; Hack, 1941; Kadar, 1966; Glennie, 1970; Clos-Arceduc, 1972; Cooke and Warren, 1973), grouped amongst draa by I.G. Wilson (1972a, 1972b, 1972c), are large ridges of mobile sand lying nearly parallel with the dominant sand-driving wind or with the resultant of two or more comparably effective modal winds. They are the typical dune form in the Australian deserts (Clapp, 1926; Madigan, 1936, 1938, 1946; D. King, 1956, 1960; Wopfner and Twidale, 1967; Jennings, 1968; Mabbutt, 1968, 1971, 1977; M. Brookfield, 1970; Folk, 1971a; Twidale, 1972a, 1972b), and are plentiful in the Sahara and other African arid regions (Cornish, 1914; Bagnold, 1931, 1933; Kadar, 1934; Aufrkre, 1935; Gevers, 1936; Brosset, 1939; Capot-Rey, 1943; Monod, 1958; H.T.U. Smith, 1963; McKee and Tibbitts, 1964; Goudie, 1969, 1970; Servant and Servant, 1970; Warren, 1971, 1972, 1976). Longitudinal dunes are numerous in the Saudi Arabian deserts (Bagnold, 1951; Holm, 1960; Glennie, 1970) and occur in many others (Blanford, 1876; Doubiansky, 1928; Hack, 1941; Striem, 1954; R.B. Johnson, 1967; Hanna, 1969; D.B. Krinsley, 1970; Stone et al., 1973; Higgins et al., 1974; Tsoar, 1974). Climatic change during the Quaternary has rendered inactive but left topographically fresh many tracts of longitudinal dunes (Grove and Pullan, 1963; Pullan, 1964; Grove and Warren, 1968; Flint and Bond, 1968; Grove, 1969; Verstappen, 1970; Warren, 1970; Alexandre-Pyre, 1971 ; Goudie et al., 1973; Lancaster, 1981).

32

Fig. 1-19. Air photograph (6.5 by 7.5 km) showing longitudinal dunes in Simpson Desert, Australia. Wind from lower right to upper left. Note tuning-fork junctions.

There are several varieties of longitudinal dune, generally increasing in morphological complexity with growing size. The smallest and simplest (Fig. 1-19), with a transverse wavelength in the order of 500 m, are exemplified by forms in the Australian and Sinai deserts (e.g. Madigan, 1936; Tsoar, 1974). These ridges are straight to meandrine in plan, with crests usually a little more sinuous than their bodies, and of nearly symmetrical cross-section. Heights seldom exceed 30m. The crest is actually a chain of local summits and avalanche faces which rise up from a broad and more gently sloping plinth but shift and change their facing with the wind of the day or season (e.g. McKee and Tibbitts, 1964; I.G. Wilson, 1972c; Tsoar, 1974). The dunes join downwind at “tuning-fork” junctures, just as marine erosion grooves (Stride et al., 1972; Lonsdale and Spiess, 1977), whereas new ridges arise centrally in the corridors between established forms. The larger forms (e.g. Holm, 1960; H.T.U. Smith, 1963), with transverse wavelengths ranging to perhaps 6 km, are ridges more than 100 m in height and often more than 100 km long (Fig. 1-20). They may be chains of simple transverse dunes, pyramidal dunes, or smaller downwind-convergent longitudinal dunes. Most

33

Fig. 1-20. Air photograph (10 by 10 km) showing complex longitudinal dunes, Grand Erg Oriental, Sahara. Dominant wind from upper left toward right, but with evidence for reversals.

longitudinal dunes consist of sand of a finer texture than the debris in the corridors between, where bed-rock or clay layers, gravel, or bimodallydistributed relatively coarse sands abound. No finer material is permitted by the wind to linger in the interdune corridors. It is no surprise that the internal structure of these large dunes should be ill-known. Bagnold’s (1954b) widely quoted theoretical model suggests an internal structure composed of two kinds of deposit (Fig. 1-21a). Beneath the plinth are gently dipping strata which may be either cross-laminated (ballistic ripples) or parallel laminated. In the upper and central portions appear sets of avalanche layers dipping in opposite directions and at high angles to the dune axis. These divergent dips represent the shifting of the localised

34

Relatively coarse-grained sand (smooth beds, rippler. ribur, small transverse dunes)

Reiatively fine-grained avalanched sand

.

.

/ I

L

I

Fig. 1-21. Internal structure of longitudinal (seif) dunes. a. According to Bagnold (1954b). b. As observed after trenching a dune, Zallaf Sand Sea, Libya (after McKee and Tibbetts, 1964).

avalanche faces as the wind changes direction. The excavation of a small Libyan seif dune by McKee and Tibbitts (1964) tends to support this model (Fig. 1-21b), and Glennie (1970) provides some confirmatory data. But Bagnold’s model cannot be valid for the larger and more complex longitudinal dunes. Depending on their shape, the larger forms could resemble internally either (1) a field of transverse dunes, (2) a complex of simple longitudinal dunes, or (3) a complex of equant dunes. Four broad themes- directionist, residualist, transformationist, and vorticist- can be traced in explanations advanced for longitudinal dunes. The precise relationship of dune trend to wind direction has long been contentious, but the analyses by Dubieff (1943, 1952), I.G. Wilson (1971), and Mainguet and Canon (1976) for the Sahara, and particularly by M. Brookfield (1970) for Australia, go far towards proving the approximate parallelism of the forms with the dominant or resultant sand-driving wind (see also Striem, 1954; McKee and Tibbitts, 1964; Tsoar, 1974). Given this parallelism, are longitudinal dunes erosional or constructional forms? Several early workers suggested that they are residual features formed by the scouring of large furrows in thick alluvial deposits, the mobile surface sand

35

being a veneer (e.g. Blanford, 1876; Aufrere, 1928). Although there are local observations supporting this view, espoused up to the present (D. King, 1956, 1960; Folk, 1971a), most of the evidence suggests that the forms are essentially constructional (e.g. McKee and Tibbitts, 1964; Mabbutt and Sullivan, 1968). If the dunes are constructional, do they arise of themselves or by transformation of other dune types? Cornish (1908) thought that longitudinal dunes could arise by the breaching of partly stabilized transverse forms. In his influential book of 1941, Bagnold (1954b) argued that the dunes grew from barkhans which had been elongated in one wing by powerful cross-winds, an idea extended by Capot-Rey and Capot-Rey ( 1948) and recently resuscitated by Lancaster (1980). Madigan (1936) objected so far as Australian deserts were concerned, since he could not find the required transitional forms. Recently, Verstappen ( 1968) suggested that longitudinal dunes may be transformed parabolic forms. According to Twidale (1972a, 1972b), the Australian longitudinal dunes arise from streamwise drifts generated at obstacles in the wind path. A major objection to this idea is that the dune wavelength is much greater than the drift spacing. Although drifting at obstacles may help to localize the dunes, it seems clear that some independent mechanism selects the ultimate dune spacing. It is now widely felt that longitudinal dunes depend on a transverse instability of the wind flow. This notion was first voiced by Madigan (1936, 1946), who opined that the Australian dunes had grown from sand streamers of the sort visible on road surfaces or when snow is driven across ice, but could not successfully resolve the problem of the large scale difference between streamers and dunes. Bagnold’s (1953) proposal as reinforced by Hanna (1969) is more powerful. Bagnold suggested that the forms are Table 1-1 Occurrence and character of longitudinal vortices in the atmospheric boundary layer Authority

Vortex transverse wavelength (km)

Ratio of vortex wavelength to vortex depth

Remarks

Plank. 1966

0.3-5.0

2

wavelengths smaller in mornings than afternoons

Kuettner, 1959

2-8

2

cloud streets

Konrad, 1968

1.5

1.8

clear air convection over Ocean in morning

Markson, 1975

2.0

2.5

cloud streets over Ocean

4.8

1.9

clear air convection over land

36

constructed as sketched in Fig. 1-2a by probably heat-induced secondary currents in the atmospheric boundary layer. This idea was supported by Mabbutt et al. (1969) and, blended with residualist views, by Folk (1971a, 1971b, 1976, 1977) with a reference to the supposedly analogous behaviour of paint rolled out (McEwan and Taylor, 1966). Glennie (1970) also favoured secondary currents, but implied that these arose because of transverse roughness variations, when again dune wavelength may be expected to scale on boundary-layer thickness. As Hanna (1969) has noted, the agreement in scale between dune wavelength and the wavelength of measured atmospheric secondary flows (Table 1-1) lends some support to Bagnold’s concept. But it remains unclear whether the instability vortices have a wholly gravitational origin. The steeper flank of the Australian dunes is invariably towards the convex side of the wind streamlines (Mabbutt et al., 1969), a feature consistent with the inflectional model summarized in Fig. 1-3 and espoused by Wipperman (1969). The crucial experiment, yet to be undertaken, is to measure atmospheric conditions during sand-driving above an actual dune field. That large vortices however caused are associated with the ridges is suggested by the arrangement of accompanying smaller dunes (e.g. H.T.U. Smith, 1963, fig. 13). Unfortunately, Glennie’s (1970, fig. 74) claim to evidence of this kind (see also Cooke and Warren, 1973) is unacceptable, as it can be argued that the dominant wind is now separating from larger and apparently relict older features as it blows obliquely across them. TIDAL CURRENT RIDGES

Although lacking decisive evidence as to their origin, Off (1963) gave the name tidal current ridges to groupings of large sand shoals of compressed sigmoidal to linear plan to be found in estuaries, at the heads of bays and gulfs, and off promontaries and capes. These structures resemble longitudinal desert dunes in scale, parallelism with flow, and the superimposition of smaller sand waves and dunes (Van Veen, 1935), and seem to be their counterparts in the tidal shallow-marine environment. Off (1963), Allen (1966c, 1968b), Swift (1975), and Swift and Ludwick (1976) give general reviews. Figure 1-22 depicts tidal current ridges on the floor of the North Sea off the Norfolk coast (Houboult, 1968; V.N.D. Caston, 1972). Most are of the linear sort, lying parallel with each other at a fairly even transverse spacing or wavelength. They are representative of the ridges as developed in the shallow seas around the British Isles and elsewhere (Van Veen, 1935, 1936, 1938; G.F. Jordan, 1962; Off, 1963; Houboult, 1968; Caston and Stride, 1970; V.N.D. Caston, 1972; Stride, 1973; Lapierre, 1975; Swift, 1975; Hunt et al., 1977). The complex of banks ranging southeastwards from Haisborough Sand to Hearty Knoll (Fig. 1-22) is not untypical of the sigmoidal type

37

Fig. 1-22. Tidal current ridges (Norfolk Banks) in the southern North Sea. Morphology based on Admiralty Hydrographic Department Chart Nr. 1049; inferred sand transport directions (bold mows) from Caston and Stride (1 970).

of ridge, present locally in the open sea (e.g. Van Veen, 1936; Cloet, 1954) but best developed in estuaries and near islands (Newel1 et al., 1951, 1959; Illing, 1954; Robinson, 1956, 1960; Newell and Rigby, 1957; Jakobsen, 1962; Reineck, 1963; M.M. Ball, 1967; Schou, 1967; Ludwick, 1970, 1973; Gohren, 1971; Park, 1974; Dorjes and Reineck, 1977). Tidal current ridges typically are about 4 km apart transversely and 15 m in height, the crests commonly reaching to within a metre or so of the sea surface. Their wavelength (Fig. 1-23) is to a first approximation proportional to the square of the water depth (Off, 1963; Allen, 1966c, 1968b), and their length can exceed 50 km (e.g. Fig. 1-22). Most linear banks and some of the sigmoidal kind are asymmetrical in cross-section, the steeper sides facing consistently in the same direction within each array, despite the extreme length of the ridges (e.g. G.F. Jordan, 1962; Houboult, 1968; Stride, 1974). Most ridges bear sand waves, as Van Veen (1935, 1936) was early to discover. Those to be found on the linear banks, and on many sigmoidal ones with arms of grossly unequal length, face the bank crest on each side

38

I

-L-

0

t I

2

I

4

I

,

6 8 ,oo

2

4

Ridge height, d (sfnoximum

6

8

io~

2

4

6 8

water-depth, h I ( m 1

Fig. 1-23. Geometry of tidal current ridges (data of Off, 1963).

but lie obliquely to the crest on similar trends (e.g. V.N.D. Caston, 1972). On the equal-armed sigmoidal banks lie symmetrically arranged sand waves or dunes facing in the same direction as the closure of the crest (e.g. Gohren, 1971; Park, 1974). Seismic profiling and shallow coring tell something of the internal structure of tidal current ridges (McKee and Sterrett, 1961; Seibold, 1964; Imbrie and Buchanan, 1965; M.M. Ball, 1967; Houboult, 1968; Park, 1974). Many prove to be wholly constructional features, resting on a level substrate which extends beneath them between exposures on the floors of the adjacent channels. Multiple internal reflectors are commonly evident, dipping in the same direction and at a similar gentle slope to the steeper side of the ridge. Evidently the banks grow or move partly in the same direction as the steeper face. Even though large sand waves are commonly superimposed, the shelly sands making up the banks are cross-bedded on a modest scale and commonly bioturbated. Cross-bed dip directions show little consistency. Houboult (1968) records foresets from the Norfolk banks dipping down, along and up the ridge faces. Tidal current ridges occur in a complex hydraulic regime which is so far ill-understood. But it is clear that the linear banks lie approximately parallel with the strongest tidal flows (e.g. Houboult, 1968), and that the sigmoidal ones are coupled with mutually evasive flood and ebb currents, each segment closing in the direction of the dominant tidal flow (Van Veen, 1936, 1950;

39

Robinson, 1956; Jakobsen, 1962; Schou, 1967). Moreover, V.N.D. Caston ( 1972) has persuasively demonstrated how the sigmoidal and linear banks

may be related as stages within an evolutionary morphological series. Off (1963) sketched an hypothesis of the origin of tidal current ridges which involved transverse instabilities in the tidal flows as the cause of “bands of slower current” in which the structures accumulated, although his analogy with river channels is perhaps far-fetched. Allen (1968b, 1968g), Houboult (1968), and Caston and Stride (1970) backed this implied role of secondary currents, for which Houboult could adduce some confirmatory field evidence. On the sea over the channels between ridges, he found long foam and debris lines which he took to indicate the surface convergence of the flow in paired vortices similar to those sketched in Fig. 1-2a. Over or near the crests, were zones where wave properties changed, suggesting surface divergence and a corresponding bottom convergence close to the ridge crests. However, the apparent secondary flow has a much larger scale than that believed to be associated with sand ribbons in similar depths, and its cause is mysterious. The asymmetry of the Norfolk ridges suggested to Caston and Stride that the vortices of each pair had unequal strengths. The stronger must lie on the western side of the ridge, in order to explain the steeper northeastern face and the reflectors suggesting lateral migration in that direction. Stride ( 1974) later showed that the steeper side of linear banks tended to face the direction in which the tidal current rotates relative to the direction of net sediment transport, and argued that the asymmetry depends on this through a lag effect (see also Postma, 1967; Huthnance, 1973). McCave (1979) has doubted both the secondary-flow model and Stride’s (1974) lag effect, on the basis of measurements of the profile of velocity at the North Hinder Lightship, 3 km to the west-northwest of the North Hinder Bank in the Southern Bight of the North Sea. According to him, the near-bed current deviates in direction from the velocity at 10m below the surface in a manner inconsistent with the presence of a secondary flow. This is correct only if, as McCave assumes, the measurements came from the cell characterized by a bottom-current directed toward the crest of the bank. As the North Hinder Lightship is sited in a trough flanking the bank, however, it is -quite possible that the next cell outward was sampled, in which case his observations support the presence of a secondary flow. McCave’s study cannot be regarded as resolving the question of the hydrodynamic controls on tidal current ridges. Many shallow-marine cross-bedded sandstone and limestone formations may have arisen partly as tidal current ridges (e.g. Sedimentation Seminar, 1966; Narayan, 1971; Pryor, 1971; D.D. Carr, 1973), though such an origin is not proved until the form of the banks is demonstrated. An exceptionally large quarry revealed to Allen and Kaye (1973) a mud-bounded asymmetrical shoal of longitudinally transported cross-bedded calcarenite measuring 6 m in height and about 800m wide across the base. Although the quarry was too small to reveal more than one shoal, similar deposits abound at the

40

same stratigraphic level, suggesting that a complex of banks resembling tidal current ridges exists in the area. Small shoals which seem to be ridges possibly of the sigmoidal type are described from late Precambrian quartzites in north Norway (H.D. Johnson, 1977a).

RIDGE-AND-FURROW MOULDS

On the underside of some turbidite sandstones, particularly if thin and fine grained, are preserved the moulds of small, closely packed, longitudinal ridges and furrows originally shaped in mud (Fig. 1-24). These have been called longitudinal ripple-load-casts (Kelling and Walton, 1957), rill marks (Dzulynski and Slaczka, 1958), longitudinal ridges (Craig and Walton, 1962), furrow casts (McBride, 1962; Potter and Pettijohn, 1963), dendritic ridges (Dzulynski and Walton, 1963; Enos, 1969a), and longitudinal ridges and furrows (Dzulynski, 1965; Dzulynski and Walton, 1963, 1965; Kemper, 1968). In the same category fall some of Pettijohn and Potter’s (1964) flute

Fig. 1-24. Ridge and furrow moulds, Silurian rocks, Southern Uplands, Scotland. Current from left to right. Specimen approximately 0.35 m long. Photograph courtesy of E.K. Walton (see Dzulynski and Walton, 1965).

41

casts, together with the flute moulds Kuenen (1957) described as being “fine-textured” or resembling “rep tilean scales” and “fern fronds”. It is clear from the moulds (Fig. 1-24) that the original ridges are narrow and sharp-crested, joining at intervals downcurrent at “tuning-fork” junctures. Their average transverse spacing or wavelength varies between a few millimetres to a maximum of about 0.06 m and is typically about 0.01 m. The furrows between ridges are broad and range from shallow and flatbottomed to deep and rounded. Some furrows are smooth and even along their length, whereas bthers have a coarsely granular appearance. Many furrows are crossed transversely at fairly regular intervals by evenly spaced curved ridges that are concave downcurrent and bound shallow flute-like hollows, the arrangement with the main ridges creating a ladder-like effect. Ridge-and-furrow moulds are often the only structure present beneath turbidite sandstones, varying from straight to meandrine in plan and covering the sole completely (Kuenen, 1957; McBride, 1962; Potter and Pettijohn, 1963; A.M. Anderson, 1976). Unusually large exposures.(e,g. .Kruit et al., 1975) reveal lines of convergence and divergence amongst the ridges which allow them to be divided between linear zones in each of which a similar orientation is maintained. Ridge-and-furrow moulds, or structures very like them, are occasionally associated with other sole marks, for example, isolated flute moulds (Dzulynski, 1963; Parkash, 1970) and various wave-like structures (Pettijohn and Potter, 1964). Craig and Walton (1962) did much to clarify understanding of the origin of ridge-and-furrow moulds. Using the then relatively new concept of turbidity currents, they suggested that the structures were “the result of scour at a late phase of current flow when movement near the base of the flow occurred in lines or stringers”. Dzulynski and Walton (1963) found experimentally that the structures could be produced when the crenulated front of a layer of water or of a small turbidity current advanced over weakly cohesive mud, the crenulations and ridges agreeing in wavelength. From these and later experiments there grew up the idea that the ridges and furrows were erosional structures dependent on gravity-induced secondary flows generated at the heads of turbidity-currents (Dzulynski, 1965; Dzulynski and Walton, 1965; Dzulynski and Simpson, 1966a, 1966b). The lobe-andcleft structure of gravity current heads (J.E. Simpson, 1969, 1972; Allen, 1971b) was not at that time understood, however, and the instability was limited strictly to the visibly overhanging current nose. According to our model (Fig. 1-6), the unstable zone extends much further back into the head. The furrows can be associated with the lobes in the model and with the bottom-divergent secondary flows lying back from them. The link with lobes, noticed by Dzulynski (1965), is supported by the expectation that the flow is most powerful behind these bulges (Allen, 1971b). The ridges, where there has been less erosion, must therefore be associated with the weaker currents flowing in the tunnels entered through the clefts. J.E. Simpson

42

(1972) found that as the head advanced, the clefts repeatedly joined up and reformed at new points on the lobes, in a manner consistent with the ridges and their downcurrent-pointing junctures having originated at these features. That such geometrical and kinematic features of the nose and near-nose of turbidity currents can be preserved suggests that the flows creating ridge-and -furrow moulds were relatively small and gentle, a view supported by Simpson’s experimental results on the scaling of the clefts. It seems possible that the mud beds were not eroded in a conventional sense but, being weakly cohesive, were moulded plastically by the current with little accompanying loss. If they were corraded to produce the furrows and ridges, then the tools responsible have left no individual traces of their work. Clefts seem to occur at more than one characteristic transverse spacing (Dzulynski, 1965; J.E. Simpson, 1969, 1972), implying that a hierarchy of secondary flows exists in the head of a gravity current. Such hierarchies could explain the patterns of converging and diverging currents which can

Fig. 1-25. Pattern of secondary currents recorded by ridge-and-furrow moulds on the underside of a turbidite sandstone in the Tertiary deep-sea fan deposits of the San Sebastian area, northern Spain (inferred from photograph bottom of p. 36 in Kruit et al., 1975). In order to facilitate comparison with the original photograph, the reader sees the current as though looking upward through the sea bed. If the ridge-and-furrow moulds (spacing approximately 2 centimetres) represent the smallest lobes and clefts developed at the turbidity current head, then the larger scale patterns suggest the occurrence also of lobes and clefts of intermediate (spacing 0.1-0.2 m) and larger (spacing 0.25-0.75 m) sizes.

43

sometimes be inferred (Fig. 1-25) from ridge-and-furrow moulds on large bedding surfaces (J.M. Clarke, 1917; Kruit et al., 1975). The frequent addition of ladders of flute-like features suggests that the secondary currents were accompanied by a mode of longitudinal instability. The model given in Fig. 1-6 may also explain (Allen, 1971b) why some flute moulds occur in regularly spaced longitudinal clusters (Kuenen, 1957; Dzulynski, 1963; Dzulynski and Walton, 1965). Presumably the clusters were scoured by the vigorous flows behind lobes, the currents at the loci of clefts being too weak materially to affect the bed.

WAVE-RELATED FURROWS AND RIDGES

A readily disturbed balance between erosion and deposition exists at the margins of lakes, seas, and oceans. Where erosion prevails, and the margins are muddy, wave-controlled scour shapes a characteristic spatial sequence of forms elongated perpendicular to the coastline, which assume a scale possibly related to wave size and a horizontal extent dependent on bed slope and

Fig. 1-26. Schematic development at the edge of a retreating tidal marsh or mud bank of erosional furrows and ridges related to wave action.

44

water-level range. I have seen this sequence bordering small Swedish lakes and on the Louisiana shore, but it is most spectacularly developed under a large tidal range, as on the North Sea coasts. Where net erosion prevails here (Fig. 1-26), the salt marsh and high tidal-flat muds are cut into deeply embayed cliffs, which give way downslope to mazes of anastomosing furrows with intervening mounds, in turn displaced seaward by yardang-like whalebacks and pillars rising from a plain of rippled sand veneering a level surface abraded into mud. That the features are erosional is clear from many details of their form. Lamination appears on the sides of embayments, for example, and on the flanks of the mounds is exploited in the formation of encircling terraces and overhangs. Plant roots and the shells of deeply burrowing bivalves (e.g. Scrobiculuriu) are commonly exposed along the crests of the mounds. Not only is rippled sand abundant on the floors of the furrows between mounds, but gravel and shells are often to be found. The sides and floors of the furrows are smooth and commonly criss-crossed by striae and small grooves, suggesting that the muddy substrate was corraded by this debris. Strong wave surges can in fact be observed between mounds when partly inundated, and the presence of gravel and shells testifies also to the current strength. There are several mainly early allusions to the presence of these features on intertidal flats (Steers, 1934; Guilcher, 1958a; J.R. Marshall, 1962; G. Evans, 1965), and more details are given by Wohlenberg (1954), Inglis and Kestner ( 1958), V.J. Chapman ( 1960), Hawkes ( 1962), Greensmith and Tucker (1966), Kidson and Manton (1973), Reineck (1974b), Kestner (1975), Larsonneur (1975), and Augustinus (1978, 1980). Typically, the mounds are about 0.5 m apart transversely and about 0.25 m deep. Although these features generally lie at a high angle to the coastline, and nearly at right-angles to the crests of refracted waves, most authors explicitly or implicitly associate them with tidal current-action. Hawkes attributed the structures to corrasion during wave backwash. Forms similar to those in Fig. 1-26 are known to be developed on glacial tills (Steers, 1946), beachrock (Emery and Cox, 1956; Russell, 1959; McLean, 1967; Alexandersson, 1969, 1973), Mississippi delta mudlumps (Morgan and Andersen, 1961), and other hard substrates (Swinnerton, 1927; Cloud, 1959; Kaye, 1959; Shiells, 1963) in the littoral zone. Figure 1-27a shows examples with gravel fills from a marine rock-platform (calcretized mudstone of Devonian age), and I have also found them on chalk platforms. The instances shown in Fig. 1-27b were scoured into plastic mud by sand accompanied by a little gravel and shell. The presence of tools, and the observed action of waves, has led to the widespread acceptance of these littoral structures as due to wave-controlled corrasion, though rilling by fresh water is assigned importance by McLean. The structures that Shiells described are recent, as they lie at right-angles to the coast and are not definitely preserved within a rock sequence. Instances of sublittoral furrows and ridges are known. Forms spaced

45

Fig. 1-27. Erosional furrows and ridges related to wave action. a. In hard red mudstone with calcite nodules and veins, Red Marls (Devonian), Swanlake Bay, Dyfed, Wales. Hammer 0.33 m long points seaward. b. In recent intertidal muds undergoing erosion, seaward side of Scolt Head Island, Norfolk, England. Trowel 0.28 m long points seaward. Note rippled sand in furrows and weakening of ridges seaward.

46

about 4 m apart were found by Groba (1959) and Seibold (1963) to have been cut into tills on the Baltic Sea coast in water to depths of 2-3 m. Norrman (1964) attributed to corrasion under wave-action a series of slightly smaller structures encountered on a clay surface in the shallows of Lake Vattern. Neev and Emery (1967) observed large areas covered by furrows and ridges when water-level fell in the Dead Sea. Whatever mechanism governs the wave-induced corrasion of cohesive substrates into ridges and furrows aligned with the direction of wavepropagation, it seems necessary to suppose that the vigorous oscillatory wave-currents are accompanied by steadier secondary or perhaps masstransport flows which serve to concentrate into parallel zones the debris acting as tools, so permitting the bed to be eroded differentially. These currents cannot be associated with the short-crestedness of the waves, or with their reflection at the coast, for in these cases the near-bottom mass transports converge and diverge only along shore-parallel zones (Carter, 1972; Carter et al., 1973). Possibly the furrows and ridges are caused by Langmuir circulations (Fig. 1-9) that impinge on the coast. This idea is supported by the apparent dependence of the scale of the structures on the size of the waves, but two difficulties remain. Firstly, a unique directional relationship must exist between wind and wave in order for these secondary flows to arise and, secondly, furrows and ridges appear generally to be much smaller in wavelength than Langmuir vortices, at least as ordinarily developed. A point in favour of the idea is that in lakes (Norrman, 1964; Neev and Emery, 1967), the structures mark the shore exposed to the greatest fetch and the generally stronger and more persistent winds. Furthermore, the larger structures seem to be associated with the bigger fetches. Wave-formed furrows and ridges have a seemingly scanty fossil record. Subfossil examples may occur within Holocene tidal-flat and lagoonal sequences (Kestner, 1962; Van Loon and Wiggers, 1975), and on Quaternary raised beach platforms (J.A. Wright, 1964). The most convincing of older examples are described by Pannekoek (1960) from the Psammites du Condroz (see also Van Straaten, 1954b), and by Macar and Ek (1969, and J.D. Bradshaw (1966). Possibly the erosional grooves and ridges described by Barnes (1965), Goldring (1971), and Baldwin and Johnson (1977) are of a related origin. Unless a sequence of forms like that in Fig. 1-26 can be seen, the exact origin of erosion grooves in shallow-marine sequences seems difficult to determine. WAVE-RELATED GRAVEL STRIPES

On sheltered sandy beaches under calm conditions, I have often met with large numbers of equispaced stripes of granules and fine pebbles trending up and down slope which lie in ranks between contour-parallel gravelly zones

47

Fig. 1-28. Gravel stripes overlying fine to medium-grained sand, North Beach, Tenby, Dyfed, Wales. Trowel 0.28 m long points seaward.

(Fig. 1-28). The stripes can be several metres long but are only 0.1-0.3 m in transverse spacing. They are slightly elevated and the material composing them is apparently moving freely over the close-packed and less mobile sand between and beneath. How these structures arise is unknown, but a roughness-related instability of the wave swash and backwash may be suggested.

SPUR-AND-GROOVE

Where hermatypic corals and salt-water algae flourish, no clear-cut distinction is possible between wholly erosional sublittoral features attributable to furrows and ridges and structures of a similar character in the formation of which the growth of these organisms has played a substantial if not predominant role. These organically-related structures are called spur-and groove, and their existence has been known since coral reefs first attracted the attention of such investigators as Charles Darwin and Agassiz. Spur-and-groove abound along the edges of coral atolls and reefs, where marine algae commonly also flourish (Crossland, 1922; Teichert and Fairbridge, 1948; Tracey et al., 1948; Newell et al., 1951, 1959; Doty and Morrison, 1954; Emery et al., 1954; Munk and Sargent, 1954; Guilcher, 1956; Newell, 1956; Newell and Rigby, 1957; Cloud, 1959; Goreau, 1959; Wiens, 1959; Shinn, 1963; Muller, 1964; Tracey et al., 1964; Maiklem, 1968;

48

Bird, 1971; Purdy et al., 1975; Roberts et al., 1975; Faure and Montaggioni, 1976; Rigby and Roberts, 1976; Sneh and Friedman, 1980). The spur-andgroove are arrays of regularly spaced ridges and hollows which extend perpendicularly out from the reef crest into depths of 20-30m. The spurs have steep and often overhanging sides up to 20m in height. Where wave-action is intense, each spur terminates to seaward in a massive prow-like feature, but otherwise the ridge crest falls gently to the sea floor. The grooves between vary from narrow to broad and flat; their floors are usually strewn with coral and other debris, or covered by a sheet of rippled carbonate sand. The wavelength of spur-and-groove ranges from 10 m to as much as 100 m, depending on water depth and wave climate. The spur-and-groove associated with algal reefs and biostromes are generally much smaller in scale (Eardley, 1938a; Carozzi, 1962; G.R. Davies, 1970b; Stoddart, 1971; Hofmann, 1973; Logan et al., 1974), the structures somewhat resembling externally the furrows and ridges developed by waves. The algal spur-and-groove also lie at right-angles to the water’s edge. Spur and groove appear to be the expression of a complex organo-physical system in which vigorous wave-generated currents can maintain and perhaps enlarge the grooves by corrasion, while organic growth either builds a spur upward and outward or modifies a pre-existing erosional ridge (e.g. Tracey et al., 1948; Emery et al., 1954; Newell, 1956; Cloud, 1959; Shinn, 1963). The system may be similar physically to that involved in the production of the erosional furrows and ridges. Thus coral spur-and-groove generally appear only on the windward side of an atoll or reef (Munk and Sargent, 1948), take a transverse spacing related to wave size (Roberts et al., 1975), and broadly agree in wavelength with oceanic Langmuir circulations (e.g. Faller and Woodcock, 1964; Scott et al., 1969). Fossil spur-and-groove should be detectable, but are so far known only amongst algal bioherms. These are groups of parallel linear mounds which, from their internal structure, have clearly grown upward from an initial substrate, generally while debris (some derived from the bioherms) was accumulated by currents in narrow channels between (P. Hoffman, 1967, 1973, 1974; G.M. Young, 1974; Young and Long, 1976; Button and Vos, 1977; Eriksson, 1977). They are commonly interpreted as lying at right-angles to shore. GLACIAL FLUTINGS

Glaciated terrains commonly display a variety of fairly regularly spaced ridges and hollows that evidently are related to ice flow, as they are elongated approximately parallel with the direction of glacier-movement as shown by accompanying bed-rock striae. The term fluting is usually applied to the more elongated of these features where developed on surfaces underlain by till or stratified drift (Fig. 1-29). Flutings range from small features

49

Fig. 1-29. Air photograph showing glacially fluted till in Athabasca area, Alberta, Canada. Ice moved from left to right. Each square land-holding has side of approximately 400m. Photograph courtesy of J. Shaw, and reproduced by permission of Government of Alberta, Department of Mines, Energy, and Resources.

with heights in the order of 0.1 m and transverse spacings comparable with 1 m, to large ridges and hollows many kilometres in length, up to 20 m in height, and in the order of 500m apart transversely (e.g. Dyson, 1952; Hoppe and Schytt, 1953; Gravenor and Meneley, 1958; Lemke, 1958; Baranowski, 1970; J. Shaw, 1975; Boulton, 1976; Aario, 1977a, 1977b; Ehlers and Stephan, 1979; Heikkinen and Tikkanen, 1979; Moran et al., 1980). Large boulders are commonly found at the up-glacier ends of the smaller flutes, but analogous bed-rock hills are not known to accompany the larger features. Grooves and ridges comparing in size and shape with the larger flutings formed in tills are also known to have been sculptured in crystalline bed-rock (H.T.U. Smith, 1948). The larger flutings as they shorten along their crests grade into the widely distributed glacial landforms known as drumlins (e.g. Ebers, 1926; Gravenor, 1953, 1974; Reed et a]., 1962; Vernon, 1966; Trenhaile, 1971, 1976; A.R. Hill, 1971, 1973a; Finch and Walsh, 1973; Gluckert, 1973; M.J.C. Walker, 1973; G.F. Mitchell, 1976;

50

Aario, 1977a, 1977b; Finch, 1977; Rose and Letzer, 1977; Heikkinen and Tikkanen, 1979; Menzies, 1979a, 1979b). These streamlined hills composed of till or partly of stratified material are generally 10-20m in height and 250-500 m apart transversely, being usually 4- 10 times longer than wide. Their shape has been compared to an ellipsoid (Reed et al., 1962), but a leminscate loop with the blunt end facing up-glacier is a better fit in plan (Chorley, 1962), as is true for yurdungs (Mainguet, 1968, 1972a). The magnetic and particle fabrics of the sediments composing drumlins and flutings have a strong preferred orientation approximately parallel with the elongation direction of these landforms (e.g. Hoppe, 1951; Donner and West, 1957; H.E. Wright, 1957; Gravenor and Meneley, 1958; Andrews and King, 1968; A.R. Hill, 1971; Shaw and Freschauf, 1973; J. Shaw, 1975, 1977; Boulton, 1976; Morris and Morland, 1976). However, Shaw and Freschauf (1973), followed by Heikkinen and Tikkanen (1979), emphasize that there are systematic deviations from strict parallelism, the fabrics in plan showing a regional herringbone pattern related to the distribution of the landscape ridges and hollows (Fig. 1-30a). The particles not only plunge up-glacier, but are inclined away from hollows and towards ridge-crests. The streamlined form, regular spacing, flow-parallel orientation, and fabric properties of drumlins and the larger glacial flutings led Shaw and Freschauf (1973) and Aario ( 1977a) to propose that these landforms are (a)

Clast fabric

4

2

I

- ' *

-

,

I

-

-

-

.

Fig. 1-30. Glacial flutings and their origin. a. Schematic representation of clast long-axis fabrics in fluted till, and the shape of fluted bedrock. b. Possible motion in transverse section of glacier during formation of fluted till. c. Possible motion in transverse section of glacier during formation of bedrock flutes.

51

deposited by till-rich glaciers in which have been developed transversely periodic near-bed motions (Fig. 1-30b), which are or resemble secondary flows like those in Fig. 1-1. Shaw and Freschauf also suggest that glacially formed bed-rock grooves may arise in response to similar motions, but in a regime of differential erosion which permitted negligible till accumulation (Fig. 1-3Oc). These proposals are an advance on the rheological explanation of drumlins developed by Smalley ( 1 966b), Smalley and Unwin (1968), Menzies (1979a), and Whittecar and Mickelson (1979), who merely defined some of the conditions which possibly attend formation of these landforms. But the Shaw-Freschauf theory is itself far from complete, being almost wholly kinematic. Whatever the extent to which ice is capable of lateral movement, perhaps as a consequence of thermal convection (Hughes, 1976), Shaw and Freschauf imply that the motion of glaciers is at times subject to a mode of transverse instability. It is worth noting that an associated longitudinal instability may occasionally be developed, since drumlins are shortcrested and commonly en-echelon. An approach to flutings explicitly from instability may prove fruitful. The Shaw-Freschauf theory also accounts for the smaller morainic flutings. However, when these occur in the lee of large boulders, as is commonly the case, the explanation suggested by Dyson (1952), and elaborated by Boulton (1 976) and by Morris and Morland (1976), appeals more. According to this notion, the shape and fabric structure of boulder-related flutings is consistent with the lateral and upward inflow of mobile till into the spaces which open up in the lee of boulders as the glacier over-rides them. TROUGH BANDING IN LAYERED IGNEOUS ROCKS

Many workers have described, notably from layered basic igneous rocks (e.g. Wager and Deer, 1939; Hess, 1960; Upton, 1960; Emeleus, 1963; E.D. Jackson, 1971), what has come to be termed trough banding, and this structure is particularly clearly seen in the spectacularly exposed Skaergaard Intrusion of East Greenland (Wager and Brown, 1968). Trough banding of the Skaergaard Intrusion appears in the form of sharp-based layers, between 0.1 and 1.0 m thick, in which the content of ferromagnesian minerals declines upward. The layers are remarkably concordant and apparently much longer than wide. In transverse section they are weakly concave-up to flat and with upturned margins, the width generally measuring a few tens of metres. They lie directly above each other, occasionally with a slight and normally erosional offset, to form a vertical stack of several tens that is separated laterally from similar stacks at the same stratigraphical level by vertical zones of largely unbanded rock. The lenses in each stack appear to be elongated in the direction of the axis of the broadly conical (inverted) intrusion, and dip radially inward toward that axis.

52

Wager and Brown (1968) suggested that the trough banding of the Skaergaard Intrusion was formed by the action of intermittent flows, in the nature of turbidity currents, that travelled inward down the axially dipping walls of the magma chamber as it shrank through cooling. Another possibility is that the laterally alternating stacked lenses and unbanded pillars record the existence of Taylor-Gortler vortices within the boundary layer of convection currents existing within the magma. The lower walls and floor of the shrinking magma chamber appear to have been concave-up, and the high apparent viscosity of the magma would have put the Reynolds number almost certainly within the laminar range. It may be suggested from their cross-sectional shape that the trough bands formed where hot and relatively inviscid fluid from the outer part of the boundary layer descended toward the surface of solidification and diverged over this bed. This idea in no way contradicts McBirney and Noyes’s ( 1979) recent important critique of layering mechanisms in basic igneous intrusions, but adds a further dimension to their discussion.

SUMMARY

Transverse modes of instability cause secondary flows in fluids under shear, in which a circulatory motion organized into counter-rotating streamwise cells becomes superimposed on the primary motion. Sand ribbons found on the rocky or gravelly floors of rivers, tidal seas, and deserts are explicable in terms of secondary flows, which heap up the mobile grains into streamwise ridges. The cause of these secondary flows may be the transverse variations of bed roughness that can develop when limited amounts of sediment are available for transport. A variety of erosional grooves and ridges, some found in rivers, others in the desert, and still others in the seas and oceans, point to the differential action of secondary flows where substrates are weak enough to experience generally corrasion. Transverse roughness variations may again promote these motions. Longitudinal desert dunes take a shape and scale relating them to secondary motions affecting the entire atmospheric boundary layer. Their cause may be either an inflectional instability promoted by the rotation of the Earth, or a gravitational instability connected with the rise of air heated at the desert surface. A secondary flow model is also able to explain tidal current ridges. The least understood secondary motions are those which appear to be responsible for longitudinal furrows beneath turbidites, wave-related ridges and stripes, the flutes and grooves observed on till sheets, and the trough banding of layered igneous rocks.

53

Chapter 2

FREE MEANDERING CHANNELS AND LATERAL DEPOSITS INTRODUCTION

A sideways twisting course is often taken by a laterally restricted flow of fluid of a sufficient size and speed when constrained by gravity against a deformable medium. Natural instances of this habit of motion abound, the term meandering being appropriate to unitary flows (Ferguson, 1975). Unquestionably the best known are single-channel rivers wandering in alluvium (e.g. F.A. Melton, 1936; Fisk, 1944; E.W. Lane, 1957), as reviewed recently by Callander (1978). Indeed, for Strabo (Russell, 1954), the River Meander (Buyuk Menderes) in southwest Turkey was the type of “everything winding”, that is, meandering. Less familiar but as important sedimentologically are the meandering channels which serve as the arteries and veins of intertidal flats and salt marshes alluviated by the sea (e.g. Dury, 1972). Meandering is not restricted to free-surface flows in alluvial settings. A thread of water will wind over a tilted glass plate (Tanner, 1962; Gorycki, 1973a). The Gulf Stream meanders (D. Hansen, 1970; Robinson et al., 1974), as do the atmospheric jet streams (Reiter, 1963). Turbidity and other currents seem able to construct meandering channels on deep-sea fans and elsewhere on the ocean floor (e.g. Komar, 1969; Cleary and Conolly, 1974; Egloff and Johnson, 1975; Chough and Hesse, 1976). On land many rivers meander through bed-rock channels containing only trifling amounts of alluvium (Dury, 1964a, 1964b, 1965). Run-off over limestone commonly engenders meandering gutters (e.g. Zeller, 1967a, 1967b; Miotke, 1968), chiefly through the mass-transfer of the rock into the carbonated water. Supraglacial streams typically form meandering channels (e.g. Zeller, 1967a; Knighton, 1972b; Ferguson, 1973b), mainly by ice-melting assisted perhaps by corrasion. This chapter discusses the meandering channels formed by rivers and by tidal streams in an alluvial context; these channels are preservable sedimentary structures. During meandering a characteristic suite of deposits is produced, typified by a distinctive arrangement and structure. Several names have been applied to these (Van Straaten, 1954a; Reineck, 1958a; Allen, 1963b), but the terms lateral-accretion deposit and lateral-accretion structure seem most appropriate. Examples of lateral accretion structure are generally hierarchical, for superimposed on the gross elements expressing channel migration are smaller structures due to the common bedforms. Furthermore, a range of lithologies usually is present. The facies to which lateral accretion deposits contribute is, with its upward-fining cyclothems, one of the most important and distinctive in the geological record.

54

FLUVIAL AND TIDAL MEANDERS

Meander settings Traditionally, meanders are ranged between two end-members. In one limiting setting (Fig. 2-la) the channel lies in bed-rock or ice, associated with little or no alluvium. Such channels are called incised (Jefferson, 1902; Dury, 1964a) or intrenched (Hack, 1965), though Kirkby’s (1972) non-committal “non-alluvial” is most appropriate. The second limiting setting (Fig. 2- Ic) shows channels in contact everywhere with alluvium previously deposited in or near them. These are Jefferson’s (1902) “meanders on flood plains”, the spilling meanders of Blench (1957), the free meanders of Dury (1964a) and Carlston (l965), and the appropriately named alluvial meanders of Hack (1965) and Kirkby (1972). At least one intermediate setting demands recognition (Fig. 2-lb). It is exemplified by the confined alluvial meanders of Galay et al. (1973) and Mollard (1973), as foreshadowed by E.W. Lane (1957) in his intermediate class “where the stream form is partly determined by the rock of the earth’s crust and partly by the stream itself”. Confined alluvial meanders have their lateral growth restricted by relatively resistant terrace deposits or bed-rock. Only confined alluvial and alluvial meanders are of concern in what now follows. Many rivers display confined alluvial meanders. Good examples (Figs. 2-2, 2-3) occur on the Beaver River (Blench, 1969; Mollard, 1973) and the

/

Flow

Fig. 2-1. Schematic settings for meandering channels. a. Incised into bedrock or other cohesive substrate. b. Laterally confined between bedrock walls. c. Freely meandering in alluvium.

55

Red Deer River (Neill, 1964, 1967; McPherson, 1969). Other cases are the Klaralven (De Geer, 191I ; Sundborg, 1956), the Oulanka (Koutaniemi, 1979), the Oka (Shantzer, 1951), the San Joaquin and Lower Missouri (F.A. Melton, 1936; Schmudde, 1963), and parts of the Omo (Butzer, 1971). Tidal meanders of any kind are ill-known, and I am unable to cite any explicit descriptions of the confined alluvial type of this origin. Examples may nevertheless exist in the Nigerian and eastern North American tide-lands (Allen, 1965e; Daboll, 1969.; Farrell, 1970; S.C. Harrison, 1972), where creeks cut back into resistant Pleistocene and older deposits. Alluvial river meanders are much described. Typical examples are found on the Pembina River (F.A. Melton, 1936; Blench, 1969) and the Qu'Appelle River (Mollard, 1973), which follow a tortuous path flanked by a broad floodplain with many abandoned meander loops (Fig. 2-4). Further examples in the Americas are the Mississippi (Fisk, 1944), Yukon (Wahrhaftig, 1965), Minnedosa (Galay et al., 1973), Assiniboine (Mollard, 1973), White (Brice, 1974a), Beatton (Hickin, 1974; Nanson, 1980), the Amazon (Tricart, 1977), and Rio Tebicuary (Rich, 1942). Many Papuan rivers exemplify the type (Speight, 1965a, 1965b; Blake and Ollier, 1971), as do the Taieri in New Zealand (A.P. Grant, 1950), the Meander (Russell, 1954) and Jordan (Schatt ner, 1962) in the Near East, and the Omo in Africa (Butzer, 1971). Tide-shaped alluvial meanders are little known. Fig. 2-5 is representative

Fig. 2-2. Air photograph (6 by 4.5 km) showing the confined meanders of the Beaver River, Saskatchewan, Canada. Flow from right toward lower left. Original photograph supplied by the Surveys and Mapping Branch, Department of Energy, Mines and Resources.

56

Fig. 2-3. Part of the Red Deer River, Alberta, Canada. River flow from top toward bottom of photograph, which represents an area measuring approximately 2.5 by 3.75 km. Photograph courtesy of C.R. Neill, and reproduced by permission of Government of Alberta, Department of Mines, Energy, and Resources.

57

Fig. 2-4. Air photograph (4 by 6km) showing the alluvial meanders and many cut-off channels of the Qu'Appelle River, near Broadview, Saskatchewan, Canada. River flows from bottom toward top. Original photograph supplied by the Surveys and Mapping Branch, Department of Energy, Mines and Resources.

58

Fig. 2-5. Meandering tidal channels in mangrove swamps, near Sombreiro River, Niger delta, Nigeria. Picture represents an area measuring approximately 3 by 4.5 km. Photograph reproduced by permission of Government of Nigeria.

of channels found in the mangrove-inhabited intertidal flats of low latitudes (see Allen, 196%; MacNae, 1966, 1968; Coleman et al., 1970; Dury, 1972). All of the channels are meandering, but whereas the larger form a net, the

59

smaller are dendritic, as with rivers. In higher latitudes, where the intertidal flats lack standing vegetation, meandering is invariably associated with dendritic channel systems (e.g. Van Straaten, 1954a; Pestrong, 1972a, 1972b; Bridges and Leeder, 1976). In the essentially supratidal salt-marsh environment, however, mixed reticulate and dendritic meander networks are found (e.g. Steers, 1934, 1960; Langbein, 1963; Myrick and Leopold, 1963; Pestrong, 1965; Land and Hoyt, 1966). As in lower latitudes, larger channels tend to monopolize the reticulate networks. Analysis and description

It is one thing to formulate a qualitative conception of meandering, but more difficult to define and analyse real meanders in a way leading to quantitative treatment. Fig. 2-6a illustrates a meandering channel. Since the edges of the water surface define the channel margins, in order to draw the channel and measure channel width ( W ) , we must also define the discharge-condition in the channel. Taking river and tidal channels as expressed on air-photographs or maps, the discharge-condition generaIly implied is that of bankfull or near-bankfull flow. The channel centreline possesses a series of inflection points, I,,I,, ...,I, which, following Brice (1964), may be joined by a smooth curve, the meander-belt axis. Developing E.W. Lane’s ( 1957) treatment, the

Pool

Riffle

Bar

Riffle

Fig. 2-6. River channel and talweg meanders. a. Definition diagram for river meanders. b. Meandering thalweg in a straight channel, showing relationship to pools and riffles (crossings).

60

meander belt lies between tangents to the outsides of the curves or meanders of the active stream. The meander-belt margins are the tangent-lines themselves, the meander-belt width ( M ) being the distance between opposite margins. These conceptions harmonize with general usage (Jefferson, 1902; Hjulstrom, 1942; Leopold and Wolman, 1960; Nagabhushanaiah, 1967; Zeller, 1967a; Chang and Toebes, 1970; Chitale, 1970). For Matthes (1941), however, the meander-belt embraces cut-off as well as active channels, and so can be wider than the meander-belt in Fig. 2-6a. Carlston (1965) uses “meander width” synonymously with meander-belt width. Meanders themselves next claim attention. Following Matthes ( 1941) and E.W. Lane (1957)’ a meander comprises two consecutive meander loops, in one of which, to the right of the meander-belt axis looking downstream, the flow is anticlockwise, and in the other of which, to the left of this axis, the flow is clockwise. With tidal channels, however, “downstream” may become a matter for choice. In every case the channel segment lying between every second inflection point comprises one meander. Each loop embraces a body of sediment called a point bar, the surface of which may show curved ridges and swales called meander scrolls (e.g. Nanson, 1980). The meander wauelength ( L ) is the distance measured along the meander-belt axis between one inflection point and the next but one downstream (Carlston, 1965; Zeller, 1967a; Chang and Toebes, 1970). Wavelength has also been measured between points of tangency on the meander-belt margins (Matthes, 1941; Inglis, 1947; E.W. Lane, 1957; Chitale, 1970). Alternatively, the spacing of inflection points at the base of a meander loop-Brice’s (1974b) “loop length’’-may be used to measure meander size, where the loop length is about one-half the wavelength (Jefferson, 1902; Popov, 1965; Kondrat’yev, 1969). Finally, meander size may be specified by the meander-path length ( A ) , the distance along the channel centreline between alternate inflection points (Chitale, 1970; Ferguson, 1973a). Other measures may be useful. The meander-loop length ( A ) , roughly Brice’s (1964, 1974a, 1974b) “height of arc”, is the distance along the axis of a meander loop betwen the meander-belt axis and the channel centreline. The loop axis carries midway the centroid, a reference point used by Brice (1974a) in studying meander migration. The meander-loop length is roughly equivalent to one-half of the meander width of E.W. Lane (1957) and Nagabhushanaiah ( 1967), or one-half of the so-called meander amplitude (Leopold and Wolman, 1960; Leopold et al., 1964; Carlston, 1965; Chang and Toebes, 1970). Meander-loop shape may partly be described by the meander-loop radius (r,,,),measured at the channel centreline. Also expressive of shape is the meander-loop central angle ( O ) , introduced independently by Popov ( 1965) and Brice (1974b). It is measured between normals to the channel centreline at inflection points. Kondrat’yev (1969) uses a whole suite of descriptive angular measures.

61

Of these measures, meander wavelength particularly has been criticized (Carlston, 1965; Speight, 1965a), for how should one choose the “typical” meander where no two meanders are exactly the same? Carlston met this difficulty by calculating an average wavelength, but even this procedure leaves considerable room for error and subjectivity. Attempts have therefore been made to objectify the assessment of meander scale by evaluating spectra and autocorrelograms for channel direction and direction-change series (Speight, 1965a, 1965b, 1967; Toebes and Chang, 1967; Chang and Toebes, 1970; Thakur and Scheidegger, 1970; Ferguson, 1975, 1977a). The outcome has been most encouraging. The results based on the different series and methods agree satisfactorily and, at least in the case of Speight’s Australasian streams, there is evidence of more than one significant modal meander wavelength. It is even possible to extract numerical measures of meander regularity from the direction and direction-change series. These techniques may seldom be applicable to palaeochannels, however, because high-quality information is required about relatively long segments of channel (see Ferguson, 1977b). In describing meander planimetric form, two aspects are of interest: the shape of the channel centreline, and the degree of parallelism of the channel margins. Four types of plan are recognized, following Brice ( 1974a, 1974b) in preference to Chitale ( 1970), namely simple symmetrical, simple asymmetrical, compound symmetrical, and compound asymmetrical (Fig. 2-7). Some of Brice’s compound asymmetrical loops and Hickin’s (1974) T bends are whole SYMMETRY SYMMETRICAL

ASYMMETRICAL

BANK CONFORMITY

I

Fig. 2-7. Classification of meander shapes, in terms of number and symmetry of bends, and conformity of banks.

62

meanders in terms of Fig. 2-6a. Parallel-sided and beaded are terms useful in describing the relationship between the margins of loops (Fig. 2-7). In a parallel-sided loop, the channel is of virtually constant width (K.S. Richards, 1976c) and the margins are similarly curved. However, the margins of a beaded loop are distinctly non-parallel and usually are oppositely curved. Ahnert (1960) first singled out beaded meanders, though he did not use this term. All river and most tidal meanders seem to be parallel-sided, at least at high discharges. Simple symmetrical fluvial meanders appear on the Pop0 Agie (Leopold and Wolman, 1957) and the Mississippi, notably near Greenville, Mississippi (Fisk, 1944, 1947). Many symmetrical tidal meanders are shown in Fig. 2-5. The Beaver and Red Deer Rivers (Figs. 2-2, 2-3) and the Klaralven (Sundborg, 1956) abound in asymmetrical simple meanders, which in planimetric form unequivocally indicate the flow direction (Raisz, 1955). Indeed, their asymmetry is frequently so marked that it amounts to the almost complete suppression of alternate quarters of a sinusoidal meander path. Compound symmetrical and asymmetrical meanders appear on numerous rivers (e.g. Schattner, 1962; Brice, 1964, 1974a, 1974b; Butzer, 1971; Hickin, 1974) as well as on many tidal channels (e.g. Fig. 2-5). Beaded meander loops are recorded from tide-lands in middle latitudes (e.g. Ahnert, 1960; Langbein, 1963; Dury, 1967; S.C. Harrison, 1972) and nearer the Equator (Allen, 1965~;Hervieu, 1968; see also Fig. 2-5). Generally, only the larger channels take the beaded form. No comprehensive classification of channel planimetric form has yet been advanced within which meandering channels may adequately be fitted and subdivided. Existing schemes fail in that the attributes of individual meanders are not distinguished clearly enough from those of meander belts and even of valleys. Schumm ( 1963a) considered only single channels, recognizing straight, transitional, regular, irregular, and tortuous patterns. All but the first are meandering, as this term is used here (Ferguson, 1975), and the last three categories combine aspects of meander shape with meander-belt crookedness. Chitale's ( 1970) scheme has similar limitations. In Dury's ( 1969) classification, only irregular and meandering channels are distinguished, presumably by appeal to a certain but unspecified regularity of appearance. Rust ( 1978) distinguished meandering from braided channels. The cross-sectional shape of a meander loop systematically changes from one station to another downstream (Figs. 2-6a and 2-8). Near an inflection point, the high-stage channel is relatively shallow and uniform in depth. These shallows constitute a rijfle or crossing where bars may emerge at low flows. Proceeding downstream into the bend, however, the cross-section grows increasingly asymmetrical and triangular, with a gradual outward shift of the fairway towards the outer concave bank and an increase in the maximum depth. Such a curved deep, called a pool, lies close to the apex of each loop. The surface of the adjacent point bars on the inner convex bank

63

0

C

C'

2 4 6

t Depth

(m)

'L/

c'

Depth (m)

Depth

00 - 2 m 2-4m

0 4 - 6 m

a

6-8m

Fig. 2-8. Secondary currents in a meander of the R. Desna, U.S.S.R.,illustrated by measured streamwise (U') and transverse (U,)components of velocity in representative cross-sections. After Rozovskii (196 1).

may be either convex-upward, straight, or concave-upward. This pattern of cross-sections is reversed as the flow passes out of the bend. Hence the river thalweg which connects the points of maximum depth in successive crosssections, swings from one channel margin to the other as each meander is traced round, as is especially clear at low flow (e.g. Grant, 1948; Hickin, 1974). The thalweg also oscillates vertically, descending from riffles into pools and either flattening out or ascending from pools to riffles. This distinctive three-dimensional geometry is shown by meandering rivers from the smallest (Wolman and Leopold, 1957; Leopold and Wolman, 1960; Wiethe, 1970; Leopold, 1973; Knighton, 1974), through those of intermediate scale (Ripley, 1927; Van Bendegom, 1947; Sundborg, 1956; Rozovskii, 1961; Nilsson and Martvall, 1972; Paulissen, 1973; R.G. Jackson, 1975), to the most majestic (Ripley, 1927; Fisk, 1947; NEDECO, 1959; Tietze, 1975). Tidal meanders are similar (Myrick and Leopold, 1963; Land and Hoyt, 1966; Dury, 1967; Reineck, 1970a; Pestrong, 1972a; Bridges and Leeder, 1976), though the beaded examples usually have a thalweg divided at

64

inflection points by mid-channel bars (Ahnert, 1960; Myrick and Leopold, 1963). In so-called straight channels (Fig. 2-6b), a riffle-pool topography and, consequently, a weakly meandering thalweg usually appear (Hensen, 1943; Leliavsky, 1955; Wolman, 1955; Kinoshita, 1957; Shamov, 1959; Fahnestock and Maddock, 1964; Leopold et al., 1964; Harms and Fahnestock, 1965; Popov, 1965; Kennedy, 1966; A.G. Anderson, 1967; Dolling, 1968; Maddock, 1969; Keller and Melhorn, 1974; Yang and Stall, 1974; K.S. Richards, 1976a). Alternate, side, or transverse bars (Allen, 1968g), firmly to loosely attached to alternate banks, define the sinuous fairway. The unstable behaviour of artificially straightened rivers (Noble and Palmquist, 1968; Yang and Stall, 1974; Lewin, 1976), drainage ditches (Dury, 1964a), and laboratory sand-bedded channels (e.g. Tiffany and Nelson, 1939; Quraishy, 1944; Friedkin, 1945; Wolman and Brush, 1961; Ackers, 1964; Ackers and Charlton, 1970b, 1970c; Schumm and Khan, 1971, 1972) leave little doubt that the riffle-pool systems of straight and of meandering channels are morphologically and dynamically equivalent, as Leopold and Wolman ( 1957) had tentatively concluded. The general topological and dynamical equivalence of the two forms of channel now seems agreed upon (Dury, 1969; Chang et al., 1971; Keller, 1972; K.S. Richards, 1976a; Keller and Melhorn, 1978), setting aside Tinkler’s unsupported views (Tinkler, 1970, 1971; Keller, 1971). Channel crookedness is the ratio of a characteristic channel length measured between two inflection points to either the air-line distance, the valley length, or the meander-belt axial length between the points. Early crookedness measures are Friedkin’s (1945) sinuosity, the ratio of thalweg length to air-line distance, and E.W. Lane’s (1957) tortuosity ratio, the stream channel (centreline) length compared with the valley length. Other early proposals are the ratio of thalweg length to valley length (Leopold and Wolman, 1957), and the ratio of meander-path length to meander wavelength within one meander (Leopold and Wolman, 1960). Measures involving thalweg length are seldom practical, however, and a restriction to single meanders presupposes a regularity of channel that is unlikely to exist. Later workers have stressed the contribution to overall crookedness that may come from the curvatures of meander belts and confining valleys (Brice, 1964; Mueller, 1968; Mansikkaniemi, 1972). We may therefore recognize sinuosity, defined as the ratio of channel length (centreline) to meander-belt axial length, preferably measured over numerous consecutive meanders (Brice, 1964; Dury, 1969), and tortuosity, which is the ratio of channel length (centreline) to air-line distance. The two measures will be numerically equal only for a precisely rectilinear meander belt; the tortuosity otherwise will generally exceed the sinuosity, though in many practical cases the difference may be negligibly small.

65

Hydromorphological relationships Engineers favouring “regime” theory (Blench, 1957), and geomorphologists stimulated by Leopold and Maddock’s (1953) outstanding work, found that the geometry of river and tidal channels depended fairly conservatively on discharge, both at-a-station, downstream within one system, and between comparable systems. The relationships involving channel width, depth, mean velocity and sediment load were originally classed under the term “hydraulic geometry”, but a grouping with other relevant dependencies under “hydromorphological relationships” may perhaps be more useful because, under the concept of hydromorphology, we can more readily look beyond the descriptive toward dynamic meanings. The dependence of width, depth and flow velocity upon discharge is now known for many rivers (e.g. Leopold and Maddock, 1953; Wolman, 1955; Leopold and Miller, 1956; Brush, 1961; Hedman, 1970; Thornes, 1970; Stall and Yang, 1972; Knighton, 1972a, 1974; Bray, 1973; Neill, 1973a) and a few tidal channels (Langbein, 1963; Myrick and Leopold, 1963; Pestrong, 1965; Dury, 1967, 1972). In terms of the conventional power functions (linear in logarithms):

W = aQ“

(2.1)

H =be“

(2.2)

U = cQp

(2.3) where W is channel width, H is mean channel depth, U is mean flow velocity averaged over the cross-section affording W and H, and Q is discharge. By continuity, Q = WHU, whence the intercept coefficients ( a , b , c ) and the exponents (m,n,p) conform to (Leopold and Maddock, 1953): abc= 1

(2 -4)

m+n+p=l

(2.5)

At a station, W, H, U and Q are instantaneous values. When downstream changes are considered, W, H, and U at the various stations take values appropriate to a selected level of discharge, for example, bankfull. The at-a-station exponents vary widely between sites on a river (e.g. Knighton, 1974), largely in response to bank strength. Because bed roughness varies with discharge, eqs. (2.1-2.3) prove in detail to be non-linear (K.S. Richards, 1973, 1976b), an observation which may weaken some theories of hydraulic geometry (Langbein, 1964; T.R. Smith, 1974). The exponents for downstream change seem more conservative. Average values for North American mid-western rivers are m = 0.50, n = 0.40, and p = 0.10 (Leopold and Maddock, 1953). The corresponding set for tidal channels reads approximately m = 0.75, n = 0.20, p = 0.05 (Langbein, 1963; Myrick and Leopold, 1963), the difference perhaps reflecting the fact that these

66

-E

lo4

-

I .

o Dury (1965)

f0

Hack (1965)

;

0 3 -

0 L

a

0

f

I02

-

10'

-

2

0

loo

O

,oo-a-Drainage basin area, A (m')

Fig. 2-9. Meander wavelength as a function of drainage basin area for a sample of North American, English, and French rivers. Data of Dury (1 965) and Hack ( 1 965).

channels are arteries as well as veins. Park (1977) has recently reviewed the hydromorphological exponents. Of special interest in palaeohydraulics are the alluvial meander wavelength-discharge relationship and, since discharge reflects drainage-basin area, the wavelength-area dependence. Only Dury (1958, 1964a, 1964b, 1965) and Hack (1965) assembled data linking river meander wavelength with basin area upstream, but really large basins unfortunately were excluded (Fig. 2-9). The visual best-fit line reads: L = 0.23A0.345

showing that wavelength gradually increases with area. Although wavelength also increases gradually with discharge (Inglis, 1947, 1949; Leopold and Wolman, 1957; Dury, 1964a, 1964b, 1965, 1976; Carlston, 1965; Speight, 1967; Zeller, 1967a; Ackers and Charlton, 1970b), Ackers and Charlton's (1970b) careful critique shows that we are far from the goal of an accurate dependence based on reliable and compatible observations. Observers have measured wavelength differently, and the quoted discharges seldom came directly from on-site rating curves. On the basis of Jefferson's (1902) and his own data, Inglis linked wavelength to the square-root of discharge, a relationship accepted and embellished by Leopold and Wolman, Dury, and Zeller. Carlston rejected this analysis, producing several rather consistent relationships:

L = 170Qi,46 L = 24.5Qt.62 L = 120Qi:

67

Mean discharge of month of maximum discharge, Omm(m3a-~)

2 I02

, , ,/ : 2

4 68i01

/ , 2

I

,,

4 6 EI02

,

, , ,,

,

2

4 6EiO3

2

Bankfull discharge,

, , ,,

,

4 6ElO4 2

I

,

4 6 E

4(m3s-I)

2

2

10

* Mean annual discharge, Om, (m3

d)

Fig. 2-10. Meander wavelength as a function of three measures of discharge in a sample of North American rivers. Data of Carlston (1965).

where the meander wavelength, L , is the mean of 6-8 observations, Q ,, is mean annual discharge, Qb is bankfull discharge, and Q , , is the mean discharge of the month of maximum discharge (Fig. 2-10). Ackers and Charlton (1970b) suggest that bankfull flow may control meander geometry in rivers. How the wavelength of tidal alluvial meanders varies with discharge is unknown quantitatively. Equation (2.1) with m = 0.5 combined with eqs. (2.7-2.9) suggest that river meander wavelength scales almost linearly with channel width. Observation strongly supports this conclusion. Adjusted for Carlston’s ( 1965)

68

criticisms, the data of Inglis (1947, 1949) show wavelength to be approximately 12.1 times width, a value supported by Leopold and Wolman’s (1960) sample. Mackay (1974) obtained a ratio of 13.6 from the Mackenzie River. Ackers and Charlton ( 1970c) determined experimentally a ratio of roughly 11, but with a weak dependence on discharge. Schumm’s (1968a) sample of American and Australian rivers gives an exceptionally large average ratio (24.7) and a wide range of individual values (8.3-87.9). The analogous ratio for riffle-pool systems in straight channels broadly agrees with the Inglis 104

8 6 4

2 0

Lsopold and Wolrnan (1960)

j 10; %

4 6 2 10’ 8 6 4

2 100

4 6ElOo 2

2

4 6EI01

4 6ElO2 2

2

4 6SlO3 2

4 6 ElO4

Channel wldth, W (m)

-

Slnuoslty 0100-125

(b)

v .

A125-175 I 75 -3 0

V V

A

-W-

0

v.j

0

4 0

.

mv 0

0

vA

0

q A

2

4

6 8

vA A

2

4

o

0

o

0

0

O=%

oo A

0

A 0

eq

6 Bl02

0

2

4

6 8 10s 2

4

,

6 8104

Channel width,Wh)

Fig. 2- 1 1. Shape of meanders in plan and profile. a. Meander radius as a function of channel width in a sample of rivers in the U S A . (Leopold and Wolman, 1960), and in the Mackenzie River, Canada (Mackay, 1974). b. Maximum channel depth in a meander loop as a function of channel width. Data largely courtesy of M.R. Leeder (1973), but with his points for the Mississippi replaced by four fresh observations and with observations from the Oredven (Nilsson and Martvall, 1972) and the Wabash River (R.G. Jackson, 1975). Note that, for each meander radius, the most sinuous rivers tend to have the largest maximum channel depths.

69

value (Engels, 1905; Leopold and Wolman, 1957; Dury, 1964a; Komura and Shen, 1970; Dury et al., 1972; Keller, 1972; Keller and Melhorn, 1974, 1978; Harvey, 1975; K.S. Richards, 1976a). Thalweg sinuosities in an experimental model of the River Rhine have a wavelength almost exactly 12 times flow width (Meyer-Peter, Hoeck and Miiller, 1937). The only tidal data is for the locally beaded channels of the Crooked River, Florida (Dury, 1972). Their wavelength-width ratio is 7.1 - 14.1 for widths measured between pools and 9.7-21.0 at pools. Tidal and river channels therefore seem similar in their wavelength-width relationships. Radius of meander curvature also scales with channel width, in a way bound up with changes of pool depth (Fig. 2-1 la). Leopold and Wolman’s (1960) large and widely cast sample, together with Mackay’s (1974) data, strongly suggest that the meander radius/channel width ratio is rarely less than 2 or larger than 6, with a preferred or average value of roughly 3.25. Hickin’s (1974) analysis from the Beatton River strongly supports the lower limiting value of the ratio suggested by these data. At variance are observations from the White and Wabash Rivers (Chang and Toebes, 1970), which afford a somewhat larger typical value for the ratio and show a weak dependence on discharge. As meander radius falls for a given width (or discharge), the sinuosity generally increases and the maximum depth, h in pool or near-pool cross-sections also tends to rise (Fig. 2-1 lb), a feature made clear by the observations of Nilsson and Martvall (1972), Leeder (1973) and R.G. Jackson (1975). Since Fargue’s (1908) day it has been appreciated that channel depth generally increases relative to width with decreasing radius of bend curvature, other factors being equal (e.g. Nwachukwu, 1973; Winkley, 1973). Empirical relationships for depth prediction were developed by several early workers, as reviewed by Chatley (1931), and Leliavsky (1955), and their use has continued (Simons, 1971; Apmann, 1972). As an example, Ripley (1927) derived a general formula yielding complete and quite realistic channel cross-sections. Radius, width, and depth relationships in tidal channels seem to be similar to those for rivers (Dury, 1967, 1972; Bridges and Leeder, 1976). The sinuosity of alluvial rivers apparently rises to a maximum at intermediate valley slopes from low values at both small and large slopes. Immamura (1935) noted from Japan that for constant channel width, the meander-belt width, a surrogate for sinuosity, at first decreased steeply and then more gradually with increasing slope. Chitale (1970) later gave a similar result in sinuosity terms. On this descending limb of the sinuosity-slope graph, there is a threshold slope for each discharge below which the stream meanders and above which the flow is braided, that is, divided laterally between more than one channel (E.W. Lane, 1957; Leopold and Wolman, 1957; Henderson,’ 1966; Chitale, 1973; Chang, 1979). The ascending limb of the graph is less satisfactorily documented. However, the sinuosity of the Mississippi River (Schumm et al., 1972) increases going from the gently

graded deltaic course upstream towards the steeper valley below the Arkansas confluence. Laboratory experiments suggest that natural channels might at sufficiently low slopes become virtually straight, having only a meandering thalweg (Ackers and Charlton, 1970c, 1970d; Shahjahan, 1970; Schumm and Khan, 1971, 1972). The preceding simple correlations conceal effects apparently linked to sediment calibre. A change in the coarseness of the sediment load, for example, dramatically alters sinuosity (Schumm, 1968a, 1968b, 1969; Schumm and Khan, 1972). A general awareness of sediment influences has come partly from direct studies of rivers (E.W. Lane, 1957; Leopold and Wolman, 1957, 1960), and partly from analyses of channel stability and efficiency (e.g. E.W. Lane, 1955; Stebbings, 1963; Shen, 1971a), but the mechanisms of sediment influence remain elusive. Indeed, there is some conflict about which sediment is significant, that exposed in banks, or that potentially transportable on the bed, though modern opinion would favour the former. Schumm (1960a, 1960b) found from the Great Plains that:

( W / H ) = 255D,-’.08

(2.10)

where D, is the weighted mean percentage of silt and clay in the river bed and banks. Though similar streams generally do flow deeper and narrower between cohesive as compared with cohesionless banks, the formula may be criticized because: (1) the correlation is partly spurious ( W and H are implicit in D,) (M.A. Melton, 1961), (2) bed and bank mud contents are uncorrelated (Ferguson, 1973c), and (3) a limited category of streams is covered (S.J. Riley, 1975). Schumm (1963a, 1963b, 1967, 1968a, 1971, 1972) later proposed that:

P = 0.94Dp,25

(2.1 1) (2.12) (2.13)

and Ferguson (1973c), using the Great Plains sample (Schumm, 1960a), advanced the correlation: W = 33.1 Qi:8Do,,o.66

(2.14)

in which P is the sinuosity, Q,, is the mean annual flood discharge, and D, is the mean bank mud percentage. Equation (2.14) confirms that channel width decreases with increasing bank strength, and the other formulae show that whereas sinuosity increases with increasing bank erosion resistance, the meander wavelength decreases. Experimental data on the effects of sediment calibre generally support the field evidence (Friedkin, 1945; Nagabhushanaiah, 1967; Ackers and Charlton, 1970a; Shajahan, 1970).

71

FLOW PROCESSES IN MEANDERS AND CHANNEL BENDS

Superelevation of the water surface A horizontally curved path is forced upon water flowing round a tidal or river meander, or following a bend in an open, laboratory channel. As J. Thomson (1876) was early to show, one result of the curvature is that each fluid element is affected by a centrifugal acceleration which must be balanced by an opposite fluid pressure, expressed by a tilting of the water surface transversely to the streamwise motion (see also Wittman and Boss, 1938; Van Bendegom, 1947; Rozovskii, 1961). The water level at the concave bank therefore exceeds that at the convex shore, by an amount called the superelevation. But as the Earth is rotating, it may also be necessary to include the Coriolis force in determining the superelevation. Furthermore, if a secondary motion emerges in the fluid due to the curvature, the friction force may also contribute significantly. The approximate transverse water-surface slope which determines the superelevation may be calculated (friction neglected) by considering the following forces acting on a unit mass of water with a horizontal streamwise velocity u following a path of constant radius, r, measured positively outwards. The centrifugal force is u2/r outwards. The Coriolis force (Vol. I, Chapter 1) is 2wu sin l, where w is the Earth's angular velocity (7.29 X rad s - I ) and 5 is the latitude. In the Northern Hemisphere, the Coriolis force acts in the positive direction of Y in anticlockwise meander loops, but in the negative sense in clockwise bends; these directions of action are reversed in the Southern Hemisphere. For equilibrium, the sum of the centrifugal and Coriolis forces must be balanced by a pressure force g(dy/dr) per unit mass, where g is the acceleration of gravity, y is water-surface height above a datum, and d y / d r is the transverse water-surface slope. Now for each r in a real meander, u is some function u ( y ) over the depth. Hence the transverse slope may be written in a similar manner to Van Bendegom (1947): (2.15) where U is u( y ) averaged over the depth at r, and k , and k , are averaging constants which, for realistic u(y), may each be taken as unity. Since the Coriolis force may be either added or subtracted, the transverse slope, and therefore the superelevation, could differ between clockwise and anticlockwise bends in the same meander belt. Bend radius and latitude chiefly set the relative importance of the centrifugal and Coriolis terms, noting that U departs little from the general order of 1 m s - ' . In practice, we may neglect the Coriolis term when 2 w sin 5 is an order of magnitude or more smaller than U/r, as with all equatorial channels, and all meanders in middle and high latitudes but the larger ones and of r,/W in excess of approximately

72

10. The Coriolis force may nonetheless introduce an asymmetry into meander belts and control the direction of wholesale lateral migration of channels (e.g. Eakin, 1914; Kabelac, 1957; Dinga, 1970), because of possible dynamic inequalities between clockwise and anticlockwise bends, and cannot be neglected for slow flows in large channels (Heu, 1967). The superelevation follows by integrating eq. (2.15) without the Coriolis term for plausible forms of U ( r ) . Shukry (1950) and Ippen and Drinker (1962) assumed that U varied as l / r , as in a free vortex (J.R.D. Francis, 1975). Others considered the forced-vortex case (J.R.D. Francis, 1973, in which U increases with r (Leopold et al., 1960; Ippen and Drinker, 1962). The integration has also been performed for U = const. (Leopold et a]., 1960; B.C. Yen, 1965), and for a parabolic dependence of U upon r (Blue, Herbert and Lancefield, 1934). C.L. Yen and B.C. Yen (1971) integrated the equation for a cross-channel variation of U that accounted for the friction due to a secondary flow. However, the shape of the water surface and the magnitude of the superelevation vary little with U( r), and for rough purposes we may assume that r = rm and U = Uav,where U,, is the streamwise velocity averaged over the whole cross-section. The superelevation by is then equal to U:W/gr,,,. It is convenient for well-developed meander loops (e.g. Fig. 2-8) to assume a vertical concave bank and a rectilinear point-bar radial profile. Referring to Vol. I, eq. (1.34), we may then take U as varying with (h/h,,)'/* and therefore with ( r - rin/rex - rin)'/*,whence: A y = - K: [W-

gw

rin(1n r e x

- In 'in)]

(2.16)

where h is the depth at radius r , hex is the depth at the concave bank of radius rex, the radius of the convex bank is rin, and the velocity at the concave bank is Kx.Whichever formula is used, the superelevation in river and tidal meanders proves to be relatively small, in the general order of 0.1 m, and hence is negligible compared with depth for all but small steep streams. Calculated superelevations generally agree satisfactorily with observation (Blue et al., 1934; Shukry, 1950; Ippen and Drinker, 1962; C.L. Yen and B.C. Yen, 1971).

Secondary flow A key feature of the motion of a real fluid in a curved open channel is a secondary flow in the form of a vertically flattened helical spiral. As an

accompaniment to the general downstream movement, near-bed fluid travels inwards towards the convex bank while that near the free surface flows across the channel to the concave shore (Fig. 2-12a). This type of secondary flow was predicted by J. Thomson (1876) and confirmed experimentally by him using markers of sand, dye, threads and seeds (J. Thomson, 1877, 1879). Indeed, the motion is an everyday experience, appearing whenever a cup of

73

Fig. 2-12. Secondary flow in (a) curved open channel, (b) curved pipe of circular cross-section, and (c) curved conduit of square cross-section.

tea or a vessel of liquid is stirred with a smooth circular movement. Secondary currents also accompany fluid flow through curved pipes and ducts (Fig. 2-12b,c), oppositely rotating helical spirals lying one on each side of the plane of curvature, equivalent to the free surface in open-channel flow (e.g. Hawthorne, 1954a; Tunstall and Harvey, 1968; M. Rowe, 1970; Greenspan, 1973; Collins and Dennis, 1976; Murata et al., 1976; Humphrey et al., 1977; Agrawal et al., 1978; Masliyah, 1980). J. Thomson (1876) correctly ascribed the secondary flow in bends to friction (see also Wittman and Boss, 1938; Van Bendegom, 1947; Rozovskii, 1961). Referring above to the forces acting on a unit mass of water in curving channel flow, we notice that the pressure force varies only with the transverse water-surface slope. Therefore at each radius it is constant with depth, the magnitude depending on the average of u( y ) . But the centrifugal force depends on the local streamwise velocity u which, because of bottom friction, generally decreases towards the bed from a maximum near the free surface. Hence near the bed, where u is less than U,the centrifugal force is less in magnitude than the pressure force, and the fluid consequently drifts towards the inner, convex side of the channel. Near the free surface, however, u exceeds U,and the centrifugal force therefore is the larger. Hence surface fluid travels outwards, completing the helical spiral. Mathematical studies of secondary flow at high Reynolds numbers in curved open channels are numerous (De'Vriend, 1981). The early work of Mockmore ( 1944) assumes inviscid flow and arbitrary velocity distributions. Van Bendegom's ( 1947) analysis, though merely sketched, is more realistic, and indicates the relative importance of downstream and transverse surface velocities and the corresponding bed shear stresses. At the bed the shear stress vector makes with the mean flow an inward-directed angle proportional to h / r , where h is the flow depth at a radius r . Many later analyses rest on the equations of motion of a turbulent fluid in a curved open channel, generally simplified by assuming that (1) the flow is steady, (2) the bend, of uniform curvature, is long enough that the flow is independent of angular distance, (3) the channel width/depth ratio is large, and (4) the eddy viscosity is constant (Einstein and Harder, 1954; Rozovskii, 1961; Shen,

14

1961; Ananyan, 1965; B.C. Yen, 1965, 1972; De Vriend, 1972; Apmann, 1972; Kikkawa et al., 1973; Engelund, 1974; Gottlieb, 1974, 1976; Ikeda, 1974, 1975). Rozovskii proposed that the bed shear stress vector due to the secondary flow deviated from the mean flow by an angle 6, where: tan6= ll(h/r) (2.17) and h and r have their previous meanings. Recent work by Zimmermann (1977), however, proves that the numerical coefficient has a weak inverse dependence on bed roughness, Rozovskii’s value of 11 equating to a DarcyWeisbach friction factor of approximately 0.04, a good average for a sand bed. Van Bendegom (1947) and Engelund (1974), in contrast to Rozovskii, gave the numerical coefficient as 10 and 7, respectively. The coefficient for curved Couette flow, of some importance experimentally, is apparently 2-3 times larger (Engelund, 1975). Less is known of how the secondary flow either develops on entering a bend or decays on leaving it, no doubt because otherwise discardable terms must be retained in the equations of motion. However, Rozovskii (1961) derived from these equations both numerical and approximate analytical solutions to the problem. Given a flow entering a uniform bend from a long straight reach, he deduced that approximately full development occurred when:

Y = k 3 W f )”*(v4

(2.18)

where y is the angular distance from the bend entrance, f is the DarcyWeisbach friction coefficient, and h and r are, respectively, a characteristic depth and bend-radius. The coefficient k 3 varies with the definition of “approximately full development”, but is given as 2.3. An analogous equation predicts the decay of a fully developed secondary flow after entering a straight. Later, Muramoto ( 1967) sketched the flow development, but from vorticity considerations. He recognized a generating region, an intermediate developing region, and a region of full development, each with a unique structure. Fox and Ball (1968), and Francis and Asfari (1971), using numerical techniques, also calculated the changing velocity structure. The mean streamwise velocity in the generating region broadly follows the freeyortex law, the maximum hugging the convex bank. The position of the vortex core gradually shifts across the channel through the developing region until, in the zone of fully developed flow, the velocity maximum borders the concave bank, as in a forced vortex. The fully developed flow has been treated as having a two-layer structure (e.g. Einstein and Harder, 1954), in which an inward-thickening boundary layer partly wraps round a core of fluid- the main spiral vortex-behaving essentially inviscidly.

75

Laboratory and field observations on secondary flow A legion of experimenters have confirmed the predicted character and development of the secondary flow in open-channel bends. Field studies have also given results generally in agreement with theory, though the evidence here is less substantial. The change in the transverse distribution of the downstream velocity component from that similar to a free vortex near a bend entrance, to that resembling a forced vortex further round the curve (or even in the subsequent straight or reversed loop), is amply proved for rigid rectangular channels (Yarnell and Woodward, 1936; Mockmore, 1944; Braden, 1947; Shukry, 1950; Rozovskii, 196 1 ; Francis and Pierce, 1967; Muramoto, 1967; Fox and Ball, 1968; Francis and Asfari, 1971; Kikkawa et al., 1973; Mosonyi et al., 1975; Siebert and Gotz, 1975; Varshney and Garde, 1975; Choudhary and Narasimhan, 1977) and for trapezoidal ones (Rozovskii, 1961; Ippen and Drinker, 1962; B.C. Yen, 1965; C.L. Yen, 1970; Barela, 1972; Deslauniers and Frenette, 1972). Figure 2-13 shows some of B.C. Yen's results. Sand fed to a channel bed, though causing spatial variations of cross-section, has no substantial effect on the velocity pattern (Martvall and Nilsson, 1972; Onishi et al., 1972; Hooke, 1974, 1975; Krishnappan and Lau, 1977). In Martvall and Nilsson's work on compound bends (Fig. 2-14), an especially marked delay occurs between the flow entering a curve and becoming fully developed. The lag amounts to nearly one-half of the meander-path length. A similar behaviour of the vortex core marks river meanders, where the largest streamwise velocities (and erosive powers) near the concave bank

A'

w

A

Fig. 2-13. Secondary flow measured in a right-angled bend of a trapezoidal laboratory channel. On the left is seen the streamwise flow, given in terms of the velocity averaged over a vertical, Ur, compared to the mean flow velocity in the cross-section, U,,,,,,,. On the right the local transverse velocity, K , is compared to the mean velocity in the cross-section. After B.C. Yen ( 1 965).

16

Fig. 2-14. Patterns of (a, c) surface flow velocity and (b, d) flow depth observed by Martvall and Nilsson ( 1 972) during two runs in a doubly meandering trapezoidal laboratory channel carrying sand.

tend to occur in the downstream half of each loop. This is seen in the Iowa (Blue et al., 1934), and may be suggested for the Mississippi (Vogel and Thompson, 1933). Leopold and Wolman (1960) found evidence for the downstream transition from free to forced vortex behaviour in Baldwin Creek, Wyoming, as did Rozovskii (1961) for the River Desna. Indications of the transition come also from the Snov (Rozovskii, 1961) and Orealven (Nilsson and Martvall, 1972), and clear proof is available from the Wabash River (R.G. Jackson, 1975). In the Wabash, as in Martvall and Nilsson’s (1972) experiments, a spatial lag on the order of one-quarter to one-half of the local meander-path length separates the channel inflection point and a

77

forced-vortex velocity distribution. Whether a similar lag occurs during flow in the larger tidal channels is not yet known, but the form of beaded channels suggested to Ahnert (1960) an upstream lag during flood reversing to downstream on the ebb. Observation amply confirms the predicted structure and strength-variation of secondary flows. The results in Fig. 2-13 (B.C. Yen, 1965) typify those obtained experimentally (see also Shukry, 1950; Rozovskii, 1961 ; Fox and Ball, 1968; Onishi et al., 1972; Kikkawa et a]., 1973; Ikeda, 1974, 1975). Prus-Chacinski ( 1954) in particular explored the strength of secondary flows, finding experimentally that tan S increased with declining bend radius, and Rozovskii (1961) later confirmed eq. (2.17) in full. Although some workers explicitly reject the concept (Vogel and Thompson, 1933; Matthes, 1941), and others remain hesitant (Bluck, 1971), there can be no doubt from the wealth of field data (e.g. Fig. 2-8) of the general occurrence of secondary currents in river bends (Blue et a]., 1934; Eakin, 1935; Van Bendegom, 1947; Van Ti1 and Tops, 1953; Leopold and Wolman, 1960; Rozovskii, 1961; Hey and Thorne, 1975; R.G. Jackson, 1975; Bridge and Jarvis, 1976, 1977; Bathurst et al., 1977; Hickin, 1978; Dietrich et a]., 1979). Rozovskii finds that their strength also varies according to eq. (2.17), and Jackson gives further supporting evidence. Low-stage secondary flows in Wabash bends are generally the weaker and, moreover, seem to develop more quickly, in accordance with eq. (2.18). Bluck ( 1971) indirectly gives evidence for these effects, though his observations are interpreted in terms of questionable “bar head” and “pool” currents. He records that the high-stage cross-stratification in the River Endrick has a greater angular divergence relative to the channel centre-line, and is developed after a longer spatial delay, than the succeeding low-stage structures. Two models exist for the flow in river meanders (Fig. 2-15a,b). In I.G. Wilson’s (1973), the channel at the apex of each loop is occupied by a single spiral vortex, whereas at each crossing a double spiral with bed-divergent currents obtains. Hey and Thorne’s (1975) model resembles Wilson’s at the meander apex, except for a subsidiary vortex rotating in the opposite sense to the main one, but has bed-convergent flow at crossings. Aspects of each model receive support. A single Wilson-type vortex seems to mark the tips of meanders in Baldwin Creek (Leopold and Wolman, 1960), the Desna, Snov and Yulya-Ioki (Rozovskii, 1961), and the Wabash (R.G. Jackson, 1975), whereas there is an additional subsidiary spiral in the Dove (Hey and Thorne, 1975) and Severn (Bathurst et al., 1977), as well as in the Klaralven, to judge from salt injections (Sundborg, 1956) and my observations on logs being floated downstream. The subsidiary vortex is also known experimentally (Einstein and Harder, 1954; Einstein and Shen, 1964; B.C. Yen, 1965; Onishi et al., 1972). In bends of very large width/depth ratio, however, several equal vortices may occur side by side (Eakin, 1935; Francis and Asfari, 1970), and in curves of small ratio, spirals can be piled

78

Fig. 2-15. Hypothetical and actual patterns of flow in meandering open channels. a. Limiting streamlines according to I.G. Wilson (1973). b. Limiting streamlines according to Hey and Thorne (1975). c, d. Alternative models to (a) and (b). Remainder of figure shows sense of rotation of secondary flow (observer looking downstream) in Bozeman and Helm Bends of Wabash River during (e) high stage and ( f ) low stage, as inferred from observations of R.G. Jackson (1975).

vertically (Chacinski and Francis, 1952; Prus-Chacinski, 1954; Soliman and Tinney, 1968). Flow at crossings is less well known. A fairly convincing bed-convergent double vortex is described from the Dove (Hey and Thorne, 1975), and a similar pattern (Fig. 2- 15e) marks the Bozeman-Helm crossing on the high-stage Wabash (R.G. Jackson, 1975). At low stage, however, this crossing yields a Wilson-style pattern (Fig. 2-150. Thus neither model is completely representative of real bends, and neither may be valid for every flow stage. The models of Fig. 2-15c, d may better represent meander flow patterns. The first of these-a "high-stage" model-reconciles Hey and Thorne's ( 1975) local observations but uses simpler kinematics. A local flow separation along the convex side of a bend downstream from the apex is often reported experimentally (J. Thomson, 1879; Mockmore, 1944; Shukry, 1950; Leopold et al., 1960; Ippen and Drinker, 1962; Soliman and Tinney, 1968; Tunstall and Harvey, 1968; Hurd and Peters, 1970; Thandveswara and Seetharamiah, 1971 ; Deslauniers and Frenette, 1972;

19

Martvall and Nilsson, 1972; Hooke, 1974, 1975). Limited separation at the same position can occur in river meanders, particularly at sharp or obstructed bends, as is shown by direct observation and by sedimentary structures (D.K. Davies, 1966; Taylor et al., 1971; Teisseyre, 1978). In small tidal meanders (Leeder and Bridges, 1975; Bridges and Leeder, 1976), breakaway is favoured by a declining bend radius/width ratio (see also Bagnold, 1960) and an increasing Froude number. A criterion for separation, r m / W < (0.5 13Fr), where Fr is the Froude number based on the maximum mean flow velocity and maximum depth, may be derived from their data. Flow separation leads to additional energy losses in bends (Bagnold, 1960; Leopold et al., 1960) and reduces the flow width. However, only small vigorous streams are significantly affected, and the secondary flow may well restrict separation to a surface layer, as in Mockmore’s (1944) channel, thus minimizing its influence on the bed.

+

Theories of meandering

Investigators continue to puzzle over the still elusive question of why river and tidal streams meander in alluvium. Although the following sketch merely touches on this topic, there still remains the even wider problem of why any restricted fluid stream should meander. The idea that meandering is a response to some kind of self-perpetuating transverse oscillation of the flowing water mass underpins several theories (De Geer, 1911 ; Exner, 1921; Hjulstrom, 1942, 1949; Fujiyoshi, 1950; Werner, 1951 ; A.G. Anderson, 1967). Fujiyoshi’s equation for meander wavelength, and also Werner’s when stripped of arbitrary “corrections”, give wavelength values both broadly consistent with experience and proportional to the square root of discharge (see eqs. 2.7-2.9). Anderson finds the same discharge dependence but introduces factors of uncertain meaning. Several workers link meandering with sediment transport, stream loads, and orderly debris transfers between bank and flow (Matthes, 1941; Friedkin, 1945; Ackers and Charlton, 1970a, 1970c, 1970d; Hooke, 1974, 1975). These processes express a necessary condition for meandering, but a consideration of them has not so far led to the prediction of meander scale. Meander initiation at chance boundary irregularities has often been advanced (Exner, 1919, 1921; Prus-Chacinski, 1954; Leliavsky, 1955; Htikonson, 1973). Usually this idea is developed in conjunction with an analysis of the role of the secondary flow generated by the irregularity in further localized erosion and deposition. However, instead of being induced at an irregularity, cross-channel winds may generate the secondary flow (Wu, -1975a, 1975b). Alternatively, the action of irregularities invites the treatment of meandering as a stability problem. Since irregularities would be randomly distributed, there must be mechanisms of wavelength selection operating in a stream, so that a dominant wavelength will eventually appear. Quraishy

80

(1944, 1973) early saw meandering as a spontaneous interaction between a flow and deformable bed. Meandering could be a response of the deformable river boundary to secondary flows (Thomson, 1876; Leliavsky, 1955; Tanner, 1960, 1963; Shen and Komura, 1968; Komura and Shen, 1970; Gorycki, 1973a; Quick, 1974). Komura and Shen on this basis calculated wavelengths in excellent agreement with observation. Assuming that the angular deflection of a stream varies with the strength of the secondary flow scaled by the streamwise flow velocity, Quick graphed flow paths in many respects like meanders in plan, but failed to obtain recurving forms or calculate wavelengths. Many workers treat meandering as a stability problem (Reynolds, 1965; Hansen, 1967; Callander, 1969; Sukegawa, 1970; Engelund, 1971; Karcz, 1971; Engelund and Skovgaard, 1973; Hayashi, 1974; Parker, 1976). General conditions for meandering and braiding are defined, but only the analyses of Hansen, Hayashi, and Parker yielded an expression for wavelength. Modest to good agreement with observation can be demonstrated. Meandering is sometimes associated with the Coriolis force (e.g. Eakin, 1914; Matschinski, 1966; Neu, 1967). This cannot be an essential control, however, since rivers meander as much in equatorial as in high latitudes. The idea that meandering maximizes stream energy losses has received little support (Jefferson, 1902; Inglis, 1949), but its antithesis, that meandering minimizes the loss and that meanders are therefore the most probable form of a river, is for some persuasive (Chatley, 1940; Bagnold, 1960; Leopold et al., 1960; Langbein and Leopold, 1966; Leopold and Langbein, 1966; C.T. Yang, 1971b; Chang, 1979). These ideas were developed in parallel with the view that thermodynamic analogies are applicable to landscape development (Leopold and Langbein, 1962; Scheidegger and Langbein, 1966; Yang, 1971a) and with the belief that rivers are nondeterministic phenomena (Thakur and Scheidegger, 1968, 1970; Surkan and Van Kan, 1969; C.T. Yang, 1971b, 1971c; Stall and Yang, 1972; Cherkauer, 1973). Meandering is not inconsistent with these notions, but meander attributes have yet to be deduced quantitatively from them. Tellingly, the meander planimetric form accepted as completely random yet the most probable- the sine-generated curve (Langbein and Leopold, 1966)-is rigorously explicable in a deterministic way (Gedzelman, 1974). Yalin (197 1, 1972) relates meandering to the scale of macroturbulence in rivers, calculating wavelengths in almost as good agreement with observation as Komura and Shen (1970). SEDIMENTATION PROCESSES IN MEANDERS AND CHANNEL BENDS

Sediment particle equilibrium on a point bar

The surface of a point bar inclines downwards and outwards, usually to within a small distance of a concave bank, whereas the secondary current in

81

the flow passing round the channel acts inwards over the bar, contrary to this outward slope. Hence a sediment particle travelling in substantially continuous contact with the bar, or one lying stationary on the bar surface, must be acted on by forces usually having both transverse (radial) and mean flow (streamwise) components. These in the general case are fluid drag, the particle immersed weight, friction and, possibly, lift. Their resultant dictates whether the particle in following the loop will spiral either inwards or outwards or remain parallel with the mean flow. Several largely independent attempts have been made to analyse these forces, with a view to calculating the equilibrium transverse profiles of point bars. Equilibrium may be either static, when the particles lie everywhere in incipient motion, or dynamic, when there is zero net sediment transport across the mean flow direction. If the dynamic equilibrium-profile is calculable, then other bar sedimentological features can be predicted. Consider as in Fig. 2-16 a single spherical sediment particle of diameter D and density u travelling in water of depth h (measured positively downwards) at a radial distance r over the surface of a point bar of negligibly small streamwise slope contained in a sufficiently large uniformly curved channel (superelevation neglected). The particle is assumed to be moving in substantially continuous contact with the bar surface, at a speed small compared with the flow (see Bagnold, 1956, 1966). When the bar is dynamically stable, the net flow of bedload across the streamwise x-direction is zero, and the radial forces acting on the particle are limited to the immersed weight and fluid drag components, lift being neglected in the light of Bagnold's (1973) observations. The weight force, Fg, is: (2.19) in which p is the density of water, g is the gravitational acceleration, and p is

Fig. 2-16. Definition diagram for secondary flow and particle stability in a meandering open channel.

82

the local transverse slope angle of the bar. The fluid drag, F,, may be writ ten:

F~ = r (0/2)’7,

(2.20)

sins

in which T, is the mean bed shear stress along a limiting bed streamline and S is the deviation angle previously used. Because of equilibrium: +r(0/2)~(u

- p>gsinp=

77(~/2)’.,

sin8

(2.21)

Noting that p is generally very small, so that sin p = tan /3 = dh/dr, and that the streamwise mean bed shear stress, 7, = 7, cos6, we can write from eq. (2.2 1):

dh dr

33pSh2 2D(u-p)r

(2.22)

after introducing eq. (2.17) and the conventional hydraulic equation (see Vol I, eq. 1.32), ?y = pghS, where S is the local water-surface slope. Equation (2.22) states that, with a fully developed secondary flow, the bar transverse slope is a steeply increasing function of flow depth, an increasing function of water-surface slope, and a decreasing function of particle size and bend radius. This analysis was given by Allen (1970b, 1970c), independently of Van Bendegom (1947) and NEDECO (1959). Several others have analysed the forces acting on a particle in dynamic equilibrium (C.L. Yen, 1970; Engelund, 1974, 1975; Ikeda, 1974, 1975; Bridge, 1976, 1977; Zimmermann and Kennedy, 1978), as Allen (1978) has pointed out in a general review. Yen’s and Ikeda’s analyses include lift, and give broadly similar results to eq. (2.22), with the noteworthy difference that the bar slope is . followed by Bridge came to the remarkable proportional to D - ‘ I 2Engelund conclusion that: dh h tana -= k4(2.23) dr r in which k , is a numerical constant relating to the deviation angle and tana is the dynamic friction coefficient due to mutual encounters between grains. Since t a n a varies with D either but little (Bagnold, 1954a, 1956, 1966) or not at all (Bagnold, 1973), eq. (2.23) is tantamount to saying that bar slope is independent of sediment calibre, which seems physically implausible. The Engelund-Bridge analysis is suspect, despite its apparent numerical success (Bridge, 1976, 1978). A test of eq. (2.22) demands more information than is usually available from either the field or laboratory. Hooke (1974, 1975) experimented with meanders 1 m wide in the form of a sine-generated curve. Quartz sand of geometric mean diameter 0.0003 m was fed to the channel under three different aqueous discharges, and bed elevation and mean bed shear stress

83 0.5

-0

(0)

04

$015

A A

v v >

0

A

0

0.1

02

0 .

0.0020 m 3 s-I 0.0035 m3s-‘ 0.0050 m3s-I

0.3

0.4

0

A

05

.

19 January 1974 2 February 1974 25 February 1974

0 0

01

Predicted dh/dr

02

03

04

Predicted dh/dr

Fig. 2-17. Observed as compared to predicted (eq. 2.22) transverse slopes for point bars in sand-bed meanders. a. Laboratory channel I m wide (Hooke, 1974, 1975). b. River South Esk, Scotland (data by courtesy of J.S. Bridge).

were mapped. Figure 2-17a compares measured local values of dh/dr with values predicted using eq. (2.22) and the experimental data. Agreement is satisfactory, considering the presence of bedforms in the real flows, except for small depths, when the equation underestimates the slope, and for large depths at the highest discharge, when the predicted slopes can exceed the angles of repose of the sand. A similar deviation of observed from theoretical values was noted by Zimmermann and Kennedy (1978) for their equation predicting the transverse bed slope. A second test was made with data generously supplied by Dr. J.S. Bridge and Dr. J. Jarvis (pers. comm., 1976; see also Bridge and Jarvis 1976, 1977) from a meander of the River South Esk, Angus, Scotland. They measured bed profiles, mean grain sizes, flow depths and water-surface slopes in a cross-section with a fully developed secondary flow on three dates in 1974 when the river was near bankfull, the condition when eq. (2.22) may be regarded as valid. The predicted and observed transverse slopes agree to the right order (Fig. 2-17b). Since dunes cover most of the bed, the discrepancies may partly relate to the difficulty of obtaining reliable estimates of grain size and bar slope. Transverse shape of point bars and meandering channels In the case of a train of uniform meanders carrying a single grade of sediment, the local water-surface slope in eq. (2.22) must from geometrical considerations be related to thexentreline slope, S,, and radius of curvature, r,, by S = S,(r,/r). Substituting for S in eq. (2.22) affords (2.24)

84

which, upon separating variables and integrating, gives h=

20(u -p)r 33pS,rm{

(2.25)

1 - 2 0 ( u - p)Cr}

for the equilibrium transverse profile, h ( r ) , of each point bar where the secondary flow is fully developed, C being an integration constant to be found from the conditions of the problem. A real channel may exist provided that C < 1/20( u - p ) r . Introducing as reference values r, and the centreline depth, h ,,,, eq. (2.25) becomes: (2.26)

from which C is excluded. Equations (2.25) and (2.26) imply that, with a uniform bedload sediment, the point-bar transverse profile is convex-up and of a steepness inversely proportional to calibre of load. Van Bendegom ( 1947) calculated convex-up profiles, though not from an explicit equation, but NEDECO (1959) using his work derived a relation similar to eq. (2.26). The analyses of C.L. Yen (1970) and Ikeda (1974, 1975) also afford convex-up profiles which, in at least Yen's case, have power-law form (Apmann, 1972). Using assumed velocity distributions, Suga ( 1967) calculated the profile as a power function under each kind of equilibrium. Integration of eq. (2.23) given by Engelund ( 1974, 1975) and Bridge (1976) also affords a power function:

h = Crk4ta"a

(2.27)

centreline depth, h,, eq. (2.25) becomes: (2.28)

upon introducing the previous reference variables. Russian workers have used a power function similar to eq. (2.28) for bar shape (Saplyukov, 1973). Although relations like eqs. (2.26) and (2.28) may readily be fitted to measured profiles, in order to predict point-bar shape under prescribed conditions, we must know the integration constant C. It is expected that these conditions will include the aqueous and sediment discharges and the sediment calibre. Ideally, C will be calculated so that the two discharges are simultaneously conserved. With Q , as the given fluid discharge and assuming vertical channel sides:

Q,= [rcxh( r ) . U(r ) - d r

(2.29)

where U is the local mean velocity in the vertical, and rex and Tin are the prescribed radii of the concave and convex banks, respectively (Fig. 2-16).

85

Calculating U conventionally (see Vol. I, eq. 1.35) (2.30) in which f is the local Darcy-Weisbach friction coefficient, and substituting from eq. (2.25) for h( r ) in eqs. (2.29) and (2.30), we obtain: rcx

Qf

=J

r(8gS,,rm) f I/2

r,n

2D(a - P ) 33pS,r,,{ 1 - 2 D( u - p ) C r }

3/2

-dr

(2.31)

when upon integration C follows by interpolation between trial values. It is more difficult to calculate C with the sediment discharge, Q,, also conserved, partly because it is not clear which flow-sediment transport relation should be used, and partly due to uncertainty about the local ratio of sediment loads. But if the local sediment transport rate is treated as a power function of the local velocity U (Vol. I, eq. 2.32), Q, will be approximately conserved so long as U is large compared with the sediment “erosion velocity”. Figure 2-18 gives transverse profiles calculated from eq. (2.25) for a fixed discharge value, two values of the sediment calibre, and a range of channel radii. These profiles satisfactorily resemble natural meanders as seen in sections far enough downstream that fully developed secondary flow may be

STRUCTURES Current ripples and cross-lamination

rn m

Dunes and cross-bedding

t-----l

P = 3.45

Upper-stage plane beds and parallel bminotion

P = 1.011 0 100 200 300400 500

P = 1.35

P = 1.74

P ~2.53

P.3.51

Fig. 2- 18. Computed meander cross-section and bedform distribution with increasing channel sinuosity for (upper sequence) aqueous discharge= 5000 m3s I , D=0.00025 m and (lower sequence) aqueous discharge = 5000 m3 s I , D =0.001 m. Note that current ripples appear only for the finer sand and at a sinuosity of 1.26; otherwise dunes and upper-stage plane beds alone are present. ~

86

assumed (e.g. Fisk, 1947; Wolman, 1955; Rozovskii, 1961 ; R.G. Jackson, 1975), but by assumption have vertical banks and, because of the extreme thalweg position, show exaggerated maximum depths. Equations (2.26) and (2.28) each provide a good forced fit to natural profiles (e.g. Bridge, 1976), given a careful choice for the proportionality constant and the exponent, respectively. Only Van Bendegom (1947), Engelund ( 1974), and Bridge ( 1977) have calculated the three-dimensional channel geometry.

Processes and rates of meander growth Plausibly, an aqueous flow in a straight channel of uniform surroundings will scour both banks equally until a stable, non-eroding cross-section is achieved (Vol. I, eqs. 1.37, 1.38). Reference to eqs. (2.25) and (2.30), however, suggests that such stability may never arise should a local curvature in plan accidentally develop. For the flow depth and velocity will be the higher at the concave bank, with the consequence that this bank will go on eroding while a point bar grows in harmony beneath the slower, shallower flows along the convex shore. Experience amply supports this interpretation. Many erosion processes affect the concave banks of river and tidal meanders, operating in a balance set by: (1) channel scale and shape, (2) the lithology and vertical-lateral sequence of bank deposits, (3) flow regime, (4) climatic setting, and (5) season. The processes are all favoured by the large flow velocities and stresses known or inferred to occur along meander concave banks (Parsons, 1960; Apmann, 1972; Hooke, 1974, 1975). The direct processes include the corrasion of cohesive banks (A.R. Hill, 1973b), the gouging of banks by drift-ice (D. Gill, 1972), the entrainment of sand or gravel particle by particle (NEDECO, 1959), the pick-up of fracturebounded blocks of cohesive sediment (A.R. Hill, 1973b), and the melting of permafrost cements (D. Gill, 1972). Block and particle entrainment is promoted by freeze-thaw (S.S. Harrison, 1970) and by wetting and drying (Twidale, 1964), both of which progressively loosen the bank. Water waves may enhance the river or tidal erosion (D. Gill, 1972; Bridges and Leeder, 1976). The indirect erosion processes tend to be catastrophic and are often precipitated by the action of the direct ones, which tend to steepen or even undercut banks. Large usually subaqueous flowages of liquidized sediment are frequent from banks of poorly coherent sand and gravelly sand (Turnbull et al., 1966; J.M. Coleman, 1969). These failures generally occur during falling stages, for flood water is then returning to the channel via the ground and pore pressures are high. Rotational slides, sometimes stepped, typify the failure of predominantly cohesive banks (Eardley, 1938b; Fisk, 1944, 1947, 1952a, 1952b; Sundborg, 1956; NEDECO, 1959; Turnbull et al., 1966; Kesel et al., 1974; Bridges and Leeder, 1976). These slides also tend to occur as stage falls, as the result of high pore-water pressures, strength loss conse-

87

quent upon thorough wetting, and the increase of bank weight due to draw-down. A third catastrophic erosion process is expressed by the sudden collapse of moderately cohesive banks into a jumble of blocks (Twidale, 1964; Pestrong, 1965, 1972b; Bluck, 1971; A.R. Hill, 1973b; Piest et al., 1975). In cold climates, the incidence of warm weather precipitates the solifluction of thawed mud into the channel from cohesive banks (Eardley, 1938b; Sundborg, 1956) and the spalling of flakes or slabs of melted sand and gravel (Eardley, 1938b). Short-term local erosion rates on meander concave banks vary extremely widely, both from site to site and time to time (Wolman, 1959; Twidale, 1964; Daniel, 1971; A.R. Hill, 1973b; Kesel et al., 1974; D.J. Hughes, 1977). This reflects partly the episodic nature of some of the erosion processes and partly the fact that they seldom work alone. The general tendency, however, is for the larger rates to be linked in time with flood flows and in space with moderately tight bends. Teisseyre ( 1980) gives further data. Bank erosion rates measured over periods of a few years are more consistent, taking the general order of 0.001-0.1 channel widths per year, where width can be regarded as a surrogate for a reference average flow velocity. These rates come from direct surveys (Leopold and Wolman, 1957; NEDECO, 1959; Crickmay, 1960; Alexander and Nunnally, 1972; Leopold, 1973), the analysis of charts, maps, and/or air photographs (Duncanson, 1909; De Geer, 1911; Tow], 1935; Sundborg, 1956; Schmudde, 1963; Noble and Palmquist, 1968; Swenson, 1970; Handy, 1972; Brice, 1974a; Kulernina, 1975; J.M. Hooke, 1977; Laczay, 1977), and vegetation studies (Eardley, 1938b; Dietz, 1952; Hickin and Nanson, 1975). Archeological evidence may help establish longer term channel shifting (Bareis, 1964; Lathrap, 1968). There is little quantitative understanding of how bank erosion rates depend upon flow conditions, bank materials, and channel form. Rates are qualitatively greater, however, for incoherent banks than for strong cohesive ones. Recently, Popov (1965) and Kondrat’yev (1969) observed that the time-rate of change of the meander central angle (Fig. 2-6) was greatest at a sinuosity in the order of 1.5. It follows that the bank erosion rate must reach a similar maximum. This was demonstrated by Hickin and Nanson (1975) who, in an elegant dendrochronological study, found the erosion rate to increase with decreasing r, / W to a maximum when this ratio was approximately equal to 3 (Fig. 2-19a). A number of unusually small and tight bends, however, afforded rates again low. Records of the Klaralven (Sundborg, 1956), Watts Branch (Wolman and Leopold, 1957; Leopold, 1973), and the White River (Brice, 1974a) go far towards showing that the decrease of erosion rate with increasing r , / W is a general feature of meandering streams (Fig. 2-19b-d). Data come also from the Mississippi (Fisk, 1947; Carey, 1969) and the Des Moines (Handy, 1972), but are too few to suggest a pattern (Fig. 2-19e). The trends seen in Fig. 2-19 bear out theoretical analyses of meander erosion (Saplyukov, 1973; Allen, 1977a).

88

f

0 3 0.01

I\

J

0 0

2

4

6

8

rm/ W

10

12

rm/ W

Fig. 2-19. Maximum local rate of meander migration (channel widths per year) as a function of the relative meander radius. a. Beatton River, British Columbia (Hickin and Nanson, 1975). b. Klaralven, Sweden (Sundborg, 1956). c. Watts Branch, Maryland, U.S.A. (Wolman and Leopold. 1957; Leopold, 1973). d. White River, U.S.A. (Brice, 1974a). e. Des Moines and Mississippi Rivers. U.S.A. (Fisk, 1947: Carey. 1969: Handy, 1972).

Evolution of meander loops A1though some awareness of meander growth-patterns emerged early (e.g. Davis, 1902; Lobeck, 1939), it is but recently that many essentials became known, partly by experiment (Tiffany and Nelson, 1939; Friedkin, 1945), and partly from detailed field studies (Lathrap, 1968; Daniel, 1971; Lewin, 1972; Brice, 1974a, 1974b; Hickin, 1974; Hickin and Nanson, 1975). As a meander train develops from an initially straight channel, each bend may move downstream (change of phase) as well as increase in loop-length (increase of amplitude). Evolution under ideal conditions may afford either uniform meanders changing only in phase, or lead to the simultaneous cut-off of grossly amplified loops and a renewal of the development cycle.

89

These behavioural modes are evident in real meanders but are complicated by the inhomogeneity of the channel boundary and by the unsteady channel processes. Most has been learned from the pattern and age of point-bar meander scrolls (Figs. 2-2, 2-3, 2-4). Each scroll is formed and ultimately added to the bar by the slow downcurrent growth around the convex bank of a feature rampart-like at the level of the bar top but of an as yet unknown form in the .deeper channel (Sundborg, 1956; Nilsson and Martvall, 1972; Nanson, 1980). Scroll bars are therefore not isochronous. Each in the Beatton River took on the order of 20 years to form (Hickin and Nanson, 1975), and several may at one time be accreting in a loop, as I have noted on the Klaralven, Sweden. But as scrolls form rapidly compared with meander loops, they are an acceptable guide to former channel position and can safely be used in meander reconstruction. Schematic evolutionary patterns can be depicted in terms of meander scrolls, as representing earlier channels, and by continuous scroll orthogonals (Figs. 2-7, 2-20), which Hickin (1974) called erosion path lines. One orthogonal, that recording maximum total channel movement, may be singled out as the meander-loop erosional axis, although a unique axis is not identifiable when a loop changes only in phase, for orthogonals are then uniform (Fig. 2-200. River meander-loops illustrating the schematic patterns are described by Lathrap (1968), Brice (1974a, 1974b), Hickin (1974), Hickin and Nanson (1975), and R.G. Jackson (1975), though Hickin has misinterpreted compound-loop growth. The scrolls A - A and B-B' in Fig. 2-20c, d reveal such loops at a critical stage. Earlier, a single characteristic radius of curvature is (01 Simple symmetrical

(b) Simple asymmetrical

( c ) Compound symmetrical

( d ) Compound symmetrical

(e) 'Rebounding' loop

( f ) Phase growth only

Fig. 2-20. Schematic evolution of meander loops.

90

Fig. 2-21. Definition diagram for the evolution of meander loops.

identifiable, but afterwards there are two, and therefore two erosional axes must appear. Hickin used at all stages a single continuous axis to describe his compound loops. A compound loop may eventually divide (Fig. 2-20e), by the “rebound” of the weakly curved segment (Lathrap, 1968). The resulting channel is shaped like the human ear (Lathrap, 1968) or the letter T (Hickin, 1974). Lewin ( 1972) reports similar metamorphoses, attributing them to the formation of additional pools in a simpler prior meander. Rebound seems common and may be forced upon an over-lengthened channel by the discharge. Regular models of meander planimetric form are ably summarized by Ferguson ( 1973a). Of appealing simplicity is the uniformly curved circular arc (Bates, 1939; Chatley, 1940; Chitale, 1970), though fitting real loops ill (e.g. Langbein and Leopold, 1966). The sine curve (e.g. Bluck, 1971) is perhaps a worse fit, with the particular objection that a recurved channel is unobtainable. It is more difficult to discriminate between the remainder: ( 1) Fargue’s (1908) spiral, of linearly varying curvature (see discussion in Leliavsky, 1959, (2) the sine-generated curve, in which the channel direction is a sine function of distance along the channel (Fargue, 1908; Langbein and Leopold, 1966; Leopold and Langbein, 1966; Daniel, 1971), and (3) Von Schelling’s (1951) equation for the most probable path of a particle in a plane, to which the sine-generated curve closely approximates. These three models describe real meanders about equally well (Langbein and Leopold, 1966; Ferguson, 1973a) and, since none has any physical basis, may therefore be used as convenience dictates. Flow and sedimentation in channel bends are well enough understood that several general features of a dynamical model of meander evolution under simplified conditions can be stated. Let the heavy solid curve in Fig. 2-21 be part of a rectilinear train of regular alluvial meanders at one instant during development. The train may be described by: z =f,(x,t)

(2.32)

91

the solution of which is desired, where z is the normal distance from the x-axis, f l stands for a periodic function, x is distance along the meander belt

axis (positive downstream), and t is time. Uniformly spaced inflection points, I,,I,, ...,I,,, occur where this curve cross the x-axis. Further evolution will generally involve a change of both phase and amplitude. Let the dashed curve be the meanders after the elapse of a small time-increment A t , and let the arrows between the curves represent bank erosion. We see that the directions of these vectors . define further uniformly spaced points, R,,R2,...,R,l,about which the channel has merely been rotated. At these stations the channel is temporarily stable, experiencing erosion on neither bank. Hence the instantaneous form and evolution of the train depends on the operation of another periodic function: (2.33) E =f2( x ,t ,d , rm,Q , D ,S , k , ) Here E is the normal bank erosion rate (positive when measured to the left of the flow direction), d is a lag distance measured parallel with the x-direction between related inflection and rotation points, r, is the local radius of channel curvature, Q is the fluid discharge (assumed steady), D is the calibre of the bed sediment (assumed uniform), S is the valley slope, and k , describes the resistance to erosion of the bounding alluvium. Equation (2.33) also appears in Fig. 2-21. The role of several variables requires explanation. The lag distance is vital, for without it a change of phase is impossible (Allen, 1974b). Putting L as the meander wavelength, the loops can simultaneously increase in amplitude and advance downstream only when 0 < d < L/4. Amplitude alone changes when d = 0, whereas only phase varies when d = L/4, and the other possibilities do not generally match real meander behaviour. Equation (2.18) affords a preliminary physical justification for the lag distance. Equation (2.33) includes the local radius of curvature, because from eqs. (2.25) and (2.30) it follows that the bank erosion rate partly depends on the appropriate flow depth. The channel width required for calculation of the local cross-section may be assumed uniform 'over the train. It may be obtained from the prescribed discharge, bed sediment and alluvium, by using the condition that at each rotation point the channel is temporarily noneroding. One important implication of the presence of rm in eq. (2.33) is that f , includes both dz/dt and d2z/dt2. It is therefore unlikely that eq. (2.33) can be solved analytically, though a step-wise graphical or numerical solution seems possible. Grain size and bedform on point bars

In developing eq. (2.25), the calibre of the sediment supplied, though considered uniform, was implicitly treated as an independent variable. This

92

is correct, because the transverse profile presents a merely local problem, and the sediment grades entering a bend are controlled by: (1) sorting over the whole upstream channel and, (2) the character of the source debris, the weathered mantle in the case of rivers and the offshore sediments for many tidal meanders. Sediments broadly ranging in calibre are likely to reach real bends. What distribution over a point bar surface will the grades tend to assume? Solving eq. (2.25) for D and differentiating partially with respect to h and r, we find that: --

-

ah

66(a - P)s",r",~

{ 2( u - p ) r + 66p ( u - p)Sn,rmCrh}' 33pSmrmh

aD -

ar

r2{2(a- p)

+ 66p(a - p)SmrmCh}

(2.34)

(2.35)

Therefore under a fully developed secondary flow, particles will be arranged such that D increases outward across the bar towards the thalweg. Fining towards the thalweg would seem possible only across exceptionally tight bends, where r varied similarly to h. Natural bends filling this bill are exceptionally rare, so that coarsening towards the thalweg should be the rule. Allen ( 1970b, 1970c, 197la) and Bridge ( 1975a, 1975b) also reached this result from a relation similar to eq. (2.22) and an assumed bar profile, but wrongly treated sediment calibre as a dependent variable. More recently, Bridge ( 1976) calculated the cross-channel grading by combining an expression derived similarly to eq. (2.22) with Engelund's eq. (2.27) for the bar profile. Despite a predicted outward coarsening, his analysis may be invalid, as two seemingly incompatible expressions for d h/dr are involved. Records of grain-size distribution On point bars are few but tend to support the result from eq. (2.25). Some rivers show an outward and downward coarsening over a major portion of a bar (Wiethe, 1970; Bluck, 1971; Masson, 1973), suggesting a mutual adjustment over a short distance between sediment and flow. A substantially longer relative distance has been necessary for adjustment in other bends, a well-defined coarsening towards the thalweg occurring only in the downstream part (Nilsson and Martvall, 1972; Erkek, 1973; R.G. Jackson, 1975; Bridge and Jarvis, 1977). Upstream the textural trends are weak and confused, or the calibre is substantially uniform across the channel. Only at riffles should there be cross-channel uniformity of grade, because in theory there are no curvature-induced transverse forces to promote cross-stream differentiation there. That nearuniformity of texture persists well downstream into some bends points to the delayed development of the secondary flow, and is consistent with the comparative tightness of these loops. If the construction and character of point bars depended on turbulence as Leighly (1932) proposed such delays should not be observed. Nansen (1980) gives further data on grading.

93

Far less is known of grading over tidal point bars. However, texture on large bars (Land and Hoyt, 1966) varies much as in rivers; the thalweg gravels of tidal gullies are well documented (Van Straaten, 1950b, 1954a; Reineck, 1958a; G. Evans, 1965). The prediction of bedform distribution in natural channel-bends is difficult, because: (1) the bed resistance coefficient is also a response to flow, (2) there is no generally accepted scheme for calculating roughness, and (3) the larger types of roughness may be expected to lag the unsteady flow. Allen ( 1970b, 1970c) and Bridge ( 1975a, 1975b) nevertheless essayed this using an assumed bar profile, the force balance equations (2.19-2.21), a steady discharge and fully developed secondary flow, and an assumed characteristic Darcy-Weisbach coefficient for each bedform type. To grasp the kind of result obtained, substitute eq. (2.25) into the conventional hydraulic equations for bed shear stress and stream power, written in terms of flow depth. Then: ro =

2 0 ( (J - p ) g r s

33Smrm{1 - 2 0 ( -~ p ) C r } 2( (I - p ) D r 33rm{1 - 2 0 ( 0 - p ) C r }

(2.36) (2.37)

in which q,is the bed shear stress and w the flow power. The stress and the flow depth increase equally with radius of curvature, but the power grows even more rapidly. Referring to Vol.1, Fig. 8.22, for example, and to Bagnold’s (1966) universal criterion for an upper-stage plane bed, Vol. I, eq. (7.4), such sequences inwards from the thalweg as: (1) upper-stage plane bed + dunes + ripples, and (2) upper-stage plane bed + dunes + lower stage plane bed may be expected, depending on grain size and discharge. Allen and Bridge calculated many such bedform sequences. Further sequences have been calculated for the theoretical bar profiles shown in Fig. 2-18. They bear out the preceding analysis, except for the poor representation of low-power forms, a consequence of assuming vertical banks. Although bedforms are widely reported from river channels, R.G. Jackson (1975) and Bridge and Jarvis (1977) stand alone in having mapped areal distributions. The maps (Fig. 2-22) from the Wabash differ slightly from those originally given, to account for Jackson’s failure to distinguish kinds of plane bed, and the limitations of his low-resolution echo-sounder. In this revision, his depth and velocity measurements have proved invaluable, and where the secondary flow appears to be fully developed, there are bedform sequences similar to those calculated (Fig. 2- 18; Allen, 1970b, 1970c; Bridge, 1975a, 1975b). It is telling in support of Stein’s (1965) work that Jackson generally records the tallest dunes in mid-channel positions, though he also claims an increasing height towards the thalweg.

94

( a ) High stage

( b ) Intermediate

0

KEY

?Lower-stage plane beds/rippies

TO

500 m

BEDFORMS

0

Dunes

?Upper-stage plane beds

Fig. 2-22. Distribution (partly inferred) of bedforrns in the Bozernan and Helm Bends of the Wabash River (modified after R.G. Jackson, 1975).

LATERAL ACCRETION STRUCTURES AND DEPOSITS

An integration of the preceding morphological and dynamical evidence affords a general conception of the three-dimensional geometry and faciessequence of river and tidal point bars. In essence, the bar deposit is expected to overlie a laterally extensive erosion surface formed through meander migration, and should comprise an upward-fining facies-sequence transected by gently inclined curved bedding surfaces which denote episodes of channel shifting. The geometry constitutes a “lateral accretion structure”, and the facies assemblage a “lateral accretion deposit”, because sedimentation occurs on a surface inclined across the direction of the effective currents, the strata being built “sideways” with respect to them. Observations supporting these ideas accumulated earliest from small meandering gullies on intertidal flats (Figs. 2-23a, 2-24b), at first in Germany (Trusheim, 1929; Hantzschel, 1936; Reineck, 1958a, 1970b; Reineck and Wunderlich, 1969), and later in the Netherlands (Van Straaten, 1950b, 1954a) and elsewhere (G. Evans, 1965; Le Gall and Larsonneur, 1972; Bridges and Leeder, 1976). The lateral deposits are rarely thicker than 1.5 m and consist of interbedded curved layers of sand and mud, generally convexup radially but in places sigmoidal or concave. The sand layers, usually thickest and most numerous towards the base, vary from parallel-laminated to current rippled (commonest), both ebb and flood directions often being preserved. A profusion of burrowing invertebrates inhabits the deposit. Underlying the whole is an irregular erosional surface, generally overlain by a gravel of bivalve and other shells mixed with pebbles of muddy sediment derived from cut banks. Erosional surfaces more discordant than those usually underlying the sand layers appear locally. They can reflect either stages in channel planimetric evolution, as controlling the influence of flow

95

Cross- lamination Parallel lamination

-

Flood tide

C--

Ebb tide

Orientation of current-directional structures

Invertebrate burrows

/

T

Lateral accretion structure Mud

0

Sand

Crass-lamination

Erosion surface Upward-fining Crass-bedding

Mud c l a d lag

I Loferal accretions 1 -

Orientation of current-directional structures

Parallel lamination

Fig. 2-23. Models for the sequence of lithologies and sedimentary structures in point bars. a. Mixed mud-sand tidal gully. b. Sand-bed river. The orientation of the master bedding (lateral accretions) is in each case compared with that of the smaller scale directional structures.

separation on deposition and erosion in these relatively small meanders, or extreme events such as violent rainstorms (Bridges and Leeder, 1976). Storm tides could also cut such discontinuities. Closely related. conceptions of lateral accretions in river meanders have been separately developed by Bernard and Major (1963) and Bernard and others (1970), by Allen (1963a, 1964, 1965a, 1965b, 1970b, 1 9 7 0 ~1971a), by Visher (1965a, 1965b, 1972), and by Bluck (1971), Bridge (1975a, 1975b),

96

and R.G. Jackson (1976). These models, most of which depict threedimensional aspects of the deposits, are foreshadowed in the work of F.A. Melton (1936), Nanz (1954) and Sundborn (1956). Fig. 2-23b shows one of a wide range of possible models for river point bars. It is considered representative of intermediate to large sand-bedded rivers with bends growing mainly in amplitude. The stratigraphic section is in the downstream half of the bend, where the secondary flow may be considered fully developed. The basal erosion surface, with flutings, pot-holes and other scours, was cut as the meander loop grew laterally. It dips outwards slightly, since the channel became narrower and deeper as sinuosity increased for the fixed valley slope. The basal surface is diachronous. Coeval portions form a series of nested arcs imitating the channel in planimetric form, the oldest and shortest lying beneath the bar core. Sediments in the lateral accretion deposit fine upwards in general but interfinger in detail. At the base is the coarsest debris supplied from upstream, mixed with clasts formed by erosion of concave banks. Internal sedimentary structures appear upwards in order of declining flow power, an arrangement which reflects the distribution of bedforms over the bar surface, in turn revealing the inward decline of current strength. The relative abundance of the different structures changes laterally, in response to the varying channel sinuosity. Curved bedding surfaces generally sigmoidal in radial profile define the lateral accretion structure. There are at least three kinds: ( 1) non-discordant and marking vertical transitions between sediments differing in sedimentary structure and/or grade, (2) erosional and slightly discordant, generally with the coarser deposit and/or the sedimentary structure of greater flow-power above, and (3) strongly discordant and extensive, often descending to large basal scours. These surfaces define interfingerings on several scales, and they depend on the unsteady channel flow, which varies daily, seasonally, and over still longer periods. For Bridge ( 1975a, 1975b), the third type of surface forms during the annual flood, but a discharge event even more extreme may actually be necessary. Where the secondary flow was not fully developed, the deposit may be either vertically uniform in texture or even upward-coarsening over an interval (R.G. Jackson, 1975, 1976). However, the sequence of structures should differ from that in the fully developed section only as the bed sediment changes. Lateral accretion in large tidal channels is modelled in a similar manner to Fig. 2-23b (Oomkens and Terwindt, 1960; Noorthoorn Van der Kruijff and Lagaaij, 1960; Klein, 1965), with ample support coming from later work (Land and Hoyt, 1966; Howard et al., 1975; Barwis, 1978). The chief contrasts are that (1) the cross-bedded facies may include foresets of opposed dip and other features indicative of markedly unsteady currents, and (2) the upper bar is likely to be dominated by richly bioturbated, interbedded muds and sands with wave and current ripples.

Fig. 2-24. Lateral deposits in fluvial and tidal sediments. a. Lateral deposit in Catskill Formation (Devonian), Rip Van Winkle Trail, Haines Falls, New York State (see Allen and Friend, 1968). Approximately 1-1.5 m of red mudstone are followed by an erosively based sandstone which passes up into interbedded sandstone and mudstone. The master bedding in the sandstones and interbeds dips at about 20" to the left and involves at least one major erosional discordance, evidence for which can be seen upward and slightly to right of left-hand figure. The master bedding is truncated near the top of the photograph by mudstones and thin sandstones parallel with the base of the main sandstone. The person (not possessed of bilocatory powers!) is 1.7 m tall. b. Lateral deposit constructed by a meandering tidal gully (seen passing between the stakes), intertidal mud flats, Jade, Germany. Approximately 1.5 m of the mud cliff is exposed above the water level.

TABLE 2-1 Some examples of lateral deposits in shallow-water (mainly fluvial) sediments from the stratigraphic record Authority Sundborg, 1956 Allen, 1965a Moody-Stumt, 1966 Beutner et al., 1967 Allen and Friend, 1968 Geology Extra-Mural Group, 1968 Cummins and Rundle, 1969 Johnson and Friedman, 1969 Gradzinski, 1970 Beuf et al., 1971 Cotter, 1971 Dodson, 1971 Maberry, 1971 Puigdefabrigas, 1973 Derr, 1974 Van Gelder, 1974 Hobday and Mathew, 1975 Nami, 1976 Elliott, 1976a Elliott, 1976b Karl, 1976 Padgett and Ehrlich, 1976

* Truedip.

Age and area Quaternary, Sweden Devonian, Wales Devonian, Spitsbergen Carboniferous, U.S.A. Devonian, U.S.A. Carboniferous, Scotland Quaternary, England Devonian, U S A . Cretaceous, Mongolia Devonian, N. Africa Cretaceous, U.S.A. Cretaceous, Canada Creticeous, U S A . Miocene, Spain Jurassic, U S A . Devonian, Ireland Permo-Carboniferous, S. Africa Jurassic, England Carboniferous, England Carboniferous, England Cretaceous, U S A . Carboniferous, Morocco

Exposure 2D 2D and 3D 2D 2D 2D 2D 2D 2D 2D 3D 2D 2D 2D 3D 2D 2D 2D 3D 2D 2D 2D 3D

Thickness (m) 7 1 .O-2.7 0.5-6.25 13.5 7 5 3 3+ 1.O- 8.5 10 10 5 < 12 <2 4 3 6 3-4 7 (3.5 3+ 5

Slope (">

7 4- 14* 4- 15* 15 22 20 4 23 5- 10 12 5-10 15 11 18 20 15 12 15* 5 6 10 ?

Fig. 2-25. Panorama taken from cliff-top looking eastward down on to foreshore at low tide, to show curved upper edges of laterally deposited sandstones in a palaeomeander, flat-lying beds, Scalby Formation (Middle Jurassic), Burniston Wyke, Yorkshire coast, England. The palaeomeander has a maximum exposed extent of the order of 125 m. Photographs courtesy of M.R. Leeder.

Lateral accretions no longer coupled to active rivers were first described by Sundborg (1956), from a Klaralven terrace, and by Allen (1965a) from the Old Red Sandstone, in which three-dimensional developments could be examined. Fluviatile lateral accretions were afterwards widely recognized (Table 2-1, Fig. 2-24a). These sequences, up to 13.5 m thick, vary from chiefly conglomerates with sandstones to mainly mudstones with sandstones of the finer grades. They generally fine upwards. The lateral accretion surfaces dip as steeply as 23”, though dips of about 10” are normal, and range in kind as in the model (Fig. 2-23b). The third type (Allen and Friend, 1968; Puigdefabrigas, 1973; Elliott, 1976a) is associated by Elliott with high-stage events. If he is correct in identifying 8-12 scroll bar deposits as lying between his adjacent discontinuities, then each such event, in terms of Hickin and Nanson’s (1975) work, could be something like the 100-year rather than the annual flood. It has been fully demonstrated that currents flowed nearly parallel with the discontinuities in lateral accretion deposits. The remarkable three-dimensionally exposed instances (Fig. 2-25) described by Beuf et al. (1971), Puigdefabrigas (1973), Nami (1976), Padgett and Ehrlich (1976), Nami and Leeder (1978), and‘Puigdefabrigas and Van Vliet (1978) are fully consistent with the flow-geometry relationship depicted in Fig. 2-23b. From washouts in rocks of the same general age as Nami studied, Black ( 1928) had earlier reported what are recognisable lateral accretions, and had referred to channels which, running parallel with the modern coast, “may then be quite clearly seen to meander”. The only tidal lateral accretion listed in Table 2-1 is Van Gelder’s (1974), which agrees well with the model (Fig. 2-23a). Other possible examples are recorded by Hobday et al. (1971). Although meanders occur on deep-sea fans, lateral accretions are not yet recognized in the deposits, but should be expected.

SUMMARY

Meandering river and tidal channels are similar in their distinctive geometry and flow dynamics. The constraining of the fluid discharge into a horizontally curved path generates a helical spiral secondary flow in each meander loop. In response, the outer side of the channel deepens and the concave bank scours, with the result that the meander loop changes in phase and amplitude in growing toward some limiting condition. In harmony, deposition on the inner bank gives rise to a lateral accretion deposit, marked internally by a characteristic geometry (lateral accretion structure) and spatial arrangement of sedimentary facies. The key to understanding the facies and geometry of these accretions, together with channel developmental patterns, seems to be a consideration of the response of the sediment carried round the channel bend to the transverse forces associated with the secondary flow, whichin turn is dependent on the channel form and discharge.

101

Chapter 3 AN OUTLINE O F FLOW SEPARATION INTRODUCTION

The brief discussion in Vol. I, Chapter 1, showed flow separation (Vol. I, Fig. 1-9) to be intimately involved with the development of an adverse (positive) pressure gradient in a boundary-layer flow, usually on account of some change in flow geometry (Prandtl, 1952; Schlichting, 1960). Where pressure increases down-current, fluid particles moving near the flow boundary are retarded and, eventually losing all their kinetic energy in conquering friction, gradually pile up. The stream is consequently forced obliquely away from the boundary by this piled-up fluid, in which a reverse motion may appear. In practice, the flow separating from the boundary in one place, becomes rejoined or reattached to it at another, a more or less closed region of rotating fluid arising between the two. The combination of a region of rotating flow with a stream temporarily freed from its flow boundary- that is, a separated flow-is associated with many sedimentary structures, and may contribute significantly to the determination of their geometry and often to the texture of the deposits marked by them. Important examples are ripples and dunes, about which much has already been said, together with flute marks and obstacle marks. The complex shapes assumed by these structures are matched harmoniously by equally complex patterns of currents and flow forces in the accompanying separated flows. We shall here review the simpler kinds of separated flow, in preparation for a return to ripples and dunes, and for a discussion of flute marks. Further details appear in P.K. Chang’s (1970) comprehensive general survey, and in the review by Brown and Stewartson (1969), restricted to laminar flows. Complex types of flow separation exist where strongly threedimensional bluff bodies are mounted on flow boundaries, for example, pebbles or massive colonial corals resting on muddy substrates. These flows and the obstacle marks they help to create will be discussed separately. The flow separation accompanying the production of sedimentary structures generally occurs at a low flow speed, in water below the velocity for cavitation, and in the air at subsonic speeds. There are features on meteorites and tektites, however, which seem to be related to separation at supersonic and hypersonic speeds, and it will be necessary briefly to review separation under these conditions. SEPARATION IN INTERNAL AND EXTERNAL FLOWS

An externalflow is one where the solid boundaries of interest are wholly enveloped by the fluid, which theoretically extends to infinity. An example is

102

a sand grain sinking through a large volume of still water. Separation shown by a ring of rotating fluid on the upper side of the grain may occur if the relative motion generates a sufficiently adverse pressure gradient. The character of the separated flow in this case depends only on the properties of the fluid and grain. The ultimate flow boundaries, which must in practice exist, are sufficiently far removed from the grain that they can be ignored. An internalflow is one strongly confined by solid boundaries or by solid boundaries in combination with a free surface, the fluid being wholly enveloped, as for example a river or the meltwater filling an englacial tunnel. Separation may occur in these flows wherever they change direction sufficiently rapidly as a body, as we saw in Chapter2, and at any abrupt boundary discontinuity, for example, a step up or down (rock ledge or dune), or a cavity (pot-hole). The character of the separated flow now depends not only on the nature of the fluid and the boundary geometry, but also on the kind and degree of boundary constraints (Kline, 1959; Ackeret, 1967). These substantially affect the shape of a region of rotating flow and seem to be amongst the controls on dune steepness. STREAMLINE MAPPINGS

Figure 3- 1 epitomizes two-dimensional separation, the criterion for which is that aU/ay = 0 at the wall, where U for a turbulent flow is understood to be the local temporal mean velocity. This criterion is satisfied in Fig. 3-la at the point S, which is a separation point. Here two limiting streamlines converge, and a streamline departs obliquely from the bed. This streamline passes through the fluid and reattaches itself at A, an attachment point, dividing into two. At A we again find that aU/ay = 0 at the wall, whence the criterion distinguishes attachment as well as separation. The streamline connecting S with A through the fluid is the separation or free streamline. It divides off a closed region of rotating flow, called a separation bubble, from the outer unidirectional stream. Figure 3-lb depicts part of the flow as expressed by limiting streamlines in the xz-plane. Because the flow is two-dimensional, the point S is but one of an infinite number of similar points which together define a transverse line S'S" on the flow boundary. This line is a singular separation line because the limiting streamlines are orthogonal to it; strictly, S should also be described as singular. Similarly, the infinity of points corresponding to A in Fig. 3-la define in Fig. 3-lb a singular attachment line A'A", on which A is a singular point. A real flow claimed as two-dimensional is never more than nominally of this kind, and many practical flows $re in fact strongly three-dimensional. Flow separation in these instances creates patterns of motion of much greater complexity than appear in Fig. 3-1 and, in addition, severe problems of definition and verification (Eichelbrenner and Oudart, 1954, 1955;

I03 Y t

x

Fig. 3- 1. Schematic representation of flow separation in a two-dimensional boundary layer. a. Streamlines and velocity profiles in the flow plane. b. Limiting streamlines in the flow boundary.

Maskell, 1955; Legendre, 1956; Eichelbrenner, 1957; Oswatitsch, 1958; Thwaites, 1960; Cooke and Brebner, 1961; Rosenhead, 1963; Perry and Fairlie, 1974, 1975; Hunt et al., 1978). We now find a tangential rather than orthogonal relationship between limiting streamlines and separation or attachment lines. The preceding simple criteria for attachment and separation break down, for non-zero velocity gradients and bed shear stresses are detectable along separation and attachment lines in three-dimensional flows. Moreover, these lines no longer comprise an infinite number of singular points, but merely a few, of two distinct kinds, obeying a precise topological rule (Coddington and Levinson, 1955; Kaplan, 1958; Rosenhead, 1963; Hunt et al., 1978).

A'

Fig. 3-2. Types of nodal point. a-c. Separation points. d-f. Attachment points.

104

Some of the patterns assumed by limiting streamlines in the neighbourhood of one of these kinds of singularity appear in Fig. 3-2 (Legendre, 1956; Rosenhead, 1963; E.S. Taylor, 1967; Allen, 19688). They share the property that the streamlines have but one kind of relationship to the point, being either all “point-seeking” (Fig. 3-2a-c) or all “point-fleeing” (Fig. 3-2d- f). Such singularities are called nodalpoints (Rosenhead, 1963). Those in the top row are all separation points, those below being all of attachment. The patterns shown in Fig. 3-2c, f are associated with separation and attachment lines, respectively, S’S” and A’A’. Aside from the singular point, each of these lines consists only of what Maskell (1955) distinguishes as ordinary points (of separation or attachment), at which the velocity gradient remains finite. The respective separation and attachment lines are also called ordinary, to distinguish them from the singular lines-E.S. Taylor’s ( 1967) “cylindrical points”-of the two-dimensional case. The second type of singularity to be found in three-dimensional separated flows is a saddle point (Rosenhead, 1963). Here some streamlines are point-seeking, whereas others are pointfleeing (Fig. 3-3). Amongst these patterns, the separation lines (ordinary) are those containing outward-directed streamlines, while the attachment lines, also ordinary, are defined by inward-directed flows (Eichelbrenner, 1957). By the definition of a limiting streamline, the mappings of these streamlines in three-dimensional flows are required to obey definite topological rules with respect to the relative numbers of nodal points (of all kinds) and of saddle points (of all kinds) (M.J. Lighthill, in Rosenhead, 1963; Perry and Fairlie, 1974, 1975; Hunt et al., 1978). These rules are hard to prove from real flows, because of the limitations of even the best flow-visualization techniques, but can be readily demonstrated from theoretical patterns (e.g. Eichelbrenner, 1957; Davey, 1961). For example, the rule for a smooth rounded body like a sphere in external flow is that the number of nodal points exceeds the number of saddle points by two. Figure 3-3e shows Davey’s (1961) calculated limiting streamlines for a flow attaching to a

Fig. 3-3. Saddle points (a,b) of separation, and (c,d) of attachment. e. Davey’s (1961) calculated pattern of limiting streamlines for a flow attaching to a surface with two rounded protuberances.

105

surface carrying two rounded, flow-facing protuberances. The mapping includes three attachment points, two nodal ( A N ) and one a saddle point (As). Our rule here requires that one more nodal point be present, presumably at a distance; it would be satisfied if the flow were external and the protuberances lay on the leading surface of a spherical body, with separation to the rear from a single nodal point (e.g. Fig. 3-2a). Hunt et al. (1978) discuss the topological rules governing nodal and saddle points for other boundary conditions, as well as providing many elegant practical examples. ROLLERS AND VORTICES: CLOSED AND OPEN SEPARATION

Separation bubbles are either rollers or vortices, accordingly as they either fully or partly close themselves off from the outer stream (Allen, 1970f). We note first that separation streamlines unite in the third dimension to form surfaces of separation. If a surface of separation and the flow boundaries combine in such a way as totally to enclose the fluid within a separation bubble, then that bubble is a roller (Fig. 3-4a). Fluid particles trapped within rollers follow recirculating paths, whence the limiting streamlines are reflexed; the separation may then be described as closed. Whereas rollers typify nominally two-dimensional and some moderately three-dimensional separated flows, vortices characterize strongly three-dimensional ones (Fig. 3-4b). A vortex is entered by many of the streamlines of the outer flow, in addition to the free streamlines which separate along the ordinary separation line. Fluid particles typically follow spiral paths in vortices and the limiting streamlines within the separation bubble normally are inflected. A vortex draws fluid from the outer stream and, at its terminus, discharges fluid back into the main flow; the separation may therefore be described as open. Very little is known about the flow patterns involved in the transition

Fig. 3-4. Idealized (a) roller and (b) vortex developed downstream of negative steps in a flow boundary.

106

between two-dimensional and three-dimensional separation. In a numerical study, however, Sykes (1980) has shown for hummocks and cavities of rounded form that, as the degree of three-dimensionality increases, a nodal point within the body of the separated fluid gradually moves closer to the bed until it reaches and joins the bed. SEPARATION IN TWO DIMENSIONS

External flows A low-speed fluid travelling parallel with a flat plate having sharp leading and trailing edges arranged transversely to flow, separates on both sides of the plate along the leading edge, and again at the trailing margin (Fig. 3-5). The captive leading-edge bubbles (W.D. Moss, 1972) are stable whether the flow be laminar or turbulent and resemble bubbles as commonly developed on plates (e.g. Gaster, 1969; Ojha, 1969). The trailing-edge bubbles are stable only at small Reynolds numbers (Hoerner, 1950; Roshko, 1954a, 1954b, 1955b, 1961; Acrivos et al., 1965), when they too are symmetrically disposed. The flow reattaches within the fluid at what might be called a free point and again along the rear face of the plate (Viviand and Berger, 1965a, 1965b; Mueller and O’Leary, 1970). A similar attachment and rearward separation marks both steady and unsteady low-speed flow past bluff plates (Taneda, 1956a, 1972; Taneda and Honji, 197l), square cylinders (Mulhearn, 1973), and circular cylinders arranged at right-angles across the flow (Tritton, 1950; Taneda, 1956a, 1972; Grove et al., 1964; Coutenceau and Bouard, 1977a, 1977b). With cylinders, the separation bubbles lengthen with increasing Reynolds number (Fig. 3-6), while the velocity of backflow U,, increases relative to the external flow velocity U,. Numerical studies yield generally similar results (e.g. Hamielec and Raal, 1969; Dennis and Chang, 1970; Pruppacher et al., 1970; Nieuws-

Fig. 3-5. Separated flows associated with a boundary layer forming on a thick flat plate of finite length.

107

AA A

e 0 0

8

A

*

A

0.15

A

*O

*

0

,"

f

A A

0

0.10

0

0

gA 8"

A

B

Taneda (19560) Grove et at. ( 1 9 6 4 ) o Coutenceau and h a r d (1977)

Grove et al. ( 1 9 6 4 )

A

o Coutenceau and h a r d (19770)

I

50

I00

Reynolds number, U, D / u

150

0

50

100

150

Reynolds number, U ' D/Y

Fig. 3-6. Features of the separated flow downstream of a circular cylinder arranged transversely to a fluid stream. a. Relative length of separation bubble as a function of Reynolds number. b. Relative maximum backflow velocity in separation bubble as a function of Reynolds number.

tadt and Keller, 1973). At Reynolds numbers greater than the order of 100, depending on the degree of confinement of the cylinder by the boundaries of the whole flow, the separation bubbles are shed periodically into the wake as a vortex street (Roshko, 1961 ; Sonneville, 1976). Cavity flows Of more relevance to sedimentary structures is low-speed flow in a two-dimensional cavity, a motion much studied on account of its practical importance (Wieghardt, 1953; Baturin, 1959). A two-dimensional cavity is specified completely by its shape, streamwise length L , and height H . Two alternative boundary conditions are involved in the experimental and numerical study of cavity flows. Under the first, the cavity is treated as open along one face to a stream flowing past. The second takes the cavity to be completely closed but with a lid moving in its own plane. Figure 3-7 summarizes schematically the results of many experiments on the flow in rectangular cavities (Wieghardt, 1953; Roshko, 1955b; Baturin, 1959; J. Fox, 1960; Tani et a]., 1961; Maul1 and East, 1963; R.D. Mills, 1965a, 1965b; Weiss and Florsheim, 1965; Haugen and Dhanak, 1966; Jarrett and Sweeney, 1967; Kistler and Tan, 1967; Pan and Acrivos, 1967; Reiman and Sabersky, 1968; Fenton and White, 1971; Raithby et a]., 1978; Rockwell and Knisely, 1979). Under the first boundary condition, the flow separates from the upstream edge and reattaches on the downstream face

108

s -

A

Fig. 3-7. The separated flow in transverse rectangular cavities at (a,c,e) small Reynolds numbers, and (b,d,f) large Reynolds numbers. No particular Reynolds number is implied by (g), which shows the downward weakening of the vortices in a deep cavity. Based on many sources.

just below the rim. In shallow to square cavities, the flow comprises a single large roller, the centre of rotation of which shifts with increasing Reynolds number towards the geometrical centre of the cavity. The Reynolds number also has some effect on the number and relative size of the secondary corner eddies (Burggraf, 1966a) which generally accompany the \main vortex. The velocity of backflow reaches up to 30% of the velocity of the outer stream and increases relatively with the Reynolds number. In deeper cavities, chains of vortices are created by the driving action of the outer flow, the rollers, tending to a square section, growing weaker as they become further removed from the open top. Similar flow patterns exist under the second boundary condition, where the moving lid takes the place of the surface of separation. Small vortices again arise in the cavity corners. Little work has been done on cavities of non-rectangular cross-section. As the apical angle is reduced in a cavity of triangular section, a solitary roller gives way to a train of increasingly smaller vortices (Henry et al., 1964;

109

Mueller and O’Leary, 1970; Rotem et al., 1970). A single vortex occurs in round-bottomed cavities (Chung and Viegas, 1961). Maul1 and East (1963) and Kistler and Tan (1967) are the only workers to have studied nominally two-dimensional cavity flows other than in the plane of flow, finding the motion to be moderately three-dimensional. Limiting streamlines deviate by upwards of 20” from the streamwise direction, and both saddle and nodal points can be mapped in the flow pattern. Because of the simplicity of the boundary conditions, numerical studies of cavity flows are remarkably successful, supporting the experimental results for both small and large Reynolds numbers (R.D. Mills, 1965a, 1965b; Weiss and Florsheim, 1965; Burggraf, 1966a, 1966b; Pan and Acrivos, 1967; Ratkowsky and Rotem, 1968; Mehta and Lavan, 1969; L.F. Donovan, 1970a, 1970b; Mueller and O’Leary, 1970; Roache and Mueller, 1970; Rotem et al., 1970; V. O’Brien, 1972; Bhatnagar and Wong, 1974; Nallasamy and Prasad, 1977; Olson and Tuann, 1979). Many of the higher Reynolds number solutions depend on the suggestion by Batchelor ( 1956) and Squire (1956) that the flow is divisible between an outer region of boundary-layer type, in contact with the cavity wall, and an inner inviscid core. Steps and walls Laboratory work and other observations soon showed that low-speed flow separation could occur both upstream and downstream from a bluff wall or other thin obstruction arranged across a boundary-layer flow, and also at both upstream-facing and downstream-facing steps (Cornish, 1897; Dobrowolski, 1924; Prandtl, 1927b; Rehbock, 1930). Strong positive pressure gradients usually exist in front of bluff walls or upstream-facing steps within boundary layers. Separation under these circumstances has been little-studied, though of practical importance, creating Scorer’s (1955) “bolster” vortices in which, for example, sand can be trapped on the upwind sides of escarpments and ridges. Wieghardt (1953), Ringleb (1961), Bradshaw and Galea (1967), and Good and Joubert (1968) have established experimentally the main features of the motion (Fig. 3-8a). At other than very small Reynolds numbers, the flow separates 2-3 step or wall heights ahead of the obstruction and reattaches on the vertical part of the surface. We now find that the flow ahead of a step or wall is less constrained than that in a cavity. In particular, the upstream separation point takes a position controlled by a strong interaction between the outer flow and the separation bubble, an interaction that is weak in a cavity confined on three sides. The calculation of separated flows ahead of walls and steps is therefore more difficult and uncertain than the prediction of cavity flows (Lighthill, 1953; Barrows, 1963; Robertson and Huang, 1969; Kiya and Arie, 1972; Taulbee and Robertson, 1972; Haussling, 1977; Dennis and Smith, 1980). Low-speed separation at a vertical wall or thin barrier arranged trans-

Fig. 3-8. Schematic representation of flow separation (a) upstream of a positive step, and (b) at a transverse wall.

versely across a boundary-layer flow creates a large roller (Prandtl, 1927b; Arie and Rouse, 1956; Kapur and Reynolds, 1967; Acrivos et al., 1968; Good and Joubert, 1968; Bradshaw and Wong, 1972; Kiya and Arie, 1972; Narayanan, 1972; Narayanan and Reynolds, 1972). Because of the upthrust imparted to the fluid at the forward face of the wall, the crest of the roller lies nearly two wall-heights above the flow boundary, while its centre of rotation occurs at about the height of the wall itself (Fig. 3-8b). The bubble for the same reason is usually relatively long, in the order of 15-20 wall-heights, but can be shortened under severe boundary constraints. The maximum velocity of backflow is 20-30% of the velocity of the external stream. Studies of flow separation at single two-dimensional downstream-facing steps are confined either to those with right-angled corners or with gently sloping risers similar in profile to a dune or ripple. A roller is formed at such a step (Fig. 3-9), whether the separating flow is laminar or turbulent, the geometry of the separation bubble changing with Reynolds number and boundary-layer thickness. Generally, there are accompanying secondary separation bubbles, as in cavity flows. At a right-angled step there is typically a large secondary bubble in the bottom corner, and usually others just beneath the surface of separation at the edge (Moffatt, 1964). Secondary

(0)

(b)

Fig. 3-9. Effect of (a) vertical and (b) sloping risers on flow separation at a tranwi’se negative step.

vortices may also occur in these positions with gently sloping risers, but they are seldom as well developed. If a laminar flow is started up at a two-dimensional downstream-facing step or a transverse ridge, a roller of gradually increasing size is shaped to lee (Honji, 1975; Longuet-Higgins, 1981). The size of the roller ultimately developed beneath a steady laminar stream increases gradually with Reynolds number and boundary-layer thickness (Tani, 1958; T.W.F. Moore, 1960; Tani et al., 1961; Nash et al., 1963; Goldstein et al., 1970; Mueller and O'Leary, 1970; Roache and Mueller, 1970; Denham and Patrick, 1974; Thomas et al., 1981). At very small Reynolds number, the roller is less than the step-height in length, but at moderate numbers is in the order of 10 times longer. Backflow velocities are small compared with the outer flow. A turbulent low-speed flow passing over a single downstream-facing step separates as a long flat roller similar to that sketched in Fig. 3-9 (Wieghardt, 1953; Tani, 1958; Tani et al., 1961; Raudkivi, 1963; Henry et al., 1964; Heskestad, 1966; Naib, 1966; Allen, 19688, 1969b; Butte and Pichon, 1970; Etheridge and Kemp, 1978). Experiments with right-angled steps show that the length L of the separation bubble grows with a decrease in the thickness h of the flow, normalized by the step-height H , as illustrated in Fig. 3-10. However, shorter and less rapidly changing bubbles arise at steps with risers sloping at about 30" from the horizontal (Fig. 3-10). The greatest velocities 8.5

8.0

7.5

7.0

L/H 0

65

0

6-0

5-5

5.0 Allen Allen 0.2

0.4

0.6 0.8 1.0

2

4

6

8 1 0

20

b/H

Fig. 3-10. Experimental variation in the relative length of the separation bubble to lee of a transverse negative step as a function of relative step-height, with the slope of the riser as a third variable. After Allen (19688, 1969b).

112

0.30-

0.25

-

0.20 -

0.15

-

0.10

urneon

a

0.05 -

-L-

O

5

6

7

8

9

10

II

L/ H

Fig. 3- 1 1. Experimental values for the backflow velocity 0.008 m above the bed and half-way along the separation bubble to lee of a transverse negative step, 0.04 m tall, as a function of the relative length of the separation bubble. Data of Allen (1968g).

of backflow at steps are in the order 20-40% of the main-stream velocity. Allen ( 1968g) found experimentally that the maximum backflow velocity gradually increased with increasing bubble length and, therefore, with decreasing flow thickness (Fig. 3-1 1). Thomas et al. (1981) give more data. In practice, a truly two-dimensional separated flow cannot exist downstream of a two-dimensional step, because of the constraints inevitably arising from side walls. Allen (1968g, 1969b) examined the patterns of limiting streamlines on both right-angled and sloping steps, finding weakly three-dimensional separation in all cases (Fig. 3- 12). Nodal and saddle points existed in alternation along each reattachment line, showing that the separation bubble was divided transversely into a number of cells, as exist in the separated flow in a two-dimensional cavity (Maul1 and East, 1963; Kistler and Tan, 1967). A reduction in flow thickness relative to step height rapidly increases the number of these cells per unit span. A separation phenomenon resembling that at a step occurs when a plane full jet (Bourque and Newman, 1960; Sawyer, 1960, 1963; Newman, 1961; Rajaratnam and Subramanya, 1968; Madjirsky, 1969; Exley and Brighton, 1971) or a half-jet (Abramovich, 1963) reattaches to an adjacent boundary. For the turbulent half-jet, Abramovich calculated a separation bubble about six times longer than the normal distance of the jet from the boundary, with backflow velocities of up to 40% of the main stream, in good agreement with experiments at steps (e.g. Naib, 1966). A double-step configuration presents downstream-facing two-dimensional steps arranged symmetrically about the plane of flow and directly opposite

1 I3

o Nodal point

Saddle point

-O

005 m

Fig. 3- 12. Experimentally determined limiting streamlines on a two-dimensional negative step 0.022 m high with sloping riser in a water stream of velocity 0.29 m s- and depth 0.064 m.

’

each other, one on each side of a conduit or channel (Mehta, 1979). At small Reynolds numbers and for right-angled steps (Fig. 3-13a) the separated flow comprises symmetrically arranged equal bubbles increasing in length with the value of the number (Hung and Macagno, 1966; Macagno and Hung, 1967a; Durst et al., 1972, 1974). At moderate and large numbers, however, the arrangement is unstable, one of the bubbles being nearly twice as long as the other (Abbott and Kline, 1962; Filetti and Kays, 1966; Durst et al., 1972, 1974). More bubbles may arise further downstream, so that the outer flow meanders unpredictably (Fig. 3-13b). Separation is suppressed if the slope of the step is reduced to about 4” relative to the mean flow direction (Schlichting, 1960). Mehta (1981) reports ‘further work on double steps.

Fig. 3-13. Flow separation in rectangular conduits with steps on opposite walls. a. Stable symmetrical flow pattern formed at small Reynolds numbers. b. Unstable “meandering” pattern of separation found at moderate and large Reynolds numbers.

1 I4

AXISYMMETRIC FLOWS

These are three-dimensional flows with the special property of being symmetrical about the mean flow direction, so that they are completely described by reference to any cross-section containing this axis. It is therefore not surprising that separation under axisymmetric and under twodimensional conditions are closely related. Axisymmetric separation in external flows at small Reynolds numbers is shown by spheres and by bodies of revolution such as spheroids, cones, and spherical caps. In laboratory and numerical experiments, a ring-like separation bubble marks the rear of such bodies, the motion in an axial section resembling that in the trailing vortex of Fig. 3-5 (Taneda, 1956b; Margarvey and Maclatchy, 1968; Masliyah and Epstein, 1970; Masliyah, 1972; Dorrepaal et al., 1976; Collins, 1979; Han and Patel, 1979). As with circular cylinders (Fig. 3-6), the bubble increases in length with increasing Reynolds number until, at a critical value, it is periodically shed to form a kind of vortex street. Narasimhan (1967) finds that separation at large Reynolds number on a cone pointing downstream is strongly influenced by the apical angle; the annular bubble increases in length as the apical angle is increased. This motion resembles that at a step with sloping riser (Fig. 3-9b), when again the presence of right-angled corners lengthens the separated region (Fig. 3-10). Little is known of separation patterns in annular cavities. J.F. Stevenson (1973) calculated for small Reynolds numbers a motion like that in Fig. 3-7c. The axisymmetric flow corresponding to separation at a two-dimensional downstream-facing step (Fig. 3-13) is the stable annular roller developed at an expansion in a circular pipe (Hieu and Hebrard, 1977; Cherdron et al., 1978; F.T. Smith, 1979). At a right-angled expansion, and for small Reynolds numbers, the bubble length and backflow velocity both increase as before with increasing number (Macagno and Hung, 1967b; Back and Roschke, 1972). Where the expansion is more gradual, shorter bubbles are found for a given Reynolds number than in the right-angled case (Chaturvedi, 1963; Golia and Evans, 1973), as noted for two-dimensional steps (Fig. 3-10) and axisymmetric external flows.

SEPARATION IN THREE DIMENSIONS

External flows Three-dimensional separation in external flows has been studied for closed bodies of revolution, chiefly prolate spheroids, and for swept-back and delta-shaped wings. A prolate spheroid of large axial ratio placed in a stream with its major

1 I5

Fig. 3-14. Flow separation involving vortices on a delta wing gently inclined relative to an air stream. After Cooke and Brebner (1961).

semi-axis parallel with flow gives rise to an axisymmetric type of separation (Cooke and Brebner, 1961). On progressively tilting the spheroid, however, the flow around the body exhibits a reproducible sequence of threedimensional patterns which have been explored both theoretically and experimentally (Maskell, 1955; Eichelbrenner, 1957; Eichelbrenner and Michel, 1958; Thwaites, 1960; Wang, 1972; Han and Patel, 1979). The asymmetrically arranged rollers formed to the rear at small angles of incidence are succeeded at moderate angles by powerful vortices, to be followed by rollers again as the spheroid becomes increasingly bluff. The case of a delta or swept-back wing is o f greater sedimentological relevance, for many bedforms have crests that are finely skewed to flow. As Roy (1952) was early to indicate, a symmetrical pair of large and powerful vortices (Fig. 3-14) arises on the upper surface of a delta or swept-back wing at low incidence, in response to flow separation along its leading edge (Kuchemann, 1953; Thwaites, 1960; Cooke and Brebner, 1961 ; WerlC, 1961; Tani, 1964; Kuchemann and Weber, 1965; Batchelor, 1967; Garodz, 1971 ; Bippes, 1977; Szodruch, 1978). That the vortices persist far downstream (P.R. Owen, 1970) is shown by the internal twisting visible in the vapour trail from each pair of jet engines on a four-engined aircraft (Scorer, 1978). Large volumes of fluid from the outer flow enter each vortex, which is commonly treated as having an inviscid core. In contrast to the sluggish backflows found in rollers (e.g. Fig. 3-1 l), the flow speeds observed within vortices approach that of the outer stream. Cavity flows

We are almost totally ignorant of flow separation in cavities comparable in span and streamwise length, which is unfortunate in view of its relevance to pot-holes, flute marks, and meteorite cavities. Engineering studies on the

I I6

design of settling tanks (e.g. Clements, 1966; Price and Clements, 1974) suggest that complex patterns are likely to prevail. In tanks of rectangular plan, paired rollers and a variety of corner vortices have been noticed. So far as rectangular cavities are concerned, vortices triggered by edge-related secondary flows (Fig. 1-4) may occur provided that two of the sides are parallel with flow. Vortices could also accompany rollers in cavities of circular or oval plan, for reasons explained in the following discussion on separation at steps. Steps and related shapes

Separation at skewed steps and at skewed ramps or walls mounted on flow boundaries has received more attention from sedimentologists than engineers. Jarocki (1949) noticed that a vertical wall of even height placed at a moderate skew across the bottom of a flow channel created a vortex which

X

t z 0,'"

0 Attachmrnt 2 lina

Step edge (separation)*

Id)

lo1

If)

Fig. 3-15. Flow separation at negative steps. a. General features of separated flow illustrated by limiting streamlines, and definition diagram for angles of attack and return. b-g. Observed limiting streamlines for separated flows formed at negative steps with vertical risers 0.025 m high at step-height Reynolds numbers in the order of 1.1. lo4. Rollers alone are present in (b), (d) and (0. In (c) a vortex alone is seen, and in (e) and (g) vortices are the dominant flow structure. Small rollers appear to be present proximally in the separated regions of (e) and (g), to judge from the shape of the limiting streamlines and the behaviour of the bottom comer eddy. After Allen (1968g).

1 I7 36C

34c

320 300 280

-

260

m

f 240 n m ;220

.$.2 0 0 ?1 180

r

5 160 0

4' 140

ROLLERS

*

f

120

100 80 60

40

20 0

20 40 6 0 80

100 120 140 160 180 200 220 240260 280 300 320 340 360 Measure of shew, 201 (degrees)

Fig. 3-16. Experimental determination of the angle of return in separated flows formed at a right-angled negative step, as a function of the angle of skew, with a parameter describing the shape of the separation bubble as a third variable. After Allen (1968g).

passed downstream into the main flow. A similar flow pattern was found by McCullough et al. (195 1) at a finally angled wedge-shaped ramp, the vortex again escaping from the ramp, and by Mulhearn and Bradley (1977) at an obliquely-placed low-porosity wall. D.T. Hopkins (in Dzulynski and Walton, 1965) saw vortex-like motions at steps skewed across the flow. Allen (1968g) has contributed most on low-speed separation at threedimensional steps, studying single steps of uniform height and constant skew, combinations of equally-skewed steps arranged symmetrically about the plane of flow, single steps of spanwise-changing height, and steps of unequal skew combined in pairs. He argued from considerations of pressure that, for infinitely long skewed steps of uniform height, a simple relationship connected the direction of limiting streamlines in the separation bubble and the degree of skewness. Referring to Fig. 3-15a, this relationship is that /? = 2a,where /? is the so-called angle of return, measured to the right of the positive x-direction (direction of outer stream) and downstream from a limiting streamline in the separation bubble at a point of reflection or inflection, and a is the angle of skew of the step measured downstream from

118 1.0

0.8 0.7

i /

ROLLERS

0.6

0.5 0.4

0.3

02

lU,l

& I . . .

0.1

0.08 DO7

0.OE 0.05 0.04

O.O? 0.02

20

40

60

80

100

120

140

160

180

Angle of skew, u (degrees)

Fig. 3-17. Experimental relationship of backflow velocity to the angle of skew in separation bubbles formed at negative steps 0.025 m high. Velocity measured 0.008 m above bed half-way across bubble. After Allen (19688).

the edge of the step and to the right of the flow-direction. It was further argued that the separation bubble is a roller when 45" < a < 135" but a vortex when 0" < a < 45" and 135" < a < 180". Figure 3-15b-g shows a range of experimental flow patterns produced using right-angled steps of uniform height arranged in an open water channel. In some cases the separation bubble comprises more than one flow cell. The patterns of limiting streamlines observed in the cells broadly support the theoretical predictions, but reveal systematic departures from them, explicable in terms of the constraints exercised by adjacent cells, the walls, and the free surface. The effectiveness of these constraints on each cell is given by the value of the group H L / S h , where H is the step height, L the streamwise length of the cell, S the spanwise length, and h the flow depth at the step edge. Figure 3-16 gives experimental angles of return and skew using H L / S h as a parameter, together with the theoretical existence fields of rollers and vortices. As H L / S h is raised the experimental points deviate increasingly from the theoretical relationship /3 = 2a, and many cells appear to be rollers, where the angle of skew would indicate a vortex. An increasing boundary constraint clearly suppresses the development of vortices able to escape from the step. The speed of backflow at a downstream-facing step also varies systematically with the degree of skew. Figure 3-17 shows experimental values of the

1 I9

backflow velocity measured parallel with limiting streamlines at either reflection or inflection and referred to the speed of the main flow. Strongly skewed steps create vortices that are more powerful than the rollers formed at a small or moderate skew. There is a harmonious increase in the vigour of the secondary vortices produced in the bottom corners of the steps (Fig. 3- 15 b-g).

PRESSURE AND STRESS IN LOW-SPEED SEPARATED FLOWS

Distribution of temporal mean values As we have already said, flow separation is associated with the presence of strong pressure gradients both within the fluid and along its boundaries. Those developed on the solid boundary are depicted schematically in Fig. 3-18 in terms of the pressure coefficient Cp = ( p , - p ) / i p U 2 , where p , is the temporal mean pressure at the wall, p is the static pressure, p is the fluid density, and U is either the temporal mean flow velocity or the velocity of the stream outside the boundary layer, according to circumstances. Laboratory results on the pressure distribution ahead of a two-dimensional upstream-facing step or wall (Fig. 3-18a) are given by Good and Joubert (1968), Kiya and Arie (1972), and Taulbee and Robertson (1972). From a small value far upstream, the pressure coefficient very gradually increases to a maximum in the order of 0.4 in the vicinity of separation, another maximum accompanying reattachment on the vertical face. The slightly lower values of the coefficient between separation and reattachment are related to the backflow. Taulbee and Robertson’s numerical model predicts pressure values similar to those measured.

8

Boundary-layer flow

Separated flow

I

Boundary-

I

I

layer

I

Separated flow

j

Readjustment region

Fig. 3-18. Properties of separated flows. a. Schematic distributions of velocity and pressure in the separated flow ahead of a positive step or transverse wall. b. Schematic distributions of velocity, mean boundary shear stress, pressure, and the intensity of pressure fluctuations in the separated flow downstream of a negative step.

120

Corresponding experimental data exist for two-dimensional right-angled steps (Tani, 1958; Tani et al., 1961; Nash et al., 1963; Raudkivi, 1963; Mueller et al., 1964; Macagno and Hung, 1967a) and for ripple and dune-like shapes (Raudkivi, 1963, 1966a; Henry et al., 1964; Vanoni and Hwang, 1967; Khanna, 1970), in which three regions of flow can be distinguished (Fig. 3-18b). Pressure is low and relatively uniform in the boundary layer ahead of the step-edge. In the separated region the wall pressure coefficient decreases rapidly towards the bottom corner of the step from the order of 0.2 to 0.4 near to reattachment, passing through a weak minimum where secondary separation occurs. The third region, that of reattachment or readjustment, shows the pressure gradually to decrease downstream towards boundary-layer like values as the new boundary layer grows beyond the reattachment point. Notice that the pressure maximum occurs just downstream from reattachment as shown by the division of the free streamline. On ripple and dune beds, the boundary-layer region is strictly speaking absent, the separated and readjustment regions alternating along the flow. From the previous criterion, a U / a y = 0, it follows that the temporal mean bed shear stress is also zero at each separation and reattachment point on the shapes sketched in Fig. 3-18. Bradshaw and Wong (1972) found that the stress increased rapidly downstream from reattachment on a flat plate carrying a step. On beds shaped like ripples or dunes, Raudkivi (1963, 1966a) also found the mean bed shear stress T~ to increase sharply between reattachment, on the lower stoss-side of each feature, and the crest downstream where separation next occurred. Experimental data are not available for the separated regions of steps and ripple-like shapes, but the temporal mean bed shear stresses here are likely to be small, on account of the sluggishness of backflow. Taking the direction of the main flow as positive, the stresses in the separated region of course assume negative values. Pressure fluctuations Although the temporal mean pressure in a steady separated flow is stable locally, the instantaneous pressure values fluctuate considerably with time, the magnitude, scale, and frequency of these fluctuations being of interest in connection with the entrainment of granular sediment, and with the plastic deformation or liquefaction of a weakly cohesive bed. Experimental data are available for high Reynolds numbers from an axisymmetric pipe expansion (Rouse and Jezdinsky, 1966) and for the separation bubble downstream from a bluff wall (Narayanan and Reynolds, 1968, 1972). The results in the two cases are qualitatively similar. The magnitude of the pressure fluctuations may be expressed by the quantity ( P ’ ~ ) ’ /i ~p U / 2 ,where ( P ’ ~ ) ’is/ ~the root-mean-square value of p’,

121

the fluctuating part of the pressure. At the wall, this quantity reaches its maximum value, in the order of 0.1, a little upstream from reattachment (Fig. 3-18b). This value is much higher than is ordinarily observed from attached turbulent boundary layers (Willmarth, 1975). By correlating pressure fluctuations between pairs of variously spaced flow-aligned points, the scale of the eddies that are causing the fluctuations can be established. The commonest eddy scale at reattachment approaches the height of the wall or step. The pressure fluctuations cover a broad range of relatively low frequencies, indicating that the eddies are being convected past the bed at speeds ranging up towards the mean flow speed. These observations combine to show that, in the vicinity of reattachment, the flow boundary is being subjected to frequent and substantial “pushes” and “pulls” as eddies travel past it. VORTEX-PRODUCTION AND TURBULENCE IN LOW-SPEED SEPARATED FLOWS

Rolling up of a free shear layer The eddies described above as detectable in a separated flow from pressure measurements are present because the viscous layer which detaches from the boundary at the edge of the step or crest of the wall proceeds to roll up into transverse billow-like vortices which increase in size and change in other important respects as they are carried along (Roshko, 1976). Ultimately, at a sufficient downstream distance, these vortices develop into random turbulence. Vortex development is associated with a significant change in the circumstances of the viscous layer in the course of its separation (Laursen and Toch, 1959; Townsend, 1976). Upstream from the edge of the step in Fig. 3-19, the retarded layer is a boundary layer, marked by a zero velocity at the bed and by a continuously declining velocity gradient outward to the edge of the layer. Downstream from separation the viscous layer is radically different (e.g. Baum, 1964; J.P. Lamb, 1967; Wygnanski and Fiedler, 1970; Patel, 1973; Brown and Roshko, 1974). The velocity profile now has a point of inflection, and so meets Lord Rayleigh’s (1880) criterion for inviscid instability. Moreover, the separated viscous layer, or free shear-layer, gradually increases in thickness downstream as it entrains more and more of the surrounding fluid as the result of vortex growth. It is for this reason that it is often described as a mixing layer. At reattachment a new attached viscous layer begins to grow. The separated flow shown,in Fig. 3-19 closely resembles the idealized case of two infinite streams of fluid in relative motion separated by a plane interface, where the fluids may be either miscible or immiscible and may differ in viscosity (or each be inviscid) and/or density. Only if the curvature

122 Boundary layer

Free shear-layei

I

Boundary layer

Boundary layer

Fig. 3-19. Schematic development of boundary layers and the layer of free shearing in the separated flow downstream of a negative step.

of the free shear-layer is high do important quantitative differences appear (Castro and Bradshaw, 1977). Kelvin-Helmholtz instability is the name given to the type of unstable behaviour which the interface may display (H. Lamb, 1932; Chandrasekhar, 1961; Betchov and Szewczyk, 1963; Gerwin, 1968). If the fluids are both incompressible and inviscid, any relative motion between the layers causes instability (H. Lamb, 1932), though compressibility modifies this picture (Lessen et al., 1965). Viscosity stabilizes the interface, but only at small Reynolds numbers and with respect to disturbances of relatively small wavelength (Esch, 1957; Hughes and Reid, 1965; Lessen and KO, 1966; Wazzan et al., 1967; Hayakawa and Unny, 1974). The interface is stabilized in the inviscid case if the upper fluid is less dense than the lower (Menkes, 1959; Esch, 1962; Davey and Roshko, 1972). It would appear that when the fluids are immiscible, interfacial tension has the effect of slightly stabilizing the arrangement (Thorpe, 1969~).So far as separation under natural conditions is concerned, the stabilizing effects of viscosity, gravity, and interfacial tension can generally be ignored, as large Reynolds number prevail.

Fig. 3-20. Instantaneous shadowgraph showing vortices developed between coflowing (left to right) streams of helium (upper layer, velocity 5 m s-I) and nitrogen (lower layer, velocity 1.9 m s-I) at a common pressure of 4 atmospheres. Photograph courtesy of A. Roshko and reproduced by permission of Cambridge University Press. See also Brown and Roshko (1 974).

123

Figure 3- 19 depicts a reattaching free shear-layer only in a time-averaged sense, no impression being given of the quite remarkably coherent and ordered structure that exists within it due to its aforementioned rolling up into flow-convected vortices. In Fig. 3-20 appear examples of these vortices. They were generated between juxtaposed streams of helium and nitrogen flowing in the same direction but at different velocities (Brown and Roshko, 1974). Theoretical study of the rolling-up process began early. Rosenhead ( 1931) idealized the free shear-layer as an infinitely thin vortex sheet, which rolled up into regularly arranged transverse vortices into which most of the vorticity became concentrated. Michalke ( 1965a) reviewed several later analyses on broadly these lines (see also Damms and Kuchemann, 1974). He showed that a shear layer of finite thickness also would roll up into vortices (Michalke, 1965a, 1965b; Michalke and Wille, 1966), established that twodimensional vortices grew more rapidly than three-dimensional ones (Michalke, 1969), and pointed out that vortices could ultimately break down under axial disturbances (Michalke and Timme, 1967). J.L. Robinson (1974), Corcos and Sherman (1976), Patnaik et al. (1977) and Jimenez ( 1980) have also calculated the character of the vortices; Moore and Saffman (1975), Takaki and Kovasznay (1978), Acton (1980), and Aref and Siggia (1980) have further considered their breakdown or merger. The vortices (Fig. 3-20) are well known fom laboratory work. They occur as ring-like features in the mixing layer of a round jet (Freymuth, 1966; Michalke and Wille, 1966; Becker and Massaro, 1968; Beavers and Wilson,

(C)

9

Vortex path Vortex amalgamation

0 0.005

0.010

0.015

0.020

0.025

Time (s)

Fig. 3-21. Development of the free shear-layer in a separated flow. a. Downstream expansion and velocity distribution in the layer. b. Development and eventual amalgamation of vortices in the free shear-layer. c. Observed travel and amalgamation of vortices in an experimental free shear-layer established between coflowing helium (velocity= 10.6 m s ) and nitrogen (velocity=4.0 m s I). After Brown and Roshko (1974).

'

~

124

1970; Crow and Champagne, 1971; Kamoi and Tanaka, 1972; Liu, 1974; Lau and Fisher, 1975; Petersen, 1978; Yule, 1978; Bruun, 1979), as transverse structures in that generated in a half-jet or at a downstream-facing step (Tani, 1958; Sato, 1959a, 1959b; Tani et al., 1961), and as transverse structures in the mixing layer between coflowing streams (Clark and Markland, 1972; Brown and Roshko, 1974; Winant and Browand, 1974; Browand and Weidman, 1976; Dimotakis and Brown, 1976; Chandrsuda et al., 1978). Striking proof of the roll-up of a natural free shear-layer is given by W.S. Cooper’s ( 1958) smoke visualizations amongst transverse coastal dunes. Vortices similar to those listed were recorded by Pierce (1961) during the acceleration of a salient edge, by Thorpe (1968, 1969a, 1969b, 1969c, 1971, 1973a, 1973b, 1973c) from between counterflowing liquids, by Woods (1968) and Thorpe et al. (1977) at thermoclines, and by Scorer (1969) as atmospheric billow clouds. See also Hussain and Clark ( 1981). Vortex growth and progression toward disorderliness are best known from studies with coflowing two-dimensional fluid streams merging at the trailing edge of a splitter plate (e.g. Brown and Roshko, 1974; Dimotakis and Brown, 1976). Figure 3-21a shows the flow pattern that results, the local “vorticity thickness”, ,a of the free shear-layer being defined by (U, U,)/(dU/dy),,, where (dU/dy),,, is the local maximum value of the velocity gradient. In both coflowing streams and half-jets, the free-shear-layer thickens approximately as 0.1-0.15 times the downstream distance (e.g. Wygnanski and Fiedler, 1970; Brown and Roshko, 1974; Dimotakis and Brown, 1976). The rate of thickening is greater if the two streams are not parallel (Hackett and Cox, 1970), as may occur in a region of threedimensional flow separation. Figure 3-2 1b summarizes schematically the instantaneous developing structure of the layer, as it has been revealed visually by Freymuth (1966), Clark and Markland (1972), Brown and Roshko ( 1974), Winant and Browand ( 1974), Browand and Weidman ( 1976), and Dimotakis and Brown (1976). An initial region where a dye thread (say) becomes undulose and locally swollen is followed downstream by a second region in which the varicosities break and roll up into vortices while the portions of dye between become greatly thinned. In a third region still further downstream, the vortices flatten and pair up, rotating round each other in the process, or otherwise amalgamate. As Brown and Roshko (1974) showed by tracking individual vortices (Fig. 3-21c), structures that have amalgamated once become involved in at least one and sometimes two later fusions. Pairing or amalgamation in fact is the chief process whereby the vortices (or vortex-complexes) grow in temporal and spatial scale during their convection. As the cascade of amalgamations is unfolded, the vortices become increasingly three-dimensional under the influence of growing nonlinear effects (Browand, 1966; Crow and Champagne, 1971; Miksad, 1973; Clark and Markland, 1972; Brown and Roshko, 1974). On suitably averaging, however, the local vortex spacing is found to lie between 3.1 and 5.0

I25

times the local shear-layer thickness, 8, (Brown and Roshko, 1974; Dimotakis and Brown, 1976), in rough agreement with Moore and Saffman’s (1975) theory for vortex stability. Hence the non-dimensional local vortex period, TU,/S,, also lies between 3.1 and 5.0, where T is the measured temporal mean period at a station in the free shear-layer and U, is the vortex convection velocity, approximately equal to +(U , U,) (Browand, 1966; Crow and Champagne, 1971; Miksad, 1972; Brown and Roshko, 1974; Dimotakis and Brown, 1975). With increasing downstream distance, then, the shear-layer widens and its vortices increase in diameter, increase in spacing, and decrease in frequency. Hussain and Clark (198 1) add more data. We cannot expect that conditions in the curved reattaching free shearlayers at downstream-facing steps (Fig. 3-19) and bedforms such as ripples and dunes are completely identical with those existing between coflowing parallel streams. Whereas the length of the former is finite and controlled by flow thickness and step or bedform height, the downstream extent of the latter is theoretically indefinite. In a reattaching free shear-layer, vortex evolution under the control of the Kelvin-Helmholtz instability mechanisms proceeds only for so long as the vortices lie upstream of reattachment. Other mechanisms must operate if they are to grow and develop beyond reattachment, as Bradshaw and Wong’s (1972) analysis suggests. On the other hand, in a non-reattaching free shear-layer, indefinite vortex evolution would seem possible. Up to a position close to reattachment, however, conditions in a reattaching free shear-layer should closely resemble those in the nonreattaching case. For the layer thickness (U,,,, - U,)/(dU/d y),,,,, where U,,, is the maximum velocity in the outer flow, grows almost linearly over most of the length of the bubble, to judge from available velocity profiles (Tani, 1958; Abbott and Kline, 1962; Raudkivi, 1963; Henry et al., 1964; Naib, 1966). It is only very close to reattachment that this length rapidly assumes very large and therefore physically meaningless values. According to Tani’s ( 1958) visualizations at a downstream-facing step, the shear-layer vortices are already comparable in diameter and spacing with the step height by the time they have traversed the first half of the separation bubble, in good agreement using the above measure of layer thickness with the scaling factors for non-reattaching layers. Tani’s scales are also in agreement with the independent conclusions of Rouse and Jezdinsky (1966) derived from pressure correlations.

+

Velocity fluctuations and Reynolds stresses Whatever the character of the flow which detaches from a wall, the edge of a step, the start of a half-jet, or the trailing edge of a splitter plate in an arrangement of coflowing fluids, the effect in the free shear-layer of vortex development is to increase velocity fluctuations and to create measurable Reynolds or turbulent stresses additional to the mean stress. These fluctua-

I26

tions must strongly influence the motion of sediment particles contained in the free shear-layer, together with the response to flow of sedimentary boundaries in the vicinity of reattachment, towards which the vortices are ultimately swept. Hot-wire and hot-film anemometers have been used to establish the magnitude of velocity fluctuations in the separated flows formed downstream from walls and related shapes (Arie and Rouse, 1956; Raudkivi, 1966b). The turbulence intensities attain maxima within the free shear-layer and remain high in the flow downstream from reattachment. Comparing the root-mean-square value of the longitudinal fluctuations with the velocity of at its largest is in the order of the external flow, we find that ( a ’ 2 ) ’ / 2 / U m 0.22, with the relative intensities of the transverse and normal fluctuations attaining maxima not far below this value. The Reynolds stress is also rather high, Arie and Rouse measuring values of m/U; in the order of 0.02, where is the temporal mean value of the product of u’ and 0’. At downstream-facing right-angled steps (Raudkivi, 1963; Tani, 1958; Tani et al., 1961; Mueller et al., 1964; Butte and Pichon, 1970; Etheridge and Kemp, 1978) and axisymmetric pipe expansions (Chaturvedi, 1963) the largest value of ( i i ” ) ~ U mgenerally lies between 0.15 and 0.22, while the maximum value of u ‘ v ‘ / U ~can attain 0.02 (Fig. 3-22a). Each quantity gradually decays downstream from reattachment. Turbulence intensities and stresses closely similar to these are also measured at half-jets (Liepmann and Laufer, 1947; Browand, 1966; Wygnanski and Fiedler, 1970) and in coflow-

0

0.05

0

0.25m

I

Fig. 3-22. Measured distributions of local mean velocity, fluctuating velocity, and mean bed shear stress at (a) a two-dimensional negative step beneath an air stream of velocity 28 m s (after Tani et al., 1961), and (b) over a bed shaped like current ripples beneath a water stream of mean velocity approximately 0.35m s - ’ (after Raudkivi, 1966a).

’

127

ing fluids downstream from splitter plates (Browand and Weidman, 1976), again pointing to the qualitative similarity between these flows and reattaching free shear-layers, as well as to the rear of bluff bodies (Narasimhan, 1967). The intensities and stresses are much larger than in the corresponding boundary-layer flows (e.g. Laufer, 1951, 1954; Blinco and Partheniades, 1971; Blinco and Simons, 1974). Little is directly known of velocity fluctuations and turbulent stresses above ripple and dune beds, though the available results point to magnitudes and distributions similar to those observed at steps and walls. Figure 3-22b presents Raudkivi’s (1966a) data. The turbulence intensity reaches a maximum about half-way along the separation bubble but along the stoss-side declines only gradually. The mean bed shear stress rapidly grows and may attain a maximum actually at separation, as Chaturvedi (1963) shows. Khanna (1970) obtained results for a ripple-like shape that are similar to. Raudkivi’s, though whether separation with backflow. occurred is uncertain. FLOW SEPARATION AT HIGH SPEEDS

Fluid compressibility (or lack of it) has little influence on low-speed flow separation but at high speeds is important. Separation of high-speed water streams is often accompanied by cavitation within the core of the separation bubble, as McCormick (1962) observed at a wedge. Clouds of water-vapour bubbles arise, violent collapse of which near to a flow boundary can cause its rapid erosion. But the flow speeds required for cavitation are large and in nature are unlikely to arise beyond the internal drainage systems of glaciers or the most violent surface floods. High-speed separation in gases such as air differs qualitatively from low-speed separation in that: (1) oblique shock waves form at reattachment and under some circumstances also at separation, (2) pressure gradients are generally steeper, and (3) streamlines tend to be straighter and to bend more rapidly. Lighthill (1953) discusses some of these differences. Moreover, at the very highest velocities, when the motion is hypersonic rather than supersonic, only laminar flow may be possible. Separation at supersonic speeds seems to govern the fluting and pitting of meteorites and tektites as they traverse the atmosphere. Flow separation at supersonic and hypersonic speeds has been explored theoretically and in the laboratory at upstream-facing right-angled steps and at ramps and wedges (Bogdonoff and Kepler, 1955; Chapman et al., 1956; Thomann, 1959; Charwat et al., 1961a, 1961b; Vasiliu, 1962; Ginoux, 1965, 1969, 1971; Zukoski, 1967; Nestler et al., 1969; Law, 1974; Wilcox, 1975), in both deep and shallow two-dimensional and axisymmetric cavities (Johannesen, 1955; Thomann, 1959; Charwat et al., 1961a, 1961b; Hahn, 1969; Nestler et al., 1969; Hodgson, 1970; McGregor and White, 1970), and at downstream-facing right-angled steps (Chapman et al., 1956; Carlson, 1959;

128

Thomann, 1959; Naysmith, 1958, 1961; Chanvat et al., 1961a, 1961b; Ginoux, 1965, 1969, 1971; Roshko and Thomke, 1966; Scherberg and Smith, 1966; Hama, 1968; Sandford and Ginoux, 1968; Roache and Mueller, 1970; Mukerjee et al., 1971; Back et al., 1972; Lamb and Hood, 1972). Whitehead and Keyes (1968) experimented on high-speed separation on swept-back wings. These studies permit the following generalizations. At an upstream-facing step, the length of the separation bubble is greater for laminar than for turbulent flows, but in each regime increases with ascending Reynolds number. At downstream-facing steps, the bubble shortens with increasing Reynolds number, an important shock wave, the lip shock (Hama, 1968), forming nearly parallel with the separation streamline. A single separation bubble can exist in a relatively much shallower cavity under high-speed than under low-speed conditions. One important effect associated with the lip shock is that separation occurs well away from where the flow boundary changes direction, for example, well below the edge of a downstream-facing step or inboard from the leading edge of a wing (e.g. Whitehead and Keyes, 1968). The pressure continues to rise for a substantial distance downstream from reattachment, where a second shock wave is formed. Thomann (1959) detected three-dimensional effects in high-speed separated flows similar to those known at low speeds. Near to reattachment at downstream-facing steps, where streamlines are concave-outward, Ginoux (1971) found sets of longitudinal vortices that may be either the response of a reattaching flow to transverse perturbations, or an expression of localized Taylor-Gortler instability (Tobak, 1971). AXISYMMETRIC TURBULENT JETS

Jets are not conventionally regarded as separated flows, unless associated with particular kinds of boundary constraint, yet it is useful to consider them here, as they include free shear-layers near to their origins and take properties influenced by vortex-production in these layers. Of most interest in connection with sedimentary structures are turbulent axisymmetric jets (Abramovich, 1963; Hinze, 1959; Laursen and Toch, 1959; Pai, 1954, 1957; Rajaratnam, 1976; Townsend, 1976). Figure 3-23a shows in axial section the temporal mean flow in a steady turbulent jet issuing in a normal direction from a circular orifice in a plane wall into a large volume of the same but nominally stationary fluid. The jet comprises at least two regions (Fig. 3-23b). The initial development region has an inner irrotational core, in which the axial flow velocity agrees with that at the orifice, surrounded by an annular free shear-layer growing in thickness linearly downstream. Beyond is the fully-developed region, also growing linearly, in which the radial profiles of axial velocity may be assumed

129 -140

000391

I I II

(d) I4O

X/<

000195

-120 c

ii c

I

Fully-developed region

0.000977

I

r'" I

r/a

r/a 25 2 0 15 10 5

3snQsTs

5

m

15 2025

smmmm US

Fig. 3-23. Flow in an axisymmetric jet. a. Schematic representation of streamlines and velocity in an axial section. b. Regions of flow in the jet. c. Calculated distribution of local velocity relative to the velocity at the orifice for b=O.O81. d. Calculated distribution of local velocity relative to the axial velocity at the same height for b=0.081.

similar, so that the flow is self-preserving. The maximum axial velocity decreases downstream in this region until, at an infinitely large distance, the jet has become infinitely wide and of zero velocity. The turbulence generated in the development region is joined further downstream by new turbulence created as the result of the growth of eddies near the borders of the jet as it entrains the surrounding fluid (Hinze, 1959; Townsend, 1976). The entrainment eddies seem to be yet another manifestation of Kelvin-Helmholtz instability. They have been visualized in the fully-developed regions of jets at higher Reynolds numbers by A.J. Reynolds (1962), Keffer and Baines (1963), Becker and Massaro (1968), and Crow and Champagne (1971). The entrainment is shown in Fig. 3-23a by streamlines parallel with the wall directed symmetrically toward the jet. The entrainment velocities are small, however, compared with the jet velocities. A very simple mathematical model of an axisymmetric turbulent jet becomes possible by assuming: (1) that the axial velocity measured in any normal cross-section of the fully-developed region follows the Gaussian

130

normal probability function, and (2) that the jet in this region is selfpreserving (e.g. Laursen and Toch, 1959). The axial velocity U ( r ) at a distance x from the orifice is assumed in the fully developed region to obey: U = U, exp( -r2/2u2) where U is the axial velocity at a radial distance r fom the axis of the jet, U, is the axial velocity at r = O , and u is the standard deviation of the distribution. The linear spread of the jet is expressed by: u = bx

(3-2)

where b is a numerical constant to be found experimentally. From a consideration of the constancy of momentum flux throughout the jet, the axial velocity at r = 0 is then found to be:

U, = ( a U o / b x ) (3.3) where a is the radius of the orifice and U, is the velocity at the orifice. The length, x,, of the irrotational core becomes: xo = (3.4) whence b = a / x o . The fully-developed jet therefore widens at a rate proportional to b and experiences a hyperbolic decline in the velocity at its axis with distance along its length. The motion is fully determined if a , U,, and b are known. As a first approximation (see Kotsovinos, 1976), this picture of the axisymmetric turbulent jet is well supported experimentally (e.g. Hinze and Van der Hegge Zijnen, 1949; Albertson et al., 1950; Alexander et al., 1953; Forstall and Gaylord, 1955). The Gaussian normal probability function describes the velocity very well in the more central parts of the jet but tends to underestimate it near the edges. Different authors have found slightly different values for the constant b, the figure of 0.081 obtained by Albertson and his associates being representative. The value of x o / a is about 16 at the lower Reynolds numbers in the range for a turbulent jet, rising to a constant value of approximately 8 at very high Reynolds numbers. As Abramovich (1963) emphasized, the turbulent jet in a still fluid has a particularly simple velocity structure. The isotachs (Fig. 3-23c) are nested curves, whereas the graphs for U / U , =const. are straight lines radiating from a virtual origin within the irrotational core (Fig. 3-23d). A practical boundary to the jet is formed by 2.440, at which U - 0.05 U,. Most naturally occurring jets emerge into a cross-stream rather than into a still fluid, with the result that they take a form distorted in comparison with our simple model. Following Moussa et al. (1977), we may expect the jet axis to bend over in the direction of the cross-stream, the cross-sectional shape to vary along the axis from circular at the orifice to kidney-like further downstream, and a wake perhaps with a vortex-street to appear in the lee. Few properties of the jet are now readily described. The position of the axis,

131

at least, can be described on the basis of formulae established from laboratory experiments (e.g. Keffer and Baines, 1963). These relationships are reviewed by Rajaratnam (1976), who points out that they differ slightly in response to Reynolds number effects, the ratio of the jet velocity to the cross-flow velocity, and the criteria used to define the position of the jet. Rajaratnam (1976) also summarizes a number of analytical methods which have been proposed for the prediction of jets in cross-streams.

SUMMARY

Flow separation in both low-speed and high-speed flows is expressed by the occurrence of a region of rotating fluid separated from the external stream by a viscous layer that for a short distance is freed from the flow boundary. Separation occurs in response to adverse pressure gradients, usually found where a flow boundary undergoes a sharp change of direction. The flow pattern in a region of separation is governed by the flow geometry, by the properties of the flow and fluid, and by the proximity of boundary constraints. Generally, the pattern of motion in real cases is threedimensional, even when the flow geometry is nominally two-dimensional. Separation and reattachment occur at ordinary lines on which lie saddle and nodal points. The free shear-layer separating the rotating fluid from the external stream is unstable and rolls up into powerful vortices that, by pairing or otherwise amalgamating, grow in size and period during convection downstream. Consequently, the free shear-layer and the reattached flow are characterized by velocity and pressure fluctuations of a much greater magnitude than typify the corresponding attached boundary layers. They constitute a dynamic environment likely to have its own distinctive sedimentological expressions.

This Page Intentionally Left Blank

133

Chapter 4 SEDIMENTATION FROM JETS AND SEPARATED FLOWS INTRODUCTION

The purpose of this chapter is to examine the fate of sediment particles that enter zones of free shearing (Chapter3). Such zones are persistent features in the flow to lee of current ripples and dunes in one-way aqueous streams, avalanche-fronted bars and Gilbert-type deltas in rivers and lakes, transverse dunes in the desert, and many flute marks and related features on beds of cohesive mud or soluble rock. In all but the case of flute-like marks, the behaviour of the grains controls the construction, by settling and avalanching, of cross-strata accumulated within the forms, and commonly influences the development of patterns of smaller scale structures that may accumulate upon or within the cross-strata in response to the temporal-mean pattern of separated flow. Transient zones of free shearing that grow with time arise during wave-action on rippled beds, for the bottom current repeatedly reverses itself over the ripple crests. Where sediment has been rapidly deposited, as by turbidity currents, or is disturbed so that an originally metastable grain-fabric is destroyed, pore waters commonly are expelled upward through channels or fissures which penetrate to the sediment-water interface. From each fissure or channel issues a jet of water which will construct a sand volcano around the vent if the current has successfully entrained particles from the underlying deposit. The characteristics of this kind of sand volcano can be understood in terms of jets, which are wholly bounded by zones of free shearing (Chapter 3). We so far lack a wholly satisfactory model for the behaviour of particles in turbulent fluids, whether stationary, as in the case of a suspension stirred randomly in a jar, or in translation, as in a jet or passing over a dune. This is because such problems are the most difficult in the field of the fluid dynamics of multiphase systems, even when' for simplicity the particles are assumed to be small or neutrally buoyant. These simplifications are rarely justifiable in nature, where grains commonly are large compared with turbulence scales, and take falling velocities that are not invariably very small fractions of the velocity of the impelling fluid. Hence reliance must still be placed on empirical results and on calculations to an order of magnitude. Broadly, we wish to gauge two possible effects: (1) the extent to which the free falling velocity of a particle changes in the presence of turbulence, and (2) the rate at which turbulence may diffuse grains.

134

PARTICLE FREE FALLING VELOCITY IN THE PRESENCE OF TURBULENCE

A grain in a turbulent fluid is subject to accelerations and decelerations because of the surging of the turbulent eddies past it. We can describe the particle in terms of its shape, size, and excess density, and can specify the turbulence by spectra of length and time scales ranging generally from the very small to the very large. For small relative velocities, an exact equation of particle motion can be written in four terms (Corrsin and Lumley, 1956; Tchen in Hinze, 1959; Houghton, 1963; Chao, 1964). One term is the Stokes drag and a second the effect of the pressure gradient in the fluid. The third is the virtual mass of the accelerated grain, and the fourth the additional drag, or Bassett force, arising with the unsteady motion. The equation is non-linear in its general form. It means that when grains occur in a turbulent fluid, they attempt to follow the surging motion of the fluid. But they cannot do this precisely or without lag, on account of their weight and inertia. Large particles tend to follow only the large eddies, and if sufficiently weighty may disregard even them, whereas small grains can follow both the large and small disturbances (e.g. Kuboi et al., 1972). The terminal falling velocity of a single particle in a turbulent environment is therefore not expected to equal that in a still fluid; nor should we expect grains of mixed sizes to diffuse equally, or grains to diffuse at the same rate as fluid momentum (Gitterman and Steinberg, 1980). The falling velocity of grains in turbulent fluids is often significantly less than in still fluids (Bouvard, 1951; Kada and Hanratty, 1960; Brush et al., 1962; Houghton, 1963; Businger, 1965; Baird et al., 1967; Field, 1968; Murray, 1970a; Bouvard and Petkovic, 1973; Meek and Jones, 1973; Herringe, 1976), and the interaction of grains and turbulence is actually exploited in at least one technique for measuring sediment size-distributions (Beck et al., 1973). In the case of a fluid oscillated vertically-perhaps the simplest “turbulent” motion possible- Houghton found that dispersed grains could be prevented altogether from either rising or falling buoyantly by a suitable choice of frequency and amplitude. In the more realistic environment produced by oscillating a grid in still water, Murray achieved reductions over the still-water terminal falling velocity of up to 30% with grains equivalent to mineral-density sands. The degree of reduction increased with increasing still-water terminal falling velocity and with the frequency of grid oscillations. The reductions to be expected for sands in rivers were, moreover, calculated to be of the same order as those obtained experimentally, and Murray therefore cautioned against the use of still-water values in predicting grain behaviour under natural conditions. Turbulence has more possible effects in the case of loosely aggregated mineral flocs, such as particularly occur in tidal waters. M.W. Owen (1971) points out that the terminal falling velocity of flocs under highly turbulent conditions may be reduced because their break-up under shear takes place

135

faster than their formation due to collision. With weak turbulence, however, the falling velocity may be increased because of net floc grobth. SEDIMENTATION FROM JETS

The transport in turbulent jets of scalar particle attributes such as concentration, size, and falling speed may be explored mathematically by an extension of the same principles as govern momentum transport (Vol. I, Chapter2; this Vol., Chapter 3) (Hinze, 1959; Goldschmidt and Eskinazi, 1966; Singamsetti, 1966; Melville and Bray, 1979). For the fully-developed region of a two-phase axisymmetric jet, and with gravitational effects neglected, we may expect the radial distribution of a particle property to follow the Gaussian normal probability function, and its axial distribution to vary reciprocally with distance from the orifice. Only if the particle and fluid-momentum diffusion coefficients are equal, however, will the “particle jet” and the “momentum jet” spread at the same rates. Singamsetti has shown why the particle coefficient should under some conditions exceed the momentum coefficient. Because inertia causes particles to be flung out of rotating eddies, it is only in the Stokes range, when grains largely follow the fluid, that the particle and momentum coefficients will be closely comparable. At larger particle Reynolds numbers, the grains should spread the faster and yield the larger coefficient. But the particle diffusion coefficient cannot grow indefinitely. Grains with sufficiently large falling velocities, for example, the coarser mineral-density sands in water and probably all sand-size grains in air, will pass almost unaffected through turbulent eddies. Because of this gravitational effect, their diffusion coefficients should be smaller than the momentum coefficient. A maximum must exist in the diffusion coefficient-Reynolds number relationship for mineraldensity solids. Experimental work partly confirms these predictions. Working with quartz sands diffused in a powerful submerged water jet, Singamsetti (1966) found that particle and momentum coefficients compared only at small Reynolds numbers. At a Reynolds number of 35, however, the particle coefficient was approximately 1.75 times the momentum coefficient. Murray (1970a) detected a similar effect, but also found that for some grains the particle coefficient was the smaller. Brush (1962) and Brush et al. (1962) using jets found particle diffusion coefficients as small as only 0.15 times the momentum value. Particle coefficients smaller than the momentum value were also measured from fast two-phase jets by Goldschmidt and Eskinazi (1966) and Hetsroni and Sokolov ( 1971). Increasing particle concentration causes departure from theoretical expectation (Melville and Bray, 1979). The nature of the deposit formed by a jet transporting grains more dense than the fluid is expected to vary with (1) the size and orientation of the jet, (2) its strength, (3) the concentration and falling velocity of the grains, (4)

136

Fig. 4-1. Definition diagram for the settling of mineral-density sand from an axisymmetnc water jet to form a sand volcano.

the flow duration, and ( 5 ) the environment of the jet. Consider in Fig. 4-1 an axisymmetric grain-laden water jet discharging vertically upward into an extensive body of stagnant water at the same temperature. The jet at the orifice has a uniform velocity U, and contains sediment particles of a single still-water falling velocity W and uniform concentration C,. Thus we ignore any effects which might in reality cause the grains to vary in concentration across the width of the channel leading to the orifice (Komar, 1972a). The grains become dispersed through the jet as the medium is entrained consequent on vortex development, whence the local grain concentration must decline both axially upward and radially outward. But the grains cannot travel upward beyond that height at which the maximum jet axial velocity just equals their falling velocity. Neglecting turbulence effects, and referring to eqs. (3.3) and (3.4), this height is: xw

='(b 1 +$)

in which a is the radius of the jet orifice and b is the previous numerical coefficient relating to the rate of spread of the jet. Now grains should settle from the jet along its borders at most levels lower than x w , sinking to the bed along paths probably inclined slightly inward, on account of the entrainment. Hence the radius of the jet at x w affords an estimate of the maximum radial distance on the bed, rw, at which the particles should alight. Extending our previous simplification that the momentum jet spreads

137

as kbx, where k is a numerical constant relating to how the edge of the jet is defined, we have:

rw = a

+ kbx,

(4.2)

approximately. On substituting eq. (4.1) into eq. (4.2), we find that the limiting radial distance from the orifice for particle deposition is inversely related to falling velocity. If rw, W, and-a can be measured, and a value for k assumed, we can at once estimate the fluid discharge from the jet. Clearly, the deposit can yield no particles for which W > U,, whence by measuring the largest falling velocity represented, an absolute upper limit can be placed on U,.Grains for which W = U, do not accumulate at the rim of the orifice, however, but at some distance off, on account of the persistence of U, to the top of the irrotational core (Fig. 3-4). The local particle deposition rate on the bed depends on the particle flux at the orifice and the local concentration along the border of the jet, which should decline with increasing jet radius (Fig. 4-1). Hence the local deposition rate of our uniform grains should also decline radially outward from the orifice. A vertical jet which has entrained sediment of mixed sizes should therefore construct around its orifice a symmetrical cone-shaped body of sediment within which grain size declines radially outward (Fig. 4-1). Because grains for which the falling velocity is limiting are not deposited immediately at the rim of the orifice, any lamination found beneath the flanks of the cone may be expected to turn down into perhaps a funnel-shaped crater with the orifice at its base. The flanks cannot steepen indefinitely, however, but must in time assume a limiting slope set by the conditions required for avalanching. SAND VOLCANOES

Cones of sediment having the appearance and origin just described are recognized as mud or sand volcanoes. Dionne (1973a) points out that this name is applied to structures representing at least four origins: (1) by the expulsion of air or gas from sediments, (2) by the extrusion of water or fluidized mud from deposits undergoing dewatering, perhaps after liquidization or slumping/sliding, (3) by the upward movement of diapirs of mobilized sediment, and (4) by normal volcanic processes. The fourth category is somewhat obscure, but our model (Fig. 4-1) includes many structures of the second kind, to which the name sand volcano may be applied even though the sediment involved often is chiefly silt. Sand volcanoes conforming to the model have no special environmental distribution, inasmuch as dewatering occurs in very many sedimentary sequences, but they are certainly most conspicuous in turbidite and deltaic deposits, which have accumulated often very rapidly and so are prone to liquidization or failure.

Fig. 4-2. Sand volcanoes (up to 0.1 m across) on top of turbidite sandstone, Hawick Rocks (Silurian), Wigtown, Scotland. Photograph courtesy of B.R. Rust.

Sand volcanoes amongst turbidites were recorded as early as the middle of the last century, but were mistaken for trace fossils (Brindley et al., 1973). There are two associations in this facies: (1) on the tops of single turbidite beds which may show little or no other evidence of dewatering, and (2) on the tops of thin to thick beds or complexes of beds involved in slumps or slides. Volcanoes belonging to the first association (Fig. 4-2) are less than 0.12 m across and commonly little more than pimples (Warren, 1963; Dzulynski and Walton, 1965; Rust, 1965; Burne, 1970; Brindley et al., 1973; Bruck and Reeves, 1976; Crimes, 1977). They usually occur scattered or in small clusters, one volcano occasionally overlapping an earlier one. Typically, the cone consists of silt, and has moderately steep sides and a small central crater. The crater overlies an infilled vent, which occasionally can be traced downwards into a chimney-like and sometimes branched feeding channel. The volcanoes capping some beds are asymmetrical all in the same direction. Such cones are comet-like in plan, the grains having been spread out in a broadening plume. As Burne has suggested, the parent jets were probably bent over by a current flowing over the top of the dewatering sediment. It may prove possible to use Rajaratnam’s (1976) equations for a jet in a cross-stream in the further interpretation of these asymmetrical cones. The volcanoes associated with disturbed beds (Gill, 1957, 1979; Gill and Kuenen, 1958; Burne, 1970; Lovell, 1974; M.H. Rider, 1974; Okada and

139

Whitaker, 1979) are generally more majestic, some ranging up to 3 m across, with a large central crater of diameter about one-third the width of the cone. Large and powerful jets of some persistence were evidently involved. Oldershaw ( 1960) and Walter ( 1972) recorded moderately large volcanoes from the tops of thick beds of Precambrian graywacke in Australia, but it is not certain if these beds had ever been caught up in slides or slumps. Walter noticed that the sand in the cones decreased in grain size radially outward, the only published record of grading of any kind in sand volcanoes. Sand volcanoes amongst deltaic sediments are best known from the Upper Carboniferous of Ireland (Nevill, 1957; Gill and Kuenen, 1958). Examples in possibly fluvial settings occur in the Old Red Sandstone of Norway (Reineck and Singh, 1973) and in the Ordovician proglacial deposits of the Sahara (P. Allen, 1975). Gill and Kuenen’s magnificent examples reach up to 4.5 m across and occur often in enormous profusion on the tops of slumped beds, commonly of great thickness and lateral extent (Fig. 4-3). The cones are well-laminated internally, as Nevill found in his examples (Fig. 4-4), and the craters overlie vents with complex infillings indicative of multiphase cone growth. Many of the larger cones lie near to fracture surfaces within or bordering the slumps. Most of the cones were built subaqueously, though

Fig. 4-3. Sand volcanoes on the top of a large slump, Namurian sandstones and shales, County Clare, Ireland. Compass-clinometernear bottom of picture measures approximately 0.06 by 0.09 m. The volcano on the left consists mainly of silt and is relatively tall, the crater being ill-defined. The volcano on the right, with a small parasitic cone, is relatively flat and of fine sand, with a well-defined crater. Photograph courtesy of M.W. Hardman.

140

Fig. 4-4. Slightly simplified axial sections through sand volcanoes from the tops of slumps, Namurian sandstones and shales, Slieveardagh Coalfield, Tipperary, Ireland. The volcano in (a) grew episodically while maintaining a relatively constant discharge. Growth was also episodic in (b) but from a gradually slackening flow. After Nevi11 (1957).

some with rilled flanks, and one steep-sided mound covered in bulbous sediment driblets, could have arisen partly subaerially. The jet model (Fig. 4-1), of course, applies only to well-submerged volcanoes. P. Allen’s sand volcanoes are even larger, ranging up to 15m in diameter, and surmount sand-filled drainage pipes. In some cases they are associated with what may be large diapiric structures. Several workers have discussed structures which are less clearly sand volcanoes in the present sense. Bailey and Weir (1932) reported a questionable example from amongst the Jurassic deep-water boulder beds of northeast Scotland. A structure resembling the diapiric cusps of Selley and Shearman ( 1962), Selley et al. (1963), and Selley (1969) is described by H.D. Johnson (1977b) from the top of a bed of liquidized cross-bedded shallow-marine sandstone. Although neither a crater nor vent is reported, the apex of the diaper is regarded as having been breached by sandy water, on account of the occurrence of “rill” marks on the flanks. These radial structures seem more like accommodation folds, however, such as may form on rising domes (see Ramberg, 1967, fig. 76), as they are bold and well-rounded. There is much evidence from modem environments and the laboratory to associate the origin of sand volcanoes with the movement of ground or formation water through unconsolidated sediment and, in particular, with sediment dewatering, either at the original site of deposition or after a slump or slide (G. Evans, 1965). Small sand volcanoes surmounting narrow ramifying chimneys carrying water upward have often been noticed at the sediment -water interface during the settlement of flocculated mud (Coe and Clevenger, 1916; Kindle, 1916; Twenhofel, 1921; Schofield and Keen, 1929; Dangeard et al., 1964; Dangeard and Giresse, 1965; Kuenen, 1968; Migniot, 1968; Karcz et al., 1974). Neumann-Mahlkau (1976) reported how a large

141

body of rapidly accumulated sediment dewatered to yield volcanoes. Several workers noticed eruptions on the tops of small experimental slumps after these came to rest (Rettger, 1935; Gill and Kuenen, 1958; Van der Knaap and Eijpe, 1968). Sand-laden water boiled out of the surface of the Turnagain Heights Slide, caused by the Alaskan earthquake of 1964 (W.R. Hansen, 1965). Sand volcanoes and structures allied to them, for example, spring pits-with-mounds, can be formed when externally derived water flows up through silt or sand (Quirke, 1930; G. Thomas, 1958; Williamson, 1960; Bondesen, 1966). SEDIMENTATION FROM SEPARATED FLOWS WITH NORMAL GRAVITY

General

Sedimentation to leeward of ripples, dunes, bars, and Gilbert-type deltas can be analysed using as a model the sediment-transporting, horizontal, turbulent half-jet with two-dimensional flow (Fig. 4-5). This concept was introduced implicitly by Jopling in 1962 and subsequently elaborated by him (Jopling, 1963, 1964a), partly as a device for prediction and palaeohydraulic interpretation (Jopling, 1965b, 1966a, 1966b, 1966c, 1967). Allen (1965f, 1968e, 1968f, 1968g) independently suggested a similar model. Prior to these investigators, Reineck ( 1961) had developed a substantial insight into some of the mechanisms controlling sedimentation in the lee of bed features associated with separated flows. The flow above the free shear-layer originating at the crest of the sediment body (Fig. 4-5b) corresponds in the half-jet to the irrotational core (Fig. 4-5a), the curved reattaching free shear-layer to the linearly expanding shear layer of the half-jet, and the separation bubble with backflow to the semi-infinite medium from which the half-jet entrains fluid. Grains denser ,Suspended

load

irrototlonol

Fig. 4-5. Half-jet model of sedimentation to the lee of ripples and dunes. a. General features of a half-jet. b. Flow velocity, grain concentration, mean streamlines and a representative grain path to lee of a ripple or dune.

142

than the fluid must now behave in a more complicated way than in a verticai jet, since gravity acts normal to the general motion. Add to this the presence of a boundary-layer flow upstream from the sediment-body crest, and it is clear that the grains where they enter the half-jet must be heavily concentrated near the bed, in a zone where the fluid velocity-gradient is steep. Therefore in order to predict the sedimentation to leeward, we must know not only (1) the distribution of temporal mean velocity and turbulence overall, but also, at the crest of the bed feature, (2) the concentration of grains of each falling velocity, C,( y ) , and (3) the tangential grain transport velocity, VWx(y ). We cannot otherwise associate particle fluxes with particle trajectories in the separated and reattached regions, nor calculate rates and textural trends to lee. Grain size and concentration in the approaching boundary layer

One approach to the specification of the two-phase flow at the crest of a subaqueous bed feature is to ascribe to it (somewhat arbitrarily) a two-layer character based on mode of sediment transport (Jopling, 1963; Allen, 1968g). The flow is divided between a lower layer containing the densely arrayed bedload grains, and an upper one bearing the suspended particles. Mineral-density particles are assumed. In the upper layer (Fig. 4-5b), C , ( y ) may either be measured or calculated using eq. (2.36, Vol. I) (Brush, 1965a; Jopling, 1965b, 1966a, 1967). Jopling obtained V,,(y) by assuming that grains and fluid had the same velocities, distributed logarithmically. Note that in this layer the transported grains are strongly differentiated as to falling velocity (Fig. 4-5b), in accordance with eq. (2.36, Vol. I). The character of the lower layer is more difficult to assess. Jopling (1963, 1964b, 1965b, 1966a) evaded the problem by characterizing this stratum as a “heavy fluid layer”, the grains in which were supposed merely to slurry over the crest of the bed feature and settle collectively. My observations (Allen, 1965f, 19688) indicate instead that the grains originating in the bedload layer behave in substantially the same way as those provided from higher up. Moreover, under the conditions giving the bedforms under discussion, the suspended load is not necessarily dominant. In the absence of measurements, it is reasonable to suppose with Bagnold (1954a, 1956) that the total local grain concentration in the bedload layer declines with increasing distance upwards from the static bed, perhaps exponentially (Fleming and Hunt, 1976). The vertical distribution of particle falling velocities, however, may strongly depend on the conditions of grain shearing. Under viscous conditions ( B a < 40), the different grain sizes present should take concentration profiles of a similar form (Fig. 4-5b), since nominally there are no forces to promote grading. The overall mean grain transport velocity should be in the order of one-sixth of the mean fluid velocity (Bagnold, 1966). However,

143

under inertial conditions ( B a > 450), the larger grains should drift under the action of the dispersive pressure towards the outer boundary of the layer, where the strain is a minimum. Hence these grains will have a maximum concentration at some distance from the bed, where the grain transport velocity is also likely to be a maximum (Fig. 4-5b). The overall mean grain transport velocity under inertial conditions is likely to be only about one-ninth of the mean flow velocity (Bagnold, 1966). We are on slightly stronger-ground in describing the two-phase flow over an aeolian dune, the adoption of a two-layer structure being unnecessary. The wind velocity, approximately equalled by the grain transport velocity, is well-described by the logarithmic profile, and a similar function is appropriate to the vertical variation of grain flux (Horikawa and Shen, 1960; Kawamura, 1964; Sharp, 1964; Chiu, 1967). The distribution of grain size within the curtain of wind-driven particles is less simple and has not yet been fully described. Both Sharp (1964) and Chiu ( 1967) found one grain-size maximum near the bed (creep load) and another at a substantial distance upwards. Grain dispersal beyond the crest of the bed feature

Jopling ( 1963, 1965b, 1966a, 1967) approached this problem for subaqueous bed features by means of his largely theoretical “path-line” method (see also Nevin and Trainer, 1927), which he applied in reverse (Jopling, 1966b) for palaeohydraulic interpretations. Given C,( y ) and V,.J y ) , and the overall distribution of temporal mean velocity, the method consists in calculating the trajectories followed by grains as they are spread beyond the crest of the bed feature. The calculations are restricted to suspended grains from the upper layer, and it is assumed that each trajectory is the vector resultant of the particle still-water falling velocity at infinite dilution and the component in the x-direction of the temporal mean flow velocity. Jopling concluded that the streamwise distance or path-length travelled by grains between the crest of the feature and the bed further downstream (1) grew larger with increasing grain transport velocity, (2) increased with the height above the crest at which the trajectory was commenced, and (3) shortened with increasing grain falling velocity (grain size). In particular, he proposed first a semi-logarithmic (Jopling, 1965b) and later a logarithmic (Jopling, 1967) relationship between path-length and starting height. Jopling further concluded that both the grain size and deposition rate of the settled material spread from the upper layer declined downstream. By combining calculated trajectories with known grain fluxes, Jopling (1965b, 1966a, 1967) estimated and compared with measured values the grain size and deposition rate of sand accumulated on bottomsets. But his experimental sediments proved coarser than the calculated ones, the discrepancies being significant because of the very gradual decline of grain size with distance downstream.

144

Although Jopling obtained a qualitatively correct description of grainsettling to lee of a subaqueous bed feature, his account is severely limited because he arbitrarily ignored the bedload layer and discounted the effect of turbulence on (1) the falling velocity of the grains, and (2) their dispersal, particularly within the free shear-layer. In aqueous environments, as we have seen, turbulence may substantially reduce falling velocities and must be expected to play a dispersive role comparable with that of the mean flow itself. Similar criticisms apply to the model of delta sedimentation proposed by Bonham-Carter and Sutherland (1967, 1968). Jopling's neglect of turbulence can perhaps be justified only for aeolian bed features. In analysing the growth of transverse desert dunes, Bagnold (1954b) had earlier advanced the idea of a lag distance between a change in the wind flow at a dune crest and the response by deposition of the transported grains, to which Jopling's path-length is closely related. Bagnold saw the lag distance as a characteristic length measured between crest and point of maximum deposition rate. The corresponding Jopling path-length would seem to be the modal value in the case of a uniform sand. Allen (1965f, 1968e, 1968f, 19688) adopted an empirical approach to the problem of grain-settling to leeward of subaqueous bed features, recognizing that turbulence could not be neglected even if quantification was not yet possible. Two kinds of experiment were made. Diffusion in the highly turbulent free shear-layer was explored by releasing small quantities of narrowly-graded particles into the flow at a point above the crest of a sloping step; the grains were trapped where they subsequently landed, with the aid of a smear of grease. In the second type of experiment, sand was discharged over a bed feature whose leeward slope was replaced by a

(bl

(dl

(cl

v (a1

Grains injected

0 ///////////n,One square csntimetre

(eI

0

.

N/nr,a, 0 . 5 0 - 1.00 0.25 0.50 0.125-0.50 0.063-0.125 0.0315 0.063

-

-

'I

Fig. 4-6. Experimental dispersal of grains from a point source into the separated flow to lee of a transverse negative step with sloping riser. a. Definition diagram and schematic laboratory set-up. (b)y=0.0081 m, L$/ W=2.57. (c)y=0.0081 m, U v / W=5.81. (d)y=0.0081 m, U v / W = 14.4. (e) y=O.O081 m, Uv/W=4.55. (f) y=0.0137 m, W=4.45. (g) y=0.0165 m, W =4.42. After Allen (1 9688).

uv/

q,/

I45

collector of the same shape divided transversely into a large number of narrow compartments, thus enabling grains which shared the same horizontal path-length to be collected. Deposition rates for the sediment in bulk and for the constituent grades could thence be derived. The striking ability of the free shear-layer to disperse grains originating at a point source is amply proved (Fig. 4-6). In these experiments the number of grains, N , captured on a square of side 0.01 m in the lee of the step is compared with the maximum number, Nma, trapped during the same run. The parameters are the height, y , of the point source above the crest and the ratio U , /W , where U, is the temporal mean flow velocity at the source (assumed equal to the grain transport velocity) and W is the grain still-water falling velocity. As Jopling ( 1965a, 1965b, 1966a, 1967) found, an increase of flow velocity increases the path-length, as does an increase of starting height. However, the path-length is clearly a statistical quantity, properly described only in terms of central tendency and spread. The extent of diffusion of the

Transport rate '8 50.0325kg m-1s-1

=- 2.225

Transport rate =0,0278kg m - k ' na=-0.916

\

-

1

8\

'm

k. I

Bed-stack phi mean size 0.19 A 0.95 A\

10-2

10-1

100

2.38

10-2

?,1

10-1

100

Distance downstream from crest, x (m)

Fig. 4-7. Experimental dispersal of three quartz-sand bed-stocks (Size in phi is -log, of particle diameter in millimetres) downstream from a body shaped like a current ripple or dune. After Allen (1968f, 1968g).

4

1.00 to 1.50 #

0.00

-0.50 to

10-2

10-1

I00

10-2

10-1

I00

10-2

10-2

10-2

10-2

10-2

10-1

I00

Distance downstream from crest. x (m)

Fig. 4-8. Experimental dispersal of quartz sands (half-phi grades) downstream from a body shaped like a current ripple or dune. Bed-stock phi mean diameter=0.95, dry-mass sediment transport ratez0.0325 kg m-' s - ' (see middle graph in Fig. 4-7 for behaviour of bed-stock as a whole). After Allen (1968f, 19688).

147

grains in these experiments is clearly substantial, particularly at large values of U , / W and y , and the concept of a unique path length is questionable. The spread as well as the central tendency of the experimental grain dispersions is systematically related to flow conditions (Allen, 19688). In the second set of experiments, bed-stocks were chosen so as to afford a wide variety of modes of transport behaviour (ratio of suspended load to bedload) and grain-shearing characteristics. The most reliable results come from three quartz sands measuring respectively 0.19, 0.95 and 2.38 phi in mean size. The bedload layers afforded by these sands became wedge-shaped as they entered the free shear-layer, partly due to loss of grains from beneath and partly due to the incorporation of particles into rapidly growing vortices, able to carry off many grains to places far downstream. Figure 4-7 shows for comparable total-load transport rates how the local deposition rate of these three sands in the lee of the bed feature declines with downstream distance. The similar variation in the deposition rate for each 0.5 phi grade is illustrated in Fig. 4-8 from an experiment with the 0.95 phi bed-stock. For both the bulked sands and grades, the local deposition rate, R , in dry weight is well described (except close to the origin) by a relationship of the form: R = mx”

(4.3)

or, alternatively:

in which x is distance measured downstream from the crest of the bed feature, and Rref and xrelare reference values (Allen, 1968e, 19680. The other terms, m and n < 0, are respectively a dimensional coefficient and an exponent. For the coarser bed-stocks, the deposition rate declines less steeply over the bottomset than over the slipface (Fig. 4-7), apparently because the finer grains, probably almost wholly from the suspended load, behaved differently from the coarser particles presumed to come from the lower layer (Fig. 4-8). Two sets of values for m and n are then required, the subscript “s” indicating the slipface and “b” the bottomset. The subscript + denotes values applying to a 0.5 phi grade. Figure 4-8 illustrates an important effect restricted to the coarser bedstocks. The deposition rate of the coarsest one or two 0.5 phi grades is a maximum in either the second or third collecting compartment downstream, and not in the first immediately adjacent to the crest as with the finer grades. Clearly, the largest grains had advantages of starting height and transport velocity over finer particles, and thus conform to the bedload model shown in Fig. 4-5. The 2.38 phi bed-stock behaved substantially viscously and did not show the effect. Both rn and n vary with bed-stock and flow conditions (Allen, 1968e, 19688). The coefficient decreases steeply with increasing total load transport

148 10

,

8 6 4 -

2 -

\

-

'L

.' *

i -

B 0.8 a

06-

Bed-stock mean phi size ( n , )

-

W

0

049

A 0.95

0.4 -

0

2.38

\A

\

Half-phi grades (nd I A

0.2 -

0.1

'1

0.95 phi bed-stock 2.38 phi bed-stock

I I

I

2

4

6

810

20

Velocity ratios. U , / W , ,

40

,

,

,

60

,

,

80 100

U,/W

Fig. 4-9. Experimental values for the exponent in eq. (4.3) as a function of velocity ratio, for the bed-stocks yielding Fig. 4-7, and for the half-phi grades of the intermediate and finest grained of the bed-stocks. After Allen (1968f, 19688).

rate, its product with the rate retaining a constant order of magnitude. The exponent n for sand in bulk is systematically related to flow and bed conditions as described by the ratio Um/Wm, where Urn and W, are the mean flow velocity above the crest of the bed feature and the arithmetic mean falling velocity of the bed-stock respectively (Fig. 4-9). A similar correlation with Urn/W is found for the separate grades. The description of particle dispersal embodied in eq. (4.3) differs less from Jopling's than might appear, since the formula effectively describes the path-length frequency in terms of weight. It can be changed into a true probability density using standard methods (Miller and Kahn, 1962), provided that we define the path-length domain; an appropriate interval is from x = D/2, where D is the average grain-size of the bed-stock, to x = L , where L is the length of the separation bubble. An average or median path-length may then be calculated. These measures of central tendency grow larger with increasing Um/Wm, but depend on the mode of transport of the bed-stock (Allen, 19688).

Avalanching in the lee of ripples, dunes, bars and deltas The steady transport of sediment over the back of a ripple, dune, bar, or Gilbert-type delta should create a steady downward rain of particles to

I49

leeward. But as eq. (4.3) states that the deposition rate declines downstream, the effect of grain settlement is progressively to steepen the leeward slope, as it were by rotating it upwards about some point between crest and reattachment. Steepening cannot proceed indefinitely, however, since there is a limiting slope, the angle of initial yield, +;, above which a surface underlain by the grains is unstable in the gravity field. A grain avalanche may consequently descend the slope from the place where this angle is first exceeded, leaving some or all of the leeward surface inclined at the lowervalued residual angle after shearing, denoted by Gr. That part of the leeward slope characterized by +r is the slip face, at the bottom of which avalanches come to rest (Fig. 4-5b). The process of differential settlement followed by the relief of instability should persist for so long as the rain of grains from above continues. Avalanching lowers the slope, whereas the downward rain steepens it, these tendencies opposing each other. But as avalanches have a limited capacity to remove debris, travelling at a finite velocity, there should be a critical total-load transport rate at the crest of the bed feature above which avalanching becomes continuous. Hence the slip face may build forward either in discontinuous jerks, as one discrete avalanche after another descends, or in a continuous manner, as the result of the sustained and general downward flow of grains. This building process (Allen, 1970a) may be analysed on the following general lines. Consider a bed feature with a slip face inclined at time t = 0 at a uniform angle &, measured downward from the horizontal, and subject to a steady rain of grains giving a distribution of R ( x ) and (dR/dx)(x) with greatest magnitudes in an area at or very near the crest. Let it be assumed that the grains underlying this slope are everywhere at rest. After the elapse of a time t, the surface in this area has attained because of differential settlement the larger inclination +i. It is readily shown that: tan+; = t a n + - L j t g - d t r

Y

(4.5)

in which y is the dry-weight sediment bulk-density. If +r, +i and R ( x ) are known, eq. (4.5) is immediately soluble for t. Referring to eq. (4.3) and the controls on rn and n, we should expect t to decline rapidly with increasing total-load transport rate. But t as given by eq. (4.5) cannot itself be the observed period of avalanching, for no avalanche travels infinitely fast. Its time of descent on a slip face of height H in the absence of a rain of grains is t , = H/sin +J', where V is the mean velocity of the avalanche measured parallel with the slope, expected to depend on both sediment and fluid properties, as well as on the mass of grains involved (Bagnold, 1954a). The observed period of avalanching is therefore: p=t+t,

(4.6)

150

for t > t,. When t = t,, however, the slope-steepening tendency of grain settlement is exactly balanced by the slope-lowering effect of avalanching, which must now be continuous, there being grains in downward motion at every moment. Continuous avalanching is therefore defined by t < t , and its threshold by p,, = 2t,. These general phenomena have been described many times, notably from desert dunes and from subaqueous bed features produced in the laboratory. Reporting on grain transport over Libyan barkhans, Beadnell (1910) described how “the bulk of this sand falls on the upper part of the leeward slope, equilibrium being adjusted from time to time by a downward sliding of the superficial layers”. Later work on aeolian dunes has substantiated and amplified this result (A.D. Lewis, 1936; McKee, 1945, 1957a; Bagnold, 1954b; Cooper, 1958; Logan, 1960; Gripp, 1961, 1968; Gripp and Martens, 1963; Inman et al., 1966; Sharp, 1966; Beheiry, 1967; Kaiser, 1971; McKee et al., 1971; Hunter, 1977). Dry sand grains behave individually and an avalanche takes the form of a narrow sand-flow. These originate at points generally close to the crest of a dune and each descends the slip face over a usually narrow front. Each flow deposits a long narrow tongue of sand with a gently convex-up top and a concave-up surface of shearing beneath, left exposed higher up the slip face. Low transverse ridges (?kinematic waves)

Fig. 4-10. Sand-flow (avalanche) tongues on the slip face of an active aeolian dune, Kelso Dunes, Mojave Desert, California, U S A . Photograph courtesy of R.P. Sharp, reproduced by permission of the Geological Society of America (see Sharp, 1966).

151

Fig. 4-1 1. Sand-flow (avalanche) tongues to lee of a dune-like sand body formed in a water channel. Scale marked in centimetres and flow from left to right. Note counter-currentripples on bed downstream of slip face but upstream of reattachment zone (hollows near to right-hand edge of photograph).

often mark the upper surfaces of sand-flows and their deposits (Lewis, 1936; Sharp, 1966; Kaiser, 1971). Many such tongues, the younger overlapping the somewhat faded older ones, mark the slip face of an active dune (Fig. 4-10). Grains which are partly damp or salt-encrusted behave coherently, however, yielding avalanches which include raft-like slabs and submerged masses of bonded particles (Cornish, 1897; Humphries, 1966; McKee et al., 1971; Hunter, 1977). Grain settlement in the lee of experimental subaqueous bodies likewise causes oversteepening relieved periodically by avalanching (A.L. Smith, 1909; Nevin and Trainer, 1927; Luders, 1929; Johansson, 1963, 1976; Jopling, 1964a, 1966a; Allen, 1965f, 19688). The avalanches (Fig. 4- 1 1) resemble aeolian sand-flows but are locally relatively broader (Allen, 1965f; Melieres et al., 1970; Hunter, 1976). The period of avalanching on experimental subaqueous sand bodies decreases with growing sediment transport rate until, at a critical value of the rate, the sediment flow.down the slip face becomes continuous and general (McKee, 1957a; Johannson, 1963; Allen, 19650. The behaviour of a sand body 0.15 m in height formed of fine-medium grained quartz sand illustrates this well (Fig. 4-12). A decrease in the period of avalanching until the

152 1.0

’

I

0.6 -

I ’

r

7

1

0.8

08 0

OE

0.4-

04

-‘u

5 I

E

,.z

c” 0.2-

P

9

02

i

c

0

e

2

c

f

a

-

.c

0 04

Ek e

CONTINUOUS AVALANCHING

0

j- 0 0 8 a

f

01

008

c

s

-

0.06

006

Q

u)

-

0.04

00 4 Threshold of motlon

0.02-

0 02 I I

0 01

0

0

01

02

03

04

I

05

I 1 ,

06

07

08

Mean flow velocity, U ( m

09

1.0

II

12

1.3

s-1)

Fig. 4- 12. Frequency of avalanches observed to lee of an experimental dune-like sand body, as a function of mean flow velocity (i.e. sediment transport rate). Bed-stock mean size= 1.10 phi. Data of Allen ( I 9650.

attainment of continuous flow is also evident when granular materials are rotated in a drum with a horizontal axis (Allen, 1970a), t being inversely proportional to the angular velocity of the drum for given Gr and I$~.This system has the attraction that t , is nominally a constant for each kind and quantity of material, allowing eq. (4.6) to be examined for many values of t. A plot of ( p - t ) against t is then a straight line of zero slope intercepting the ordinate at t,. Representative data (Fig. 4-13) from amongst Allen’s ( 1970a) results confirm this, avalanches flowing continuously when t becomes comparable with ( p - t). With some materials, however, ( p - t ) is a weakly increasing function of t, perhaps reflecting the increasingly dynamic character of the environment as the drum speed is raised and the grainpacking changed slightly. Grading in avalanche deposits

When sand grains of mixed sizes are poured into a conical heap, the larger particles generally accumulate preferentially around the skirts of the cone, while the finer remain near the apex. This experiment illustrates a phenomenon to be observed when many systems of cohesionless particles of mixed

153 10

5

0

5

2

0 (C)

+Continuous for

* * 0

avalanching

.

.

t r0.75 s

** * *

*.

2

4 Value of

6

810

20

40

60

80 100

t imposed in drum expsrlment (s)

Fig. 4-13. Avalanche period in drum experiments (data of Allen, 1970a). (a) 0.003 m glass beads in 50%aqueous glycerol. (b) 0.003 m glass beads in air. (c) 0.00037 m quartz sand in air. (d) 0.00104 m quartz sand in water. (e) 0.00027 m quartz sand in air.

sizes experience strain. The separation of the component grades is variously called grading (sedimentology), flow differentiation (igneous petrology), and segregation (many technological fields). An early account of grading was given by H. Richardson (1903). That particulate materials became graded when strained was first appreciated by investigators concerned with the handling or storing of solid fuels, crushed ores, fertilizers, and crystalline drugs. R.L. Brown (1939) gave an important early review of the problems raised by grading during the handling of coal; a later and more general review is due to J.C. Williams (1976). Grading similar to that in the experiment described above is known to occur during the filling and emptying of bins, hoppers and bunkers, and tableting dies (Sherman and Kaiser, 1937; D.R. Mitchell, 1938; R.L. Brown, 1939; Stock, 1944; Spain, 1955; Fowler, 1960, 1961; J.C. Williams, 1963, 1968; Van Denberg and Bauer, 1964; Matthee, 1967; Ahmad and Pilpel, 1969, 1970; Lawrence and Beddow, 1969). A particle mixture will segregate in a rotating drum, the larger grains moving to the periphery (Donald and Roseman, 1962). Williams and Shields (1967), Ridgway and Rupp (1971), and Sallenger (1979a), finds that the larger grains migrate upwards to the

154

free surface when a mixture avalanches down a sloping channel. A similar grading arises during the simple shearing of a mixture in a shear-cell, even though the grains involved may differ in diameter by no more than a few percent (Scott and Bridgewater, 1975). Grading by diffusion occurs when sufficiently small particles settle through a static heap of large grains (Bridgewater et al., 1969; Bridgewater and Ingram, 1971; Bridgewater and Scott, 1974; Masliyah and Bridgewater, 1974; Cooke et al., 1978). Large particles regardless of their relative density will travel upwards to the free surface of a mixture if the mass is strongly vibrated (H. Richardson, 1903; J.C. Williams, 1963; Ahmad and Smalley, 1973). See also Bridgewater ( 1980). A differentiation of the mixture commonly occurs when magma abounding in phenocrysts is intruded as a sill or dyke. In differentiated dykes and sills, the phenocryst concentration is invariably a maximum at or near the centre of the body (e.g. Bhattacharji and Smith, 1964; Bhattacharji, 1967; Heimlich and Manzer, 1973), and it is not uncommon for a size grading also to be present, the larger crystals clustering near the centre (Drever and Johnston, 1958; Baragar, 1960; Simkin, 1967; Gibb, 1968). A similar size grading has occasionally been noticed from clastic dykes (Diller, 1889; Peterson, 1968; Eisbacher, 1970). The graded character of the deposits left by avalanches on the slip faces of ripples, dunes, bars, and Gilbert-type deltas is well-attested in the field and the laboratory. Two classes of grading may be recognized, taking the surface of the slip face, or the boundaries of a cross-stratum, as a reference. Tangential grading is a systematic textural change in the streamwise direction along the length of a cross-stratum or over the surface of a slip face. It is called rezlerse when grain size increases in the streamwise sense, but normal where the grain size declines in this direction. The second class is named perpendicular grading. This is reverse if the coarser grains are concentrated along the outer surface of the cross-stratum, but is normal where they cluster near the lower boundary. Reverse tangential grading seems typical of slip-face deposits formed in air (Fig. 4-14). Bagnold (1954b) has described in his book first published in 1941 how he demonstrated this experimentally using sand split into grades, each being dyed a different colour. The coarser grains of a mixture were seen to migrate to the snout and top of a sand-flow and, outpacing the finer particles which had moved to lower levels, to stop further down the slip face (see also McKee, 1945). Hunter (1977) found the grading in modern aeolian dunes of small size. Reverse tangential grading is typical of water-laid cross-strata formed of gravelly and relatively coarse sands (Allen and Narayan, 1964; Johansson, 1965, 1975; Basumallick, 1966; Boersma, 1967; Gellatly, 1970; N.D. Smith, 1970), and it has often been produced under laboratory conditions (Luders, 1929; Johansson, 1963, 1976; Jopling, 1964a; Allen, 1965f, 19688; Brush, 1965a). Normal grading, however, results using

155

Fig. 4-14. Segregation in a mixture of small (white) and large (dark-coloured) beads poured through a fixed funnel into a narrow vertical container with transparent walls. Photograph courtesy of J.C. Williams.

bed-stocks of fine-grained sand (Allen, 1968g), and should characterize cross-stratified sands of a similar texture in the field. Allen and Narayan (1964) found a lack of tangential grading in some shallow-marine crossbedded sandstones. Whether there is a predominant mode of perpendicular grading is not clear. Clear-cut normal grading is figured by J.C. Williams (1968), who poured a mixture of large and small grains in air (Fig. 4-14). In a small aeolian dune, however, Hunter ( 1977) found reverse grading in avalanche deposits near the dune crest but normal followed by reverse grading close to the toe. In water-laid sands, Allen and Narayan (1964), Basumallick (1966), and Johansson ( 1976) identified reverse grading, whereas Boersma (1967) in addition detected normal grading. McCabe (1977) found both normal and reverse grading in large water-laid cross-strata. Brush ( 1965a) followed by Reineck and Singh (1973) propose that only reverse grading is possible. Judging from laboratory experiments, the controls on grading are: (1) the nature of the fluid medium, (2) the character of the transported sediment, (3) the sediment transport rate, and (4) the scale of the sand body. The first three factors combine to determine the streamwise deposition-rate and grain-size gradients that will characterize the grains settling to lee of the bed feature, together with the size, frequency and behaviour of the slip-face avalanches. The fourth factor also influences avalanche behaviour and, together with avalanche size, controls the thickness of each cross-stratum. The settling grains tend to impose a final grading that is reverse, due to the fact that the coarser ones first accumulated preferentially near to the

156

crest. In experiments (Allen, 1965f, 1968g), the use of coarse bed-stocks leads to reverse grading, the strength of which declines with increasing total-load transport rate. This is partly explained by the reduction with increasing transport rate of the grain-size gradient within the settling particles. A bed-stock of fine-grained sand, however, gives normal tangential grading, under conditions of continuous avalanching, and the grain-size gradient in the resulting cross-strata is only a little less steep than within the settling cloud. The avalanching could have been unable to invert the textural gradient because of the sustained high rates of deposition. In contrast, Jopling (1965b) attributes normal grading to the retardation of avalanches by the backflow. Bagnold (1954a) suggests that grading (or lack of it) in slip-face deposits may depend on the mechanics of sand-flows. According to eq. (1.28, Vol. I), the collision-related forces under conditions of viscous granular shearing (Ba < 40) are independent of grain size and, therefore, cannot induce either tangential or perpendicular grading within flows attributable to this regime. The steady mean speed of a flow of uniform thickness h , however, should be : V = 0.000483( gh 2/v)

(4.7)

in which 17 is the dynamic viscosity of the fluid medium. Inertial effects dominate a sand flow once Ba>450, when the shear stress and dispersive pressure should vary as D 2 for a given strain (Vol. I, eq. 1.29). The steady mean speed of a uniform flow is then expected to be: V = O.O044(g s i n ~ # + ) ” ~ ( h ~ / ~ / D )

(4.8)

in which g is the acceleration due to gravity. Bagnold argues that the larger grains of a mixture will then migrate under the influence of the dispersivepressure gradient towards the free surface of the flow, where the strain is least. The smaller grains will correspondingly move towards the surface of shear, where the strain approaches a maximum. Komar (1972a, 1972b, 1976b) has extended Bagnold’s ideas to the distribution of phenocrysts in sills and dykes, obtaining results consistent with experience. Bagnold’s ( 1954a) suggestions are only partly consistent with the observed grading of cross-stratified deposits, and receive but limited support from experiments on avalanching. Both Bagnold (1954a) and Allen (19688) confirmed the form of eq. (4.8) for inertial sand-flows, but Allen obtained velocities proportional only to the seven-tenths power of thickness from the viscous regime (Fig. 4-15). Ridgway et al. (1968), and Ridgway and Rupp (1970, 1971) also experimented on sand-avalanching, but used a smooth chute. Internal shearing was said to be lacking under these conditions (see also Augenstein and Hogg, 1978). Dilatation nonetheless occurred and there was much grain-mixing during flow, even when marked particles of a single size were used. When a mixture of sizes avalanched in the chute, the larger

157

I

I

0.4 -

-

0.2

I

/*

-

I

E

. 0.1

b

-

0

g

0.08-

D

c.” -

0.06-

0

004-

0.02

-

/

/

8

A

0.01 0.0004

0.001

0002

0004 0006

Water, D = 0.00019 m Water D = 0.00045 m

0.01

Avalanche thickness, h

002

0.04

(m)

Fig. 4-15. Experimental determination of avalanche speed on rough slopes as a function of avalanche thickness and fluid medium.

grains invariably moved up rapidly towards the free surface of the flow. Hence internal shearing may not be necessary to effect grading, though there remains the possibility that the development of grading is enhanced, at least under inertial conditions, by Bagnold’s dispersive-pressure mechanism. Middleton (1970) rejected Bagnold’s (1954a) explanation of grading, mainly because a concept having only statistical validity cannot be applied to the individual elements of a continuum. He proposed instead that grading (reverse perpendicular) arose because the smaller grains tended to filter down between the larger ones during flow, thus displacing the larger grains towards the free surface. What Middleton here invokes is the mechanism of percolation, which occurs spontaneously when sufficiently small particles are poured on to a static heap of large ones (Bridgewater et al., 1969; Bridgewater and Ingram, 1971; Bridgewater and Scott, 1974) and which, when size differences are less marked, is promoted by vibration (H. Richardson, 1903; R.L. Brown, 1939; J.C. Williams, 1963, 1968; Williams and Shields, 1967; Ahmad and Smalley, 1973; Harwood, 1977) or strain (Scott and Bridgewater, 1975), in what might be called “kinematic sieving”. Both strain and vibration act to dilate the grain mass, freeing particles from each other and widening the gaps between them, so that substantial relative movement becomes possible. An additional mechanism may .contribute to grading when strain is sustained, as during sand flow. Large grains at the free surface not only have a relatively high velocity, permitting them to outstrip smaller and slower

I58

particles beneath, but they also find themselves shearing past a grain-layer which, because it comprises smaller particles, appears to them comparatively smooth. If the lower layer were to stop, the coarse particles above would tend to travel onwards, since the surface of the lower layer was insufficiently rough to arrest them. H. Richardson (1903) long ago deduced that inverse tangential grading arose in a poured sand and gravel mixture “because the irregularities of the heap are rough relative to sand grains (which are therefore detained), but smooth compared to the larger stones (which therefore roll to the bottom).” As well as perhaps aiding reverse tangential grading in avalanche deposits, Richardson’s mechanism of overpassing (or like seeking like) may also contribute to the development of grading in mountain scree-deposits built up by rock-fall (Kirkby and Statham, 1975; Statham, 1976). SEDIMENTATION IN THE FAR LEE: SHELL-PEBBLE LAGS AND RIPPLE FANS

Some of the grains projected beyond the crest of a bed feature alight on the bottomset or even on the nearby parts of the bed still further downstream (Fig. 4-5b). In these regions, where the reattaching flow predominates, large and powerful vortices generated in and convected along the free shear-layer “explode” in succession against the bed (Allen, 1965f, 19688; A.J. Sutherland, 1967), they or their remnants being redistributed downstream or into the backflow. Provided that the fluid forces operating in the regions affected by reattachment are large enough, some or all of the grains which reach the bed after passage through the free shear-layer also undergo redistribution. But if all grains alighting on the bed are rearranged, the substrate across which the bed feature is spreading must itself be eroded in the vicinity of reattachment. Debris won from the substrate may then become mingled and redistributed with the grains that alighted on the bed. Hence bottomset deposits may comprise material from at least two possibly different sources. Unless ripples, dunes and bars are migrating under conditions of large net deposition rate, substantial erosion occurs in the regions of reattachment. Erosion at reattachment less often accompanies growth of Gilbert-type deltas. One frequent result of scour at reattachment is the accumulation of lag deposits formed of debris too coarse to be entrained or swept far. Such deposits, locally amounting to an almost complete armouring, commonly mark the backs of the larger current ripples (Guy et al., 1966) and dunes (Fig. 4-16) as sheets of granules or pebbles, frequently in marine environments accompanied by shell and other organic debris. These deposits are preserved as layers of clasts no more than one particle thick on the erosion surfaces beneath sets of cross-strata. The winnowing of fines at reattachment combined with lee-side avalanching are effective mechanisms for differentiating sediment texturally. Their action is reinforcing, because reattachment

159

Fig. 4-16. Ebb-oriented dunes (wavelength about 12 m) with stoss-side shell and pebble lags, Barmouth Estuary, Wales. Flow from upper left to lower right.

affects the lower slopes of a ripple or dune, to which same level earlier avalanching will have brought the coarser debris. A major role played by the larger reattaching flows is to build grains into distinctive patterns of current ripple marks related in orientation to the directions of limiting streamlines. Although the transport path of a given bedload particle depends on both the bed shear-stress vector and the transverse bed slope (Howard, 1977), it is reasonable so long as the slope is small to treat grains as following limiting streamlines and, therefore, to regard the ripple crests as streamline orthogonals. These ripple patterns, called ripple fans (Allen, 1968g), are best known as arrangements of current ripples in the troughs and on the stoss sides of water-laid dunes. Their occurrence is of course restricted to dunes formed of medium or finer grained sands, and probably is also limited to the smaller overall stream powers characteristic of the dune existence-field (Vol. I, Fig. 8.22). With larger overall powers, the local values probably demand plane-bed transport. However, rippling is also suppressed by the appearance of pebble lags. Ripple fans commonly mark transverse aeolian dunes and, to judge from the internal features; are frequently associated with Gilbert-type deltas. Fig. 4-17 shows schematically the main kinds of ripple fan (Allen, 1968g). Those associated with the longer-crested dunes can usually be divided transversely into a number of cells along imaginary streamwise lines, called seams, towards which the ripples have a component of facing. Seams usually

160

Dune crest and sllp-face

-.

Ripple Croat and slip-face

#

Inferred near-bed flow

Main current

Fig. 4-17. Idealized ripple fans developed in the separated flows to lee of subaqueous and aeolian dunes.

coincide with the crests of spurs, but are also found on areas that are flat on a scale larger than ripples. Figure 4- 18 is a foreshortened view of sinuous long-crested intertidal

Fig. 4-18. Ripple fans in the troughs of fairly regular sinuous-crested intertidal dunes (wavelength about 6 m),Barmouth Estuary, Wales.

161

Fig. 4-19. Ripple fans (conventions of Fig. 4-17) associated with dunes. a. Dune approximately 0.5 m high at depth of 790 m beneath current from lower left, sea floor west of Strait of Gibralter, Atlantic Ocean (after Melieres et al., 1970), b. Dune approximately 0.5m high at depth of 910 m beneath current from left, sea floor west of Strait of Gibralter (after Melieres et al., 1970). c. Dune a few decimetres high beneath current from bottom to top in depth of 4531 m, Drake Passage (after Heezen and Hollister. 1971). d. Dune about 0.3 m high preserved on bedding surface in shallow-marine sandstones (Grks Armoricain, OrdovicianSilurian), Camaret, Pres’qu’ile de Crozon, France (after Bates and Kirkaldy, 1976).

dunes (Allen, 1968g), in the troughs and on the stoss sides of which appear ripple fans like those in Fig. 4-17a. M.E. Tucker (1973) also recorded ripple fans from mainly sinuous to catenary intertidal dunes, claiming that the fans arise late during tidal run-off. Barwis (1978) provides another record. Apparently long-crested dunes in the deep sea also possess ripple fans. Melieres et al. (1970) figured examples (Fig. 4-19a, b) from depths of 790 m and 910 m beneath the Mediterranean Undercurrent west of Gibraltar, and Heezen and Hollister (1971) illustrate a further instance from a depth of 4531 m (Fig. 4-19c) in Drake Passage. A magnificent fossil example (Fig. 4-19d) occurs in the shallow-marine Gres Armoricain of Brittany (Bates and Kirkaldy, 1976; D.E.B. Bates, pers. comm., 1976). Another appears in Fig. 4-20, and Puigdefabrigas ( 1974) shows more. Figs. 4-21 and 4-22 illustrate ripple fans typical of the spurs of catenary dunes (Fig. 4-17b) and the sharper inflections in the crests of long-crested dunes generally (Allen, 19688; Farrell, 1970). Belt (1968) and Collinson (1972) report from Upper Palaeozoic continental deposits ripple fans surmounting spur-like features comparable to those in Figs. 4-21 and 4-22. Lunate and other strongly three-dimensional dunes shaped in water (Figs.

162

Fig. 4-20. Part of the curved crest (C), slip face (SF), and ripple fan (F) associated with a strongly three-dimensional dune preserved on bedding surface in Upper Stromness Flagstones (Devonian), Bay of Skaill, Orkney, Scotland. The portion of the rim shown makes an acute angle of about 30' with the main current direction, from lower right to upper left. Wave action shortly after the dune was active has slightly modified the current ripples which make up the fan. Hammer toward left gives scale. Photograph courtesy of N.G.T. Fannin.

Fig. 4-21. Sharp-crested spur at saddle on sinuous-crested dune, Barmouth Estuary, Wales. Scale 0.5 m long parallel with main current from upper left to lower right.

163

Fig. 4-22. Spur and ripple fans associated with inflection in otherwise straight dune crest, Barmouth Estuary, Wales. Scale 0.5m long parallel with main current flowing toward observer.

Fig. 4-23. Ripple fan associated with strongly three-dimensional dune, Barmouth Estuary, Wales. Scale 0.5 m long nearly parallel with main current away from observer.

164

Fig. 4-24. Unsymmetrical ripple fan associated with the unsymmetrical lobe of a strongly three-dimensional dune, Barmouth Estuary, Wales. Scale 0.5 m long parallel with main current direction away from observer.

Fig. 4-25. Bold spurs and grooves to lee of a strongly oblique dune, as seen from downstream, Wells-next-the-Sea, Norfolk, England. Scale 0.5 m long.

165

Fig. 4-26. The same dune as in Fig. 4-25, but looking across the main current, from nght to left.

4-17c, 4-23, 4-24) usually carry well-developed ripple fans in the troughs (Reineck, 1963; Allen, 19688; Singh and Kumar, 1974). In plan the crests of the current ripples normally lie along concentric ovals, the slip faces dipping away in all directions from a centre. Gall (1971) and M.E. Tucker (1977) show fans similar to these from continental Triassic sandstones. Ripple fans related in character to those of strongly three-dimensional aqueous features are occasionally reported from aeolian dunes (Cornish, 1900, 1901, 1914, 1934; Capot-Rey, 1943; McKee, 1945, 1966b; Sharp, 1963; Hunter, 1977). Figure 4-17d is based on the small dunes with spurs that Cornish described. The orientation of the crests of the ballistic ripples is very variable, the ripples locally trending at right angles to the dip of the slip face. Aqueous dunes markedly oblique to flow usually carry rows of bold, regularly arranged spurs to lee (Cornish, 1901, 1914; Guy et al., 1966; Allen, 1968g; Knight and Dalrymple, 1975). Well-ordered ripple fans mark these spurs (Figs. 4-17e, 4-25, 4-26), but similar fans are occasionally found on oblique dunes lacking the features (Fig. 4-27). The structures often called ripple scours (Potter and Glass, 1958; Potter, 1963; Van der Linden, 1963; Pettijohn and Potter, 1964; Simon and Hopkins, 1966; Hobday and Horne, 1977) may in part be fossilized ripple fans developed on oblique dunes (Allen, 19688). They are associated with cross-bedding. McCabe (1977) discovered in association with Carboniferous cross-bedded sandstones fea-

166

Fig. 4-27. Ripple fans to lee of an oblique dune, but not associated with spurs and grooves, Wells-next-the-Sea, Norfolk, England. Scale 0.5 m long and current from upper left to lower right.

tures which he suggests are spurs, though in a sediment generally too coarse to yield ripple fans. Two lines of evidence show that ripple fans are a rather precise visualization of the patterns of limiting streamlines characteristic of the separated flows to lee of dunes, bars, and Gilbert-type deltas. Ripple fans arise experimentally because of flow separation to the lee of sand bodies resembling dunes or Gilbert-type deltas (Luders, 1929; Jopling, 1961, 1964b; Johansson, 1963, 1976; Allen, 1965f, 1968g). The ripples fashioned by backflow face the slip face of the bed feature; they are called either regressive (Jopling) or counter-current ripples (Allen). In that part of the fan shaped by the reattached flow, the ripples of course face in the direction of the general flow. Bottomset climbing-ripple cross-lamination and counter-current ripple forms all attributable to backflow are known in two-dimensional section from many cross-bedded sediments (Botvinkina et al., 1954; Allen and Narayan, 1964; Johansson, 1965, 1975; Boersma, 1967; Gradzinski, 1970; Duff and Walton, 1973; De Raaf and Boersma, 1971; Narayan, 1971; Jonker, 1972; T. Elliott, 1976b; Hunter, 1977; Martinez, 1977), including some attributable to Gilbert-type deltas and others to aqueous or aeolian dunes (Fig. 4-28). Commonly, the cross-laminated bottomsets extend for large streamwise distances beneath the slip-face deposits, indicating that the rippling beneath the backflow can be persistent in time

167

Fig. 4-28. Vertical flow-parallel section through cross-bedding sets with counter-current cross-lamination in the bottomset zone, excavation in alluvium of R. Rhine, Amerongen, The Netherlands. Scale 0.3 m long. Photograph courtesy of J.R. Boersma, and reproduced by permission of the Royal Geological and Mining Society of The Netherlands (see Boersma, 1967).

(cf. M.E. Tucker, 1973). There is even field evidence of a three-dimensional nature to support the proposed interpretation of ripple fans and bottomsets in terms of counter-current structures (Boersma et al., 1968; Aario, 1972). Perhaps the most telling proof comes from comparisons (Allen, 19688) between ripple fans on modem dunes (Figs. 4- 18, 4-2 1-4-27) and patterns of limiting streamlines generated experimentally during flow separation on downstream-facing steps shaped like the dunes (Fig. 3.15). For example, a step with a lobe-shaped riser gives limiting streamlines which radiate in all directions away from a symmetrically placed nodal reattachment point, precisely as is suggested by the ripple fan of a lunate dune. Again, a skewed step with spurs is found to generate a transverse series of streamwise vortices rotating in opposite directions in pairs, as may be inferred from the corresponding dune. In character a ripple fan is harmonious with the bedform with which it is associated, illustrating in a striking way the close inter-relationship existing between bedform and flow pattern (Allen, 1969b; I.G. Wilson, 1972~).A

168

map of limiting streamlines and their accompanying singularities is an excellent guide to the location of sites or net erosion or deposition, to where ridges and hollows exist, and to the shape and orientation of these features. The method is not limited to bedforms, but can be successfully applied at much larger scales (I.C. Wilson, 1971). GEOMETRY AND STRUCTURE OF LEE-SIDE DEPOSITS

What proportion of the height of a ripple, dune, bar, or Gilbert-type delta will consist of bottomsets, and what will be the shape and structure of the lee-side deposits as a whole? One obvious control on the nature of cross-strata as seen in streamwise vertical profiles is the ratio of the characteristic grain path-length to the height of the bed feature (Allen, 1968e, 19688). As this ratio increases, a growing proportion of the sediment load settles on the bottomset zone and a growing proportion of the cross-stratified set may be expected to consist of bottomsets. It will be recalled from the discussion of eq. (4.3) that the path-length is strongly dependent on the ratio Um/Wm. In the case of Gilbert-type deltas with constant flow and sediment, the same control is exerted by the ratio of flow depth at the front of the body to the depth at the crest (Jopling, 1965a). The path-length/height ratio, however, is both more general and flexible. Current ripples and aeolian dunes, for example, do not take properties related to flow depth. We should here emphasize that bottomsets originate wholly from the settling grains only when the sediment body is spreading over an inerodible substrate. This is true of small laboratory deltas built over the rigid floor of a flume, and would also correctly describe Gilbert-type deltas that spread across a cohesive floor. It is not true of current ripples and dunes, which march across a floor formed of deposits similar to themselves. Because of backflow-erosion in the zone from reattachment to the lowest point in the trough, the bottomsets of ripples and dunes may be formed partly or even wholly of grains which, instead of having passed over the crest, were scoured up from the back of the bedform in front. The second control on cross-strata in profile relates to backflow processes. We first note that the limiting streamline extending with the backflow from reattachment to the foot of the slip face is a bedload transport path for any grains that may be supplied from the settling cloud or by erosion of the substrate beneath. But this path, beginning where the separation streamline divides on the bed, is of limited length and so the backflow in places may carry less than the theoretically allowable sediment load. If the origin of distance along this path is put at reattachment, and the direction of backflow is taken as positive, we must distinguish between two sediment-transport functions, J , ( x ) and J,(x). Here Jt is the theoretical transport rate in the

169 b

(a)

(b)

f

B

-

Vague stratifkatlon

f

x;,-

5 2

e "C

0 2 'ti-

i t

"

E

Sand-flow (stippled) with groin-fail stratification

L

0

Sand-flaw stratification Flow deoth at bedfarm crest Bedform height

Fig. 4-29. Controls on the geometry of cross-bedding. a. Controls on the shape and structure (in the plane of flow) of subaqueously formed cross-bedding. b. Smaller scale features of cross-bedding in relation to increasing relative grain path-length, the two lower figures applying particularly to the aeolian case.

backflow, but J, is the actual rate allowed by the availability of sediment. It is only downstream in the backflow from the station where J, = J, that bottomsets can accumulate, and the position of this station is independent of the sign of d J,/dx. Hence the feather edge of the bottomsets may be located anywhere beneath the backflow, or even downstream fom the backflow zone. Now J, at any x is the integral from x = 0 to x of the sum of R(x),the function describing the settling grains, and the function representing the eroding capability of the backflow. As both R and J, increase with the characteristic path-length for a given flow geometry, the one neutralizing the effect of the other, the factor which controls the location of J, = J, must be the flow-geometry itself acting through the relative strength of backflow (Fig. 3-10). For each path-length/height ratio, the point where J, = J, should advance toward the slip face as the flow depth at the crest of the feature decreases relative to the height. Figure 4-29a summarizes these controls. The effect of increasing the relative depth is to increase the length of bottomsets without changing the relative thickness of the bottomset zone. Growth of the relative path-length, however, increases the relative thickness of the bottomset zone. Since a decline in relative height and an increase in the relative path-length is most likely to be caused by an increase of overall stream power, bottomsets accumulated under local plane-bed conditions are most likely to arise when

170

Fig. 4-30. Sand-flow (avalanche) and grain-fall cross-bedding in modern small aeolian dunes, Hunters Cove, Oregon. a. Lower portion of the interior of a dune, as seen in a vertical section in the flow plane, and a horizontal section on which the pencil rests. The horizontal surface reveals sand-flow units (light tone) separated by grain-fall sand (dark tone). Wind from right to left. b. View from above on to a horizontal surface similar to that in (a). Wind and dip of stratification toward top. Photographs courtesy of R.E. Hunter (see Hunter, 1977). with (a) reproduced by courtesy of the International Association of Sedimentologists.

171

the relative depth is small and/or the relative path-length is large. As well as bottomsets, two other kinds of stratification may be formed to lee of bed features. They are both associated with Bagnold’s (1954b) encroachment deposits, and were clearly distinguished by Gripp (1961). Sandflow cross-strata (Hunter, 1977) are long, narrow layers which range up and down the slip face on the sites of the tongues left by sand flows. As Gripp has shown, they are found to range from plano-convex to doubly-convex in section when a sand tongue is dissected with a knife or where the back of a dune has been scoured by the wind (Fig. 4-30) (Sharp, 1966; Hunter, 1977, 1980a; Borowka, 1979, 1980). A common associate is grain-fall cross-strata (Hunter, 1977), produced by the settlement of particles discharged over the crest of the feature (Gripp, 1961; Jopling, 1965b; Allen, 19688, 1970a). Grain-fall cross-strata are generally much thinner and finer-grained than sand-flow cross-strata. Figure 4-29b suggests how the relative importance of the two types may change with increasing path-length/height ratio. When avalanching is continuous, at large enough relative path-lengths, no distinction can be made amongst the faint and irregular strata (Allen, 19650 between grain-fall and sand-flow deposits. Hunter ( 1976) has pointed to slight differences between aeolian and aqueous sand-flow cross-strata, but their generality is uncertain.

SUMMARY

Free shear-layers arise as the result of flow-separation on ripples, dunes, bars, and Gilbert-type deltas, and also during the flow of natural jets. The intense turbulence in these layers has a profound effect on the behaviour of sediment transported over bed features and in natural jets, and brings about considerable diffusion of grains. Sand volcanoes built by jets on the tops of compacting beds or dewatering slumps can be explained in terms of a simple quantitative model in which flow and sediment properties are combined. The cross-strata accumulated to lee of bed features present a more difficult problem, however, as gravity in this case acts normal to the direction of particle transport. Laboratory experiments suggest that the geometry and structure of lee-side deposits depend on the characteristic path-length assumed by grains projected beyond the crest of the bed feature, and the strength of backflow in the separated region. An increase of path-length increases the relative importance of bottomset deposits, whereas an increase in backflow strength reduces the length of bottomset strata.

This Page Intentionally Left Blank

I73

Chapter 5 FLOW AROUND A BLUFF BODY: OBSTACLE MARKS INTRODUCTION

Patterns of flow and flow-force of great complexity arise in a stream once a surface-mounted bluff body assumes spanwise and streamwise dimensions that compare with its height. The body diverts the flow, which must locally accelerate to pass by, and vortex lines become stretched and crowded. Flow separation may occur on the upstream side of the body, the resulting vortices being stretched along the flanks, to cluster around the wake downstream. The wake itself is complex. Near the body, a strongly three-dimensional separation bubble may be present, attached partly to the rear of the body and partly to the flow boundary. A three-dimensional motion should also characterize the far wake, in which the flow disturbed by the body gradually reassumes the properties of the adjacent undisturbed boundary layer. Further complexities are introduced if the body is permeable, or if the flow is oscillatory or rotary. Upstream as well as downstream separation may be reduced or prevented if the body allows some of the flow to bleed through it, as with a tussock of vegetation, though the wake must persist. A steady streamline configuration and force-pattern cannot arise where a bluff body is affected by oscillatory or rotary currents, though symmetrical equilibrium scour-features may result. Finally, a large bluff body in a deep planetary boundary layer is unlikely to create a symmetrical flow disturbance because of the influence of Coriolis force. The above sketch will already have suggested some of the consequences of bluff-body flow in the presence of a deformable sedimentary boundary, and where the approaching stream itself bears sediment. If separation occurs upstream of the body, and the flow is accelerated around the sides, a local scouring or partial suppression of deposition may create a furrow surrounding the body. The presence of a wake, with its inevitable velocity defect, suggests that sediment may be preferentially accumulated, or scour minimized, to lee of the obstacle. A wide range of sedimentary structures called obstacle marks (Dzulynski and Walton, 1965; Karcz, 1968) conform broadly to this description. Examples abound in most depositional environments, from deserts and coastal dune complexes, to rivers, intertidal flats and beaches, and the oceans. The first recorded obstacle marks were found by James Hall (1843) in a littoral sandstone and on a modern beach, where wave-generated currents had shaped crescentic grooves around shells and pebbles and deposited “tails” of sand to lee. Hydraulic engineers also find it necessary to study bluff-body flows, since uncontrolled scour at bridge abutments and piers, river training

I74

works, harbour moles and jetties, and marine pipelines and drilling platforms endangers life and property. Equally undesirable is the uncontrolled drifting of snow or sand across roads and railways. Highway engineers have therefore studied permeable bluff bodies, as a basis for designing drift fences. GENERAL FEATURES OF BLUFF-BODY FLOWS

Two-dimensional flow past a bluff body A bluff body causes a diversion and local acceleration of the flow past it. A good impression of the extent of the local increase of velocity comes by examining the flow of a uniform frictionless stream past a transverse circular cylinder (Batchelor, 1967; Carstens and Sharma, 1975). Streamlines in the plane of flow appear in Fig. 5-la. The local flow velocity U can be resolved between a radial component U, and a tangential component U,, where:

U = (U,'

+u y 2

and it can be shown that:

in which U, is the velocity far upstream, a is the cylinder radius, and r and 0 are polar coordinates. Figure 5-lb depicts the ratio U/U'. Equation (5.2) shows that the flow is retarded along the stagnation streamline ending at the attachment point. Equation (5.3) reveals that the tangential velocity at the surface of the cylinder grows with increasing distance from attachment, to reach a maximum of 2Um when 0 = 90". But in reality a thin boundary layer forms on the cylinder because of fluid viscosity, with flow separation occurring somewhere on the flanks. Achenbach ( 1968) found experimentally that the position of the symmetrically arranged separation points, as measured by the polar angle e,, varied in a complex manner with the cylinder Reynolds number, Re = U , D / v , in which v is the kinematic viscosity and D the diameter (Fig. 5-lc).

Two-dimensional flow past a surface-mounted impermeable bluff body We cease to have analytical methods for predicting the flow in its entirety once a bluff body becomes surface-mounted (but see Hawthorne, 1954b; Gradowczyk et al., 1968; Hjorth, 1975; Smith et al., 1977), though the

I75 160

150

-

140

Q

f

130

g 120

EB 110

(0

100

90

80 0

70 104

2

4

6 8 los

2

4

6 8

2

I

*

L

4

6

E

7

Reynolds number,

Fig. 5- 1. Features of flow around bluff bodies. a. Streamlines for the flow of an inviscid fluid around a transverse circular cylinder. b. Local velocity relative to that of undisturbed stream for inviscid flow around a transverse circular cylinder. c. Experimental values of the separation angle on a transverse circular cylinder as a function of Reynolds number (data of Achenbach, 1968).

boundary-layer flow ahead of a cylinder or other bluff body is calculable (E.S. Taylor, 1959; Johnston, 1960a, 1960b; Hornung and Joubert, 1963; Perry and Joubert, 1965; Sowerby, 1965). These calculations yield limiting streamlines which closely resemble the flow pattern ahead of the cylinder in Fig. 5-la, but ignore effects related to secondary flow in the vicinity of the body. But a pattern of secondary flow must arise because of the velocity gradient in the boundary layer (Tison, 1940, 1961; Lighthill, 1956, 1957;

Fig. 5-2. Some features of the fluid motion around a right-circular cylinder mounted on the bed and extending through the free surface of a unidirectional current.

176

Toomre, 1960; Moore and Masch, 1965; Karcz, 1968; Richardson, 1968). Consider the flow in Fig. 5-2 in which a right-circular cylinder extends from a plane flow boundary through the free surface. Line AA‘ in the plane of symmetry consists of attachment points at each of which the local flow stagnates and the local dynamic pressure, pU2/2, in which p is the fluid density, is a maximum. But as U increases outward within the boundary layer, the gradient of the dynamic pressure on AA‘ is negative. Hence there must arise a secondary flow of fluid driven from A towards A’ by this pressure gradient, the magnitude of this flow being the solution of a( V2/2)/ay = -a( U2/2)/ay, where V is the velocity of the secondary flow (Moore and Masch, 1965). In ordinary boundary layers, we should therefore expect V to increase in magnitude towards the bed. This simple result is possible because we considered only the flow in the plane of symmetry, but a similar attack shows that diving flows will arise elsewhere near the front and sides of the cylinder. For example, limiting streamlines directed downward may be expected on the flanks of the cylinder and, in the plane of symmetry, streamlines within the body of the flow should also dip towards the bed. At A’ in Fig. 5-2, the secondary current turns upstream, to be checked at a singular separation point, S, where the oncoming boundary-layer flow offers sufficient resistance to overcome its motion. From S a primary separation line composed of ordinary points should curve downstream around the flanks of the cylinder. Using vorticity considerations and empirical data, Belik (1973) showed that in turbulent flows the distance d between A’ and S varied as: -=0.73( d D

0.19

7 urnaxh )

(5.4)

where D is the diameter of the cylinder, U,, is the maximum velocity of the undisturbed flow, and h is the flow or boundary-layer thickness. The bracketed term is the boundary-layer Reynolds number, ranging in Belik’s experiments between approximately l o 4 and 10’. What precisely one sees (Fig. 5-3) when visualizing a bluff-body flow depends on the shape of the obstacle (spheres, cylinders, cubes, and plates have all been studied), its attitude to flow, the Reynolds number, and the technique of visualization chosen. The valuable analyses of Morkovin ( 1972), Hunt et al. (1978), and Mason and Sykes (1979), point to configurations that are present in most flows, and Fig. 5-4 is a tentative attempt to depict some of them. The diversion and slowing of the boundary-layer ahead of the primary separation lines S, is well-established and in good agreement with theory (Keutner, 1932; Prandtl, 1952; Johnston, 1960b; Belik, 1973; Hornung and Joubert, 1963; Allen, 1966a, 1966b; Sedney, 1972, 1973; Hjorth, 1975; Melville, 1975; Castro and Robins, 1977; Hunt et al., 1978; Mason and Sykes, 1979). Several investigators have described the vigorous downflow to

177

Fig. 5-3.Visualization in Plaster of Pans of limiting streamlines near a right-circular cylinder mounted on the flow boundary beneath a unidirectional water stream (flow from top toward bottom), at a Reynolds number based on cylinder diameter of 11250.

I78

Fig. 5-4. Idealized flow configurations associated with the flow of a unidirectional current past a wall-mounted right-circular cylinder. a. Limiting streamlines and the main separation and attachment points and lines (the pattern to one side only of the plane of symmetry is shown). b. Development of vortices upstream of the cylinder in the plane of symmetry. c. Rising flow immediately to rear of cylinder.

be observed on the upstream side of the body, particularly in the plane of symmetry (Masch and Moore, 1960; Mochizuki, 1961; Sachs, 1972; Hjorth, 1975; Melville, 1975; Castro and Robins, 1977; Mason and Sykes, 1979). Mulhearn (1973) and Hjorth (1975) have illustrated the attachment line AA’ on the leading surface of a bluff body. Between one and seven vortices may be formed between the body and the primary separation point (Fig. 5-4a, b), each in downstream succession associated with a progressively higher streamline in the boundary layer (Gregory and Walker, 1951; Prandtl, 1952; Thwaites, 1960; Mochizuki, 1961; Schwind, 1962; D.M. Sykes, 1962; Hornung and Joubert, 1963; Halprin, 1965; Peake and Galway, 1965; Allen, 1966a, 1966b; Furuya and Miyata, 1972; Sachs, 1972; Sedney, 1972, 1973; Belik, 1973; Hjorth, 1975; Castro and Robbins, 1977; Hunt et al., 1978; C.J. Baker, 1979). Even though but one vortex may be seen in the plane of symmetry, others rapidly develop laterally, giving attachment and separation lines such as A , , A,, A, and S, and S, in Fig. 5-4a. Thus pairs of oppositely rotating vortices curve around the body, assuming flow-parallelism where they flank the wake. The flow configurations lying downstream from bluff bodies are less well understood, partly because of the difficulties of visualization in these highly unsteady regions. Several workers show on the bed two nodal separation points with swirl (sometimes called foci) within the near-wake separation bubble (Prandtl, 1952; Mochizuki, 1961; Furuya and Miyata, 1972; Belik, 1973; Sedney, 1973; Castro and Robins, 1977; Hunt et al., 1978). The flow from these points (Fig. 5-4a,c) is vertically upward either towards the free surface or, if the obstacle is wholly immersed, towards a free shear-layer at the level of the top of the body (e.g. Moore and Masch, 1965; Belik, 1973; Hjorth, 1975). These flows appear to be fed from below by fluid which originates relatively high up in the oncoming boundary layer but which dips

179

obliquely towards the bed around the flanks of the body (e.g. Mochizuki, 1961; Hunt et a]., 1978). The far-wake expands gradually downstream and appears to contain large vortex structures capable of sweeping the bed in directions away from the plane of symmetry (Schlichting, 1936; W. Jacobs, 1938; Schultz-Grunow, 1956; Smith et al., 1977). At Reynolds numbers less than the order of lo3 based on the body, regular arch-shaped vortices are shed into the wake to form chain-like patterns (Gregory and Walker, 1951; Mochizuki, 1961; Furuya and Miyata, 1972; Mason and Sykes, 1979). Turbulence marks the far-wake at higher Reynolds numbers. The dynamics of flow near an obstacle may usefully be contrasted with the distribution of temporal-mean velocity in its vicinity (Fig. 5-5). Although the flow is slowed near the front of the body, and a velocity defect marks the wake (Fig. 5-5a, b), the flow vorticity is greatly enhanced because of the stretching and clustering of vortex lines upstream (P.D. Richardson, 1968). Consequently, a sharp increase in turbulence intensity is locally detectable, together with the powerful vortices already described. Hjorth ( 1975), experimenting with cylinders, confirmed the increase in temporal-mean velocity near to a bluff body mounted on a plane boundary, as suggested by the theory of frictionless flows (Fig. 5-l), as well as a heightening of turbulence intensity where the velocity had been raised. Together with Melville (1975), he also detected substantial local increases in the mean bed shear stress on

fl B

------B--

(b)

_-

Edge of wake

(12’

J

-_

Cylinder diameter = 0 . 0 5 m Cylinder height =O.I m -3-Meon bed shear stress rebtlve to undisturbed boundary layer

Cylinder diameter=0.075m Cylinder height =O.I m

Fig. 5-5. Features of the flow around a wall-mounted right-circular cylinder in a unidirectional water stream. a. Distribution of velocity in the plane of symmetry, with the exception of the middle profile, which shows the velocity measured close to the lateral circumference of the cylinder. b. Distribution of velocity within the boundary layer, in a plane parallel with the bed about one-third of the boundary-layer thickness from the bed. c. Measured distributions of mean bed shear stress for cylinders under different flow conditions (after Hjorth, 1975).

180

the boundary supporting the cylinder (Fig. 5-5c). One pair of maxima lay symmetrically upstream of the cylinder, and a second weaker pair occurred to the rear. The wake is generally highly turbulent on account of vortexproduction in zones of separation and free shearing. However, because a surface-mounted bluff body stands in a boundary layer, the wake decays more rapidly than if the same obstacle were in a uniform stream. Hence a surface-mounted obstacle may materially increase turbulence in a flow while having little effect on its temporal mean characteristics. For example, the velocity defect in the wake of a cube-shaped building in the atmospheric boundary layer decays as x - 3 / 2 instead of as x - ' , where x is downstream distance (J.C.R. Hunt; 1971). Two-dimensional and axisymmetric bodies in uniform streams yield decay relations of x - 2 / 3 and x - '1' respectively (Laursen and Toch, 1959; Townsend, 1976). Two-dimensionalflow past a surface-mounted permeable body Commonplace examples of permeable bluff bodies are tussocks of grass, waterweed or seaweed, bushes, trees and hedges, snow fences, and clusters of buildings or other engineering structures. Permeable obstacles are characterized by overall dimensions and by an internal arrangement of smaller solid elements that define spaces (porosity) also internal to the body. Whether the body is an entity for present purposes depends on its solid elements being sufficiently closely spaced that they interfere in a fluid stream. Theoretically, interference persists up to an infinitely large dispersion, but in practice it seems that the critical spacing is about six times the projected width of the elements (Breusers, 1971; Collinson, 1971a; Wise, 1971; Hanlon, 1972; Sachs, 1972; Li and Shen, 1973; P.R. Owen, 1973). The interference partly blocks the flow, with the result that a permeable obstacle diverts some of the fluid streaming past it, while allowing the remainder to pass through its internal spaces. Hence a pressure rise is detectable on the upstream side of a permeable surface-mounted body, but the rate of rise and the pressure maximum are less than if the obstacle were solid. Similarly, because of bleed through the body, the pressure to leeward is not as high as if the body were impermeable, and the velocity defect is 1ess.marked. A permeable surface-mounted obstacle therefore has a different drag coefficient than the corresponding solid body. Studies of the flow at permeable bodies of simple structure show that: (1) the turbulence intensity of the fluid entering the wake is reduced relative to that in the oncoming stream (Taylor and Batchelor, 1949), (2) the drag coefficient declines as the permeability increases (Elder, 1959; Castro, 1971; Koo and James, 1973), and (3) the obstacle has greatest effect when its constituent solid elements lie en echelon (Li and Shen, 1973). Castro's experiments with plane perforated plates in a uniform stream show that the effect of bleeding fluid through interstices is to reduce the scale and alter the

181

( d ) Porosity= 0.305

( a ) Porosity >0.305

Fig. 5-6. Schematic representation of unidirectional flow past a transverse porous-permeable plate (after Castro, 1971).

position of the leeward separation bubble (Fig. 5-6), until the bubble seems to disappear when the apertures exceed in total area about one-third of the overall area. Visualizations by the South African National Building Research Institute (1969) suggest that a similar ratio marks the disappearance of separation in the lee of a surface-mounted permeable obstacle. The way in which the character of a permeable bluff body controls the distribution of temporal mean velocity in its vicinity is best known from field and laboratory studies on wind breaks and snow fences (Finney, 1934; Nageli, 1941; Pugh, 1950; Rider, 1952; Jensen, 1954; Pugh and Price, 1954; Mellor, 1965; Tabler and Veal, 1971; Mulhearn and Bradley, 1977). The accounts by Finney, Nageli, and Jensen are particularly comprehensive, and Plate (1971b) gives a useful review. Some of Jensen’s (1954) results are summarized in Fig. 5-7, in which the fractional velocity defect, (UudU d b ) / U u d , at y = 0 . 4 H appears as a function of x / H for a slatted fence.. Here u,d is the undisturbed temporal mean flow velocity far upstream of the fence at a distance of 0.4 fence heights H above the ground, and u d b is the velocity of the disturbed flow, either upstream or downstream, at this height. The magnitude of the defect declines rapidly with increasing permeability of the fence and, on the upstream side, the length of the affected region shows a harmonious decline. The defect for the corresponding solid obstacle (a wall) appears for comparison.

Surface-mounted bluff bodies in oscillatory and rotary flows The bluff bodies considered so far have all been subject to unidirectional currents. Very little is known of obstacle behaviour in oscillatory and rotary flows, however, of which there are many natural examples. Wells and Sorensen (1970, 1971) and Abad and Machemehl (1974) investigated flow and scour at surface-mounted bluff bodies subjected to oscillatory wave-generated currents, but with somewhat inconclusive results.

182

-20

-16

-12

-8

-4

0

4

8

12

16

20

24

28

32

36

40

Horizontal distance. x

Fence height, H

Fig. 5-7. Measured distributions of relative velocity upstream and downstream of porouspermeable transverse walls mounted in a unidirectional turbulent boundary layer. Data of Jensen ( 1954).

Perhaps the most important governing parameter is the ratio of the orbital diameter of a near-bed water particle to the streamwise length of the obstacle. Large ratios should favour the full development of the velocity defect and the leeward separated flow. As with vortex ripples (Vol.1, Chapter 1 l), the separation bubble should be forced to detach itself from the body at each reversal of flow, contributing to a highly disturbed local environment. Small values of the ratio, however, should lead to less turbulence near the obstacle, since a weaker separation will occur. There seems little reason to suppose that the ratio will materially influence the acceleration of the flow as it is diverted by the body, and eqs. (5.2) and (5.3) should continue to provide broad predictions. Given a symmetrically arranged obstacle, patterns of velocity and shear should be symmetrically disposed relative both to the plane of flow and the plane bisecting the body and normal to the direction of wave propagation. Any slight asymmetry could be attributable to mass-transport, in the absence of other steady currents. We can only speculate on the effect of a surface-mounted obstacle on rotary currents, such as the tide makes in shallow open waters. Considering temporal-mean magnitudes only, a bilaterally symmetrical pattern. of flow speeds and forces should arise if the current vectors have a markedly elliptical envelope. Only axial symmetry is possible when the envelope is a circle. BLUFF BODIES IN PLANETARY BOUNDARY LAYERS

Since Coriolis force grows with flow speed, the deflection of flow due to the Earth’s rotation increases upwards within the thick benthic boundary layer created in the oceans by friction between tidal or thermohaline currents and the bed. The bottom current in the Northern Hemisphere must be

I83

Fig. 5-8. Limiting streamlines around the Taylor column generated in the benthic boundary layer by a low circularly cylindrical bump (seamount). After Hogg (1973).

directed at 45" to the left of the geostrophic flow, whereas in the Southern Hemisphere it must lie at 45" to the right. An obstacle comparable in scale to the boundary-layer thickness cannot then create a symmetrical distribution of flow velocity and force (Carstens and Sharma, 1975; Mason and Sykes, 1979). Firstly, the attachment line corresponding to AA' in Fig. 5-2 must be curved and not straight. Secondly, an observer looking downstream should find the larger flow velocities and stresses to the left in the Northern Hemisphere, but to the right in the Southern Hemisphere. The truth of these inferences is confirmed by the work of Hogg (1973) and P.A. Davies (1972) on the stationary Taylor columns which can be created within ocean currents by large obstacles like knolls or seamounts. Since the column forms almost directly above the body, and is a zone of closed streamlines, the combination acts as if much or all of the flow thickness were encompassed by an obstacle. Figure 5-8 shows near-bed streamlines calculated for a body in the Northern Hemisphere. Note the concentration of streamlines on the left, indicative of above-average bed shear stresses.

GENERAL IMPLICATIONS FOR SEDIMENTATION

Figure 5-9 summarizes the above as qualitative distributions of bed shear stress in the vicinity of surface-mounted obstacles classified as to permeability and pattern of flow. Areas marked by plus signs have stress values exceeding the average, whereas values less than average occur where minus

184

Fig. 5-9. Summary of the effects of bluff bodies on mean bed shear stress in different types of boundary-layer flow.

signs appear. Characteristic obstacle marks should arise on a sedimentary bed in response to these patterns. The tendency where stresses exceed the average is either for the erosion rate to rise above the average (the entrainment threshold is assumed at least locally exceeded), or for the deposition rate to fall compared with that at a distance on the bed, in each case because the transporting ability of the flow has been raised. In both instances the obstacle mark should include negative relief. We might expect a bilaterally symmetrical crescent-shaped furrow in the case of a unidirectional flow, a pair of opposed sausage-shaped grooves in an oscillatory current, a continuous circular moat in a circular-rotary or strongly multidirectional flow, and an asymmetrical crescentic furrow beneath a planetary boundary layer. Substantial negative features should be lacking from obstacle marks generated by bodies so permeable as to have afforded no flow separation, since the fluid is inadequately accelerated at their flanks. The tendency in zones of below-average stress, where the transporting power of the flow has been reduced, is either for the erosion rate to fall relative to that on the distant bed, or for the deposition rate to rise compared with the average. Positive features should emerge in these zones. They are simplest in the case of permeable obstacles, being either flow-aligned tails or circular aprons of sediment formed in the wake. Positive and negative structures can be combined in obstacle marks formed at solid bodies. Beneath a unidirectional current, for example, the U-shaped furrow embracing the body can accompany an upstream drift, formed where the approaching boundary layer was retarded prior to separating (Queney and Dubief, 1943), as well as a poniard-shaped tail constructed in the wake to leeward.

185

But in order to reach the wake, the transported sediment must be carried well above the bed (suspension, high saltation), since the principal separation line is an effective barrier to bedload grains (Fig. 5-4). There is another circumstance under which a solid obstacle may fail to yield a mark combining both drifts and a furrow. If erosion is by sand-blasting or directly by fluid stresses, and the obstacle is small in scale compared with the boundary layer and the grain saltation path, there is little if any tendency for furrowing upstream and only a downstream tail may arise. There is no generally accepted classification of obstacle marks, but three broad categories are identifiable: ( 1) current crescents, ( 2 ) current shadows, and (3) scour-remnant ridges. Peabody (1947) gave the name current crescent to U-shaped furrows fashioned around such obstacles as clay pebbles, stranded wood, and fruit stones as currents eddied past them. The arms of the crescent point downcurrent, embracing one or more flow-aligned sediment ridges. Figure 5-10a-e illustrates schematically a number of different forms of simple current crescent, ranging from wholly erosional to wholly depositional in origin. We can furthermore assign to the class the furrows or moats formed at bluff bodies by oscillatory, rotary and multidirectional currents, and by planetary boundary layers. Bagnold (1954b) used the term sand shadow for a large wind-aligned sand accumulation leeward of an

( a ) Sand-laden flow -----Original - - - - _ _bed _______

( b ) Fast sand-laden flow

( c ) Erosive flow

( d ) Fast flow with bedload only

( e l Fast flow with suspended and bed loads

(f

-

1 Fast sand-laden flow

- - - - - Original __

bed

( 9 ) Fast sand-laden flow

Fig. 5-10. Varieties of current crescent and shadow formed by unidirectional currents, depicted in the plane of symmetry and in plan. Morphology depends on current strength, the grade of sediment transported, and the nature of the flow boundary.

186

obstacle. By introducing the less specific name “current shadow”, his concept can be widened to include accumulations of mud or sand in water as well as flow-aligned ridges created by differential erosion (Fig. 5-10f, 8). A current shadow may comprise a single ridge of sediment, a ridge bifurcating once or more or more downstream, or a group of parallel ridges. Furrows upstream or on the flanks must be lacking however. Scour-remnant ridges (Allen, 1965d) are relatively small and generally simple ridges of sediment which gradually taper and lose height downcurrent in the lee of an obstacle. They result from differential erosion but are distinct from erosional current shadows.

CONTROLS ON THE CHARACTER OF OBSTACLE MARKS

The above mainly hydrodynamic evidence, combined with field and laboratory results, shows that obstacle marks depend for their character on: (1) the substrate supporting the bluff body, (2) the approaching boundary layer, (3) the transported sediment, (4) the size of the obstacle in relation to boundary-layer thickness, and (5) the shape and orientation of the body. Experimental studies of obstacle marks, particularly those due to scour, have been made almost exclusively by bridge engineers. Moreover, these workers have restricted attention mainly to bluff bodies of simple geometry in the presence of sand beds affected by unidirectional flows. Karcz (1968), Neill ( 1973b) and Shen (1971b) survey part of this work, but the most comprehensive reviews are by Hjorth (1975), Melville (1975), and Breusers et al. (1977). A recent study at subcritical-supercritical Froude numbers is by Jain and Fisher (1980). Corroborative field data are scanty (Neill, 1965, 1973b; Karcz, 1968; Holmes, 1974), partly because of the difficulty of collection, especially where flood-scour at bridge piers is involved. Hence we can obtain only a general insight into the controls on naturally occurring obstacle marks, which lack regularity of form and arise in gravelly and muddy as well as sandy sediments. A further review is by Jain (1981). The degree of streamlining of a symmetrically arranged bluff body profoundly affects the extent of lateral and upstream scour (Keutner, 1932; Tison, 1940, 1961; Laursen and Toch, 1953; Hawthorne, 1954b; Dietz, 1972; Hjorth, 1975). Slender bodies of bicusped or biconvex cross-section predictably promote the least scour, whereas sharp-angled obstacles of square or rectangular shape are invariably fronted by deep furrows. Flow separation occurs at every sharp edge on these bluff forms, increasing their effective width and drag. Keutner (1932), Laursen and Toch (1953, 1956), and Hawthorne (1954b) all found that even a slight skew given to a slender obstacle caused a dramatic increase in the depth of scour upstream. The pattern of scour and accretion, like the body itself, is no longer symmetrical about the plane of

187

flow. Ridges accumulate either immediately to lee or far down the wake. The scour hollow may extend for some distance downstream beyond the trailing edge of the body. Melville (1975) and Breusers et al. ( 1977) review a plethora of empirical formulae for the depth of scour in front of a bluff body as a function of obstacle geometry and flow and bed conditions. The formulae are divisible between four groups, on the basis of form. Some are valid only when the flow conditions do not permit general sediment entrainment (clear-water scour), whereas others may apply both to this condition and to scour accompanying general transport. According to the simplest formulae, the equilibrium scour depth is a power function only of the size and shape of the body. For a right-circular cylinder, Larras (1963) and Breusers (1965) give:

H, = 1.050°.75 and :

(5.5)

H , = 1.40 ( 5-6) respectively, where H , is the scour depth relative to mean bed level, and 0 is the cylinder diameter. These formulae, valid for general sediment transport, make the relative scour either a constant or nearly so. The more complex equations make scour depth also a function of sediment and/or flow properties. The formula of Shen et al. (1969): H, = 0.000223(

urn,,, D , 0.619

in which the group in brackets is the obstacle Reynolds number, is fairly representative, besides sharing a common basis with Belik’s (1973) eq. (5.4) predicting the scale of forward separation. It too applies to general sediment motion and, with Neill’s (1973b) field data and Knight’s (1975) laboratory results taken into account, is valid for 1.8 X 10’ < R e < 2.5 X lo’. Figure 5-11 shows this formula together with the extensive data of Bonasoundas (1973) and Knight (1975), covering both clear-water and general scour. The local width of the scour furrow created by a circular cylinder in a loose sand bed is fairly constant at each scour condition but increases with scour depth (Bonasoundas, 1973). Estimated in the plane of symmetry as the length L, (Fig. 5-1 l), the width is given approximately by H,/tan $+, where $+ is the residual angle after shearing. The equivalence is approximate because (1) the local scour depth varies slightly with polar angle, and (2) backflow within the scour can maintain side-slopes exceeding c$~.On account of their strength, muddy sediments can yield scours with vertical or even overhanging sides (e.g. Nicolett, 1975). The numerical model developed by Gradowczyk et al. (1968) is fairly successful in predicting scour dimensions. Belik’s (1973) eq. (5.4) compares in form with eq. (5.7) but grossly

188

3

2

16'

B

-

6

I

E

a-

a

5

3

b

2

" fa

B

I 10-2

-

0

O

0

oo

B 0

6 -

a Bonasoundos (1973) 0

4 -

lo3

Knight (1975b3

0

2

3

4

2

6 e l O 4

Reynolds number,

3

4

6 B l O 5

',*an Y

Fig. 5-11. Depth of scour in front of a right-circular cylinder rooted in a sand bed, as a function of cylinder Reynolds number. Equation (5.7), for mobile-bed scour, is a limiting relationship, applying when sand is in movement over the whole of the bed. Clear-water scour implies that only sand within the zone of influence of the cylinder is in transport.

underestimates the scale of equilibrium scour hollows, presumably because of the influence of side-slope collapse in the case of sand beds and the effect on the vortices of the scour itself (Knight, 1975). Bed shear-stress distribution within the hollow (Melville, 1975; Melville and Raudkivi, 1977) is rather different than on the corresponding flat bed (Fig. 5-5c). The greatest stresses lie in a wide arc just downstream from the lip of the scour. Melville's measurements of local velocity show that normally only one large vortex is present in the upstream part of a scour furrow. A second and generally smaller vortex may occasionally be found immediately downstream from the lip, as suggested by the presence of a slight ridge of sediment probably expressing separation (e.g. Keutner, 1932; Francis et al., 1968; Karcz, 1968; Melville, 1975). Beginning with an undisturbed flat bed, the depth of scour at an obstacle affected by a steady flow increases with time until equilibrium is reached, at first rapidly and then more gradually (Laursen and Toch, 1956; Laursen,

I89

1963; Vinje, 1969; Breusers, 1971; Dietz, 1972; M.A. Gill, 1972; Bonasoundas, 1973; Melville, 1975). Equations of exponential form best express this dependence. The obstacles so far considered have all been passive in the sense that their position remained fixed while scour proceeded around them. When erosion begins around a body which merely rests upon a sand bed, the obstacle first becomes undercut (Bagnold, 1937; B.M. Abbott, 1974) but eventually may gradually slide upstream and downward, perhaps even turning over, into the developing furrow (Johansson, 1960, 1976; Fahnestock and Haushild, 1962; Koster, 1977). This interaction can give an imbrication to stones and other objects (Vol. I, Chapter 5). Johansson (1976) found that the imbrication angle increased with flow velocity, and could be as large as about 42". The dependence can be better stated by reference to eq. (5.7), for the larger the Reynolds number, the deeper is the scour relative to the scale of the body, and the greater the angle through which the object can be tipped before streamlining limits further descent.

CURRENT CRESCENTS IN AEOLIAN ENVIRONMENTS

Snow and mineral sand are the most important naturally occurring wind-blown sediments, and forms of current crescent are known from both kinds of material. Cornish (1902, 1914) was the first to make a detailed study of current crescents in snow. He observed that crescent-shaped hollows with arms pointing downwind formed during snow-storms around boulders, the bases of trees, and isolated buildings, all as the result of differential deposition. In the case of the smaller crescents, developed at trees and boulders, a poniardshaped tail of snow had accumulated preferentially in the shelter of the obstacle. Figs. 5-12 and 5-13 illustrate similar structures as described by Allen (1965d) after more snow had built around the shovelled-up remains of an earlier fall. Further examples are discussed by Dobrowolski (1924), Seligman (1936), Pedgley (1967), and Bonasoundas (1973). The larger of Cornish's crescents, like some studied by Seligman (1936) and Pelevin (1965), have partly encircling drifts that apparently accumulated in the vicinity of the principal separation line (Fig. 5-4a), but leeward tails can be lacking. Mellor (1965) described from a building in the Antarctic a remarkable structure composed of a continuous moat encircled by a large apron of accumulated snow (see Fig. 5-9). Figure 5-14 shows a current crescent formed from wind-blown sand drifted around an obstacle partly embedded in an extensively deflated sand beach. A curved furrow to the front and sides of the obstacle, together with the wake zone, have here been kept free from accumulating sand. Bourcart (1928), R.B. Gordon (1972), and Whitney (1978) describe similar structures.

190

Fig. 5-12. Current crescent formed by differential deposition of snow around mass shovelled up from an earlier fall, Brown University Campus, Providence, Rhode Island, U.S.A. Pencil 0.18 m long points in wind direction.

Fig. 5- 13. Current crescent formed by differential deposition accompanied by slight erosion around snow mass shovelled up from earlier fall, Brown University Campus, Providence, Rhode Island, U.S.A. Pencil 0.18 m long points into wind. Scour-remnaht ridges on floor of crescent point to spiralling air-flow within groove.

191

Fig. 5-14. Current crescent formed by deposition of sand around a somewhat battered 5 gallon drum, beach west of Holkham Gap, Norfolk, England. Wind from lower right toward upper left.

Cornish (1902, 1914), Dobrowolski (1924), and Seligman (1936) interpreted their aeolian current crescents by reference to the flow at a bluff body. Allen (1965d) found scour-remnant ridges within the furrows he described, and so could demonstrate directly the occurrence of a horse-shoe vortex at each obstacle. The ridges indicate a pattern of currents similar to that in the upstream part of Fig. 5-4a. CURRENT CRESCENTS IN AQUEOUS ENVIRONMENTS

River and shallow tidal flows

Many workers have made current crescents in the laboratory using sand beds and one-way aqueous streams (Keutner, 1932; Hawthorne, 1954b; Dietz, 1972; Bonasoundas, 1973; B.M. Abbott, 1974; Carstens and Sharma, 1975; Hjorth, 1975; Melville, 1975; Futterer, 1977). Invariably on the flanks and upstream side of the obstacle is an embracing U-shaped to almost moat-like scour hollow, the arms of which may terminate downstream in delta-like deposits. The larger forms of crescent display a single tail to leeward, which grows bolder as the flow strength is raised.

192

Fig. 5-15. Large current crescent formed on a river sand bar around a block of cohesive soil from a nearby bank, Laiture delta, northern Sweden. Flow from upper left to lower right. Photograph courtesy of V. Axelsson (see Axelsson, 1967).

These essentially accretionary structures have their counterparts in natural river environments. Arnborg (1958) could observe active crescents on a river bed, the furrows containing small concentric ridges indicative of multiple horse-shoe vortices. Peabody (1947), Friend ( 1965), Sengupta (1966), Conybeare and Crooke (1968), Karcz (1968), Slatt and Hoskin (1968), Picard and High (1973), and Teisseyre (1977) all describe current crescents with tails formed because of differential deposition in the vicinity of stones or other obstacles, and now preserved on mainly dried-up stream beds. Karcz found the depth of scour to be only about one-half the obstacle breadth, the ratio being substantially less than eqs. (5.5)-(5.7) would suggest, presumably because the natural obstacles are broadly equant in shape rather than tall and cylindrical. Figure 5-15 (Axelsson, 1967) gives the essence of the larger current crescents found in river environments, at trees on floodplains (Jahns, 1947; Underwood and Lambert, 1974), at dense mats of vegetation (McGowen, 197I), and around stranded ice (Klimek, 1972). Accretionary current crescents of these kinds have little chance of preservation except when formed high up in river channels or on floodplains,

193

where large deposition rates prevails. McGowen ( 1971) has figured the kinds of bedding produced during the partial infilling of large crescents as floods wane. The maintenance of conical moats around tree trunks during flood plain accretion creates Underwood and Lambert’s ( 1974) centroclinal crossbedding, in which each inward-dipping lamina resembles the frustrum of an inverted cone. This structure should be sought around the casts of trees in coal-bearing rocks. Small accretionary current crescents, however, are fairly commonly preserved in parallel-laminated fluviatile sandstones (e.g., Fahrig, 1961; Gall, 1971; De Omenaca, 1974). Tidal currents locally behave like river flows. Several workers have from tidal flats and sand banks described crescents formed around shells and other obstacles (Gripp and Martens, 1963; Hartwell, 1970; Gebelein, 1977). Many fluviatile current crescents arose through the differential scouring of cohesive mud in the neighbourhood of stranded mud clasts and stones, partly exhumed pedogenic concretions, and resistant burrow-infillings (e.g. Peabody, 1947; McKee, 1954; Pettijohn and Potter, 1964; Diessel et al., 1967). Figure 5-16 illustrates examples found by Friend (1965) as moulds

Fig. 5-16. Current crescents formed by differential erosion of mud beds and preserved as moulds beneath sandstones, Wood Bay Series (Devonian), Spitsbergen. a. Current from lower right toward upper left. b. Current from lower left toward upper right. Photographs courtesy of P.F. Friend (see also Friend, 1965).

1 94

beneath a sandstone in the Old Red Sandstone of Spitsbergen. Similar to these in character and origin are the current crescents occasionally preserved beneath turbidites (Dzulynski and Sanders, 1962b; Lanteaume et al., 1967). Sengupta (1966) and Karcz (1968) interpreted fluviatile current crescents in terms of the vortices and velocity defects created during flow around bluff bodies. Internal scour-remnant ridges indicative of forward separation have yet to be described from such crescents in the field, but rearward separation similar to that in the model (Fig. 5-4) is clearly proved by the patterns of convergent-divergent current ripples that are preserved (Fig. 5- 15).

Sand beaches Many beach sands include a small admixture of stones or shells which, when exposed in the wave swash-backwash zone, create backwash-oriented current crescents preserved generally in association with parallel laminations and parting lineations (Fig. 5-17). Further examples are given by Plessman (1961), Pettijohn and Potter (1964), Allen (1966b), Martins (1967), and Cepek and Reineck ( 1970). Karcz ( 1968) has discussed some of the complications that can be introduced into their form when the obstacle penetrates the free surface of the flow, with the result that transient surface waves arise. Fossilized current crescents plausibly of littoral origin are known (J. Hall, 1843; Seilacher, 1953; Vortisch, 1973).

Tidal seas and the deep ocean Current crescents resembling those found in shallow-water environments are now well known from those parts of the ocean floor swept by vigorous thermohaline and tidal currents. Depths of occurrence range from a few tens of metres on the continental shelf to more than 4 km on the lower continental rise and elsewhere. The crescents have formed around lava pillows (Heezen and Rawson, 1977), around stones in some instances ice-rafted (Heezen and Hollister, 1964, 1971; Pratt, 1968; Kelling and Stanley, 1972; Werner and Newton, 1975a, 1975b; Johnson and Lonsdale, 1976; Schlager et al., 1976; Bouma et al., 1977b; Werner et al., 1980), and at various organic obstacles (Pratt, 1968; Neumann and Ball, 1970). Some of Werner and Newton’s so-called comet-marks (see also Johnson and Lonsdale, 1976; Bouma et al., 1977b) resemble the aeolian crescent shown in Fig. 5-14, in that sediment is lacking from both the wake of the obstacle and the crescent-shaped area in its immediate vicinity. Evidently the mobile sediment travelled only as bedload, otherwise it would have penetrated beyond the primary separation line shown in Fig. 5-4. However, in most cases (e.g. Werner et al., 1980) a sand tail lies downstream of the object creating the current crescent. Probably the largest current crescents to be found in tidal seas are those associated with wrecked ships (G.F. Caston, 1979).

195

Fig. 5-17. Small current crescents formed by wave backwash around cockle shells (about 0.02 m across) resting on fine sand, coast near Burnham Overy Staithe, Norfolk, England. Seaward toward top of photographs. In (c) traces of the landward-pointing swash-formed crescent remain preserved.

Since the first report was given by Heezen and Johnson (1963), current crescents in which ridges are combined with furrows ranging from short arcs to almost complete moats have been widely described at abyssal knolls and seamounts (Lowrie and Heezen, 1967; Pratt, 1968; Heezen and Johnson, 1969; Johnson and Johnson, 1970; Johnson et al., 1971; Davies and Laughton, 1972; Ruddiman, 1972; Roberts et al., 1974; Johnson and Lonsdale, 1976; Normark and Spiess, 1976; Von Stackelberg et al., 1976, 1979; Lowrie et al., 1978). Like the smaller crescents, the forms associated with these large obstacles occur beneath persistent thermohaline currents, but their scale is measured in kilometres or even tens of kilometres. Some of the forms

196 37'30' N

4000

I

'

39O25' N

37O25' N 39O20' N

I

67°KYW

67O05'W

67°00'W

KEY

cGenerolizbd bottom current

Furrow/moat

Turbid woter -1700-

Depth contour

Fig. 5-18. Furrows, moats, and sediment drifts formed at knolls and seamounts within the benthic boundary layer. a. Knauss Knoll, Central Atlantic Ocean (after Lowrie and Heezen, 1967). b. Mytilus Seamount, Central Atlantic Ocean (after Johnson and Lonsdale, 1976). c. Seamounts southwest of Faroe Plateau, North Atlantic Ocean (after Johnson et al., 1971).

represent differential deposition (Lowrie and Heezen, 1967; Roberts et al., 1974), whereas others seem due to the non-uniform erosion of evenly deposited sediments (Normark and Spiess, 1976). Davies and Laughton (1972) give a model for current crescents at seamounts and knolls with affinities to that advanced in Figs. 5-4 and 5-9. Figure 5-18 shows examples of these larger forms. Knauss Knoll (Fig. 5-18a) is a small feature on the continental rise near Hudson Canyon in the path of the Western Boundary Current affecting the western Atlantic Ocean. The large accretionary ridge or fore-drift upcurrent of the knoll is attributed by Lowrie and Heezen (1967) to deposition where the current is decelerated on approaching the obstacle. The furrow associated with this knoll is small and restricted to the southeast flank. In the same general area but much larger is Mytilus Seamount, investigated by Johnson and Lonsdale (1976) using current meters, side-scan sonar, and a seismic profiler (Fig. 5-18b). Strata crop out on the ocean bed over an extensive area upcurrent from the seamount, but at its foot is a zone of murky waters concealing a thick

197

accumulation of mud. Likewise skirting the eastern side of the seamount is a wide erosional channel swept by axial currents directed south-southeast. Figure 5-18c shows two of a number of seamounts with bordering crescents and ridges investigated by Johnson and Johnson (1970) between the Faeroe Plateau and the Mid-Atlantic Ridge. Like similar features in the Rockall Trough (Roberts et al., 1974), the sedimentary deposit is thickest on one or more of the upcurrent, right-hand (looking downcurrent), and downcurrent sides, in general agreement with Hogg’s (1973) model (Fig. 5-8). In much shallower waters differential scour probably related to locally accelerated currents has exposed igneous dykes to view on the sea bed, where they stand like castle walls above adjacent moats (G.F. Caston, 1975).

CURRENT SHADOWS IN AEOLIAN ENVIRONMENTS

Impermeable bodies Erosional furrows fail to arise at obstacles in the aeolian environment where the substrate is erosion-resistant, and only tails, generally accretionary, can here be formed (Fig. 5-19a). Gripp and Martens (1963) and R.B. Gordon (1972) figure examples found on beaches where sand driven by the wind over the damp surface had been trapped in the lee of stones or dense seaweed clumps. Trusheim ( 1935) illustrates shadows from relatively continuous spreads of sand. Long snow-drifts in the lee of buildings seem of a related origin (Roots and Swithinbank, 1955). The thin but vigorous Martian winds have locally shaped features similar to Fig. 5-19a in the shelter of stones strewn on the planetary surface (Mutch et al., 1976a, 1976b). These tails have an obscure and possibly complex origin. Mutch and his colleagues interpret them either as erosively modified dust accretions, or as wholly erosional forms produced when an even deposit burying a stony surface was extensively deflated. If the second suggestion is correct, the forms should be regarded as scour-remnant ridges. Greely et al. (1974) describe and analyse in terms of laboratory experiments the tails, in some cases depositional but in others erosional, that exist downwind from many Martian volcanic craters.

Permeable obstacles The result of partly checking a snow-bearing wind at a tussock of grass is a poniard-shaped snow shadow to leeward (Cornish, 1902, 1914; Seligman, 1936; Pedgley, 1967). The retardation provided by large bushes can result in long and complex snow drifts, as Cornish (1902, 1914) found on the Canadian prairie. The most impressive shadows, however, are formed from sand trapped by

198

Fig. 5-19. Current shadows (a) downstream of snow masses, pencil 0.18 m long and parallel with wind blowing toward observer, Brown University Campus, Providence, Rhode Island, U.S.A., and (b) in the lee of a tussock of brown seaweed (scale 0.15 m long), R. Severn, near Lydney, Gloucestershire, England.

199

Fig. 5-20. A ballistically rippled sand shadow in the lee of a tussock of vegetation. Wind toward observer. After a photograph by Stone (1967).

grass tussocks and bushes in coastal dune complexes and deserts (Fig. 5-20). They include the sand shadows, sand-shadow dunes, or turret dunes formed at small tussocks (Passarge, 1904; J.S. Bradley, 1957; W.S. Cooper, 1958; Logan, 1960; Gripp and Martens, 1963; Beheiry, 1967; Hayes, 1967; Stone, 1967; Depuydt, 1972; Schreiber et al., 1972; Carter, 1978b; Whitney, 1978), the somewhat larger knob or elephant-head dunes of Russell (1932), Beheiry (1967), and Stone (1967), and the even larger nebkha or shrubb-coppice dunes of Capot-Rey (1957a) and Stone (1967) respectively. These intergrading and overlapping forms show in a striking manner that a sand shadow of increasing size can arise only if plant-growth keeps pace with sand supply. Hesp (198 1) also describes sand shadows at tussocks. The wind-flow over sand shadows is largely indicated by the patterns of superimposed ballistic ripples (J.S. Bradley, 1957; Gripp and Martens, 1963; Beheiry, 1967). To leeward of the most permeable tussocks and bushes, the ripple crests are almost rectilinear and strike more or less directly across the crest of the shadow. Where the vegetation is more dense, however, the ripples face inwards slightly towards the axis of the shadow (e.g. Fig. 5-20), suggesting an inwards and upwards but still largely downstream flow of air such as appears in the mid-wake of Fig. 5-4a. Greely et al. (1974) produced similar ripple fans experimentally at model Martian craters.

200

CURRENT SHADOWS IN AQUEOUS ENVIRONMENTS

These structures are best known from river channels and floodplains, where they occur as flow-aligned drifts of sand in the shelter of cobbles and boulders (Arnborg, 1958; Karcz, 1968; Klimek, 1972; Teisseyre, 1977), as downstream-tapering sand ridges to lee of grass tussocks and bushes (Ahlmann, 1924; Doeglas, 1962; Karcz, 1968), and as narrowing plumes of gravel in the wake of dense brushwood tangles (Froehlich et al., 1972). Excavations by Karcz (1968) suggest that the ridges are bedded internally in harmony with their external form. Fluviatile sand and gravel shadows can be fossilized. Mr. D.H. Dales (pers. c o r n . , 1979) has found shadows in New Red Sandstone gravels of southwest England (Fig. 5-21a). I have noticed them in gravelly fluvioglacial deposits in New York State as wedges of faintly bedded sand lying downstream from the larger stones, and also in the Old Red Sandstone of southern Britain (Fig. 5-21b). The marine environment seems to be poor in current shadows. Gennessaux (1966), Jindrich (1969), and G.R. Davies (1970a) found that sand shadows up to 4 m long formed in the shelter of sponges, mollusc shells, and other large objects on the floors of current-swept channels. The current shadow shown in Fig. 5-19b formed to lee of a tussock of seaweed attached to a partly buried holdfast. Heezen and Hollister (1971) record mud shadows in the lee of coiled faeces, manganese nodules, and other debris on the ocean floor at depths of more than 3 km. SCOUR-REMNANT RIDGES

The structures thus named by Allen (1965d) are small simple ridges of either snow, sand or mud preserved to leeward of resistant objects such as ice fragments, shells and stones, or the remnants of crusts of hardened snow, hardened mud, and ice-cemented or salt-hardened sand. The ridges invariably taper downcurrent and usually narrow in this direction. In length they seldom exceed 0.1 m and in height 0.02 m. Their shape in transverse crosssection harmonizes with the spanwise profile of the projecting obstacle upstream. Scour-remnant ridges are wholly erosional in origin, arising chiefly as the result of sand-blasting and rarely by the direct action of fluid stresses. This mode of origin is in many cases proved by the circumstances under which they are found, for example, where a sand beach is seen to be undergoing rapid deflation, and in other instances by the exposure of discordant bedding on the ridges and their surroundings (e.g. Heezen and Hollister, 1971). Reineck and Singh (1973), however, claim that the structures can be partly depositional. Figure 5-22 exemplifies scour-remnant ridges formed by the attack of a strong wind upon sun-crusted snow (Allen, 1965d). Cornish (1902, 1914),

20 1

Fig. 5-21. Current shadows in fluviatile deposits of the stratigraphic record. a. Current shadow of pebbly sand to lee (right) of a cobble in Tor Bay Breccia (Permo-Triassic), Paignton, Devon. Lens cap 0.07 m across and current from left to right. There may have been a furrow in front of the cobble, to judge from the nest of pebbles there, making the shadow part of a current crescent. Photograph courtesy of D.H. Dales. b. Flat mudstone boulder (marked by arrow) with long, internally stratified current shadow to lee (right), medium to very coarse grained sandstones, Brownstones Group (Devonian), Ross-on-Wye, Gloucestershire, England. Boulder approximately 0.75 m long with current from left to right.

202

Fig. 5-22. Scour-remnant ridges formed formed around pieces of hardened snow, Brown University Campus, Providence, Rhode Island. Pencil 0.18 m long points in wind direction from right to left.

Fig. 5-23. Scour-remnant ridges formed at pebbles and shells scattered through fine sand, coast near Burnham Overy Staithe, Norfolk, England. Trowel 0.28 m long points in wind direction.

203

Dobrowolski ( 1924), and Seligman (1 936) record similar features. Of a similar character are the scour-remnant ridges (Fig. 5-23) formed when deflation attacks damp beach sand containing scattered stones or shells (J.S. Bradley, 1957; Fisk, 1959; Milling and Behrens, 1966; Martins, 1967; Heezen and Hollister, 1971; Depuydt, 1972; Wunderlich, 1972; Carter, 1978b). Scour-remnant ridges also arise on beaches where salt-hardened crusts are breached (McKee, 1957b; Gripp and Martens, 1963). In all cases the erosion is accomplished by saltating grains. The downstream slope of the ridge crests should therefore be relatively constant and should compare with the angle of impact of the saltation, for the ridges must have attained an equilibrium geometry once their downstream slopes permitted no steeper than glancing impacts. A striking uniformity'of slope is evident in any set of scour-remnant ridges (e.g. Wunderlich, 1972). Observed ridge slopes (5- 12') are broadly consistent with Tsuchiya and Kawata's (1971) and White and Schultz's (1977) experimentally determined impact angles of about 8" (quartz sand) and 14' (glass beads) respectively. R.W. Berry (1973), however, has reported scour remnant ridges from a beach that are not associated with either stones, shells or salt crusts. He suggested that non-uniform compaction of the sand led to the development of the structures. Examples of scour-remnant ridges have been photographed from many parts of the ocean bed swept by vigorous thermohaline currents (Heezen and Hollister, 1964, 1971; Owen and Emery, 1967; Hollister and Heezen, 1972; Kolla et al., 1976; Hollister et al., 1978). The most convincing of these as purely erosional structures are described by Owen and Emery in association with transverse sastrugi-like features. The combination is strongly reminiscent of the effects of deflating a ripple-marked beach sand. SCOUR FEATURES IN COMPLEX CURRENTS

The character of the scour features produced by oscillatory, rotary, and multidirectional currents is little known. Even under the action of uniform progressive waves in the laboratory a variety of patterns of scour can arise. Of those generated at an upright circular cylinder by Wells and Sorensen (1970, 1971), the most common are (1) a symmetrically arranged arcuate furrow on the side facing the oncoming waves, and (2) a solitary, usually oval hollow adjacent to one of the flanks. Occasionally there is a weakly developed tail of sand pointing in the direction of net sediment movement. The two much more subordinate patterns were found to be (1) a uniform shallow moat encircling the whole cylinder, and (2) a pair of sausage-shaped furrows arranged symmetrically about the plane of flow. S.M. Stanley (1975) also made scour marks in the laboratory under wave action, while studying the orienting abilities of semi-infaunal bivalves. He found complex patterns of hollows and ridges,

204

Fig. 5-24. Conical moat shaped by wave-action in fine sand around a wooden post, Barmouth Estuary, Wales. Scale 0.15 m long.

symmetrical both about the plane of flow and about the plane normal to the direction of wave propagation. Real waves, represented by broad spectra of heights and propagation directions, appear to produce only moats at obstacles on sand beds (Fig. 5-24). The moat illustrated here is almost perfectly axisymmetric, like the obstacle that created it. The examples studied by Dorr and Kauffman ( 1963), shaped by large boulders, are less perfectly axisymmetric and their inward-sloping sides carry patterns of radial ripples, of a form indicative of swirling currents. Dorr and Kauffman also described rippled-marked, doughnut shaped bodies of sandstone, called “rippled toroids”, that might have been moulded by these hollows. Although the toroids seem to have been shaped by swirling currents, they were not interpreted as obstacle marks. Slatt and Hoskin (1968) report moats around large obstacles in a wave-affected environment. The problems of scour around obstacles exposed to rotary currents has become crucial in recent years in the North Sea, where it is necessary to mount drilling rigs and platforms on a mobile sand bed. T.N. Watson (1974) distinguishes two kinds of scour. One occurs locally around each supporting leg, resulting in a conical scour-pit resembling the moat in Fig. 5-24, while the other, due to the assemblage of legs, is expressed by a general lowering of the sea bed, in response to the heightened mean velocity and turbulence.

205 SUMMARY

An obstacle projecting up into a boundary layer bends and concentrates vortex lines. This results in the creation, on the upstream side of the body, of one or more vortices which locally increase the mean bed shear stress where they curve round the flanks of the obstacle before joining the wake. In the near-wake, flow separation occurs provided that the obstacle is neither streamlined nor more than moderately permeable. The far-wake of a bluff body is characterized by a streamwise-declining velocity defect, and by boundary stresses that are smaller than average. Current crescents, current shadows, and scour-remnant ridges are sedimentary structures which depend on flow at bluff bodies. They occur in environments ranging from rivers to the deep ocean. In current crescents a U-shaped furrow related to the upstream vortices is combined with one or more sediment ridges dependent on processes in the wake. Current shadows involve only accretionary sediment ridges and are commonly related to permeable obstacles. Scour-remnant ridges likewise lack upstream furrows; they are erosional in origin and seem to depend either on corrasion or directly on fluid stresses. Erosional obstacle marks seem to have the greatest chance of preservation. Many kinds of obstacle mark are useful palaeocurrent indicators.

This Page Intentionally Left Blank

207

Chapter 6

HEAT AND MASS TRANSFER: ICE DUNES, KARREN, AND RELATED FORMS

INTRODUCTION

A transport process is any process whereby matter or energy is conveyed parallel with the boundary of a fluid stream through the action of the stream. Much of the above is concerned with one particular transport process, that involving the conveyance of mineral solids by wind or moving water. But this flow creates sedimentary structures only when it is accompanied by a process that involves the movement of grains across the interface between the stream and its sedimentary boundary. This kind of process is one of transfer which, in the context of sediment movement, is called either erosion, when debris moves from bed to stream, or deposition, when movement is from stream to bed. We saw in Vol. I, Chapter2 that erosion and deposition can be described by time and space derivatives of the sediment transport rate. There are, however, other kinds of transfer process, many of which also yield forms that may properly be called sedimentary structures, namely, ice ripples and related forms, Karren or lapiaz, and a range of sculptural features preserved on tektites (glassy), meteorites (stony or metallic) and, observed in recent years, on the heat-shields of space vehicles. Karren are regular sculptural features developed where carbonate rocks, chiefly limestones, are exposed to water streams in cave systems, on the Earth’s surface, and beneath soils. Similar forms occur locally on surfaces of gypsum or halite, though unusual climatic circumstances are clearly necessary for their development. Certain features developed on surfaces of ice or hardened snow are genetically related to Karren. These structures all depend on mechanisms referable to the general transfer process called muss transfer, whereby matter is removed from a solid surface into a neighbouring fluid as the result of direct chemical and/or physical dissolution, the shape and position of the interface consequently changing. The dissolution rate depends on the properties of the solid and of the fluid, as well as on the character of the fluid stream. As with particle erosion and deposition, the material transferred experiences no change of state during the transfer. Ice ripples and tektite, meteorite and heat-shield structures depend on more complex mechanisms, grouped as heat-with-mass transfer (ablation). In these, energy is conveyed from a fluid to a neighbouring solid or liquid, causing the solid or liquid to lose mass because o f a change of state. The melting of ice into water or warm air is a simple example. The more complex mechanisms, however, involve chemical reaction as well as at least one

208

change of state, as is commonly true of tektites, meteorites and heat-shields that attain high temperatures in travelling through the Earth’s atmosphere. They are controlled by a wider range of material constants than is the case in simple mass transfer. Heat and mass transfer are intensively studied by engineers because of their great practical importance, helpful introductory accounts being given by J.T. Davies (1972), Kay (1963), and Knudsen and Katz (1958). A valuable treatment with a mathematical bias is by Bayley et al. (1972), and other useful advanced texts are by Kays (1966), Kreith (1965), and Levich (1962). Coulson and Richardson’s (1962, 1965) books give a sound theoretical coverage, but with a strong practical flavour. Patankar and Spalding (1970) show how problems can be solved computationally in these difficult fields. An important early review is by Drew (1931). Schlichting (1971) recently sketched some important modern issues of heat-transfer and boundary-layer research. The principles of heat and mass transfer have not so far been much applied to the natural features listed above, despite their obvious and decisive relevance, though the studies of a class of limestone features by Curl (1966a), of meteorites by D.T. Williams (1959), and of ice ripples by Ashton and Kennedy (1972) stand as striking demonstrations of what can be achieved. REGIMES AND MECHANISMS OF HEAT AND MASS TRANSFER

There are two modes of heat and mass transfer: free or natural convection and forced convection. In free convection there exist no external forces causing fluid motion, though circulatory currents may result directly from the transfer, as during the evaporation of water from a stagnant pool into stationary air. In forced convection, transfer results from the externally motivated flow of a fluid phase. Limestone dissolution into a water stream is an important example. Forced convection occurs under laminar as well as turbulent conditions, each regime being represented naturally. The freeconvection transfer-rate is much the smaller, however, as may be discovered by comparing the effects of stirring sugar into coffee or tea and merely sprinkling the crystals into an undisturbed cup. Turbulent motion as the result of free convection rarely occurs naturally outside of the ocean and atmosphere. The chief mechanisms of mass and heat-with-mass transfer are as follows: Mass transfer (1) Physical dissolution of solid into liquid. (2) Chemical dissolution of solid into liquid. (3) Sublimation of solid into gas. Heat-with-mass transfer (ablation) (4) Melting of solid into liquid of identical composition.

209

(5) Melting of solid into liquid or gas of different composition. (6) Vapourization of liquid into gas. (7) Melting or vapourization followed by chemical reaction with fluid phase. The driving force in mass transfer is the concentration gradient of the substance undergoing transfer. The diffusing substance moves from areas of high concentration- the solid-liquid or solid-gas interface- to sites of lower concentration. In heat-with-mass transfer, either thermal energy is extracted from the fluid phase and used to change the state of the other phase (or phases) that are present, or frictionally generated heat is employed to this effect. The ultimate driving force is the temperature gradient, but this can be moderated by, for example, the concentration gradient of any vapour phase or gaseous reaction product, or by the thermal properties of the diffusing substance in its transformed state. Natural examples of several of these mechanisms are easily found. The solution of halite or gypsum from a rock surface exposed to a stream of water illustrates the first mechanism. Ice can sublime in air, exemplifying the third mechanism. The most important natural instance of the second mechanism is the dissolution of calcium carbonate, the chief constituent of carbonate rocks, into water containing dissolved carbon dioxide. The process (Fig. 6-1) involves the solution of calcium carbonate at the solid-liquid interface and its reaction to form calcium bicarbonate, with carbonic acid produced elsewhere in the system at an air-water interface (Curl, 1968; Roques, 1969). Since the aggressive species in this complex reaction is the carbonic acid, the transfer rate is seldom controlled by the solubility of the calcium carbonate itself (in the absence of reactants). The fourth and fifth

WATER H 2 0

.. . . . 'AIR

:cop

'_'

'1.1 .1 x \

. . . . . . .. .. ..

(Cop)

(HCO;)

(OH-)

H20

H

I \ \ \ \ \ \ \ \

Fig. 6-1. Summary of limestone dissolution into a thin film of water in the air. After Roques (1 969).

210

mechanisms are illustrated by the melting of ice in water to give ripple-like forms on the undersides of river ice-covers, and meandering channels on the surfaces of glaciers. When tektites and meteorites enter the Earth’s atmosphere, the aerodynamic heating apparently produces on the outside of the body a thin layer of melted material which then partly vapourizes, perhaps to the accompaniment of oxidation reactions. A combination of ablation mechanisms is involved. There are two possible scales for heat and mass transfer. Transfer is on a molecular scale, by conduction (heat) or in an analogous manner (mass), in laminar free and forced convection. The transfer rate is correspondingly very small. Much higher transfer rates are possible in a turbulent fluid, however, because of the movement of eddies transversely across the flow (e.g. Hanratty, 1956; Toor and Marchello, 1958; Sirkar and Hanratty, 1970). Generally, the transverse turbulent fluctuations of larger scale and lower frequency are the most effective in heat and mass transfer. They sweep contaminated fluid in bulk from the flow boundary to far-distant stations, in the process bringing fresh fluid to the interface supplying the mass or energy. The transfer rate in turbulent flows therefore depends strongly on the average time that a quantity of fluid spends in contact with the flow boundary. The bursts and sweeps present in the inner parts of the turbulent boundary layer (Vol.1, Chapter6) must be amongst the chief agents of transfer in turbulent forced convection. In turbulent free convection eddies related to the rolling-up of free shear-layers could play the decisive role. CONTROLS ON HEAT AND MASS TRANSFER

Coefficients and parameters The rate of mass or heat transfer in any system can be expressed in terms of properties of the system and of the materials involved (Knudsen and Katz, 1958; Kreith, 1965; J.T. Davies, 1972). If we measure a mass-transfer rate of RM moles per square metre per second in a system in which the concentration difference of the diffusing substance is AC moles per cubic metre, then: in which k M is a mass-transfer coefficient having the dimensions of velocity. Assuming steady-state conditions, the mass-transfer rate is also related to the concentration gradient, through Fick’s law of diffusion: dC RM=-D (6.2a) dY dC R M = - ( D M + D )(6.2b) ME dy

21 1

in which y is distance normal to the flow boundary supplying the diffusing substance, D, is the molecular diffusivity of mass, and DME is the eddy diffusivity of mass. The negative sign is used because the transfer-rate is positive in the direction of decreasing concentration. Similarly, if we measure a heat-transfer rate of R H joules per square metre per second in a system in which the temperature difference in degrees Kelvin is AT, then by Fourier's law, assuming steady-state conditions: (6.3a)

R,=-(K,+K

HE

dT dy

)-

(6.3b)

in which KH and K,E are the thermal conductivities of the fluid phase in joules per square metre per second per degree Kelvin under stagnant/laminar and turbulent conditions, respectively. Clearly, eq. (6.3) corresponds exactly to eq. (6.2) for mass transfer. To obtain a formal analogy between the two, we divide eq. (6.3) by pc, where p is the fluid density and c is the heat capacity of the fluid phase in joules per kilogram per degree Kelvin: (6.4a) (6.4b) where KH/pc and KHE/pc are thermal diffusivities:

with the same dimensions as the diffusivities of mass. By writing: -R H - -kHAT PC

analogous to eq. (6.1), the heat flux can be related to a heat-transfer coefficient k, corresponding to the mass-transfer coefficient k,. The diffusivities D , and D , are molecular diffusivities depending only on the materials forming the system. For example, the mass diffusivities of calcium bicarbonate in water at 10°C (Curl, 1966b) and of sodium chloride in water at 20°C (Coulson and Richardson, 1965) are 6.6 X 10-"m2s-' and 1.35 X 10 m2s - I respectively. Coulson and Richardson ( 1965) quote the mass diffusivt) of water vapour into air at 25OC as 2.56 X 10-'om2s-'. Kreith (1965) and Bayley et al. (1972) give extensive tables of the thermal properties of common substances. In contrast, the eddy diffusivities, DME and DHE,are not constant, but depend on the properties of the system, particularly the Reynolds number. They should be orders of magnitude larger in value than the corresponding molecular diffusivities.

-'

212

The relationships sketched above can be extended analytically with such difficulty that it has long been usual to solve problems of heat and mass transfer with the help of empirical correlations based on dimensional considerations (e.g. Knudsen and Katz, 1958; Kay, 1963; Kreith, 1965). The choice of variables for non-dimensional groupings in heat transfer is made from the following: in which U and L are a velocity and length characteristic of the system, g is the acceleration due to gravity, 77 and p are the fluid viscosity and density, respectively, k,, is the coefficient of thermal expansion of the fluid, DH is the molecular thermal diffusivity of the fluid, AT is the temperature difference, and k H is the heat-transfer coefficient it is desired to calculate. The corresponding list for mass transfer reads:

u,L , g , T , p , Ac,D M , k M in which AC is the concentration-difference in the system, DM is the molecular mass diffusivity characteristic of the combination of substances, and k M is the desired mass-transfer coefficient. Buoyancy forces can generally be neglected during forced convection, whereupon we obtain for heat transfer the groupings

NU=-kHL , R e = - ULP , P r = - 17

DH 17 pDH in which the Nusselt number, Nu,is a non-dimensional form of heat-transfer coefficient, the Reynolds number compares inertial with viscous forces, and the Prandtl number, Pr, compares the molecular momentum diffusivity with the molecular thermal diffusivity. The corresponding non-dimensional groups for mass transfer are:

S h = -kML , R e = - ULP , sc=- 17 DM 17 pDM in which the Sherwood number, Sh, is a non-dimensional mass-transfer coefficient and the Schmidt number, Sc, compares the molecular momentum diffusivity with the molecular mass diffusivity. Hence the transfer coefficient depends on the character of the system, as described by Reynolds number, and on the materials involved, represented by the Prandtl or Schmidt numbers. Essentially, the Prandtl and Schmidt numbers compare the growth of the velocity boundary layer with the thermal and mass boundary layers. When Pr = 1 and Sc = 1, the boundary layers are equal in thickness and develop at the same rate. If Pr > 1 and Sc> 1, however, the velocity boundary layer is the thicker and the faster to develop. Instead of the Nusselt and Sherwood numbers, the groups k H / U(Stanton number, S t ) and k M / Uare commonly used in correlations.

213

Buoyancy forces cannot be neglected in free convection, since fluid motion occurs because of density differences created by the temperature or concentration gradient. The customary groupings now are, for heat transfer:

NU=-k n L , GrH= k TE L3ATgp2 , P r = DH

v2

v

PDH

and, for mass transfer:

in which Gr is a Grashof number and A p is the density-difference. Note that the product of GrHwith Pr is the Rayleigh number encountered in Chapter 1. The corresponding mass-transfer Rayleigh number is formed by the product GrM.Sc. The Grashof number compares the product of buoyancy and inertial forces in the system with viscous forces.

Analogy between momentum, heat and mass transfer Osbome Reynolds (1874, 1883) proposed that the mechanisms of momentum transfer and heat transfer are the same, and the analogy has since been extended to mass transfer. For example, eqs. (6.2a) and (6.2b) are of the same form, a flux being given as the product of a diffusivity with a “concentration” gradient. For comparison, the equation of momentum transfer under the simplest conditions of laminar flow is:

in which T is the momentum flux, and v is the kinematic viscosity, otherwise the molecular momentum diffusivity. The laws of momentum, heat and mass transfer are the same. Hence if we know the laws governing momentum transfer, commonly expressed as relations involving friction coefficients, we can immediately use the analogy to calculate mass and heat transfer rates. The power of Reynolds’ analogy has continued t o attract investigators, who have extended and refined his work (e.g. Chilton and Colburn, 1934; Sherwood, 1940; knudsen and Katz, 1958; Gamer et al., 1959; Kay, 1963; Kreith, 1965). At its simplest, the analogy is:

(6.7) where f is the Darcy-Weisbach friction coefficient, valid only when Pr = Sc = 1. Many important turbulent systems do not meet these conditions, so that the analogy is more difficult to state (Sherwood, 1940; Knudsen and Katz, 1958). For example, although the Prandtl number of air is 0.69 under ordinary conditions, thus broadly satisfying eq. (6.7), that of water is 7.0

214

(J.T. Davies, 1972). The Schmidt number for sodium chloride in water at 20°C is 745 (Coulson and Richardson, 1965) and for calcium bicarbonate in water at 10°C is 1985 (Curl, 1966b). The simple analogy cannot apply under such conditions, for the thermal and mass boundary layers are now very much thinner and slower to develop than the velocity boundary layer. Laminar boundary layer on a flat surface The local rate of heat and mass transfer from a laminar boundary layer developing on a flat surface is known theoretically to be determined by, in mass-transfer terms: (6.8a)

Sh, = 0.332S~‘/~Re;/~

(6.8b)

where the Sherwood and Reynolds numbers employ the streamwise distance x from the start of the boundary layer (Fage and Falkner, 1931; Knudsen

and Katz, 1958; Kay, 1963; Kreith, 1965; Bayley et al., 1972). So long as the flow is sufficiently thick that the boundary layer can go on developing, the local mass-transfer rate declines with increasing distance along the surface. Theories of mass transfer to thin films of fluid are explained and justified experimentally by Kramers and Kreyger (1956), Atkinson and Taylor (1963), and Oliver and Atherinos (1968). The local mass-transfer rate is again a decreasing function of streamwise distance. Turbulent boundary layer on a frat surface The heat or mass transfer to a turbulent boundary layer on a smooth flat surface is given by the simple Reynolds analogy (eq. 6.7) only when the Prandtl or Schmidt number equals unity (Kay, 1963; Kreith, 1965; Bayley et al., 1972; J.T. Davies, 1972). It follows from the equation for the local friction coefficient in a turbulent boundary layer that the local rate of transfer declines with increasing streamwise distance. The rate of decline, however, is more gradual than in a laminar boundary layer, and the transfer proceeds much more rapidly for the same Reynolds number. The simple analogy for smooth surfaces was modified by L. Prandtl, G.I. Taylor, T. von K h h and many others in an attempt to overcome its restrictions (Knudsen and Katz, 1958; Kay, 1963; Kreith, 1965; Bayley et al., 1972; J.T. Davies, 1972). The Prandtl-Taylor analogy rests on the idea that the turbulent boundary layer comprises two layers, an inner viscous one, and an outer fully turbulent part. Von Karman’s modification uses a three-layer structure, of viscous sublayer, buffer layer, and an outer fully turbulent layer. In mass-transfer terms, this analogy is written as: -kM-

1

+

f/8 5( f/8)’l2( (Sc - 1) In[ 1

+

+ d( Sc - l)]}

215

where f is the local value. Sherwood and Ryan ( 1959) find the Von Kiumhn analogy unsatisfactory, and Greenwald (1972) points out that, so far as mass transfer is concerned, the properties of the boundary layers are inevitably modified as the result of mass transfer. Kader and Yaglom (1972) give the following equation, rewritten here for mass transfer: Sh, =

Rex(f/W’ 2.12 ln(Rexf) 12.5Sc2l3 2.12 In Sc- 7.2

+

+

(6.10)

for the local transfer rate from a smooth surface. Agreement with experiment is excellent. Much less is understood of transfer from rough flat surfaces into turbulent boundary layers. Yaglom and Kader (1974) and Kader and Yaglom (1977) give a complex but general expression which is well-supported experimentally, and Brutsaert ( 1975) describes a comprehensive theoretical model. For transfer from surfaces with a wavy roughness into air, the equation: (6.11) developed by Verma and Cermak (1974a, 1974b), is useful. Here ShH is the Sherwood number based on the wave-height H, and U* is the shear velocity. The transfer rate from a rough surface is substantially greater than from a smooth surface under comparable flow conditions, provided that the roughness elements do not penetrate the viscous sublayer. Luminarflow in a conduit There are two parts to the problem of transfer to a laminar flow in a closed conduit of finite length and arbitrary but uniform shape, a problem named after Graetz (1885), its first investigator. The entrance region, in which the transfer boundary-layer is still developing, must be separately considered from the fully-developed region, where the transfer boundarylayer fills the conduit. General surveys of these topics are given by Knudsen and Katz (1958), Kay (1963), Kreith (1965), Kays (1966), and Bayley et al. (1972). A representative experimental study is by Linton and Sherwood (1950), and a theoretical one is given by Sellars et al. (1956). In the entrance region, the local heat or mass transfer rate gradually declines with increasing streamwise distance, as the boundary layer progressively thickens. The rate in the fully-developed region is constant and depends only on conduit Reynolds number. Turbulent flow in a conhit The problem of transfer to a turbulent flow in a conduit is similarly bipartite. It is thoroughly reviewed by Knudsen and Katz (1958), Kay

216

(1963), Kreith (1965), Kays (1966), Bayley et al. (1972), and J.T. Davies (1972). Important experimental and theoretical studies of transfer in smooth tubes at large Prandtl or Schmidt numbers are given by Linton and Sherwood (1950), Levich (1962), Marangozis et al. (1963), Kolar (1965), Lawn (1969), Sleicher et al. (1970), Mizushina et al. (1971), Notter and Sleicher (1971a, 1971b, 1972), Kader and Yaglom (1972), and Pinczewski and Sideman ( 1974). The local transfer rate declines with increasing streamwise distance in the entrance region but is constant in the fully-developed part. Levich proposed a correlation for turbulent flow in very rough circular conduits. It was confirmed experimentally by Mahato and Shemilt (1968), who gave the formula: S h , = 13.4

+ 0.125( f/4)”4Re1,(d/k)1’2

(6.12)

for the fully-developed region, where the Sherwood and Reynolds number employ the conduit diameter d and k is the equivalent sand roughness height. Note that the transfer rate now declines with increasing roughness, in contrast to the increase possible when the roughness elements lie within the viscous sublayer. Kolar (1965) and Dawson and Trass (1972) also discuss transfer from rough surfaces. Free convection

Correlations are here achieved using the Rayleigh number alone, or the corresponding quantity formed as the product of the Grashof with the Prandtl or Schmidt number. There is, however, a wide choice of boundary conditions. The most general problem is that of the free convection induced by heat and/or mass transfer from an inclined interface of infinite extent which may face either downward or upward (J.S. Turner, 1973). If transfer increases the density of the fluid near the interface, then a downward flow along the surface should occur whether the surface faces upward or downward. Similarly, if the fluid density near the surface is lowered, the fluid should stream upward along the surface, regardless of the facing of the surface. Free convection from vertical and horizontal surfaces then become limiting cases of this general problem. Most work has been done on laminar free convection from horizontal surfaces. Bandrowski and Rybski (1976) give a theory of mass transfer from upward-facing and downward-facing plates of finite extent, and Sani (1965) reports a theoretical study of combined heat-with-mass transfer. Heat transfer from finite plates is considered by Clifton and Chapman (1969). Several investigations of mass transfer from horizontal surfaces have been made (e.g. Fenech and Tobias, 1960; Husar and Sparrow, 1968; Wragg, 1968; Wragg and Loomba, 1970; Goldstein et al., 1973; Lloyd and Moran, 1974). In the case of finite horizontal plates, the overall Sherwood number is correlated

217

with the Rayleigh number by:

Sh = 0.54Ra’I4

(6.13)

where the length term in these numbers is the plate area divided by perimeter (Lloyd and Moran, 1974). In turbulent free convection, the coefficient in eq. (6.13) becomes 0.13 and the exponent 1/3 (Lloyd and Moran, 1974; Long, 1976); bursts and sweeps (Vol. I, Chapter 6) can be observed (Perry and Hoffmann, 1976). Convection in horizontal layers of fluid cooled from above was studied by Spangenberg and Rowland (1961) and by Berg et al. (1966). Free convection at inclined surfaces has attracted but little attention (Sparrow and Husar, 1969; Lloyd and Sparrow, 1970), despite its generality.

HEAT AND MASS TRANSFER IN SEPARATED LOW-SPEED FLOWS

An important case of separation in external flows arises during fluid motion around a sphere or cylinder. Many workers have studied heat transfer from single spheres and circular cylinders (e.g. Paltz et al., 1931; Small, 1935; Schmidt and Wenner, 1941; Giedt, 1949; Eckert and Soehngen, 1952; Aufdermauer and JOSS, 1967; Galloway and Sage, 1968; J.S. Lewis, 1971), and the parallel case of mass transfer has also attracted attention (e.g. Garner and Grafton, 1954; Hsu and Sage, 1957; Garner and Suckling, 1958; Garner et al., 1959; Garner and Keey, 1959; Linton and Sutherland, 1960; Galloway and Sage, 1968). The local transfer rate (Fig. 6-2a) rises to. two maxima, at the forward attachment point/line (stagnation point/line), and where the separated flow reattaches downstream. It is a minimum close to separation, the position varying with Reynolds number. The overall transfer rate grows with increasing Reynolds number, harmoniously with a decline in

1

Reynolds number order 105-106

r 0

c

e

0

1 0

ReattaFhment !

CJ‘ 0

0

45

135 angle (degrees)

90 Polor

180

Distance from edge of step (separation)

Fig. 6-2. Schematic variation in local rate of mass transfer (a) at a circular cylinder at right angles to a fluid stream, and (b) at a two-dimensional negative step.

218

the relative importance of transfer from upstream of separation as compared with the region downstream. A certain amount is known about heat transfer from separated flows at cavities and downstream-facing steps. Chapman ( 1956) showed theoretically that in laminar flow the overall heat transfer rate from a cavity is less than the rate from the corresponding boundary-layer flow, a result reminiscent of external flows at low Reynolds numbers (Fig. 6-2a). Experimental studies of heat transfer from separated flows in cavities show that the local rate of transfer is largest close to reattachment, in agreement with Burggraf's (1966a, 1966b) theory, the rate generally exceeding by several times that in the corresponding boundary-layer flow (Seban and Fox, 1963; Jarrett and Sweeney, 1967; Fenton and White, 1971). Spalding (1967) tackled the difficult problem of turbulent heat transfer from the separated flow at a downstream-facing step. His conclusion (Fig. 6-2b) that the local rate peaks close to reattachment, and that this maximum exceeds by several times the value in the corresponding attached boundary layer, is amply justified experimentally (Ede et al., 1956; Seban, 1964; Filetti and Kays, 1966; Krall and Sparrow, 1966; Zemanick and Dougall, 1970). However, the degree to which the maximum rate exceeds the boundary-layer value apparently declines with increasing Reynolds number and relative step-height. Under turbulent conditions, the overall transfer-rate from the separated flow at a step also exceeds the corresponding attached boundary-layer value, a result harmonious with observations from external flows at large Reynolds numbers (Fig. 6-2a). Seban and Caldwell (1968) found that the effect on heat transfer of a sphere mounted on a smooth surface was similar to that of a downstream-facing step, the maximum local rate of transfer in the separated region exceeding that in the adjacent boundary layer. HEAT AND MASS TRANSFER IN HIGH-SPEED FLOWS

The nature of heat and mass transfer in high-speed flows is important to an understanding of the surface sculpturings and in some cases the shapes assumed by meteorites, tektites, and space-vehicles during their journey through the Earth's atmosphere. Mass and heat transfer under these conditions obey similar laws to the low-speed case, but with complications linked to aerodynamic heating at large relative velocities, the dissociation of the atmospheric gases at high temperatures, and the rarified nature of the high atmosphere. Kreith ( 1965) helpfully sketches this field, and Spalding ( 1961) surveys most of the mechanisms of heat-with-mass transfer that are involved. Transfer in flows of boundary-layer type has been much studied (e.g. Thomas and Whipple, 1951; Gadd et al., 1958; G.W. Sutton, 1958; Bethe and Adams, 1959; McFarland and Harmon, 1961; Spalding, 1961). Many analyses explore the stable shapes assumed by axisymmetric bodies as the result of heat transfer through a boundary layer (Christensen and Buhler,

219

1959; G.W. Sutton, 1959; Kubota, 1960; Turcotte, 1960; Simpkins, 1963;

D.T. Williams, 1963a, 1966; Karashima et al., 1968; Welsh, 1970; Lipfert and Genovese, 1971). This shape is a parabola, the local radius of the body being a power function (exponent of order 0.5) of the axial distance from the nose (stagnation point) where the mass-transfer rate is a maximum. Under high-speed as under low-speed conditions, the local heat-transfer rate in a cavity is greatest near to reattachment on the downstream wall, where it exceeds the rate in the corresponding attached boundary-layer flow; the overall rate ordinarily exceeds that in the boundary layer only in turbulent flows (Larson, 1959; Thomann, 1959; Charwat et al., 1961b; Burggraf, 1966a, 1966b; Hahn, 1969; Nestler et al., 1969; Hodgson, 1970; R.A. White, 1971). High-speed heat transfer at steps is qualitatively like that in low-speed flows. At upstream-facing steps the local rate is a maximum close to where the flow attaches on the forward-facing surface (Thomann, 1959; Nestler et al., 1969; Inger, 1972). The local rate at downstream-facing steps peaks near to reattachment, where it usually exceeds by several times the corresponding boundary-layer value (Gadd et al., 1958; Carlson, 1959; Naysmith, 1958, 1961; Thomann, 1959; Scherberg and Smith, 1966; Sandford and Ginoux, 1968; Back et al., 1972; Lamb and Hood, 1972). An isolated protuberance on a flat surface locally enhances the transfer rate (Bloom and Pallone, 1957).

INSTABILITIESACCOMPANYING MASS OR HEAT-WITH-MASS TRANSFER

A flow causing mass transfer or heat-with-mass transfer can shape its boundaries into rhythmically arranged mounds and hollows only if an initially unstable interaction occurs between surface irregularities and the local flow properties that control the local transfer-rate. That such interactions should arise is suggested by the discovery that both the local transferrates and, for example, the local turbulence intensity, lag downstream changes of bed-shape (Seban and Dougherty, 1956; Back et al., 1964; Moretti and Kays, 1965; Graham and Deissler, 1967; Ashton, 1972a; Ashton and Kennedy, 1972). Where a turbulent flow expands and decelerates, the local intensity of turbulence rises, and with it the local rate of mass or heat transfer. The opposite effect accompanies acceleration. Hence the problem of bedforms arising because of mass or heat transfer resembles in essence that of the production of bedforms during the transport of solids, extensively discussed in Vol. I, Chapter 7. Here we saw that stable wavy beds can exist only if particular degrees of lag arise between the bed shape, the local flow properties, and the local sediment transport rate dependent on those properties. Our present problem differs mainly in that, as there is no granular transport, the bed can respond only by erosion.

220

' ( b ) CLASS

Downstream distance

' ( c ) CLASS

B

.

Downstream distance ( d ) CLASS D

C Moss transfer

Downstream distance

Mass transfer

Downstream distance

Fig. 6-3. Development of transverse bed waves by mass transfer into a unidirectional stream.

First consider transversely arranged sinusoidal bed waves on a surface undergoing mass transfer beneath a unidirectional stream (Fig. 6-3). Assume that the local mass transfer-rate also varies sinusoidally downstream, on the same wavelength as the bed features but not necessarily on the same phase. By considering Fig. 6-3 we see that bed waves are damped when 0 < 6 < 77/2 and 377/4<6<27~, where 6 is the phase difference between the bed and mass-transfer waves, but augmented when 77/2 < 6 < 377/4 (Table 6-1). For bed waves to grow in amplitude or be stable, the transfer rate must peak somewhere in the troughs, the features moving upstream if the maximum lies upstream of the trough-point but downstream if the maximum occurs downstream. Most known bed waves match Class C in Table 6-1. Analyses to establish the phase relationship between the bed and mass-transfer waves, and therefore the stability of bed undulations, have been made for ice ripples by Ashton (1972a) and Ashton and Kennedy (1972), and for cross-hatching (bedforms resembling rhomboid ripple marks) on space-vehicles by Inger (1969, 1972), Inger and Williams (1972), and several others (see Swigart, 1974). See Hanratty (1981) for another review. Table 6-1 is for a two-dimensional bed, but we can perhaps extend the underlying analysis to the case of a channelized flow in a substrate subject to mass transfer, when meandering should occur by analogy with granular beds (Chapter 2). Vertical undulations are now accompanied by undulations in the horizontal plane, but at twice the wavelength.We find that meanders travelling downstream can arise only when the maximum of the larger of the two local values of the horizontal mass transfer rate occurs in the downstream part of each bend (as there are two banks at each station, there are two local values of ,the transfer rate but, because of secondary flow, one of these values is the larger). If as well there are stable vertical undulations on

22 1 TABLE 6-1 Stability and response of a wavy bed undergoing mass loss through melting or solution

Class

A

Phase difference between bed and mass-transfer rate

Bed feature celerity

6=0

c=o

O<S
c
6 =n/2

B

n/2<6
CCO

Rate of change of amplitude of bed feature

do dt da =O dt da - >o dt -( 0

Physical interpretation

Damping Neutrally stable Augmenting ? N o known bed waves

C

6=n

c=o

n <6 <3a/4

c>o

da dt

-> O

Augmenting Bed waves known

6=3n/4

D

3n/4<6<2n

c>O

da dt da

-= O

Neutrally stable

-(

Damping

dt

0

the bed, expressing the occurrence of pools and crossing, we should expect from Table 6-1 a crossing in the upstream half of each bend and a pool in the downstream half. Rayleigh-Taylor instability should commonly accompany mass transfer and mass-with-heat transfer, since each causes local changes in fluid density. Spangenberg and Rowland (1961) and Berg et al. (1966) demonstrate convection in horizontal layers of fluid cooled from above; the occurrence of convection when horizontal fluid layers are heated from below is well known. A fluid into which there is mass transfer from a horizontal roof seems comparable with the cooled fluid layer. Streamers of fluid dense with dissolved solute should descend at regular intervals from this ceiling into the less dense fluid below, the streamers originating at separation points at which the roof should retreat less than at the attachment points between. Sparrow and Husar (1969) and Lloyd and Sparrow (1970) show the occurrence of instabilities during convection from inclined heated surfaces facing upward. Transverse waves existed in the stream of warmed fluid at inclinations of the surface in excess of 76" from the horizontal, but at lower slopes there arose paired longitudinal vortices. Descending but otherwise similar

222

Fig. 6-4. Transverse flow patterns likely to accompany development of longitudinal features as a consequence of Lamb-Taylor instability.

waves or vortices should form during mass transfer from inclined downwardfacing surfaces. By analogy with heat transfer in the presence of TaylorGortler vortices (McCormack et al., 1970), the largest mass-transfer rates should occur where limiting streamlines diverge. Lamb-Taylor instability, a variety of gravitational instability, affects bodies decelerating in the Earth’s atmosphere if they partly melt to give an outer liquid layer. The gas-liquid interface can become unstable, the motion in the fluid layers taking the form of paired longitudinal vortices, even when the adjacent solid surface is convex (Feldman, 1959). The largest rates of mass transfer occur where streamlines on the gas-liquid interface diverge and the liquid layer is thinnest (Fig. 6-4). The resulting longitudinal bed waves are stable and stationary only if the local rate of mass transfer becomes uniform over the surface. CLASSIFICATION OF KA RREN

Karren are organized morphological features resulting from the. dissolution of soluble rocks, of which limestone, dolomite, halite and gypsum are the most important. Closely allied to them in morphology and origin are pseudokarren, formed under certain conditions during the weathering of igneous rocks and some sandstones. The early work of Heim (1878), Chaix (1894, 1904), Eckert (1900), Chaix and Chaix (1907), Cvijic (1924), Lindner (1930), and So& (195 1, 1960) led to the classifications of limestone and dolomite Karren advanced by Bogli (1961) and Bauer (1962), and summarized by Jennings (1971), Sweeting (1972), and Bogh (1978). These classifications recognize not only the mor-

223

phological differences between Kurren but emphasize the influence of such environmental factors as lithology, geological structure, altitude and aspect, the amount and distribution of the precipitation or stagnant or flowing water causing the dissolution, and the presence or absence of a soil or organic cover. The difficulties that these classifications afford in practice stem from the fact that Kurren, like many other kinds of sedimentary structure, are hierarchically organized, with small forms occurring on larger ones, and TABLE 6-11 Classification of Karren Spi?z&arren

Inland form I

Solution boslns (kameni?zasl

Y

I

sE

k

I

Rlnnsnkarren

Tri??karren

I Rundkorren

I"

\

224

these commonly on larger ones still. The difficulties are only partly avoided by Bogli’s (1961) separation of simple forms from complexes of forms, or by Pluhar and Ford’s (1970) distinction between features of “larger” and “smaller” scales. An explicitly hierarchical classification seems desirable. Table 6-11 presents a classification of Karren, in which the commoner forms are divided between three orders on the basis of superimposition and general scale. The smallest Karren, with dimensions typically in the order of 0.01-0.1 m, are those of the third order. The first-order Karren are the largest, with dimensions ordinarily or 1- 10 m; typically, they are accompanied by forms representing a lower order or orders. FIRST-ORDER K A R R E N

Flachkarren Several well-illustrated accounts of these have been published, chiefly from European localities (Corbel, 1957; Parry, 1960; R.J. Jones, 1965; Packer, 1965; Sweeting, 1966, 1974; P.W. Williams, 1966; T.M. Thomas, 1970; Goldie, 1973; Purdy, 1974; Schunke, 1976). These Karren comprise flat-topped blocks of rock bounded on all sides by solution-widenedjoints or

Fig. 6-5. Fluchkurren (with Rundkurren) in level-bedded Carboniferous Limestone, Malham Tam, Yorkshire. Joint spacing order of 1.5-3 m.

225

fractures (Fig. 6-5). The blocks, combined into limestone or dolomite pavements, are square to rectangular or diamond-shaped in plan, depending on the fracture or joint pattern affecting the strata. The dimensions of the tops of the blocks are fairly constant at any one site but, as Goldie found, vary between sites partly under a lithological control. At some sites, the sides of the blocks are measured in decimetres, whereas elsewhere the blocks are several metres long. The tops of the blocks vary in character. In the British Isles (e.g. Parry, 1960; Sweeting, 1966), the rounded grooves known as Rundkarren are normally found on the tops, though in exposed areas, such as parts of the Burren in Ireland (P.W. Williams, 1966), only a pitting may be present. Roughly pitted tops seem characteristic of Grecian and Alpine Fluchkurren (Bogli, 1961; Schunke, 1976). Packer (1965) reported large pock-marks from forms developed on dolomite beds. Purdy (1974) emphasized and extended an earlier observation of Smith and Albritton (1941) that many Fluchkarren are slightly concave-up, the top of each block having a raised though commonly breached rim. It is not nowadays disputed that Flachkurren are the result of dissolution, though it is recognized that some of the features originated not from bedding surfaces but from surfaces of erosion, for example, glaciated pavements. Only those forms with rough pitted tops have clearly formed through direct exposure to rain or snow-melt, in some instances after the removal of a protective cover of till from a rock surface (P.W. Williams, 1966). Although examples marked by Rundkarren have also been attributed to dissolution directly beneath the atmosphere (e.g. Parry, 1960; Purdy, 1974), most workers believe that Fluchkurren of this kind arose beneath a cover of soil or peat (e.g. R.J. Jones, 1965; P.W. Williams, 1966; Sweeting, 1966, 1972, 1974). Purdy rejected Sweeting’s (1 966) interpretation because, in small-scale experiments, he could give the top of a limestone block a raised but breached solution rim by directly exposing it to acid rain, provided that the fluid accumulated as one or more meniscus-bounded pools. However, the essence of Purdy’s effect seems to me to lie in the fact that the acid liquid so acts on the block as to tend to drain from its top at just one or two points along the rim. The rim is rapidly lowered at those points while the remainder gradually becomes a drainage divide. There are no physical reasons why the same effect should not occur on the top of a block of rock buried under a shallow soil; except when the ground was thoroughly soaked, the water-table trapped by the block would be convex-up, like Purdy’s meniscus, with a similar tendency to drain radially and to exploit points of weakness on the rim. In conclusion, it is doubtful if Fluchkurren can be precisely interpreted in every case. Many occur in places where there have been substantial changes of climate and land-use over the period likely to have been involved in their formation.

226

Kluftkarren

These are widened joints or fractures associated with Flachkarren or with Spitzkarren (Fig. 6-6). They are typically 0.2-0.5 m wide at the top and 1-2 m deep, but exceptionally reach a width of 3 m and a depth of 22 m (Eckert, 1900; Chaix, 1904; Lindner, 1930; Lattman and Olive, 1955; Parry, 1960; Bogli, 1961; Howard, 1963; Packer, 1965; R.J. Jones, 1965; Sweeting, 1966; P.W. Williams, 1966; Pluhar and Ford, 1970; T.M. Thomas, 1970; Cooke, 1973; Schunke, 1976; Wirth, 1978). The cleft tapers downward linearly only when the maximum width is very small compared with the depth; the wider and deeper examples taper with an obvious trumpet-like flare. Kluftkurren are generally associated with smaller structures (Fig. 6-7), typically either Rillenkarren or Rinnenkarren (Table 6-11) accompanied by cockling or solution ripples (e.g. Bogli, 1961; Jennings, 1971; Pluhar and Ford, 1970; Cooke, 1973). Where Rundkarren mark adjacent Flachkarren, large vertical grooves, occurring singly or a few close together, descend the walls of the cleft (e.g. Sweeting, 1966, 1972, 1974). At some sites the clefts are filled to the top with soil (Lattman and Olive, 1955; Howard, 1963), at others reveal soil and growing plants only at the bottom (e.g. Parry, 1960), and in still other places seem empty.

Fig. 6-6. General view of Kfuftkurren, Carboniferous Limestone, Malham Tam area, Yorkshire. Note horizontal solution ripples on walls of the widened joints. Rucksack gives scale.

221

Fig. 6-1. View obliquely down into Kluftkarren (note convex sides) associated with Rinnenkurren and, on the horizontal surface (with hammer 0.35 m long). Rundkarren. Carboniferous

Limestone, Malham Tarn, Yorkshire.

Whether developed on bare rock or beneath soil, Klufrkarren are shaped by water descending largely from the level of the intervening Flachkarren. The downward-tapering form of the clefts shows that ( 1) differential dissolution is involved, and (2) the local temporal-mean rate of dissolution declines downward over the walls, the largest values occurring at the top. In addition, the convexity of the walls of well-developed Klufrkarren indicates that the rate is a weakly non-linear function of the downward distance. Hence we may compare the dissolution of the limestone or dolomite bounding a cleft with the response of a soluble bed of finite length to a boundary-layer flow developing with increasing distance along the bed. Whether the boundary layer is laminar, eq. ( 6 . Q or turbulent, eqs. (6.9, 6.10), the local rate of mass transfer declines with increasing streamwise distance, the rate decreasing

228

rapidly at small distances but more gradually over the larger ones. The fact that in practice dissolution takes place into a thin film of water streaming down the rock surface is not an objection to the use of these equations as models. Since the Schmidt number is large, the mass-transfer boundary layer should be thinner than the water film over the first few metres of the flow. At greater depths within the cleft, however, one of the thin-film models would be preferable (Kramers and Kreyger, 1956; Atkinson and Taylor, 1963; Oliver and Atherinos, 1968). Spitzkarren

These are assemblies of upward-pointing pyramidal to projectile-shaped bodies of rock separated by interconnected clefts or, in some instances, basin-like depressions (Table 6-11). Individual pinnacles seldom exceed 2 m across at the base, but can be grouped to form much larger complexes. Spitzkarren formed from carbonate rocks occur in three distinct settings: ( 1) on bare rocks in inland, particularly mountainous, karst areas, (2) beneath a soil cover in inland karst, and (3) on coastal carbonate rocks exposed in the intertidal zone and a little above. Similar features occasionally arise during the weathering of granite (Klaer, 1956). The ablative ice-forms known as penitentes much resemble Spitzkarren (Seligman, 1936; Lliboutry, 1964, 1965).

Fig. 6-8. Spitzkurren,Akiyoshidai, Japan. Photograph courtesy of M.M. Sweeting.

229

Figure 6-8 illustrates Spitzkarren from bare inland rocks (Eckert, 1900; Cvijic, 1924; Bogli, 1961, 1978; Jennings and Sweeting, 1963; Wilford and Wall, 1965; Chinese Academy of Geological Sciences, 1970; Corbel and Muxart, 1970; Sweeting, 1972, 1979; Rossi, 1976; Longman and Brownlee, 1980). Jakucs ( 1977) figures similar structures from exposed halite. The forms resemble pyramids or upturned projectiles. Their steep sides comprise several convex to flat facets intersecting at sharp ridges that culminate upward in one or a few peaks. The facets usually carry Rillenkurren and, commonly, solution ripples as well (Table 6-11). Spitzkarren formed beneath a soil are less regular than those produced in the open and lack sharp-edged facets (Bauer, 1962; Howard, 1963). Their shapes are much smoother and more rounded; steeply inclined Rundkarren may be recognizable. Those formed on coastal limestones are the least regular of all (Guilcher, 1953, 1957, 1958b; Tracey et al., 1964; Blackburn et al., 1965; Coetzee, 1975; Rigby and Roberts, 1976; Ley, 1979). As shown in Fig. 6-9, coastal Spitzkurren are jagged, pyramidal masses of rock with locally overhanging sides roughened by cockling or irregular pits. Flat-bottomed solution basins more commonly lie between these pinnacles than between the other kinds of Spitzkarren. The pinnacles can attain 1 m in height but are generally shorter. The end-product of the growth of Kluftkarren, and the attendant narrow-

Fig. 6-9. Small Spitzkarren developed on moderately dipping Carboniferous Limestone, Gower coast, Wales.

ocz

230

Fig. 6- 10. Schematic evolution of Spitzkorrenfrom a jointed limestone (or other soluble rock) subjected to seepage or precipitation.

ing of the Fluchkurren between, could be the Spitzkarren of bare or soilcovered rocks (Fig. 6-10). Similarity of process and physical environment, as well as similarly of form, may therefore exist between Spitzkarren and the terminal shapes of prismatic bodies ablated in axially symmetric flows. With the rock structures, water originating from above essentially acts axially upon rectangular fracture-bound prisms of limestone, creating pyramidal to projectile-shaped forms. When prismatic bodies are ablated experimentally (Christensen and Buhler, 1959; D.T. Williams, 1963b), the intermediate shapes take flat leading faces and convex sides, like Fluchkarren and Kluftkarren, and the terminal forms sharp cusps. We cannot press this model too far, however, for many coastal Spitzkurren, and some inland forms, have been partly shaped by the downward and lateral growth of solution basins (Table 6-11). SECOND-ORDER K A R R EN

Solution basins These are formed on level to gently sloping rock surfaces and are circumscribed hollows holding moisture or standing water for a period. Solution basins are frequently developed on inland exposures of limestone, richly calcareous sandstone, and dolomite (Cvijic, 1924; Udden, 1925; Smith and Albritton, 1941; Zotov, 1941; Frye and Swineford, 1947; Bogli, 1961; Jennings and Sweeting, 1963; P.W. Williams, 1966; Miotke, 1968; Pluhar and Ford, 1970; Avias, 1972; Lowry and Jennings, 1974) and on coasts are common intertidally and in the spray zone (Emery, 1946; Guilcher, 1953, 1958b; Common, 1955; Corbel, 1957; Revelle and Emery, 1957; Kaye, 1959;

23 1

Fig. 6-1 1. Solution basins on level surfaces of Carboniferous Limestone, intertidal zone, Pendine, Dyfed, Wales. Coin approximately 0.03 m across.

232

Corbel and Muxart, 1970; De Vaumas, 1970; Kelletat, 1974; Coetzee, 1975; Soares de Carvalho, 1975). There are many pseudokarren similar to solution basins. Solution basins (Fig. 6-11) are typically on the order of 0.1-0.4 m wide and 0.01-0.1 m deep, but occasionally reach depths of 0.5 m and widths of 3 m. In plan they are circular, oval, or amoeboid; the larger ones commonly arose by the coalescence smaller basins. The margin of a solution basin is often scalloped on the scale of 0.01 m or so. From the scallops roundbottomed flutes descend over the concave sides of the basin to the generally level floor, each flute joining its neighbours along sharp ridges originating at the cusps on the rim. These marginally sculptured solution basins practically never hold a permanent soil, though in inland settings they may contain scattered mosses and at times algae (e.g. P.W. Williams, 1966), and on the coast often shelter a rich flora and fauna (e.g. Emery, 1946). A rounded rim and a circular to oval shape in plan typify basins holding soil (e.g. Sweeting, 1966, 1972). Solution basins represent the dissolution of rock by stagnant water trapped in hollows on the surface. Except where a soil is developed, lateral dissolution greatly exceeds downward lowering, presumably because on the floor there is inhibition by the accumulated debris (insoluble rock matter, wind-blown dust, organic matter) (cf. Kaye, 1959). The marginal scallops and flutes resemble Rillenkarren but are explicable by the downward streaming of water during basin-filling only in the case of the deeper basins. In shallow basins, some kind of instability must accompany dissolution, though its cause is mysterious. Three possibilities arise. The marginal sculpturing may be related to either (1) convection cells in the stagnant water due to cooling at the surface consequent on evaporation, or (2) Taylor-Gortler instability in the flow of water dense with dissolved solute down the concave sides of the basin, or (3) the action of wind-generated wavelets. The second possibility is particularly promising, in view of the findings of McCormack et al. (1970). Shallow pan-like to deep cauldron-shaped features resembling limestone solution basins commonly arise during the weathering of granites and syenites (Branner, 1913; Twidale and Corbin, 1963; Dragovich, 1968; Dzulynski and Kotarba, 1979), basalts (Wentworth, 1944; Bartrum and Mason, 1948), olivine dolerites (D.L. Reynolds, 1961), and some sandstones (Jutson, 1939; Emery, 1946; Mainguet, 1972a). The depressions occur on steep as well as mild slopes and may contain soil and growing plants. Commonly they are grouped, descending the rock face like stairs. These pseudokarren seem to be related in origin to solution basins. They can be explained by a heightened chemical attack consequent on moisture and organic acids becoming trapped.

233

Trittkarren Bogli (1960, 1961, 1978) gave this name to step-like solution features developed in descending series on mildly sloping rock surfaces (Table 6-11, Fig. 6-12). Chaix and Chaix (1907), Bauer (1962), Jennings (1971), Sweeting (1972), and Soares de Carvalho (1975) describe further examples. The steps follow the contours of the slope and their edges are generally either bowshaped or strongly scalloped. With increasing slope the features become closer horizontally. Deep armchair-like forms ( Trichterkarren) have occasionally been recorded, notably from steep slopes, but the step-height rarely lies outside the range 0.0 1-0.1 m. As contour-following forms, Trittkarren must lie transverse to the currents that shape them, but which factors control their occurrence and spacing remain unknown. The structures could be related to the transverse ribs of supercritical flows (Vol. I, Chapter lo), to judge from the decrease of spacing with increase of slope. Sinter terraces around hot springs are similar (Grange, 1937; Calder, 1972; E.F. Lloyd, 1972). Rillenkarren These are amongst the most distinctive of Karren types and one of the earliest of the minor solution forms to be systematically described (Heim, 1878; Eckert, 1900; Chaix, 1904; Cvijic, 1924). They are cosmopolitan, occurring in areas of mountain karst where the climate is severe (Eckert,

Fig. 6-12. Trittkarren, Carboniferous Limestone, west coast of the Burren, Co. Clare, Ireland. Photograph courtesy of M.M. Sweeting.

234

1900; Chaix, 1904; Cvijic, 1924; Lindner, 1930; Bogli, 1951, 1960, 1961; Corbel, 1957; Bauer, 1962; Miotke, 1968; Bauer and Zotl, 1972; Pfeffer, 1976), amongst tropical karst (Wilford and Wall, 1965; Twidale, 1966; Chinese Academy of Geological Sciences, 1970; Corbel and Muxart, 1970; R.C. McDonald, 1976; Rossi, 1976; Sweeting, 1979), and to a lesser extent amongst the karst of relatively arid regions (Jennings, 1971; Lowry and Jennings, 1974; Dunkerley, 1979). Rillenkarren frequently accompany Kluftkarren (e.g. Pluhar and Ford, 1970) and Spitzkarren (e.g. Sweeting, 1972), and forms resembling them commonly decorate the margins of solution basins (e.g. Emery, 1946; Frye and Swineford, 1947). Rillenkarren occur on steep, bare rock surfaces as groupings of sharpcrested ridges and downward-trending round-bottomed furrows (Fig. 6- 13). Ridge spacing ranges generally between 0.01 and 0.05 m. On any extensive rock surface the furrows join downwards to form a number of fan-like or more complex and dendritic “drainage systems” of an extreme lateral compression, or they may fade out on smooth surfaces. The divides between these systems, commonly forming the edges of slope facets as well, e.g. Spitzkarren, are usually marked by ridges from which other ridges branch downward. The furrows in some instances have rough or slightly pitted surfaces, but otherwise carry transverse solution ripples. Ridges and furrows can be as short as 0.5 m and are seldom longer than a few metres. They

Fig. 6- 13. Rillenkarren, Akiyoshidai, Japan. Photograph courtesy of M.M. Sweeting.

235

commonly weaken downward, either as they merge into still-larger grooves or fade out on smooth rock. Sweeting ( 1972) accurately reflects prevailing views, recently supported experimentally by Glew and Ford (1980), in stating that Rillenkarren “form the most quickly of all karren and appear on rocks that have been exposed to rain or meltwater for only a few years, or even months”. That the fan-like or dendritic systems into which Rillenkarren are grouped serve to collect and drain water from the rock face is strongly suggested by their similarity to the rills of badlands underlain by clay (Schumm, 1956a; Gavrilovic, 1972; Stewart et al., 1972; Gerber and Scheidegger, 1973; Yair, 1973) or volcanic ash (Segerstrom, 1950; Norrman, 1972). The downward weakening of these systems is consistent with the progressive development of the boundary layer that is expected to originate at the top of a slope with Rillenkarren. Rinnenkarren

This is another cosmopolitan minor solutional feature of karst areas (Heim, 1878; Eckert, 1900; Chaix, 1904; Cvijic, 1924; Bogli, 1951, 1960, 1961; Corbel, 1957; Balms, 1962; Bauer, 1962; Jennings and Sweeting, 1963; Maurin and Zotl, 1966; Sweeting, 1966, 1972; Miotke, 1968; Cooke, 1973; Waltham and Ede, 1973; Lowry and Jennings, 1974). Rinnenkarren (Fig. 6-14) often occur with Rillenkarren and like them are fan-like to dendritic and restricted to steep slopes. Furthermore, the furrows are round-bottomed and frequently separated by sharper-crested ridges; in some cases the intervening surfaces are flat. Rinnenkarren differ by being much the larger structures. Transverse spacings range between 0.02 and 1 m, and furrows can be as much as 15 m long. That Rinnenkarren are related to streaming water rather than to rain-beat is shown not only by their similarity to badland drainage rills, but also by their presence in limestone and gypsum caves (McGregor et al., 1963; J.C. Coleman, 1965; Geze, 1965; Waltham, 1974; Pise et al., 1975), where there is independent evidence of vadose modification. Systems of dendritic to parallel grooves up to 5 m in spacing and 1-2 m in depth are commonly produced during the weathering of basalt (Palmer, 1927; Bartrum and Mason, 1948) and granite (Fleury, 1919; Klaer, 1956; Twidale, 1964, 1968; Wall and Wilford, 1966b; Twidale and Bourne, 1976a, 1976b). These structures, which resemble Rinnenkarren, reflect the heightened chemical attack ensuing where both moisture can linger and intermittent streams of water can flush away both the insoluble and dissolved products of weathering. Rundkarren

Generally dendritic systems of rounded grooves and ridges called Rundkarren (Fig. 6-15) abound on limestone pavements in the British Isles (e.g.

236

Fig. 6- 14. Rinnenkarren on moderately sloping surfaces of Carboniferous Limestone, Hutton Roof, E n a s h Lake District. Handle of hammer 0.35m long points downslope.

237

Fig. 6-15. Rundkarren developed on nearly horizontal Carboniferous Limestone in (a) general view and (b) close-up, Malham Tarn, Yorkshire. Joints spaced in the order of 2 m apart.

238

Parry, 1960; R.J. Jones, 1965; Sweeting, 1966, 1972, 1974; P.W. Williams, 1966; Goldie, 1973; Purdy, 1974) and in karst elsewhere on surfaces of mild to intermediate slope (G.H. Hudson, 1910; Smith and Albritton, 1941; Frye and Swineford, 1947; Bogli, 1961; Bauer, 1962; Jennings, 1971 ; Avias, 1972). They are generally found with Fhchkarren, one and in places two or three systems of furrows centripetally draining each block of rock before breaching the rim. The grooves are 0.1-0.2 m deep and wide and usually smooth; lengths range up to 3 m. The master drainage furrows commonly pass down into vertical grooves on the sides of Khjtkarren. Rundkarren are widely accepted as drainage features etched slowly into the rock while buried under soil or peat (e.g. Bogli, 1961; Bauer, 1962; Sweeting, 1966; P.W. Williams, 1966; Wirth, 1978). However, Parry (1960) believes that the features are relict and undergoing burial, while Purdy (1974) regards them as being shaped in the open.

Maanderkarren and related forms Muanderkarren (Fig. 6- 16) are rare forms best developed where long, isolated runnels have arisen on exposed limestone surfaces of mild to intermediate slope (Chaix and Chaix, 1907; Bogli, 1961, 1978; Zeller, 1967b;

Fig. 6- 16. View from above of Miianderkarren draining across a flat and nearly level limestone surface, Tw&enen, Muotatal, Switzerland. After a photograph by Bogli (1978).

239

Miotke, 1968; Lowry and Jennings, 1974). The channels are in the order of 0.1 m across and up to three times deeper than wide. The meanders, as regular as any developed by ordinary rivers, can take an extreme sinuosity, though detrital sediment is totally lacking. They are beaded in plan (Fig. 2-7), resembling the tidal meanders described by Ahnert (1960). The “point bars” of Maanderkarren are steep-sided, cusp-like ridges that strike out boldly into the flow. They may be undercut upstream, and some downstream channel movement probably occurs, though downcutting apparently predominates. Only Zeller (1967b) has attempted to study the hydraulics of Miianderkarren. In the Silbern area of Switzerland, he found them to occur on slopes between 0.06 and 0.5, and inferred that they depended on supercritical streams. Many cave conduits have strong meandering tendencies that are dependent on hydraulic rather than structural controls (Balazs, 1962; Ongley, 1968; Deike and White, 1969; V.R. Baker, 1973b). Even cut-offs are known (Colingridge, 1962). Fig. 6-17 shows the meander wavelength of these passages plotted against the width. The ratio is about ten, consistent with

I

I

I

l

l

I

I

I

l

l

I

I

I

i

I

I

L

A A

/

ICE CHANNELS Leopoid ond Wolmon (1960) A Knighton (1972b) Porker (1975) 0

CAVE CONDUITS A

A

I

I

I

I

I

Ongley (1968) Deike and White (1969) Baker (1973 b)

I

I

l

l

16‘ Channel or conduit width (rn)

Fig. 6-17. Wavelength of meandering ice channels and limestone cave conduits, as a measured function of channel or conduit width.

240

data for ordinary rivers (Chapter 2). Baker calculated for six conduit reaches the relationship between meander wavelength and the contributive surface drainage area, obtaining a trend similar to Fig. 2-9. Evidently ordinary rivers and cave conduits are similar hydromorphologically, although in the first case the transfer process is two-way and the flow has a permanent free surface, whereas in the second the transfer is but one-way and conduits may be full during effective flows. Glacier ice is another natural material in which meanders can be shaped by transfer. Leopold and Wolman (1960), Zeller (1967b), and Price (1972) gave early accounts of meandering supraglacial streams, and further details come from Dozier (1970), Knighton (1972b), Ferguson (1973b), and G. Parker ( 1975). Supraglacial meandering channels are generally larger than Muanderkarren, with widths attaining the order of 1 m. In shape, however, the two kinds are very similar. Supraglacial meanders are typically beaded, the “point bars” again being sharp ribs. Bed slopes are high, and supercritical flow seems to be the rule (Leopold and Wolman, 1960; Zeller, 1967b; G. Parker, 1975). Figure 6-17 shows that supraglacial meanders follow the same trend as cave conduits and ordinary rivers, and Zeller (1967b) indicates that Miianderkarren also follow it. There are some hydromorphological differences from ordinary rivers, however, since Ferguson’s investigation shows that channel-width in ice meanders decreases and sinuosity grows with increasing bed slope. Park ( 1981) discusses their hydraulic geometry. A theory of supraglacial meanders was developed by G. Parker (1975), who considered the stability of an ice channel containing a stream of water able to freeze on to the walls in some places but melt them in others. Provided that there is supercritical flow, and the water surface and bed are in phase, the channel is unstable and the meanders grow in amplitude with progressive incision. The meander pattern should be stationary. These conclusions receive general support from the field.

Roof pendants Projecting downward from the roof in many caves are fairly regularly arranged rock masses having roughly the form of inverted cones or pyramids (Table 6-11) to which the name pendant is given (Bretz, 1942; Bogli, 1961, 1978; Colingridge, 1962; Wilford, 1966; Ollier and Trattman, 1969; Jakucs, 1977). Their sides, smooth to slightly irregular and pitted or ridged, range from a few centimetres to a metre or so in length, the largest pendants occurring in the bigger chambers. In some cases pendants are associated with large tubular cavities called bell holes (Wilford and Wall, 1965; Wilford, 1966; Ollier, 1975). Opinions differ as to the origin of pendants. Curl (1966b) and perhaps Bretz (1942) favour their origin by mass transfer during free convection when the chamber is filled with sufficiently still water, a plausible explana-

24 1

tion in view of the flow patterns seen when liquids are cooled from above (Spangenberg and Rowland, 1961; Berg et al., 1966). Water dense with dissolved limestone should be found in a boundary layer that originates at the root of each pendant and flows downward to separate from the rock at the tip. The corresponding flow of fresh and aggressive water within the body of the chamber should be upward towards the head of each roof cavity. Ewers (1966) and Ollier and Trattman (1969), however, see pendants as remnants left between ramifying tunnels created during the widening of a bedding surface, and Jakucs (1977) treats them as due to corrasion not corrosion. COCKLING

The essence of these common but rarely described third-order Kurren is shown in Fig. 6-18 and in illustrations given by W.E. Davies (1957) and Miotke (1968). Cockling is confined to exposed surfaces of limestone or dolomite that are seldom affected by prolonged streams of water but which are repeatedly wetted, as by the tide or wave-spray, or by rain-splash or mist. They can often be seen on coastal Spifzkurren (e.g. Guilcher, 1953), and inland on joint faces or in Kluffkarren. The structures are equidimensional to slightly elongated cup-like pits which intersect along generally knife-edge but

Fig. 6- 18. Dense cockling on near-vertical surface of Carboniferous Limestone exposed intertidally, Gower coast, Wales. Hammer handle is 0.03 m across.

242

occasionally flat ridges to give the rock surface a crinkled or cindery appearance. An individual pit is seldom wider than 0.03 m and may be no more than a few millimetres across. Lichen or algae occur in some pits but others show only bare rock. There is an apparent gradation between the rather poorly ordered equidimensional forms of cockling and solution ripples (Jennings, 1971), a form of transverse Karren. Intermediate forms are illustrated by Wilford and Wall (1965). Sweeting (1966), and Lord Medway et al. (1967).

TRANSVERSE K A R R E N AND RELATED FORMS

Cave flutes and scallops

These third-order Kurren (Table 6-11) are amongst the best known of all solution forms, occurring on the walls and floors of passages chiefly in limestone caves (G.H. Hudson, 1910; Bretz, 1942; J.C. Coleman, 1945, 1947, 1965; W.E. Davies, 1957; Curl, 1959, 1966a; Rudnicki, 1960, 1962; Bogli, 1961, 1978; Colingridge, 1962; Eyre, 1963; Glennie, 1963; Renault, 1963; T.D. Ford, 1964; Moore and Nicholas, 1964; Gkze, 1965; Ollier and Trattman, 1969; White and White, 1970; Goodchild and Ford, 1971; Ollier, 1975; Jakucs, 1977) and occasionally in gypsum caverns (McGregor et al., 1963). Scallops (Fig. 6- 19) were defined by J.C. Coleman ( 1965) as “small asymmetrical cups, close set and often overlapping with a steep downstream face”. The term flute is restricted by Curl (1966a) to forms that are longer-crested (i.e. more two-dimensional) than scallops but otherwise similar to them. Bretz ( 1942) compared flutes and scallops morphologically to current ripple marks. Like J.C. Coleman (1945, 1947), he appreciated that their crests lay transverse to flow, and recognized that the steeper slopes faced downstream. The wavelength of most scallops and flutes is in the order of 0.05-0.1 m but larger forms have also been recorded (Renault, 1963; White and White, 1970). Scallops have a breadth not much greater than their wavelength (Renault, 1963), and are more plentiful than the long-crested flutes into which they merge (Curl, 1966a). We now know that flutes and scallops depend on a self-stabilizing interaction between a one-way turbulent aqueous stream and a limestone bed able to respond by mass-transfer to the flow (cf. Gkze, 1965; Jakucs, 1977). Eyre ( 1963), Glennie ( 1963), and Moore and Nicholas ( 1964, personal communication, 1969) suggested from general observations that these forms declined in wavelength with increasing flow velocity, a conclusion supported by Rudnicki’s (1960) experimental results obtained using Plaster of Paris as a practical substitute for limestone (Schmidt number of 1000-2000 at ordinary temperatures). Bretz ( 1942) before them, and Ollier and Trattman (1969) subsequently, proposed that scallops and flutes depended on vortex

243

Fig. 6-19. Scallops in a West Virginia limestone cave. a. Flow away from observer. The stylolites standing proud of the surface are approximately 0.3 m apart. b. Flow toward observer. Photographs courtesy of D.C. Ford.

244

Fig. 6-20. Crest lines (polygonal pattern of heavy lines) and limiting streamlines (arrows, direction inferred from minor solutional marks) on scallops formed experimentally by prolonged solution of a flat bed of hardened Plaster of Paris beneath a turbulent water stream. Current from bottom to top. Mean flow depth=O.O74m; mean flow velocity= 0.85 m s - ’.

action, hinting that the forms caused flow separation. Allen (1972) confirmed this in experiments that gave the pattern of limiting streamlines on the scalloped bed shown in Fig. 6-20. Rudnicki (1960), Allen (1971c, 197Id), and Blumberg and Curl (1974) showed in the laboratory that scallops and flutes arose at defects in a soluble bed, provided that a critical defect-size was exceeded. The marks were thereafter amplified by the flow, until the bed became fully covered and a statistically (or otherwise) stable assemblage arose, the average wavelength remaining constant in time. The marks were found to grow downstream (Allen, 1971c), and to propagate downward into the bed at an angle of approximately 61 O from the horizontal (Blumberg and Curl, 1974). In travelling downstream, scallops and flutes conform to the analysis given in Fig. 6-3, the maximum local mass-transfer rate being observed to occur on upstream faces (Allen, 1971c; Blumberg and Curl, 1974). In the last respect, the marks also conform to what we know of heat and mass transfer in separated flows (Allen, 1971c), in which the bed and mass-transfer profiles are out of phase.

245

Curl (1966a) analysed the relationship between flute dimensions and bed and flow conditions. He showed that the wavelength, L , was effectively independent of the Schmidt number and a function only of the Reynolds number. Using rather limited empirical data, he proposed that: V

= 22500

(6.14)

where U is the mean flow velocity and v the kinematic viscosity. The term on the left is the flute Reynolds number, and the wavelength is inversely proportional to the flow velocity. This form of relationship is strongly supported by the experiments of Allen (1971~)and Goodchild and Ford (1971), who produced scallops, the more three-dimensional bed feature, and by Blumberg and Curl (1974) who worked with flutes. Goodchild and Ford’s mark Reynolds number is significantly smaller than Curl’s, however, because they measured the velocity differently. Allen’s limiting mark Reynolds number agrees well with Curl’s on allowing for bed three-dimensionality (Blumberg and Curl, 1974). In later work, Blumberg and Curl proposed an alternative form of eq. (6.14), in which U is replaced by the shear velocity and the numerical constant becomes 2200. R.M. Thomas (1979) explicitly interpretes the wavelength of scallops and a wide variety of other transverse bedforms in terms of the factors which also scale the structures associated with the viscous sublayer in the turbulent boundary layer (Vol. I, Chapter 6). Lithology has some influence on the wavelength of limestone scallops and flutes (Goodchild and Ford, 1971; Bloomberg and Curl, 1974), but the nature of the control is not known. Features similar in all but size to limestone flutes and scallops are well known from ice caves (Sharp, 1947; Lliboutry, 1964, 1965; Curl, 1966b; Thoren, 1969; Halliday and Anderson, 1970). Taking a wavelength ordinarily between 1 and 2m, these ice waves presumably depend on an interaction between a stream of warm air and the cave walls similar to that occurring between limestone and flowing water. The features described by Leighly (1948), however, appesr to have been much more symmetrical than typical ice waves, and his interpretation in terms of convection seems more appropriate. It resembles that advanced above for limestone pendants. Ice ripples There is a remarkable similarity between ice ripples, formed by melting at an ice-water interface, and the flutes and scallops of ice and limestone caves. Figure 6-21 depicts the essential nature of these transverse features, as recorded experimentally and from the undersides of river ice-covers (Carey, 1966, 1967; Larsen, 1969, 1973; Ashton et al., 1970; Ashton, 1972a, 1972b, 1978, 1979; Ashton and Kennedy, 1972). Ice ripples decrease in wavelength with increasing flow velocity according to a relationship of the same form as

246

Fig. 6-21. Ice ripples on underside of river ice cover (block sawn out and overturned), February 1970, Cedar River, Iowa. Flow depth= 1.3 m; mean flow velocity=0.46 m s - ’. Photograph courtesy of G.D. Ashton, reproduced by permission of American Society of Civil Engineers.

eq. (6.14), but with a numerical constant of 61000 (Fig. 6-22). According to Ashton (1972b), their wavelength is also weakly related to flow depth. It has been shown analytically and confirmed experimentally that ice ripples depend on an interaction at an ice-water interface such that the streamwise profile of the melting rate is out of phase with the bed wave (Ashton et al., 1970; Ashton, 1972a; Ashton and Kennedy, 1972; Gilpin et al., 1980). Under steady conditions, the maximum heat and mass transfer rates are located on the upstream sides of the ripples, and the forms propagate downstream, in accordance with Table 6-1. In the field, however, ice ripples growing in amplitude with time but travelling upstream (Case B, Table 6-1) have at times been recorded (Carey, 1967). This could be a feature of unsteadiness, the ripples having been measured while adjusting to a changed flow. An important result of the work of Gilpin et al. (1980) is the discovery that an ice-water interface will remain unrippled, provided that the ice layer is thin enough and the shear stress exerted by the aqueous stream sufficiently small.

Solution ripples Jennings (1971) gave this name to transverse ripple-like solutional features present on steep surfaces of bare limestone (Fig. 6-23). Similar forms were

241 1

I

I

I

\

o

I

I

l

l

RIVER ST. CROlX Carey (1966, 1967)

p\

% \ O\

LABORATORY

O

bAshton and Kennedy ( 1 9 7 2 )

"P 0.

0

OoWo\

I

I

I

1

I

I

I

0.I Mean flow velocity (m s d )

Fig. 6-22. Wavelength of ice ripples in laboratory experiments and in a river, as a measured function of mean flow velocity.

described from steep and in places overhanging surfaces by Wilford and Wall (1969, Wall and Wilford (1966a, 1966b), and Jennings (1967). Solution ripples have wavelengths ranging from a few millimetres up to 0.03 m and sinuous crests as much as 0.25 m long. They are asymmetrical in vertical profile, lying transversely to streams of water flowing down the rock. On underhanging to vertical slopes, the downstream side is the steeper (relative to the ripple base), but on overhangs the steep side faces upstream. Solution ripples, regarded as third-order forms (Table 6-11), are commonly to be found on Kluftkarren or within vertical grooves. No details of the origin of solution ripples are known, beyond their restriction to watered surfaces. A relationship to cave flutes and scallops may be suggested, however, on the grounds of their asymmetry and crestal pattern. The reversed asymmetry of the forms present on overhangs is possibly related to solution into meniscus-held pools trapped on the upwardfacing sides. Wall and Wilford (1966a) suggested that surface tension played a role (unspecified) in the formation of solution ripples.

248

Fig. 6-23. Solution ripples in Carboniferous Limestone, Malham Tarn area, Yorkshire. a. Ripples partly developed on an initially smooth vertical joint. b. Mature ripples on wall of Kluffkurren.Graduations on hammer handle approximately 0.025 m apart.

249

Dirt polygons

The surface of a late-lying snow patch commonly reveals a pattern of adjoining shallow depressions individually in the order of 0.3-0.5 m across (W.E. Richardson, 1951, 1954; F.K. Ball, 1954; Richardson and Harper, 1957; Ashwell and Hannell, 1966; Jahn and Klapa, 1968). These structures, due to the ablation of the snow, are called “dirt polygons” because along their ridged margins there is usually a concentration of the mineral and organic debris that was deposited along with the snow. Individual depressions range from equidimensional to elongate in plan. Dirt polygons form quickly, especially under sunny conditions (Ashwell and Hannell, 1966). The patterns have been interpreted as resulting from convection, by Richardson (1954) who followed Leighly (1948), and were later connected with wind eddies (Richardson and Harper, 1957). Jahn and Klapa (1968) stressed the importance to the formation of dirt polygons of slow melting under strong wind action. Their emphasis is supported by the occurrence of many groups of polygons composed of individuals that are asymmetrical in profile and with common directions of elongation and facing (e.g. Jahn and Klapa, 1968). Dirt polygons may therefore be allied to cave ice-waves and to ice ripples. As regards the dirt rims, F.K. Ball (1954) showed that debris that was originally uniformly dispersed in the snow could be concentrated at the edges of the polygons if, on reaching the melting surface, the particles followed paths normal to this surface. It was left to Jahn and Klapa (1968) to show that this could occur only if the particles adhered to the snow through the action of surface tension on a thin melt-water film.

STRUCTURES RELATED TO HIGH-SPEED FLOW

Cross-hatching

This term describes regular patterns of diamond-shaped waves found on solid bodies (glass, plastics, camphor, etc.) subjected to high-speed flow in the laboratory or as the result of travelling through the Earth’s upper atmosphere (Canning et al., 1968; Laganelli and Nestler, 1969; McDevitt and Mellenthin, 1969; Nachtsheim and Larson, 1971; Stock and Ginoux, 1971a, 1971b, 1972; E.P. Williams, 1971; Nachtsheim and Hagen, 1972; White and Grabow, 1973; Stock, 1975a). The waves strikingly resemble rhomboid sand ripples (Vol.1, Fig. 10-13) but generally have lengths measured only in millimetres; the similarity even extends to the spur-like features present on some cross-hatchings (e.g. E.P. Williams, 1971). Crosshatching waves have streamwise symmetry and elongation. Five main points can be made about cross-hatching (White and Grabow,

250

1973; Swigart, 1974; Stock, 1975b): (1)a transitional to turbulent flow is demanded, (2) the waves can form not only in subliming, melting or charring materials, but also in those able to respond to the fluid shear only by viscous deformation involving relaxation and creep, (3) the wavelength varies inversely as the fluid pressure, (4) the waves travel slowly downstream, and ( 5 ) the semi-angle describing the waves in plan is given very closely by sin-' (l/Ma), where Ma is the Mach number based on flow properties at the edge of the boundary layer (see Vol. I, eqs. (10.24, 10.25) applicable to rhomboid ripples). Cross-hatching has been attributed to an interaction between TaylorGortler vortices and shock waves (Tobak, 1970), to differential ablation in a turbulent boundary layer (Inger, 1969, 1972; Inger and Williams, 1972), to the instability of a liquid melt-layer (Nachtsheim, 1970; Nayfeh and Saric, 1971; White and Grabow, 1973), and to inelastic deformation of the solid material (Probstein and Gold, 1970; Gold et al., 1971; Stock, 1975b). Experimental evidence most favours of the origin of cross-hatching by inelastic deformation. If this theory is true, then heat-with-mass transfer must merely augment an effect possible because the material has already become sufficiently soft under the action of high temperature. Ring waves on tektites and meteorites Many button-shaped tektites (G. Baker, 1956, 1958, 1959, 1961, 1963; Chapman and Larson, 1963), and some meteorites (Chapman et al., 1962), display low waves, measuring a few millimetres from crest to crest, arranged in a concentric or spiral ring-like pattern centred at the stagnation point on the convex leading face of the body as it traversed the Earth's atmosphere. Similar ring waves arise experimentally when spheres of frozen glycerine or oil are melted in air streams (Chapman and Larson, 1963; Chen and Ostarch, 1971; Kuzyk and Chen, 1972). The waves travel slowly downstream and are believed by Kuzyk and Chen to express the instability under restricted conditions of the liquid melt-layer. Ring waves arise on a tektite comparatively late during flight, after a substantial amount of glass had already been fused on the leading face and driven outward to the equator, where it solidified to create a thick encircling flange (G. Baker, 1956, 1958). The waves not only transect flow lines in the glass but decorate the flange itself. Pits (regmaglypts) on meteorites The more intensely ablated parts of many iron and stony meteorites (Nininger, 1936a, 1936b, 1959; Henderson and Perry, 1958; D.T. Williams, 1959; Krinov, 1960; Mason, 1962) show minor surface sculptural features that range from vague wave-like markings to adjoining bold depressions of a

25 I

similar size, shape and orientation relative to the stagnation point on the body and that closely resemble limestone solution scallops (Fig. 6-19). The depressions are polygonal in plan and join along rounded to sharp ridges spaced from a few millimetres to several centimetres apart. Many wellpreserved meteorites showing such depressions have a surface covering of what may be presumed to be solidified threads of melted material, apparently oriented in the local direction of the flow accompanying ablation. Similar threads, also flow-oriented, were made experimentally by D.T. Williams (1959), who ablated ceramic blocks in a rocket blast. The streamline patterns suggested by the meteorite threads compare with those shown in Fig. 6-20, and suggest that flow separation occurred in the surface pits during ablation. Supporting evidence comes from the experiments of D.T. Williams (1959, 1963b). These observations and experiments strongly suggest that meteorite pits represent an interaction between the ablating surface and the gas stream, during which flow separation locally occurred. The precise nature of the interaction is not clear, except that it is consistent with the properties of separated flows (Fig. 6-2b), but it may be related to that responsible for ring waves on tektites, since both waves and polygonal depressions are occasionally associated (G. Baker, 1959; Chapman et al., 1962; O’Keefe, 1963).

SUMMARY

Mass transfer and heat-with-mass transfer are processes whereby solid surfaces are wasted in the presence of a fluid, either stagnant, as during free convection, or in motion, as with forced convection. Wasting rates depend on material, fluid, and flow properties, and can be described for many kinds of flow geometry by correlations involving a non-dimensional transfer coefficient with the Schmidt (or Prandtl) number, the Reynolds number and, in cases of free convection, the appropriate Grashof number. When wasting involves a self-stabilizing interaction between the solid and the stagnant or moving fluid, a variety of wave-like surface forms can arise, either equidimensional or with a longitudinal or transverse orientation relative to flow. There is a wide range of naturally occurring wave-forms related to mass or heat-with-mass transfer. The most diverse and widespread are Kurren, produced when soluble rocks, particularly limestone and dolomite, dissolve into water at surface exposures, beneath soils, or in caves. Other wave-like forms arise during the sublimation or melting of ice and hardened snow, and as tektites, meteorites, and other bodies ablate in the Earth’s atmosphere. Our knowledge of these natural structures is at present largely descriptive, for so far little has been done to apply the principles of wasting processes to their understanding.

This Page Intentionally Left Blank

253

Chapter 7 FLUTE MARKS, MUD RIPPLES, S I C H E L W A N N E N AND POTHOLES INTRODUCTION

A vigorous debris-laden current. acting on a cohesive substrate of mud or rock will commonly shape the surface through corrasion (or corrasion combined with grinding) into hollows of a distinctive size and shape. These depressions may lie either sparsely distributed or closely packed on the surface, or they may be concentrated into bands. In shape the hollows strongly resemble, on the one hand, current ripples and dunes (Vol. I, Chapter8) and, on the other, cave flutes and scallops (this Vol., Chapter6). There are genetic affinities, too, for the marks depend on a transfer process entering into an eventually self-stabilizing interaction between the bed shape and the flow over the bed as the ultimate control on local wasting. Flowseparation phenomena are important in the interaction as expressed by flute marks, mud ripples and Sichelwannen. These structures have two contrasted modes of preservation. Sichelwannen and potholes are most familiar to glaciologists and geomorphologists, who see them chiefly as surface hollows. Flute marks and mud ripples, however, are known to sedimentologists almost exclusively as moulds from the undersides of sandstone beds. These raised welt-like features, wrongly called casts, represent original hollows infilled by sediment. FLUTE MARKS

General Figure 7-1 depicts the ideal flute mark (Allen, 1971c) as an upstreampointing heel-shaped hollow of length L , breadth 8,and depth H , aligned parallel with flow and with a steeper downstream than upstream side. Distally, a broad rounded median ridge is commonly observable, encircled laterally and proximally by the principal furrow. On the flanks, close to the either sharply cusped or rounded rim, lie lateral furrows and sharp to rounded internal ridges. The surface of the hollow is usually smooth but may bear faint subparallel scratches. The counterpart of the hollow as here described is a flute mould, variously referred to as “casts of mud furrow” (J.M. Clarke, 1917), Fliesswiilste (Hantzschel, 1935a), Zapfenwiilste (Rucklin, 1938), “flow marks” (Rich, 1950), “flute casts” (Rich, 1951; Crowell, 1955; Kuenen, 1957), “scour fingers” (Bokman, 1953), “scour casts” ( Kingma, 1958), and “vortex casts” (Wood and Smith, 1959). Of these terms, flute cast

254 Median ridge

,Lateral

furrow

Fig. 7-1. Idealized flute mark with chief dimensions and morphological features.

is most commonly applied (e.g. Potter and Pettijohn, 1963; Pettijohn and Potter, 1964), though Conybeare and Crook (1968) use flute mould, preferring exactness of meaning over deference to popular usages. Since flute marks ordinarily occur in companies, classifications of them should draw attention to the properties of the collective as well as of the individual, though it is as well to recognize that the spectrum of variation is continuous. Rucklin (1938), Dzulynski and Sanders (1962a, 1962b), Dzulynski (1963), Dzulynski and Walton (1965), Ricci-Lucchi (1970), and Allen (1971~)all stressed the patterns assumed by flute marks as well as the features of individuals. Ten Haaf (1959) and Pett and Walker (1971), however, emphasized individual marks. Figure 7-2 illustrates the classification which I believe the evidence justifies. Assemblages are divided between isolate and conjugate. Marks cover all parts of the surface in a conjugate assemblage. An isolate one includes residual areas of unmarked bed, and the flutes that are present may be distributed either randomly or in some kind of pattern of clusters or bands. Isolate flutes vary most, and four main kinds are recognized in Figs. 7-2 and 7-3. There seem to be at least three varieties of parabolic mark-simple, bulbous or voluted, and peniform-and three kinds of asymmetrical flute, here called simple, corkscrew and twisted. Most conjugate flutes are of the parabolic type, but with generally segmented rims. It is worth emphasizing with Pett and Walker (1971) that flute-mark assemblages rarely comprise just one type of individual. We should also note that although flute marks are particularly common in rocks of turbidite facies, they are by no means confined to this setting. Examples have been

255

I

FLU ZE ( 0 ) Clustered

MA RKS ( c ) Oblique

( b ) Longitudinal

I

( d ) Parabolic-transitional

t ( e l Parabolic I ( f ) Spindle-

I

( i ) Long- crested

I

I ( i ) Parabolic-tronsitronol

(k) Porobolic

I

MUD

R/PPLES

I

Fig. 7-2. Classification of flute marks and mud ripples as seen in plan.

recorded from fluviatile, deltaic and shallow-marine deposits, commonly in association with structures, for example, mud cracks, indicating exposure. Parabolic flute marks To judge from described moulds (Fig. 7-4), mQst flute-mark assemblages are dominated by the simple-parabolic variety, with bulbous and some peniform shapes also present, together with rare asymmetrical forms (J.M. Clarke, 1917; Rucklin, 1938; Pringle and Eckford, 1945; Kuenen, 1953b, 1957; Potter and Glass, 1958; Ten Haaf, 1959; Plessman, 1961; I.C. Rust, 1961; Bouma, 1962; Craig and Walton, 1962; Dott and Howard, 1962; Dzulynski and Sanders, 1962b; McBride, 1962; Misra and Awasithi, 1962; Dzulynski, 1963; McBride and Kimberley, 1963; Potter, 1963; Pettijohn and Potter, 1964; Dzulynski and Walton, 1965; D. Richter, 1965; Enos, 1969a; Ricci-Lucchi, 1969a, 1970; Negendank, 1970; Teraoka, 1970; Wezel, 1970; McCabe and Waugh, 1973). The marks are isolate in some assemblages but conjugate in others. The flutes are parallel and fairly uniform in size on a given surface, ranging in average length from a few centimetres in some

256

~~

(d)%lndle-ahaped

I61 Comet-shaped

I

(f

1 Asymmetrical

:ig. 7-3. Features of individual flute marks, in plan and profile.

Fig. 7-4. Large conjugate parabolic and asymmetrical flute marks preserved as moulds on underside of thick sandstone bed, Smithwick Formation (Carboniferous), Marble Falls, Burnett County, Texas, U.S.A. Current from top toward bottom. Photograph courtesy of E.F. McBride and reproduced by permission of Springer-Verlag.

257

assemblages to between 0.5 and 1 m at the other extreme; forms no less than 1.5 m deep are recorded by Winn and Dott (1979) from beneath deep-water conglomerate beds. A staggered arrangement is often conspicuous amongst conjugate forms. Individual parabolic marks frequently carry bold lateral furrows and ridges (e.g. I.C. Rust, 1961). Structures closely resembling conjugate parabolic flutes are occasionally found on limestone surfaces acted on by vigorous sand-laden rivers ( M a s o n and Campbell, 1935; M a s o n , 1940a; Rich, 1950). It is possible, however, that the sculpturing is due more to corrosion than corrasion. Indeed, the structures resemble cave scallops as well as mud-bed flute marks.

Spindle-shapedflute marks These marks (Fig. 7-5) are fairly common, both as isolate structures and in conjugate assemblages (Rucklin, 1938; Rich, 1950; Rabien, 1956; Kingma, 1958; Radomski, 1958; Dzulynski and Sanders, 1962b; Dzulynski, 1963; Pettijohn and Potter, 1964; Dzulynski and Walton, 1965; D. Richter, 1965; Schroder, 1965; Backhaus, 1967; Colton, 1967; Allen and Friend, 1968;

Fig. 7-5. Comet-shaped and some spindle-shaped flute marks preserved as moulds on underside of sandstone, Catskill Formation (Devonian), Juniata River, Newport, Pennsylvania, U.S.A.Width of bed approximately 0.25 m. Current from lower left toward upper right.

258

Conybeare and Crook, 1968; Ricci-Lucchi, 1969a, 1970; Beaudoin, 1968; Parkash, 1970; Kruit et al., 1975; Andrews and Laird, 1976). Spindle-shaped flutes are ordinarily between 0.05 and 0.15 m in length but are many times longer than wide. The proximal ends vary from sharply pointed to moderately rounded, and the lateral rims from straight to slightly curved. Many marks are shallow and flat-floored, whereas others have a depth as much as one-half to two-thirds of the width. A median ridge and lateral structures are conspicuously absent.

Comet-shaped flute marks McBride (1962) described as comet-shaped a type of sharply-pointed flute mark with wavering divergent margins. Such marks (Fig. 7-5) are rare and more often isolate than conjugate (Rucklin, 1938; Cummins, 1958; Dzulynski and Sanders, 1962b; McBride, 1962, 1966, 1970; Colton, 1967; Allen and Friend, 1968; Laird, 1972). The flutes are seldom more than 0.1 m long and are usually rather shallow. A staggered arrangement is typical of clustered marks. Comet-shaped with parabolic flute marks accompany the rectilinear meandering grooves described by Dzulynski and Sanders ( 1962b). These

Fig. 7-6. Asymmetrical flute marks seen as moulds in Plaster of Paris, from an original sandstone slab (Silurian, Gotland, Sweden), Department of Historical Geology and Palaeontology, University of Uppsala, Sweden. Current from bottom toward top. Width of surface approximately 0.17 m.

259

structures were attributed in Vol. I, Chapter 6 to the activities of sublayer streaks in the turbulent boundary layer. Asymmetrical flute marks Asymmetrical flute marks are common both as isolate structures and as contributors to conjugate assemblages. Figure 7-6 illustrates simple forms resembling those figured by Dzulynski and Walton (1965). Such marks reveal on one flank a train of lateral furrows and ridges that diminish in size outward. Examples of the corkscrew type (Fig. 7-3), with some resemblance to gastropod shells viewed apically, can be found in most conjugate assemblages of dominantly parabolic flute marks (e.g. Dzulynski and Walton, 1965). The twisted kind of mark (Fig. 7-3), included in Ten Haaf's (1959) voluted class, is comparatively rare but Kuenen ( 1957) figures examples. Patterns of flute marks It is not uncommon for flute marks to occur in patterns (Fig. 7-2), either in clusters, parallel longitudinal bands, or in parallel lines or bands oblique to flow. Clustering is often seen, which may express either some random circumstance in the origin of the marks, or the spawning of new flutes by matured ones. Kuenen (1957) and Dzulynski and Sanders (1962b) have illustrated flute marks concentrated into parallel bands. Dzulynski ( 1963) and Dzulynski and Walton ( 1965) described oblique arrangements. MUD RIPPLES

Several workers have described from sandstone soles the moulds of structures that strongly resemble in size and shape the more two-dimensional kinds of current ripple (Vol. I, Chapter 8), but which arose on a mud bed in response to erosion (Dangeard et al., 1961; Dzulynski and Kotlarczyk, 1962; Dzulynski and Sanders, 1962b; Dzulynski, 1963; Potter and Pettijohn, 1963; Pettijohn and Potter, 1964; Winterer, 1964; Dzulynski and Walton, 1965; Grumbt, 1966; Lanteaume et al., 1967; Negendank, 1970). The name mud rippZes is appropriate for these features. Flute marks occasionally appear with them, and there are forms that approach flute marks in threedimensionality. The likelihood on these grounds of a genetic affinity between mud ripples and flute marks is acknowledged in Fig. 7-2. Figures 7-7 and 7-8 show moulds of representative mud ripples. Typically, mud ripples occur in conjugate assemblages as forms of uniform wavelength, ranging as an average between 0.02 and 0.40m. The crests are long and straight to gently winding, and junctures resemble those of current ripples. Mud ripples are relatively flat but strongly asymmetrical in vertical profile,

260

Fig. 7-7. Mud ripples preserved as mould on sandstone sole, Normanskill Shales (Ordovician), Green County, New York State, U.S.A. Current from lower left to upper right. Photograph courtesy of E. Chown.

Fig. 7-8. Mud ripples preserved as moulds on sandstone sole, Krosno-Beds (Oligocene), Wernejowka, Polish Carpathians. Ripple wavelength approximately 0.04 m. Current from bottom to top. Photograph courtesy of S. Dzulynski.

26 1

with a steep lee side and much gentler upstream-facing surface. Mud ripples are divisible between two intergrading types, according to the superimposed minor features. Figure 7-7 is typical of ripples that are covered with equant-polygonal to strongly elongated smaller marks (e.g. Dzulynski and Walton, 1965), the longer of those superimposed forms having strong affinities with transversely ornamented ridge-and-furrow moulds (Chapter 1). The smoothly rounded and pillow-like polygonal marks are invariably restricted to the lee sides and troughs of the mud ripples. The elongate features, however, develop gradually with increasing downstream distance over upstream faces. These marks point upcurrent and, as in transversely ornamented ridge-and-furrow moulds, lie nested together with parallel to flaring margins. The second type of mud ripple is shown in Fig. 7-8 (e.g. Dzulynski and Walton, 1965). The surface is much smoother, and minor features are restricted to small spindle-shaped marks, occurring singly or in clusters a few at a time. Dzulynski (1963) and Winterer (1964) describe forms of an intermediate character; these have equant to elongated marks in superimposition, chiefly on the steep leeward faces, and may be associated with large flute marks. Structures intermediate in character between typical mud ripples and typical flute marks are described by Dzulynski (1963) and Grumbt (1966). POTHOLES

Potholes are shallow hollows to deep shafts drilled into rock surfaces by the cutting action of suspended stream-borne debris, or by the combination of corrasion with grinding by stones too large to be suspended but small enough to roll or slide. The forms contribute to the modern landscape and attracted early attention, being first described from the glaciated headwaters of the RhGne by de Charpentier in 1841. Many descriptions have since been published, chiefly from northwest Europe and North America (Bragger and Reusch, 1874; McKellar, 1890; Gilbert, 1905; Lugeon, 1915; Elston, 1917; Fuller, 1925; Rosberg, 1925; Marr, 1926; P.B. King, 1927; Ljungner, 1930; Alexander, 1932; Maxson and Campbell, 1935; Riley, 1943; Angeby, 1951, 1952; Higgins, 1956; Johnson, 1956; Hattin, 1958; Dahl, 1965; Gjessing, 1965, 1967; Schwenk, 1965; Holtedahl, 1967; Morgan, 1970; Putzer, 1971; Aghassy, 1978; Augustinus, 1978; Buckle, 1978). Pothole moulds are seldom reported from the older geological record (Shrock, 1948), though in my experience they are fairly common in fluviatile deposits, occurring beneath sandstones eroded into mudstone (Dixon, 1921; Allen, 1974a), and are also to be found in shallow-marine deposits (Aigner and Futterer, 1978). Potholes vary widely in form. Some are cauldron-shaped and about equally wide and deep, the smooth sides sloping inward at a moderate to steep angle toward a rounded floor (e.g. Marr, 1926; Higgins, 1956). Most

262

resemble a vertical circular to oval cylinder closed at the bottom, but with locally overhanging and occasionally deeply undercut sides (e.g. Brogger and Reusch, 1874; Angeby, 1951 ; Dahl, 1965; Gjessing, 1967). Although some cylindrical potholes have a similar depth to width, the majority are many times deeper than wide. As shown in Figs. 7-9 and 7-10, many potholes have sides marked by spiral grooves and ridges, grading to regularly arranged ripple-like features, commonly with undercut lee faces (Brogger and Reusch, 1874; Ljungner, 1930; Angeby, 1951 ; Schwenk, 1965; Gjessing, 1967; Morgan, 1970; Sugden and John, 1976). Traces of similar features are visible on the floor of the pothole shown in Fig. 7-11, a mould from the fluviatile Old Red Sandstone. Most cylindrical potholes terminate downward in a cone-shaped pit, though a number have a flat floor, and some, as described by Angeby (195 1) and Morgan (1970), a central pinnacle (Fig. 7-1 1) or radial bar. The size of potholes is extremely variable. Hattin (1958) described a field of some 400 forms, none of which was wider than 0.42m or deeper than 0.25m. Potholes range upwards from this order of size to giants in the neighbourhood of 10m wide and 20m deep (e.g. Riley, 1943; Dahl, 1965; Holtedahl, 1967). Most are in the order of 2-5 m deep and 1 m across.

Fig. 7-9. Pothole with spiral grooves on wall, developed on steeply sloping rock surface, Skagerrak coast, Norway. Matchbox gives scale. Photograph courtesy of J. Gjessing (see Gjessing, 1967).

263

Fig. 7-10. Pothole approximately 0.6 m deep and wide with spiral flutes on floor and lower walls, drilled in horizontal rock surface, Skagerrak coast, Norway. Photograph courtesy of J. Gjessing (see Gjessing, 1967).

Potholes have two principal locations: (1) on the rock beds of active rivers, particularly at rapids and waterfalls (e.g. Angeby, 1951; Putzer, 1971; Buckle, 1978), and (2) on glaciated bed-rock surfaces distant from active

Fig. 7-11. View from below of mould of pothole and associated furrow, Lower Old Red Sandstone, Lydney, Gloucestershire, England. Current creating pothole flowed from top toward bottom. Specimen 0.55 m long.

264

drainage. Augustinus (1978) has figured potholes from a modern muddy intertidal flat undergoing erosion. The geographical settings of potholes are very varied, particularly in lowland Scandinavia with its extensive glacierformed landscapes, prompting Rosberg (1925) to divide potholes generally between shore, moulin and waterfall potholes, canyons produced by pothole erosion (potholes in lines), and inverted potholes and series of potholes. Later classifications, however, stressed pothole mechanics (e.g. Ljungner, 1930; Alexander, 1932). Alexander divided potholes between eddy holes shaped by rotary currents, gouge holes fashioned by currents that plunged at a shallow angle into a depression, and plunge-pool holes sculptured by vertically descending streams of water. Certain-kinds of local condition appear to assist pothole development. As noted by Angeby (195 I), Dahl (1965) and Gjessing (1965), they particularly favour the leeward sides of rock ribs defined by joints or by the occurrence of hard bands, and are also associated with general depressions in the rock surface, and with groove-like channels. Partly on the basis of laboratory experiments, Aigner and Futterer ( 1978) suggest that the potholes they describe from shallow-marine sediments were formed by the enlargement of scours initiated at shells lodged on a muddy substrate. Many potholes appear to have been fed by a channel entering obliquely from upstream, and were sometimes emptied by another on the downstream side. The pothole of Fig. 7-11 has a conspicuous feeding channel, but lacks signs of an exit groove. Gjessing (1967) described a large pothole with an exit channel trending upward across the steeply inclined rock surface into which the cavity had been drilled. Occasionally, giant potholes are joined in lines, as if a series of deep shafts had been scoured by a stream exploiting the same fault surface or large joint (Holtedahl, 1967).

SICHEL WANNEN

Ljungner (1930) gave the name Sichelwannen to bow-shaped furrows, with arms generally pointing in the direction of glacier flow, that occurred in association with erosional grooves and potholes on the extensive glaciated bed-rock of southern Sweden. These forms are widely described from Scandinavia (Johnson, 1956; Dahl, 1965; Gjessing, 1965; Holtedahl, 1967), and are reported from the glaciated Precambrian rocks of the Canadian Shield (C. Bernard, 1971a, 1971b). A few examples occur in western Scotland (M.J. Gray, 1981). Figure 7- 12a shows schematically the general appearance of isolate Sichelwannen and their variation in profile and plan. In plan the forms are bilaterally symmetrical to moderately asymmetrical bow-shaped furrows, in the order of 1-2 m broad and long. All forms are relatively shallow, but the vertical profile is very variable, some furrows having a long straight lee side

265

Fig. 7- 12. Sichelwannen. a. Schematic types. b. Distribution on ice-smoothed rock surface. Elvegkd Skjomen, Narvik area, Norway (after Dahl, 1965).

and strongly convex stoss of greater dip, but others a steep lee side (even overhanging locally) and a long upstream surface of gentle slope. The sharpest rims appear on forms with relatively steep lee surfaces. Some asymmetrical forms reveal smaller ridges and furrows in the longer arm of the trough, somewhat similar to the trains of grooves shown by simple asymmetrical flute marks (Fig. 7-6). Sichelwannen usually occur in large localized assemblages, on the upstream and downstream sides and the flanks of hills and roches moutonPes present on the glaciated surface. Figure 7-12b shows part of an extensive field of large isolate Sichelwannen described by Dahl (1965). Most of the forms lie haphazardly on the flanks of a bed-rock ridge, pointing slightly downslope. Some occur in a curving band that trends obliquely across the slope, and there are others, perhaps joint-localized, in transverse rows. Dahl ( 1965) and Holtedahl ( 1967) give photographs suggesting that Sichelwannen are commonly localized by joints in the bed-rock. Gjessing (1965, fig. 14) illustrated a remarkable assemblage of Sichelwannen in which the troughs, pointing downslope, lie on a surface sloping irregularly at 45" and more. Sichelwannen in places join together laterally in small clusters (Fig. 7- 13) that strongly resemble barchanoid sand dunes (Holtedahl, 1967). The packing is locally so close as to create extensive conjugate assemblages reminiscent of whole dune fields (Ljungner, 1930).

266

Fig. 7-13. Sichelwunnen on almost vertical ice-smoothed rock wall, Skorpo Island, Hardangerfjord, Norway. Ice flow from right to left. Photograph courtesy of H. Holtedahl (see Holtedahl, 1967).

267

ORIGIN OF FLUTE MARKS

Two pertinent observations The erosional origin of flute marks has long been held. J.M. Clarke ( 1917). in an early description of turbidite sedimentary structures, proposed that flute moulds were “the natural casts of deeply marked strand slopes rilled and eddied by the ebbing tide”. Whereas his environmental interpretation would not now be accepted, there is still no evidence to contradict his appreciation of the erosional nature of flute marks. Decisive evidence for their erosion was given by Rucklin (1938), who produced flute marks experimentally on mud beds, and by Kuenen (1953a, 1953b, 1957), who observed from the field their cross-cutting relationship to underlying deposits and their discordantly bedded coarse infillings. These findings have since been widely confirmed. For example, flute marks with terraced surfaces that can only record the scour of a laminated deposit are well known (e.g. Ten Haaf, 1959; Dzulynski, 1963). The second fundamental observation bearing on the origin of flute marks relates to their initiation at, and localization by, prior inhomogeneities of shape, or defects, in the eroded surface. One important class of defect is provided by organic markings on or within mud beds. Evidence for the partial erosion of such markings is often cited (Ten Haaf, 1959; Seilacher, 1962; Crimes, 1973), but it is less widely appreciated that wasting is

Fig. 7-14. Underside of siltstone bed in Sonyea Formation (Devonian), Hector Township, Schuyler County, New York, U.S.A.,showing gradation from unmodified Fucoides graphicus (G), current-modified F. graphicus (M), to flute marks (F). Current modifying F. graphicus flowed from upper right toward lower left. Width of surface approximately 1.2 m. Photograph courtesy of G.W. Colton.

268

commonly localized at and by such marks. Colton (1967), however, was able to demonstrate a continuous series of sedimentary structures which began with unmodified organic traces, ranged through recognizeable traces with varying degrees of scour to lee, and ended in flute marks (Fig. 7-14). Other workers have recorded evidence of organic marks or other defects that have caused scour (Kingma, 1958, p. 12; Dzulynski and Sanders, 1962b, pl. VIB; Dzulynski, 1963, pl. XLVI; Pettijohn and Potter, 1964, pl. 72A; Grumbt, 1966, pl. IV, fig.2). Since defects can localize erosion, and since it would appear that flutes can develop by the sufficient enlargement of these scours, we must conclude that the marks arise by a process of differential erosion, the rate on the floor of the hollow exceeding that on the surrounding bed. This conclusion appears so simple as to be not worth mentioning, yet it is fundamental to an understanding of flute marks. A n elementary theory of flute marks Any theory of flute marks must ultimately explain: (1) the shape and orientation of individual marks, (2) the relative homogeneity of marks in each assemblage, and (3) the patterns assumed by assembled marks. Allen (1968c, 1968d, 1969a, 1969c, 1971c, 1972, 1973, 1975) has taken steps towards a theory of these features. Although the shape and growth of an individual flute mark cannot yet be fully predicted (but see Carter et al., 1977 for general ideas), an elementary model is available to describe the increase of flute depth with continuing erosion (Allen, 1968c, 1971~).Figure 7-15 shows a mud bed in a position AB at the start of erosion at time t = 0. A defect in the surface AB (defect size small enough to be neglected) gives rise to a flute mark having the longitudinal profile CD after the elapse of some time t > 0. Let the uniform erosion velocity parallel with the y-direction be V, on the bed surrounding the mark, and let the corresponding velocity at the deepest point on the mark be V,. Then after the elapse of time t:

Current

A

____)

x

B t=O

I

Fig. 7-15. Definition diagram for evolution of a flute mark.

269

Then after the elapse of time t:

and:

the relief of the surface being: H=Y2 -YI where H is the depth of the mark. At time t : (dH/dt) = V, - Vl

or: (dH/dt) = Vl(k - 1)

(7.3)

(7.5)

where k > 0 is the erosion-velocity ratio. Equation (7.5) confirms the previous inference that flute marks record differential erosion. Clearly, when k > 1, a mark is growing monotonically, but when 0 < k < 1 the relief on the bed is being damped. A mark is of constant depth, or neutrally stable, only when k = 1. Although simple, eq. (7.5) is of value, since V, is in principle directly related to boundary-layer and bed properties, whereas V, depends on a probably complex and possibly time-dependent bed shape and flow configuration. The depth ultimately attained by the mark increases according to this model with the erosionvelocity ratio and the duration of the erosion process. The character of an assemblage of flute marks should depend on: (1) the size, shape and distribution of the defects localizing erosion, (2) the resistance to erosion of the mud bed, and (3) the strength and duration of the eroding current. Defect shape should influence the size and symmetry of the marks, at least during their earlier growth stages. Defect size may control the growth-rate of a mark, that is, whether the disturbance represented by the defect can be damped or amplified in relief under the action of the particular current. During the earlier growth stages of an assemblage, the spatial distribution of defects should exert a strong influence on the density of flute marks on the bed, and on whether the ultimate forms are isolate or conjugate. Flow conditions and duration should also partly determine the ultimate size and density of the marks, through the control of the former on instantaneous growth rate. Flow conditions could exert a third kind of influence. Recalling that the scale of cave flutes and scallops is inversely related to flow velocity (Curl, 1966a; Blumberg and Curl, 1974), do flow conditions in some manner control the ultimate size of conjugate flute marks? There is a marked similarity of form between cave scallops and conjugate flute marks in mud beds, and each kind of structure is. dependent

270

on a transfer process (Allen, 1971~).However, Sestini and Curcio (1969, and later Tanaka (1970), noticed that the largest flute marks in turbidites tended to occur beneath the thickest sandstone beds, which suggests that the largest marks are the product of the fastest, thickest, and longest-lived currents. The control on size in conjugate flute assemblages may differ from that with cave structures. Allen (1971~)proposed that defects of three classes could initiate flute marks on a mud surface: (1) hollows caused by burrowing, grazing, or resting organisms, (2) forward-facing or backward-facing steps, due to various causes (e.g. failure of mud expressed by microfaults, prodding or asymmetrical ploughing by organisms), and (3) objects distributed through the body of the bed which differed in resistance from the mud (e.g. empty or sand-filled cavities, pebbles, the hard parts of organisms, or early-diagenetic or pedogenic concretions). The growth of flute-mark assemblages dependent on defects of the third class must obviously differ from that in the other two cases, since marks arising from defects of this sort can be progressively accumulated with the descent of the erosion surface. As an example of how flute-mark assemblages might develop, Fig. 7-16 suggests alternative paths for marks created by a uniform steady current acting for duration T and initiated at defects of the first class, assumed to be circular depressions (e.g. organism burrow tops). Let these defects be of an initial size Lo distributed about a mean size L,, (a Gaussian normal probability density is a plausible model), and let the lower limit of size

I

w

Duration of eroalon, 1

Fig. 7-16. Alternative evolutionary paths for an assemblage of surface defects growing into flute marks.

27 I

exceed any critical size for amplification. Each defect will have a nearest neighbour at a distance Y, and the population of defects can be characterized by a mean nearest-neighbour distance r, (a Poisson probability density is suggested). Since all the defects initiate marks growing at all times, r,, should be closely related to the instantaneous mean flute-mark length, Lmt,once the marks have grown sufficiently that they are largely or wholly conjugate. If the defects lay at the corners of squares with two sides parallel with flow, L,, would equal rm at the moment when conjugacy was attained. If flow was parallel with the diagonal of the square arrangement, L,, would equal r, at this moment. Should the flow conditions impose a limiting flute-mark length of Lmf,then marks dependent on a population of defects for which r, or 0 rm was less than L,, would approach this limit asymptotically from below. An assemblage growing from a population of defects for which r,, or 0 rm was greater than LmI,however, would initially exceed LInfin mean length, but later approach this asymptote from above. Allen (1971~)has discussed for this model the effect of other parameters. Can the above asymptotic mean flute-mark length ever be approached from defects of the third class? These defects, being circumscribed objects differing from the embedding mud in resistance to erosion, presumably give rise in many cases first to current crescents (Chapter5) and then to flute marks, as the body is undercut and then swept away. Only in the case of cavities can flute marks be formed directly. If every defect intersected by the

c

E

4

-

f

W

-c 0

s

E

0 CL 0 L

0

>

a

~

~~

~

-

Duration of erosion, t

Fig. 7- 17. Alternative evolutionary paths for an assemblage of defects distributed threedimensionally and giving rise to flute marks.

212

descending erosion surface localized a flute mark, the mean flute-mark spacing would decrease monotonically with time, since more and more marks accumulate on the sedimentary surface as time passes. The mean length may increase over a short initial period, but the conjugate state should be reached at a mean mark-spacing smaller than the characteristic nearestneighbour distance for the defects, again because of their progressive surface accumulation. Figure 7- 17 shows some possible development paths. Theoretically, the marks are infinitely small after an infinitely long period of erosion. Some influence must be given to flow conditions, however, and there is possibly some limiting flute size, smaller than L,, as previously used, that is attainable. This limit, if it exists, represents a balance between the influence of the flow alone and the influence of the defects, and so depends on both defects and flow. Only the flow is suggested to determine L,,, as plotted in Fig. 7-16.

Mass-transfer analogy Allen (1971c, 1973, 1975) urged the analogy between the erosion of a mud bed through corrasion and/or fluid-stressing and the wasting of a soluble solid by mass transfer, and argued that an insight into the growth of mud-bed flute marks was obtainable experimentally by studying the enlargement of defects in soluble beds. Plaster of Paris mixed with water sets to give hard beds (hydrated calcium sulphate) that are easily shaped and yet dissolve only slowly in a turbulent water stream. Figure 7-18 depicts, as “Plasticine” moulds, stages in the growth by differential solution of an axisymmetric defect cut into the smooth surface of a Plaster of Paris bed exposed to a turbulent water stream. The amount of erosion at each stage is given by the non-dimensional age of the mark, V , t / L o , in which V , is the temporal-mean solution velocity on the bed surrounding the mark, t is the duration of the solution process from the start of the run, and Lo is the diameter of the initial defect. There results a bilaterally symmetrical and monotonically growing structure that closely resembles a simple-parabolic flute mark in shape and orientation relative to flow. From many such experiments, Allen (1971d) established that the length L of isolate solutional marks varied as: 7/16

L

LO

-‘

for values of the term in brackets between about 10 and 10 -3, where U is the mean flow velocity and v is the kinematic viscosity of water. The maximum breadth B of the marks increased with time, varying as: -= B LO

6.3(

Z)

415

(7.7)

273

Fig. 7-18. Evolution of shallow circular defect 0.0091 m in diameter in a bed of hardened Plaster of Pans dissolving into a turbulent water stream, as shown by a series of Plasticine moulds. Current from bottom toward top, and all photographs to a single scale. a. Initial defect. b. V l r / L o=0.069. c. V , r / L , =0.16. d. V , r / L , =0.33. e. V , r / L , ,=0.53. f. V , r / L , ,= 0.77. g. V,r/L,,=1.06. h. V,t/L,=1.57.

214

for B / L o >2.8 and Vl:t/Lo>0.36. The maximum depth H at first decreased slightly, but subsequently increased according to:

z)

2/3

-= H

HO

12.3(

where Ho is the maximum depth of the initial defect, for H / H o > 1.18 and V l t / L o> 0.96. The marks in plan shape tended to a power law with an exponent in the order of one-half, a remarkable parallel with findings on the stable shape assumed by axisymmetric bodies undergoing ablation in external flow (Christensen and Buhler, 1959; G.W. Sutton, 1959; D.T. Williams, 1963a, 1966). Bilaterally symmetrical hollows closely resembling simple-parabolic flute marks were also created by the action of a turbulent stream on defects in the form of short transverse slots (Fig. 7-19a, b, g, h). Slots skewed to flow, however, yielded structures (Fig. 7- 19c-1) closely resembling simple asymmetrical flute marks, although the asymmetry became less with increasing mark age, and eventually disappeared. The mark afforded by a short strongly skewed slot (Fig. 7-19e, f) had a twisted beak-like proximal part. A train of lateral ridges and furrows typified over a large range of ages the mark generated at a long strongly skewed slot (Fig. 7-19kJ). This mark closely resembled the asymmetrical flute marks of Fig. 7-6 and those figured by Dzulynski (1963, pl. XLIII). Defect spacing, and the pattern and orientation of clusters of defects, appear from mass-transfer experiments strongly to influence flute-mark development (Allen, 1973, 1975). When simple axisymmetric defects lie close together in pairs or trios, the following sequence of growth stages is observed: (1) the independent growth of a flute-like mark at each defect until the mark length or breadth is of the same order as the defect-spacing, (2) increasing interference between the now partly-conjugate marks and (3) development of a single, large, bilaterally symmetrical mark by the gradual elimination of unsymmetrical features from the compound form of stage 2. Figure 7-20 illustrates this sequence. Notice that one pattern of defects affords a peniform mark during the second growth-stage. Together with the experiments on single axisymmetric defects (Allen, 1971c), the work with clusters showed that the shape of the primary defect (or defect complex) causing a flute mark remains evident in the mark only over a certain initial growth period, just as can be inferred from the rock record (e.g. Dzulynski and Sanders, 1962b, pl. VIB). Writing D as the greatest overall horizontal dimension of a defect or defect-complex (Allen, 1975), the critical value of V , t / D for the disappearance of evidence of the parent lies between 0.34 and 0.87, with a closely defined mean near to 0.62, that is, at about the age at which eqs. (7.6-8) become valid. At greater ages, the mark no longer reveals its genesis by the shape.

275

Fig. 7-19. Evolution of straight shallow slots in a bed of hardened Plaster of Paris dissolving into a turbulent water stream (current from bottom toward top), as shown by Plasticine moulds. a, c, e, g, i, k. Initial defects. b, d, f, h, j, 1. Flute marks developed from the slots after the solution of approximately 0.0095 m of Plaster of Paris from the surrounding bed. All photographs to a single scale (slot in g is exactly 0.089 m long).

277

Not all solutional marks belong as do those in Figs. 7-18-7-20 to a class of monotonically growing marks, the class for which k > 1 after the initial growth stage. Allen (1971~)showed that defects could be too small relative to flow conditions to afford marks that eventually grew in all dimensions, a parallel observation being made by Gilpin et al. (1980) for defects of an ice-water interface under stable flow and thermal conditions. Such stable defects gave marks that at first increased and then decreased in length and breadth with increasing time, but which declined in depth at all times ( k < 1 at all stages). Figure 7-21 gives a selection grown from axisymmetric defects. They closely resemble spindle-shaped flute marks (Fig. 7-9, particularly Rucklin's (1938, fig. 3) Fluchzupfen and many of the sharp-nosed flutes of Pett and Walker (1971), differing further from parabolic flute marks, or the marks shown in Fig. 7-18, by the general lack of a median ridge or lateral ridges and furrows. The critical defect size in metres for monotonic growth appears to vary as: 1.25hU -'I8 L,, = 5.90h ( 7)

(7.9)

in which Lo,, is the critical size and h is flow depth. As Allen (1971~) showed, this equation defines for given flow conditions the downstream distance required for the viscous sublayer to roll up into vortices and so become turbulent. Like the wavelength of cave flutes, the critical defect size for mass-transfer flute marks is inversely proportional to the flow velocity. Assemblages of flute-like marks develop from random defects in a manner that is qualitatively consistent with the model sketched above. Those shown in Fig. 7-22a, b comprise marks of a substantial individual age but are only partly conjugate. Numerous asymmetrical marks representing a second generation of structures have begun to form in the assemblage of Fig. 7-22b. The marks of Fig. 7-22c are wholly conjugate, and include peniform types.

Flute marks on mud be& The experimental production of flute marks directly on mud beds presents many difficulties, but a start has been made on this task. Rucklin (1938) Fig. 7-20. Evolution of pairs and trios of equal, shallow, circular defects cut into hardened Plaster of Paris dissolving into a turbulent water stream (current from bottom toward top). a, b, c. Pair of defects at right angles to stream and with centres 0.03 m apart at, respectively, V , t / L , =0, 1.61, and 5.65. d, e, f. Pair of defects at 45" to stream and with centres 0.03 m apart at, respectively, V , t / L , =0, 1.39, and 3.30. g, h, i. Pair of defects in line along stream and with centres 0.03 m apart at, respectively, V , r / L , =0, 1.41, 3.33. j, k, 1. Trio of defects with centres 0.025 m apart at, respectively, V , r / L , , =0, 1.74, and 4.67. m, n, 0. Trio of defects with centres 0.025 m apart at, respectively, V , r / L , =0, 1.55, 4.84. The photographs are at the same scale in each set. In all cases value of L , is the greatest overall dimension of the defect arrangement.

278

Fig. 7-21. Plasticine moulds showing flute marks evolved from defects of less than critical size in a bed of hardened Plaster of Paris dissolving into a turbulent water stream. a. V l t / L o = 0.364. b. V l t / L , =0.491. c. V l t / L , =0.793. d. V l r / L o=0.972. Note the shallowness of the marks and the lack of a sharp rim. Current from bottom toward top. All photographs to a single scale, with bed in (a) measuring 0.05 m wide.

used fairly strong mud beds acted on by sheet flows, obtaining some marks that resembled flutes from the geological record, but many disordered structures. Dzulynski ( 1965) made structures resembling comet-shaped and spindle-shaped flute marks where an experimental turbidity current followed a curved path over a mud bed, but his experiments were not quantitative and the erosional origin of the marks was never proved. Allen (1969a, 1969c, 197lc) attempted to explore separately the effects of fluid-stressing and corrasion as mechanisms of erosion. The mechanisms themselves, however, are not mutually exclusive. Fluid-stressing is most effective on weakly cohesive mud beds, formed by allowing an aqueous dispersion of clay to settle and the deposit to age for a period. One assemblage of marks (Fig. 7-23b), made by allowing a vigorous turbulent current to attack such a bed, comprises conjugate to near-conjugate

Fig. 7-22. Rubber latex moulds of flute mark assemblages made by the dissolution of a flat bed of hardened Plaster of Paris carrying random defects into a turbulent water stream. Each bed is 0.48 m long with current from left to right. a. Mean flow depth=0.054 m, mean flow velocity=0.29 m s-I, duration=5.27X lo5 s. b. Mean flow depth=0.060 m, mean flow velocity=0.47 m s - ' , duration=5.24X lo5 s. c. Mean flow depth=0.156 m, mean flow velocity=0.47 m s-I, duration=6.08X lo5 s.

280

Fig. 7-23. Plaster of Paris moulds of flute marks made by the fluid stressing of a weakly cohesive bed of kaolinite mud. Current left to right. a. Mean flow depth=0.072 m, mean flow velocity=0.60m s-I, length of bed depicted=0.54m. b. Flow conditions as in (a) with bed length=0.28 m.

28 1

parabolic flutes with median ridges and, in some cases, lateral ridges and furrows. A few spindle-shaped marks also appear. In a second assemblage (Fig. 7-23a), symmetrical and asymmetrical marks are combined with generally more subdued transverse features transitional between flute marks and mud ripples (e.g. Dzulynski, 1963). Although resembling simple parabolic flute marks in general shape, the features of Fig. 7-23 differ in one important respect, namely, they carry small equan t-polygonal to elongate marks like those noted from many mud ripples (e.g. Fig. 7-7) and apparently allied to ridge-and-furrow. Typically, flute marks have surfaces that if not smooth are merely lightly scratched. These experiments, coupled with allied ones (Allen, 1971c), showed that the superimposed features resembling ridge-and-furrow are related to individual vortices in the flow, each vortex deforming and/or eroding the soft bed into a characteristic minor mark. Two important inferences follow. Firstly, a current may create on a weak bed its own defects from which to grow flutes, and prior populations may not be needed. Secondly, as we can also infer from the mass-transfer studies and from experiments to be described next, flute marks record an integral property of a current, and not an instantaneous flow pattern or condition. Corrasion demands the presence in the flow of dispersed particles sufficiently large as to behave to some extent inertially, and is most effective with relatively strong mud beds. Figure 7-24 shows as moulds a number of flute marks made by the corrasional enlargement of small defects introduced on to beds of stiff modelling clay. These marks are smooth, unlike those fashioned by fluid-stressing (Fig. 7-23), and so closely resemble typical flute marks. There is also a general resemblance between the experimental and natural marks. Those created from axisymmetric defects (Fig. 7-24a-d) are bilaterally symmetrical, usually with a weak median ridge and paired lateral ridges and furrows. Skewed slots gave asymmetrical marks with in one case a group of lateral furrows (Fig. 7-24e, f). Technical difficulties prevented these marks from being grown to a large size, but some evidence for the existence of a critical defect-size for sustained growth was obtained. None approached the size of typical flute marks, however, and it is important that more experiments involving the corrasion of mud beds should be made.

A model for flute marks It has been shown above that structures closely resembling natural flute marks can be created by differential solution or erosion at defects. Two more observations are required in order that we can see which mechanisms control this differential wasting. Experimentally, flute marks are coupled with separated flows, in detail containing either a roller and a number of vortices or a pair of vortices. This was suggested by Rucklin (1938) and by D.T. Hopkins (in Dzulynski and

282

Fig. 7-24. Plaster of Paris moulds of flute marks made by the corrasion of a stiff clay bed by a fast sand-laden current (mean flow velocity 1.48 m s - I in all cases). a. Vl t / L , =O. 196, initial defect a circular pit 0.0096 m diameter and 0.0030 m depth. b. V l t / L , =0.095, initial defect a circular pit 0.01 18 m diameter and 0.0044m depth. c. V l t / L , =0.064, initial defect a circular pit 0.025 m diameter and 0.0046 m depth. d. V l t / L , =0.061, initial defect a circular pit 0.027 m diameter and 0.0072 m depth. e. V l t / L , =0.098, initial defect a slot 0.032 m long and 0.0044 m deep skewed at 60" from line of flow. f. V,t/Lo=O. 195, initial defect a slot 0.046 m long and 0.0036m deep inclined at 30" from line of flow. In each case Lo is the overall streamwise defect length. All photographs to a single scale, with (a) 0.06 m across.

283

Fig. 7-25. Limiting streamlines drawn on rubber latex moulds of idealized flute marks shaped in beds of hardened Plaster of Paris exposed to a turbulent water stream in order to reveal associated flow configurations. a, b. Plan and elevation of narrow parabolic mark of length 0.235 m and depth 0.027 m in current of 0.155 m mean depth and 0.463 m s - mean velocity. c, d. Plan and elevation of spindle-shaped mark 0.296 m long and 0.013 m deep in current of mean depth 0.154 m and 0.466 m s mean velocity. Current from bottom toward top in all cases.

'

~

'

Walton, 1965) and has since been firmly established by mapping the minor marks on flutes generated during fluid-stressing (Allen, 1968d, 1969a), by mapping on flute marks created in Plaster of Paris beds the current crescents

284

Fig. 7-26. Mould of part of asymmetrical flute mark accompanied by erosively deepened longitudinal ridges and furrows, Lower Palaeozoic, southeast Ireland. Current from left toward right. Note how ridges and furrows bend in toward the nose of mark, as in Fig. 7-25a, c, indicating the concentration of vorticity. Coin approximately 0.03 m across.

formed at entrapped air bubbles (Allen, 1971c, 1973, 1975), and by establishing limiting streamlines on experimental models of ideal flute marks (Allen, 1971d). The limiting streamlines on an ideal parabolic mark (Fig. 7-25a, b) show the presence of a proximal roller and two flank vortices. Another noteworthy feature, suggestive of the concentration of vorticity that accompanies flow separation, is the “focussing” of the limiting streamlines that lead into the proximal part of the mark. The same effect is evident in the ridge-and-furrow associated with a real mark (Fig. 7-26). The spindle-shaped model (Fig. 7-25c, d) contains only a pair of vortices. The second observation concerns the local growth of flute marks. Figure 7-27 shows in longitudinal profile stages in the growth of flute marks generated from a long transverse slot in a Plaster of Paris bed, an axisymmetric defect in a Plaster of Paris bed, and an axisymmetric defect in a strong mud bed exposed to corrasion. Growth was invariably downstream and downward into the bed. The value of k is in the order of 1.5 for both plaster and mud beds, with the maximum growth-rate occurring on the upstream-facing side of the mark, close to flow reattachment. A model for flute growth on mud beds must clearly be very similar to that

-

Current

0.04-

p

285

0.03-

\

c

8

-e w

-3.80

0.02-

-

0.01

01 0

- 0~0100I

E

\

( a ) Transverse slot (Plaster of Paris) "

0.02

"

0.04

"

0.06

"

0.08

~

"

"

"

"

"

"

0.12 044 016 048 Downstreom distance, x (m)

0.20

0.22

0.05 0.06 0.07 0.08 0.09 Downstream dlstance. I (ml

0.10

0.11

0.10

"

-

5

.-c

f

Ooo50-

w

( b ) Circular pit (Plaster of Paris)

0 0

0.01

0.02

- 0,0100r

0.03

0.04

s -7 --

Current

\

I

00050

/

-

/o

-0,052

-

o

.

l

l

2 '0,194

( d ) Circular pit (Stiff mud) E

O 0

0.01

0.02

003

0.04

005

0.06

0.07

008

OQS

I

I

0.10

0.11

Downstream dlEtOnC0. x (m)

Fig. 7-27. Longitudinal profiles at various non-dimensional ages illustrating the evolution of defects exposed to turbulent currents. a. Transverse slot in bed of hardened Plaster of Pans, mean flow depth=O.I75m, mean flow velocity=0.37m s - ' . b. Circular pit in bed of hardened Plaster of Paris, mean flow velocity= 1.15 m s-I. c. Circular pit in stiff clay exposed to sand-laden current of mean velocity= 1.48 m s - I.

already proposed for cave flutes (Chapter 5), which rested on the properties of turbulent separated flows (Chapter3). The rolling-up of the free shearlayer, and the convection of the resulting vortices toward the reattachment region, creates on the upstream face of a flute mark an environment in which the turbulence intensity and the fluctuations and magnitudes of the pressure and bed shear stress are all generally in excess of the values for the corresponding boundary layer. Just as an increase in the local mass-transfer rate over the corresponding boundary-layer value is inevitable in this environment, so also is an increase in the rate of mud-bed erosion through fluid-stressing. The model for corrasional flutes, however, is less straightforward. The agitated environment close to reattachment will inevitably cause dispersed particles to make more frequent and vigorous contact with the bed, raising the local erosion rate above the boundary layer value, but there may also be effects related to the steepness of the paths of grains as they approach the surface of the flute. In cutting wear (Vol. I, Fig. 2.8), there is

286

one angle of attack for which the mass of mud removed per particle impact is a maximum, a constant particle impact velocity being assumed. Since this is but a small to intermediate angle, a cusp may be expected to form close to reattachment, where the separation streamline is steeply inclined to the bed. Tellingly, some parabolic flute marks reveal such a cusp (e.g. Fig. 7-4). ORIGIN OF MUD RIPPLES

Experimentally, mud ripples can be formed only by the fluid-stressing of a weakly cohesive mud bed. Allen (1971~)made them by al1owing.a vigorous water stream to act on a smooth mud bed formed by the settlement and ageing of various aqueous clay dispersions (Fig. 7-28). The wave-like features eroded on the bed are relatively flat and strongly two-dimensional, closely resembling natural mud ripples (Fig. 7-8). They further resemble the natural

Fig. 7-28. Plaster of Paris mould of mud ripples made by the fluid stressing of a kaolinite mud bed. Current from bottom toward top. Mean flow depth=O.O78m; mean flow velocity= 0.55 m s - I . Specimen 0.15 m wide. Compare with Fig. 7-7.

287

forms in that most carry superimposed equant-polygonal depressions in the troughs and flow-aligned elongate marks resembling spindle-shaped flutes or ridge-and-furrow on the upstream faces. These superimposed marks are best developed on the weaker beds. On the strong muds, however, they are occasionally restricted to the leeward faces of the ripples, as in the natural structures described by Dangeard et al. (1961) and Winterer (1964). Observation of the erosion process suggested that each superimposed mark is the product of a short-lived interaction between a coherent vortex-structure in the flow and the deformable bed. In the trough of a mud ripple, where the reattaching flow approaches the bed steeply, the marks assumed an equantpolygonal form as vortex after vortex struck the bed at a steep angle, spread out in all directions from the point of impact, and in so doing squeezed and stripped slivers of mud from the surface, each new form partly obliterating older ones. The vortices yielded flow-aligned marks on striking the upstream face of a mud ripple, because of their convection in the re-forming boundary layer. Allen’s (1971~)experiments led to a relationship between the size of mud ripples and flow conditions different from that for cave flutes and scallops (eq. 6.14). Figure 7-29 shows the mean wavelength of mud ripples, L,,, as a function of the hydraulic radius, r , of the experimental channel. The mean

0

I

I

0.01

0.02

0.03 Hydraulic

0.04

1

I

0.05

0.06

007

radius. r (m)

Fig. 7-29. Wavelength of mud ripples as an experimental function of hydraulic radius of flow. Data of Allen (1971~).

288

wavelength in metres is given approximately by: L , = 0.050 0.80r

+

(7.10)

where the intercept may express a threshold condition. There was no correlation between wavelength and flow velocity. These findings suggest, in the light of the apparent relationship between flute size and turbidite thickness (Sestini and Curcio, 1965; Tanaka, 1970), taken with the occasional coexistence of mud ripples and flute marks (e.g. Winterer, 1964), that the two kinds of structure are genetically related, the one recording mainly the fluid-stressing of weak muds and the other chiefly the scouring of strong beds. ORIGIN OF POTHOLES

Historically, two views of potholes have been taken: (1) all potholes are due to the action of violent streams, existing either at or beneath the surface of the ground, and (2) those found in glaciated areas distant from modem drainage record the activities of glacier moulins. The moulin interpretation of potholes, popularized by Brogger and Reusch (1874) and by Upham (1900), states that those present in glaciated areas were eroded by waterfalls that plunged down glacier crevasses to reach the bed-rock. This interpretation has been widely applied (G.K. Gilbert, 1905; Fuller, 1925; Man, 1926), and has continued to receive support even in recent years (e.g. Faegri, 1952). But there are grave objections to the glacier-moulin interpretation, first voiced by Alexander ( 1932) and since amplified by Angeby’s ( 1951) studies of potholes from river rapids, primarily because the potholes found in glaciated areas, either buried or exposed, differ in no essential way from those currently being shaped by streams or arising in laboratory experiments intended to simulate river entrenchment (Shepherd, 1972; Shepherd and Schumm, 1974). The other objections, extensively considered by Alexander (1932) and C.G. Higgins (1957), are that: (1) few or no glacier crevasses are likely to remain stationary for long enough to permit the degree of erosion demanded by the size of most potholes, (2) even if the crevasses were in motion, no one bed-rock site is likely to be precisely re-occupied by a series of moulins, and (3) the ice is unlikely to have been so thin that the crevasse would have provided an uninterrupted shaft to bed-rock. Alexander (1932) convincingly developed the idea that potholes in glaciated terrain are the product of sediment-charged meltwater flowing between the base of the ice and the bed-rock surface, a notion also championed by Streiff-Becker ( 195la, 195Ib). Alexander showed experimentally that the current enters a pothole at the periphery as a gently declined jet (from the entry channel if one is developed), spirals downward around the walls to

289

reach the base, and finally rises vertically along the axis to escape. This result is consistent with the downward-spiralling grooves, ridges and ripple-like features found on many potholes (e.g. Figs. 7-9, 7-10), and is further supported by Angeby's (1951) experiments on the flow-pattern within a full-scale pothole exposed on a temporarily dry river-bed. The internal spiral features so prevalent in potholes are inexplicable by the vertical jet of the moulin hypothesis, which is now rarely invoked as an alternative to Alexander's views. ORIGIN OF SICHEL WAN N E N

That Sichelwannen cannot be due to surface streams is at once evident from their independence of topographical features; for instance, they are commonly to be found pointing along the strike of near-vertical rock walls, or on hills of bold relief. Sichelwannen have instead been generally attributed to a subglacial process. Ljungner (1930) thought that they were formed by sheets of meltwater flowing in confined spaces between the base of the ice and the bed-rock, the erosion being accomplished by a kind of fluid-stressing. Although the suggested erosion mechanism is hardly plausible, there is no telling evidence against his proposed site of origin. Hjulstrom (1935) also favoured a subglacia1 origin for Sichelwannen, but stressed the probable role of cavitation erosion (Vol. I, Chapter 2) in shaping the structures, particularly near obstructions to flow, such as erratic blocks trapped in the ice-roof but touching the bed-rock surface and, we may here add, partly opened cracks or joints on the rock floor. He pointed to experiments indicating a close spatial association between cavitation damage and the occurrence of flow separation (e.g. De Haller, 1933; Schroter, 1933), though the association was not explicitly discussed. Subsequent work has amply proved that cavitation erosion is a most effective mechanism, particularly where separation is possible, for example, at downstream-facing steps or bluff bodies (e.g. Price, 1947; Rao and Thiruvengadam, 1961 ; McCormick, 1962; Brown, 1963; V.E. Johnson, 1963; Kenn, 1966, 1968; Kenn and Minton, 1968). Dahl (1965) also regarded cavitation as playing a significant role in the shaping of Sichelwannen, emphasizing the laterally confined nature of the meltwater flows involved. Although subglacial meltwater flows mainly under hydrostatic control, and probably often attains the high speeds necessary for cavitation (Barnes, 1956), erosion by cavitation cannot be the only mechanism of wasting involved in forming Sichelwannen. Their smoothness is quite unlike the pitted and fretted appearance typical of, say, concrete damaged by cavitation (e.g. Kenn, 1966). Corrasion by the stream-borne debris should also occur, as Hjulstrom ( 1935) himself appreciated, and could have been predominant, as Holtedahl ( 1967) appeared to believe.

290

The close resemblance between Sichelwannen and corrasional flute marks has not prevented several workers from attributing the former to abrasion either by ice or an ice-water paste (Johnson, 1956), a mysterious highly viscous substance which appears to be a mixture of water, ice and debris (Gjessing, 1965), or by debris-laden ice (Boulton, 1974, 1975). Boulton’s theory, the most closely reasoned of this group, associates Sichelwannen with differential abrasion at the glacier bed arising because of the diversion of the debris-laden basal ice around some obstruction, either a large erratic halted for a time against the bed-rock, or a band or local patch of abnormally hard rock. It also strongly links Sichelwannen to topographic situations favouring the development of subglacial cavities. The main difficulties confronting Boulton’s (1974, 1975) idea are: (1) the lack of a reported association between Sichelwannen and remnant erratics or obstructions related to rock hardness, (2) the abundant occurrence of the forms on exposed as well as sheltered surfaces (relative to ice-movement), and (3) the substantial parallelism between glacial striae within and without Sichelwannen (e.g. Holtedahl, 1967). The presence of striae within Sichelwannen does not necessarily mean that the forms have been wholly shaped by ice, but rather that ice may have been the last agent to act upon them. Indeed, had the structures been wholly sculptured by the ice, patterns of striae suggestive of flow separation (e.g. Fig. 3-15) would be expected, particularly in forms with steep or overhanging lee sides. The balance of present evidence is thought to favour the production of Sichelwannen by subglacial meltwater flows, though that evidence is not decisive and there remains a case for a critical examination of these intriguing structures. SUMMARY

Typically, flute marks are bilaterally symmetrical heel-shaped hollows eroded into mud beds by debris-laden currents acting either on prior defects on or within the bed or, if the mud is insufficiently strong, on self-created defects. Mud ripples closely resemble two-dimensional forms of current ripple. They are known experimentally to depend on the erosion of weak muds by fluid-stressing, and their wavelength increases with flow depth. Forms intermediate between flute marks and mud ripples occur, and it is possible that the two kinds of structure are genetically related, since there is weak evidence to suggest that the size of flute marks increases with the thickness and speed of the current. Sichelwannen closely resemble flute marks in appearance but are much larger, occurring on rock surfaces in glaciated regions. They can be attributed to a subglacial environment but direct evidence for their origin is lacking. The balance of present evidence favours their corrasion by debris-laden meltwater flowing violently under

29 1

hydrostatic pressure in confined spaces between the bed-rock and the glacier above. More work is needed on these structures. Flute marks, mud ripples, and Sichelwannen all appear to depend on mechanisms associated with flow separation. Potholes also are common on the bed-rock of glaciated regions, but are frequently found as well on the beds of surface streams, particularly at rapids. Potholes are shaped by debris-laden water which, entering the hole as a gently declined jet, spirals downward around the walls before rising axially to leave the structure.

This Page Intentionally Left Blank

293

Chapter 8

LIQUIDIZATION, LIQUIDIZED SEDIMENT, AND THE SEDIMENTATION OF DENSE PARTICLE DISPERSIONS INTRODUCTION

Our ordinary experience, in walking over beaches, sand dunes, and dried-up river beds, is that cohesionless sand and coarse silt deposits have considerable shear resistance, supporting large loads without yielding. Yet circumstances can arise naturally, or be induced artificially, which cause these materials to lose their strength and become like viscous liquids, when they may fail disastrously. The mechanisms effecting this change of state, from solid-like to liquid-like, are those of liquidization and their products are liquidized sediments (Allen, 1977c). Cohesionless deposits which change their state are capable of moving on slopes in obedience to body forces and beneath sedimentary covers in response to pressure gradients. Upon the withdrawal of the liquidizing mechanism, however, redeposition of the particle dispersion commences and, if a packing more dense than before is assumed, layer thickness is ultimately reduced and pore fluids escape. The duration of this process of sedimentation powerfully influences the extent of deformation under a given set of forces. Subaerial slopes underlain by cohesionless materials commonly fail catastrophically during earthquakes, the debris travelling swiftly over large distances after being liquidized ( e g Dobry and Alvarez, 1967; Seed and Wilson, 1967; Seed, 1968; P.A. Gilbert, 1976). These failures are attributed to a mechanism of liquidization called liquefaction (Casagrande, 1936), essentially a break-down of the fabric of the material to such a degree that grains are no longer mutually supported but become temporarily separated and dispersed in the pore fluid. Neither an inflow of pore fluid nor a change of volume of the deposit is required for liquefaction. Flat-lying sands and silts often become liquefied over depths of many metres during earthquakes, with startling results: spouts of water mixed with sand and mud build volcano-like forms on the ground surface, sediment is forcibly injected into fractures, huge buildings tilt on their foundations and sink as one into the liquidized sediment, and buried objects, such as large pipes or partly empty storage tanks, rise buoyantly to the surface (Oldham, 1899; Fuller, 1912; Gee, 1934; Poddar, 1952; Duke and Leeds, 1963; Steinbrugge and Flores, 1963; Reimnitz and Marshall, 1965; Kawakami and Asada, 1966; Yamada, 1966; Foster and Karlstrom, 1967; Seed and Idriss, 1967; Ambraseys and Sarma, 1969; Dixon and Burke, 1973; Adams, 1976; Espinosa, 1976; Seed et al., 1981). It is probably in such circumstances that most of the penecontemporaneous soft-sediment deformations that abound

294

in the geological record are created (Henderson, 1935; Kuenen, 1948b, 1958, 1965b; Shirley, 1955; E. Williams, 1960, 1961, 1963; Selley et a]., 1963; Selley, 1969; Allen and Banks, 1972; Lowe and Lo Piccolo, 1974; Lowe, 1975). Cohesionless deposits underlying subaerial slopes often become liquidized for no obvious reason, the effect being called spontaneous liquefaction. Good examples occur amongst the often disastrous failures experienced by waste tips and spoil heaps (Bishop, 1973), and the retrogressive flow-slides in the highly sensitive quick clays (Smalley et al., 1975) of the Canadian and Scandinavian lowlands (Tavenas et al., 1971 ; Mitchell and Markell, 1974). In some of these cases, liquefaction apparently was due to an internal build-up of water to such an extent that the weight of the grains was eventually transferred entirely to the pore fluid, the material in consequence losing all shearing strength. Cohesionless sediments beneath subaqueous slopes can also be liquefied, in some instances spontaneously and in others because of earthquakes (e.g. Koppejan et al., 1948; Terzaghi, 1957; Andresen and Bjerrum, 1967; Bjerrum, 1971; P.A. Gilbert, 1976), or perhaps because of pressure fluctuations related to surface wave-action (Henkel, 1970; Mitchell et al., 1973; Moshagen and Tdrum, 1975). The undermining or withdrawal of support to the slope may also cause liquefaction (Peck and Kaun, 1948). Morgenstern (1967), Van der Knaap and Eijpe (1968), and Middleton (1970) urge that such subaqueous slope-failures may grow into turbidity currents, a potent agent for the transfer of coarse sediment from shallow to deep water. Hendry ( 1973) attributed bedding in certain subaqueously formed conglomerates to the episodic liquefaction of the parent deposit. The other chief mechanism of liquidization is fluidization, of particular interest to chemical engineers (Davidson and Harrison, 1963, 1971 ; Davidson and Keairns, 1978; Harrison, 1974; Kunii and Levenspiel, 1969; Leva, 1959; Reboux, 1954; Zenz and Othmer, 1960). This mechanism demands that fluid be forced upward through the grain-mass until the downward-acting immersed particle weight is balanced by the fluid drag. The grains if cohesionless then lose mutual support, the bed expanding, but maintain a constant average distance above the ground provided that the fluidizing flow persists. Clearly, externally supplied fluid is essential to fluidization, whereas if fluid enters a grain-mass during liquefaction, it does so merely passively and without playing an essential part in the change of state. Several geological roles are given to fluidization, particularly in regard to volcanic phenomena (D.L. Reynolds, 1954, 1969; J.B. Lewis, 1969; Schumm, 1970). The mobility of pyroclastic flows is attributed at least partly to fluidization, either by exsolved gases or entrapped air in terrestrial instances (Fenner, 1923; D.L. Reynolds, 1954; McTaggart, 1960, 1962; M.C. Brown, 1962; R.V. Fisher, 1966; Pai et al., 1972; Yokoyama, 1974; Sparks, 1976), to fluidization by exsolved gases in the lunar case (O’Keefe and Adams, 1965),

295

and in subaqueous examples to fluidization by steam generated from engulfed water (Niem, 1977). The evidence for gas-fluidization is strong, notably the discovery that hot debris may continue to evolve gases even after deposition (Gibson and Tazieff, 1967; I.L. Gibson, 1970). Kent (1966) suggested that cold rock avalanches achieve extra mobility as the result of being fluidized by engulfed air, an idea rejected by Shreve (1966, 1968a, 1968b), who regarded the air as merely forming a lubricating cushion. Middleton and Hampton (1973, 1976) believe that in the deep-water environment there occur “fluidized sediment flows”, that is, flows of concentrated particles created through liquefaction but which afterwards are in some way self-fluidizing. Lowe (1975, 1976) has rightly dismissed this notion, but on uncertain grounds. In this chapter we review mechanisms of liquidization, explore the properties and behaviour of liquidized sediments, and discuss the sedimentation of particle dispersions after liquidizing mechanisms are withdrawn. Two subsequent chapters will cover sedimentological phenomena partly related to liquidization, namely soft-sediment deformation structures (Chapter 9), and turbidity currents, pyroclastic surges, and pyroclastic flows (Chapter 10). The range of problems here raised well exemplifies the necessity, early demanded by Brush (1965b), of “a combined knowledge of basic physics, soil mechanics, and fluid mechanics” -a tall order by any standard! In these three chapters, the terms liquidization, liquefaction and fluidization refer to acts and mechanisms; the words liquidized, liquefied, and fluidized refer to the state of a material; and the terms liquidized sediment, liquefied sediment, and fluidized sediment refer to the material itself. Terms of general meaning- liquidization, liquidized, and liquidized sediment- are particularly necessary, in view of the continuing confusion in the sedimentological literature between liquefaction and fluidization and between liquefied and fluidized sediments.

VARIETIES OF LIQUEFACTION

Case-history analyses (Seed, 1968; Ambraseys and Sarma, 1969; P.A. Gilbert, 1976) points to three main kinds of liquefaction: (1) static, (2) dynamic, and ( 3 ) cyclic. These qualifying terms can be criticized on various grounds, but are brief and in many ways apposite. Static liquefaction follows from the sufficient increase of the pore-fluid pressure in a stationary mass of cohesionless grains. The single application to the mass of a sufficiently large impulse or load causes dynamic liquefaction. Cyclic liquefaction results from the repeated action of a reversing load, as during an earthquake, or during the passage of a train of water waves.

296

STATIC LIQUEFACTION

Consider in Fig. 8-1 a superficial layer of grains of solids of density u and uniform fractional volume concentration C, the pores being filled to a certain horizontal level with standing water of density p. The shearing resistance Txzat the level AB is: T,, = c

+ ( w ah,, + ( 1 - c ) ph ,-,I g

-

pgh

,-,) tan +

where c is the granular cohesion, h,, and h , are the thicknesses above AB of the granular and aqueous layers, respectively, g is the acceleration due to gravity, and 9 is the friction angle of the material (Lambe and Whitman, 1969). Under what conditions is T,, reduced sufficiently for failure to occur? The first term in eq. (8.1) is zero for unconsolidated sands and coarse silts, which are cohesionless, and the term in curly brackets-Terzaghi’s (1925) effective stress-is therefore the only one with any influence. It comprises two parts: (1) the total weight at the level AB of a unit column of grains plus any water, and (2) the pore-fluid pressure at that level which, since the system is in static equilibrium, is simply the hydrostatic pressure. In the system as depicted, the fluid pressure at a given level cannot exceed the total weight at that level. Hence the shearing resistance must remain positive because the effective stress is positive, and continuing stability is likely. But if the mass lay beneath an impermeable cover, we could by raising the hydrostatic

Fig. 8-1. Definition diagram for a partly water-saturated cohesionless sediment.

297

pressure so diminish the effective stress that failure became inevitable. Similarly, we could lower the effective stress sufficiently by inducing a seepage of water through the mass. Thus the mass can be made to fail under the action of exceedingly small body forces or pressure gradients, since the effective stress can be reduced to zero or even made negative by the means suggested. wnetner or not there is catastrophic failure depends on grain packing and fabric. If the concentration is high, shear strains arise only as the result of either grain elastic deformation, crushing or dilatation, or some combination of these. Crushing is inconsistent with a small effective stress. The immediate effect of dilating close-packed grains is to decrease the pore-fluid pressure, and so, referring to eq. (8.1), to increase shearing resistance (e.g. 0. Reynolds, 1885, 1886). Should the concentration be low, however, the supports between grains tend to be destroyed by the smallest shear strains and the fabric undergoes progressive collapse. If any subsequent change of volume of the mass is possible, the tendency will be for decrease. As the fabric collapses, the particle weights become transferred to the intergranular fluid, the pressure in which consequently rises monotonically, and the affected material changes state, becoming a two-phase “fluid” deforming under the slightest force. Figure 8-2 models this process. A uniform number of twodimensional particles occupying a constant space are shown first in a mutually supportive packing, next in an arrangement in which about half of the original number are “floating”, and finally in a packing in which no particle touches another. Equation (8.1) is strictly true only if (1) the grains are incompressible, and (2) the yield stress of the solids, which connects the contact area between grains and the intergranular shearing resistance, is independent of the

(a)

(bl

(el

Fig. 8-2. A model for sand liquefaction. The same ellipses, representing sedimentary particles, have been packed into a fixed rectangle in such a way that in (a) each ellipse touches at least one other, as with grains that give each other mutual support in a solid-like sand, in (b) some grains have been disconnected, as in a partly liquefied sediment, and in (c) no grain touches another, as in a fully liquefied sand.

298

confining pressure. Bishop and Skinner (1976) emphasize that real materials do not obey these conditions, and point out that, at sufficiently large pore-fluid pressures, the stress carried by grain contacts can be important in determining stability. To account for this factor, the term in curly brackets in eq. (8.1) should read: where A is the total projected contact area between grains per unit area at the level AB. Now A is of order 0.01-0.1 for natural cohesionless sediments, whence the third term is negligible only when the pore-fluid pressure compares with the effective stress as given in eq. (8.1). Static liquefaction is illustrated well by the local phenomenon of flowsliding, the failure of slopes underlain by well-sorted coarse silts to fine sands poor or lacking in clay minerals, followed by a protracted surge of liquidized debris. These slides are common on the banks of the estuaries of the Rhine and Schelde (Koppejan et al., 1948), occurring chiefly at low tide during periods of unusually large tidal range, probably in response to seepage-related pore-fluid pressures (see eq. 8.1). Slides of a similar character and cause typify the margins of the Norwegian fiords (Bjerrum, 1971), and are also known to involve the point-bar sands of the Mississippi River (P.A. Gilbert, 1976). Many of the quick-clay flow-slides of the Canadian lowlands appear to exemplify static liquefaction (Mitchell and Markell, 1974). As with the disastrous Saint-Jean-Vianney flow-slide, which followed heavy rain and surface flooding, they are perhaps triggered mainly by excessive pore-fluid pressures. Bishop (1973) summarizes a number of failures of waste tips and spoil heaps which may also represent cases of static liquefaction. In one of these, the failure of the fly-ash tip at Jupille, Belgium, the pore fluid seems to have been moist air and the trigger the removal of support to the slope. DYNAMIC AND CYCLIC LIQUEFACTION

General effects of earthquakes and related disturbances The general effect of earthquake-induced shear waves on a layer of cohesionless sand or coarse silt overlying bed-rock is to subject elements in the layer to repeated horizontal shaking. Each element experiences a periodically reversing shear stress, T,,, while confined under a constant normal stress, S, controlled by the amount of sedimentary overburden and the level of the water table (Fig. 8-3). The frequency, amplitude, and duration of shaking vary with earthquake magnitude, distance to epicentre, and the character and thickness of the strata through which the shocks have travelled. Cyclic liquefaction related to earthquakes is mainly associated with those of magnitude 6 and more (Seed, 1968; Seed and Idriss, 1971). The maximum

299

6

Unconsolidated deposit

Bedrock

Fig. 8-3. Schematic representation of the behaviour of an element in loose sediment subjected to earthquake shocks.

ground surface acceleration during such events is in the order of 0.2g, and the frequencies of earth-shaking fall mostly in the range 0.1-10 Hz (C.F. Richter, 1958). Maximum horizontal ground surface velocities are therefore commonly in excess of 0.1 m s - ’ . Strong shocks are generally felt for periods in the order of 10-100 s, and there may be weaker aftershocks at intervals of a few minutes. Laboratory work (Goodman and Appuhn, 1966) suggests that the magnitude of the ground acceleration and the amplitude of the ground motion increase with depth below the surface, but in real cases the succession of strata must be the factor determining the profile of displacements and accelerations. Case histories reveal that, given favourable circumstances, cyclic liquefaction can simultaneously affect cohesionless deposits lying within areas measuring hundreds and even thousands of square kilometres (Seed, 1968; Ambraseys and Sarma, 1969; Seed and Idriss, 1971). The phenomenon is therefore of regional rather than local importance. On the supposition that the column of water-saturated cohesionless sediment above an element at a depth h below the ground surface behaves as a rigid solid, Seed and Idriss (1970, 1971) calculate that the maximum shear stress experienced by the element during an earthquake is: where y is the bulk density of the sediment (including pore water) and amaxis the maximum ground surface acceleration. In reality, the column is not rigid, and the above value of ( T,Jmaxmust be reduced by a factor inversely related to h and also dependent on lithology. At a depth of 30m, for example, the observed maximum shear stress is less by a factor in the order of 0.5. When ( qz),,,= exceeds the static shear strength of the sediment, liquefaction commences and extensive deformation become possible. Ambraseys and

300

Sarma (1969) and P.A. Gilbert (1976) show that the static shear strength also increases with h , as representing the overburden pressure, but that it is extremely sensitive to grain concentration, decreasing steeply, as Bjerrum et al. (1961) found experimentally, as the packing grows looser. At loosest possible random packing, a cohesionless sand or silt has negligible static shear strength. Cyclic loads apparently able to cause liquefaction are imposed on the sea bed by surface waves (Henkel, 1970; Mitchell et al., 1973; Moshagen and T&-um, 1975; Madsen, 1978). It can be shown (Wiegel, 1964; Mitchell et al., 1973) that the deviation of the bottom pressure from the still-water value is:

(8.3) where H, L and T are respectively the wave height, wavelength, and wave period, x is distance in the direction of wave propagation, t is time, and d is water depth. Because of the pressure difference between wave crest and trough, the passage of a wave induces a time-dependent shear stress in the bottom sediment. According to eq. (8.3), the magnitude of the stress is negligible for L>0.5d but increases to a maximum dependent on H at a depth that is a small fraction of L . Storm waves have heights in the order of 10 m and frequencies in the order of 0.1 Hz, comparing with some earthquake vibrations. Henkel (1970) and Mitchell et al. (1973) show that such waves could trigger the failure of low-strength sediments in water depths of the same order as the wave height. Dynamic liquefaction depends on events of a more local character than earthquakes and storms, for example, explosions, the fall of massive bodies, or the sudden advent of tsunami or river flood waves. The general effect of these agencies may not be dissimilar to that of earthquakes, but with two possible differences: (1) any induced ground vibrations are probably shortlived, and (2) stressing in some cases may be related to compressional rather than to shear waves. Whereas the effects of tsunami can be felt over fronts measuring tens or hundreds of kilometres, the sudden impact of a massive body or a river flood wave may affect an area of but a few tens of square metres. Further details of the response of cohesionless sediments to impulsive loads appear in Krizek (1971b), who also discusses clay soils (Krizek, 1971a).

Laboratory studies of cyclic liquefaction Because of its relevance to constructional engineering in earthquake zones, cyclic liquefaction is extensively studied in the laboratory, at two sample scales and using two main kinds of test. Broadly, a cyclically reversing shear

301

stress, with a frequency in the order of 1 Hz, is applied to a confined sample of cohesionless and usually water-saturated sand or coarse silt until either complete liquefaction occurs or a stable condition arises. Pore-water pressure and cyclic strain are measured throughout each experiment. Much work has rested on adaptations of the simple-shear and triaxial tests familiar in soil mechanics, which use samples with dimensions in the order of 0.1 m (Lambe and Whitman, 1969). A sample in a simple-shear test is cyclically stressed horizontally while confined under a known vertical load (Seed and Lee, 1965; Peacock and Seed, 1968; Finn et al., 1969). In the triaxial tests which many workers have favoured (Seed and Lee, 1965, 1966; Lee and Seed, 1967a, 1967b; Castro, 1969; Finn et al., 1969; Seed and Peacock, 1970; Lee and Albaisa, 1974; Wong et a]., 1975; Ladd, 1977), the sample is confined under a uniform all-round load while cyclically stressed in a single direction. Partly on account of the small sizes of the samples employed, and partly because the adapted simple-shear and triaxial tests have often given conflicting results, several investigators have preferred a kind of simple-shear test in which a large sample with dimensions in the order of 1 m is stressed either on a horizontal shaking table or by repeated impacts (Florin and Ivanov, 1961; Seed and Goodman, 1964; Goodman and Seed, 1966; Yoshimi, 1967; Finn et al., 1970b; Prakash and Gupta, 1971; Seed and Silver, 1972; Seed et al., 1975; De Alba et al., 1976). Figure 8-4 epitomizes the main results of these tests (e.g. Seed and Lee, ( a ) LOW-CONCENTRATION

DEPOSIT

'U ( b ) HIGH-CONCENTRATION A

Time,

t

DEPOSIT Confining pressure

.C

F

+ v)

0

2 0

Time,

t

Fig. 8-4. Summary of behaviour of cohesionless materials at relatively low and relatively high concentrations when cyclically loaded.

302

1966; Lee and Seed, 1967a, 1967b; Peacock and Seed, 1968; Finn et al., 1969; De Alba et al., 1976). Complete liquefaction is obtained with samples having a low grain concentration (Fig. 8-4a). The pore-fluid pressure at first rises rapidly but tends to level off before increasing steeply again to become constant at the value of the confining pressure, the effective stress having fallen to zero. The sample experiences negligible deformation during the period of pressure rise but, coincident with the attainment of the confining pressure, suddenly displays the very large cyclic strains consistent with general liquefaction. These large strains can be maintained even when the amplitude of the applied cyclic stress is greatly reduced. Presumably the monotonic pressure increase reflects the progressive collapse of the system of mutual supports between the grains, as in the model of Fig. 8-2. Samples of high grain concentration behave differently in several respects (Fig. 8-4b). Substantially larger maximum shear stresses must be applied in order to obtain measureable strains. The pore-fluid pressure rises gradually with increasing number of loading cycles, but may level off at a value significantly less than the confining pressure, or may equal the confining pressure only at certain instants during the loading cycle. Similarly, the cyclic strain increases gradually before becoming of constant amplitude. Even though the effective pressure may become zero, such samples cannot be said to be liquefied in the sense that they are capable of extensive deformation.

Factors influencing cyclic liquefaction The laboratory work summarized above shows that cyclic liquefaction in cohesionless sediments is favoured by: (1) increase in amplitude of the cyclic shear stress, (2) increase in number of loading cycles, (3) decrease in confining pressure, (4) decrease in sample grain-concentration, and (5) decrease of grain size. It is disfavoured by the presence of clay minerals, which confer cohesion, whence muddy sediments (e.g. Koutsoftas, 1978; Taylor and Morrell, 1979) are as difficult to liquefy as gravels. Some of these influences are illustrated in Fig. 8-5, based on the data of Finn et al. (1969) for a medium grained sand in simple shear. The possible field of behaviour is limited by the grain concentrations in closest possible and loosest possible random packings, which are here given notional values as they were not measured. The experiments also reveal that loading frequency has little effect on liquefaction behaviour, at least in the range 0.1-10 Hz, that typifying earthquake shear waves. The sample history, however, exerts an important but as yet poorly understood influence (Lee and Seed, 1967b; Finn et al., 1970a; Ladd, 1977). Although the ultimate effect of cyclic loading typically is to increase packing density (e.g. Linger, 1963; Prakash and Gupta, 1971; Silver and Seed, 1971a, 1971b; Seed and Silver, 1972; Lee and Albaisa, 1974), the tendency towards liquefaction is not always reduced by repeated episodes of such stressing, although repeated low loadings generally are

303 0.62

I

l

l

1

I

I

1

1

1

I

1

1

1

1

1

1

1

1

I

1

1

,

0.65

0.64

0.63 c

0 .+

1c 0 . 6 2 0

c

--

0.61

0 0

c

0.60

0.59 In all runs S = 1.96 x lo5 N m-2

0.58

0.57

0.56

I

2

1

1

1

1

I

4 6 8100 2

I

I

I

I

4 6810i

I

2

1

1

1

1

4 6ElO2

I

2

I

l

l

,

4 6EI03

I

2

I

I

L

4 6 ElO4

Number of cycles to liquefaction

Fig. 8-5. Resistance to liquefaction of a quartz sand of median diameter 0.0004 m in simple shear, at a constant confining load and as a function of particle concentration and magnitude of cyclic stress. After Finn et al. (1969).

effective (Seed et al., 1977). Finn et al. (1970a, 1970b) found that some samples could be reliquefied and that those which had experienced large cyclic strains could be liquefied more easily than before, even though of heightened grain concentration. The effect is -probably not confined to the laboratory. The Niigata area in Japan has experienced many large-magnitude earthquakes, yet the unconsolidated deposits there are still liable to liquefy under shock (Seed and Idriss, 1970, 1971; Ambraseys and Sarma, 1969). One effect of the 1964 earthquake, for example, was apparently to increase some strata in proneness to liquefaction but to decrease others (Kishida, 1966). Subtle changes in grain packing and fabric may explain these effects (Finn et al., 1970a). Proneness to liquefaction can also be discussed in terms of the actual or potential volume change during stressing (Geuze, 1948; Castro, 1969; Castro and Poulos, 1977). The curve in Fig. 8-6 shows the locus of states in which a given material will deform at constant grain concentration, constant effective

304

I -+E

l

I/ 2!

W

DILATA N T MATERIALS

-

F I R M

C O N TRACTIVE

MATE R I A L S

QUICKSANDS

Fig. 8-6. Summary of response of cohesionless sands to cyclic loads, as a function of grain concentration and confining pressure.

confining stress, and constant shear stress. It is, alternatively, the graph of the maximum liquefaction concentration, a function of the confining pressure and the material under study. Below it lie contractive materials, capable of complete liquefaction, whereas above come dilatant ones, which either increase in shear resistance during loading or lose but little strength. As in Fig. 8-5, the possible fields of behaviour are bounded by the grain concentrations for loosest possible and closest possible random packing. A material starting out in state A will move along the path AA’ to the curve when monotonically or cyclically loaded. One commencing in state B will move to B’ on the ordinate, affording a quicksand. A monotonically loaded sample starting out in stateC, however, will move to the right towards the field boundary, increasing in strength in the process. Points on the ordinate may be reached instantaneously by contractive materials when cyclically loaded, Estimation of liquefaction potential

Engineers naturally regard it as vital to be able to estimate in earthquake zones the liquefaction potential of the deposits upon which structures are to be raised. These procedures are explained and reviewed in numerous publication (Finn, 1966; Idriss and Seed, 1967; Seed, 1967; Ambraseys and Sarma, 1969; Kurzeme, 1970; Seed and Idriss, 1970, 1971; Seed and Peacock, 1970; Yoshimi and Kuwabara, 1973; Castro, 1975; Christian and Swiger, 1975; Lee and Focht, 1975; Seed et al., 1975; Finn et al., 1976, 1977; Castro and Poulos, 1977), and could aid future sedimentological studies of softsediment deformations.

305 VARIETIES OF FLUIDIZATION

Whereas the pore fluid in liquefaction is essentially passive, in fluidization it is the vital and active agent, providing by its upward movement the force that sustains the particle weight after bed-expansion past the stage when grain contacts can exist. Several varieties of fluidization may be distinguished, according to the origin of the fluid phase and whether or not the fluidized mass is in translational motion. The simplest variety is stationary (conventional) fluidization in which a fluid stream is forced upward through a static grain-mass supported from below (Fig. 8-7a). Although the fluidized mass is stationary in the sense that there is neither horizontal motion nor vertical movement of its centre of gravity, internal motions, of individual grains relative to each other, and others of a gross circulatory nature or resembling turbulence, are not precluded. In contrast, the term translational fluidization covers all those modes in which the fluidized material is in horizontal motion. Flow-fluidization (Fig. 8-7b) describes the translation of grains over a sloping bed upward through which a fluid is discharged at a rate sufficient to balance the particle weight (Siemes and Hellmer, 1962; Douglas and Walsh, 1966; Douglas et al., 1967; Botterill et al., 1970; Botterill and Van der Kolk, 1971; Douglas and Sayles, 1971; Botterill et al., 1972; Botterill and Bessant, 1973; Botterill and Abdul Halim, 1978; Singh et al., 1978). Apparently, there are no known natural counterparts, but their occurrence is not impossible. The term bulk sevfluidization (Fig. 8-7c) is appropriate to the kind of fluidization that Kent (1966) envisaged for avalanches, in which debris is supported by the internal upward flow of fluid engulfed at the snout of the moving mass, rather in the manner of turbidity currents (Fig. 1-6b). The third type of translational fluidization is grain sev-fluidization. Here the fluid phase comes from the

(01 Stationary

( b ) Flow-fluidization

fluldlzation

( d ) Grain self-fluidization

( c ) Bulk self-fluidization

Fig. 8-7. Main classes of fluidization. Here, V is the superficial fluid velocity and superficial velocity at which fluidization occurs.

Ynr the

306

fluidized particles themselves, as is proposed for flows composed of magma fragments from which gases are exsolved. STATIONARY FLUIDIZATION

Regimes of fluidization

The regime of fluidization depends on the properties of the granular solid and fluid involved and on the geometrical boundary conditions, as summarized in numerous textbooks and reviews (Davidson and Harrison, 1963; Davidson and Keairns, 1978; Harrison, 1974; Kunii and Levenspiel, 1969; Leva, 1959; Mathur and Epstein, 1974; Reboux, 1954; Vanecek et al., 1966; Zenz, 197 1 ; Zenz and Othmer, 1960). Four regimes are recognized which, for the purpose of discussion, are considered to arise in a vertical tube containing a monodisperse granular bed supported on either a porous plate or the sides of a funnel (Fig. 8-8). The boundary conditions in natural cases of fluidization are in some cases similar to this, for example, when debris is fluidized in the shaft of a volcano, or in a conduit allowing water to escape from a sedimentary slump. They are otherwise different, as during selffluidization. In the static-bed, packed-bed or fixed-bed regime the fluid has a superficial velocity V , calculated on the basis of the empty tube, less than the ( b ) Incipient fluidization

l a ) Fixed-bed

Id1 Aggregative

: c ) Particulate fluidization

fluidization

f

Chonneling

Porvoids

Bubbling

Fig. 8-8. Main types of stationary fluidization.

Slugging

Spouting

307

superficial velocity V,, which will just effect fluidization (Fig. 8-8a). Particles consequently remain supported at grain contacts, though the apparent immersed bed weight is less than the true weight. The regime of incipient fluidization (Fig. 8-8b) is attained when V equals V , , , the bed for the first time becoming fluid-like. The immersed weight is just balanced by the total fluid drag. Were the grains at all closely packed at the start, the bed will have expanded slightly in order for fluidization to have occurred. But there is a fractional volumetric grain concentration C,, which permits incipient fluidization without bed expansion. This concentration is closely comparable with the concentration in loosest possible random packing. Two almost alternative and ostensibly different regimes are encountered as V is raised above Vmf,depending on the properties of the system. The fluidization of solids by liquids is normally in the particulate regime (Fig. 8-8c). With increase in the superficial velocity, the bed expands in harmony as the grains interact with the flow so as to maintain a uniform separation distance. This striking uniformity can persist to remarkably small values of the grain concentration, the fluidized bed retaining a well-defined top though, of course, occupying an increasingly greater fraction of the tube. The fluidized bed is strongly non-uniform in aggregatiue fluidization, normally shown by gas-solid systems (Fig. 8-8d). Four kinds of nonuniformity are recognized. The fluid passing through a channelling bed, is confined to fairly straight, circular to oval conduits while much of the intervening grain-mass continues in the fixed-bed state. Channelling is typical of beds of particles that are fine (e.g. wheat flour, quartz silt) or of such a composition (e.g. clay minerals) that surface forces are significant (e.g. Matheson et al., 1949; Brekken et al., 1970). Grain-free bubbles of gas trailing wakes behind them- the combination resembles a long-stalked mushroom-are present in a bubbling bed. The bubbles, originating at the apertures in the supporting porous plate, usually grow larger upward, as the result of coalescence and the absorption of more gas. At a sufficiently high superficial velocity, the bubbles may become large enough to fill the width of the container, the bed then being described as digging (Stewart and Davidson, 1967). Rowe (1971) gives an excellent description of bubbles and their associated phenomena. Typically, the bubbles are relatively thick and globular, as depicted in Fig. 8-8d, but systems are known in which very flat and irregular bubbles are produced. Hassett ( 1961) reported such bubbles, which he called paruoids (partial voids) from beds of glass ballotini fluidized with water. I have observed trains of analogous flat, irregular voids separated by sheets of gas bubbles in “Guinness”- the internationally known stout of Ireland-that has been freshly drawn. Hassett’s parvoids rise by the fall of ballotini from the roof of the void and then accumulation on the floor below; those in Guinness descend by the opposite process. The spouting fluidized bed, claimed by some as not representing fluidization at all (Mathur and Epstein, 1974), arises when the container has but a single narrow basal

308

orifice. The grains entrained by the fluid jet from the orifice are carried up and deposited at the periphery of the container, from there to sink downward to further entrainment by the jet. Grains can experience considerable rounding and size-reduction if extensively recirculated in a fluidized bed (e.g. Gwyn, 1969). It is commonly said that liquid and gas fluidization differ in some fundamental way, but this is not borne out experimentally (Wilhelm and Kwauk, 1948; Matheson et al., 1949; E. Johnson, 1950; Lawther and Berglin, 1957; Cairns and Prausnitz, 1960; Harrison et al., 1961; Hassett, 1961; Simpson and Rodger, 1961; J.W. de Kock and L.S. Leung in Davidson and Hamson, 1963; Davies and Richardson, 1966; Reuter, 1966; Lawson and Hassett, 1967; Stewart and Davidson, 1967; Crowther and Whitehead, 1978). There are many liquid-solid systems that fluidize aggregatively, and numerous gas-solid systems that fluidize in a particulate manner. Simpson and Rodger, in particular, obtained a single correlation representing an extremely wide range of fluidized systems. It is too complex to be discussed here, but shows that aggregative fluidization is favoured by: (1) large solids density, (2) low fluid viscosity, and (3) large solids diameter (in the absence of intergranular cohesive forces). Thus lead shot can be fluidized aggregatively in water, though not in glycerol, and small plastic particles will respond particulately in dense gases. The reasons for particulate behaviour in some systems, but aggregative behaviour in others, remain mysterious but may be connected with the instability of fluidized beds to small disturbances. Rice and Wilhelm (1958) found the unsupported lower surface of a fluidized bed to be theoretically unstable (Rayleigh-Taylor instability) and proposed that this was related to aggregative behaviour. Later investigators, mainly working with linearized equations, stressed the stability of a fluidized bed to small internal disturbances (R. Jackson, 1963a, 1963b, 1971; Murray, 1965; Pigford and Baron, 1965; Molerus, 1967; Anderson and Jackson, 1968). These studies show that fluidized beds are unstable to small disturbances in the form of compression waves, which are the only waves leading to variations of particle concentration, that is, to such phenomena as bubbles. Such disturbances are amplified in both liquid-solid and gas-solid systems, however, but in the former case have growth rates orders of magnitude smaller than in the latter. A particulate bed interpreted in these terms therefore only appears to be uniform. Harrison et al. (1961) and Davidson and Harrison (1963) approached the issue by considering the stability of bubbles. They argued that if the rising velocity of a bubble exceeds the falling velocity of the grains in its wake, then the bubble will tend to fill up and, consequently, to diminish. No such tendency exists when the grain falling velocity exceeds the bubble rising velocity. It follows that the bubbles that can exist in a liquid-fluidized bed are very much smaller than those that can be present in a gas-fluidized

309

system. If the bubble and grain sizes were similar, the bed would seem uniform and the regime would be identified as particulate. A different approach again, from energetics, is followed by Doichev (1974) and Doichev et al. (1975). They argue that the regime (particulate or aggregative) actually observed in a given system is that for which the centre of gravity of the fluidized bed is a minimum. Knowing the properties of bubbles, a criterion of regime can then be found by comparing the average fluid velocity within the bed under an assumed particulate regime with that under an assumed aggregative one. It follows that the boundary between the two regimes is: (8.4)

in which u and p are the densities of the solids and fluid, respectively, g is the acceleration due to gravity, D is the particle diameter (assumed spherical), TJ is the fluid dynamic viscosity, y is the bulk density of the fluidized bed, and Cmf is the fractional volume grain concentration at incipient fluidization (Fig. 8-9). Particulate fluidization is observed when the left-hand side of eq. (8.4) is the smaller, and aggregative fluidization when it is the larger. The first bracketted term on the left is the Galileo number, Gu, used by some workers as a criterion for the existence of bedforms (Vol. I, Chapter 8). Equation (8.4), resembling the theoretical stability criterion of Molerus (1967), is consistent with most earlier work (e.g. Simpson and Rodger, 1961)

0 1 0.450

1

0.500

I

0.550

I

0.600

0.

0

Minimum particle concentration at fluidization, Cmf

Fig. 8-9. Stability of stationary fluidized beds, according to Doichev's (1974) criterion.

3 10

and has good experimental support (Doichev, 1974; Doichev et al., 1975). As regards granular materials of sedimentological interest, C,, can be taken as equal to the concentration in loosest possible random packing, for which a value of 0.55 is typical (Vol.1, Chapter4). The right-hand side in eq. (8.4) therefore has a value close to 180. Given the particle-size range and density of natural debris, we see that fluidization by water is ordinarily particulate, whereas fluidization by air or hot volcanic gases is normally aggregative. Rietema and Mutsers ( 1978) have further considered the stability of fluidized beds.

Minimum fluidization velocity Consider in Fig. 8-10 the upward flow of fluid through an initially well-packed bed of height h formed of monodisperse cohesionless grains supported on a porous plate in a vertical tube with pressure tappings. As the fluid superficial velocity rises above zero, the pressure drop A p across the bed increases linearly along the path AB, reaching a maximum value at B. The sharp decrease between B and C is associated with a slight expansion of the bed, as the originally tightly packed grains unlock. Incipient fluidization is attained at point C, the superficial velocity being V,,, the concentration C = Cmr,and the bed height h,, > h. Provided that the fluidization is particulate, and no grains are swept from the tube, the pressure drop subsequently is constant, following the path CE. On decreasing the velocity, however, the pressure drop follows the path ECD, while the bed height becomes constant at hmf.On raising the superficial velocity again, no further

Superficial velocity, V

Fig. 8-10. Pressure drop as a function of superficial velocity during the fluidization of a cohesionless bed.

311

increase of bed height is observed as fluidization occurs, and the path DCE is retraced identically. Thus when the initial concentration is C,, , hysteresis disappears from the system. It is worth pointing out that the bed does not fluidize instantaneously in response to a sufficient increase in the superficial velocity. As V,, is exceeded, a wave of fluidization is observed to pass upward through the fixed bed, just as a wave of change marks any sudden shift in V in an already fluidized bed (Slis et al., 1959). As Richardson (1971) emphasizes, real systems tend to deviate from this idealized behaviour (e.g. Leva et al., 1951), and it is not always easy to measure V,, from an experiment of the kind just described. Although some ingenious practical alternatives have been proposed (e.g. Verloop and Heertjes, 1973), it is a common practice to calculate V,, on some theoretical or empirical basis. At incipient fluidization, the pressure drop across the bed must equal the immersed bed weight:

A P = C m , ( a - P)ghrn,

(8.5) If now the pressure drop can be written in terms of fluid and particle characteristics, then the minimum superficial fluidization velocity follows. Several solutions have been proposed based on an analysis of flow through the tortuous passages of a fixed bed. The Carman-Kozeny equation (Scheidegger, 1960) affords, as developed by Davidson and Harrison (1963): V,, = 0.001 14

(0 -

P W 2

II for uniform spheres at Reynolds numbers in the viscous range. Other developments from the Carman-Kozeny equation are explained by Leva (1959), Kunz (1971) and Richardson (1971). An equation appropriate to both inertial and viscous conditions was proposed by Ergun (1952) and extended by Wen and Yu (1966a, 1966b). It reads (Lowe, 1976): V,, = -

150k211 3.5kIDp

+[ (

150k2q ) 2 3.5k,Dp

-p)gD + ( a1.75k,p

where the numerical constants k , and k, are functions of particle shape and C,, respectively. For uniform spheres, k, = 10.3 and k, = 7.83, but values of 14 and 11, respectively, are suggested by Wen and Yu for general use. Notice that V,, is independent of bed thickness in this equation and in eq. (8.6). Further discussion of Ergun’s equation appears in Leva (1959), Kunii and Levenspiel ( 1969), Richardson (1971), and Broadhurst and Becker (1975). The minimum superficial fluidization velocity is one to two orders of magnitude smaller than the particle free falling velocity. Figure 8-11 compares values of V,, for mineral-density solids in water at 20°C from eq. (8.7) with values for W , from Rubey’s (1933) general settling law (Vol.1,

312

Particle dlometer. D (m)

Fig. 8- 1 1. The minimum fluidization velocity and falling velocity of quartz spheres in water at 20°C.

Chapter2). For small particles W, is approximately 100 times V,, but for large grains it is but 10 times larger. Beginning with Pinchbeck and Popper (1956), several authors have shown that the ratio W,/V,, is correlated with the Galileo number, ranging from approximately 75 for Ga < 1, corresponding to the Stokes range, to about 10 for Gu> los, when conditions are inertial (Richardson, 1971). At small values of the number, the ratio is somewhat sensitive to Cmf.The Galileo number involves the solid and fluid densities, the particle diameter, and the fluid viscosity. It will be recalled that the number appears also in eq. (8.4), a criterion of fluidization regime. Large values of W, / V,, therefore correspond to particulate fluidization, whereas small values equate with the aggregative regime.

Bed expansion It is important sedimentologically as well as in chemical engineering practice to know how the height and average grain concentration within a bed change as the superficial velocity varies. For some years it has been customary to express this relationship by an empirical correlation of the form of eq. (2.22) of Vol.1, given above for the sedimentation of a particle

313

dispersions (Hancock, 1937; Lewis et a]., 1949; Lewis and Bowerman, 1952; Richardson and Zaki, 1954a; Whitmore, 1955, 1957; Richardson and Meikle, 1961a, 1961b; Kramers et al., 1962; Godard and Richardson, 1968; Capes, 1974; Wakeman and Stopp, 1976; Singh and Sen Gupta, 1980). Surprise should not be occasioned, because it is easily shown that fluidization and sedimentation are fundamentally identical (e.g. Lapidus and Elgin, 1957; C.C. Harris, 1959a, 1959b; Anderson, 1961); for example, the superficial velocities in the two cases are the same when measured relative to the grains. Richardson's ( 1971) version of the Richardson-Zaki correlation for particulately fluidized uniform spheres reads, with V, as the interstitial fluid velocity : ( V / V i )= (1 - c)"

(8.8)

where d is the width of the fluidization chamber, log V , = (log W, - D / d ) , and the empirical exponent n is a function of particle shape, the ratio D / d , and the Reynolds number Re = W, D p / v , as follows: n = 4.65 20( D / d ) , Re < 0.2 (8.9a)

+ n = [4.4 + 18(D / d ) ]Re-O.O3,

0.2 < Re < 1

(8.9b)

n=[4.4+ 18(D/d)]Re-'.',

1 < Re < 2 0 0

(8.9~)

< 500

n = 4.4ReV0.', 200 < R e

(8.9d)

n = 2.4, Re > 500

(8.9e)

How grain shape affects the exponent is less satisfactorily understood, though Richardson and Zaki (1954a) show that at large Reynolds numbers

0.6

1

0 1

10-4

C,,.0~55

'

2

"

4

I

'

6 el0-3

'

2

4

6 Bl0-z

I

2

" "

4

6 8

lo-^

'

2

'

I

'

4 6 f 00

Vdoclty ratlo. W W ,

Fig. 8-12. The relative falling velocity of particles in a dispersion as a function of concentration and exponent in the falling velocity-concentration equation.

314

the value increases with decreasing particle sphericity (see also Whitmore, 1955, 1957). The exponent changes with the Galileo number in much the same manner as its variation with the Reynolds number (Richardson, 1971). Figure 8-12 depicts eq. (8.8) at a range of values of n, for D/d negligibly small and a maximum concentration of C = 0.55. The graph is bounded at one limit by the condition C = Cml,whence: Vmf = W,( 1 - Cmr)”

(8.10)

affording a means of estimating the minimum fluidizing velocity. The other bound is the condition C = 0, whence V = W,. Hence in Fig. 8-11 the field of fluidization is bounded below by the curve of Vmf and above by the curve for W,. When V > W, particles must be swept away by the fluid, eroded in Kezdi’s (1979) terms, whence a field of hydraulic transport (elutriation) can be identified (Leva and Wen, 1971). Finally, when V < Vmf, we have what Lowe (1975) has generalized as the seepage regime, during which the finest particles of all may be carried upward out of the bed, or suffused (Kezdi, 1979). Equations (8.8) and (8.9) for the particulate regime are reliable to concentrations as small as about 0.1, but may be somewhat in error at very small values (Happel, 1958; Adler and Happel, 1962). However, considerable departures from eq. (8.8) arise in aggregatively fluidized systems (Richardson, 1971), particularly those involving deep beds of fine particles. An equation for the expansion of freely bubbling beds is given by Godard and Richardson ( 1969). Polydisperse systems The emphasis has so far been on systems involving grains of a single density and size, or at least of a relatively narrow size range. Most natural granular materials are polydisperse, consisting of a wide range of particle sizes and often of densities. How do these materials behave when fluidized? The equations describing the incipient fluidization of monodisperse particles are applicable to mixed sizes, provided that a valid average grain size is calculated (Leva, 1959; Chiba et al., 1979). Polydisperse systems tend to fluidize more gradually, however, than systems involving only one particle size. Complete fluidization is at first local in occurrence and even an apparently fully fluidized bed may contain pockets of unmobilized grains. Of particular importance in polydisperse systems are segregation and elutriation. Segregation, also called stratification or classification, is the vertical and, to a much smaller extent, horizontal ordering of the grains in a fluidized bed according to size and/or density. Most early references to segregation are either incidental or qualitative (Parent et al., 1947; Verschoor, 1950; Leva et al., 1951; Osberg and Charlesworth, 1951; Hall and Crumley, 1952), but

315

several detailed studies have since been made of both particulate systems (Jottrand, 1954; Richardson and Zaki, 1954b; Scarlett and Blogg, 1967; Garside and Al-Dibouni, 1974; Wakeman and Stopp, 1976; Juma and Richardson, 1979) and gas-fluidized beds, chiefly of the bubbling variety (Thomas et al., 1961; Rowe et al., 1972a, 1972b; Nienow et al., 1978). The degree of segregation depends on the spread of grain sizes and/or densities and on the vigour of fluidization, as measured either by V/Vmf or (1 C)/( 1 - Cmf).In particulate systems there is negligible segregation provided that V/Vmf is close to unity and the settling velocities of the grains differ by less than about two-fold. With increase of V/Vmf the particles of smaller size or density ascend into the upper part of the bed, those of greater density or size remaining in the lower part. A slightly different sequence is observed from bubbling beds. Maximum segregation occurs when V/Vm, takes an intermediate value, the classification being negligible for values close to unity and also for very large values. Pruden and Epstein (1964), and Gibilaro and Rowe (1974), present theories of segregation. For every polydisperse system a value of the superficial velocity exists at which the smaller or less dense particles begin to be entrained and carried away by the flow, leaving a bed enriched in the denser or larger grains. This is the process of elutriation (Fig. 8-11), reviewed by Leva and Wen (1971), and both particulate and aggregative systems are affected. Segregation and elutriation are time-dependent processes, and cannot be expected to go to completion in beds that are only briefly fluidized (e.g. Hanesian and Rankell, 1968). BULK SELF-FLUIDIZATION

Kent’s (1966) bulk self-fluidization of cold avalanches, to which Shreve (1966, 1968a, 1968b) objected, should not be finally dismissed without quantitative assessment. Consider in Fig. 8-13 a bed of uniform slope p beneath water or air down which flows an avalanche of uniform normal thickness h and length L measured along the bed. The flow travels at a steady velocity U parallel with the bed and consists of grains of a single free falling velocity W, at a uniform concentration C > Cmf.Because of the viscosity of the medium, the snout of the avalanche overhangs the bed, and medium is squeezed beneath the flow (Allen, 1971b). Superimposing a velocity - U on the avalanche, bringing it to rest, the streamlines for the motion will appear as in the diagram. The streamline terminating at S is a stagnation streamline that originates at an asymptotic height hs far upstream. By continuity, the discharge of medium per unit width into the space beneath the avalanche is: q = h,U (8.11)

316

! /

Fig. 8-13. Definition diagram for bulk self-fluidization.

assuming the medium to be incompressible. If the inflow is deflected uniformly upward amongst the grains, then the vertical superficial velocity becomes: h,U cos /3 V= (8.12) L Substituting from eq. (8.8) and from hs = k , h , where k , << 1 is a numerical constant, we obtain: U=

LW,( 1 - , ) ' I k , h cos p

(8.13)

for the speed of the avalanche if bulk self-fluidization is to occur during flow. Now we can also calculate U from the appropriate equations of motion, say from the Chezy-type relationship for uniform steady flow: (8.14) in which y is the avalanche bulk density, p is the density of the medium, and f is the total Darcy-Weisbach friction coefficient. Substituting eq. (8.14) into eq. (8.13) and rearranging, we obtain: (8.15) as the criterion for bulk self-fluidization. Evidently this state is favoured by a short avalanche length, a large avalanche thickness, a small free falling velocity for the component grains, and a high grain concentration. Now let us assume mineral-density solids and insert into eq. (8.15) practical values of the quantities involved, say, L = 50 m, h = 1 m, C = 0.4, n = 3, k , = 0.01, f = 0.08 and sin p = 0.1. We find that W, must be comm s-' if bulk selfparable with or smaller than approximately 3 X fluidization is to occur. An avalanche in water must therefore be composed of silt-sized particles and one in air of even finer dust. Bulk self-fluidization as envisaged by Kent (1966) can on these grounds arise only in avalanches composed of very small or very light particles; the upward movement of an

317

engulfed medium through an avalanche of coarse mineral debris has no power to fluidize the flow. There is a reason why cold bulk self-fluidization may not occur even with very fine or very light grains. To judge from J.E. Simpson’s (1969, 1972) experiments on gravity currents, the interface beneath the avalanche in Fig. 8-13 will be subject to Rayleigh-Taylor instability, tending to roll up into longitudinal billows (Allen, 1971b). Hence the medium squeezed beneath the avalanche will not be discharged uniformly upward over the base of the flow, as assumed above, but will tend to rise in the form of large bubbles. These may significantly stir the debris, and could elutriate fines, but will not fluidize the bulk of the material on account of the extreme non-uniformity of the superficial velocity. Is bulk self-fluidization more likely in an avalanche of hot grains that heat and expand the entrapped medium as it rises from beneath? The possibility exists for atmospheric avalanches but can at once be dismissed for aquatic environments unless perhaps the water is heated to boiling. Assuming that the pressure within an atmospheric avalanche is the ambient pressure, it follows from the gas laws that hot grains increase V in eq. (8.12) by the factor O,,/O,, where O,, and Om are the absolute temperatures respectively of grains and air. Pyroclastic debris frequently has an initial temperature comparing with 1250”K, whence a five-fold increase in vertical superficial velocity arises. The enhanced superficial velocity remains inadequate to fluidize other than dust, however, and bulk self-fluidization fails to explain the readier flow of hot than cold sand (McTaggart, 1960). GRAIN SELF-FLUIDIZATION

Several workers give grain self-fluidization a significant role in the matron of pyroclastic flows and in ignimbrite deposition, on the basis of relationships comparing with eqs. (8.6) and (8.7) above (D.L. Reynolds, 1954; McTaggart, 1960; O’Keefe and Adams, 1965; Pai et al., 1972; Sparks, 1976). Chiefly because of the ill-sorted nature of ignimbrites, Sparks proposes that pyroclastic flows are merely semi-fluidized, the coarser debris being transported and segregated according to size and density within a “lubricating” matrix of self-fluidized fines. He therefore suggests that the transported materials are divisible between three phases: (1) debris too coarse to be self-fluidizing (analogous to a fixed bed with seepage), (2) self-fluidized fines, and (3) particles small enough to be elutriated, which form the dust cloud observed to rise above the dense lower part of a pyroclastic flow. The degree of flow expansion, however, and the downward extent of selffluidization, remained uncertain, but can be modelled in a simple system as follows. Consider in Fig. 8-14 a deep laterally extensive layer of magma particles of uniform solids density u, free falling velocity W,, and fractional volume

318 . . . . . , . . . . . . . . . . . . .. . . _ . .. . . . . . . . . .. . . . . , . . . . . . . _ .. . . . . . . .' . C = ' C ( y ) .': '. . . . . . .. . . . . . , . . :.. . . . . .. . , .;.. . .. .. ., . .. :. :. . ' .

.

.

Self-fluidized layer

,

-y=Ymt,

C=Cmf-

Non-fluidized layer

Fig. 8-14. Vertical variation of grain concentration in a self-fluidized layer.

concentration C(y ) overlying an impermeable base, where y is distance measured upward from the base. The particles evolve gas at a uniform temperature 8°K and mass-rate m kg kg-ls-', rn being the gas evolution coefficient. The volumetric gas production within an element in the bed is, from the gas laws: amCR8 (8.16) 4= wherep is the gas pressure and R the gas constant per kilogram, equal to the universal gas constant (8.314 JK-'mol-') divided by the gas molecular weight. To find at any height in the bed the upward superficial velocity of the gas discharged, we integrate eq. (8.16): (8.17) where V is the superficial velocity. But eq. (8.8) also affords the superficial velocity, whence: (8.18)

the subscript signifying the concentration at y. This equation is generally soluble only numerically, but has an analytical solution under one restrictive condition. Two layers, the lower non-fluidized and the upper self-fluidized, exist within the bed shown in Fig. 8-14, assuming sufficient depth and no particle agglomeration. In the lower, the superficial gas velocity is less than Vmf,and the particle concentration is equal to or more than Cmf.In the upper layer, however, ( V - Vmf) increases with ascending height, and so the concentra-

319

tion must be less than C,, and C ( y ) must be a monotonically decreasing function, becoming zero at infinitely large height. Corresponding to C,, , there is a height ymfdefining the thickness of the lower, non-fluidized zone. The critical bed height follows on the plausible assumption that C( y ) = const = Cmf,whence from eq. (8.18): (8.19) which is shown in Fig. 8-15 for C,, =0.55, p = 1.014X lo5 NmP2 (atmospheric), u = 1500 k grn-3, m = 5 X kg kg-ls-', R = 3.615 X l o - ' JK kg-', and 8 = 1250°K. The value of the gas evolution coefficient is chosen on the assumption that the particles contain 5% of gas by weight, evolved over a period of 100 s. Following Sommer's (1977) work on the Bandelier Tuff, New Mexico, the gas constant is calculated for a molecular weight of 23. The values of n come from eq. (8.9). Since the dense lower layer of a pyroclastic flow is in the order of 1- 10 m thick, and these critical heights for fluidization correspond to particles of medium sand to granule size on the basis of the density and the gas mixture assumed, it is apparent that only debris of fine sand and sub-sand grades can be self-fluidking. Coarser

10

lo-' I

10-3

I

10-2

10-1

I00

10'

Free falllnq velocity, W,

102

103

104

(m 6')

Fig. 8-15. Thickness of the non-fluidized part of a self-fluidized grain mass,as a function of particle free falling velocity and for a particle fractional volume concentration of 0.55.

320 A 4 0

n u El 0

n

0

Y'Ymf

c

r .-m 0

I

Y'Ymt

Y'Ymf

CXCmt

c

Grain concentration, C

Fig. 8-16. General form of vertical profile of grain concentration in self-fluidized beds, as a function of particle free falling velocity.

particles must either be supported by the self-fluidized fines or by Bagnoldian intergranular forces (Vol. I, Chapter 1). As Sparks (1976) showed, debris finer than medium to coarse sand rarely composes more than 40% by weight of pyroclastic flow deposits. Self-fluidization seems to sustain the lesser proportion of the flow. Numerical integrations of eq. (8.18) show that C ( y ) for y >ymf has the form sketched in Fig. 8-16. As expected on physical grounds, the local concentration decreases upward, at first rapidly but then more gradually. The initial rate of decrease is inversely related to the value of ymf,that is, the concentration declines upward more gradually in a dispersion of large grains than in one of fines. Alternatively, at a given height, a coarse bed is expanded less than one of fine-grained debris. Therefore the bulk density of the dispersion also declines upward, and self-fluidization affords gravitationally stable dispersions, at least of monodisperse solids. Equation (8.18) is clearly also relevant to the grading of pyroclastic flow deposits. The preceding analysis, like that of Sparks (1976), is deficient because particulate fluidization is assumed, whereas the low-viscosity gas and highdensity solids involved would, in a stationary bed, have behaved aggregatively. The justification offered here is that shearing probably breaks down bubbles as fast as they are formed, whence the regime in a pyroclastic flow would effectively be particulate. In small-scale studies of flow-fluidization, Botterill and van der Kolk (1971) and Botterill et al. (1972) found evidence for bubble suppression.

32 1 APPARENT VISCOSITY OF LIQUIDIZED SEDIMENTS

Controls and means of measurement The apparent viscosity of liquidized sediments powerfully affects their extent of deformation under the action of natural forces. Studies of grain dispersions produced other than by fluidization (reviewed by T.F. Ford, 1960; Happell and Brenner, 1965; Jeffrey and Acrivos, 1976; Rutgers, 1962a, 1962b; Ward, 1955) and of fluidized beds (reviewed by Davidson et al., 1977; Leva, 1959; Schugerl, 1971) show viscosity to depend on: (1) grain concentration, (2) grain size and size-distribution, (3) grain shape and surface roughness, (4) particle and fluid compositions, (5) the relative density of the solids, and (6) the manner in which the liquidized material is created. Great problems confront attempts to calculate the viscosity theoretically, and neither are consistent, accurate and readily comparable experimental results easily obtained. Of the chief methods of laboratory measurementrotating cylinder, torsion pendulum, capillary, and rising/falling sphereonly the second and fourth are readily applicable to a fluidized bed. The most complex rheological properties are shown by dispersions of very small particles in which surface forces are significant (e.g. Burke, 1935; Metzner and Whitlock, 1958; Kearsey, 1962; Greenberg et a]., 1965; Umeya et al., 1969; Mishra et al., 1970). The larger and nominally cohesionless particles of present interest fortunately behave in a generally simpler manner. Non -fluidized dispersions Grain concentration undoubtedly has the strongest influence on the apparent viscosity, qdisprof a non-fluidized grain dispersion, for example, a liquefied sand or a stationary mixture of neutrally buoyant particles in a fluid. Equations for this dependence can usually be put in polynomial form: qrel = qdisp/q= 1

+ k , C + k2C2+ k3C3+ ...

(8.20)

in which qrelis the relative viscosity, q is the viscosity of the fluid phase, C is the fractional volume particle concentration, and k , ,k , , k , . .. are constants. A major problem is to find closed forms of eq. (8.20) applicable to the full natural range of concentrations and, particularly, accurate close to the upper limit, where qrelchanges very rapidly with C. Einstein (1905, 1906, 1911) gave the first theoretical equation for the relative viscosity of a particle dispersion: Vrel -1+kC (8.21) where k = 2.5, assuming that C is very small and that the grains are smooth, rigid, uniform, neutrally buoyant, perfectly wetted spheres. Hatschek (1910) obtained this relationship with k = 4.5, but Brenner (1958). rederived Ein-

322

stein’s equation. Eirich et al. (1936a) and Cheng and Schachman (1955) concluded experimentally that Einstein’s formula failed at concentrations greater than 0.02-0.03, and Ward and Whitmore (1950a) found large variation in the value of k, which for their uniform spheres was approximately 4. Terms in C to a higher order mark theoretical formulae describing the apparent viscosity of monodisperse systems at intermediate concentrations (Guth and Simha, 1936; Vand, 1948; Simha, 1952; Kynch, 1954, 1956; Simha and Somcynsky, 1965). Vand’s popular equation: Yrel -

1

+ 2 s c + 7 . 3 4 9 ~ 2+

o(c3)

(8.22)

is well-supported experimentally up to concentrations of approximately 0.3 (Ward and Whitmore, 1950a). Several theoretical and semi-empirical equations exist for monodisperse systems at large as well as lesser concentrations. Mooney (1951) gave: (8.23) In qre1= 2.5C/( 1 - k C ) expandable as a power series, in which k, to be determined experimentally, ranged between 1.35 and 1.91 according to himself, and between 1.0 and 1.47 according to Sweeney and Geckler (1954). Lewis and Nielsen (1968) found that eq. (8.23) agreed well with their experimental data. Simha (1952), with an extension by D.I. Lee (1969), and Kynch (1956) developed complex theoretical models of relative concentration. Happel’s ( 1957) model: (8.24) “Ire1 - 1 5.5kC

+

where k is a tabulated coefficient increasing steeply with C, is well-supported up to concentrations of approximately 0.4 by the work of Ward and Whitmore (1950a), P.S. Williams (1953), and Sweeney and Geckler (1954), but at higher values underestimates the relative viscosity. A model with good experimental support for concentrations as high as 0.4 is also described by Allen and Kline (1968). Statistical mechanical concepts are used by Sather and Lee (1972) to derive an approximate equation for relative viscosity. This equation is in excellent agreement with reduced experimental data (Rutgers, 1962a, 1962b; D.G. Thomas, 1965), but is awkward in practice. R.L. Hoffman’s (1972, 1974) model for very high concentrations is less successful than the equation: (8.25) in which k = 9/8, n = 1, and C,, is the maximum possible concentration, proposed by Frankel and Acrivos (1967), who stressed the asymptotic nature of the viscosity-concentration relationship. Sather and Lee (1972) list asymptotic forms obtained from the models of Simha (1952), where k = 1/20, and Happel (1957), for which k = 1/80, the exponent being 3 in each case. 2 0.8. There is excellent support for eq. (8.25) at C/C,, The literature yields many empirical equations for relative viscosity (e.g.

323

Arrhenius, 1887; J.V. Robinson, 1949, 1951; T.F. Ford, 1960; Rutgers, 1962a, 1962b; Gay et al., 1969). Oliver and Ward's (1953) equation: (8.26) ?re1 = 1/(1 - kC) advocated also by Ward (1955) and Higginbotham et al. (1958), is simple and acceptable for concentrations up to about 0.3. The constant lies close to 2.5 but varies between systems. A good correlation over nearly the whole natural concentration range is given by: Yrel -

1

+ 2.5C + 10.5C2 + 0.00273 exp( 16.6C)

(8.27)

due to D.G. Thomas (1960). Figure 8-17 shows eqs. (8.24), (8.25) and (8.26), Oliver and Ward's (1953) relation being given for k = 2.5, and the asymptotic form of Frankel and Acrivos (1967) for G.D. Scott's (1960) value of C,,, = 0.637 (uniform spheres in random close packing). The equations indicate that the relative viscosity increases rapidly with increasing concentration. The rise is approximately ten-fold at a concentration of 0.45. At C = 0.601, Scott's (1960) value for uniform spheres in loosest random packing, the relative viscosity is approximately 60. If the asymptotic forms of the Simha (1952) and Happel (1957) equations had been used instead of eq. (8.25), relative viscosities

V

V

I

V L

V

I

V 7

V

I

" V

".

" 1

""

I "

Particle cancentration. C

Fig. 8-17. Relative viscosity of a dispersion of neutrally buoyant spherical particles in a Newtnnian fliiirl a t rpct a c a thenrptiral fiinrtinn nf nartirlp rnnrentratinn

324

respectively of 1.6 X lo3 and 6.4 X lo3 would have resulted for this packing. Relative viscosities in the range 10'- lo3 have been measured from sphere dispersions close to the maximum concentration (e.g. Vand, 1948; P.S. Williams, 1953). The effects of grain size and size-distribution are less well understood. Experimental work reveals an increase with decreasing grain size in the relative viscosity of monodisperse systems of particles smaller than about 5 X 10 - 5 m (Hauser and le Beau, 1939; Robinson, 195 1 ; Eveson, 1957). For larger grains, the best data suggest that relative viscosity is independent of size (Ward and Whitmore, 1950a; Metzner and Whitlock, 1958), though Moreland (1963) claims a continuing decrease, and others (Matheson et a]., 1949; P.S. Williams, 1953; B. Clarke, 1967) point to the opposite effect. The result of adding small grains to a system of substantially larger ones is to reduce its relative viscosity (Matheson et al., 1949; Eveson et al., 1951; Eveson, 1959), as theory predicts (Mooney, 195 I ; Rajagopal, 1960). The large particles behave as though dispersed in a continuous medium provided by the small grains. When size is continuously distributed, however, the shape rather than range of the distribution curve seems most influential (Eveson, 1958).

100,

80

'

I

I

1

I

I

I

-

60 -

40

j 20

-

-

i ?

-"

2.

c 0

;.

-t

10

-

8 -

L

0

a

6 4 -

KEY Gloss rods (0.00003x 0.0007 m ) A Gloss plates (0.0001 x 0,0004m) v Gloss s p h e r e s ( 0 . 0 0 0 0 5 6 - 0 . 0 0 0 0 7 6 m) Crushed quortz ( ditto )

2 -

I

/ I

0

005

,

0.10

I

I

0.15

0.20

0.25

030

I

0.35

0.40

I

0.45

0.50

0.55

Porticle concentrotion, C

Fig. 8- 18. Relative viscosity of various solids dispersed in water, as an experimental function of particle concentration, shape, and (?) size. Data of B. Clarke (1967).

325

The relative viscosity of a dispersion rises noticeably at a given measured concentration as the grains become less spherical and their surfaces roughen. Increased surface roughness enhances inter-particle friction, particularly at larger concentrations, but also raises effective particle size, so that the dispersion behaves as though more concentrated than is actually the case. We saw in Vol. I, Chapter 5 that an elongated grain rotates when in a sheared fluid, the volume swept by the particle representing an increase of size above the nominal value. The effective volume is also raised by fluid trapped in hollows on the particle surface, or by edges and projections. These effects are well illustrated by B. Clarke’s (1967) data on the relative viscosity of aqueous dispersions of crushed quartz, and glass spheres, plates and rods (Fig. 8-18). The markedly non-spherical but relatively smooth rods (axial ratio 23.3) and plates (axial ratio 4.0) afford the largest relative viscosities. The quartz, presumably of much smaller axial ratio but angular shape and rough surface (Krinsley and Doornkamp, 1973), gives values less than for the rods and plates but much greater than for equivalent smooth glass spheres. The observations of Ward and Whitmore (1950b) and Whitmore ( 1957) also suggest that particle roughness and angularity significantly raise relative viscosity. Eirich et al. (1936b) found that the relative viscosity of rod dispersions increased very steeply with axial ratio, but only at large ratios. This finding supports theoretical models for dispersions of nonspherical particles (Eisenschitz, 1932; Kuhn, 1932; Peterlin, 1938; Kuhn and Kuhn, 1945; Brodnyan, 1959), though none is applicable at large concentrations. Fluidized beds

Fluidized beds should on the face of it differ but little in apparent viscosity from non-fluidized dispersions. Investigations to date, however, show that this expectation is only true under restricted circumstances. Several workers give reliable measurements of the apparent viscosity of gas-fluidized beds of quartz sand and resin or glass spheres, from which relative viscosities can be derived. Hagyard and Sacerdote ( 1966), fluidizing resin spheres with air in conventional equipment, obtained apparent viscosities in the order of 0.1-1.0 Ns m-* at grain concentrations close to the minimum for fluidization. These results imply relative viscosities comparable with 5 X 103-5 X lo4, two to three orders of magnitude more than for non-fluidized dispersions (Fig. 8- 17). Apparent and relative viscosities of the same general order as obtained by Hagyard and Sacerdote are also afforded by the work of Schugerl et al. (1961), Siemes and Hellmer (1962), Botterill and Van der Kolk (1971), Botterill and Bessant (1973), and Singh et al. (1978), all of whom except Schiigerl studied flow-fluidized beds. Grace (1970) analysed Rowe and Partridge’s (1965) data on gas-fluidized beds to obtain apparent viscosities also in the order of 0.1-1.0 Ns m-*, again

326

6 -

4 Prudhoe and Whltmore (1964) 0 GS = 8.4 x lo-'

2 -

104 8 -

Hagyard

6 -

Rlqby et 01. (1970) G0=8.6~103 A GS = 1.9x 1 0 3 x lo2 GS ~ 4 . 5 Gu = 3 2 x 10'

4 -

f G c

-

2 -

-

103

--l a

:I

0

4 -

B

2 -

-g.-

and Sacsrdote (1966) oG0=6.5xIO6

0

I02

-

8 6 4 2 -

-

10' 8 6 4 -

0

0.1

0.2

0.3

0.4

0.5

0.6

Relative concentration,

0.7

0.8

0.9

1.0

C/Cmox,C/Cmf

Fig. 8-19. Relative viscosity of various fluidized solids as an experimental function of particle concentration and Galileo number. Two theoretical curves for neutrally buoyant dispersed particles in a Newtonian fluid at rest are also given.

indicating relative viscosities some orders of magnitude greater. Many of these investigators found that apparent viscosity decreased steeply with increasing superficial velocity (Schugerl et al., 1961; Siemes and Hellmer, 1962; Hagyard and Sacerdote, 1966; Botterill and Van der Kolk, 197l), implying a sharp fall with decreasing grain concentration, eq. (8.8). Figure 8-19 gives Hagyard and Sacerdote's data recalculated on the plausible assumption that for their resin spheres C,, = 0.6, together with, for comparison, eqs. (8.24) and (8.25) for C,, = 0.6. The gas-fluidized and the nonfluidized systems are strikingly different. There is apparently less difference in relative viscosity between particulately fluidized beds and non- fluidized dispersions. Prudhoe and Whitemore ( 1964) conventionally fluidized glass spheres in a large-viscosity oil. Relative viscosities calculated from their results (Fig. 8-19) agree well with eq. (8.24), which itself closely fits laboratory dispersions of neutrally buoyant grains (Happel, 1957). Rigby et al. (1970) fluidized glass beads and a quartz sand in water, obtaining apparent viscosities that fell steeply with increasing superficial velocity. Figure 8- 19 shows these results, recalculated on the assumption that C,, =0.6. The relative viscosities are roughly one

327

order of magnitude greater than the values given by eq. (8.24) but much less than for Hagyard and Sacerdote’s (1966) air-fluidized beads. What explains the much greater relative viscosity of gas-fluidized as compared with liquid-fluidized beds, and fluidized as compared with nonfluidized systems? The answer seems to be inertial effects. Hagyard and Sacerdote’s (1966) resin spheres have a density nearly lo3 times more than the fluidizing phase. In the experiments of Prudhoe and Whitmore (1964) and Rigby et al. (1970), however, the density differences are similar, in the order of 2, but the liquid phases differ in viscosity by nearly 400 times. Inertial effects are therefore best measured by the Galileo number, which in Fig. 8-19 varies over a range of approximately 10’. The Galileo number for Prudhoe and Whitmore’s (1964) fluidized beds is small and it is not surprising that their relative viscosity compares with the theoretical value for a dispersion of neutrally buoyant particles. The influence of the Galileo number is also evident in the data of Schugerl et al. (1961), which show that, for constant density difference, the larger particles afford the greater apparent viscosity. Davidson et al. (1977) attribute the large relative viscosity of (gas) fluidized beds to energy dissipation arising from particle collisions, and use Bagnold’s (1954a) results in a quantitative exploration of this idea. They therefore imply an inertial explanation for the effect seen in Fig. 8-19, but note certain limitations to a Bagnoldian approach. SEDIMENTATION

General

When a liquefying mechanism is withdrawn, or a fluidizing stream is sufficiently reduced, the dispersed grains proceed to settle out, forming a deposit with a new pattern of texture, packing, and fabric. This is the process of sedimentation, in the chemical engineer’s restricted sense. It occurs after natural liquefaction or fluidization, and during deposition from turbidity currents and some other high-concentration flows. Consider the settling of grains originally dispersed throughout a liquid contained in a vertical-sided vessel closed beneath (see Acrivos and Herbolzheimer, 1979, for effects of sloping sides). In the simplest case (Fig. 8-20a), clear liquid A appears above the original dispersion B, while a deposit D more dense than B forms from the bottom. The interface between A and B descends at a constant velocity to meet the interface between B and D rising from below, until the last of the original dispersion has been consumed and A directly overlies D. A summary of events appears in Fig. 8-20b as plots of interface height, y , against time. Only with compressible particles or those possessed of strong surface forces (e.g. flocculated clay minerals) will the interface AD continue to sink after the completion of

328 CLASS

CLASS 1

n

I C L A S S lU

fal

Fig. 8-20. Classes of behaviour during the static sedimentation of monodisperse grains, illustrated by the changing appearance of the sedimenting column and the movement of interfaces.

sedimentation. Another possible but more complex history is seen in Fig. 8-20c, d. A fourth layer, C, of intermediate but non-uniform concentration, appears between layers D and B, consuming the latter before itself being consumed. Interfaces BC and CD are vague, however, and the plot for the top of the dispersion is smooth. A third possible history is seen in Fig. 8-20e,f, but with the difference that interfaces BC and CD are sharp, affording discontinuities on the highest height-time curve. The above generalizations rest on many laboratory experiments such as appear in Fig. 8-21 (Egolf and McCabe, 1937; Steinour, 1944; Lewis et al., 1949; Gurel et al., 1955; Hanratty and Bandukwala, 1957; McLaughlin, 1959; Oliver, 1961; Richardson and Meikle, 1961a; Michaels and 'Bolger, 1962; Shannon et al., 1964; Obiakor and Whitmore, 1967; Harris et al., 1975; Smiles, 1976), the chief departures from the ideal of Fig. 8-20 occurring with very small particles in electrolytes. How is sedimentation to be further analysed? Kynch (1952), in a celebrated analysis (see also Lapidus and Elgin, 1957, and Wallis, 1962, 1969), approached the problem from continuity, on the single major assumption that the falling velocity, W , of a given particle in a given dispersion depends only on the local grain concentration, C , ranging from the free falling velocity, W,, at zero concentration to zero at maximum possible density. Consider a fixed horizontal surface at height y above the

329

Fig. 8-21. Behaviour through time of an actual Class1 sedimenting system (glass beads in water). Interfaces indicated by arrows and phases by convention adopted in text.

base of a dispersion settling in a vessel closed beneath, as in Fig. 8-21. The volumetric particle flux across this surface is: s=cw (8.28) downward per unit area and time, whereas that of interstitial fluid is: F = Vi(l - C) (8.29) upward, where V, is the average fluid velocity. Since the container is closed beneath: S+F=O (8.30) for there can be no net flow. The continuity equation for the dispersion can be shown to be:

(8.31) which, on account of eq. (8.28), can be written as:

ac ac+ v(c)-=o at aY

(8.32)

where: d v(c)=-#w)

(8.33)

330

If on a height-time graph portraying the settling of the dispersion, curves are drawn through points of equal concentration, the coordinates ( y , t ) and ( y d y,t dt ) of two adjacent points on the curve are related by:

+

ac

+

aC

-dy +-dt=O at aY Combining eqs. (8.32) and (8.34), the slope of such a curve is:

(8.34)

*=

(8.35) V(C) dt and the curve is a straight line, as C,and therefore V , are constant along it. Figure 8-20f shows examples of these curves, drawn as dashed lines, on the supposition that the dispersion was initially uniform. They are therefore parallel in region B, since C, and therefore V , are constant. In region C, however, the slope decreases, for the concentration increases downward from interface BC toward interface CD. Discontinuities in particle concentration of two kinds exist in settling dispersions (Kynch, 1952). The most obvious are represented by interfaces such as AB, BC, and AD in Fig. 8-20. These cannot be analysed by the equation of continuity, eq. (8.31), but must be described by a relationship analogous to that for a shock wave and stating that the particle flow into one side of the interface or shock shall equal the flow out on the other side. Taking interface AB in Fig. 8-20: VA B = -

A ’

- ‘B

B‘

-A‘

(8.36)

where VA, is the velocity of the interface and the subscripts A and B denote particle fluxes and concentrations in the two layers. Since W in eq. (8.28) is negative, and the particle flux is zero in layer A, then VAB also is negative as observed. The velocity VA, is the slope of the straight line joining the points ( C4, SA)and (C,, S,) on the curve of S( C). Kynch’s other discontinuity is an infinitesimally small change in particle concentration, for which eq. (8.36) for VA, reduces to eq. (8.35) for V. A line of constant concentration in such as Fig. 8-20f therefore describes the propagation upward within the dispersion of a very small discontinuity. From a consideration of eqs. (8.35) and (8.36), the entire history of sedimentation of a uniform dispersion can be predicted if we know W(C) and the concentrations typifying the several possible layers. Monodisperse systems For these, the easiest to handle, a wide choice for W ( C ) is available, depending on particle concentration and Reynolds number. The most general equation is the Richardson-Zaki relationship for uniform dispersions

33 1

presented in eqs. (8.8) and (8.9). Other variants are given by Maude and Whitmore (1958) and Davies et al. (1976), and Anderson (1961) offers another useful correlation. Relationships applicable at small Reynolds numbers are due to Brinkman (1949), Hawksley (1951), Happel (1958), and Oliver (196 1)' amongst others. Oliver's equation, reading:

W = W,(l

- 0.75C'/3)(1 - 2.15C)

(8.37)

agrees particularly well with experiment at very large as well as very small concentrations. An equation useful at low concentrations in the Stokes range is that by Famularo and Happel (1965). The Richardson-Zaki equation is used here, on account of its simplicity and generality. We can now model the history of a suspension and complete the analysis of Kynch (1952) and Wallis (1962, 1969). Substituting eq. (8.8) for W into eq. (8.28), we obtain: S = W,C(l-

c)"

(8.38)

for the variation of particle flux with particle concentration in a given system. Figure 8-22a shows this equation for n = 2.4 and C, = 0.637 (closest possible random packing), the absolute value of S being plotted. If the point ( S o , C,) represents the initial dispersion, then, following eq. (8.36), the slope of the straight line connecting the origin with this point is VAB,the velocity (downward relative to rest) of interface AB. Similarly, the slope of the straight line connecting (CD, 0) with (Co, S o ) is the velocity, VBD, of the interface between layers B and D. Note that VAB and VBD have opposite signs, as is observed. Since all parts of the graph of S ( C ) are directly accessible from (CD,O),only layers A, B and D can exist during sedimentation. This type of system, with a maximum of three layers and interfaces that are sharp, is referred to Class1 in Fig. 8-20. Sedimentation histories belonging to Classes I1 and I11 in Fig. 8-20 arise only when the graph for S( C) carries an inflection point at a concentration

Grain concentration. C

Groin concentration. C

Fig. 8-22. Grain flux as a function of grain concentration in a monodisperse sedimenting system behaving according to (a) Class I only, and (b) more generally (all classes achievable).

332

sufficiently small in comparison with C,. A direct shock can be transmitted from the initial state in Fig. 8-22b to the state represented by C, only when 0 < C, < C , or when C, < C, < C,. There is a “sheltered” region, C, < C, < C,, lying between the point where a straight line from C, is tangent to the curve and the intersection with the curve, within which the graph has an inflection point (C,, S,). Sedimentation of Class I1 is obtained if (C,, So)lies on a concave upward part of the sheltered curve. The interface AB descends at the velocity given by the line connection C = 0 and C = C,, while the settled state is propagated upward at the velocity given by the line joining C = C, with the tangent point C = C,. The region C appearing between layers B and D has a gradational boundary BC and particle concentrations intermediate between C, and C,. Class I11 systems arise when (C,, So)lies where the sheltered part of the graph is convex upward. The particle concentration in region C ranges from C, upward to a value given by the tangent from (C,, So)to the curve, since this is the fastest continuity wave in region C just equal to the velocity of the interface BC. The bounds of these classes of sedimentation can be defined in terms of C,, C , and n as follows. Writing eq. (8.38) (negative value of W, neglected) for porosity, P = ( 1 - C), and differentiating, we obtain:

(8.39) Examining Fig. 8-21b, another expression for d S / d P is: dS dP

S3-0 P, - P,

(8.40)

where P, and P, in the S( P ) curve correspond to states C, and C, in the S ( C ) graph. Eliminating d S / d P we obtain a quadratic equation with the solution: C,(n

+ 1) * [ c h ( n + 1)2- 4 n ~ , ] ” *

(8.41) 2n written in terms of concentration. The larger root is the tangent point C, in Fig. 8-22b, as stated by Wallis (1969), whereas the smaller is the intersection point C , . The triple point ( n , , , Ctr)in the n-Co plane where the fields for the three classes meet is obtained when the term in square brackets in eq. (8.41) equals zero. We then have:

C=

(8.42) and, equating the terms within these brackets:

(8.43)

333

find that: (8.44) as obtained by Wallis (1969) for the generalized inflection point C2. Since C, can be measured, we can predict n,, and C,, for any monodisperse system. Figures 8-23 and 8-24 summarize calculations based on eq. (8.41). The first graph shows that n,, is a steeply decreasing function of C, and that real values for C, lie near the upper bound of the ordinary range of n in the Richardson-Zaki equation. Taking G.D. Scott’s (1960) value of C, = 0.637 for equal spheres in closest possible random packing, we find that n l r = 4.032 and that Class I1 or Class I11 sedimentation is possible only for larger values of n. The second graph shows the existence fields at this value of C,, from which it is clear that, for ordinary values of n , sedimentation according to Classes I1 and I11 is limited to restricted conditions of grain size, fluid medium, and initial concentration. Naturally occurring sands and coarse silts yield values for C, substantially below Scott’s result for uniform spheres, and it is doubtful, referring to Fig. 8-23, that sedimentation other than 10

9

7

L

E

a

8

0

5

w 4

3

2

I

0 Particle concentration in deposit, CD

Fig. 8-23. The triple point between sedimentation according to Classes I, I1 and 111, defined in terms of the sedimentation equation exponent at the triple point and the concentration in the deposit.

334

7

4

3

2

0I 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.01

Initial particle concentration. C.

Fig. 8-24. Theoretical existence fields for sedimentation classes in monodisperse systems, assuming that C, =0.637 (closest possible random packing).

Class I is possible, whatever the initial concentration (large if dispersion resulted from liquefaction, but possibly small if fluidization was involved). Finer grained sediments, however, may often behave according to Class I1 or Class 111, as they commonly take values for n in excess of 4.65. Dixon et al. ( 1976) have challenged Kynch’s ( 1952) assumption that W depends only on C, on the grounds that inertia is thereby neglected. They contend theoretically that only Class1 sedimentation is possible when inertia is not ignored. Critical experiments should establish the truth of this claim. Polydisperse systems Regrettably little work has been done on the sedimentation of initially uniform dispersions of particles of mixed sizes and/or densities, despite its relevance to natural sedients and to many industrial materials and processes. Phillips and Smith (1969, 1971) experimented on binary systems of spherical particles that differed in size by up to 7: 1 and in density by up to 11 : 1 at total concentrations ranging up to 0.5. Figure 8-25 gives intermediate stages in the histories of the three classes of sedimentation they distinguished, where DN and DT indicate respectively a dispersion and a

335

CLASS 1

Fig. 8-25. Classes of behaviour observed during the static sedimentation of bidisperse mixtures of spherical particles in Newtonian fluids at rest.

deposit, the subscript 1 denotes the faster-moving species in the mixture, and the subscript 2 the slower-moving species. The faster species is not necessarily the one with the larger free falling velocity. Class1 sedimentation typifies mixtures of low concentration or where size and/or density differences between species are small. A deposit of mixed species is overlain by a dispersion also of mixed species, succeeded in turn by a dispersion composed only of the slow species, as noted also by Richardson and Meikle ( 1961a), Lockett and Al-Habbooby ( 1973, 1974), and Mirza and Richardson (1979). The final deposit is a layer of mixed species overlain by one of pure species 2. Class I1 sedimentation, also described by Richardson and Meikle (1961a), affords a tripartite deposit, of species 1 overlain by a layer of mixed species, succeeded by a layer of species 2. In Class I11 sedimentation the original mixed-species dispersion is gradually contracted by the ascent of the boundary capping a pure dispersion of species 1. The fully segregated end-product is a layer of pure species 1 overlain by a layer of pure species 2. According to Richardson and Meikle ( 1961a) and Phillips and Smith ( 1969, 1971), Class 111 sedimentation is typical of moderate and large concentrations when substantial size and/or density differences exist between species. Richardson and Meikle, for example, studied glass (u = 2921 kg m-3) and polystyrene (u = 1045 kg mP3) spheres of equal free falling velocity in a liquid ( p = 969 kg mP3). There was complete segregation of the smalldiameter glass below the large-diameter polystyrene. An important difference exists between sedimentation according to Class I and that according to Classes I1 and 111. In the first case the velocity of both species in the mixture is downward relative to rest, but in the latter only the faster-moving species invariably travels downward. The upward travel relative to rest of the slower-moving species is restricted to an initial phase in Class 11, since ultimately a mixed-species deposit appears above the layer of

336

pure species 1 . In Class I11 sedimentation, the slow-moving species travels upward faster than does the interface capping the deposit of species 1, whence for a time a dispersion of pure species 1 is seen. We therefore have evidence, in these two classes of sedimentation, for the upward flushing relative to rest of sufficiently slow-moving particles. Some progress has been made toward a theory of sedimentation in polydisperse systems, beginning with Jottrand (1954) and Pruden and Epstein (1964), who sought criteria for separation by size and/or density. T.N. Smith (1965, 1966, 1967) and Phillips and Smith (1969) developed theoretical models for the sedimentation of binary, discontinuous polydisperse, and continuous polydisperse systems of particles in the Stokes range. These analyses take into account the buoyancy, drag and pressure forces acting on the particles, together with particle interactions. They explain, for example, why particles of small settling velocity can be flushed upward through the sedimenting dispersion by action of the pressure gradient and fluid drag, this kind of elutriation being represented experimentally by Classes I1 and 111 of Fig. 8-25 (Richardson and Meikle, 1961a; Phillips and Smith, 1971). Calculations from the model are involved, however, and the agreement with experiment is but modest. A more practical but empirical approach is described by Lockett and Al-Habbooby (1973, 1974) (see also Mirza and Richardson, 1979), who postulate that the behaviour of a single species in a polydisperse system is a function of the sum of the concentrations of all the species present, and can be described using the Richardson-Zaki relation, eqs. (8.8) and (8.9). Suppose that we have species 1,2,...rn occurring at concentrations of C,,C2,... C,,, in a dispersion, and that these species have free falling velocities of W,m,W2,,... W,,,,. If the mixture settles in a vessel closed beneath, the interstitial fluid velocity relative to rest is: m

-+) +) F

(1

1

(8.45)

(1

since under the given conditions the fluid flux, F, is equal to the total solids flux ZYS, eqs. (8.28) and (8.29), the absolute values of the fluxes being considered. The settling velocities of the species in the dispersion are related to the fluxes by:

w

’

S S =1 -2 ,...

w

C,’ * - c 2

w

=-s m

(8.46)

w m

and, referring to eqs. (8.8), (8.28) and (8.29), the slip velocities are given by:

337

i

:

v, + w,= w,,1 - x c v, + w2= w241

)"-I

-d.jf12-'

(8.47)

to :

where n , , n 2 ,. . . n m are the appropriate exponents. Given the free falling velocities, exponents, and initial concentrations, we can solve this system of equations to obtain the settling velocities of the species and the movement of the boundaries limiting the upward occurrence of each. This theory, like T.N. Smith's (1965), predicts for large size and/or density differences the flushing of the slower-moving species into the upper parts of the dispersion. Lockett and Al-Habbooby found generally excellent agreement between their theory and experiment in the case of binary systems, but there are no results available for more complex mixtures. Experiments show that the particles of a polydisperse system will settle collectively at a single velocity and without segregating if the total concentration is sufficiently large. R. Davies (1968) and Davies and Kaye ( 1972), studying binary and ternary mixtures, concluded that this occurred at concentrations as low as 0.3, provided that the species were similar in size and initial concentration. As size and concentration differences increased, however, the critical total concentration for collective behaviour steadily rose, and some mixtures segregated even at total concentrations as large as 0.55. Lockett and Al-Habbooby (1973, 1974) found experimentally and theoretically that there was a critical total concentration for a mixture at which the species settled at the same velocity and without segregating. They interpret the effect hydrodynamically, whereas Davies sees collective behaviour as due to particle interlocking. The hydrodynamic interpretation is preferable, for under the mechanical theory *the critical concentration depends only on the size ratio and not on the relative abundance of the species. Graded systems We assumed initial uniformity in considering the sedimentation of monodisperse and polydisperse systems. These models have several applications to natural deposits, yet there are many systems of cohesionless granular sediments that are non-uniform, displaying vertical gradients of texture and/or concentration. The vertical changes may be either continuous, as in a bed without strongly differentiated internal lamination, or discontinuous, as in an unbroken sequence of layers or beds. How do such systems behave after

338

(a) ,

. . . ., .. . .' . .

,

. . _. , . . .

Fig. 8-26. Definition diagram for the structure and sedimentation of a discontinuously graded, horizontally layered, cohesionless sediment.

being liquidized but not homogenized? Consider first a discontinuous graded system composed of grains of a single density. Figure 8-26a shows a series of infinitely extensive horizontal layers, each treated as a uniform dispersion, characterized by postliquidization concentrations of CI,C2,. . . C,,,, free falling velocities W,,, W,,, ... W,, and exponents n,,n,, ... nnr in the Richardson-Zaki relationship, eqs. (8.8) and (8.9). On withdrawing the liquidizing mechanism, the upper boundary of thejth layer descends at the velocity:

w = W. ( 1 J

Jw

-,,)',I

(8.48)

whereas that of the ( j- 1)th layer falls at:

the initial periods of acceleration from rest being negligibly small, Now the strata can remain in contact only if w/ 2 w/-!, otherwise expanding layers of fluid will appear between them. Hence the cnterion for continuing contact between layers is W,/y-,2 1, which from eqs. (8.48) and (8.49) may also be written: (8.50)

We see from this that contact persists if, when n is uniform, C does not increase upward, and if, when C is uniform, n does not decrease upward. There are narrowly restricted combinations of vertical changes in C with

339

vertical changes in n also satisfying the criterion. When eq. (8.50) is not satisfied, thejth and the ( j- 1)th layers gradually separate, an expanding layer of fluid appearing between (Fig. 8-26b). But the j t h layer is now supported only by the fluid, whence grains should shower from beneath into the growing fluid layer. If 7 is the velocity of the boundary between thejth layer and this layer, then, applying eq. (8.36): v . = - s. - S!J (8.51) J

J

c; - q.

where the prime denotes the fluid layer. Again ignoring acceleration periods as small, the boundaries of the fluid layer should separate at a speed of ( V , - W,-,). We cannot yet calculate 7 , but a simple experiment, in which we invert a layer of water above a layer of sand in a sealed jar, confirms that C', is small and that is positive. Equation (8.50) is a necessary condition for layer stability, for when not satisfied we find that layers of contrasted bulk density alternate vertically. Each sediment stratum in the initial dispersion, because of its greater bulk density, is potentially unstable above the fluid layer developing beneath, and hence could rupture, its collapse being hastened as the fluid rushed up through the resulting breaches. Equation (8.50) is probably also a sufficient condition for instability, for liquidized sediment layers would have negligible shear strength. If a layer had escaped liquidization, however, rupture could probably be resisted at least for an initial period. The experiments described suggest that an unliquidized sand layer does not rupture until reduced to a critical thickness, for grain-interlocking gives a certain strength. Additional strength comes from the reduced pressure developed above as the (permeable) layer gradually sinks under its own weight (see eq. 8.1). In contrast, the deposit of grains wasted from the initial layer is invariably loosely packed, generally rupturing as soon as inverted. The curious inversions of properties found by Kishida (1966) after the Niigata earthquake may have this explanation. Hence a system of liquidized layers failing throughout to satisfy eq. (8.50) should not sediment overall according to the kchardson-Zaki model. Instability, spreading upward from below, should rapidly set in, promoting a much shorter sedimentation time because of the disruption of the layers and their descent as substantial masses. Allen (1977~)considered the sedimentation of a continuously graded polydisperse system, on the supposition that the particles were of a single density, experienced only vertical motions, and were uniform at each level. The time-rate of change of the concentration, aC/at, at the level of a selected particle was found to be: (8.52)

340

where W is the local particle falling velocity, and aW/ay is the falling velocity gradient, with y measured positive downward. Equation (8.52) can only be solved numerically, since C depends on both y and t and W is a complex function of C, but its physical meaning is easily grasped by considering the key term aW/ay. When aW/ay is a constant, and C ( y ) is a constant initially, the dispersion expands or contracts, according as a W / a y is positive or negative. When a W/ay is positive, the local concentration declines faster near the base of the dispersion than the top. Hence during sedimentation an originally gravitationally stable bulk-density gradient can be destabilized, and an initially unstable gradient can be further steepened. When aW/ay is negative, however, the dispersion contracts, faster near the base than near the top. Originally stable bulk-density gradients are made even more stable, and initially unstable ones may be stabilized. There are important differences between discontinuous and continuous graded systems. For example, whereas W,/W,-, < 1 in a discontinuous system means potential instability, the corresponding statement for a continuous one, aW/ay > 0, does not necessarily have this implication. FLUIDIZATION AFTER LIQUEFACTION

It is asserted by Middleton and Hampton (1973, 1976), but denied by Lowe (1976)' that a sediment once liquefied may during a subsequent translation be fluidized by its own escaping pore fluids. This is a concept of self-fluidization that differs from Kent's (1966) notion, since there is no requirement for the supply of fluid from an external source. We here offer a simple proof in support of Lowe's counter-assertion. We can treat a translatory flow of liquefied sediment as though the flow were a stationary settling dispersion, since the effects of bottom slope and loss of settling grains beneath the moving mass apparently are negligibly small. Self-fluidization is possible only if there exists within the dispersion and upward superficial velocity, V , relative to rest, that exceeds V,, for the grains. Now from eqs. (8.28) and (8.29), this superficial velocity is: v = CW (8.53) where C is the fractional volume grain concentration of the dispersion and W is the falling velocity of the dispersed grains. For self-fluidization: (8.54) v > V,, whence: (8.55) substituting for W from eq. (8.8) and introducing eq. (8.10) for V,,. Since C

34 1

is in practice always smaller than Cmf,which compares with the concentration in loosest possible random packing, the criterion can never be satisfied. Self-fluidization as conceived by Middleton and Hampton, is therefore impossible, at least in a monodisperse system. The only sense in which an “internal” fluidization can be said to occur is in polydisperse systems containing grains of such small settling velocity that these fines either remain at rest or become flushed upward as already discussed. Lowe (1976) attempted to show that Middleton and Hampton’s selffluidization is physically impossible, at least for monodisperse systems, by comparing a “superficial rate of fluid escape” from a sedimenting dispersion with V,, calculated using eq. (8.7). He derived eq. (8.53) for the rate of escape but, because of his use of eq. (8.7), found his criterion of selffluidization to be not satisfied only in one limit. Moreover, Lowe incorrectly interpreted his escape rate as a flux upward relative to rest across the upper boundary of a dispersion (interface AB in Fig. 8-20). Equations (8.28) and (8.29) clearly show that there is a zero upward flux of fluid in layerA in a stationary settling dispersion. We therefore cannot accept Lowe’s ( 1975, 1976) further contention that a layer of fine sediment could be uniformly fluidized as the consequence of the sedimentation after liquefaction of a coarse layer beneath, the particle densities being equal. For fluidization demands that there is an upward flow relative to rest of an externally supplied fluid, and no such flux is available as a consequence of the settling of liquefied grains. SUMMARY

Liquidization is a general term to describe those mechanisms bringing about a change of state from solid-like to liquid-like or “quick” in a cohesionless granular sediment. Two mechanisms of liquidization are of particular sedimentological importance. Liquefaction is the in situ disruption of the system of mutual supports between grains, usually as a consequence of either seismic shock or the build-up by other means of high pore-fluid pressures, with the result that shear strength is lowered or reduced to nothing. Fluidization is the mechanism whereby a quick condition is achieved by forcing a fluid from an external source upward through the sediment, until the immersed weight of the grains is balanced by the total fluid drag. It is a necessary condition for fluidization that the fluid phase be in upward motion relative to rest, but this is not a necessary condition for liquefaction. Liquefaction is most likely to occur in sediments that are superficial, cohesionless, fine grained, and loosely packed. Fluidization also is easiest with cohesionless fine-grained sediments that are loosely packed. Its onset, and the subsequent expansion of the bed, can be described in terms of particle and fluid characteristics.

342

Once a mechanism of liquidization has been withdrawn, we are left with a particle dispersion, commonly of high concentration, that proceeds to settle out and form a new deposit, with the consequent release of pore fluid. This process of sedimentation is dynamically similar to fluidization, differing only in the frame of reference appropriate to its analysis. The sedimentation of a monodisperse system occurs on three possible modes, depending on particle Reynolds number and concentration. During the sedimentation of polydisperse systems, particles of sufficiently small settling velocity can either remain stationary in the dispersion (effectively they are fluidized) or be flushed upward (elutriated) to form a fine grained top to the deposit. The sedimentation of dispersions in which settling velocity declines upward, that is, graded systems, is likely to be accompanied by instability phenomena.

343

Chapter 9

SOFT-SEDIMENT DEFORMATION STRUCTURES INTRODUCTION

Stratigraphical and sedimentological studies over many years have shown that soft sediments often become deformed non-tectonically. The structures induced take myriad forms and are increasingly called soft-sediment deformations. It is clear from field evidence, and consistent with experiment and theory, they were created either during deposition or shortly after burial started. Certainly most, and possibly all, soft-sediment deformation is associated in time with the earliest stages of sediment consolidation, when the deposit is weakest and pore fluid is being expelled most rapidly. By interrupting the normally gradual process of pore-fluid expulsion, the factors causing sof t-sediment deformation may also abruptly and significantly enhance that process, provided that pore fluid is mobilized. For this reason Lowe ( 1975) categorized most soft-sediment deformations as water-escape structures, aqueous environments being alluded to because it is within these that soft-sediment deformations chiefly arise. At the same time, it should be clearly understood that the mobilization of pore fluid is generally a consequence of deformation and seldom the direct cause. Under the circumstances described, at or close to the sediment-fluid interface, the only forces available to cause soft-sediment deformation are weak in ordinary geological terms. Hence the deposits affected must at the time have been either liquid-like or solids of insignificant yield strength compared to ordinary rocks. Liquefaction and fluidization, described in the preceding chapter, are two mechanisms available for changing natural sediments to a lKquid-like state, and there are good reasons for believing that at least liquefaction is significant in the production of many kinds of softsediment deformation. We shall here apply our previous summary of liquefaction, fluidization, and sedimentation, together with other evidence, to an understanding of soft-sediment deformation structures. The application is incomplete, however, because natural sediments are more complex than the relatively simple systems so far studied by civil and chemical engineers. Soft-sediment deformation structures tell more about the early consolidation history of sediments than about their depositional environment, for very few varieties seem specific to a particular depositional setting. The structures are most prevalent, however, in water-laid sediments, and arise most frequently where high sedimentation rates prevail to promote the loose packing of sands and silts (Vol. I, Chapter 4), for example, in deep-water basins affected by turbidity currents, storm-influenced shallow-marine environments, deltas, and river floodplains.

344

KINEMATICS AND DYNAMICS OF SOFT-SEDIMENT DEFORMATION

It is first worth summarizing the properties of the materials involved in soft-sediment deformation, framed in terms of the history of possible states over the duration of the process (Fig. 9-1). The description hydroplastic (Shrock, 1948; Elliott, 1965; Lowe, 1975) is appropriate for the original material, of a significant yield strength and effective viscosity. The vertical component, V, of the pore-fluid superficial velocity relative to rest is less than the minimum fluidization velocity, Vmf, and so lies in the seepage regime (Fig. 8-1 1). Gravel or cohesive mud is unlikely to lose its hydroplastic state during deformation, for as we have seen these materials resist both liquefaction and fluidization. Liquidization is almost inevitable with loosely packed cohesionless sands or coarse silts, and may occur either directly because of deformation or as the result of another external factor. The liquidized sediment has a negligible yield strength but a large effective viscosity. This is unlikely to be smaller than the order of 0.1- 1.0 Ns m-* for a liquefied water-logged quartz sand or for a sand fluidized by water under conditions close to minimum fluidization (Figs. 8- 17, 8- 18, 8- 19). However, the effective viscosity of fluidized sand declines steeply with increasing superficial velocity. Once the liquefying or fluidizing

Fig. 9-1. Summary of the rheological history of unconsolidated sediments that become liquidized.

345

mechanism is withdrawn, a liquefied or fluidized sediment can no longer be said to exist, and we have only a dispersion that must proceed to settle out. Until this process is completed, and a hydroplastic condition is fully regained, liquidized and hydroplastic materials will coexist. The limits in time on deformation need not in theory coincide with any of the significant time-points singled out in Fig. 9-1. In practice, however, its start and finish when there is liquidization are likely to coincide more or less exactly with the maximum bounds on the liquidized state. The duration of the liquidized state therefore controls the total strain experienced by elements during soft-sediment deformation and the length of their translation path. This magnitude has two parts, the duration of the liquefied or fluidized state, and the duration of the dispersed (sedimenting) condition. The liquidized state is attained immediately; a liquidizing mechanism becomes operative perhaps only during dynamic liquefaction. In cyclic liquefaction, the more important case, laboratory work (Chapter 8) indicates that periods of shaking respectively in the order of 10s and 100s are necessary for the full liquefaction of loosely packed and moderately packed water-logged sand. Time is also necessary for the complete fluidization of a deposit, for a “fluidization wave” must gradually spread through it. Hence the rheological properties of a sediment could progressively change between the onset of a liquidizing mechanism and the attainment of full liquidization. Consequently, deformation may begin before the liquidized state is fully attained. The liquefied state as defined in Fig. 9-1 can probably exist only for an instant, with sedimentation starting almost immediately afterwards. When water-logged sand in a jar is liquefied by being shaken, and the shaking is continued, sedimentation begins almost at once, proceeding until the whole mass is rigid. The bed contracts more when shaking is continued after liquefaction than when it is stopped, but the start of settlement is not significantly delayed. In contrast, the only bound on the duration of the fluidized state is the availability of fluid supplied externally, either from a different bed or set of beds or another part of the same bed. This state may therefore exist for seconds, minutes or even hours, during which deformation may proceed continuously. Examination of the grain size of the sediment suspected of having been fluidized will afford an estimate of the minimum unit discharge of fluid from the external source, but only the positive identification of the source (e.g. a slumped bed) will permit the duration of flow to be calculated. The duration of the dispersed (sedimenting) state as defined in Fig. 9-1 is readily found by applying Kynch’s (1952) eq. (8.36) over the thickness of the dispersed layer. For uniformly dispersed grains of a single size and density, the duration is:

346

".0.01

0.02

004

0.1

0.2

0.4 0.6

I

0.02 0.04

0.1

0.2

0.4 0.6

I

Initial thickness of resedlmentlng loyer, h, (ml

Fig. 9-2. Time required for the resedimentation of a bed of liquidized sand, as a theoretical function (eq. 9.1) of initial thickness of the layer, particle falling velocity in the dispersion, and concentration difference between dispersion and deposit. Particle concentration in deposit assumed to be 0.60.

where h , is the initial layer thickness, AC is the grain concentration difference between the dispersed and deposited sediment, C , is the concentration of the deposited grains, and W is the falling speed of the dispersed particles (Allen and Banks, 1972; Lowe, 1976; Allen, 1977~).Equation (9.1) affords order-of-magnitude values for non-uniform, polydisperse systems, provided that characteristic values of AC, C, and W are available. Alternatively, it may be applied incrementally to improve the estimate. Figure 9-2 shows how T varies with layer thickness, concentration difference, and free falling velocity, W being substituted for from eq. (8.8). In most practical cases T is in the general order of 1- 100 s, being greatest for thick layers of fine sediment of high concentration. Soft-sediment deformation occurs in response to stresses originating in four main ways: (1) from gravitationally unstable vertical profiles of sediment bulk density, (2) non-uniform confining loads, (3) presence of the sediment on a slope (downslope component of body force), and (4) fluid flow, either at the ordinary sediment- fluid interface or internally. In addition also to recognizing these, Lowe (1975) attempted to isolate three modes of deformation, corresponding in part to states shown in Fig. 9-1. Hydro-

347

plastic deformation is recognizable from the excellent preservation of the (deformed) laminae and by the lack of evidence for other than local liquidization. Lowe's concepts of liquefied and fluidized deformation appear to coincide with deformation in the liquidized state, as this is defined in Fig. 9.1. It may be doubted that varieties of liquidized deformation can ever be confidently distinguished, and useful precision is lost through his failure to distinguish properly between the liquefied, fluidized, and dispersed (sedimenting) states. Lowe proposed the elutriation of fines as one criterion for his fluidized deformation, but fines can also be flushed from highconcentration dispersions (T.N. Smith, 1965, 1966, 1967; Lockett and AlHabbooby, 1973, 1974), such as may arise through liquefaction. Another criterion of fluidized deformation proposed by Lowe is the apparent lack of preserved lamination. Although lamination is almost certain to disappear during fluidization involving a large bed expansion, it may also be lost through percolation and other forms of grain diffusion when a highconcentration dispersion due to liquefaction experiences a large total strain (Scott and Bridgewater, 1975). Because the criteria seem equivocal, later reference will generally be made only to liquidized deformation, in addition to hydroplastic deformation. Some kinds of soft-sediment deformation dependent primarily on liquefaction involve the production of regular folds, either within the one sedimentation unit or at the interface between two, the process being wholly internal to the single or paired layers. By continuity, the anticlines must ascend at a rate inversely proportional to their width, and similarly for the descent of the synclines. If the rate of anticlinal ascent equals or exceeds the settling speed of grains dispersed in these folds, then those particles are fluidized, for they either remain stationary relative to the ground or ascend, though more slowly than the fold crests. If it can be established that fluidization occurred in the cores of the anticlines-and the process is favoured by their commonly being the narrower folds-we can go on to estimate the minimum rate of folding as a criterion for fluidization. In the simple model sketched in Fig. 9-3, the synclines, of width LAB,descend at a speed VAB, while the anticlines, of width L,,, ascend at the speed VcD.

Fig. 9-3. Definition diagram for soft-sediment deformation at the interface between two horizontal sediment layers when fluidization is involved.

348

Applying continuity, and substituting the grain settling speed for Vcn, the criterion:

is obtained for fluidization. The lengths involved, and the order of magnitude of W , can all be estimated from the affected deposit.

CLASSIFICATION OF SOFT-SEDIMENT DEFORMATION STRUCTURES

The nomenclature of soft-sediment deformation structures has developed haphazardly and often with little regard for significant observable differences between structures. No comprehensive classification of them has so far been published, though Ricci Lucchi (1969~)and Lowe (1975) have made a start on this important task. Lowe’s categories are based on different primary criteria, however, which leads to the difficulty that certain structures can be assigned to more than one category. The earlier classifications of Elliott (1965) and Swarbrick (1968) are too restricted to be applicable generally. Classifications of soft-sediment deformation structures to be useful must inevitably rest on a combination of criteria, but with only one kind of

TABLE 9-1 Classification of soft-sediment structures

I. Gravitationally unstable profiles of bulk density 1. Continuous profiles (single sedimentation units) (convolute lamination) 2. Discontinuous profiles (a) single sedimentation units (dish and pillar structures) (b) paired sedimentation units, upper layer not pierced (load casts) (c) paired sedimentation units, upper layer pierced (ball-and-pillow structures) (d) multilayer complexes of sedimentation units, with more dense layers pierced (sand balls) II. Non-uniform confining loads 1. Single sedimentation units (complexly deformed cross-stratification) 2. Paired sedimentation units (folding and faulting due to laterally spreading sand bodies)

III. Downslope component of body force I . Slides (internal stratification substantially undisturbed) 2. Slumps (considerable disturbance of internal stratification, usually much overfolding and internal thrusting) I V. Fluid flow (usually sediment-bearing) 1. Shear stress essentially horizontal (simple deformed cross-stratification) 2. Shear stress steeply inclined to general bedding (eroded and/or bent up laminae)

349

criterion given primacy, either structure geometry, the kinematics of deformation, or the origin of the deforming stresses. Because we here emphasize the mechanics of origin, the classification given in Table 9-1 groups softsediment deformation structures under primary categories representing causative stresses. The lesser criteria vary from class to class as the case demands, but much emphasis is put on the number of sedimentation units or other kinds of layer involved in deformation, as this attribute is important theoretically. This is particularly the case in Class I which covers structures related to gravitationally unstable profiles of sediment bulk density. Essentially, these are recognized (Artyushkov, 1963a, 1963b; Anketell and Dzulynski, 1968a; Anketell et al., 1970; Allen, 1970f; Lowe, 1975) as expressions of kinds of Rayleigh-Taylor instability (Chandrasekhar, 1961; Ramberg, 1967, 1968a, 1968b). Whether the profile of density is continuous or discontinuous is important to the theoretical treatment of this instability.

DEFORMATION STRUCTURES RELATED TO GRAVITATIONALLY UNSTABLE VERTICAL PROFILES OF BULK DENSITY

Convolute lamination

This name is given to laterally extensive series of more or less regular folds developed throughout or confined to the upper part of a single sedimentation unit (Figs. 9-4 and 9-5). Characteristically, the folds strengthen upward from the undeformed base, or from some unaffected higher level, there being little or no evidence for dicollement, and may die away toward the top. The folds increase in wavelength with the thickness of the bed or deformed zone (Kuhn-Velten, 1955; Ten Haaf, 1956; Crowell et al., 1966),

Fig. 9-4. Syndepositional convolute lamination (slightly schematic) in turbidite sandstone of Pic0 Formation (Pliocene,), Ventura Basin, California, U.S.A. After Crowell et al. (1966).

350

Fig. 9-5. Syndepositional convolute lamination (note erosional truncations and evidence of earlier folding within fold limbs), River Ganges alluvium, Bhagalpur, Bihar, India. The deformed layer is normally graded, from sandy up to silty, and sandy sediment, in crosslaminated sets climbing at a low angle, reappears above the erosion surface truncating the folds toward the top of the section. Length of bed shown approximately 0.47 m. Photograph courtesy of A. Chakrabarti (see Chakrabarti, 1977).

and their degree of development is similar within any one unit, horizontal extents as great as 750 km2 having been claimed (Sutton and Lewis, 1966). Largely following Fleuty (1964), the folds range from gentle (Angelucci et al., 1967; Mutti and Ricci-Lucchi, 1972), through open (Conybeare and Crook, 1968; Chakrabarti, 1977), to close, isoclinal, box-like, or even resembling an elastica (Ten Haaf, 1956; Dzulynski and Smith, 1963; Einsele, 1963). Strong asymmmetry and recumbency are scarce, most folds being either symmetrical or weakly to moderately asymmetrical, with seldom a barely overturned limb (Lamont, 1938; Kuenen, 1953b; Ten Haaf, 1956; Holland, 1959; Fagan, 1962; Einsele, 1963; Dzulynski and Walton, 1965; McKee et al., 1967; Lindsey, 1971; Tyler, 1972; Chakrabarti, 1977). Asymmetrical folds have axial surfaces that lean on average in the palaeocurrent direction (Kuenen, 1953b; Ballance, 1964b; Crowell et al., 1966; Scott, 1966; Sutton and Lewis, 1966; B.G. Jones, 1969; Chakrabarti, 1977). Anticlines are generally sharper than synclines and may have cores of either blurred and highly distorted laminae or even structureless sediment (e.g. Tyler, 1972). Many workers describe the folds three-dimensionally as like basins and upright cones or domes (Kuenen, 1953b; Ten Haaf, 1956; Kingma, 1958; Webby, 1959; Wood and Smith, 1959; H.G. Davies, 1965; Scott, 1966;

35 1

Parkin, 1976; Chakrabarti, 1977). These are in some instances associated with, or subordinate to, cylindrical folds aligned either parallel with or athwart the palaeocurrent direction (Dzulynski and Smith, 1963; Sutton and Lewis, 1966; Anketell and Dzulynski, 1968a). Convolute lamination is typically found in cross-laminated very fine sands or coarse silts that contribute to graded beds in the order of 0.1-1.0 m thick, either turbidites (e.g. Kuenen, 1953a, 1953b; Ten Haaf, 1956; E. Williams, 1959; Wood and Smith, 1959; Bouma, 1962; McBride, 1962; Dzulynski and Smith, 1963; Einsele, 1963; Crowell et al., 1966; Angelucci et al., 1967; Jawarowski, 1971) or their fluvial and deltaic analogues (e.g. McKee, 1954; Einsele, 1963; J.M. Coleman and Gagliano, 1965; Grumbt, 1966; McKee et al., 1967; Stanley, 1968; Coleman, 1969; P.F. Williams, 1969; Karcz, 1972; Picard and High, 1973; Friend et al., 1976; Chakrabarti, 1977). Also affected often are horizontally laminated fine or very fine sands, and interlaminated clean with muddy silts. Convolute lamination occurs in deposits lacking obvious normal grading (Dott and Howard, 1962) and one case is reported from a reversely graded bed (H.G. Davies, 1965). Some soft-sediment deformations in coarse-grade, often cross-bedded sandstones have affinities with convolute lamination (Sutton and Watson, 1960; Selley et al., 1963; A.D. Stewart, 1963; Selley, 1964; Friend et al., 1976; Allen, 1977~). The work of Kuenen (1953b), Ten Haaf (1956), and Nagtegaal (1963, 1965) allows three kinds of convolute lamination to be distinguished, on the basis of the relative timing of deposition and deformation (Fig. 9-6). Post-depositional convolute lamination (B. Smith, 1916; Rich, 1950; Natland and Kuenen, 1951; Ten Haaf, 1956; Holland, 1959; Webby, 1959; Bouma, 1962; Fagan, 1962; Dott and Howard, 1962; McBride and Kimberley, 1963; Angelucci et al., 1967; Rattigan, 1967; T.E. Smith, 1967; Conybeare and Crook, 1968; Ricci Lucchi, 1970; Trettin, 1970; Dunbar and McCall, 1971 ; Jawarowski, 1971; Mutti and Ricci-Lucchi, 1972; Tyler, 1972; Banks, 1973b) arises some time after the start of burial. The folds have greatest amplitude in the middle of the convoluted zone and die away upward and downward toward undeformed laminae. They lack other than

-s7zimE

( a 1 Postdepositional convolute laminotion

(b 1 MetadepmMonol convolute lamination

;

(c 1 Syndepositional convolute lominatbn

Fig. 9-6. Types of convolute lamination.

352

normally expectable internal discordances (e.g. between cross-laminated sets). Metadepositional convolute lamination arises either just before or immediately after deposition ceases. The folds are truncated either by the unit top, on which sand volcanoes may lie above anticlines, or by an internal erosion surface close beneath. Many workers record this structure (Lamont, 1938; McKee, 1954; Van Houten, 1954; Walton, 1955; Kuenen and Sanders, 1956; Kingma, 1958; Webby, 1959; Bouma, 1962; Dott and Howard, 1962; Murphy and Schlanger, 1962; Einsele, 1963; Nagtegaal, 1963; H. G. Davies, 1965; D. Richter, 1965; Grumbt, 1966; Hubert, 1966a; Pescatore, 1966; Angelucci et al., 1967; McKee et al., 1967; Okko, 1967; Wunderlich, 1967; Conybeare and Crook, 1968; J.M. Coleman, 1969; Ricci-Lucchi, 1969c, 1970; P.F. Williams, 1969; McBride, 1970; Teraoka, 1970; Wezel, 1970; De Raaf and Boersma, 1971; Jawarowski, 1971; Tyler, 1972; Picard and High, 1973; Trewin and Holdsworth, 1973; Rascoe, 1975; Boll et al., 1976; Harvey, 1980). Figures 9-4, 9-5 and 9-6c depict syndepositional convolute lamination, formed episodically to continuously during deposition of a bed. The chief evidence for this is the erosional thinning of groups of laminae from synclines toward anticlines, concluding in many instances with truncation of anticlinal crests. As in the metadepositional variety, the folds as a whole may be cut by either the top of the bed or a planar erosion surface just beneath. Syndepositional convolute lamination seems nearly as common as the metadepositional kind (Kuenen, 1953b; Ten Haaf, 1956; Kingma, 1958; Webby, 1959; Wood and Smith, 1959; Prentice, 1960; Dott and Howard, 1962; McBride, 1962; A.D. Stewart, 1962b; Dzulynski and Smith, 1963; Nagtegaal, 1963; Ballance, 1964b; Coleman and Gagliano, 1965; Sanders, 1965; Seilacher and Meischner, 1965; Crowell et al., 1966; Hubert, 1966a; Sutton and Lewis, 1966; Ricci-Lucchi, 1970; Chakrabarti, 1977). Whatever the explanation for convolute lamination, all workers seem agreed that the sediment when deformed was either hydroplastic or liquidized. Probably the latter was most often its state, judging by the smoothness of folds, the scarcity of micro-faults, and the extreme thickness variations shown by individual laminae. From the predominant basin-and-dome form of the folds, we may infer that the primary deforming forces acted essentially vertically, creating in the horizontal an isotropic pattern of shear stress vectors distributed about scattered centres. In cases where the folds lean from the vertical, however, a subordinate horizontally directed force, possibly either fluid drag or a downslope component of the sediment weight, probably also existed. The localized expulsion of pore waters from a bed that is rapidly accumulating is regarded by Migliorini (1950) as the cause of convolute lamination, and by Ten Haaf (1956) and Chakrabarti (1977) as a contributory factor. That such expulsion occurred in some instances seems undoubted,

353

but does not of itself provide a driving force, and cannot explain the postdepositional structure. Under special circumstances, as on beaches (De Boer, 1979), the expulsion of entrapped air may be the cause of convolute lamination. For Rich (1950) and Kuhn-Velten (19554, convolute lamination results from the downslope slip of an overlying sedimentary layer. The chief objections are that (1) horizontal rarely exceed vertical movements within fold limbs, and (2) folds neither invariably nor consistently lean from the vertical. The effect of fluid drag on rapidly accumulating sediment was thought by Prentice (1960) and Sanders (1960) to explain syndepositional convolute lamination. The deposit according to Sanders becomes locally and periodically cohesive, the hardened masses being dragged forward and simultaneously eroded to given the anticlines, while grains accumulate further in the continuously renewed troughs of liquid-like material between. No satisfactory explanation was offered for the alternation of cohesive with liquid-like states. Another essentially hydrodynamic explanation of syndepositional convolute lamination stems from Kuenen ( 1953b), who suggests that deformation is initiated and sustained by high fluid pressure in the troughs of current ripples and low pressure at their crests. Holland (1959) sees the structure as related to “some irregular distribution of pressure or suction, drawing up the anticlinal convolute folds and depressing the laminations between”, an idea elaborated by Chakrabarti (1977). The chief difficulty posed by these ideas is the postulated coupling between folds and pressure fluctuations. In Holland’s model, fluctuations are convected essentially at the speed of the depositing current, and in Kuenen’s at the ripple celerity. In each case, however, the convection speed must have been vastly greater than the rate at which the anticlines could have built downstream. Inspection of syndepositional convolute lamination (e.g. Kuenen, 1953b; Crowell et al., 1966) shows that each anticline during growth was crossed by numerous ripples, whence the required phase relationship between bedform and folds was seldom attained. Two further objections to Kuenen’s model are that (1) fold wavelength correlates with fold-layer or bed thickness and not with ripple wavelength, and (2) syndepositional convolute lamination is not restricted to crosslaminated deposits. The same objections confront Kuenen’s alternative proposal that the folds reflect differential loading by the ripples; they are joined by the further problem that the folds are rarely ripple-like in plan. These difficulties are not critical for Dzulynski and Smith’s (1963) idea that longitudinal patterns in convolute folds are related to secondary flows in the depositing current. A radically different explanation is offered by E. Williams (1960, 1963), who believes that convolute lamination is due to the laminar flow of liquidized sediment around unaffected portions of the deposit clinging to the

354

floor and roof of the layer, to become the cores of the folds. The fold geometry negates this idea. Finally, convolute lamination may be an instability (Rayleigh-Taylor) phenomenon, arising either during or after sediment accumulation, that is driven by a gravitationally unstable gradient of bulk density. This possibility, more plausible than any other, was sketched by Anketell et al. (1970), who attributed the unstable gradient to vertical changes in grain concentration, apparently as imposed during deposition. A related idea specific to normally graded beds was developed by Allen (1977c), who showed using eq. (8.52) that, during their sedimentation after liquefaction, the local grain concentration and bulk density could decrease more rapidly in the lower than the upper part, and so reverse an originally stable gradient or further steepen an originally unstable one. Although developed for the postdepositional structure, the explanation is applicable to the other varieties. As regards the syndepositional type, for example, each increment of rapidly deposited sediment is required to become liquidized almost immediately upon deposition. This could easily be accomplished by the vibratory action of pressure fluctuations in the turbulent current. Field evidence tends to support these theories. Ramberg’s ( 1968a, 1968b) calculations for a viscosity-dominated system (Model V) similar to a graded layer afford a constant fold wavelength/layer thickness ratio close to 3. Crowell et al. (1966) measured a ratio of approximately 2 from the turbidites of the Pic0 Formation. Perhaps most telling is the consistency between the three-dimensional form of the folds, with their essentially axial symmetry, and the pattern of forces expected of a system deforming in the gravity field but without net horizontal translation.

Load casts A horizontal layer of dense fluid superimposed over a layer of light fluid is unstable in the field of gravity, for the potential energy of the system is not a minimum (Rayleigh, 1883). The Rayleigh-Taylor instability of sediment layers contrasted and arranged in this way is latent, however, provided that their yield strengths remain sufficiently large, but becomes actual upon liquidization. At one stage highly controversial (Prentice, 1956, 1960; Kelling and Walton, 1957, 1961; Kuenen and Prentice, 1957; Sullwold, 1959; Holland, 1960), load casts are now recognized as one of the commonest soft-sediment deformations representing the instability of discontinuous layered systems. Kuenen (1953a, 1953b, 1957) describes them as “swellings in the shape of slight bulges, deep or rounded sacks, knobby excrescences, or highly irregular protuberances” to be found on the undersides of sands overlying muds or beneath gravels or coarse sands superimposed on finer sands. Load casts were first reported by Fuchs (1895), who called them Fliesswiilste and reproduced them experimentally, and later by Sorby ( 1908), Kukuk, (1920), and Shrock (1948). These interfacial markings appear in

355

Fig. 9-7. Vertical section through load casts beneath volcanogenic sand bed overlying mud, Langdale Slates (Ordovician), English Lake District. About one-half natural size. After Sorby (1 908).

fluvial (McKee, 1954; D.K. Davies, 1966; Sarkar and Basumallick, 1968; McCracken, 1969; P.F. Williams, 1969), deltaic (Kukuk, 1920; Potter, 1963; Potter and Pettijohn, 1963; Dott, 1966a; Kepferle, 1977) and shallow-marine (Emery, 1950; Pannekoek, 1960) deposits, but are commonest in turbidites (Henderson, 1935; Hills, 1941; Natland and Kuenen, 1951 ; Kuenen, 1953a, 1953b, 1957; Sutton and Watson, 1956; Ksiazkiewicz, 1958; Sullwold, 1959; Ten Haaf, 1959; Wood and Smith, 1959; Lindstrom, 1960; Bouma, 1962; Murphy and Schlanger, 1962; A.D. Stewart, 1962b; Dzulynski, 1963; Ballance, 1964a; Crowell et al., 1966; McBride, 1966; Scott, 1966; Conybeare and Crook, 1968; Ricci-Lucchi, 1970; Negendank, 1970, 1972; D. Roberts, 1972; Behrens, 1973). Load casts occasionally appear in lake sediments (Danilov, 1973; Sims, 1973), and even in layered igneous bodies (Wells, 1962; Roobol, 1972; Dawson and Hawthorne, 1973; Goode, 1976; Thy and Wilson, 1980; C.A. Lee, 1981; Parsons and Butterfield, 1981) and pyroclastic successions (Crowe and Fisher, 1973). Figure 9-7 reproduces Sorby’s (1908) specimen of load casts in vertical section from the Borrowdale Volcanic Series of the English Lake District. It shows rounded pockets of coarse ash that bulge downward into volcanic mud, which in its turn projects upward but in sharper, diaper-like shapes. Faint laminae in the coarse ash follow the margins of the pockets, while a bolder layering in the mud remains generally conformable to the shapes of the diapers, except perhaps locally where there may have been slip in response to extreme shear. Hills (1941) and Ballance (1964a) depict similar relationships. In these examples the mud at the heads of some diapers is drawn out into long streaks, to make Kelling and Walton’s (1957) “flame-

356

Fig. 9-8. Photograph from below of load casts formed experimentally by collapse of a layer of soft sand mixed with Plaster of Paris into a layer of mud, when both became liquidized in response to a sequence of shocks. Specimen 0.3 m across.

structures”, Sullwold’s (1959) “load waves”, and Lamont’s (1965) “anticrests”. The pockets and diapers of Fig. 9-7 are relatively symmetrical about near-vertical axes, but in other cases lean markedly from the vertical and in a consistent direction, normally that of the palaeocurrent (A.D. Stewart, 1962b; Ballance, 1964a; Dionne, 1971b; Dunbar and McCall, 1971; Crowe and Fisher, 1973). These asymmetrical load casts are called squamiform by Ten Haaf (1959) and termed flow casts by Prentice (1956). The flame structures associated with load casts penetrate but do not pierce the upper of the sediment layers involved. Figure 9-8 shows the appearance of load casts in plan from an example made experimentally by sifting sand mixed with Plaster of Paris on to mud and then vibrating the layers. The downward protuberances of sand are

357

roughly equant with a tendency toward polygonal form, many similar examples occurring in the geological record (Kelling and Walton, 1957; Allen, 1960; Lindstrom, 1960; Dzulynski, 1963; Behrens, 1973). A subparallel elongate form is generally restricted to structures that are asymmetrical in vertical profile. The wavelength of load casts at mud- sand interfaces is usually in the range 0.01-0.1 m but can reach the order of 10 m (Emery, 1950; McCallien et al., 1964). Large features resembling load casts are described by Reinhardt and Cleaves (1978) from gravels overlying saprolite. Francis and Howells (1973), and Needham (1978), describe spectacularly large load casts from volcanic sequences. The necessity for sediments to have little if any strength if load casts are to form has long been appreciated. Sorby (1908) wrote of the mud in Fig. 9-7 as in a “creamy semi-liquid condition” when the ash was imposed. Shrock (1948) described his lower sediments as either hydroplastic or highly viscous. Sims (1973, 1975) is able to link the production of load casts and other soft-sediment deformations in modern lake deposits to historical earthquakes, which presumably liquefied the sediments. An understanding of the forces involved in load casting was slower to grow. Shrock (1948) in explaining load casts claims that “hydroplastic sediments, if unequally loaded with sand or gravel, yield to the weight of the superincumbent load by flowing”, a statement containing no hint that load casts form basically because the system is gravitationally unstable. This idea was introduced by Kelling and Walton (1957), though accompanied by strong overtones of Shrock‘s thought. They compared load casts to salt domes formed through gravitational instability (e.g. Nettleton, 1934; Dobrin, 1939, 1941; Parker and McDowell, 1955; J.C. Howard, 1971; Ala, 1974; Hunsche, 1978), to which delta mud-lumps (Morgan and Andersen, 1961; Morgan et al., 1968) and diapiric igneous bodies (Stephansson, 1975; Stephansson and Johnson, 1976) may be added, but claimed that unstable equilibrium was produced only when the upper projected down originally into the lower layer. Such irregularities can certainly help to localize loadcasting, as in load-casted flute and tool marks (Kelling and Walton, 1957; Ten Haaf, 1959), but cannot generally be their cause. By means of qualitative experiments and reference to theory, Dzulynski and his collaborators have gone far toward explaining load casts in terms of the post-liquidization gravitational instability of a dense overlying a light layer (Dzulynski and Walton, 1963, 1965; Dzulynski, 1965, 1966; Dzulynski and Simpson, 1966a; Anketell and Dzulynski, 1968a, 1968b; Anketell et al., 1970). From Fig. 9-9, showing the bulk density of water-saturated mineral-density sediments as a function of particle concentration, we see that a substantial driving force exists in systems of quartz sand overlying clay-mineral mud. Furthermore, following Artyushkov (1963a, 1963b, 1971), they could interpret the narrow diapirs and flame-structures in terms of the lesser effective viscosity of the upper as compared with the lower layer (cf. R.B. Smith, 1979).

358

-

P

1

1000

500

-

.

I : _. I. .' I. .:.

.'. '

.

'

I..,

. ,

.:

,

:.

I

'I

, '

1 . '

0

I

: , . I "1 ' .I

: : '. . . ;: ;;.. . I.: '.'.' I . ;. .

.I

. '

. . . ' I

. , . . ..

I I

Fig. 9-9. Bulk density of water-saturated sediment as a function of particle density (mineralogy) and fractional volume concentration.

At present there are neither theoretical nor quantitative experimental studies of Rayleigh-Taylor instability in sand-mud systems. There are two general theories, however, for the inertia-dominated case (Bellman and Pennington, 1954; Chandrasekhar, 1955, 1961; Hide, 1953, and the viscosity dominated one (Ramberg, 1963b, 1966, 1967, 1968a, 1968b, 1972a, 1972b, 1973; Berner et al., 1972). Which is now appropriate may be judged from Ramberg's (1968a) criterion for the neglect of inertia: (9.3) in which L is the load-cast wavelength, Y is the kinematic viscosity of the sediment layers (equal viscosities assumed), k = 1 for sand-mud systems, and g is the acceleration due to gravity. For a kinematic viscosity of 0.0005 m2s-', corresponding to a bulk density of 2000 kg m P 3 and an effective viscosity of 1 Ns m-2, inertia is negligible only for wavelengths smaller than about 0.015 m. As this value falls within the ordinary range for naturally occurring load casts, a purely inertial theory (Allen, 19709 may be less satisfactory than one taking both viscosity and inertia into account.

359

Pseudo-nodules and ball-and-pillow

Load-casting is never accompanied by such extreme deformation that the upper sediment layer is pierced by the diapers rising from below. There are other two-layer systems, however, and some multi-layered ones, in which the more dense layers are completely disrupted, an extensive bed or beds of sand having been reduced to a series of isolated masses embedded in more or less continuous mud of a lower density that represents one or a blend of several original strata. These masses range from saucer-like to pillow- or bolstershaped, and some even resemble cigars or sausages. They are distinctive in two other ways (e.g. Macar, 1948, 1951; Pepper et al., 1954; Rusnak, 1957; Sorauf, 1965; Howard and Lohrengel, 1969; Hubert et al., 1972; Button and Vos, 1977): (1) wrapped around their outsides are structures preserved on the original sand-mud interface, for example, animal tracks and ripple or tool marks, and (2) internal lamination closely follows the external form, except where the tops of masses are erosively truncated. Confusion reigns in the classification and nomenclature of these complex structures (Skipper and Middleton, 1975), but two criteria seem particularly useful: (1) the size of the masses, and (2) their mode of aggregation. The term pseudo-nodules (Macar, 1948) here covers a structure consisting of a single, laterally extensive row of uniformly sized sand masses, looking for all the world like a horizon of concretions. Ball-and-pillow structure (Potter and Pettijohn, 1963) describes a sheet d sand masses of various sizes packed vertically and horizontally in a mud matrix. The larger masses tend to be described as “hassocks”, “pillows”, “bolsters” or “rolls”, all of which terms are appropriate to their size. Only the smaller ones are commonly described as balls. Pseudo-nodules have a different environmental distribution than load casts, and are commonest in shallow-marine and deltaic deposits (J.R. Cooper, 1943; Macar, 1948; Macar and Antun, 1950; Van Straaten, 1954b; Rusnak, 1957; Seilacher and Meischner, 1965; Sorauf, 1965; Ager and Wallace, 1966; Grumbt, 1966; Simon and Hopkins, 1966; D. Richter, 1967; Young, 1968; Wunderlich, 1970; Dionne, 1971b; Goldring, 1971; Bialik et al., 1972; Hubert et al., 1972; Banks, 1973b; McBride et al., 1975b; Rascoe, 1975; Van Loon and Wiggers, 1976; Button and Vos, 1977; Tankard and Hobday, 1977; Vos, 1977; Weaver, 1976; H.D. Johnson, 1978; Stanley and Surdam, 1978; Weaver and Jeffcoat, 1978; Gill, 1979; Montenat, 1980). There are fewer examples from turbidites (Dzulynski, 1963; McBride, 1966; Ricci-Lucchi, 1969c) than from deposits formed in lakes (Kaye and Power, 1954; Negendank, 1972; Hubert et al., 1976) or by rivers (Selley et al., 1963; McKee, 1966a; J.M. Coleman, 1969; McArthur and Onesti, 1970; P.K. Ray, 1976; Eriksson and Vos, 1979). Figure 9-10 summarizes from these accounts the characteristics and relationships of pseudo-nodules. An undisturbed bed can in some instances be

360

Fig. 9-10. Schematic lateral passage of a continuous sand bed overlying mud into pseudonodules.

traced laterally through a load-casted zone into a row of pseudo-nodules (Hayashi, 1960; Dzulynski, 1963; McBride et al., 1975b; Weaver, 1976) and, it is claimed, even into ball-and-pillow structure (Hubert et al., 1972). The width of pseudo-nodules is 2-4 times and their length up to 8 times the thickness, which is similar to that of the parent bed. A typical width is about 0.5 m but individual masses several metres wide are known and there are many no more than 0.1 m across. Markedly elongated nodules share the same orientation, characteristically parallel with the depositional strike. The synclinal folds defined by the external form and internal bedding of pseudonodules have axial surfaces ranging from vertical to moderately leaning. Generally, the leaning direction is constant within a set. A laterally extensive erosion surface frequently forms the common top to a row of sand masses, a relationship suggestive of metadepositional convolute lamination. Where there is no such truncation, the laminae internal to a pseudo-nodule are seen around the edge to have been severely thinned and bent inward and even downward, as in the lower row of Fig. 9-10. Occasionally, internal discordances demonstrate an episodic growth (e.g. Macar and Antun, 1950; Seilacher and Meischner, 1969, similar to syndepositional convolute lamination. Figure 9-11 shows part of a sheet of ball-and-pillow structure with a lateral extent of at least 1.5 km in the middle of a Carboniferous upwardcoarsening deltaic sequence. It is one of a number of so-called “slump

36 1

Fig. 9-1 1. A zone of ball-and-pillow structures (sandstone in mudstone) overlying shales and mudstones, and overlain (apparently erosively) by sheet sandstone and interbedded sandstone and mudstone. The ball-and-pillow zone is approximately 2 m thick. Coal Measures (Carboniferous) east of Amroth Castle, Amroth, Dyfed, Wales.

sheets” discussed by Kuenen ( 1948b). In this example, sand balls and pillows occupy a zone approximately 2 m thick that is truncated in places erosively by a laterally extensive sheet sandstone. The sand masses lie in mudstone and range in apparent length from less than 0.1 m to a little over 1 m, being on average about 0.4 m across. Most are shallow, flat-lying, dish-like bodies with overturned edges followed by the internal bedding (Fig. 9-12), though a few are rod-like and some are S-shaped (Fig. 9-13). Ksiazkiewicz (1958) found similar forms amongst disrupted turbidites. This example is representative of a large number of ball-and-pillow structures, described mainly from shallow-marine and deltaic deposits (B. Smith, 1916; J.R. Cooper, 1943; Kuenen, 1948b; Macar, 1948; Pepper et al., 1954; Niehoff, 1958; Radwanski, 1960; Radwanski and Roniewicz, 1962; Potter, 1963; Potter and Pettijohn, 1963; Pettijohn and Potter, 1964; Sorauf, 1965; Gauri and Kalterherberg, 1966; Gavelin and Russell, 1967; Bogacz et al., 1968; Schiener, 1970; G.M. Young, 1970; Dionne, 1971b; Goldring, 1971; Wagner and Varker, 1971; Hubert et al., 1972; Wincierz, 1973; Humphreys and Friedman, 1975; McBride et al., 1975b; Rascoe, 1975; Rust, 1976; Brenchley and Newall, 1977; Gill, 1979). Some sheets involve sand masses of spectacular size, measuring many metres across (Howard and Lohrengel, 1969), and

362

Fig. 9- 12. A single saucer-shaped sandstone pillow (note overturned edges) embedded in mudstone. Coin approximately 0.03 m across. Same locality as Fig. 9- 1 1.

others are believed to extend over thousands of square kilometres (Pepper et al., 1954). There are other examples of ball-and-pillow structure composed of sand masses sufficiently small as mainly to be described as balls (Hadding, 193 1 ;

Fig. 9- 13. Vertically flattened sigmoidally folded sandstone bed in mudstone. Coin approximately 0.03 m across. Same locality as Fig. 9-1 1.

363

Greensmith, 1956; A.J. Smith, 1959; R.E. Elliott, 1961; H.G. Davies, 1965; Dott, 1966a; Rattigan, 1967; P.F. Williams, 1969; Jawarowski, 1971; Basu and Guha, 1972; Broekman, 1974; Ruegg, 1975; Weaver, 1976). Many are shallow-water in origin. Detached ball-like masses of heavy crystals are associated with load casts in some layered igneous bodies (Parsons and Butterfield, 1981). Pseudo-nodules and ball-and-pillow structure are no longer felt to be concretions (J. Hall, 1843), but are accepted as soft-sediment deformation structures. Chadwick ( 193I), calling them “storm rollers”, clearly implied their possible dependence upon intense wave action, a cause of liquefaction already discussed. Cooper ( 1943), Kuenen ( 1948b), Macar ( 1948), Macar and Antun (1950), and Hubert et al. (1972, 1976) regard pseudo-nodules and ball-and-pillow structure as due primarily to the downslope movement of interbedded sand and mud, while recognizing that vertical displacements had also occured. In contrast, Sorauf (1965) interpreted many of them as due to the gravitational instability of layered sediments of contrasted bulk density, and of having been involved in mainly vertical movements. Differential loading of soft mud by rapidly deposited sands is the cause according to Kaye and Power (1954), Howard and Lohrengel ( 1969), and McBride et a]. (1975b), with such triggers as earthquake shocks playing a role in some cases. Sorauf ( 1965) thought that isolated sand pillows represented differential loading by sand infilling channels. That translation on a slope is the primary cause of pseudo-nodules and ball-and-pillow structure seems unlikely. Kuenen ( 1958, 1963, 1965b) and Bogacz et al. ( 1968) experimentally produced axially symmetrical structures closely resembling many pseudo-nodules and pillows (e.g. Fig. 9- 12) by applying a shock to unconsolidated multilayers. No net horizontal translation of masses occurred during deformation. Shapes such as that in Fig. 9-13, and the similar ones recorded by Ksiazkiewicz (1958), could have resulted from the oblique descent of sand rafts, and are therefore not an acceptable criterion for the horizontal translation of a whole sheet of foundered sand masses. Other evidence of substantial horizontal displacement, for example, dkoffementor internal shear planes, is generally lacking, and only the slight leaning of some pseudo-nodules denotes a measure of horizontal movement. The most plausible explanation of pseudo-nodules and ball-and-pillow structure is that they record the Rayleigh-Taylor instability of liquidized sand and mud layers, following the arguments of Dzulynski (1966), Anketell and Dzulynski (1968a, 1968b), and Anketell et al. (1970). Pseudo-nodules clearly represent the two-layer case, but ball-and-pillow structure may not always record the disruptim of multilayers. Hayashi and Iwai (1959), Dott (1963) and Lindsey (1971) found sand balls that apparently had been detached from load casts, suggesting that some sheets of sand balls and pillows could have resulted from the repeated detachment-or sedimentary

364

stoping-of quantities of liquidized sand from the underside of a single, thick sand bed. Anketell et al. (1970) suggest that “brittle” sands could founder similarly, and Goldring (197 1) may have evidence for this in the vertical angular blocks of sand within his Grand Slump Member, a sheet otherwise of pillows and balls. Heavy mineral sags and drops

A.D. Stewart (1963), Selley (1964), and Lowe (1975) showed that heavy mineral laminae and bands in quartz sands become deformed in response to density instabilities when all are liquidized. Individual heavy mineral layers are often only a few grains thick and rarely exceed 0.01 m. Interspersed with laminae or bands of quartz or quartz-feldspar sand, they deform as groups where sufficiently close vertically. In Stewart’s and Selley’s examples, from the Torridon Group of Scotland, the heavy minerals are almost exclusively specularite according to Irving ( 1958), but chiefly magnetite, haematite and ilmenite according to Selley (1964). Their density is close to 5000 kg mP3, about twice that of quartz and feldspar. Four stages of drop production are recognized by A.D. Stewart (1963). The first involves the gentle, localized sagging of the heavy mineral layers, at a horizontal spacing of 5-10 times the layer thickness. In the second stage, heavy grains flow laterally into the sags, which consequently thicken while the arched-up portions between grow attenuated. Inward overfolds may at this stage be developed at the margins of sags. Infrequently, an arch slides into an adjacent sag, to accumulate in recumbent concertina-like folds. Figure 9-14a, b shows these stages. The third stage sees the change of a sag into a virtually independent drop, which sinks through the quartz sand while remaining attached to the parent lamina by a faint wake. Figure 9-14c illustrates such structures, though no wakes are visible in the plane of the

Fig. 9-14. Drop and sag structures in heavy mineral bands (black) within sandstones, Torridon Group (Precambrian), northwest Scotland. After A.D. Stewart (1963).

365

section. The final stage (Fig. 9-14d) shows drops that are spreading sideways, to form in some instances, according to Stewart, a vortex ring that gives rise to a secondary drop. The origin of heavy mineral sags and drops through density instability in liquidized sands was shown convincingly by A.D. Stewart (1963), who compared them to: (1) the drop-like sand masses that Kuenen (1958) produced experimentally by liquidizing a sand layer overlying mud, and (2) Thomson and Newall’s (1886) blobs and vortex rings, made by dropping a liquid into another miscible one (see also Okabe and Inoue, 1960, 1961). Figure 9-15 shows stages in the production of spherical drops-Thomson

Fig. 9-15. Successive stages in .the gravitational instability of a narrow cylinder (approximately 0.21 m long, 0.002 m diameter) of dyed glycerol mixed with a very little water and introduced by means of a capillary tube into plain glycerol at room temperature. Time elapsed (a) 12 s, (b) 27 s, (c) 72 s, (d) 128 s. The photographs are here reproduced inverted in order to facilitate comparison with Fig. 9-14.

366

and Newall’s blobs- by the instability of a narrow horizontal cylinder of dyed glycerol introduced into plain glycerol, when it will be seen that Stewart’s fourth stage only is lacking. Its reality in the case of heavy mineral drops is a little doubtful, for Thomson and Newall could make vortex rings only when the liquids had a kinematic viscosity similar to water (1 X m2 s-I). That of liquidized sand at a large enough grain concentration to permit retention of lamination is l o 2 - lo3 times greater, when only spherical drops might be produced, such as Lowe (1975) has figured. Figure 9-14d may not show vortex rings, but perhaps drops flattened as they struck a rising surface of redeposited grains. A significant contrast in scale and density difference exists between heavy mineral sags and Thomson and Newall’s drops, however, and it is not clear how these factors might affect the production of vortex rings. What time scale attaches to heavy mineral drops? Figure 9-14c shows drops about 0.01 m in diameter that apparently fell about 0.05 m. Assigning to the liquidized heavy mineral layer a bulk density of 3200 kg mP3 (Fig. 9-9), and to the quartz sand a bulk density of 1900 kg mP3 and effective viscosity of 1 Ns m-*, the drops once independent could by Stokes’ law (Vol. I, eq. 2.15) have fallen this distance in only 0.7 s. Even demanding several seconds for the drops to develop, the total time seems well within the time-scale for the sedimentation of liquidized sand beds of ordinary thickness (Fig. 9-2).

Deformation involving an ephemeral layer: passively deformed beds The deformation structures so far described have only involved sedimentary layers, which remain in some tangible form after disturbance. We now turn to cases where deformation apparently depended on the presence amongst sedimentary layers of a layer of pore fluid, ultimately expressed from the sequence and so lost to present inspection, of which Fig. 8-26 is an example. One possible case for deformation related to an ephemeral fluid layer is H.D. Johnson’s (1977b) passively deformed bedding. From the late Precambrian shallow-marine rocks of north Norway he describes repetitions of the vertical sequence: ( 1 ) intensely soft-sediment deformed cross-bedded sandstones, (2) weakly deformed cross-bedded sandstones (passively deformed bed), and (3) undeformed cross-bedded sandstones. The intensely deformed rocks, described as convolute-bedded, “form unbroken sequences up to 8 m thick” but are ordinarily between 1 and 4 m. The passively deformed beds following sharply above show no signs of internal liquidization but are warped into elongated shallow basins separated by sharper anticlines. The anticlinal hinges localize upward sand injections which in some instances seem to have pierced the bed. Undeformed sandstones bury the uneven top of the passively deformed layer.

367

The character and setting of these sequences support H.D. Johnson’s ( 1977b) argument that liquidization, probably storm-induced, occurred in a

sand layer commencing a short distance below the sea bed, the unaffected but hydroplastic sand above, which became the passively deformed bed, acting as a lid to the liquidized bed. The only account offered of the forces causing deformation is the statement that “the quasi-liquid nature of this bed causes the overlying bed to founder, particularly where there is an upward escape of pore water‘ and sand through the overlying bed”. A liquid-like state is doubtfully a cause of deformation and is a sufficient condition only in the presence of a suitable prior driving force. There could have been a driving force if either (1) the passively deformed bed exceeded in bulk density the sand beneath, or (2) a fluid layer appeared between the liquidized sand and the passively deformed bed, on account of the lid subsiding slower than the resedimenting dispersion beneath. That the second possibility cannot easily be discounted is shown by the following simple experiment. A layer about 0.10 m thick is formed by rapidly sifting fine sand into water, and on top is similarly deposited a much thinner layer of very fine sand. On jolting the container the sands are liquefied. Almost at once, puffs of grains appear above the sediment-water interface, some from circular vents and others from apparently linear sources. Small craters, a few with modest cones, are afterwards discovered on the surface. None of these effects appears if the sands are treated separately or if the order of succession is reversed. An upper layer of very fine sand is analogous to the passively deformed bed. It behaves unstably because, as a layer, it sinks more slowly than the fine sand sedimenting beneath, and exceeds in bulk density the layer of plain water accumulating above this sand. Deformation involving an ephemeral layer: dish structures

Dish structures are a recent discovery. They apparently were first described by Crook (1961) under the title “discontinuous curved lamination”, Pedersen and Surlyk’s (1977) claim on behalf of Natland and Kuenen (195 1) (and by implication Migliorini, 1950) being misjudged. Short accounts using the name “dish structure” were later published almost simultaneously by Stauffer ( 1967) and Wentworth ( 1967), but comprehensive studies became available only with the work of Lowe and LoPiccolo (1974) and Lowe (1975). Dish structures are frequent in the coarser grained deposits of turbidity currents and related high-concentration flows (Crook, 1961; Stauffer, 1967; Wentworth, 1967; Ojakangas, 1968; Hubert et al., 1970; Chipping, 1972; Corbett, 1972; Klein et al., 1972; Kruit.et al., 1972, 1975; Lowe, 1972, 1975; Mutti and Ricci-Lucchi, 1972; Lowe and LoPiccolo, 1974; D.J. Stanley, 1974; Van de Kamp et al., 1974; Nilsen and Clarke, 1975; Homewood, 1976; Knox, 1976; Hirayama and Nakajima, 1977; Nilsen et al., 1977; Hendry, 1978), and I have seen them also in the thicker mid

368

Fig. 9- 16. Vertical section through fine-grained sandstone with small dish structures. Specimen 0.035 m across. Note sharply defined bases and muddy lower zones to dishes, and also the relatively clean tops. Jackfork Group (Carboniferous), southeast Oklahoma. Photograph courtesy of D.R. Lowe.

Ordovician turbidites at Cardigan in Wales (James, 1975; Allen, 1981). The structures are rarely found in shallow-marine (Tyler, 1972; Rautman and Dott, 1977) and fluviatile (Nilsen and Clarke, 1975; Rust, 1976) sediments. Pedersen and Surlyk (1977) found dish structures in two of the coarser grained of 179 ash layers deposited from air falls amongst Eocene marine diatomites. These accounts lead to the following description. Dish structures occur in laterally extensive sheets in coarse silts and in all grades of sand, with most examples coming from normally graded beds. Each structure (Fig. 9-16) has two parts, the dish itself, and the sediment contained within the dish and bounded by the dish or dishes next above. In sections normal to bedding, dishes are substantially flat to strongly concaveup laminae or bands richer in clay, silt and sometimes organic matter than the surrounding sediment and usually of a darker colour. They lie en echelon.

369

Fig. 9- 17. Dish structure developed after convolute lamination, Jackfork Group, Oklahoma, U.S.A. Numerous examples of laminae severed or distorted between successive dishes can be seen. Specimen approximately 0.15 m across. Photograph courtesy of D.R. Lowe.

3 70

(a)

I

c

increasing bed thickness and COOrSeneSs

Fig. 9-18. Dish structures. a. Schematic vertical section through beds with dish structures, in which the dish-structured zone has a roof in sediment similar to that involved in the dishes. b. Some schematic details of dish structures developed in a previously convolute-laminatedbed (see also (a), left-hand sequence).

Dishes vary in width from about 0.02 m to over 0.5 m, and in vertical spacing from less than 0.01 m to as much as 0.08 m. They are polygonal, circular, oval or elliptical in plan, generally lacking a marked elongation. Dishes invariably have sharp bases. Usually the tops are gradational (Fig. 9-16), but some sharp upper boundaries are known (Rautman and Dott, 1977; Rust, 1976). Lowe and LoPiccolo (1974) identified two kinds of change in each dish and overlying infill: (1) size-grading, marked by an upward increase in mean sand-grain size, and (2) content grading, distinguished by an upward decrease in the amount of interstitial clay, silt and organic matter ( e g Fig. 9-16). Content grading in many instances culminates upward in a band of pale-coloured, clean-looking sand just beneath overlying dishes (Fig. 9-16 but compare Pedersen and Surlyk, 1977). The turned-up edge of one dish rarely touches the base of a dish lying above. In deep-water sands, the vertical patterns and relationships to earlier formed sedimentary structures shown by dish structures seem to reflect bed thickness and coarseness. In the thinner and finer grained beds, as Lowe and LoPiccolo (1974) noted, dish structures with relatively flat bases and narrow, sharply up turned margins are overlain by increasingly concave dishes (Sequence A in Fig. 9-18a). Parallel lamination in the lower part of the bed is often cut by the edges of dishes, and cross-lamination or convolute lamination higher up is commonly severed (Fig. 9-17). Lowe and LoPiccolo noted that, in the pale zone at the top of a dish filling, the prior laminae are not

371

uncommonly bent sharply over (?micro-faulting involved), or streaked out so as to be scarcely detectable (Figs. 9-17, 9-18b). Many of the pale zones of dishes that obliquely cut prior laminations are in fact completely structureless, suggesting an extreme of disruption. At weakly developed pale zones, however, abrupt offsets are sometimes discernible. Prior layering is seldom reported in association with dish structures in the thicker and coarser grained beds (e.g. Kruit et al., 1975). The sequence of flat grading up to concave dishes in these beds usually overlies structureless sand (Fig. 9- 18a, Sequence B). The sequence of dish shapes reported from deep-water sands may not be typical of other facies. Rust (1976) noted from a fluvial sand a weak tendency for dish concavity to decrease upward. Little attention is paid to the manner in which sheets of dish structures are limited upwards, though at least two modes of termination are recognizable. Mutti and Ricci-Lucchi (1972) and Kruit et al. (1975) show sheets truncated by planar erosion surfaces overlain by more sand (Fig. 9-18a, Sequence B, left), as is implied by Klein et al. (1972). In the second mode (Fig. 9-18a, Sequence A, Sequence B, right), the dish-structure zone terminates within the affected sedimentation unit, at a roof formed by either metadepositional convolute laminated (Lowe, 1975) or parallel laminated (Kruit et al., 1975) sand. The roof in the example of Fig. 9-19 is uneven and penetrated by irregular veins of structureless sand, which generally cut but in places follow the bedding. Some veins appear totally to envelop irregular blocks of sand, the lamination in which had been tilted or warped relative to that in unaffected parts above (view the photograph obliquely to see this). In another example reported by Kruit et al. (1975) the laminae at the edge of a large block have been bent and streaked out upward. Dish structures were treated as primary by those earliest to study them. Wentworth (1967) attributed them to antidunes, but thought that dewatering of the bed had played an unspecified part, noting as well that certain hydrodynamic difficulties stemmed from his interpretation. In Stauffer’s (1967) view, dish structures arise either internally or externally during the flow of highly concentrated debris. He like Wentworth gave an unspecified role to the pore fluid, writing that “this trapped water may be the essential factor in the formation of dish structure”. Stauffer’s interpretation was extended by Corbett (1972), who proposed that dish structures arose during dewatering by the modification of effectively primary laminations, formed during the mass-shearing of liquidized sediment. These explanations are difficult to accept, mainly because the characteristics of dish structures are inconsistent with the mechanisms advanced. Lowe and LoPiccolo (1974) treat dish structures as secondary features produced during the gradual dewatering of quick or underconsolidated beds. The dishes are said to “evolve as escaping water is forced to follow horizontal flow paths beneath semi-permeable laminations or beneath deadwater trapped in regions of closure beneath semi-permeable laminations”.

372

Fig. 9-19. Vertical section in dish-structured sandstone (below) extending up to an irregular roof beneath parallel laminated rocks. The latter are penetrated by veins of destratified (? liquidized) sand. Tertiary deep-sea fan deposits, San Sebastian area, northern Spain. Width of bed 0.45 m. Photograph courtesy of A. van Vliet (see Kruit et al., 1975).

The escaping water is regarded as generally originating within the bed in which the dish structures are developing, but an origin in earlier sediments is not excluded. The prior existence of semi-permeable laminations, which need not be laterally extensive, is critical to Lowe and LoPiccolo’s explanation. These laminae deflect horizontally the water moving upward through the bed. The horizontal flow is regarded as invariably vigorous enough to entrain any clay, silt and organic matter present in the sand beneath a semi-permeable lamina and in some instances as powerful enough to set the sand itself in motion. Lowe (1975) was later to describe the pale zones created. by this cleaning-up process as “horizontal fluidization channels”, probably a misnomer in terms of fluidization as understood above. A dish is formed as mobilized fines are filtered out and trapped by the semi-permeable lamina, consequent on some of the mainly horizontal flow in the developing pale zone below seeping upward through it. The lamina thickens by upward growth and is simultaneously extended laterally be deposition at its extremities. At the edge of the growing dish, however, the escaping flow turns upward along a vertical path. If another semi-permeable lamina at a higher level lies in this path, a further dish can form, and so on until a substantial portion of the original sedimentation unit contains dish structures.

373

Several difficulties suggest that at least one other model needs consideration. The prior existence of semi-permeable laminae does not seem necessary for dish production. Pedersen and Surlyk (1977) are emphatic that the 179 tuffs amongst which they found two with dish structures are totally without internal lamination, though ordinarily with a marked normal grading, and their photographs lack any sign of prior laminations (other than the dishes) within the two falls that preserve the structure. If dishes grow by deposition at their edges, as Lowe and LoPiccolo (1974) suggest, why is it that the structures are generally of such a modest concavity? The relative flatness of a dish is understandable where there is undeformed parallel lamination, but difficult to comprehend where the prior laminae are inclined, as in crosslaminated or convolute-laminated zones, or where the sand was apparently structureless. Since the flow around the dish is compressed at its edgecompare that about a sphere (Vol. I, Fig. 2-9)-one would expect marginal growth on much steeper upward paths than seem typical (Figs. 9-16, 9-17). The relative flatness and horizontality of dishes strongly suggests that production is in fact under a primarily gravitational control, and not that of the distribution of pore-fluid pressure in an essentially passive granular framework, as implied by Lowe and LoPiccolo (1974). Finally, the uneven roofing of sheets by metadepositional convolute-laminated (Lowe, 1975) or parallel-laminated sediment (Fig. 9- 19) shows that at least some dish structures are postdepositional (Lowe and LoPiccolo, 1974), but as well suggests that dishes did not form until most or all of the bed was already partly consolidated and slightly cohesive. The prior lamination not uncommonly offset between dishes adds to this point. It suggests that the sand masses involved in dish production were capable of independent movement, because they were largely or wholly bounded by fracture surfaces. In the face of these difficulties, it is worth asking if dish structures could result from a process of stoping within a water-saturated sedimentation unit that is slightly cohesive but far from completely consolidated. A horizontal water-filled cavity must exist in the bed before stoping can occur. Such cavities, which need only be very shallow, could be made in the bed as the result of the sedimentation after liquefaction of zones where sand had remained cohesionless. Significantly, Rust ( 1976) found dish-structured sands to overlie zones of ball-and-pillow, which could leave water-filled spaces above them as they formed and consolidated. But if no cohesionless sand remained, a cavity could be created if a limited quantity of water originating externally were forcefully injected into the bed, provided that the bed lay beneath one or more mud layers able to stretch in tension to accommodate and at least temporarily seal the newly created fluid layer. Whichever is the case, the water will probably contain dispersed fines and the cavity should appear in the lower coarser grained part of a graded sand, where the permeability is largest and the strength-giving mud content least. Even a very shallow water-filled cavity overlain by sediment constitutes a

374

potentially unstable system in the gravity field. Slightly cohesive sand will fail and fall into such a cavity in substantial masses and not grain-by-grain. The subhorizontal failure surfaces will follow prior laminations only where these are substantially horizontal, as in parallel-laminated parts of the bed. In cross-laminated or convoluted portions, the failure surfaces will be substantially independent of bedding, and will define flake-shaped rather than sheet-like masses. As the masses are released one after the other from the roof of the cavity, the cavity will progress up through the bed, to stop either where the sand is so strong that further falls are impossible, or when the cavity is suddenly emptied through a breach in its roof. Three things should happen to each mass of sand as it sinks toward the cavity floor. Some of the cavity fluid will seep upward through the sinking mass, which will filter out a quantity of the dispersed fines. Their deposition rate will be greatest over the underside of the mass and will decline inward along the flow paths. Most fines will be trapped in the central part of the mass, because the flow entering here is least deflected from the vertical. The dish-entrapped fines will therefore thin outward from the centre, as is observed (Fig. 9-16). The fluid drag exerted on the mass will be greatest around its edges, which should become turned steeply upward, in a manner similar to Kuenen’s (1958) experimental sand balls. As the developing dish structure approaches the cavity floor, where earlier dish structures lie, the intervening cavity fluid will be forced outward with rapidly increasing force. As can be seen by dropping a flat pebble a short distance through water on to sand, the outward flow could mobilize and shear the tops of dish structures already on the floor, which may be the origin of the pale zones and offset laminae recorded (Fig. 9-17), as well as replenish the cavity fluid with fines. The floor will in this way be shaped to receive each dish, while sand will be carried laterally to infill the spaces between dishes sinking in close array. Finally, the impact of the dish with the floor will promote the further consolidation of the sediment, probably as the result of settlement after liquefaction. The cavity should therefore deepen as it rises through the bed, for the roof will outpace the floor. This model, involving the instability of a two-layer system in which one layer is ephemeral, explains most of the characteristics of dish structures, notably their form, vertical succession, roofing and lack of complete dependence on semi-permeable laminae. It too presents difficulties, the chief of which is that, in those cases where prior lamination is seen, the offsets between dishes are neither as common nor as substantial as might be expected. It may nonetheless be incorrect to expect these attributes after descents of no more than a few millimetres or centimetres.

375

DEFORMATION STRUCTURES RELATED TO NON - UNIFORM CONFINING LOADS

Load-casted ripple marks Three varieties are known: ( 1) postdepositional, involving incomplete ripple marks, (2) syndepositional, involving a sequence of ripple marks, and (3) syndepositional, where one ripple grew continuously. Dzulynski and Kotlarczyk (1962), Dzulynski (1963) and Dzulynski and Walton ( 1965) have discussed load-casted ripple marks of postdepositional origin. The structure (Fig. 9-20b) in cross-section appears as a row of plano-convex or biconvex lenses of coarse silt or sand embedded in mud. The lenses are generally less than 0.1 m long and seldom thicker than 0.01 m, the thickest part usually lying close to one edge. The internal lamination varies from steep near the sharp side of the lens to almost horizontal near where the lens is thickest. Dzulynski and Kotlarczyk suggest that the structures result from the differential loading of a hydroplastic substrate, as illustrated in Fig. 9-20a, b. The mud in the troughs between ripples is effectively unloaded, whereas that beneath the ripples is loaded to an extent proportional to local ripple height and sand bulk density. If the mud had been liquidized, the ripples would have sunk much deeper, forming sand balls as in Kuenen’s (1958) experiments. Clustered load-casted ripple marks of syndepositional origin were also described by Dzulynski and Kotlarczyk (1962), Dzulynski (1963), and Dzulynski and Walton (1965). These structures are cylindrical masses of sand or coarse silt that occur in rows in the plane of bedding and in cross-section present a radial internal structure of laminated sand wedges and mud fingers (Fig. 9-21a). Dzulynski and Kotlarczyk advanced an ingenious explanation for them (Fig. 9-21b). Each mass is believed due to the loading into weak mud of a number of ripples, one after the other at much the same site, each new addition pressing downward and forward the earlier ones, until a radial structure becomes well-developed. A row of cylinders can

Fig. 9-20. Schematic development of a row of load-casted ripple marks.

316

I

II

Fig. 9-2 1. Clusters of load-casted ripple marks. a. A cluster of load-castcd.ripple marks, Kliva Sandstone (Oligocene), Polish Carpathan Mountains. b. Stages in development of cluster of load-casted ripple marks. After Dzulynski and Kotlarczyk (1962).

Fig. 9-22. Load-casted ripple marks, Kurkiselka Esker, Kiiminki, Finland. Current from right to left. Photograph courtesy of R. Aario.

311

be created if loading occurs simultaneously at several nearby sites. Dzulynski and Kotlarczyk did not explain how sand reaches all parts of the bed, nor why foundering is localized in the manner demanded by the distribution of the cylinders. Once locally weakened, however, the mud would tend to remain of reduced strength, permitting further deformation. Sand could reach all parts of the bed if there was a substantial supply in suspension. A second type of syndepositional load-casted ripple mark is described by Aario (1971) from esker silts and sands. Almost certainly the same structure is recorded by Begin (1975) from interbedded fluvio-deltaic sands and silts under the title of “asymmetric riple marks”. Figure 9-22 illustrates the structure described by Aario (1971). It consists of a laterally extensive row of inclined pouches formed of coarse-grained cross-laminated sand that fill the troughs of strongly asymmetrical synclinal folds in the deposit below. The cross-laminae steadily decline in dip from steep and even overturned at the upcurrent base of each pouch, to their normal attitude at the downcurrent top. The sediments beneath are normally graded cross-laminated sands that pass up into a thick drape of laminated silt. Aario (1971) concluded that each trough-filling sand pouch and complementary anticline was developed simultaneously with the downstream march of a ripple (Fig. 9-23). Combining ideas advanced by Kuenen (1953b) and Sanders (1960), discussed in connection with convolute lamination, he sug-

Fig. 9-23. Schematic stages in the development of syndepositional load-casted ripple marks, according to Aario (1971).

378

gested that the folds represented the combined effect of fluid drag on the rippled bed and the pressure differences existing between troughs and crests. He further concluded that the upward and downstream decrease in the intensity of deformation in the pouches resulted from a steady decline in current strength. If Aario’s explanation is correct, it can apply only to the earliest stages of pouch growth, for ripple troughs in Fig. 9-22 now lie above anticlines and not above synclines as his hypothesis demands. It is more likely that deformation began, and was maintained, as the result of differential sediment loading. The laminated silt beneath the pouches draped but did not obliterate the forms of ripples capping the cross-laminated sand further below. Thus when rippling recommenced, deposition of coarse sand began to the lee of residual mounds, infilling the troughs between. A differential loading would therefore have been combined with a latent gravitational instability, for it is reasonable to suppose that the silt would have had the lower bulk density on account of its fine grade. If liquefaction occurred the troughs would have been accentuated by a progressive rotation not dissimilar to that postulated by Dzulynski and Kotlarczyk (1962) for clustered loadcasted ripples. The liquefaction permitting, deformation to take place was possibly triggered by pressure fluctuations associated with flow separation at the ripples. Folds related to the lateral spread of sand mounds Several cases are known of layered muds that became folded as sand deltas, dunes, and complex drifts advanced across them. The muds remained hydroplastic, except locally where they were liquidized as a direct consequence of deformation. Figure 9-24 summarizes reported features and relationships.

-

Sand spreading

Fig. 9-24. Deformation by folding and faulting of layered plastic muds by a migrating sand body.

379

The largest and most extensive folds are described by R.G. Brown (1969) and I.J. Townsend (1974) from sites in the Coorong Lagoon, South Australia, where substantial aeolian sand-drifts are spreading inland from a coastal barrier. Here folds occupy belts up to 150 m wide and 1.5 km long in thick layered muds in front of the advancing and over-riding drifts. The structures appear as long exposed ridges (anticlines) in the order of 1 m high arranged en echelon, at a crestal spacing of up to 20 m, and subparallel with the leading edges of the drifts, their height declining away from the sand spreads. Open to closed and symmetrical to mildly leaning folds are typical. Some are box-like but others have swollen hinge zones. Small reverse faults and thrusts affect the hinges of some anticlines. Locally in the sands of the advancing drifts are normal faults down-throwing toward the exposed mud. A second but smaller modern example is described by W.R. Parker (1973) from a barred beach where underwater dunes travel over thin mud sheets deposited on the floors of runnels parallel with shore. Fold crests are subparallel with dune crests. A fold wavelength of about 0.5 m and an amplitude of 0.15-0.20 m are usual. The anticlines are in some cases upright and symmetrical, resembling buckle folds, but in others are strongly asymmetrical, facing the direction of dune travel. Parker noticed that the largest folds occurred where the dunes were tallest, and that dune size and intensity of folding declined in the same direction. B.G. Jones (1972b) described from the Devonian rocks of central Australia an example of the deformation of muds during the spread of a large aeolian dune. The folds resemble in scale, form and attitude those described by R.G. Brown (1969) and W.R. Parker (1973) and, like the folds in the Coorong Lagoon, appear to have been exposed to erosion during growth, since thick intraclast conglomerates appear locally in their synclinal troughs. The folding is thought in each of these cases to be due to the differential loading of a mobile mud during the spread of a substantial sand body, appeal being made partly to experimental evidence of the kind advanced by Kindle (1917b), Rettger (1935), and McKee and Goldberg (1969). These workers found that when a sand body such as a delta spread rapidly across a layered mud, some of the mud was squeezed -forward and compressed laterally in harmony, becoming shaped into folds of outward-declining amplitude arranged parallel with the edge of the advancing load. Some folds resembled buckles but others were strongly asymmetrical, with thinned or thrust-out limbs. In one experiment, Rettger produced in the sand body normal faults down-throwing toward the side of least load on the mud, just as R.G. Brown (1969) observed from the Coorong Lagoon.

3 80 DEFORMATION STRUCTURES RELATED TO A DOWNSLOPE BODY-FORCE COMPONENT

Sheet slumps formed from multilayers The stratigraphic record abounds in sheet-like bodies of deformed sediment that were emplaced apparently following the collapse and downslope translation over a substantial distance of a superficial layered deposit, either sand interbedded with mud, or mud with carbonate sediment. The sediments at the time appear to have been mainly unconsolidated and only in a few cases partly lithified. Slumps of still mushy layers of crystals have been reported from the more steeply dipping cooling surfaces within many layered igneous intrusions (Wadsworth, 1961, 1973, Irvine, 1965; Thompson and Patrick, 1968; Ghisler, 1970; Umeji, 1975). Sheet slumps (Fig. 9-25) are known from several environments and are developed on a wide range of scales. In glacially influenced settings (Fairbridge, 1947; Van Straaten, 1949; Jardine, 1965; Dionne, 1971b; Wisniewski, 1973) there occur folded and faulted silts and clays with downthrust sand masses, in sheets that rarely exceed 0.5 m in thickness and commonly die out over a few tens of metres. Thin slump sheets are also recorded from pyroclastic sequences (Crowe and Fisher, 1973). Grander slumps occur in fluviatile and deltaic deposits (Matthews, 1961; Dott, 1963; Pettijohn and Potter, 1964; Kelling and Williams, 1966; T.D. Ford, 1971; Rascoe, 1975; Gill, 1979; E.W. Johnson, 1981), in which examples occasionally reach 15 m in thickness and extend laterally over 10 km or more. Slump sheets in the general order of 1-10 m thick are also recorded from lacustrine and shallow-marine sequences (Evans and Whitaker, 1964; Spreng, 1967; Daley, 1972; Kennedy and Juignet, 1974; Adams and Cossey, 1978). By far the largest, however, occur amongst deep-water basin deposits (O.T. Jones, 1937, 1940; Straw, 1937; Earp, 1938; Newel1 et al., 1953; Sutton and Watson, 1956; Williams and Prentice, 1957; Waterhouse and Bradley, 1957; Ksiazkiewicz, 1958; Rigby, 1958; Ten Haaf, 1959; Murphy and Schlanger, 1962; Marschalko, 1963; Ballance, 1964b; Grant-Mackie and Lowry, 1964; D. Richter, 1965; Pescatore, 1966; K.M. Scott, 1966; Gregory, 1969; Helwig, 1970; G.S. Horne, 1970; Ricci-Lucchi, 1970; Morris, 1971; Yagashita, .1971; D. Roberts, 1972; Mutti and Ricci-Lucchi, 1972; Van Straaten and Tucker, 1972; Corbett, 1973; Hoedemaker, 1973; Crimes, 1975; Eisbacher, 1976; Rupke, 1976; Woodcock, 1976a, 1976b). Most of these sheets have a thickness in the order of 1 m, many are in the neighbourhood of 10 m thick, and a few exceed 100 m. Lateral extents are generally uncertain, but the thicker sheets apparently are the more extensive. Ballance described a slump about 1 m thick that passed within 200 m laterally into undisturbed strata, and referred to thinner sheets that were even less persistent. Gregory and Rupke, however, reported thick sheets apparently traceable laterally for many kilometres.

381

Fig. 9-25. Features of slump sheets, lacustrine muds and silts, Dead Sea, Israel. a. Imbricately thrust folded layers in two zones. Hammer 0.33 m long. b. Box folds with probable basal dicollernent. Hammer stuck into cliff below folded zone casts vertical shadow about 0.4 m long. Photographs courtesy of B.W. Sellwood.

382

So far as the stratigraphic record goes, “Distinction between slump structures and small tectonic structures is sometimes difficult, especially where intensive tectonic movements have later taken place or when the structure is only partially exposed” (Kuenen, 1953b). Although many features of slump sheets imply slumping, the only definite large-scale criteria of a slump origin are the interbedding of sheets with undisturbed strata and the presence of what O.T. Jones (1937, 1940) described as a “welded ” (i.e. erosional) contact at the top of each sheet. Although reported by many authors (e.g. Fairbridge, 1947; Sutton and Watson, 1956; Matthews, 1961; Jardine, 1965; Helwig, 1970; Ricci-Lucchi, 1970; Corbett, 1973; Kennedy and Juignet, 1974; Woodcock, 1976a) these criteria are easier to establish in the case of thin than thick sheets. Small-scale indicators of slumping should therefore not be neglected, for example, burrowed slump folds (Kleist, 1974; Beutner, 1975), sand volcanoes on the tops of sheets (Gill and Kuenen, 1958; Moore et al., 1976; Gill 1979), and features indicating sediment hydroplasticity (Woodcock, 1976a). The question of why and how do the sedimentary materials composing a slump sheet deform, given the initial geometry of failure, was considered by Helwig (1970). Two contrasting types of sediment are likely to be combined in the thinner sheets: (1) cohesionless water-saturated sands and coarse silts, which if liquidized fail by viscous flow or otherwise by the development of slip surfaces, and (2) cohesive muds which deform either as plastic solids or as viscous liquids accordingly as their water content is small or large. Failures reaching deeply into a layered sequence may also involve cemented sand beds which fail as brittle solids in extension. Early formed concretions, and early cemented carbonate sediments, should behave similarly in shallow failures. The major stress in slumping is gravitationally induced shear, which can cause the folding and thrusting of multilayers only if deflected from its nominally bedding-parallel sense. Helwig lists the likely causes of deflection as: (1) rotational movements in the head and tail regions of the slump, (2) transverse variations in the local flow speed of the slump related to nonuniform frictional stresses, (3) over-riding of bottom irregularities, (4) suddenly decreased slope or collision with obstacles, and (5) localized liquidization during flow or development of density-controlled instabilities. Because of the varied nature of the parent sediments, and the localized action of the stresses, variety of deformational style is the hallmark of slump sheets, including the presence of essentially unstrained masses. Typically, the folds in slump sheets are isolated either single hinges or disharmonic structures. Axial surfaces vary from steeply inclined to flat-lying, with most tending toward the latter category (Fig. 9-26a). Concentric folds, box folds, and some similar folds may all be observed in a single sheet. Most single folds have unequal limbs (Fig. 9-26b) and some a spiral form (Hadding, 1931), resembling a rolled-up carpet (Fig. 9-26c). Faults ranging from bedding-parallel slips to low-angle thrusts abound and divide up some sheets

383

ca. I m

Fig. 9-26. Structures (slightly simplified) in slump sheets. Sandstone or marker sandstone beds shown stippled. a. A large flat-lying fold, Waitemata Group (Miocene), New Zealand (after Gregory, 1969). b. Unequal folds in turbidite sandstone, Marnosa-arenacea romagnola (Tertiary). Appennines (after Ricci-Lucchi, 1970). c. Spiral fold in turbidite sandstone, Waitemata Group (Miocene), New Zealand (after Gregory, 1969). d. Imbricate structure in turbidite sandstones, Waitemata Group (Miocene), New Zealand (after Gregory, 1969). e. Imbricate structure in fluvial sandstones, Peel Sandstone (?Devonian), Isle of Man (after Ford, 1971). f. Thrusts and reverse faults in Pleistocene silts and clays, Glasgow, Scotland (after Jardine, 1965). g. Box folds in Pleistocene silts and clays, Finland (after Van Straaten, 1949). h. Overfolds with decollement, Pleistocene silts and clays, south Quebec, Canada (after Dionne, 1971 b). i. Imbricate blocks formed from a single thick turbidite sandstone in tension, Waitemata Group (Miocene), New Zealand (after Gregory, 1969).

384

internally into recognizable packets. Series of thrusts that repeat a bed in an imbricate structure are frequently observed (Figs. 9-25a, 9-26d, e). Some thrusts change into low-angle reverse faults of modest displacement (Fig. 9-260. DPcollement associated with box folds is commonest in the thinner sheets (Figs. 9-25b, 9-268, h). The brittle response of relatively competent beds is recorded by the presence of unwarped blocks bounded by joint-like fracture and bedding surfaces. The strung-out imbricate blocks of Fig. 9-261 represent a bed that failed like this while being stretched and sheared. There is no simple relationship in slump sheets between fold attitude and slumping direction. Woodcock ( 1976a, 1976b) has considerably developed the early model proposed by O.T. Jones (1937, 1940), finding that the folds face chiefly in the direction of slump movement, have axes aligned mainly perpendicular to this direction and parallel with the strike of the palaeoslope, and possess axial surfaces on average tilted gently down toward the source of the slump. The model is supported experimentally (e.g. Rettger, 1935; Blay et al., 1977) but, as Woodcock notes, has no a priori validity. Other models exist (E. Hansen, 1965; Scott and Hansen, 1967; Lajoie, 1972; B.A. Hall, 1973; Beutner, 1975; Eisbacher, 1976), which may better explain the considerable diversity of fold axial trends observed from some slump sheets (e.g. Ten Haaf, 1959; Marschalko, 1963; Helwig, 1970; Morris, 1971). In Lajoie's model, based on an observation of a slumped snow layer, fold axes lie perpendicular to the slope strike at the tail and sides of the slump, but turn parallel with the strike at the head. Eisbacher's model presents the folds as overlapping lobes, the curved axis of each turning from strike-parallel at the head to strike-perpendicular on the flanks. The relationship between the slumping direction and the path of the current that deposited the beds originally is another question. As regards deep-water deposits, Ballance (1964b) found the slumping and current directions to coincide, whereas Murphy and Schlanger (1962), K.M. Scott (1966), and Corbett (1973) established an azimuth difference of approximately 90". Presumably in many basins turbidity currents flowed parallel with the slopes on which slumping occurred (Kuenen, 1967). A further discussion is given by Woodcock ( 1976b). Studies in modem environments show that slumping of unconsolidated sediments occurs on subaqueous slopes as low as 0.5". Huge volumes of sediment can be involved, as witness the slumps described from the Mississippi delta and deep-sea fan by Walker and Massinghill (1970), Coleman et al. (1974), and Prior and Coleman (1980a, 1980b). Slumping is triggered by earthquake shocks, the build-up of pore-fluid pressure as the result of the migration of pore water, and the oversteepening of slopes by deposition or other means. Because unconsolidated sediments are involved, liquidization probably plays a significant role in most cases of slumping, but is not always a factor of over-riding importance. Oversteepening or earthquake shocks are most often invoked to explain slump sheets. See also Woodcock (1979).

385

Deformed cross-bedding

The third of the three kinds of deformed cross-bedding identified by Allen and Banks (1972) reveals a combination of folding and faulting with the local blurring or destruction of lamination. Most reported examples are from aeolian sands. The deformation in many instances occurred during the accumulation of a set of cross-strata, and is therefore metadepositional with respect to foresets rather than to the set itself. The features described are: (1) small folds ranging from disharmonic and relatively upright, through drag folds, to nappe-like forms, (2) normal faults downthrowing in the direction of foreset dip and occasional small thrusts, and (3) patches of vaguely laminated or apparently structureless sediment (W.J. Miller, 1922; Bigarella et al., 1969; Glennie, 1970; McKee et al., 1971; McKee and Bigarella, 1972; Gradzinski and Jerzykiewicz, 1974; Barrett and Kohn, 1975; Borowka, 1979). McKee et al. (1971) were able, partly experimentally, to relate these structures to the modes of gravitationally induced failure of sand accumulating to lee of dunes, the moisture content and history of wetting and drying of the sand proving to be an important control. Sand that was damp with rain or dew, or which had recently been dried out, tended to fail in a brittle manner. The superficial layer became faulted or broken up into large slabs or a jumble of blocks that moved some way downslope, occasionally producing drag folds in laminae over which it passed. Wet crusts, however, tended to fail by folding. Ahlbrandt and Andrews ( 1978) have described from cold-climate aeolian dunes a type of deformation that results from the melting of snow interbedded with the foresets of sand. An interesting parallel from an aquatic environment is afforded by the deformed cross-bedding found by Harms et al. ( 1 963) within a dune on a river point bar. The extent of deformation increases upward and downcurrent in the cross-bedding set within the dune. The deformation upcurrent takes the form of small disharmonic folds of a wide range of attitude, associated with thickened and disturbed laminae. Shear discontinuities become increasingly important amongst the folds as the set is traced downcurrent. Fluid drag is rejected as a cause of deformation, and it is suggested instead that downslope mass-movement occurred following a rise of porewater pressure within the dune, consequent on a fall of river stage in the presence of a silty drape over the bed. Dalrymple (1979) has described from intertidal dunes in the Bay of Fundy a type of deformed cross-bedding that he is able convincingly to ascribe to the flow and slumping of the loosely packed sand, after it had become liquefied as the result of the breaking of waves against the bedforms as they emerged during the tidal ebb. The volumes of sand involved are small and localized. The deformation increases in extent upward within each affected set, varying in form from gentle flexures to sharp, diaper-like anticlines

386

ranged between rounded basin-shaped folds resembling those in pseudonodules. Faults are lacking in this type of deformation. In some cases nominally of the third kind of Allen and Banks (1972), the deformation has great lateral extent and is metadepositional with respect to sets, though occasionally involving more than one bed. These cases include the elaborate folds accompanied by faulting and sometimes brecciation described by Knight (1929) and Steidtmann (1974) from the Casper Sandstone, by Rice (1939a, 1939b) from Triassic sandstones, by Peacock (1966) from the Hopeman Sandstone, and by Kiersch (1950), Sanderson (1974), Freeman and Visher (1975), and Doe and Dott (1980) from the Navajo Sandstone. With the exception of the Triassic sandstones, these rocks are almost certainly aeolian, though Visher ( 1971) argues, unconvincingly, for the shallow-marine origin of the Navajo Sandstone. Few firm explanations have been offered for the deformations described. Knight proposed downslope mass-movement into the troughs between dunes to explain folding in the Casper Sandstone. Rice proposed the collapse under their own weight of underwater sand bodies as the cause of, the Triassic structures. Sanderson contended that the Navajo dunes, though emplaced by wind, were watersaturated at the time of deformation. Peacock suggested a choice between the downslope movement of partly moist and partly dry sand, undercutting at the foot of the dune slope, and the action of earth tremors. As regards the sandstones they studied, Doe and Dott concluded that “contortion of the sand took place below a water table”, and that failure might have been triggered by “slight changes in the physical setting, such as saturation of the dunes or changes in the level of the groundwater table.” Some of these explanations are easily rejected, for they do not satisfactorily explain the substantial lateral extent of the structures.

DEFORMED CROSS-BEDDING RELATED TO FLUID DRAG

Description The other two kinds of deformed cross-bedding recognized by Allen and Banks (1972) are metadepositional with respect to sets, restricted to single sets, and of a comparatively simple shape. In one kind, the simplest of all, the cross-strata are overturned to form a recumbent fold, in some instances with smaller, disharmonic folds in the hinge zone. Cross-strata in the second kind are shaped into small folds increasing in amplitude upward within the set, without gross oversteepening in the upper part. Figure 9-27a is representative of the simplest kind of deformed crossbedding. Similar examples come from many formations to which a fluviatile origin is attributable (McKee, 1938; Botvinkina et al., 1954; Fuller, 1955; Robson, 1956; Potter and Glass, 1958; Fahrig, 1961; G.P. Jones, 1961, 1962;

387

Fig. 9-27. Deformed cross-bedding. a. Simple recumbent fold, Floral Formation (Pleistocene), Saskatoon, Saskatchewan, Canada. Photograph courtesy of H. E. Hendry. b. Complex folds, Upper Old Red Sandstone, Hook Head, southeast Ireland.

388

J.H. Stewart, 1961; McKee, 1962; Selley et al., 1963; Mountain, 1964; Tobisch, 1965; Beuf et al., 1966, 1971; Simon and Hopkins, 1966; Rust, 1968; Burollet et al., 1969; J.M. Coleman, 1969; McCormick and Picard, 1969; Selley, 1969, 1972; Banks et al., 1971; Smits, 1971; Allen and Banks, 1972; De Vries, 1973; Hobday, 1974; Hendry and Stauffer, 1975, 1977; Edwards, 1976; Haczewski, 1976; Martinez, 1977; Long, 1978). A few cases are known from rocks for which a lacustrine, deltaic or marine origin is argued (Tobisch, 1965; Gavelin and Russell, 1967; T.E. Smith, 1967; Singh, 1969; Picard and High, 1970; Gietelink, 1973; Anderton, 1976). As seen in vertical profile parallel with the palaeocurrent direction, the folds are simple, unfaulted, similar, flat-lying structures with weakly to moderately curved hinges and an upcurrent facing. Each is confined to a single cross-bedding set and is truncated upward by the undeformed erosion surface beneath the set above. Folds persist laterally for distances in the order of 10-20 set thicknesses, decaying upcurrent and downcurrent by increase in the height of the hinge above the set base and, consequently, loss of the upper limb. Hinges generally lie in the upper half of the set, but occasionally reach down to the base itself (Hendry and Stauffer, 1977). Fold axes lie on average perpendicular to the dip-azimuth of undisturbed foresets and are curved in deformed trough cross-bedded sands. Lamination remains distinct, except in the downstream parts of the more extended upper limbs. Rarely, small disharmonic folds ornament the hinge zones of the recumbent structures (Robson, 1956; Tobisch, 1965; Dott, 1966a; Beuf et al., 1971; Gietelink, 1973; Mrakovich and Cougan, 1974; Hendry and Stauffer, 1975; Haczewski, 1976). Like the larger folds, these small flexures have axial surfaces that depart but little from parallelism with the set base. Hence they resemble buckles produced when layers of differing competence are folded together (Ramberg, 1964). There is no gross oversteepening of foresets in the second kind of deformed cross-bedding. At their simplest (Fig. 9-28a), examples of this

Fig. 9-28. Deformed cross-bedding. a. Bima Sandstone (Cretaceous), Nigeria (after G.P. Jones, 1961). b. Excavation into point-bar sands of Mississippi River, Old River Locksite, Mississippi, U S A . (after Frazier and Osanik, 1961).

389

structure reveal either a single downstream-facing warp or a pair of folds, one above the other, the axial surfaces ranging in inclination from moderately upcurrent to mildly downstream (Broadhust, 1954; G.P. Jones, 1961, 1962; Mountain, 1964; Friend, 1965; Tobisch, 1965; Dott, 1966a; Gradzinski, 1970). Jones, Mountain, Friend and Gradzinski each observed a lateral passage between undistorted cross-strata and these simple folds, whereas Dott found a transition into the overturned cross-bedding first described. At the other extreme (Figs. 9-27b, 9-28b) are foresets thrown into numerous small folds, mostly with horizontal to upstream-dipping axial surfaces and hinges of small to moderate curvature (Rice, 1939b; Frazier and Osanik, 1961; Selley et al., 1963; Allen, 1964; Friend, 1965; Greensmith, 1965; Nilsen, 1965; Simon and Hopkins, 1966; Anderton, 1976; Button, 1976; Martinez, 1977; Young and Long, 1977; Hobday and Von Bruun, 1979; Miall, 1979). Both the simple and complex folds, together with forms of intermediate character, can often be found in one and the same bed (e.g. Friend, 1965). In one of Rice's (1939b) beds there was a lateral passage from complex folds into simple overturned foresets. Interpretation of simple deformed cross-bedding

Regarding deformation like that in Fig. 9-27a, three issues must be settled: (1) the pattern of translation of the elements on a cross-stratum during deformation, (2) the nature of the sediment when deformed, and (3) the nature and origin of the deforming force. In view of the shape and unfaulted nature of the folds, it is intuitively satisfying to begin by supposing that deformation was by simple shearing, whence elements experienced only horizontal translation. There could have been small downward vertical displacements if the bed had been liquidized prior to deformation, but these are very small compared with the horizontal ones, and so may he safelv neglected. As has been shown (Allen and Banks, 1972; Hendry and Stauffer, 1975, 1977), the shape of a deformed cross-stratum depends on its original form and on the pattern of translation of its included elements during deformation. Hendry and Stauffer go some way toward explaining these influences, and Fig. 9-29 was suggested by a diagram of theirs. The graphs on the right show various patterns for the total horizontal displacement, X , of an element as a function of height y above a datum. Figure 9-29a shows the change in vertical cross-sectional form parallel with the maximum dip-direction of three cross-strata, A, B, and C, under the influence of a pattern of displacements increasing linearly with height. Note that the zero displacement occurs some distance above the base of the set. Consequently, each of the final shapes, A', B', and C', bears a cusp, with B' and C' also having a hinge of large curvature near the set top. Displacement in Fig. 9-29b varies as the square-root of height above the set base. Cusps are lacking, but the folds face

390

Base of cross-bedded layer

cross-bedded layer

0

0 Base of cross-bedded layer

/Bare

of cross-bedded

layer I

Fig. 9-29. Vertical sections parallel with current illustrating patterns of deformed crossbedding, as a function of initial foreset shape and displacement function. The graphs on the right show several forms of displacement function for an element in a liquidized sand deformed by a current flowing overhead. The curves A, B, and C are foresets of contrasted shape, and the curves A , B’ and C’ the foresets after deformation according to the displacement function. Note that the form of A , B’ and C’ depends additively on the displacement curve and the initial shape.

downcurrent, instead of upcurrent, and parasitic folds can be developed. Upcurrent-facing folds, with limbs of substantial equality, together with hinges of small to moderate curvature, can arise for sufficiently large translations when total displacement varies as the square of height (Fig. 9-29c, d). A square law is also assumed in Fig. 9-29e, but the origin lies within a second, lower cross-bedding set. Essentially unitary folds arise, although the cross-strata of two sets are involved. In accordance with the supposition of simple shearing, all fold limbs are thinned and hinge zones thickened in Fig. 9-29. The folds are therefore similar. What general form of displacement law is implied by real cases of simple deformed cross-bedding? Patterns of displacement close to the linear and square-root forms are ruled out, for neither yield realistic shapes and cusps are unreported. Realistic shapes (see Fig. 9-27) are, however, given by

39 1

patterns comparing with a square law (Fig. 9-29d). Accepting that real cases never agree precisely with idealized theory- indeed, precise agreement is never expected- Hendry and Stauffer (1975) offer no physical argument for their startling claim that there is no unique or even modal displacement profile operative during the formation of simple deformed cross-bedding. The contrary seems instead to be true, for folds resembling those in Figs. 9-27a and 9-29d are so plentiful as virtually to exclude all other shapes. Where does the level of zero displacement lie during deformation? Since fold patterns similar to Fig. 9-29e are unknown, it must lie either within or above the set base. Most authors discussing simple deformed cross-bedding accept that the sediment was water-saturated at the time of deformation (e.g. Robson, 1956), though not necessarily fully submerged, and some regard it as also liquidized (e.g. J.H. Stewart, 1961; Selley, 1969, 1972; Selley et al., 1963; Allen and Banks, 1972). That the sand was liquidized is strongly urged by the smooth and unfaulted fold shapes and often greatly extended upper limbs. A liquid-like state is further supported by the smoothly flowing folds that arise when quicksands are deformed in the laboratory (Selley and Shearman, 1962; Selley, 1969). Hendry and Stauffer (1975), however, suggest that the sand was not liquidized when deformed. If this were true, shear discontinuities and other faults should be evident, representing internal slip. Such discontinuities in plenty, together with hinges often of almost knife-edge curvature, mark the deformed cross-bedding produced experimentally by McKee et al. (1962a, 1962b), but by such drastic and unrealistic expedients as dragging heavy bags over a sand delta, bulldozing it to a substantial depth, or squirting a powerful water jet at the sand. It is unlikely during such rapid and intense stressing that the sand could ever liquefy other than locally. The character of most simple deformed cross-bedding suggests instead the gradual application of quite small stresses. There are two views on the deforming force. Many authors attribute the folding to gravitationally induced downslope slip (McKee, 1938; Rice, 1939b; Fuller, 1955; G.P. Jones, 1961, 1962; Dott, 1966a; McCormick and Picard, 1969; Smits, 1971), but this explanation is discounted by the attitude, shape and lateral extent of the folds. Others claim that folding resulted from fluid drag on the upper surface of the cross-bedded sand body (Robson, 1956; J.H. Stewart, 1961; McKee et al., 1962a, 1962b; Rust, 1968; J.M. Coleman, 1969; Allen and Banks, 1972; Hendry and Stauffer, 1975; Anderton, 1976). The lateral persistence, similar form, upstream facing, and recumbent nature of the folds comply with this explanation, but there is some difference of opinion as to the nature of the fluid involved. Robson (1956) referred to the action of sand-laden waters, and Allen and Banks (1972) simply to currents, without specifying whether and under which transport-mode there was sediment present. Others saw the fluid as a dense slurry differing but little in bulk density from the cross-strata it deformed

392

(McKee et al., 1962a, 1962b; Rust, 1968; Hendry and Stauffer, 1975). Except for Rust, who believed he had found the deposits of these slurries, the suggestion appears to be made on the grounds that only such dense and frictional materials could produce sufficient drag. It seems unnecessary to look for special circumstances in order to have deformed cross-bedding. Allen and Banks ( 1972) developed a theoretical model showing that overfolds could result from the drag of ordinary river and tidal currents, provided that the sand was liquidized. The ultimate shape of a deformed cross-stratum was found to depend on the interaction of: (1) the initial form, (2) the upward rise within the dispersion of the shock bounding the layer of resettled grains, and (3) the time-dependent velocity profile generated within the dispersion by the drag. Assuming that liquidization occurred instantaneously throughout the whole of a cross-bedding set, that the dispersion was uniform in all respects, and that the instantaneous velocity profile was of linear form throughout the period of sedimentation, Allen and Banks calculated the horizontal displacement X , of an element of height y above the base of the bed as: (9.4)

where T is the applied stress, qdispis the effective viscosity of the liquidized sediment, W is the grain free falling velocity in the dispersion, and C, and C , are the fractional volume grain concentrations in the dispersion and deposit, respectively. Choosing a linear form for the original cross-stratum, the fold shape is given by:

for 0 < y < H , where x is distance measured horizontally from the upper end of the original cross-stratum, x,, is the maximum horizontal displacement, y , is the height of the fold hinge, and H is the observed bed thickness. Equation (9.4) is the square law that seems to approximate to the displacement function implied by most cases of simple deformed cross-strata, and eq. (9.5) for 0 < y < H is a portion of a parabola. Interpretation of more complex forms Far too little progress has been made with these, but the geometry (Fig. 9-28) suggests buckling as an adjustment to partly if not predominantly vertical loads. The structures could well result from the flattening, like blobs of stiff paint, of submerged sand dunes or bars on being liquidized, perhaps by earthquake shocks. That the sand was liquid-like is suggested by the commonly observed upward increase in fold amplitude, consistent with the

393

restrictive rise of a shock between a rigidified deposit and a still deformable dispersion (Allen and Banks, 1972). Dalrymple’s (1979) mechanism could be significant in shallow-marine and intertidal environments.

SUMMARY

Soft-sediment deformations arise when liquidized, hydroplastic, and sometimes more competent sediments are stressed during or shortly after deposition. The time-scale of deformation of structures involving liquidized sands is determined by the time necessary for the dispersed grains to resettle, and is commonly in the order of 10- 100 s. Many soft-sediment deformation structures are related to the presence of a gravitationally unstable profile of bulk density within a sedimentation unit or sequence of units, for example, convolute lamination, load casts, pseudo-nodules, ball-and-pillow, heavy mineral sags and drops, and dish structures. The soft-sediment deformations related to the development of non-uniform confining loads are load-casted ripples and folds developed ahead of sand bodies spreading over mud. Slump sheets and some varieties of deformed cross-bedding are an important class attributable to the action of gravitationally induced downslope shear stresses. Slump sheets arise in a variety of environments but are particularly prevalent on the flanks of deep-water basins. Cross-bedding also becomes deformed through the action of fluid drag on liquidized sand. These deformations are widespread, particularly in fluviatile deposits, and the simplest are of interest because they can be modelled theoretically.

This Page Intentionally Left Blank

395

Chapter I0 STRUCTURES AND SEQUENCES RELATED TO GRAVITY-CURRENT SURGES

INTRODUCTION

Of the many kinds of natural gravity-current surge discussed in Vol. I, Chapter 1, those whose density-excess stems from internally dispersed sediment are of most sedimentological interest, that is, turbidity currents and the surges of pyroclastic debris associated with volcanic eruptions. These flows are dissipative, losing speed for various reasons, but are only mildly so and are therefore highly mobile. Turbidity currents transport coarse debris over the ocean floor certainly for hundreds of kilometres, and movements of tens of kilometres in smaller basins and lakes are easily achieved. Eruptions yield less mobile flows- the density difference between debris and enveloping gas is greater-but transport paths measuring tens of kilometres in length are common, and travel over a hundred or so kilometres is occasionally recorded. The concept of turbidity currents as agents for sediment erosion and transport in watery environments stems from the early work of Daly (1936), Kuenen (1937), Bell (1942) and Knapp (1943), in which an important place was given, partly with experimental support, to the turbidity-current origin of the then recently discovered oceanic submarine canyons. The idea became widely accepted, however, only with the brilliant field and experimental work of Kuenen ( 1950, 1951a, 1951b, 1965a, 1966b), Kuenen and Migliorini (1950), Natland and Kuenen (1951), Kuenen and Menard (1952), and Kuenen and Carozzi (1953), and with the theoretical studies Menard and Ludwick (1951). Turbidity currents were revealed as a plausible mechanism for the emplacement beneath deep water of sheet-like sands with shallowwater characteristics. The case grew stronger with the discovery that earthquakes and river floods could trigger the orderly sequential breaking of submarine telegraph cables crossing the continental margin, evidently in response to the downslope movement of some huge and enormously powerful current or mass-movement (Kuenen, 1952; Heezen and Ewing, 1952, 1955; Heezen et al., 1954, 1966a; Heezen, 1956; Houtz and Wellman, 1962; Krause et al., 1970). The surges associated with volcanoes are related to particular eruptive modes (P.J. Francis, 1976; MacDonald, 1972). In a Plinian eruption gases and fragmented magma.are forced through the vent of the volcano to form a vertical eruption column towering upward for many kilometres. Collapse of the column on to the flanks of the volcano creates a radially spreading surge that may surmount substantial obstacles and travel outward for many tens of

396

kilometres over level ground before halting (Sparks and Wilson, 1976; Sparks et al., 1978). Sparks and Walker (1973) propose that these surges, which they call pyroclastic flows, are relatively dense, with the incandescent debris largely in a fluidized state. Somewhat similar is the eruption style of the phreatic or phreatomagmatic maar volcanoes (J.G. Moore, 1967; Waters and Fisher, 1970; Ollier, 1974), in which the explosive combination of magma with water or water-saturated deposits creates an eruption column of fragmentary material, volcanic gases, and water droplets. From the base of the column during the early stages of eruption there emerges a rapidly spreading and ground-hugging ring-shaped debris cloud called a base surge. Column collapse may feed the base surge or, if sufficiently delayed, create a second surge. Base surges are moist, cool and probably more dilute than pyroclastic flows. A similar but hot surge apparently contributes to nukes ardentes. These result from Peleean eruptions, during which the explosive breaching of a lava dome on the flanks of a volcano creates a mass of incandescent debris partly buoyed up by exsolved gases. This mixture is capable of extraordinarily rapid and forceful downward travel. Sparks and Walker (1973) suggest that a typical nuke .ardente has two components, a relatively dense basal part resembling a pyroclastic flow, surmounted by a less dense but ground-hugging cloud, their ground surge. Only the surge, they claim, can over-ride topographic barriers. The role of pyroclastic flows and nukes ardentes in the transport and emplacement of pyroclastic material has been grasped since the early observations of such as Anderson and Flett (1903), Perret (1924, 1935), and Fenner ( 1923). Several reviews have since been forthcoming (Peterson, 1970; Ross and Smith, 1961; R.L. Smith, 1960, 1963). Recognition of the importance of base surges is more recent, dating from the 1965 eruption of Taal Volcano, Philippine Islands (Moore et al., 1966; J.G. Moore, 1967), and has received some stimulus from work on atomic weapons, which also create these surges (Shurcliff, 1947; Hirschfelder et al., 1950; Penny and Thornhill, 1951; Martin and Moyse, 1952a, 1952b; E. Swift, 1962; G.A. Young, 1965). Subsequent work has shown that both turbidity currents and volcanic surges emplace thin but extremely extensive debris sheets that in many instances reveal systematic lateral as well as vertical changes in texture and sedimentary structures. These patterns are reviewed here; they are potentially a guide to the character of flows which for various reasons can never be completely observed directly in nature.

DISSIPATION OF GRAVITY-CURRENT SURGES

Debris sheets form beneath turbidity currents and volcanic surges primarily because these flows are dissipative, that is, their velocity .and sediment load decline with increasing distance from source, Equations ( 1.6 1) and

397

(1.63) in Vol. I, respectively for the steady head and uniform body of a gravity current, disclose four possible causes of dissipation: (1) density reduction through sediment loss or engulfment of ambient medium, (2) reduction in flow thickness, related to flow stretching or collapse, (3) friction at the base and upper surface of the flow, partly involving density reduction due to mixing between flow and medium, and (4) reduction in bed slope. To these we may add encounters with currents having an opposite component of flow, and descent into an ambient medium of downward increasing density, for example, a stratified ocean. The first three causes are intrinsic, and their consideration reveals something of the reason for the great mobility, that is, the mild dissipativeness of gravity currents. The remainder are extrinsic, with obvious effects, and will not be examined further. Continuing deposition has two effects on a real gravity-current surge holding grains of a range of falling velocities. Firstly, since grains of large falling velocity are likely to settle out earliest, a progressive reduction in the overall density of the current must result, leading to a reduced density difference with the ambient medium and a consequent decline in forward velocity. Secondly, a progressive reduction in effective flow thickness may be expected, since the particles as a whole will tend to settle toward the bed. Some quantitative estimation of these effects is possible using very simple models. At its simplest, a sediment-driven gravity current is a fluid slab of uniform thickness through which grains of a single falling velocity are uniformly dispersed (Fig. 10-1). If U is the instantaneous forward velocity of the current, and W is the falling velocity of the dispersed grains, then for small bed slopes Wis the rate at which the current loses thickness as the top and centre of gravity of the initial dispersion descend relative to the base of the flow. The quotient W / U is a relative measure of the instantaneous current dissipation rate due to grain settling. Accepting that values of U = 10 m s and W = 0.01 m s - ' are characteristic of, for example, natural turbidity currents, W / U is evidently a very small quantity, indicating that flowthinning due to sediment loss is only mildly dissipative. The inverse quantity,

'

Fig. 10-1. Definition diagram for a sediment-driven gravity current considered as a moving slab composed of a uniform particle dispersion.

398

U / W , where U is now taken to be characteristic of the flow over its whole path, is readily found to equal a representative flow path-length divided by the initial height of the slab, of order lo3 given the previously assumed values. Our quotient U / W is a mobility number which, multiplied by the initial flow thickness, denotes the order of magnitude of the path length. Given an initial thickness of 100 m, travel of order 100 km should be achievable by a flow characterized by U = 10 m s I and W = 0.01 m s - I . If particles of more than one falling velocity are present, however, dissipation yill result from a density change as well as flow-thinning. If AW is the maximum difference in the settling velocities, then AW/U is a measure of the dissipation rate due to differential settling. Implicit here is the assumption that the hydraulic forces due to the motion of the slab are at all times inadequate to sustain in total the load represented by the dispersed grains. In order to apply our criteria, therefore, we must explore a condition for the self-sustainment or “auto-suspension” of the current (Knapp, 1938; Bagnold, 1962; Middleton, 1966a; Pantin, 1979; Southard and Mackintosh, 1981). For if the hydraulic forces can sustain the load then there will be no deposition and no dissipation due to this cause. The required condition in our simple model may be written as the quotient m,/mth, where ma is the actual grain load in the slab, in dry mass per unit bed area, and mth is the load which can theoretically be maintained stationary relative to the bed by the forces arising from the motion (Fig. 10-1). Since we assume a uniform grain dispersion: ~

(10;l) where pi and p2 are respectively the density of the intergranular fluid (not necessarily equal to the density of the ambient medium, p , ) and the current, u is the density of the grains, and h is the slab thickness. Noting that the sediment transport rate is the product of the grain load and transportvelocity, we can write mthusing Bagnold’s (1966) theory (Vol. I, eq. 2.38) as: mth-

e.uw -s- --

W ( u - p i )g

(10.2)

on the supposition that the transport velocity equals the velocity of the slab, and that only suspension transport is involved. Here e , is Bagnold’s suspension efficiency factor, w is flow power, and g is the acceleration due to gravity. Writing the flow power using the quadratic resistance law, Vol. I, eq. (1.19), and Vol. I, eq. (1.63) for the uniform flow of the body of a gravity current, and dividing eq. (10.2) into eq. (lO.l), the condition becomes: (10.3)

399

in which fo is the Darcy-Weisbach friction coefficient for the bed, f the total friction coefficient, and S the slope. Only when ma/m,h < 1 is the dispersed sediment fully supported by the forces due to motion; otherwise a fraction of the total load is free to settle toward the bed. Equation (10.3) shows that rna/rn,, increases with increasing W, but decreases with flow thickness, density difference ( p , = pi), and bed slope, each to the power minus one-half. Self-sustainment is therefore favoured by a small grain falling velocity, and by a large density difference, flow thickness, and bed slope. For a turbidity current of h = 100 m, pz = 1100 kg mP3, W = 0.01 m s - ' , f o = 0.04, f = 0.06, and S = 0.01, we find that rn,/rn,, = 8.6, whence self-sustainment is far from being attained and dissipation through sediment loss will occur. Further calculations with eq. (10.3) suggest that self-sustainment is rare, and restricted to thick turbidity currents composed of light particles on steep slopes. Self-sustainment seems even less likely in the case of pyroclastic flows and base surges, in which particle falling velocities are generally large (Sparks et al., 1978). However, grain self-fluidization (Chapter 8) should contribute toward self-sustainment in pyroclastic flows. The lobes and clefts on the head of a gravity-current surge (Simpson, 1969, 1972) express a viscosity-related gravitational instability effect and the continuous engulfment of ambient medium by the current (Allen, 1971b). Here is another cause of dissipation, assuming that the engulfed fluid mixes at least partially with the flow. Now the problem of calculating this dissipation rate is similar to that of the bulk self-fluidization of a cold avalanche (Fig. 8-13). Using the earlier analysis, it is readily shown that the overall rate at which trapped fluid mixes upward is given by V = hsU/L, where V is the rate and L is the streamwise length of the mixing zone. Introducing U to form a quantity analogous to the previous W / U , the dissipation rate becomes h s / L . Little is known of mixing at the heads of surges, but hs is probably of order 0.01 H , where H is the head height, whereas L is of order 2- 3 H , whence h / L becomes of the general order 0.0 1- 0.00 1. Dissipation due to this cause is therefore more effective than that related to sediment loss, but as the effect is exerted over only a short length of the current, the final influence is weak. Mixing between flow and ambient medium also occurs along the upper surface of the body of a surge. The process is like the mixing experienced in jets and wakes, and is described using the velocity, measured normal to the mixing layer, with which the medium is entrained into the current. Michon et al. (1955) and Ellison and Turner (1959, 1960a, 1960b) concluded that the mixing rate depended only on the densiometric Froude number, the rate increasing with that number, whereas Lofquist (1960) and Macagno and Rouse (1962) found that the Reynolds number was also influential, the rate decreasing with this parameter. Bata (1959) and Bonnefille and Goddet (1959) detected a Reynolds number dependence. Putting V as the entrain-

400

ment velocity and U as the flow speed, V / U appears to be a very small quantity for real surges, of very large Reynolds number. Available experimental data suggest that, at the critical densiometric Froude number, values of l o p 3 or l o p 4 are unlikely to be exceeded. Mixing along the upper surface of the body of the current is probably a much less effective cause of dissipation than sediment loss. Dissipation also results from friction between the current and its bed. The effect is weak, as the total resistance coefficient is not much larger than that for the interface (Middleton, 1966c; Tesaker, 1969a, 1969b; Kersey and Hsu, 1976). Mixing accompanying the growth of Kelvin-Helmholtz instability waves (billows) on the top of the head (Simpson, 1969, 1972; Britter and Simpson, 1978; Simpson and Britter, 1979, 1980) may be a particularly important mechanism of dissipation. It implies the consumption of the body of a gravity current by the slower-moving head and the gradual transformation of the relatively dense original flow into a much more voluminous, dilute and sluggish form. Simpson and Britter’s laboratory experiments seem to suggest that, at large relative depths, the body of the current travels about 16% faster than the head. A turbidity current 10 km long where it emerged from the end of its channelized path, and with a characteristic head velocity of 8 m s-I, would therefore consume itself within a further distance of the order of 60 km. This seems a rather short distance, in the light of field studies of the distribution of individual turbidites, but it must be admitted that we know very little about the lengths and speeds of the prototype. Of the mechanisms discussed above, loss of sediment and mixing at the top of the head place the strongest restrictions on the mobility of gravitycurrent surges. These flows nonetheless are still only mildly dissipative, and would appear able to travel over distances in the order of 102-104 times their thickness. Since the thickness of the flow is likely to exceed the thickness characteristic of its own deposit to a similar degree, the horizontal scale on which sedimentary features change in surge deposits is likely to be many orders of magnitude more than the vertical scale. That this estimate is correct is suggested by laboratory experiments on sediment-driven gravity current surges. Kuenen and Migliorini (1950), Middleton (1967a), and Love11 (1971) produced flows that travelled over paths in the order of 102-103 times the deposit thickness. As is to be expected from the above, an increase in the falling velocity of the dispersed sediment reduces the mobility of the current (e.g. Riddell, 1969), and therefore diminishes the horizontal relative to the vertical scale of the resulting deposit. However, the thickness remains very small compared to the lateral extent.

40 1

TURBIDITES AND THE BOUh4A SEQUENCE

Vertical patterns

That the deposits nowadays attributed to turbidity currents (turbidites) present a characteristic vertical sequence of sedimentary features, more or less repeated from one bed to another, was first clearly appreciated by Sheldon (1928, 1929) in her study of the Portage (Devonian) rocks of New York State. Of these she wrote (1928, p. 243, 248) that: “Most of the beds are alternating shales and sandstones. As a rule the variations are systematic and appear to be due to fluctuations in the effective strength of the transporting waters. The sandstone beds begin abruptly and are rather massive at the bottom.. . Above comes shale, then the series begins again with the massive sandstone resting directly on the top of the shale.. . Thus it appears that the sandstone beds were formed as units and that the deposition of each passed through a regular succession of stages. Not all of the stages are present in every bed but the full series consists of massive sandstone at the base grading into flat sedimentation surfaces followed by minute cross bedding and ordinary ripple marks.. . It is probable that these stages depended upon the velocity of the water, the depth or volume of water and the sediment load.. . The sediment was thoroughly churned at first, then distinguishable channels and flat sedimentation surfaces developed and finally the current diminished enough so that ripples were formed.. . The tops of the beds levelled off as the currents diminished further.” Although she ultimately attributed the Portage rocks to shallow-water conditions, and to seasonal or periodic changes, whereas Kuenen (1956) and Walker and Sutton ( 1967) clearly demonstrated their turbidity-current origin in relatively deep water, this statement is a remarkable anticipation of later findings. It was lost to sight for more than thirty years. Kuenen’s vigorous championship of turbidity currents introduced a period of intense study of turbidites in the stratigraphic record. Although many descriptions of turbidite sedimentary structures resulted, few workers recognized that these structures tended to occur in a definite sequence, repeated from bed to bed. Ksiazkiewicz (1954) found that in the Carpathian flysch cross-lamination was usually restricted to the tops of sandstones. Ten Haaf (1959) epitomized the turbidites of the northern Appennines by means of an idealized upward sequence, as follows: (1) normally graded sediment resting on an eroded surface, (2) deposits with “foresets” and ripples which may in time experience soft-sediment folding, and (3) laminated mud. An important idealization based on field data was given by Bassett and Walton (1960) for the Hell’s Mouth Grits, a series of thick turbidites preserved close to source. Their model turbidite showed in upward sequence: (1) a thick normally graded part with no other internal structures, (2) a usually laminated, commonly cross-laminated and occasionally convoluted zone, and (3) silt-

402

stones grading up into mudstones. A parallel interest in deep-sea sands led Nesteroff (1961) to propose from work on abyssal plains in the Atlantic Ocean, Mediterranean Sea, and Gulf of Mexico an ideal sequence consisting of (1) normally graded sand, (2) fine sand and silt showing parallel lamination overlain by cross-lamination succeeded by horizontal lamination, and (3) mud (see Von Rad, 1968, for further examples). Hundreds of cores revealed to Nesteroff that the representation of this sequence was often incomplete, chiefly by the progressive loss of its lower members. Bouma (1962) was the first to grasp that the turbidite sequences separately and often incompletely described by large numbers of individual workers, each concerned with one particular sedimentary basin, were in fact substantially the same, and that a single idealized sequence could be used to represent turbidite formations. This important generalization- now called the Bouma sequence- followed from his detailed comparative study of turbidites chiefly in the French and Swiss Alps and the Appennines. His sequence (Fig. 10-2a) has five intervals, renamed divisions by Walker (1965), as follows: (A) graded division showing a more or less distinct normal

I

Harms 8 Fohnestock (1965) Walker (1965. 1967b)

Dlvlsion

E Pelite

D Porollel lominotion

Lower flow regime. Plone bed. no movement.

Stream power less than order 0.01 W m-2.

Lower flow reglme. Riooie bed.

Stream power iess thon order 0.5 W m-2.

C

I

A Normal groding

I I

(1968h, 1969c)

Stream power less thon order 0.01 W m-2,

Current rioole lominotion

B

Ilen

Lower flow regime. Plone bed. no movement.

Upper flow regime. Plone bed with groin movement. Upper flow regime. Antidunes

I

Division

I

I

E

I

Pelite

I I

Stream power order 0.5-5 W m-2. Stream power greoter thon order 5Wm-2.

Interoretotion Stream power less thon order 0.01 W m-2.

I I

I

I

Streom power less thon Stream power less than Stream power order I W m - 2 ,

B2 Porollel lomination (lower staoe)

I

CI Dunes

BI Porollel lamination (upper stage)

A Normol grading

1

'

Stream pow?. order 0 . 2 - 5 W m-2.

I

Stream power order 0.5 5 W m-2.

-

Streom power greater thon order 5 Wnr2.

Fig. 10-2. Ideal vertical sequences of grain size and sedimentary structure in turbidites. a. According to Bouma (1962), with later interpretations. b. In relatively coarse-grained clastic or bioclastic turbidites.

403

textural grading but no other internal structures, (B) lower division of parallel lamination in which grading may still be discernible, (C) division of current ripple lamination, usually in silt or very fine sand, (D) upper division of parallel lamination, invisible in weathered or strongly folded rocks, consisting of sandy and muddy laminae, and (E) pelitic (mud) division. Like Nesteroff ( 196l), whose conclusions were reached independently, Bouma found that many turbidites presented an incomplete sequence, composed of only some of the divisions listed. These incomplete beds Bouma divided between base cut-out sequences (e.g., B + C + D + E, C + D + E), truncated sequences, commonly due to the downward erosion of an overlying bed (e.g., A + B, A + B + C), and truncated base cut-out sequences (e.g., B + C). Bouma’s generalization is empirically sound and agrees with our understanding of turbidity-current mechanisms. Although widely accepted, it has not passed unmodified, primarily because it refers to terrigenous clastic turbidites. Kuenen (1953a) remarked that cross-bedding, which might be attributed to dunes, was rare in turbidites (implying terrigenous ones), in which kind of sediment Pettijohn (1957) found a significant scarcity of grains of very coarse sand to granule grade. Cross-bedding is restricted to coarse-grained terrigenous turbidite formations and is usually rare (Dzulynski et al., 1959; Unrug, 1963; Marschalko, 1964; Mutti and Sanuy, 1968; Walker, 1970a; Rocheleau and Lajoie, 1974; TassC et al., 1978). A deficiency in these grades is less apparent amongst bioclastic turbidites which, perhaps significantly, show cross-bedding more frequently. Hubert ( 1966a, 1966b) found that about 20% of bioclastic turbidites in the Ordovician Whitehouse Formation of Scotland included a cross-bedded division, in the shape of cross-bedded dune forms, beneath divisions C + D + E. Thompson and Thomasson ( 1969) observed amongst Carboniferous turbidites three examples of the sequence cross-bedding + B + C + D, two cases of a sequence with cross-bedding alone, and one example each of the sequences B + crossbedding and A + cross-bedding + B + C + D. Rocheleau and Lajoie (1974) report similar sequences from a coarse-grained terrigenous turbidites. Hubert (1966b) modified Bouma’s (1962) sequence to include a dune (cross-bedding) division, but made no notational innovations. Combining empirical with theoretical evidence, Allen ( 1970d) proposed the modified ideal turbidite sequence: (A) graded division, recently subdivided by Cas (1979), (B,) lower division of parallel laminations deposited from upper-stage plane beds, (C, ) division of cross-bedding, (B,) intermediate division of parallel laminations deposited from lower-stage plane beds, (C, ) division of cross-lamination, (D) upper division of parallel laminations, and (E) mud division (Fig. 10-2b). This scheme circumvents the grain-size restriction implicit in Bouma’s proposal and takes account of the textural differences in the source materials of terrigenous and bioclastic turbidites. On this scheme, a typical sequence for a terrigenous clastic turbidite would be A B, C, D E, whereas a bioclastic one might show C , + C, + D -, E (e.g. Hubert, 1966b) or C , B, -+

+

+

-+

+

404

C , + D + E (e.g. Thompson and Thomasson, 1969). Division D has proved with experience to be the least satisfactory of Bouma’s (1962) intervals, primarily because it is difficult or impossible to recognize under many common circumstances. Bouma himself recognized the difficulty of separating this division from the overlying division E, and his hesitations have been confirmed by others (e.g. Walker, 1967b, 1978; Scholle, 1971). Divisions D and E are often perforce combined. A visible textural grading normally accompanies Bouma’s structural sequence. Many workers have measured vertical grading in turbidites, including Natland and Kuenen (1951), Radomski (1958), Webby (1959), Nederlof ( 1959), Shiki ( 196l), Parkash and Middleton ( 1970), GonzalezBonorino and Middleton (1976), and Rupke (1976) from the stratigraphic record, Nesteroff (1961) and Shepard and Einsele ( 1962) in recent sediments, and Kuenen and Migliorini (1950), Kuenen and Menard ( 1952), and Middleton (1967a) from laboratory experiments. Scheidegger and Potter (1965), drawing on some of this work, showed that curves (arithmetic scales) of grain size against height above turbidite base took three forms, either concave-up, uniform (rectilinear), or convex-up (Fig. 10-3). These describe varieties of normal grading, though if portions of the concave-up and convex-up graphs are sufficiently steep, it can fairly be claimed that the beds are partly non-graded. Reverse-graded turbidites have since been detected. In the Devonian Punta Negra Formation of western Argentina (GonzalezBonorino and Middleton, 1976), only the thinner turbidites are normally graded, whereas the beds of intermediate thickness show reverse followed by normal grading, and the thickest units may be entirely reverse-graded (Fig. 10-3). These turbidites are anomalous, but Rupke ( 1976) has found reverse grading in another formation. It is well-known that the maximum grain size of turbidites is positively correlated with bed thickness (Potter and Schei+

P

o n

Grain diameter

Grain diameter

Fig. 10-3. Idealized schemes of vertical grading in turbidites.

405

.

(0)

DfSTRlBUTlOtV-GRADING

Grain diorneter

( b ) COARSE-TAU

GRADING

Grain diameter

Fig. 10-4. Varieties of normal grading in turbidites, shown by idealized grain size-frequency curves at a series of levels in the bed.

degger, 1966). Graded layers in which coarseness and thickness are often positively correlated are known from lakes (e.g. Banerjee, 1973a, 1973b; Reineck, 1974a). Attention has since shifted to the character of the size-frequency curve and its variation upward in a turbidite. Experimentally, Middleton (1967a) distinguished two-kinds of (normal) grading in turbidites formed from surges (Fig. 10-4). In distribution grading practically all percentiles in the distribution shift toward the finer grades with increasing height above the turbidite base, affording Scheidegger and Potter’s ( 1965) uniform and concave-up curves. Further experimental examples are the turbidites of Kuenen and Mighorini (1950). In beds with coarse-tail grading, only the coarsest few percent of the sediment shows an upward decrease in grain size, except near the top of the bed, where distribution grading prevails. Measures of central tendency therefore remain fairly constant vertically, to yield convex-up curves in the terms of Scheidegger and Potter (1965). Middleton found that coarse-tail grading characterized turbidites deposited from high-concentration surges, but flows sustained for a short period yield a similar effect (Kuenen and Menard, 1952).

Patterns in the direction of flow Parea (1965) and Walker (1967b) independently published reviews showing that turbidites revealed trends related to distance along the current path, their character at any station being dependent on their proximity to source (proximality). These trends involve inter-related changes in gross lithological

406

composition, sedimentary structures, and grain size. Many turbidite formations reveal a downcurrent reduction in the amount of sandstone relative to shale (e.g. Dean and Anderson, 1967; Lovell, 1969, 1970; Crimes et al., 1974; Picha and Niem, 1974; Slaczka and Unrug, 1976). The reduction is significant, however, only over distances in the order of tens of kilometres, supporting the preceding suggestion that individual turbidity currents are highly mobile and likely to deposit beds orders of magnitude longer than thick. A downcurrent reduction in the relative amount of sandstone is not universal, for K.M. Scott (1966) reports a case of an increase away from source. This evidence suggests that, in some basins, individual turbidites may at first thicken to a maximum and then thin along the current path (Meischner, 1964; Engel, 1970, 1974). The more usually observed fall in sandstone content is consistent either with a gradual reduction with increasing distance in turbidite thickness and/or with the presence of many sandstones that do not reach far from source. More important from the present standpoint are the strong correlations between turbidite thickness, coarseness, and internal sequence. In his comparative study, Bouma ( 1962) showed quantitatively that the thicker turbidites, which we have seen are the coarser grained, were more complete as regards structural sequence than the thinner ones, which tended to begin with divisions B or C rather than with A. This observation has been widely repeated (Hubert, 1967; Walker, 1967a; Ricci-Lucchi, 1969b, 1969c; Tanaka, 1970; Crimes, 1973; Crimes et al., 1974). Unrug (1963) in the Istebna Beds of the Polish Carpathians could tentatively relate the kinds of vertical sequence present to proximality. He found divisions B and C to grow in relative importance downcurrent at the expense of division A. Walker (1967b) introduced the important idea that the proximality of turbidite formations can be measured by calculating for a group of beds at a time the relative abundance of sequences that begin with division A, B or C respectively. He introduced a simple proximality index, defined as: ABC-index = A

+f B

where A and B are the percentages of beds in each group that begin with divisions A and B respectively. Walker regarded this index as unsatisfactory for turbidite formations with many sandstones, usually thin, that lacked Bouma’s middle divisions. He therefore proposed a second index, defined as: Modified ABC-index = (A- [A + El)

+f B

in which A + E is the percentage of beds 0.03 m or less in thickness with perfect gradation from division A directly into division E. Figure 10-5 is Walker’s (1967b) analysis of 3352 turbidite sandstones taken 25 beds at a time from seven long sections in five formations of different ages and settings. The median curve indicates a decreasing value for the ABC-index. Groups with large index values disclose a high proportion of

407

C

50 %

B

Fig. 10-5. The ABC-index for 3352 turbidite sandstones, considered in natural sequences of 25 beds at a time, from five formations at seven sites in various parts of the U.S.A. Data of R.G. Walker (1967b).

beds starting with either division A or division B, and therefore cluster close to the A apex or to the AB edge. Correspondingly, groups that cluster near the C apex involve turbidites that start mainly with division C and have small values of the index. Figure 10-6 using the same data shows how the average sandstone thickness increases with the modified proximality index. Walker and Sutton (1967) at the same time analysed the Middle Devonian turbidites of the Sonyea Group of New York State, finding good agreement with the patterns in Figs. 10-5 an 10-6. The data of Angelucci et al. (1967) and Tanaka (1970) indicate for other turbidite formations trends similar to that in Fig. 10-6. Few workers have related the ABC-index directly to downcurrent distance. Walker ( 1967b) concluded on theoretical grounds that the index decreased with increasing transport distance, but did not test this in the formations he studied. Love11 (1969) in the Eocene Tyee Formation found the modified ABC-index to decline downcurrent, in accordance with Walker’s model, but the reduction in the value, less than 10% over a distance of 150 km, was so small as to be hardly detectable. Crimes et al. (1974) found in Ordovician turbidites from Spain a larger reduction in the ABC-index over a

408 1.2

I

I

3

I

1

I

I

I

I

1.1

I

I

I

--

I

I0

I

I

E

. I

0.9

I I

m 0

I

1

g

0.8

I I I I I

v n

0.7 C

i:

0

5

0.6

D 0

Z 0.5

1

0.4

0.3

02

0.1

0

10

20

30

40

50

60

Modlfied ABC-index

70

80

90

100

(percent)

Fig. 10-6. Average sandstone bed thickness in each natural group of 25 turbidites, as a function of the modified ABC-index. Same data set (R.G. Walker, 1967b) as in Fig. 10-5.

downcurrent distance of 40 km. The Sonyea Group turbidites yielded to Walker and Sutton (1967) a result not unlike Lovell’s. Over a distance of 100 km in the direction toward which the turbidity currents had flowed, the value of the modified ABC-index remained relatively constant, with the maximum increasing irregularly. The sharp erosional bases of turbidites frequently reveal flute moulds representing scour and the moulds of structures due to the action of tools dragged or suspended by the current (Chapter 13). The extent to which these sole markings vary downcurrent in character and abundance is uncertain. In some formations sole markings are restricted to the thicker and coarser grained turbidites, deposited in relatively proximal positions (Bouma, 1962; Ricci-Lucchi, 1969c). Some authors give evidence suggesting that scour structures become less abundant relative to those due to tools with increasing downcurrent distance (Dzulynski et al., 1959; Hsu, 1959; Craig and Walton, 1962; Lovell, 1969; Ricci-Lucchi, 1969~).Bouma (1962) noticed no sys-

409

tematic change in the relative abundance of scour and tool marks, at least when correlated with internal structural sequence. Tanaka (1970) found that scour and tool marks frequently occurred together, but that tool marks were more prevalent on the soles of the thicker and coarser turbidites. Crimes (1973) discovered tool marks to be commonest beneath beds starting with division A and scour structures to predominate below beds commencing with division C, implying that scour structures increased in abundance distally. Slaczka and Unrug (1976) reported an acme of scour marks at an intermediate downcurrent position. It would at present seem unwise to generalize about downcurrent changes in turbidite sole structures. Pett and Walker (1971) examined in a number of turbidite formations the character of flute marks in relation to the coarseness and sedimentary structure of the lowest division of the beds carrying the marks. They found a strong tendency for marks beneath beds starting with division A to be relatively wide, bulbous and round-nosed, whereas those present beneath beds commencing with divisions B or C were narrow and pointed. Little correlation could be found between the grain size and sedimentary structure of the basal division of turbidites bearing flute marks, giving no support to Allen’s (1968h) theoretical arguments for a correlation. In the turbidites examined by Ricci-Lucchi (1969a), however, a trend of the form suggested by Allen is present though less clearly defined and shifted significantly toward the finer grain sizes. The main weakness of the studies summarized in the preceding few paragraphs is that they attempt to predict lateral changes within an individual turbidity-current deposit on the basis of the statistical properties of groups of turbidites. It is preferable, as R.G. Walker (1973) has indicated, to study individual beds which can be traced out over a wide area, either because they can be walked out, or correlated with confidence between sections. Turbidites in the stratigraphic record can in some areas be traced laterally over large distances. Hesse (1965, 1974) made a good case for being able to correlate individual beds over 115 km in the Cretaceous of the Alps. Internal structural and textural features were not closely observed, but several beds showed downcurrent thinning. Engel ( 1970, 1974) found that certain relatively thick conglomeratic turbidites in the Yugoslavian Paleocene and Eocene could be traced laterally, with downcurrent thinning, over distances of about 15 km. Rupke (1976) achieved similar correlations, but again of relatively thick beds. Individual turbidites of a more typical thickness and texture were correlated in sections distributed over an area of 20 by 40 km by Picha and Niem (1974), and over distances up to about 40 km by Hirayama and Nakajima (.1977), and by Tokuhashi (1979). Correlations over distances as great as 60 km were achieved by Ricci-Lucchi and Valmori (1980) for the thicker turbidites they studied. The beds studied by the Japanese were deposited on a channeled deep-sea fan, and in plan appear to

410 (a1 Gray turbidite

( b l Tricolor

turbidlte

Fig. 10-7. General character of the Hispaniola-Caicos Basin, and the areal distribution of the largest particle size observed in cores penetrating (a) the Gray Turbidite, and (b) the Tricolor Turbidite. After Bennetts and Pilkey (1976).

- O

5 0 km

Core piercing division

DIVISION

E

Fig. 10-8. Thicknesses and distributions of Bouma divisions in cores penetrating the Gray Turbidite, Hispaniola-Caicos Basin. After Bennetts and Pilkey (1976).

41 1

Core piercing turbidite

Fig. 10-9. Thicknesses and distributions of Bouma divisions in cores penetrating the Tricolor Turbidite, Hispaniola-Caicos Basin. After Bennetts and Pilkey (1 976).

be lobe-shaped, thinning and fining down and away from the axis of the lobe. Complete Bouma sequences appear where the beds are relatively thick, but toward the margins of the lobes the lower divisions fail progressively to appear. Something of a contrast is afforded by turbidites in the Ordovician Cloridorme Formation, Quebec. Enos ( 1969a, 1969b) could walk out some beds over distances of up to about 3 km, but concluded that the median downcurrent length of the turbidites was a mere 10 km. Parkash and Middleton (1970) traced eight beds over 3.2 km of outcrop, finding no significant systematic downcurrent change in either thickness or coarseness. The turbidites tended to have smooth soles downcurrent but to show tool and isolated flute marks proximally (Parkash, 1970). Some unusual turbidites in the Cloridorme Formation have been correlated over distances up to 12 km (Skipper and Middleton, 1975). Individual turbidites can be traced over comparably large distances in present-day abyssal plains and related environments. Correlations over distances of 10- 15 km were achieved in Hardanger Fjiord by Holtedahl(1965), over a few kilometres in the Navidad Basin by Seiglie et al. (1976), and over an area of 3 by 17 km in the Wilkes Basin by Payne et al. (1972). The abyssal plain of the Tyrrhenian Sea yielded to Ryan et al. (1965) turbidites with well-developed Bouma sequences that could be correlated over a distance of

412

about 70 km. Correlation over 55 km was achieved by Belderson and Laughton (1966) in the Madeira-Cape Verde Basin. In the Adriatic Sea, Van Straaten (1967) could recognize the same turbidites in cores 60 km apart. By far the most detailed studies are those by Bornhold and Pilkey (1971), in the Columbus Basin, to the southeast of the Great Bahama Bank, by Bennetts and Pilkey (1976) in the nearby Hispaniola-Caicos Basin, and by Elmore et al. (1979) in the Hatteras Abyssal Plain. Six lobe-shaped turbidites could be traced in the Columbus Basin over paths several tens of kilometres long. The beds, of carbonate detritus formed in the shallow waters of the Banks, become thinner and apparently finer grained downcurrent. Even more detailed observations were made on three turbidites, distinguished as “gray”, “green” and “tricolor”, in the Hispaniola-Caicos Basin. Figure 10-7 shows how grain size varies within the gray and tricolor beds, derived from respectively the west and south sides of the trough. However, there was no systematic pattern in the distribution of Bouma divisions. In the biogenic gray turbidite, the Bouma divisions fail downcurrent progressively from below (Fig. 10-8). The tricolor turbidite, with a substantial terrigenous component, has divisions with practically identical areal distributions (Fig. 10-9). The Black Shell Turbidite studied by Elmore and his associates is an order of magnitude more extensive and thicker than any of these. It is lobe shaped in plan, up to 4 m thick, and with an axial extent of at least 500 km. The axial portion is the thickest and coarsest grained, showing the vertical sequence A E, the intermediate Bouma divisions proving absent. Laterally, the turbidite is thinner and better organized internally. Van Tassel1 (1981) has further discussed the tricolor turbidite.

-

Interpretation

Sheldon’s (1928, 1929, p. 525) interpretation of the Bouma structural sequence in terms of the gradual decay of a current anticipates by more than 35 years our present concepts. “The sandstones began abruptly”, she wrote, “and showed evidence that the agitation of the waters was greatest when the basal portion of the sandstone was formed. The currents gradually diminished until, at the close of the sandstone phase, they were suitable for forming ripples”. Harms and Fahnestock (1965) and, independently, Walker (1965) interpreted the original Bouma sequence in terms of the then recently completed experiments on bedforms at the Colorado State University (see Guy et al., 1966), which confirmed and greatly extended Gilbert’s (1914) discovery that there was a sequence of bed configurations related to changing flow conditions. That parts at least of this sequence can occur in decelerating flows is confirmed by the later experiments of Kuenen (1965a, 1966a) and Banerjee (1977). Division B was attributed to deposition on a plane bed, and division C to settlement on a rippled surface; divisions D and E were related to deposition from suspension in a current too weak to cause traction.

413

Following Simons and Richardson (1961), the “lower regime” flow that gave division B was distinguished from the “upper regime” current that afforded division C. Harms and Fahnestock attributed division A to the upper part of the upper flow-regime in which, in the original open-channel experiments, antidunes were formed. Walker (1965) was at first more circumspect, merely comparing division A with the experimental antidunes, but later (1967b) offered an interpretation similar to Harms and Fahnestock’s. Figure 10-2a shows a paraphrased interpretation of the original Bouma sequence suggested by these three workers. Their use of the regime concept has little merit, however, since “regime” refers merely to total flow resistance (grains, bed shapes, acceleration losses), telling nothing of flow strength and sediment transport rate, to which bedforms are arguably much more closely related. Moreover, bedform is not uniquely determined by whether the flow is in either the upper or the lower regime. The configuration in the lower regime could be either a lower-stage plane bed or antidunes, according to grain size and flow depth, whereas an upper-regime flow could generate either current ripples, dunes, or antidunes. Allen (1968h, 1969c) therefore suggested an interpretation of the original Bouma sequence in terms of the flow power indicated by the structures (Fig. 10-2a). This scheme clearly reveals turbidity currents ordinarily to be flows of decreasing strength. Division A is difficult to interpret. Although in varying degrees compared to antidunes (Harms and Fahnestock, 1965; Walker, 1965, 1967b), perhaps mainly on the grounds of relative position, and although antidune structures are occasionally found in turbidites (e.g. Skipper, 1971), with Middleton and Hampton (1976) championing some parallel laminations as antidune structures, the lack of internal bedding makes hazardous the attribution of division A to any particular bed configuration. Since the development of antidunes requires an almost unique combination of flow depth and velocity, it seems most likely that division A records a deposition rate so large as compared to the allowable bed-load transport rate that particle segregation by size and/or density was impossible (Middleton and Hampton, 1976). As Middleton ( 1967a) found experimentally, the deposit was probably quick also, and prone to disruption by instability waves. Deposition rates measured in metres or tens of metres per hour could have prevailed during the deposition of division A, particularly as the features of the transition B + C, involving much finer grained sediment, suggest rates of centimetres and even decimetres per hour (Allen, 1971e). Natural turbidity currents are probably far from being self-sustaining, if this interpretation is correct. A striking lack in the original Bouma sequence is a division of dune-related cross-bedding. Walker ( 1965) speculated that either the current was insufficiently deep for dunes to appear, or that its flow was too short in duration. Walton’s (1967) explanation was that either dunes were formed but then erased as the current decayed, or that their development was inhibited when

414

grains of a certain modal size were present, presumably close enough to the bed for deposition. Representations then available of bedforms in the grain size-flow power plane (Simons et al., 1965) suggested to Allen (1969~)that dunes were lacking because, at the grain sizes evidently available for deposition by most turbidity currents, the range of flow power appropriate to these forms was traversed too quickly, being narrow, to permit their growth. Hence aspects of Walker’s and Walton’s suggestions were combined. Allen (1970d) later proposed on the basis of H.M. Hill’s (1966) bedform theory that the role of grain size is critical because it determines the occurrence of a triple point separating upper-stage plane beds, dunes, and current ripples in the grain size-flow power plane (Vol. I, Fig. 8-22), a suggestion supported by experimental work (Hill et al., 1969). According to this model, if the power of a turbidity current passing a fixed station follows a path in time such as AA‘ in terms of the modal grain

. . .. .. .. . .. ‘ .A . . .. . .. . . .. . . . . . . . . . Deposition r o t e too high . . . . . ,

10-5

,

I

.

I

10‘~

10-3

10-2

Grain diameter, D (m)

Fig. 10-10. Evolution of hypothetical turbidity currents as they pass afixed site, in terms of grain size and sedimentary structure. The current following the path AA’, for example, deposits parallel-laminated very fine grained sand, followed by cross-laminated very fine sand and coarse silt. Note that the boundary to division A is moveable and partly arbitrary.

415

10‘

N I

E

-? 100

c 0,

-

4

?

3m

6n

E lo-’

10-2

No bed-materiol movei 10-

10-

IO-~ Grain diameter, D

10-2

(m)

Fig. 10-1 1. Evolution of a hypothetical turbidity current at a series of sites, in terms of the grade and structure of the sediments deposited. The path connecting sites A, B, C. etc. illustrates the changing character of the leading edge of the depositional zone in the current. At point D, for example, the current deposits parallel-laminated very fine grained sand followed by cross-laminated very fine grained sand and coarse silt. The insets (b) show in streamwise profile and plan the distribution of Bouma divisions. Note that the boundary to division A is moveable and partly arbitrary.

sizes successively available near the bed for deposition (Fig. 10-lo), then the structural sequence developed is B, -, C, -, D E, that is, the original Bouma sequence in revised notation (Fig. 10-2b). With the path BB’ we have A + C, C, + D + E. The sequence A -, C , + B, -, C, -+ D --* E would result if the path in time were CC’. Paths of lower slope, or paths starting at smaller powers, would yield different Bouma sequences, of the base cut-out variety or lacking middle terms. Figure 10-10 indicates what happens to several currents at one station; the changing behavior of one current at stations spread along its path, say, that which deposited Bennetts and Pilkey’s (1976) gray turbidite (Fig. 10-8), is suggested in Fig. 10-lla, in which AA‘, BB’ etc. represent events at progressively more distal sites. The path AD records the change at the most forward depositional portion of the -+

--$

416

flow, and the whole bed may be like that sketched in Fig. 10-1lb, much as envisaged by Bouma (1962) and Meischner ( 1964). Figures 10-10 and 10-11 furnish a general key to the Bouma structural sequence, and describe a model capable of accommodating both the largely fine-grained terrigenous turbidites, though some are relatively coarse (e.g. Rocheleau and Lajoie, 1974), as well as the more often coarse-textured bioclastic ones (e.g. Hubert, 1966a, 1966b; Thompson and Thomasson, 1969). Implicit in the model, however, is the assumption of a grossly overloaded flow, in the sense of our preliminary discussion, whence the modal grain size deposited at a station on the turbidity-current path is independent of the flow power there and a function only of initial and boundary conditions. In a sufficiently large sample of turbidites, particular transitions, for example, B, 3 C,, C, -+ C,, should therefore be correlated with defineable but broad ranges of grain size. Were the current close to being self-sustaining, so that the grades deposited were closely adjusted to the prevailing power, a much closer and essentially unique correlation between structure and texture would be expected. An empirical test remains to be made. Three explanations exist for turbidite vertical and lateral grading. Firstly, Kuenen (1951a) and Kuenen and Menard (1952, p. 85), supposing a particular velocity distribution in turbidity currents, suggested that: “An upward flow at the nose of the advancing current results from the vertical velocity gradient. This flow tends to concentrate the coarsest grains in the foremost lower part. As a consequence, the first grains to settle on the bottom from the nose of the flow are also the largest that can reach this spot at any time, and as the flow continues to pass over this area the depositing material gradually decreases in size.” Secondly, Scheidegger and Potter ( 1965, 1971) and Potter and Scheidegger (1966) attributed the vertical and lateral changes to the way in which the decay of turbulence in the current controlled the sediment deposition rate and coarseness of the deposited grains, for given initial conditions. This idea was formulated mathematically to show that bed thickness and coarseness would decline downcurrent, while grain size would decrease upward at any station, assuming that a wide range of grain sizes was present in the original current. Middleton’s (1967b, p. 499) experiments on turbidity-current surges led him to suggest that: “If flows where the separation of grain sizes is not prevented by high concentration (or by some other property of the suspension), a lateral grading of the coarser grain sizes deposited in the bed is developed, because the velocity and turbulence within the current.. . are not sufficiently large to prevent deposition of the coarser particles present in the initial suspension. The lateral decrease in maximum grain size is a function of the time that has elapsed since the suspension was released from the lock, rather than being a function of decreasing velocity of the flow.” But this mechanism was explicitly reserved to laboratory-scale surges, the prototypes being regarded as mainly self-sustaining.

417

The extent to which these mechanisms operate in natural turbidity currents cannot be precisely judged at present. Scheidegger and Potter’s model, predicated upon self-sustaining though decaying currents, can seldom be applicable if the results of the above calculations on the control of mobility by sediment load are valid. These same calculations show Middleton to have been unduly conservative in restricting his mechanism to the laboratory scale. If natural turbidity-current surges are as far removed from being self-sustaining as the calculations suggest, then they are very like a slab of dispersion similar to that sketched in Fig. 10-1, from which grains of many sizes are free to settle, unhampered by forces due to any motion of the slab. Although Kuenen and Menard mistook the cause of the upward components of velocity present in turbidity current heads, a mechanism similar to the one they outlined could be operative, for upward flow results from consumption of the body by the slower-moving head as the wake is enlarged (Middleton, 1966b; Britter and Simpson, 1978; Simpson and Britter, 1979). However, this mechanism may only be effective over comparatively large distances. Under flow conditions far removed from self-sustainment, the vertical grading of turbidites should be explicable in terms of the laws governing the sedimentation of stationary polydisperse systems (Chapter 8), modified to account for flow shearing. What is known of systems of high concentration seems to be fully consistent with Middleton’s (1967b) finding that coarse-tail grading and poor horizontal grading are restricted to high-concentration flows. The rare reverse size-grading of turbidites (e.g. Gonzalez-Bonorino and Middleton, 1976) cannot be explained by these means, unless grains of a wide range of density are present, and possibly is related to patterns of flow within turbidity currents.

PYROCLASTIC FLOW, GROUND SURGE AND BASE SURGE DEPOSITS

Extent and grading Like turbidites, the deposits of volcanic surges display a remarkable lateral compared to vertical extent. Individual pyroclastic-flow deposits are commonly 10-20 m thick, though many are thinner, yet typically reach for several tens of kilometres from volcanic centres in the Mediterranean area (Sparks, 1975; Schmincke and Swanson, 1967; Alvarez et al., 1975; Barberi et al., 1978), the Atlantic region (Anderson and Russell, 1939; H. Williams, 1942; G.P.L. Walker and Croasdale, 1971), North and Central America (Noble, 1965; Fisher, 1966; Lipman et al., 1966; Smith and Bailey, 1966; Ratte and Steven, 1967; Miller and Smith, 1977; Rose et al., 1977; C.D. Miller, 1978; Kreiger, 1979), South America (Francis and Baker, 1977), Japan (Murai, 1961; Kuno et al., 1964; Lipman, 1967; Yokoyama, 1974; Taneda, 1979), and New Zealand (Ewart, 1965; R.C. Martin, 1965). Some

418

flows have travelled more than 100 km (Guest, 1969; Koch and McLean, 1975), and prove particularly voluminous (Francis and Baker, 1977). In contrast, nukes ardentes are comparatively small and seldom travel more than about 10 km (e.g. MacDonald and Alcaraz, 1956; G.A. Taylor, 1958; Moore and Melson, 1969; Sparks and Walker, 1973; Davies et al., 1978). Base surges seem to be similarly if not more restricted, being confined to within about 5 km of crater rims (Moore et al., 1966; J.G. Moore, 1967; Schmincke et al., 1973; Sheridan and Updike, 1975). Pyroclastic-flow deposits are unstratified, coarse grained and ill-sorted (Murai, 1961 ; G.P.L. Walker, 1971; Walker and Croasdale, 1971 ; Sparks, 1976; Davies et al., 1978; Taneda, 1979), and of variable lateral grading. Murai’s careful examination of a large number of flow-deposits showed little or no downcurrent decline in median grain size or change in sorting. R.C. Martin (1969, Self (1972), and Koch and McLean (1973, however, found indications of downcurrent fining. A streamwise decline in the size of lithic fragments was detected by Kuno et al. (1964), Fisher (1966), Yokoyama (1974) and Sparks (1975). A parallel decrease in pumice size was noted by Yokoyama, but Kuno observed an increase followed by a decline, the maximum size occurring at a distance from source of about one-third the maximum extent of the deposit. Sparks found no change in pumice size. Taneda observed similar maxima far both pumice and lithic fragments. Crystals are much more abundant in pyroclastic-flow deposits than in the contained pumice (G.P.L. Walker, 1972). Fisher (1966) and Lipman (1967) noticed that in some flow units the crystals declined in relative abundance away from source, though not necessarily changing in size. Whether the deposits of ground and base surges display any systematic downcurrent changes in texture and composition is uncertain, but a measure of fining is perhaps to be expected. Some pyroclastic-flow deposits thin away from source (G.P.L. Walker, 1962; Lipman et al., 1966; Smith and Bailey, 1966), but systematic thickness changes in the majority are masked by local variations related to buried topography. Vertical grading is common only in thin pyroclastic-flow deposits. Lipman et al. (1966) found some beds in the Topapah Springs Member to be compositionally graded from crystal-poor and pumice-rich in the lower part to crystal-rich and pumice-poor higher up. RattC and Steven (1967) recorded a normal size-grading of crystals above a thin reverse-graded zone from deposits surrounding the Creede Caldera, Colorado. A rather similar pattern (Fig. 10-12a), typifying thin flow-deposits, is described by Sparks (1975, 1976) and Sparks et al. (1973). The thin basal division is reverse-graded and relatively fine grained. The much thicker overlying division shows an upward decline in the size and abundance of lithic fragments, but an increase in the amount and coarseness of pumice fragments. The scanty evidence available in the work of Fisher and Waters (1970), Schmincke et al. (1973), and

419

Sand-wave

All components reverse- graded

bedding

Coarse parallel bedding

Fig. 10-12. Schematic vertical grading and sedimentary structures in (a) ground-surge deposits, and (b) base-surge deposits (very tentative). Lithic debris shown in solid black.

Sheridan and Updike (1975) suggests that the deposits of ground and base surges may be normally graded (Fig. 10-12b). Sorting in pyroclastic flows (Fisher, 1966; G.P.L. Walker, 1972; Sparks, 1976) is complex and little understood, if only because of the variability of debris in size, density and breakability. Sparks argues that the large grainconcentration in the flows prevents the deposits from becoming well-sorted, as is commonly suggested for turbidites. The principal textural grading observed (Fig. 10-12a), remarkably like that found in a Class I1 or I11 polydisperse system (Fig. 8-25) (Richardson and Meikle, 1961a; Phillips and Smith, 1969, 1971; Lockett and Al-Habbooby, 1973, 1974), is attributed by him to the buoyant rise of the relatively light pumice. The floating of pumice into the upper and faster-moving levels of a spreading pyroclastic flow may also explain the maximum of pumice size reported by Kuno et al. (1964). Although the explanation of grading proposed by Sparks is supported by what is known of stationary polydisperse systems, it is doubtful if his calculations predicated upon this suggestion are valid, as he overlooked the work on sedimentation and so over-simplified the behaviour of mixtures.

Radial grooves Base surges can fashion longitudinal bedforms in the shape of either erosional grooves or low accretionary ash waves disposed radially about a crater. As well as reporting base surges, Richards (1959, 1965) saw that the upper cone of Barcena Volcano, Mexico, bore a pattern of densely arrayed and steeply plunging radial grooves that gave place on the milder slopes below to

420

Fig. 10-13. Oblique aerial view of the east flank of BBrcena Volcano, Mexico, showing straight radial grooves (G)giving place downslope to ring-like sand waves (SW). Light-coloured areas are recent ash deposits. Photograph courtesy of A.F. Richards and U.S. Navy.

concentric ash waves (Fig. 10-13), (see also J.G. Moore, 1967). The grooves were 3-7 m wide, between 1 and 3 m deep, and of a parabolic to steeply U-shaped cross-section. They were remarkably straight and in many cases extended axially over several hundred metres. Transverse spacings were in the order of 10- 100 m. Richards attributed the grooves to erosion by tephra avalanches, amongst which he included the surges described. What are possibly related structures are recorded by Losacco and Parea (1969) from the Roman Volcanic Province as grooves of parabolic profile between 4 and 30 m wide and 2- 15 m deep arranged radially about certain craters. These forms are substantially larger than the structures described by Richards, and could have been shaped partly by rainfall and run-off. Fisher (1977) investigated the erosional grooves of Koko Crater, a mum volcano in Hawaii. Figure 10-14 is representative of them and their discordantly stratified and often cross-bedded infillings. The largest grooves measured 5-25 m apart with many smaller ones between; width at the shoulders ranged from 0.4 to 5 m and depths from 1 to 3 m. Groove axes plunged away from the crater, and in some instances were localized by former drainage lines. The infilled grooves have smooth walls and floors and in cross-section are parabolic, locally almost vertical-sided. Like Richards ( 1959), Fisher

42 1

Fig. 10-14. Complex infilled radial channel on flanks of Koko Crater, Hawaii. The first channel (to about half-way up rock face) was steep-sided and V-shaped, being filled in two stages, whereas the principal later cut is much wider and round-bottomed. Photograph courtesy of R.V. Fisher, reproduced by permission of Geological Society of America (see Fisher, 1977).

attributed the grooves to base-surge erosion, suggesting from Allen’s ( 1971b) work that the furrows and ridges recorded the action respeptively of lobes and clefts on the front of the surge. Presumably, large scale secondary flows of the kind sketched in Figs. 1-6, 1-25 were responsible. Fisher’s proposal is plausible in the light of the large size of the lobes observable at the heads of base surges. Erosional grooves may have wholly accretionary equivalents. Mattson and Alvarez (1973) describe low ash waves extending radially from Italian rnaar, and Nairn (1979) seems to record similar structures from New Zealand. From Sugarloaf Mountain, Arizona, Sheridan and Updike (1975) report the Occurrence of gently rolling subradial dunes. The flow-structures on the front of a base surge can also explain these waves. The lobes and clefts imply the existence in the leading part of the flow of transverse variations in shear stress and therefore of sediment transfer rate (Allen, 1971b). The rate was evidently positive (deposition) when the radial ash waves were formed, but

422

negative when the grooves arose. The difference is a matter of general regime, and independent of the occurrence of clefts and lobes.

Plane beds and parallel stratification Several workers find that the tephra beneath volcanic cones swept by base surges includes parallel-stratified deposits which appear to have accumulated on plane or only slightly wavy beds (Fisher and Waters, 1970; Heiken, 1971; Schmincke et al., 1973; Ollier, 1974; Sheridan and Updike, 1975). These sediments consist of irregularly interbedded ash and lapilli in layers from a few millimetres to a few centimetres thick individually. The finer grained beds generally extend laterally over several tens of metres without significant change, but the coarser ones are more variable, some being flat isolated lenses, and others showing a repeated pinch-and-swell. Reverse-grading affects some coarse layers. Closely associated with these deposits are generally finer grained crossbedded ashes. In places, isolated cross-bedded lenses appear amongst the coarser, parallel-stratified sediments.

Sand waves and cross-bedding Since the pioneering observations of Richards (1959), J.G. Moore (1967), and Fisher and Waters (1969), large sand waves associated with a range of cross-bedding structures have been widely recognized in the deposits of base and ground surges. Variously called, somewhat indiscriminately and inconsistently, “dunes”, “antidunes” and “ring dunes”, there is a tendency to interpret the structures physically in terms of the supposedly corresponding aqueous bedforms. The less committal name sand waoe is advocated here, together with a distinction between progressive, regressive and stationary types, accordingly as the bedding and successive crestal positions indicate movement downstream, upstream or essentially not at all (Fig. 10-15). The mode of occurrence of sand waves is known from both active and extinct volcanoes. Richards (1959) and J.G. Moore (1967) found the waves to be arranged concentrically around the crater of Barcena Volcano (Fig. 10-13), mantling the gently dipping ground downslope from erosional grooves. A less restricted distribution marks sand waves on the island cone present in the crater-lake of Taal Volcano (Fig. 10-16). In each case the forms decline in wavelength downslope (downcurrent). Traces of concentric structures that might be ash waves appear on Surtsey Volcano in Iceland (Thorarinsson et al., 1964), shown by Richards (1959) to have been affected by base surges. Past surge deposits also preserve evidence of concentrically arranged sand waves (Crowe and Fisher, 1973; Meyer et al., 1974), with a downslope fall in wavelength (Schmincke et al., 1973; Sparks et al., 1981). In plan volcanic sand waves have long crests that range from smoothly

423

Fig. 10-15. Bedforms and internal sedimentary structures in base-surge deposits, tentatively interpreted in terms of relative sediment deposition rate (steepness of bedform-climb) and surge temperature/moisture content. Current from left to right. Note that a cool but relatively dry surge may behave similarly to a sufficiently hot but relatively moist one.

curved to gently winding. Wavelength values (Fig. 10-17) vary from about 2 to 20m (Waters and Fisher, 1971; Crowe and Fisher, 1973; Mattson and Alvarez, 1973; Schmincke et al., 1973), the vertical form-index averaging about 15, as in aqueous dunes of a similar size (Fig. 8-6). The waves are variable in symmetry and facing, as judged from the direction of groundslope, the positions of nearby craters, and the sense of thinning of the deposit. Progressive forms have migrated downcurrent (Fig. 10-15A, B); they are asymmetrical and internally show cross-strata that are steeper on the lee-side than on the stoss side. The stoss-side cross-strata are usually the steeper in upstream-travelling or regressive sand waves (Fig. 10-15C, D, E). Stationary sand waves show a relatively symmetrical external form and internal layers which face upcurrent and downcurrent about equally (Fig. 10-15F). The slopes of external surfaces and internal partings are also variable. Crowe and Fisher (1973) record many dip values of 10-15" and less, whereas Schmincke et al. (1973) illustrate upcurrent dips of as much as 55". Downcurrent dips steep enough to reflect avalanching are generally restricted to the deposits of progressive sand waves.

424

Fig. 10-16. Concentrically arranged sand waves on surface of base-surge deposit mantling small crater in Lake Taal, Philippine Islands. After J.G. Moore (1967). Sand-wave spacing given in metres.

Cross-bedding of type A, (Figs. 10-15, 10-18) occurs in Australian and Hawaiian base-surge deposits (Ollier, 1974; Fisher, 1977) and records progressive sand waves. It consists of several superimposed and gradationally related sets of alternately fine and coarse grained lee-side layers, accompanied by generally fine grained stoss-side deposits, which include the occasional erosional parting. There is a close resemblance in both form and the lee-side concentration of coarse grains to supercritical climbing-ripple crosslamination (Vol. I, Fig. 9-14). The scale is of course greater by two orders of magnitude. Type A cross-bedding (Figs. 10-15, 10-19, 10-20a,d) resembles type A,, preserving stoss-side as well as lee-side deposits, but is restricted to what are effectively form sets. Episodic upward and forward growth is recorded by the erosional partings which frequently occur amongst the stoss-side and crestal deposits. This type of cross-bedding is present in many surge deposits (Fisher and Waters, 1969, 1970; Heiken, 1971; Crowe and Fisher, 1973;

425

Sand wave height, H (m)

Fig. 10-17. Sand wave height and length in base-surge deposits.

Schmincke et al., 1973; Sparks and Walker, 1973; Swanson and Christiansen, 1973; Sheridan and Updike, 1975; Bond and Sparks, 1976; Sparks, 1976). Cross-bedding of types B and A, are similar, but with the important difference that in the former (Fig. 10-15) successive sets are erosively related (Fisher and Waters, 1969, 1970; Swanson and Christiansen, 1973), as in subcritical climbing-ripple cross-lamination (Vol. I, Fig. 9-9). The best examples of type C cross-bedding (Figs. 10-15, 10-20b, c) are described by Mattson and Alvarez (1973) from the Roman Volcanic Province and by Nairn (1979) from New Zealand. Assuming their identification of the source-direction to be correct, the structure was made by sand waves that climbed steeply and non-erosively upward while migrating into the current. Lapilli are concentrated amongst the stoss-side layers, as Schmincke et al. (1973) found in another example, as well as in cross-bedding shaped by unquestionably regressive forms. Type D (Figs. 10-15, 10-20e, 10-21) is related to type A, through the involvement of what are best called form sets (Schmincke et al., 1973; Sparks and Walker, 1973; Nairn, 1979). The core consists of cross-beds that often coarsen downcurrent. Truncating them is an erosion surface that is steepest upcurrent and draped by asymmetrical layers, with coarse grained partings, that climb upcurrent.

426

P

N Q.

Fig. 10-18. Progressive cross-bedding in coarse ash with some coral debris (white fragments), cliffs east of Kahauloa Crater, Hawaii. Hammer toward base of cliff gives scale. Photograph courtesy of R.V. Fisher, reproduced by permission of the Geological Society of America (see Fisher, 1977).

427

Fig. 10-19. Progressive cross-bedding in coarse ash, Ubehebe Craters, Death Valley, California, U.S.A. Photograph courtesy of R.V. Fisher, reproduced by courtesy of the Geological Society of America (see Crowe and Fisher, 1973).

I

I

Fig. 10-20. Cross-bedding structures in base-surge deposits. a. Type A z , Ubehebe Craters, Death Valley, California, U.S.A. (after Crowe and Fisher, 1973). b, c. Type C, Roman Volcanic Province, Italy (after Mattson and Alvarez, 1973). d. Type A,, Oregon Tuff Rings (after Heiken, 1971). e. Type D, Graciosa, Azores (after Sparks and Walker, 1973). f. Type F, Taal Volcano, Philippine Islands (after Waters and Fisher, 1971). Arrow shows direction of base surge.

428

Fig. 10-21. Cliff section approximately 5 m thick showing type D cross-bedding (top centre of photograph), base surge deposits, Laacher See, Germany. Surge from left to right. Photograph Schmincke and reproduced by permission of International Association of courtesy of H.-U. Sedimentologists (see Schmincke et al., 1973).

In type E cross-bedding (Figs. 10-15, 10-22), described by Schmincke et al. (1973) and Meyer et al. (1974) from the Eifel, we see alternating coarse with fine layers stacked laterally and without marked climbing against step-like features scoured into often level-bedded ash. Dips in the coarse layers commonly exceed 30" and range up to 55". There is a marked symmetry about cross-bedding of type F (Figs. 10-15, 10-20f), illustrated by Waters and Fisher (1971) and Booth (1973). It is found within sand-wave forms and consists of erosively related sets with cross-beds that generally face downcurrent. The erosional partings, however, are variable in their facing. Cross-bedding may not be restricted to the deposits of pyroclastic surges. Walker and Croasdale ( 1971) report low-angle cross-beds and wave-like forms in deposits attributed to pyroclastic flows, and Nakamura and Kramer (1970) refer to cross-bedding in other coarse tephra. There seems to be an important compositional difference between the progressive and regressive forms of cross-bedding. Armoured and/or accretionary lapilli appear to be abundant only where stationary and regressive sand-wave structures predominate (J.G. Moore, 1967; Heiken, 1971; Mattson and Alvarez, 1973; Schmincke et al., 1973). The same deposits in at least one instance are vesicular (Schmincke et al., 1973), due to the tephra having

429

Fig. 10-22. Cliff section (scale marked in decimetres) showing type E cross-bedding, base surge deposits, Laacher See, Germany. Surge from left to right. Photograph courtesy of H.-U. Schmincke and published by permission of International Association of Sedimentologists(see Schmincke et al., 1973).

been wet when,deposited (Lorenz, 1970, 1974). Vesicular tuffs are not known to accompany progressive cross-bedding, in association with which accretionary lapilli are rare or absent (e.g. Fisher and Waters, 1970; Fisher, 1977). The physical significance of surge-related cross-bedding and sand waves remains obscure. Stationary and regressive forms were compared morphologically by Fisher and Waters (1969, 1970) and Waters and Fisher (1971) to antidunes on free-surface aqueous flows (Vol. I, Chapter 10). However, they did not explicitly claim that the structures were antidunes in a hydrodynamic sense, and instead drew attention to the fact that the debris carried in base surges can be wet and therefore strongly cohesive upon deposition. This suggested a possibly important difference in the way in which a surge interacted with its bed as compared with an aqueous stream moulding cohesionless sand. But cohesiveness was accepted as important only in the preservation of the bedforms, and not in their initial development. Later authors were bolder. Crowe and Fisher (1973), and Mattson and Alvarez (1973), interpreted the forms hydrodynamically as antidunes, the latter applying Kennedy’s (1963) formula for flow speed. Schmincke et al. (1973) made the same proposal, with the addition that cross-bedding of type E was attributed to “chutes-and-pools”, a configuration related in open watercourses to meandering at large Froude numbers.

430

Supercritical flow is physically possible in base and ground surges, but the presence of upstream-facing structures in the deposits is no guarantee that this actually occurred, when there is also evidence- accretionary lapilli and vesicles, to which may be added soft-sediment deformations, mud plasters, and impact structures preserving near-vertical bedding- that the grains were wet when transported and cohesive en rnusse after deposition. Upstreamfacing structures are in fact typical of the interaction between a cohesive bed and particles that are considerably more dense than the transporting medium. The sastrugi shaped on ice surfaces by blowing snow, and erosional forms in sand-blasted metals (Chapter 13), are examples that represent a wholly erosional setting. When accretion occurs, features due to upstream-building as well as with upstream-facing become noticeable, as in the climbing adhesion ripples formed when the wind for a long period drives sand grains over a moist surface to which some adhere. Internally, these ripples (Hunter, 1973) closely resemble type C cross-bedding, and there are also clear affinities with type E, the chute-and-pool structure of Schmincke et al. (1973). This comparison suggests that stationary and regressive types of cross-bedding, associated with apparently wet and therefore cool surges (temperature less than 100°C), record an unstable interaction between the moistened debris driven by the surge and a particle-capturing cohesive bed, that may have been independent of the Froude number. Flow separation (forward) was probably involved, but perhaps not in the manner pictured by Meyer et a]. (1974). The progressive type of cross-bedding suggests bedforms similar in all essential respects to small aeolian transverse dunes. Further strength is given to the comparison when we recall that there is little or no evidence for the wetness of these deposits, vesicles being unknown and accretionary lapilli sufficiently scarce as to have come from earlier tephra. Presumably the parent flows were dry and therefore rather hot. In conclusion, there is little to support the view that antidunes in the hydrodynamic sense occur in volcanic surges, and little to justify a direct interpretation of surge-generated structures using bedforms shaped by flowing water, though there appears to be a sequence not unlike that in turbidites. What we can suggest (Fig. 10-15) is that the character of sand-wave structures in surge deposits depends on the relative rate of deposition from the surge and its temperature and therefore wetness. Other structures Soft-sediment deformations occur in some surge deposits (e.g. Crowe and Fisher, 1973), an indication that the beds may have been formed in a wet state. A clearer proof of wetness is afforded by the mud plasters that form on the upflow sides of trees and buildings (Moore et al., 1966; J.G. Moore, 1967; Fisher and Waters, 1970; Waters and Fisher, 1971) and by the

43 1

adhesion ripples on the tops of some beds (Lorenz, 1970, 1974). The trees acted as bluff bodies, the eddying of the surge around them permitting little debris to accumulate immediately to lee. Sags formed as large fragments fell through a surge on to the deposit accumulating beneath have also been reported (Heiken, 1971; Waters and Fisher, 1971; Crowe and Fisher, 1973). The marginal bedding in some sags is nearly vertical, pointing to a cohesive sediment. The only sedimentary structures preserved in pyroclastic-flow deposits are related to the behaviour of the debris while cooling after deposition. Schmincke and Swanson (1967) described various features attributable to the gravitational movement of the partly welded but still-hot ash, including large slope-parallel waves due to the downhill buckling of the cooler crust. P.W. Francis ( 1970) illustrated similar structures. SUMMARY

Turbidity currents, pyroclastic flows, base surges and ground surges are gravity currents that derive their excess of density from the presence of internally dispersed particles. These flows are rarely self-sustaining, ordinarily containing much more sediment that can be supported as a load by the forces due to the motion, and are dissipative largely through particle deposition. The rate of dissipation is relatively small, however, and the flows are highly mobile, depositing beds that are orders of magnitude more extensive than thick. Turbidity currents form layers in which a definite succession of structures related to a waning current is developed vertically and laterally. The nature and completeness of the sequence depends on the initial and boundary conditions under which the current was developed. The most complete sequences are afforded by the largest currents, which are also generally the most mobile. In parallel with the sequence of sedimentary structures, turbidites become finer grained upward and laterally in accordance with their expected decay through sediment loss. The atmospheric surges related to volcanic activity differ from turbidity currents in carrying particles that are two orders of magnitude more dense than the enveloping gas, and are noticeably less mobile. They also differ amongst themselves, primarily in relative density. Pyroclastic flows appear to be comparatively dense, giving rise to poorly sorted deposits that lack depositional sedimentary structures and often any kind of vertical or lateral grading. Beds formed from base and ground surges are better stratified. Frequently they include varieties of wave-like forms and cross-bedding related to small dunes (relatively hot flows) or to an unstable interaction between wet ash particles and a cohesive particle-capturing bed (cool flows). A sequence of structures and textures resembling that in turbidites may mark these deposits.

This Page Intentionally Left Blank

433

Chapter I 1 COASTAL SAND BARS AND RELATED STRUCTURES

INTRODUCTION

In his important monograph Processes of Coastal Development, Zenkovitch (1967) aptly wrote “perhaps the origin of the submarine sand bars which extend along the water’s edge for tens or even hundreds of kilometres presents the most complicated and confused problem of the coastal zone”. This reference is to structures familiar from sandy shores as longshore bars and troughs (ridges and runnels or fulls and swales when exposed intertidally), and to what are called transverse bars, narrow ridges projecting obliquely outward from the strand. The origin of these bars is indeed a complicated issue, for the forms occur in perhaps the least straightforward of all sedimentary environments, in which tide, wind and wave interact (C.A.M. King, 1959, 1972; Komar, i 976a; Muir-Wood, 1969; Shepard, 1963; Zenkovitch, 1967; USACERC, 1977). At the coast, the water level may change drastically and on several contrasted periods through tidal action, as well as less regularly as atmospheric depressions pass by. Here waves encounter water changing in depth both in space and in time. Some of the energy of the waves incident on the coast is used in setting bottom sediment in motion and in creating sediment-transporting longshore and offshore currents. Another part is reflected from the beach, whence under favourable circumstances we may observe sedimentary features dependent on standing waves formed from the incident and reflected wave-trains. Because of the deepening of water offshore, and the irregular form of coastlines, some waves become trapped to the shore, to form what are called edge waves. These waves, either progressive or standing, contribute significantly to the complexity of the coastal environment and to coastal forms. Counting the beach &d nearby offshore as first-order morphological elements, the longshore and transverse bars we shall here discuss constitute second-order sedimentary structures, which in their turn are associated with still smaller, third-order forms, for example, tide-shaped dunes in longshore troughs, current ripples, and wave ripples. The extreme changeability of the beach and nearby offshore environment means that there is an unusually close involvement of the third-order structures with the second-order bars; most excavated sand bars include sedimentary structures representing a wide range of smaller bedforms, belying the simple shape of the bars. Fortunately, our present understanding of the bars themselves is much less confused than when Zenkovitch (1967) wrote.

434

MORPHOLOGY OF THE BARRED BEACH AND NEARBY OFFSHORE

Longshore and transverse bars occur on barred coasts as compared to those that are non-barred, where the profile across the beach and into the nearby offshore is smooth except for ripples and dunes. The transverse profile of a typical barred coast reveals a series of bars and troughs in a belt beginning in the nearby offshore and extending on to the foreshore (Fig. 11-1). The bars may be wholly intertidal where the sea bed slopes very gently and the tidal range is large, but only partly so where the range is modest or small. Relative to incident waves, each bar has an exposed side (bar face) to seaward and a sheltered side (bar k e ) to landward. Consider first a submerged bar. The bar face is a zone of landward-strengthened interaction between incoming waves and the bed, that results in landward-increasing oscillatory currents. By contrast, the bar lee experiences a decreasing interaction and a progressive weakening of oscillatory currents toward the trough. The general magnitude of the bar face and lee currents increases, however, as we pass from the deeper to the shallower bars. Next consider an intertidal bar during tidal ebb. Waves at first break lightly on the bar top and then more heavily as the water level falls. By the time the bar crest is emerging the breaking waves are “pumping” water as a series of surges landward across the bar toward the lagoon held in the trough next up the beach. There is consequently a flow of water parallel with shore along the lagoon. A further drop in water level leaves the crest finally emergent, but exposes the bar face to even heavier wave attack. Waves break on the bar face which may consequently be kept smooth by repeated swash and backwash flows, their zone of operation shifting steadily

OFFSHORE

FORESHORE

-I-BACKSHOREI I

Waves 4

Longshoie bor

Berm crest.

I

‘

Longshore trough

/

/

Waves L

/

Berm

‘ p-. I

\

\

Bar crest

Bar face

I

\

Bar lee (overwash zone) f loar

Swash-backwash zone

Breaker zone

Fig. i l - 1 . General morphological features of a barred sandy coast seen in transverse cross-section.

435

down the face, to approximately the level of the crest of the bar next down the shore. Finally, a new lagoon forms seaward of the bar, sheltering it from waves other than those in the adjacent lagoons. Bars never extend inward to the highest parts of the foreshore, which persists as a smooth, flat area affected by swash and backwash during storms and the higher tides, but exposed to wind action during neaps.

LONGSHORE BARS AND TROUGHS

Form and behaviour Longshore bars and troughs have been studied for almost 125 years. D.W. Johnson (1919), O.F. Evans (1940), and Shepard (1950) summarize the earlier European and North American work, and Zenkovitch (1967) reviews Russian and related contributions. Greenwood and Davidson-Arnott ( 1979) provide a comprehensive recent review. The term longshore bars and troughs covers systems of one or more sand ridges and associated flanking depressions aligned parallel or at an acute angle with coasts of low overall gradient, typically in the range 1 : 200 to 1 : 50. Bars and troughs that are more or less permanently submerged, as in lakes and inland seas, have often been called balls and lows (D.W. Johnson, 1919), but the term balls is inappropriate for such elongated ridges. King and Williams ( 1949) believe that intertidal shore-parallel bars should be separately distinguished, as ridges and runnels or, to use Cornish’s (1898) terms, as fulls and swales. In my opinion (but see Orford and Wright, 1978) there are no compelling morphological or dynamical reasons in favour of this distinction, and all shore-parallel bars, whether intertidal or subtidal, will here be called longshore bars. Longshore bars and troughs can arise wherever wave action is powerful enough to move sand. They occur in lakes (O.F. Evans, 1939, 1940; Wulf, 1963; Varjo, 1969; Saylor and Hands, 1971; Fox and Davis, 1970; Davis and Fox, 1971, 1972a, 1972b; Davis et al., 1972, 1975; Hands, 1976), on the shores of land-locked seas such as the Baltic and Mediterranean (Otto, 1911; W.W. Williams, 1947; King and Williams, 1949; Bruun, 1955; Ajbulatov et al., 1962; Clos-Arceduc, 1962, 1964; Davidsson, 1963; Zenkovitch, 1967; Rudowski, 1970; Wunderlich, 1971; Exon, 1975; Rapp, 1975b), on the shores of oceans of relatively small tidal range (Kindle, 1936a; Wiegel et al., 1954; Shepard, 1950, 1960; Shepard and Moore, 1960; Hoyt, 1962, 1967; Hom-ma and Sonu, 1963; Bowler, 1966; Sonu et al., 1967; Sonu and Russell, 1967; Goldsmith, 1969; Hayes and Boothroyd, 1969; Sonu, 1969, 1972, 1973; Herbich, 1970; Davis and Fox, 1971; Davis et al., 1972; Hayes, 1972; Hunter et al., 1972; McHone, 1972; Wunderlich, 1972; Hayes et al., 1973; Nilsson, 1973; Vincent, 1973; Davidson-Arnott and Greenwood, 1974, 1976; Balsillie, 1975; Davis and Fox, 1975; Greenwood and Davidson-Arnott,

436

Fig. 11-2. Oblique aerial view of straight longshore bars, Miramichi Estuary, New Brunswick, Canada. Photograph courtesy of B. Greenwood.

Fig. 11-3. Air photograph (1.35 by 1.80 km) showing three-dimensional longshore bars, Kouchibouguac Bay, New Brunswick, Canada. Original photograph supplied by the Surveys and Mapping Branch, Department of Energy, Mines and Resources, Canada, and by courtesy of B. Greenwood (see Davidson-Amott and Greenwood, 1976).

437

Fig. 11-4. Oblique aerial view looking south of intertidal longshore bars and troughs, Formby Point, Merseyside, England. Photograph courtesy of John Mills Photography Limited.

1975; Short, 1975a, 1975b; Abele, 1977; Owens, 1977; Owens and Frobel, 1977; Fox and Davis, 1978, 1979a; Owens and Bowen, 1978; Greenwood and Mittler, 1979; Hine, 1979; Hunter et al., 1979; Wrigh et al., 1979), and in enclosed seas of large tidal range, notably the North Sea (Cornish, 1898; Hantzschel, 1938, 1939; W.W. Williams, 1947; King and Williams, 1949; Pugh, 1953; Van Straaten, 1953b; Doeglas, 1955; Reineck, 1960, 1963; Gutsche, 1961; King and Barnes, 1964; Depuydt; 1972; Fuhrboter et al., 1972; Jardine, 1973; King, 1973; Loreau and Purser, 1973; Crofts, 1975; W.R. Parker, 1975; Figge, 1976; Van den Berg, 1977). These accounts permit several generalizations about the morphology of longshore bars and troughs, shown in plan in Figs. 11-2, 11-3, 11-4 and 11-5. Belts of bars and troughs range between about 300 m and 1 500 m wide. They comprise from one to 25 or 30 paired structures in a traverse normal to shore, the forms on average becoming more numerous and closely spaced with decreasing bottom slope. Water depths of 5- 10 m prevail at the outer edges of bar belts developed in large lakes and the seas and oceans, but can be as little as 1-2m in small lakes. The spacing between bar crests almost invariably increases outward from shore, exponentially according to Saylor and Hands (1971). This increase, though striking when just a few bars are

438

(d)

sea

Beadh

Land

Land

Land

Fig. 11-5. Examples of types of longshore bar redrawn from air photographs. Crestal zones shown in black. Scales very uncertain, but bars are in the order of tens of metres transversely apart. a. Part of a field of multiple parallel bars, Gelting Bay, western Baltic Sea (after Exon, 1975). b. Multiple parallel bars, Mediterranean coast (after W.W. Williams, 1947). c. Multiple parallel bars with discordances between groups of bars, Escambia Bay, Florida (after Lau and Travis, 1973). d. Inner crescentic and outer straight bars, Crystal Beach, Florida (after Balsillie, 1975). e. Paired crescentic bars, Mediterranean coast (after W.W. Williams, 1947). f. Multiple crescentic bars, Port Phillip Bay, Victoria, Australia (after Bowler, 1966).

present, is easily overlooked in belts composed of large numbers of individuals (e.g. Varjo, 1969; Exon, 1975). Bar spacing is very variable but ranges from the order of 10-50m for the innermost structures to the order of 75-300 m for the outermost ones. In some belts the bars are long, straight or smoothly curving, and almost perfectly parallel over distances of several to many kilometres, branching and rejoining but rarely. Bars in other belts are slightly sinuous in plan and have crestal zones that locally widen and shoal. The most complex bars are those variously described as arcuate, lunate or cusp-shaped (Figs. 11-3, 11-5d, f). Some examples lack obvious pattern, but others are remarkably regular, the crestal inflections retaining a nearly constant wavelength along the length of an individual bar, but increasing in wavelength outward through the series (e.g. Hom-ma and Sonu, 1963; Owens, 1977). The cusps on these strongly three-dimensional forms invaria-

439

bly point shoreward and, where the innermost bar of a series is of this type (e.g. Figs. 11-3, ll-5d), there may be outward-pointing cusps of the same wavelength and often phase on the adjoining beach. We can also generalize about the profiles of longshore bars and troughs. Most observers (e.g. Shepard, 1950; Saylor and Hands, 1971; Hands, 1976) find that bar height, water depth at the crest, and water depth in the adjoining trough all increase with increasing wavelength outward in the belt, except for the outermost bar of a series, which is often flatter than the others. Hence the bars are similar, as is shown by the uniformity of the ratio of trough depth to crest depth (Fig. 11-6), occasionally reaching Keulegan's

Depth of bor crest below meon 8eo level, h2 (ml

0

2

I

3

5

4

6

,

0 KEY

o Washington / Oregon coost 0 South Collfornh beoches AEost Coost of U. S. A.

0 A

0

m

A

. . . .

.

\

A

A

A

\

W

O

Fig. 11-6. Depth relationship for longshore bars on the coasts of the U.S.A. Data of Shepard (1 950).

440

(1948) experimental value of 1.69, and by the ratio of wavelength to crest height, which ranges between about 25 and approximately 150. Most permanently submerged bars are slightly asymmetrical, having a well rounded crest that separates a straight to weakly convex-up face from a slightly steeper lee. However, an exaggerated impression of the degree of their asymmetry can be gained from the fact that, as the bars occur on a sloping bed, the lee is always shorter than the face. Intertidal bars commonly have a broad shoulder sloping gradually landward that passes into a short lee inclined at up 30" or so. Longshore bars experience seasonally or with individual storms varying amounts of change in position and shape, the innermost forms being the most changeable. Exon (1975) reports that the outer bars of one belt in the Baltic Sea are sufficiently stable as to support carpets of sea grass and mussels on their flanks. O.F. Evans (1940) and Davidson-Arnott and Greenwood ( 1975) describe bars of a similar long-term positional stability, shown by their persistence from year to year and their oscillatory rather than migratory behaviour. Balsillie (1975) reports seasonal changes in the two-bar belt of the Florida coast, the inner bar being straight in summer but strongly cusped during the stormy winter. At many sites, storms flatten rather than erase bars. At others, storms completely smooth the foreshore and shallower offshore, the subsequent growth of bars that migrate upslope before welding on to the upper beach marking shore recovery (Davis et al., 1972; Hayes, 1972; Abele, 1977). Most bars gradually migrate onshore, though somewhat hesitantly and with short periods of reversed motion (King and Williams, 1949; Shepard, 1950; Bruun, 1955; Doeglas, 1955; Davidsson, 1963; Seibold, 1963; Bajorunas and Duane, 1967; Saylor and Hands, 1971; Sonu, 1973; W.R.Parker, 1975; Short, 1975a, 1975b). Such bars commonly lie at a very acute angle to the coast, indicating that their movement is longshore as well as upslope. Short (1975a, 1975b) found bars on the Alaskan coast that were attached at intervals of approximately 220 m and moved onshore at about 1.2 m per day. Saylor and Hands (1971) reported much slower rates for Lake Michigan bars, in the order of 1 m per month.

Controls on longshore bars Longshore bars and troughs could from their settings depend on wave action, tidal action, unidirectional longshore currents, or some combination of these three. The over-riding importance of wave action is clear from the fact that forms strongly resembling longshore bars can be made in laboratory wave tanks in the absence of tidal effects or significant unidirectional longshore currents (Bagnold, 1947; Keulegan, 1948; Hensen, 1957; McKee and Sterrett, 1961; Nayak, 1970; Carter et al., 1973), and that these forms respond to changes in water level and wave character in a similar manner to natural

44 1

L c 0

g

2 -

e 0

.c

K)-2

.

f

8 -

k

6 -

0

%4

f

s

4 -

2s 2

2

4

6

8

4

68i03

2

4

6elO4

102

Non-dimsnsional deep-water

wave height, H / D

Fig. 11-7. Nayak's (1970) criterion for longshore bars.

bars (Keulegan, 1948; Nayak, 1970; Hands, 1976). Combining his own with earlier experimental data, Nayak derived a criterion for bar occurrence in terms of the ratio of wave height, H , to wavelength, L, in deep water (wave steepness) and the ratio of wave height to the median diameter, D , of beach sediment (Fig. 11-7). Steep waves and fine sediments favour bars. The early idea that bars depend fundamentally on unidirectional longshore currents, already rejected by O.F. Evans (1940), is even more firmly refuted by this experimental evidence. However, this is not to say that longshore bars are entirely uninfluenced by coastwise currents. Many three-dimensional bars seem to occur when and where there are significant unidirectional longshore currents (Hom-ma and Sonu, 1963; Sonu, 1969, 1972, 1973; Sonu et al., 1967; Sonu and Russell, 1967). Moreover, Hensen (1957) and Gutsche ( 1961) made such bars experimentally using obliquely incident waves that created a longshore flow. The field affords no evidence that tideless conditions are necessary for the development of three-dimensional bars, as urged by C.A.M. King (1959, 1972). The tide may merely moderate the tendency for waves to form bars (Watts and Dearduff, 1954). There exist three explanations as to how waves determine the occurrence and character of longshore bars: (1) the bars occur where waves break in the plunging mode (Galvin, 1968) and each bar in a series represents waves of a particular height, the waves of each height being associated with a particular storm or season, (2) the bars represent a complex interaction between the shape of the bottom. and the shape of the waves, the one modifying the other, and (3) the bars are due to the standing waves formed from the incident train and its reflection from the beach. The first theory is one of the oldest concepts in coastal geomorphology,

442

dating to Elie de Beaumont in 1845 (D.W. Johnson, 1919; O.F. Evans, 1940). It continues to attract adherents (Shepard, 1950, 1963; King, 1959, 1972; Varjo, 1969; Dyhr-Nielsen and Sorensen, 1970; R.L. Miller, 1976), despite the fact that (1) many waves spill rather than plunge when breaking on longshore bars, and (2)most outer bars lie too deep to break even extreme waves. The second explanation, stated explicitly by Boczar-Karakiewicz ( 1975) and implicitly by Davidson-Arnott and Greenwood (1976) and by Hands (1976), depends on the fact that a wave in passing over a submerged barrier is strongly modified but in travelling into deeper water beyond tends to reform (Wiegel and Fuchs, 1955; McNair and Sorensen, 1971; Bryant, 1973; Chandler and Sorensen, 1973), a process that could be repeated several times as waves advanced through gradually shoaling water. One attraction of this concept is that bars of a given size are not treated as dependent on waves whose occurrence is limited to particular times. Instead, each series of bars is regarded as expressing a particular wave climate and sediment availability. A serious weakness is that no mechanism is apparent for actually building the bars; secondary currents must be present if bars are to be built up from a flat bed. The most plausible explanation for all but strongly three-dimensional longshore bars and troughs is that they are due to standing waves formed by the reflection of the incident train from the beach. Lettau (1932) suggested that suspended sediment affected by standing waves would move toward antinodes and be deposited as bars. Nomitsu (1943) thought that bars would arise beneath both nodes and antinodes. Bagnold (1947) attributed his experimental series of bars to a weak reflection from the beach, and noted that the structures occurred at a spacing of half the wavelength of the surface waves, beneath nodes. Noda (1969), however, found experimentally that bars occurred beneath antinodes though predicting their formation at nodes. Bowen (1975) concluded that either the nodes or the antinodes could be the sites of longshore bars. In important contributions, Mei et al. (1972) and Carter et al. (1973) investigated both mathematically and experimentally the properties of partly reflected waves in water of uniform undisturbed depth, together with the related movement of bed sediment. The work extends the theoretical studies of Longuet-Higgins (1953) and Hunt and Johns (1963) on mass transport in finite-amplitude waves to the general case of partly reflected waves (see also Dore, 1976, 1977). The outcome of their lengthy analysis is that the magnitude and direction of the mass transport in the bottom boundary layer depends on the extent to which the energy of the progressive incident wave is reflected by the beach or other barrier. With no reflection, the mass-transport velocity is uniform and in the same direction as the wave propagation, just as Longuet-Higgins found. Provided that the reflection coefficient is less than 0.414, the mass transport continues to be in the same direction as the

443 wovelength of surfoce wove

-One (01

-

___-------.. f. .___ __----. ,’ -__. ....-/.,

1 Antinode

Surfoce wove envelope

Node

wovelength of surface wove

-One (b)

-

,Surface wove envelope

Antinode Antinode

Antinode (trough)

Antiiode (trough)

Fig. 11-8. Summary of currents created by progressive waves partly reflected from a coast. a. Distribution of maximum near-bed orbital velocity in relation to nodes and antinodes on free surface. b. Distribution of mass-transport currents due to the wave motion. Adapted from Mei et al. (1972).

incident waves, but is non-uniform on a scale related to that of the wave. A non-uniform transport rate of bed sediment should result, which could shape low bars parallel with wave crests. Bars and troughs are certain to arise when the coefficient exceeds 0.414, for the mass-transport velocity is then reversed in direction each one-quarter of a wavelength, a result confirmed experimentally by Mei et al. (1972). Figure 11-8a shows that the maximum orbital velocity beneath a strongly reflected wave occurs beneath nodes. The pattern of mass transport is complex but divisible into cells (Fig. 11-8b). In the bottom boundary layer, the near-bed flow is toward nodes and away from antinodes, whereas in the outer flow it is toward antinodes and away from nodes. Sediment transported as bedload therefore accumulates at nodes, as bars with a spacing of one-half the wavelength of the incident waves. At antinodes, where the orbital velocity is a minimum, is deposited sediment fine-grained enough to have elsewhere penetrated upward in suspension into or through the bottom boundary layer. The reflection coefficient is a crucial parameter in this model of longshore bars and troughs. Under laboratory conditions (Mei et al., 1972), the coefficient increases with decreasing wave steepness but increasing sediment calibre, which leads to steeper equilibrium beach slopes (Fig. 11-9). Most barred coasts are flatter and affected by steeper waves than would be the case if a reflection coefficient of 0.414 were an absolute criterion of bar formation. Many bars may therefore depend on the non-uniform onshore mass transport promoted at smaller values of the coefficient. Does this basic model cover the more realistic case of water depth

444 0.7

0.6 c

c

m

.- 0.5 ‘0 * 0 0

-

0.4

0

c 0

-

5 0.3 0:

0.2

0.1 0

I

0

I

I

0.005 0,010 0.015

0.020 0.025

0030 0.035

I

0.040 0.045 0.050

Wave steepness in deep water, # / L

Fig. 11-9. Wave reflection coefficient and slope of upper part of beach as functions of wave steepness in deep water, for different grades of beach material. After Mei et al. (1972).

increasing outward from shore? Lau and Travis (1973) calculated the mass transport velocity due to slowly varying finite-amplitude waves reflected from a plane sloping beach. They confirmed the critical reflection coefficient of 0.414 derived by Mei et al. (1972), and found that the spacing of nodes, where bars should form, increased monotonically outward from shore, as is observed for natural bars. The origin of strongly three-dimensional longshore bars is far from clear.

. . . . . . _ .. ._... .. .. .. . .. .. . . . . .;._. . . . . . .. .. .. : . . . . . B e a c h . . . : .. . .. ... ._.. ... . ... . . . . . . . . .. .... .. .. . . . . . .. .. . .. .. _ . . ... . .. _. . . . ( a ) . . . . . . . . .: . .. . . .. .. . . . . . . . . _ . . ’

Fig. 11-10. Patterns of secondary currents associated with different types of three-dimensional longshore bar.

445

Any theory, however, must be consistent with the field observations of Sonu et al. (1967) and Sonu (1969, 1972, 1973), who found that such bars when innermost are associated with cell-like horizontal water circulations under conditions of normally incident waves, but with meandering longshore currents when arrival is oblique (Fig. 1 1-10). Three explanations demand consideration. King and Williams (1949), C.A.M. King (1959, 1972), and Riviere et al. (1961) suggest in essence that arcuate bars represent the action of two sets of waves coming from different directions, but do not elucidate a mechanism to bolster their proposal. This explanation is like that of Branner (1900) for beach cusps and has some support (Dalrymple, 1975). Clos-Arceduc (1962, 1964) developed in some detail the idea that the remarkably regular crescentic bars found off enclosed beaches represented a stationary coupling between incident waves and standing oscillations trapped between headlands. This idea is strongly supported by the experiments of Escher (1937), who made combinations of a cusped beach and cusped longshore bars by the combined action of progressive waves and standing waves at right angles. It was later extended to a demonstration that a stationary (or very slowly travelling) coupling is possible between normally (or nearly normally) incident waves and edge waves created as the result of the reflection of the incident train from a plane beach (Bowen and Inman, 1969; Guza and Davis, 1974; Guza and Bowen, 1975, 1976; Minzoni and Whitham, 1977). Since the edge waves arise by the instability of the incident train, long beaches unbounded by one or more reflective headlands could be affected, a conclusion supported by Huntley and Bowen’s (1973, 1974) detection of edge waves on such a beach. The horizontal pattern of near-bed mass transport calculated for standing edge waves is consistent with the form of strongly three-dimensional bars (Bowen and Inman, 1971; Bowen, 1973) and is not incompatible with Sonu’s field observations. Sonu (1969) compared crescentic bars to dunes formed by unidirectional currents, rejecting earlier expressions of the edge-wave theory of bars (Sonu, 1972, 1973), mainly on the grounds that the bars are generally too large to be compatible with the scale of ordinary incident waves. This particular objection loses force before recent developments in edge-wave theory, but two difficulties nonetheless remain. Under edge-wave theory, the incident waves must arrive normally or very nearly so, whereas markedly oblique waves are capable of producing the bars experimentally (Hensen, 1957; Gutsche, 1961) and in the field. Secondly, systems of multiple bars predicted under edge-wave theory seem to be characterized by a single coastwise cusp-spacing, regardless of water depth (Bowen and Inman, 1971). Hom-ma and Sonu (1963), however, found that cusp spacing increased outward in bar belts, as shown in Fig. 11-5f.

446 MINOR SEDIMENTARY STRUCTURES ASSOCIATED WITH LONGSHORE BARS AND TROUGHS

Intertidal bars and troughs The smaller scale sedimentary structures associated with intertidal longshore bars and troughs have been known for many years. They reflect the interplay between beach shape and changing water level, with its profound effect on tidal currents and on the magnitude, direction, and variety of wave-generated flow. Wave and tidal action during ebb periods seem most to influence the minor sedimentary of barred beaches. However, W.R. Parker’s (1975) division of barred beaches into two hydrodynamic environments-ridges dominated by breakers, and troughs dominated by tidal and longshore currents (Fig. 11-1 la)-is perhaps too generalized to be an acceptable framework in which to examine the distribution of minor forms, which demands the recognition of at least four morphodynamic zones (Figs. 11-1, 11-1 lb). These are: (1) the bar face, dominated by shoaling and breaking waves and by swash-backwash, (2) the bar crest and shoulder, dominated by breaking waves and wave-generated landward surges, (3) the bar lee, where the bed abruptly plunges steeply into calmer water, creating

KEY

- Wave ripples Current rippler

nn

Y

vv g

Dunes Antidunea or plane beds Rhomboid dunes a n d / o r ripples Current direction

Fig. 1 1- 1 1. Morphology, currents, and bedforms associated with longshore bars, particularly those that are oblique and intertidal. Bedform type and distribution can change rapidly in response to changing wave and tidal conditions, and may not at all instants reliably indicate the subsurface structures.

447

flow separation, and (4) the trough floor, dominated by coastwise currents and, after emergence of the bar, by waves related to the local wind. Figure 11-1 l c shows the general pattern of currents, which depends in detail on the acuteness with which the bar joins the upper foreshore. Where the angle of join is very small, essentially onshore and alongshore currents prevail, but both the bar and trough flows grow more oblique as the angle increases.

Fig. 11-12. Intertidal longshore bars, coast near Burnham Overy Staithe, Norfolk, England. a. Looking east along trough landward of bar, with bar face to left. b. Close-up of (a) toward eastern end.

448

Van Straaten (1953b) made an early systematic study of the minor surface structures of barred beaches, pointing out their marked spatial differentiation. This work was extended by Reineck (1960, 1963), who mapped a section of barred beach 2 km long, and by W.R. Parker (1975). Many others have contributed to knowledge of minor structures on barred beaches (Hantzschel, 1938, 1939; Doeglas, 1955; Hoyt, 1962, 1967; Wunderlich, 1971, 1972; Davis et al., 1972; Hayes, 1972; Abele, 1977). Figure 11-1 Id, e shows the two most commonly observed distributions of minor sedimentary structures. The bar face is almost invariably a smooth, seaward-dipping slope marked only by plane beds and belts of antidunes aligned parallel with the beach, together with swash marks, and parting lineations aligned normal to the bar. Seaward these pass into the dunes and/or ripples of the trough floor. The bar crest and shoulder are last affected during the ebb by wave-generated shoreward surges of water. Here occur plane beds, landward-facing rhomboid ripples and dunes, and, occasionally, landward-facing current ripples, usually strongly three-dimensional, flat, and tending toward the rhomboid form. Shallow overwash channels occasionally appear on the bar shoulder, terminating landward in lobes of sediment that represent deltas built on the bar lee (e.g. Owens and Frobel, 1977). The bar lee (Fig. 11-12) is seldom less than 0.15 m in height or more than 1.25 m. It is a steep landward-dipping slope, often attaining 30-35" and in calm weather showing signs of avalanches. The toe is rounded and shades off into the floor of the trough to landward. The rim varies from sharp to rounded, depending on the extent of modification of the lee by wave and current action during the ebb. The bar lee is usually straight to smoothly curved in plan and lobate only where bar-shoulder overwash flows become channelized. Water draining from the bar after the ebb commonly results in rill marks on the lee face. Wave action in the landward lagoon may create flights of clifflets on the bar lee. Trough floors vary most in space and time. Spring tides and obliquely incident waves generate strong longshore currents that build small dunes aligned across the axes of the troughs (Fig. 11-1Id). As stage falls, progressively gentler currents round off the dunes, which may eventually be masked by wave-related ripples. Under less extreme conditions, and particularly in troughs that lie high up on the foreshore, longshore-facing current ripples are generated by the flows along the troughs (Fig. 11-1le). Wave-related ripples become superimposed on them if water is ponded in a trough and the local wind is strong enough. Mud layers draping ripples and dunes are commonly deposited in troughs after stormy weather. Onshore bar movement after storms is generally more vigorous than concomitant upward growth. Hence barred beaches should internally be dominated by trough and bar-lee sediments, rather than by bar-face and bar-shoulder deposits. Excavation of exposed bars (Fig 11-13) reveals that landward-dipping cross-beds formed on the bar lee interfinger with, or pass

449

Landward

Seaward

Fig. 11-13. Vertical section showing internal structure of an intertidal longshore bar, July 1966, Crane Beach, Ipswich, Massachusetts, U.S.A. After Davis et al. (1972).

laterally into, nearly horizontally bedded sands formed on the bar shoulder (Doeglas, 1955; Hoyt, 1962; Reineck, 1963; Davis et al., 1972; Hayes, 1972; Wunderlich, 1972). The discontinuities disturbing the cross-beds record intermittent bar movement and are probably related to periods of exposure, when the lee face was smoothed and scoured by waves and currents acting in the troughs. Figure 11-14, taken from the Plum Island beach, Massachusetts (Hayes, 1972), shows the landward-dipping cross-beds of a bar that was deeply buried by bar-shoulder deposits during subsequent beach accretion. In the two North Sea beaches studied by Van den Berg (1977), however, bar-shoulder deposits, and the seaward-dipping parallel-laminated sands of the bar face, are less extensively preserved than bar-lee and trough sediment.

Fig. 11-14. Vertical internal structure (sea toward left) of an intertidal longshore bar, Plum Island, Massachusetts. Photograph courtesy of M.O. Hayes.

450

Again the bar-lee deposits are landward-dipping cross-beds, but the troughs afford cross-laminated sands related to rippling, trough cross-bedded sands formed by dunes, and occasional mud drapes. Generally longshore currents are indicated by the trough deposits. As might have been expected from the growth and onshore movement of longshore bars, trough deposits tend to be overlain by those of the bar lee.

Submerged bars and troughs Practical difficulties have held back knowledge of the surface and internal structures of submerged bars and troughs as compared with their intertidal counterparts. The distribution of surface forms, established principally by Ajbulatov et al. (1962), Rudowski (1970), Davidson-Amott and Greenwood (1974, 1976), Greenwood and Mittler (1979), and Hunter et al. (1979), is not unlike that on the intertidal features already described, with the significant difference that features recording exposure or very shallow water are lacking. We therefore concentrate on internal structures. Werner (1963), Newton (1968a, 1968b), and Exon (1975) examined submerged bars in the Baltic Sea. Exon’s rather flat and symmetrical bars are commonly structureless and bioturbated internally, with a thin outer layer of cross-laminated sediment. Occasional bars are parallel-laminated or thinly cross-bedded, landward and seaward dips being observed. A thick outer layer of wave-ripple cross-laminated sand typifies the bars sampled by Werner and by Newton. Davidson-Arnott and Greenwood (1974, 1976), and Greenwood and Mittler ( 1979), have examined the internal structure of submerged longshore bars off the considerably more energetic Atlantic coast of Canada. The observed facies (Fig. 11-15) vary spatially on a bar and with the relative position of that bar. Beneath bar faces lie seaward-dipping parallel-laminated sands, related to plane beds formed by the more extreme waves, erosively overlying cross-laminated sands that represent wave and wave-current ripples of calmer periods. There is less cross-laminated sand beneath the face of the inner bar than the outer, a reflection of the generally more disturbed conditions in shallower water. On bar crests, where wave currents are vigorous, a combination of plane beds and strongly three-dimensional dunes creates interfingering trough cross-bedded and parallel-laminated sands, with some cross-lamination during calms. The inner and outer bars differ most in terms of their lee deposits. The outer bar presents to lee the same facies as on its seaward side. The inner bar, however, has an internal structure very similar to its intertidal counterparts, consisting mainly of steeply landwarddipping cross-beds. The differences are that the submerged bar is capped by cross-laminated sand and, possibly, has fewer discontinuities amongst the cross-beds. Cross-laminated sand predominates in the troughs between bars. Bars on the considerably more energetic coast of Oregon (Hunter et al.,

45 I

Fig. 11-15. Schematic profile (a) and internal structures (b-h) at various sites in a pair of submerged longshore bars, Kouchibouguac Bay, New Brunswick, Canada. Photographs courtesy of B. Greenwood (see Davidson-Amott and Greenwood, 1974). Each photograph represents a vertical relief cast measuring approximately 0.3 by 0.45 m. -

452

1979) are typified by landward-facing cross-beds on the crests. In the troughs, cross-bedding indicative of strong longshore flows is often seen. This pattern of structures in the Canadian bars is matched by a pattern of grain size. The coarsest deposits occur in the troughs, as noticed by Brand ( 1959, Mothersill ( 1969), Saylor and Hands ( 197l), Greenwood and Davidson-Arnott (1972), and Hunter et al. (1979), but the sediments offshore are on the whole finer grained than those inshore. Fox et al. (1966) are the only workers to record the coarsest sediments from bar crests. No longshore bar deposits have been conclusively identified in the stratigraphical record, although the claim by Roep et al. (1979) is a powerful one. However, Goldring ( 1966), Allen ( 1974a), Goldring and Bridges ( 1973), De Raaf et al. (1977), and Roep et al. (1979) have all recognized in shallow-water sandstones, and attributed largely or wholly to wave-action, repeated couplets of parallel-laminated overlain by cross-laminated sandstone somewhat resembling the flank deposits of the outer bars described by Davidson-Arnott and Greenwood ( 1976).

TRANSVERSE BARS

On sandy shores where wave action is moderate or weak, transverse (finger) bars may be present instead of, or in addition to, longshore bars. Transverse bars are long, narrow, straight-crested bars that project obliquely outward from the shore into shallow water (O.F. Evans, 1938a; Zenkovitch, 1967; Niedoroda and Tanner, 1970; Niedoroda, 1973a, 1973b; Barcilon and Lau, 1973; R.W.G. Carter, 1978a). The bars occur in trains at an average spacing along the shore ranging from the order of 10 m to many hundreds of metres. Bar length is 1-3 times the longshore spacing. Bars either gradually fade away into deeper water or terminate in broad spade-like shoals; occasionally bars bifurcate toward deeper water. The sediment on the bars seems to be coarser than in the troughs between. Niedoroda and Tanner (1970) observed in the field that waves were refracted toward the bars and tended to spill in the shallows of the bar crests. They noticed that an onshore current along the bars crests was compensated by a weaker outward flow in the deeper water between bars, the two currents together forming a gyre. Laboratory experiments and theoretical calculations in which the observed current pattern was reproduced suggested to them (see also Niedoroda, 1973a, 1973b) that the bars could arise as the result of an unstable interaction between slight prominences on the sea bed and normally incident waves, provided that the water was sufficiently shallow and shoaled gradually enough. The bars that R.W.G. Carter (1978a) observed where formed on a beach adjoining a rocky headland, and he therefore proposed that they were initiated by the action of opposed longshore currents. A connection between the bars and surface

453

waves was denied by Barcilon and Lau (1973), who proposed instead a potential-flow model related to that of Kennedy (1969), in which the bars are ascribed to unidirectional longshore currents. Although observed bar wavelengths and offshore slopes appear to support this model, whereas Niedoroda and Tanner offer no mechanism for the control of wavelength, an origin of transverse bars due to wave-action is more plausible. Nothing has been published on the internal structure of these transverse bars.

BEACH CUSPS

Character and distribution

Beach cusps are amongst the oldest known and most familiar of foreshore structures, being commonest and best developed around high tide mark. They are series of regularly spaced, shallow embayments that face and plunge seaward and join at sharp, seaward-pointing horns (Figs. 11-16, 11-17). Each series occurs at a single level on the foreshore, but there may be more than one series, differing in character and age, on a given shore at any one time. Beach cusps are one of a number of partly hierarchical cusped coastal forms that range in scale up to a spacing in the order of 100-1000

Fig. 11-16. Beach cusps 10- 15 m in wavelength on a pebble beach, view at mid tide looking southeast from cliffs in centre of Swanlake Bay, near Tenby, Dyfed, Wales.

454

Fig. 11-17. Starved or juvenile beach cusps of.grave1 on a sandy base, coast northeast of Holm-next-the-Sea, Norfolk, England. Trowel stuck in sand is 0.28 m long.

km (Dolan, 1971; Hoyt and Henry, 1971; Dolan et al., 1974, 1979). The term here covers forms with a longshore horn spacing from as little as 0.1 m (shores of small lakes) to as much as 50-75 m (open ocean coasts). The smaller of these are Dolan’s “cusplets”; the larger are his “cusps” and the smaller of his “sand waves”. Beach cusps were first described by Palmer (1834) from the south coast of England, and have since been widely reported from lakes and inland seas (O.F. Evans, 1938a; Bagnold, 1940; Rudowski, 1964; Panin, 1967; Zenkovitch, 1967; Komar, 1973), and particularly from tidal seas and the open ocean (Cornish, 1898; Jefferson, 1899; Branner, 1900; D.W. Johnson, 1910, 1919; Shepard, 1935; Timmermans, 1935; W.O. Thompson, 1937; Kuenen, 1948a; Guilcher, 1949; Boye, 1954; Norris, 1956; Bascom, 1960; M i , 1958; Longuet-Higgins and Parkin, 1962; Otvos, 1964; King, 1965; Russell and McIntire, 1965; Milling and Behrens, 1966; Gadow and Reineck, 1968; Worrall, 1969; Depuydt, 1972; Schwartz, 1972; A.T. Williams, 1973a; Dolan et al., 1974; Shirai and Tsuchiya, 1974; Abele, 1977; Darbyshire, 1977; Keeley, 1977; Dubois, 1978; Fox and Davis, 1979a; Sallenger, 1979b). The work particularly of D.W. Johnson, Kuenen, Mii and Rudowski reveals at least four intergrading varieties of beach cusp. The two commonest (Fig. 1 1- 18a, b) are marked by well-defined embayments and horns. They differ by the presence in the one case (Fig. 1 1-16) of either a steadily declining slope or a slight bench further down the beach, and in the other by the occurrence lower on the beach of distinct delta-like bodies of sediment, one to each cusp, or locally to two or three cusps. The third variety, identified by Russell

455

Seaward

Seaward

Fig. 1 1-18. Schematic types of beach cusp.

and McIntire (1965) as juvenile, is represented by triangular mounds of gravel or shell debris surrounded by sand, the embayments being relatively shallow and the horns little marked (Figs. 11-17, 11-18c). Beach cusps of the fourth variety (Fig. 11-18d) are restricted to the berm crest or the crest of a bar lower down. They combine seaward-facing embayments with landwarddipping barkhan-like avalanche surfaces. Most beach cusps are symmetrical in plan, the axes of their horns and embayments lying normal to the beach. Some series consist of asymmetrical cusps, the embayments and horns pointing obliquely down the strand. The cusps sketched in Fig. 11-18c exemplify well the distribution of sediment on beach cusps. The horns generally reveal the coarsest debris, though coarse sediment often is also concentrated along the axes of the embayments.

Controls on beach cusps Beach cusps occur in sand, gravel, and mixed gravel-sand (e.g. Russell and McIntire, 1965), and are even to be found where cobbles and boulders are present. They therefore mark beaches which range in overall slope from a few degrees to the order of 20". Mii (1958) measured a weak direct

9SP OE

a

I OE

lo*

02 a a

a

a

a .

8

a

.

8 6 01

L Z 9

*

E: z

t?=

E q I; 2

I a

a

6.0

3.0

L .o 3.0 321s

I

NlV'tlD

Fig. 11-19. Wavelength and horn length of beach cusps as a function of the calibre (Wentworth grade) of beach material. Data of Mii (1958).

correlation between cusp spacing and coarseness of beach material, and another between horn length and coarseness (Fig. 1 1- 19). Guilcher ( 1949) also reported finding the largest cusps in the coarsest beach sediments. These findings are consistent with Longuet-Higgins and Parkin’s ( 1962) conclusion that sediment mobility under wave action is a necessary condition for cusp formation, and with a variety of reports suggesting some sort of control of cusp size by wave scale. D.W. Johnson ( 1910) firmly believed that the largest cusps were built by the greatest waves. Russell and McIntire (1965) found as the result of their extensive survey that the largest cusps occurred on the most exposed coasts, where the coarsest sediment tended to be found, thus implying an increase of cusp size with wave scale. Although attempts to correlate cusp wavelength with wave height are rather unrewarding, there is an excellent direct correlation with the length of the swash or surf zone. A.T. Williams (1973a) found that on Hong Kong beaches the wavelength was about twice the swash length. Longuet-Higgins and Parkin (1962) noted a less straightforward increase of cusp size with swash length. Worrall(l969) gives supporting evidence from the West Coast of Africa. He describes cusps 85-95 m in wavelength associated with powerful and prolonged swashes. See also Guza and Bowen ( 1981). Not all sea conditions favour cusp formation. Beach cusps seldom result

457

from the confused waves associated with storms, but are most favoured by calm conditions bringing regular, normally incident waves that surge on the shore rather than break by plunging or spilling (D.W. Johnson, 1910; Shepard, 1935; Kuenen, 1948a; Mii, 1958; Longuet-Higgins and Parkin, 1962; Rudowski, 1964; Russell and McIntire, 1965; Komar, 1973). Beach cusps have been made experimentally by the action of normally incident simple waves on mobile sediment (D.W. Johnson, 1910; Timmermans, 1935; Bagnold, 1940; N.C. Flemming, 1964). Cusps that trend obliquely across the beach, however, have been reported by Rudowski (1964), Russell and McIntire (1965), and Zenkovitch (1967). The fact that in some instances oblique waves were also observed shows that normal wave incidence is not a necessary condition for cusp formation. A large tidal range may weaken cusp development (Shepard, 1935), presumably because the water level shifts too quickly for there to be much sediment rearrangement. Field observations show that there are two different patterns of secondary currents associated with beach cusps. Kuenen (1948a), Norris (1956), Komar (1971), and A.T. Williams (1973a) observed that wave motion over cusps created a horizontal circulation of water and sediment from embayments to horns. Guilcher (1949) also noticed this pattern, but only at times of relatively high water level when the more steeply sloping parts of the embayments and bolder portions of the horns were covered. The opposite pattern of circulation, from the horns to the embayments, was reported by Bagnold (1940), Longuet-Higgins and Parkin (1962), Russell and McIntire (1965), and Worrall (1969). Guilcher (1949) noticed it only at times of low water, when the bolder and more steeply sloping parts of the cusps were emergent . Guilcher’s (1949) observations hint that the boldness of the cusp topography and local slope of the beach control for given wave conditions the circulation over cusps. This inference finds support in Komar’s (1971) experimental generation of cusps on an initially plane sand beach. The circulation was at first from horns to embayments, but at a critical stage in the strengthening of the topography, a circulation from embayments to horns developed. Eventually the waves and the shape of the beach achieved equilibrium, when circulation ceased altogether.

Theories of beach cusps Much early discussion centred on the question of whether beach cusps were essentially erosional in origin (D.W. Johnson, 1910, 1919), or whether deposition was significant in their formation (Kuenen, 1948a). The structures are certainly partly erosional, for bedding is often exposed in the backs of embayments, but deposition plays an undeniable role in shaping horns and deltas, adding layers to the floors of embayments, and in preserving many forms substantially whole (e.g. Mii, 1958; Otvos, 1964; Worrall, 1969). Later

458

work has concentrated on the mechanics of cusp spacing and circulation. Branner ( 1900) suggested that beach cusps resulted from the intersection of two incident wave-trains approaching from different directions. Although dismissed by D.W. Johnson (1910), and subsequently given little attention as an explanation of beach cusps, Branner’s mechanism could be operative in certain instances. The circulation over beach cusps closely resembles that in rip-current systems, and some of these systems are associated with intersecting wave trains, the spacing of the rips being related to the coastwise length of the diamond pattern of wave intersections (e.g. Inman et al., 1971, fig. 1). With this clue, Dalrymple (1975) showed theoretically that rip currents could be created by intersecting progressive waves of the same period (see also Dalrymple and Lanan, 1976). The waves set up periodic longshore variations of water level which drive longshore currents; these escape offshore as rips which could mould a beach into cuspate forms. Under this theory, cusp spacing reflects the wave length in deep water and the approach angles, being not less than one-half the wave length. Longuet-Higgins and Parkin ( 1962) introduced the idea that beach cusps might depend on edge waves (Vol.1, eq. 1.56) that interacted with the incident waves to produce horizontal gyres, but found little agreement between the observed wavelengths and the wavelengths of the edge waves as they calculated them. Komar (1973) attributed to edge waves the small beach cusps he measured from Mono Lake, California, but he did not see the waves, and again obtained only a modest agreement between his observed and calculated spacings. Later, Darbyshire (1977) and Darbyshire and Pritchard (1978) showed that the spacing of beach cusps, including LonguetHiggins and Parkin’s, was about one-half that of the edge waves that could have been generated by the incident progressive waves. Darbyshire (1977) nevertheless rejected the edge-wave model in favour of a complex explanation depending on the interaction of the incident waves refracted some way offshore. However, it is unwise to reject the edge-wave model, for Escher (1937) and Komar (1971) showed experimentally that the combination of normally incident with standing waves at right angles (effectively edge waves) will generate horizontal gyres involving rips that can mould a mobile beach into forms resembling beach cusps. A similar kind of circulation is to be expected from edge waves alone or from a combination of progressive with edge waves, and is known experimentally to form above rigid beds (Bowen, 1969a, 1969b; Bowen and Inman, 1969, 1971; Huntley and Bowen, 1973, 1975; Guza and Inman, 1975). An analysis by Sallenger ( 1979b) allows the observations of LonguetHiggins and Parkin (1962) and of Komar (1973), together with the puzzling conclusion of Darbyshire (1977) that cusp spacing is about one-half the wavelength of edge waves, all to be reconciled with edge-wave theory. Equation (1.56) in Vol. I can be rewritten:

L = ( g / 2 n ) ~ ’sin(2n

+ I)p

(11.1)

459

in which L and T are respectively the wavelength and period of the edge waves, g is the acceleration due to gravity, p is the beach slope, and n is a positive integer describing the edge-wave mode. Now edge waves may be either synchronous, when their period is the same as that of the incident waves, or subharmonic, when they possess exactly twice the period. Under field conditions only subharmonic edge waves are observed (Huntley and Bowen, 1973), the zeroth ( n = 0) mode being the the most likely to occur (Huntley and Bowen, 1973;-Guza and Davis, 1974). Now Sallenger points out that subharmonic edge waves should create cusps with a spacing of one-half the edge-wave wavelength. That this is indeed the case is strongly suggested by the data assembled in Fig. 11-20, amplifying Sallenger’s results, in which the calculated cusp spacing is taken largely as one-half of the edge-wave wavelength and the zeroth mode is for the most part used. Cloud (1966) suggested that beach cusps might express Plateau’s instability, the varicosities that develop in a cylinder of fluid in slow axial motion relative to another of similar viscosity and density (e.g. vapour trails of jet aircraft). A parallel was drawn between the breaking wave and a cylinder of fluid, but the comparison is insubstantial. Gorycki ( 1973b) suggested that beach cusps were related to the salients representing instability at the leading edge of a sheet of water-the bores of swash resulting from breaking waves -as it advanced over a flat surface. Although the salients are associated

40

1

4 0

0.8 0.6

t

-

KEY o Longuet-Hlgginr a Komar (19731

0.4 -

04

-

-

Porkin (19621

Darbyshire (1977)

+ Dubois (1978)

$a

0.2

a

/: I

I

t

,

I

I

I

l

l

I

,

Fig. 11-20. Calculated compared with observed beach cusp wavelengths. The calculated wavelength is given in most cases on the basis of subharmonic edge waves of zeroth mode. The graph plotted is the line of perfect agreement.

460

with an appropriate circulation pattern, the localized appearance of surf bores and swash is better explained by longshore variations in wave height at breaking. Hino and Hayashyi (1973) and Hino (1974) undertook a more thorough and fruitful exploration bearing on beach cusps as an instability phenomenon. They showed theoretically that the uniform wave set-up on a straight beach of uniform slope is unstable to small disturbances, so that the level of the water surface assumes a periodic longshore variation. As a consequence, horizontal circulatory currents involving rips are created under conditions of normally incident waves, and meandering longshore currents combined with horizontal circulations when the waves arrive obliquely. They also showed that the longshore period of the rips is approximately four times the surf-zone width, a result confirmed by both their own and McKenzie’s (1958) field observations of rip-current spacing. This theory is attractive as an explanation of beach cusps by reason of its generality and the fact that direct correlations between longshore cusp spacing and swash width have been reported (Longuet-Higgins and Parkin, 1962; A.T. Williams, 1973a). Quantitatively, however, the agreement between theory and observation is so far poor. Related work is described by LeBlond and Tang (1974), Dalrymple and Lozano (1978), and Miller and Barcilon (1978). Mei and Liu (1977) proposed an interesting model of nearshore horizontal circulations, combining the effects of longshore variation of wave height, which as Bowen (1969b) showed can drive circulations on a plane beach, with the influence of changing bottom topography on wave paths and breaking depth, which also can promote a circulation (Noda, 1973). They concluded that the circulation over cuspate each forms would be from horns to embayments when the first effect was dominant, just as Guilcher (1949) observed in the field when the water played over the more subdued parts of beach cusps, and Komar (1971) found in the early stages of his experiments, when little sand had been redistributed. The opposite effect, a circulation from embayments to horns, was expected under the influence of a strongly developed cuspate topography, again as was found by Guilcher and Komar. As in Hino’s (1974) model, surf-zone width proved to be an important controlling parameter. Mei and Liu’s theory is as yet at a relatively simple stage of development (but see Liu and Lennon, 1978). It suggests, however, that there may be dangers in attributing beach cusps and related forms to a single cause.

Internal structure of beach cusps Whereas some attention has been given to beach lamination on a small scale, as will shortly be explained, almost nothing is known of the large-scale structure of beach deposits, such as might be generated on a shore with beach CUSDS. This is unfortunate, because Worrall (1969) shows that beach

46 1

cusps can be abundantly preserved as surface forms, and therefore almost certainly as internal structures, within beach-ridge strand plains. W.O. Thompson (1937) concluded from his studies of a Californian beach that the deposits of a cusped beach comprise seaward-dipping laminae contained in shallow, intersecting, cusp-like embayments plunging seaward. In the deposits of cusped sand beaches, the sets of laminae are very nearly, but not quite, parallel and have dips generally less than loo, an observation supported by Otvos (1964). W.O. Thompson (1949) convincingly interpreted as beach cusps large scoop-like structures in the Lyons Sandstone (Permian) of Colorado. They are filled with parallel-laminated, sometimes faintly ripplemarked well-sorted sandstones, and are associated with rhomboid ripple marks, swash marks, and air heave structures. Possible beach cusps were found amongst parallel-laminated sandstones with antidunes in the littoral Downton Castle Formation (Silurian) of the Welsh Borders (Allen, 1974a).

BEACH LAMINATION

Morphological and dynamical background

Gently dipping parallel laminae formed on plane beds and bundled into weakly discordant, erosively related sets abound in the deposits of sandy non-barred coasts. They are occasionally preserved within intertidal longshore bars together with cross-bedding and cross-lamination. The laminae form in a complex, hierarchically structured environment of great spatio- temporal variability (Schwartz, 1968). Despite intensive research, we continue to lack a properly detailed and integrated account of how beach sediments depend on littoral processes. Sedimentologists have in the main studied beach deposits independently of the processes, except in the most general terms. Although many geomorphologists and engineers have explored the dependence of beach form on process, the sediments and stratal relationships developed as another kind of response have usually been ignored, or treated either cursorily, or in a specialized way. Attitude is a salient property of beach lamination. Plane beds on the beaches of modem non-barred coasts almost invariably dip straight out to sea, obliquity arising only where there are beach cusps. Hence the laminae expected to be present beneath should also on average dip straight out to sea (e.g. Milling and Behrens, 1966; Panin, 1967; Barwis, 1976). Experimental studies and surveys of modem beaches show that the magnitude of the dip is a function of wave characteristics and the calibre of the beach material. Bascom (195 1) found that Pacific coast sand beaches of the U.S.A. increased in steepness with increasing sediment median diameter (Fig. 11-21), the data representing mid-tide level. A similar relationship was noticed by Bagnold (1940). Field and experimental studies by C.A.M. King (1953, 1972), and

462

0

00004

0.001

0.0006

Meon grain diomrter, D

(ml

Fig. 11-21. Beach slope as a measured function of the calibre of beach material. Data of Bascom (1951).

laboratory work by Rector (1954), showed that beach slope declined with increasing wave steepness (wave energy) for a given sediment and wave period. Since Bascorn’s beaches are amongst the most energetic in the world, the scatter of points in Fig. 11-21 may be regarded as defining the smallest mid-tide slope likely to be encountered on a foreshore of a given sand. The laminae themselves, the partings between laminae, the sets into which laminae are bundled, and the erosion surfaces between those sets record a hierarchy of processes acting on several distinct time scales (Schwartz, 1968). The time-scales that are possibly relevant cover wave action (period 1-20 s), the semi-diurnal or diurnal tide (periods 4.5 X 104s, 9.0 X lo4s), individual storms with a time-scale so far as beach erosion and recovery is concerned in the order of 1 X 105s, and alternate stormy and calm seasons (period 3.15 X lo7s). There can of course be no permanent accumulation unless processes operating on these scales work within the context of a trend toward deposition of an even greater characteristic time.

Effects on the scale of waves That each beach lamina records an individual swash and/or backwash flow is a plausible working hypothesis. Swash period is of the same order as that of the parent waves, but is rarely identical or as regular, because of

463

interference between backwash draining from the beach and incoming water, and because of the combination of swashes (e.g. Dolan and Ferm, 1966; Kirk, 1975; Waddell, 1976). Swash and backwash flows have high Froude numbers, since their characteristic velocities are large but depths small (Miller and Zeigler, 1958; Dolan and Ferm, 1966; Schiffman, 1965; Ingle, 1966; P. Wright, 1976), and therefore promote the formation of plane beds and related structures (Vol. I, Chapters 8 and 10). Whether deposition or erosion is dominant in the swash-backwash zone probably depends on the extent to which the upbeach swash discharge is balanced by the downbeach discharge due to backwash (U.S. Grant, 1948; Duncan, 1964). Infiltration of water into the beach during swash is typical of a flooding tide and high water levels, and results in a relatively diminished and slower backwash, a condition favouring deposition. Efflux from’ the beach into the ascending swash augments the flow, however, and results in an enlarged and faster backwash, a circumstance that favours erosion. This condition is promoted by an ebbing tide and low water levels. Clifton (1969) found that swash-backwash flows had three possible effects: ( 1) erosion only, (2) erosion followed by a variable amount of deposition, and (3) deposition only upon an uneroded surface. The first effect suggests a strong effluent flow from the beach into the swash, while the last indicates strong infiltration, destructive of the swash. Clifton claims that all deposition occurs during backwash, but if infiltration plays the part given it by Grant and Duncan, there should be significant deposition as the swash decelerates, as well as toward the end of backwash. The fabric of parallel-laminated beach sands should therefore show not merely an across-beach preferred orientation (e.g. Curray, 1956), but diametrically opposed directions of imbrication. This could be useful in distinguishing parallel-laminated beach from river sands. The laminae that Clifton ( 1969) could relate to individual swash-backwash events were relatively coarse grained (fine-coarse sand), and graded from fine up to coarse, presumably in response either to the downward filtering of fines, or to Bagnoldian dispersive pressure while the grains were sheared together in the flow (Vol. I, Chapter 1; this vol.,. Chapter 4). Lamina thicknesses were as much as 0.018m. Clifton described each lamina in plan as having the form of an irregular ellipse elongated parallel with the beach, that is, a form similar to the parent swash. The dimensions measured in two cases were respectively 6 by 3 m and 19 by 10 m. Many beach sands are much finer grained than Clifton’s and appear to form normally graded and much thinner laminae. Brenninkmeyer’s (1973) observations suggest that it is most unlikely that every swash-backwash flow, or even many such flows, leaves a lamina on the beach. Waddell (1976) thinks that a long-period beat may control the deposition of laminae.

464

Effects on the tidal scale

The breaker and swash-backwash zones migrate first landward and then seaward across the foreshore as the tide floods and ebbs. Since erosion typifies the breaker zone, whereas deposition can take place seaward of the breakers and in the swash-backwash zone, some erosively related sets of beach laminae could record processes of a tidal period. Duncan (1964), Otvos (1965), and Strahler (1966) have developed a model of beach sedimentation on this time scale (Fig. 11-22). We can identify on the beach at any instant one erosional and two depositional zones (Fig. 1 1-22a). The finer sand scoured up in the breaker zone is carried chiefly landward, where much of it accumulates in the swash-backwash zone. Of the coarser sediment, some remains in the breaker zone, but most is transported seaward to be deposited on a broad step-like feature. According to Duncan, the distribution of erosion and deposition in the swash-backwash zone is dependent on the position and attitude of the water table within the beach (Emery and Foster, 1948; Dominick et al., 1971). At the start of the flood tide (Fig. 11-22b), the water table dips seaward and intersects the exposed

Swash-backwash I zone I

Swash-backwash

Breaker

0

Deposition

( a ) MORPHOLOGY

-

-

Swash-backwash

Swash-backwash

Fig. 11-22. Erosion and deposition associated with the movement of the swash-backwash and breaker zones across a sand beach under tidal influence. After Duncan (1 964).

465

foreshore, the efflux of water from the beach permitting only modest deposition. Heavy deposition over the whole swash-backwash zone is experienced by mid-flood, when infiltration into the beach has reversed the attitude of the water table (Fig. 11-22c). At high tide, with infiltration continuing, deposition is again heavy but restricted to the inner part of the swash-backwash zone (Fig. 11-22d). During the ebb, deposition prevails over the whole swash-backwash zone, but the site of maximum accretion shifts steadily toward its seaward limit .(Fig. 11-22e, f). The upbeach movement during the flood of the breaker zone therefore creates a seaward-dipping erosion surface on which accumulates an onlap sequence of swash-backwash laminae. An offlap sequence of laminae above an erosion surface is formed during the succeeding ebb. If wave and tidal conditions held constant, or wave height at the beach was increasing, we should expect to see only the last-formed ebb sequence. Some or all of the preceding flood sequence might be preserved below that due to the ebb if a long-term trend permitting net deposition prevailed. Measurements of beach profile changes give some indication of the scale of tide-related sequences of laminae. C.A.M. King (1951) found that the depth of sand disturbance during a tidal cycle on British beaches was but a 0.05

0

--

0.04 A

E

0

a u 0

5

-U f

0.03

0

A

0

0 V 0

0

0

A

0

r

g

0.02

n

-

KEY TO BEACHES Druridge (D=0.00040rn) Blackpool ( 0 = 0 ~ 0 0 0 2 rn) 2 A Rhosslli ( D = 0.00023 m) A Whltbeck ( 0 = 0 . 0 0 0 2 9 m ) 0

A

0.01

0

A -

I

I

I

l

l

I

I

I

,

,

L

I

I

,

,

,

Fig. 11-23. Maximum depth of sand disturbance as a measured function of wave energy density and grain size on four British beaches. Data of C.A.M. King (195 1).

466

few percent of the wave height and was strongly correlated with wave energy (Fig. 11-23). Workers studying beaches generally more energetic than King’s found depths of disturbance an order of magnitude larger than her values and as much as 40% of breaker height (Zeigler and Tuttle, 1961; Duncan, 1964; Otvos, 1965; R.D. Hill, 1966; Strahler, 1966; Schwartz, 1967; Harrison, 1969, 1970; A.T. Williams, 1971a, 1971b, 1973b). Coarseness of beach sediment also increases depth of disturbance, as may be seen in Fig. 11-23. Otvos and Williams, who each found proportional disturbances much greater than did King, worked on beaches with substantial amounts of medium to very coarse sand. Only Otvos ( 1965) and A.T. Williams ( 1971b) described the character of the sequences accumulated during tidal cycles. Otvos found upward-fining sequences of generally coarse to medium sand, the lower coarser parts being attributed to deposition on the landward side of the breaker zone and the finer upper portions to accumulation in the swash-backwash zone. Graded sequences like those of Otvos were found by Williams chiefly at mid-tide level, though examples could be seen at any position on the beach. The sequences deposited around high tide level, however, were described as mainly uniformly textured. Many workers have recorded from recent or modern beaches sequences of laminae in the general order of 0.1 m thick that could record tidal cycles (W.O. Thompson, 1937; McKee, 1957a; Soliman, 1964; Psuty, 1965, 1966; Milling and Behrens, 1966; Panin, 1967; Stapor, 1975). These sequences are erosively related, as expected under the model (Fig. 11-22), and commonly graded, in some instances compositionally as well as texturally. See also Howard and Reineck (1981). The tide has another periodicity, that of the spring-neap cycle, which under restricted circumstances can influence beach cut-and-fill (Inman and Filloux, 1960; Sakalowsky, 1975a, 1975b). Inman and Filloux studied a beach in a part of the Gulf of California where an afternoon sea-breeze stirs up vigorous waves. The high water of spring tides also occurs in the afternoon, the coincidence with the sea-breeze generating a fortnightly cycle of changes expressed on the upper beach by cut and fill of the order of 0.1 m. There result almost rhythmically arranged bundles of laminae, some rich in heavy minerals.

Effects on a storm or seasonal time-scale Much attention has been given both by engineers and geomorphologists to changes in beach profile with individual storms and with stormy seasons (Inman, 1953; C.A.M. King, 1953; Wiegel et al., 1954; Zeigler et al., 1959; Zeigler and Tuttle, 1961; McIntire and Walker, 1964; Dolan, 1965; Gorsline, 1966; Warnke et al., 1966; Kirk, 1969; Thompson and Harlett, 1969; Warnke, 1969; Niyogi, 1970; Everts, 1973b; A.T. Williams, 1974; Nordstrom and Inman, 1975; Winant et al., 1975; Steele, 1976; De Wall et al., 1977;

461 1.6

I

I

0

---

1.4

I

I

I

0

0

-

8

E

t

-

0

1.2

-

1.0

-

0.8

-

0 0

0

0 c

8

8

c ._ 0

0

5

r

0

0

5

8

0

0.6

8

-

0 0

f

5

0.4

-

r"

oo

0.2 01 0

o Florida beaches 8

0

I

0.1

0.2

California

beaches

I

I

I

I

L

0.3

0.4

0.5

0.6

0.7

1

0.8

b

09

1.0

I

1.1

Mean annual breaker height (rn)

Fig. 11-24. Maximum annual change in sand level on beaches in U.S.A. as a measured function of mean annual breaker height. There may be a concealed grain-size effect related to that in Fig. 11-23.

Kana, 1977; Birkemeier, 1979, 1981). Generally speaking, beach profiles are cut down during an individual storm or during the stormy season, built up in the ensuing period or season of calms. A consideration of the area defined by the limits of a large number of profiles for a particular beach station-the sweep zone of King and Barnes (1964)-shows that most change takes place over the middle and upper parts of beaches. The vertical change in level between storms or between storm seasons is typically in the order of 1-2m for ocean beaches exposed to substantial waves, and reaches 3 m or more for particularly stormy areas or as the result of the most severe individual storms. Gorsline was able to quantify this relationship for beaches in western Florida and, using Ingle's (1966) data, for the Pacific coast of California (Fig. 11-24). Although the waves affecting the Pacific beaches have about twice the period of those observed off the Florida coast, the Pacific waves are less effective since the Californian beaches are of fine to medium sand as compared to medium to very coarse sand in Florida. Hence the grain-size effect at the level of the storm or stormy season is similar to that noticed by C.A.M. King (195 1) for the tidal cycle. A beach can be cut down and back in a matter of a few hours during a storm (e.g. Leatherman, 1979), but takes generally several to many days fully to recover its farmer profile (Thompson and Harlett, 1969). Large cuts are favoured by the concurrence of large waves with a high tide (Kana, 1977), but even a hurricane may cause little erosion when this concurrence is not achieved (e.g. Warnke, 1969).

468 Seaward

Lamina,

STORM CYCLE

Fig. 11-25. Speculative model depicting cycles of lamination (storm, tide, swash-backwash)in beach sands.

The nature of the sedimentary sequence related to this storm or seasonal cycle is not known directly. But we may speculate that, beginning with a coarse lag deposit of pebbles and/or shells representing the storm or stormy period, it comprises a succession of tide-related upward-fining or other sequences that expresses recovery after the storm or during the calm season (Fig. 11-25). The thickness of this storm or seasonal complex should increase with the degree of exposure of the beach to wave action (Fig. 11-24), and could be as much as 2-3m thick. There may be an upward increase in the angle of dip of the laminae. The constituent sequences of laminae should also take a thickness related to wave energy (Fig. 11-23), and may on average scale with the overall thickness of the complex. Such complexes should be detectable within regressive strand-plain deposits.

Beach lamination in the stratigraphic record W.O. Thompson (1949) in describing the Lyons Sandstone gave an account of a fossil beach deposit that is one of earliest and most convincing on record. Parallel-laminated sandstones with small original dips of rather consistent direction are here organised into erosively related sets. Amongst them occur rhomboid ripples, swash marks, and air-heave structures, all indicative of the strand. Thompson likened the deposit to modern beach sands he had studied over the period of a storm. Many later workers have described parallel-laminated sandstones in sharply or erosively related sets and ascribed to them a shallow-water if not beach origin (e.g. P. Allen, 1959, 1962; Otvos, 1966; Michaelis and Dixon, 1969; Gliese, 1973; Allen, 1974a;

469

Vos and Hobday, 1977). P. Allen found the parallel laminae of Wealden sandstones to have a small original dip and often to be grouped into rhythms or sets a few centimetres thick. The laminae examined by Michaelis and Dixon had a marked normal grading. Vos and Hobday found their laminae often to be rich in heavy minerals, to have an original dip of 2-4", and to show parting lineations aligned along the direction of dip, as can be repeatedly seen on plane beds shaped by swash and backwash on beaches today. The sand bodies they studied were shown by Behr (1965) to be similar in orientation and much longer than wide, a grouping suggestive of a strand-plain or series of barrier sands. However, no sandstones of this general type have yet been studied in sufficient detail to say if hierarchical sequences like that sketched in Fig. 11-25 are preserved. Parallel-laminated sandstones of the kind described typically appear in the upper levels of upward-coarsening sequences in the order of 10m or more in thickness commencing with marine shales. Favourable exposures reveal through such sequences the presence of major bedding surfaces that in shape and slope could be the foreshore and nearby offshore of a beach (e.g. Harms et al., 1965; Shelton, 1965; Cleavinger, 1974). Similar major bedding structures are recorded by Van Straaten (1965) from large excavations in Holocene barrier islands.

SUMMARY

The coastal environment is complicated and very variable dynamically and is often complex morphologically. Barred coasts reveal, on a gently sloping sea or lake bed, series of longshore bars and troughs that lie parallel or nearly parallel with the shore, and which increase from shallow to deep water in wavelength, height above the bed, and water depth at the crest. The bars seem to be deposits formed at or close to the nodes of standing waves created by the interaction of the incident wave-train and its reflection from the beach. Strongly three-dimensional bars, however, may involve in addition an interaction between incident waves and edge waves, or other longshore variations in water level. Longshore bars and troughs are mobile features and preserve distinctive deposits. Particularly characteristic of permanently submerged forms are erosively related, inclined sets of parallel-laminated with cross-laminated sand. Intertidal bars largely consist of solitary units of landward-dipping cross-bedding. Beach cusps are familiar structures on sandy to gravelly shores. These periodically arranged seaward-facing embayments and horns increase in scale with increasing wave energy. There are many explanations of beach cusps, but none is entirely satisfactory. The most promising are that they either represent an instability of the wave set-up, or record the effects of edge waves combined with the influence of spatially changing water depth

410

on shoaling waves. Beach cusps can be preserved in strand-plain deposits, apparently as large scoop-like erosion surfaces. The middle and upper parts of the foreshore on non-barred sandy coasts are characterized by parallel-laminae arranged in erosively related sets. The laminae record swash-backwash flows of large Froude number, and the sets erosion-deposition cycles related to tides, individual storms, or stormy seasons.

47 1

Chapter 12 STORM SEQUENCES IN SHALLOW WATER

INTRODUCTION

The wind’s ability to make progressive waves on a water surface is widely familiar. Less familiar is its ability to tilt up that surface in the direction of the air flow, by virtue of the tractive force applied. The effect exists with even the lightest wind, but is strong only during storms. As a consequence of the tilting, the water at the shore stands significantly higher than is the case during dead calms. The difference between the storm and fair-weather water levels is called the wind set-up, positive in the case of an above-normal level, negative in the case of a lower stand. The wind set-up contributes significantly, and in most cases predominantly, to what is known as the storm surge, the difference due to all causes between the storm and fair-weather water levels (Heaps, 1967). Like the set-up, the surge may be either positive or negative, depending on circumstances. The other contribution to the storm surge comes from horizontal gradients of atmospheric pressure over the Earth’s surface, such as accompany cyclonic depressions. As Heaps (1967) points out, a pressure difference of one millibar between two points on the surface of a lake or sea means a difference in surface elevation of about 0.01 m. The wind has a second effect on an exposed water body, familiar to anyone who has observed with each change of wind the shifting in drift direction of barely floating objects. The wind by virtue of the tractive force applied to the surface sets up within the water body a wind-drift current acting in the same direction. The observed wind-induced current, however, is the wind-drift current modified by the flow that arises because of the tilted water surface, for the tilt will be recognized as implying the action of a pressure force opposing the wind stress. The flow due to tilt is called the gradient current, and is opposite to the wind drift. The combined motion in a bounded water body is a near-surface flow in the wind direction, and a compensating deeper and opposite flow. A storm moving onshore may therefore create a significant offshore flow near the bottom, capable of shifting wave-stirred sediment from shallow to deep water. Many coasts are affected at least once a year by significant surges. The process, if it occurs, could therefore be geologically significant. Engineers, geomorphologists and, latterly, sedimentologists now have a considerable direct knowledge of storm-surge effects at the immediate coast. Barrier beaches are overtopped and channels carved through them. If the hinterland is low-lying, as with deltas and alluvial coastal plains, water floods inland for many kilometres, building sand or gravel fans immediately

412

to landward of the barriers, but carrying blanketing muds to distant points. Rivers are backed up in their channels by surges and, if levees are overtopped, make their own contribution to the flood waters and to the catastrophic erosion and deposition that so often accompany storms. Far less is directly known of the offshore sedimentary phenomena accompanying storms. Yet it is being increasingly suggested that only storm-action can satisfactorily explain the normally graded terrigenous or bioclastic sandstones so prevalent amongst strata which on independent grounds accumulated in comparatively shallow waters. Similarly, only storms are thought able to explain the presence of normally graded sand and silt layers on the bottoms of modern shelf seas in depths as great as 60m. But at present the evidence is circumstantial and incomplete. No offshore graded layer has ever been conclusively linked with a storm and, although the combination of a wind-induced current with wave-stirring is an appealing mechanism for offshore sediment transport, the quantitative mechanics of the process as a whole have hitherto been obscure. An attempt is made in this chapter to provide a semi-quantitative model of storm action in the nearshore and offshore and to assess it in the light of supposed storm sand-layers, in which an apparently distinctive sequence of sedimentary structures and textures is seen. However, the possibility that other processes can shift sand outward from shore should not be ignored. Reimnitz et al. (1976) claim that rip currents may be powerful enough to ripple sand in depths as great as 30 m. TWO-DIMENSIONAL STEADY MODELS OF WIND EFFECTS

Wind set-up Consider the action of a steady wind of constant direction on the surface of a homogeneous body of water under uniform barometric pressure contained in a bounded basin with horizontal bottom existing in a uniform gravity field. Let the basin be sufficiently small that geostrophic effects are negligible, and the problem be restricted to the two-dimensional case. The equilibrium wind set-up at stations sufficiently distant from the walls that edge effects are negligible can be calculated for laminar flow either from the equations of motion or, leading to speedier physical insight, by considering with Hellstrom (1941) the force balance on a small element of unit width and length d x parallel with the wind (Fig. 12-1). The body forces acting on the element are the weight of water Wand the reaction R. The wind exerts a force T~- d x on the free surface, where T~ is the mean surface shear stress, while the water in the basin exerts a force T~ dx, T~ being the mean bed shear stress. Hydrostatic pressure forces: Pwg

p , =-Y, 2

2 7

P2 =-P w g (Ys + dYh2 2

473 Wind

$

$- - - - - - - $\ \ \ \ \

Fig. 12-1. Definition diagram for the forces acting on a water surface and within a water body of finite depth exposed to the wind.

act on the sides of the element, where p, is the density of water and g is the acceleration due to gravity. The sides are also acted upon by shear forces Fl and F2 related to the currents of water flowing through the element. Summing the forces parallel with the x-direction, we obtain: r;dx+P,

-P2 +rO-dx=O

(12.1)

which leads to:

(12.2) upon disregarding terms in dy, of a higher order than the first. Assuming the required water-surface tilt to be small, the flows through the two sides of the element can be regarded as equal, whence:

F, = F2

(12.3)

Summing the forces parallel with the y-direction, we have

W=R

(12.4)

Moments taken around the point 0 yield:

affording: (12.6)

when terms in dx and dy, of a higher order than the first are disregarded.

474

Equations (12.2) and (12.6) are equivalent statements of the water-surface slope. The first term of eq. (12.6) gives the slope arising from the static conditions, while the second term describes the extent to which the slope is lowered by the currents induced in the water body. To obtain this term, Hellstrom (1941) appealed to the equations of motion, finding that for laminar conditions F, = q q , where q is the dynamic viscosity of water and Usis the velocity of the water at the free surface. The equations of motion q, eq. (12.6) also reveal that for laminar conditions U,= ~ ~ y ~ / 4whence becomes: (12.7) in which k, = 3/2. Substituting eq. (12.7) for the slope in eq. (12.2), we find k , = ( T ~ / T , 1) and T,, = + T , . Equation (12.7) shows that the degree to which a water surface is tilted up by a wind is directly proportional to the wind force and inversely proportional to water depth. Hellstrom (1941) also obtained this relationship directly from the equations of motion of a laminar fluid. The same or similar derivations come from Keulegan ( 195l), Langhaar ( 195l), Van Dorn ( 1953), Ursell (1956), and Baines and Knapp (1965). A useful summary of Hellstrom’s work is given by Sibul (1955b). Ursell did not assume the set-up to be small, and therefore derived a term additional to that on the right in eq. (12.7). This new term described the rate of change of fluid momentum in the x-direction arising from the change in flow depth due to the set-up. The term is negligible under most field conditions, but can be significant at the laboratory scale. Although the laminar case is important theoretically, only the wind currents and set-up in turbulent water are of practical interest. Hellstrom (1941) attacked this case from the equations of motion and Boussinesq’s theory of turbulence, obtaining for the water-surface slope:

+

(12.8) where: (12.9) in which fo is the Darcy-Weisbach bed friction coefficient, and k , is a coefficient describing the nature of the fluid. We see that eq. (12.8) is identical in form to eq. (12.7), whence whether the fluid is laminar or turbulent makes no difference to the basic controls on the water-surface slope. However, k , is not a constant in the turbulent case, but ranges between narrow limits as k , and fo vary. As k,\lf,/8g tends to infinity, k,

475

tends to 3/2, its value in laminar flow. For k 2 / f , / 8 g tending to zero, k , tends toward unity, whence from the definition of k , in terms of shear stresses, T~ must be negligibly small compared with T ~ .Hellstrom records that Boussinesq gave k 2 for water the value of 45 m1l2s-I. For rippled sand beds, for which fo is close to 0.08, k, would then be approximately 1.16, making T~ some 16 percent of T ~ . The surface profile of a particular body of water follows by integrating either eq. (12.7) or (12.8) under the boundary conditions and constraints appropriate to that body. Consider first a two-dimensional basin with a plane horizontal bottom and vertical sides acted on by a steady transverse wind of constant direction (Fig. 12-2a). Hellstrom (1941) integrated eq. (12.8) to obtain for this case: (12.10) where K, is a constant of integration. This follows from the condition: (12.11)

ld ys (x) .dx= hd

where h is the still-water depth and d is the length of the basin in the wind direction, stating that the water mass is conserved. Substituting for ys(x ) in eq. (12.11) from eq. (12.10) and then integrating, he obtained: (12.12) as an implicit expression for K,, which may be solved by trial and error. Equation (12.10) reveals that the shape of the water surface is part of a parabolic cylinder, the set-up at any point being s = y s - h. Clearly, the set-up is negative at the upwind edge of the basin but positive at the down-wind margin. Y,

I

.

X c

I

Fig. 12-2. Definition diagram for the form of the water surface when the wind blows transversely across (a) a basin of rectangular cross-section, and (b) a sloping shelf bordering a very much larger water body.

476

Next consider the effect of wind blowing toward the shore of a twodimensional basin on the margin of which is a much smaller and shallower shelf of uniform width with a plane sloping bottom (Fig. 12-2b), such as affords a model of a continental shelf bordering an ocean. With the given notation, the shelf bottom is described by: yo = x tan P

(12.13)

where P is the slope of the shelf, and the water-surface slope by: (12.14) geostrophic effects being neglected. Hellstrom (1941) integrated eq. (12.14) to obtain for the profile of the water surface the implicit equation: (12.15) where K, is another integration constant. Hellstrom considered the boundary conditions to be applied in order to obtain K, for closed basins. Our boundary condition, however, derives from the assumption that the shelf is small and shallow compared to the basin as a whole. Hence we may assume that the depth at the shelf-edge when the wind is blowing is equal to the fair-weather depth h. Therefore putting y, = h at x = 0 into eq. (12.15), we obtain : (12.16) and, upon inspecting this equation and eq. (12.15), find three possible water-surface configurations:

h> h=

h<

k17s

P& tan P ’ k1TS

Pwg tan P ’ k1TS

Pwgtan P ’

K, < 0,

concave-upward

K , =0,

plane

K, > 0,

convex-upward

Concavity is favoured by a large shelf-edge depth and a large shelf slope; convexity comes from a combination of small shelf slope and small depth at the inner margin. The shapes of water surfaces affected by wind in laboratory channels agree well with the theory presented above, to judge from observations made by Hellstrom (1941), Francis ( 195I), Keulegan ( 195l), Johnson and Rice (1952), Sibul (1955a, 1955b), Sibul and Johnson (1957), and Tickner (1960). There is also good agreement between theory and the open-air observations

477

made by Van Dorn (1953) from a model-yacht basin intermediate in scale between a laboratory wind-wave tank and a small natural lake. Hellstrom used very viscous oils in some experiments, allowing him to test the laminar theory and to establish for this case that k , was approximately equal to 1.5. However, there are substantial differences of opinion as to the value of k , for turbulent flow, though the coefficient is certainly smaller than in the laminar case. Keulegan tentatively applied a value of 1.25. Van Dorn found the coefficient to be not larger than 1.10. Sibul(1955a) obtained a wide range of values, some smaller than unity, but a mean of 1.27, in agreement with Keulegan’s tentative assumption. Baines and Knapp (1965) found k , to be approximately 1.1, in agreement with Van Dorn. Francis (1951, 1953), however, obtained results suggesting that k , was significantly smaller than these values. The earlier work indicated that T~ was 3% or less of 5 , giving k, = 1.03. Measuring the bottom shear stress directly, he later concluded that k , was only 1.015, a result which Engelund (1973) supported theoretically.

Currents associated with the set-up Under the above assumptions, Hellstrom (1941) calculated from the equations of motion and for laminar conditions the distribution of velocity U ( y ) within a water body as the result of surface wind-action (Fig. 12.1). There are as indicated two contributions to the observed velocity field. The first reflects the wind force and exists even if the water surface is horizontal. This is the wind-drift current, calculated to be: (12.17) in which y is distance measured vertically upward from the bed. This current is proportional to the wind force and increases linearly with height (Fig. 12-3a), attaining a maximum at the surface given by U, = r s y s / q . The gradient current, deriving from the tilt of the water surface, is given by: (12.18) and has a surface value of: (12.19) The gradient current, distributed parabolically (Fig. 12-3b), therefore opposes the drift current. Adding eqs. (12.17) and (12.18), and substituting for the water-surface slope from eq. (12.7), the observed current is found to be: (12.20)

478

+

Wind 4

Wlnd (b)

-

0.9

0.8

7

Wlnd

0.9

-

0.7

d m

n

0.6

m n

0

0.5

f

:.

s 0

0.4

E a'

03

0.2

0.1

1

0

1

2

3

4

5

6

I

-4

l

I

-3

Velocity in arbllrary

I

I

-2

I

I

-I

I

0.5 10 1.5

units

Fig. 12-3. Theoretical laminar currents in a water body acted on by the wind. a. Wind-drift current. b. Gradient current. c. Observed current (summation of wind-drift and gradient currents).

seen in Fig. 12-3c. The velocity is zero at y = O and y = 2ys/3, and has a minimum value, U = -Tsy,/12 at y = y s / 3 . Since one of the assumptions is that the water body lies in a closed basin, eq. (12.20) naturally satisfies the condition that the total discharge of water through the element in Fig. 12-1 is zero. The observed current in the laminar case is expected to be a drift in the wind direction in the upper one-third of the water body, and a flow opposite to the wind in the lowest two-thirds. Hidy et al. (1966) also derived eq. (12.20), though presenting an alternative form, and Baines and Knapp (1965) give additional equivalent relationships. Equation (12.20) is of more theoretical than practical interest. So far only Hellstrom (1941) and Reid (1957) have attempted to calculate for turbulent conditions the distribution of velocity in a wind-affected water-body complying with the previous assumptions. Hellstrom (1941) based his model for turbulent conditions on the Boussinesq theory yielding the water-surface slope. His equation for the observed

479

wind-current reads:

(12.21) in which y, is the water depth and y the distance measured vertically upward from the bottom. Like the corresponding formula for laminar motion, eq. (12.21) is of parabolic form, describing a near-surface current in the same direction as the wind and a deeper opposite flow. The current now varies as the square-root of the shear stress exerted by the wind, and not as the first power, as in the laminar case, and is a function only of the relative depth. The velocity at the bottom, U,,given by the third term to the right in eq. (12.21), is generally not zero and increases as ro grows larger relative to r,, being effectively a slip velocity. The velocity at the surface, obtained by setting y =y,, increases as ro grows smaller relative to rs,Figure 12-4a shows velocity profiles calculated from eq. (12.21) for different values of k,, and

Wind

Forssblad (1947) o Urn= io rn s-1 Masch (19631 Urn= 5 . 6 4 rn a-I A Urn= 0.05 rn a-1

A

Velocity in arbitrary units

Relative velocity, U. /Urn

Fig. 12-4. Turbulent currents in a water body acted on by the wind. a. Theoretical velocity profiles according to Hellstrom's (1941) model (eq. 12.21). b. Velocity profiles observed under laboratory conditions.

480

with k, = 45 m'/2s-'. The depth at which U is zero lies generally in the upper half of the flow. Reid's (1957) model depends on the Prandtl-Von Karman mixing-length theory of turbulence, and is therefore more appealing than Hellstrom's (1941) simpler attack. The velocity profile calculated under the previous assumptions reveals a near-surface flow with the wind, lying above a slower and thicker opposiie current. The velocity increases steeply upward above the bed, being zero at the bed itself, where Hellstrom's formula yields a finite value, and is again zero at a height of about 0.65 times the flow depth, similar to the laminar case. Only near the bed is the shape of the velocity profile sensitive to the ratio of the bed and surface shear stresses. Within the body of the fluid the profile changes but little with this ratio, in contrast to Hellstrom's model. Reid's model presents many practical difficulties, however, as both the bed and surface roughness must be known. Shemdin (1973) gives another model. Figure 12.4b shows values for the local steady velocity measured by Forssblad ( 1947) and Masch ( 1963) in bounded turbulent water bodies

4

o A

Keulegan (1951) Masch (1963) Wu (1968. 1975a) Plate (1970)

J lo-' \

8

8 6 4

Keulegan (1951) 10-3

2

10-3

I

Id

KP .

10' .

4

6 0

lo2 10' lo4 Reynolds number ,

2

4

6

2

8 104

Reynaldr number.

loe L

I

2 105

4

6

8

106

Yx -

Fig. 12-5. Velocity of surface water compared with the mean wind speed, as an experimental function of Reynolds number based on surface velocity and water depth. The inset graph shows the change in the form of the relationship (broadly the laminar-turbulent transition) at a Reynolds number of approximately lo3.

48 1

v

affected by wind under laboratory conditions. The values are normalized by the mean wind speed U,.Immediately striking is the fact that the water velocity is a mere few percent of the wind speed, and that values typical of the interior fluid persist practically to the bed. The laminar model, eq. (12.20), fitted to the data is obviously unsatisfactory. A tolerably good match in the interior of the liquid arises using Hellstrom’s (1941) eq. (12.21), for k , comparable with 1.1. Under the same ratio of the bottom and surface stresses implied by this value, Reid (1957) found his equation also to give a good fit in the interior, but there exist no data by which to test its accuracy near the bed. A velocity profile like that in Fig. 12-4b was also measured by Francis (1953). Those of Baines and Knapp (1965) resemble the figured distribution but are somewhat distorted, carrying an inflection in the region of reversed flow. Masch’s (1963) plots also are distorted, but in the forward current. The presence of secondary currents may explain these deviations. The sluggishness of wind-induced currents compared to the wind is further emphasized by laboratory measurements of the surface drift (Francis, 1951; Keulegan,.1951; Masch, 1963; Hidy et al., 1966; Wu, 1968, 1975a; Plate et al., 1969; Phillips and Banner, 1974). A selection of data appears in Fig. 12-5 as a plot of U 5 / U ,against the Reynolds number U 5 y s / v ,where v is the kinematic viscosity of water. Up to a Reynolds number of about lo3, the velocity ratio increases as the square root of the Reynolds number, and the influence of viscosity is clearly significant. In a region of higher Reynolds numbers, the effect of viscosity is less marked, the velocity ratio increasing only as the one-fifth power of the Reynolds number. But as Plate (1970) points out, the trend is sufficiently marked that at large Reynolds numbers the surface current cannot be said to be a constant fraction of the mean wind speed. Keulegan’s (195 1) proportionality of 0.033 is, however, still widely quoted and used. When waves are present, as must invariably be the case, what proportion of the total current is contributed by the mass-transport due to the wavemotion alone? Bye (1967) suggested that in fully developed seas the contribution might be rather high, but in laboratory experiments, Wu (1975a) found the surface mass-transport to be only 5- 13% of the total surface current.

NATURAL SURGES AND WIND-INDUCED CURRENTS

There exists a voluminous literature describing the magnitude and frequency of storm surges as observed on coasts, and all that we can do here is to sinde out representative items by way of illustration. Bretschneider (1967) and Heaps (1967) give detailed and useful surveys of this work. In sharp contrast is our meagre empirical knowledge of the actual currents induced by storms. Storm surges frequently affect the coasts of the British Isles. The statistics

482

compiled by Lennon (1963a) and Suthons (1963) show that a surge of the order of 1 m occurs approximately once each year at many sites on the British west and east coasts. Surges of about 2 m recur once every few tens of years. Those with a magnitude in the order of 3 m affect these coasts with a frequency of once every few hundred years, for example, the great surge of 1953 in the southern North Sea (Rossiter, 1954). Reineck (1962) and Nasner and Partenscky (1975) document similar surges that have affected the German coast. The surges on the west coasts of the British Isles are related to gales accompanying deep cyclonic depressions that approach the coast from the southwest, keeping the coast to their right (Lennon, 1963b; McIntyre, 1979). The winds in these depressions rotate anticlockwise, and the effect of Coriolis force is to create the greatest positive set-up in the leading quadrant to the right of the storm track. Analyses of North Sea events (e.g. Rossiter, 1954; Shaw et al., 1976), and particularly Harding and Binding’s (1978) general survey, show that the severest surges are related to depressions travelling either eastward from northern Scotland to Denmark, or southeastward from Shetland to the Netherlands. The coastlines of the German and Flemish Bights are most affected. The shallow Baltic Sea is also subject to storm surges, though seldom in excess of 2 m above normal sea level (Hellstrom, 1941). The steep west coasts of Scandinavia rarely exhibit surges in excess of 1 m (Hellstrom, 1953; Bergsten, 1955; Gjevik and Wed, 1976). Surges are modest in the eastern Mediterranean Sea (Striem, 1974), and in the Adriatic Sea rarely exceed 1 m (Robinson et al., 1973). Tropical storms yield surges. The coastal plains bordering the Gulf of Mexico and the western Atlantic Ocean are frequently swept by hurricanes that raise sea level at the coast by upward of 3-7m above normal (e.g. Hayes, 1967; Sethuraman, 1979). Surges of as much as 7 m are also reported from the Bay of Bengal (Flier1 and Robinson, 1972; Das et al., 1974) and Hong Kong (Watts, 1959), and comparable surges affect Australian shores (e.g. Hopley, 1974a, 1974b). Shallow lakes are particularly affected by large surges. The westerly gales of winter commonly produce positive surges of 2 m or more at the eastern end of Lake Erie (Keulegan, 1951). Lake Okeechobee, Florida, has a maximum depth of about 5 m, yet surges to as much as 3 m above normal during hurricanes (e.g. Saville, 1952). Storm-induced currents are difficult to measure, particularly at sea, where they must be separated from flows due to the tide, waves, and thermohaline circulations. The latitude-adjusted near-surface wind-induced current in the open ocean was found by Durst (1924) to be approximately 0.8% of a characteristic wind speed. Hughes ( 1 956) made an extensive analysis of drifter movements to estimate the surface current as 3.3% of the wind speed measured at a height of 10 m, a proportionality remarkably close to Keulegan’s (1951)

483

experimental value. The wind component in the total surface current at Amrum Lightship in the German Bight of the North Sea was determined by Mandelbaum (1955) for winds of up to Force 5. At Force 5 the wind current was approximately 0.1 m s I . Wind-induced near-bed currents were recorded at several sites in European and North American waters. Gienapp (1973) measured the current 2 m above the sea bed near Helgoland in the German Bight during the storm surge of 2 November, 1965. An offshore current peaking at 0.81 m s - ' was measured, as compared with a calm-weather maximum of about half this value. V.N.D. Caston (1976), working amongst tidal current ridges, found a significant strengthening of the near-bed current, by between 1.4 and 2% of the wind speed at a height of 30 m for winds of between 35 and 50 knots. By chance, Murray (1970b) measured near-bed currents in 6.3 m of water 360 m off the Florida coast during hurricane Camille, 1969. This storm crossed the Gulf of Mexico on a northwesterly track to the west of the current-meter station. The pre-storm westerly current changed during the storm into an offshore flow of about 0.8 m s - I , with pulses reaching 1.6 m s - I , before the instrument failed. Later, Murray ( 1972) measured storm-induced currents in 15.6 m of water off the Mississippi Delta. Onshore winds produced offshore near-bed flows in the order of 0.2-0.3 m s - I, the storm-induced currents persisting for 36-48 hours. Smith and Hopkins (1972) obtained long records of currents 3 m above the sea bed in depths up to 80m on the stormy continental shelf off Washington and Oregon. The storm contribution amounted to about 0.5 m s-I, with a weak offshore component. At slightly shallower depths on the Texan shelf, Forristall et al. (1977) measured hurricane-induced currents as great as 1.5 m s - I , exceeding even the orbital velocities produced at that depth by the accompanying waves (maximum height 7.8 m). Figueiredo (1980) has recently described the changes in current strength induced during a period of strong winds in water 15-20m deep on the inner part of the Brazilian shelf. In harmony with an increase in the height and period of the surface waves, the surface current increased from 0.40-0.82 m s - I, while the bottom current strengthened from 0.26 to 0.34 m s - I. Further changes in current speed resulted from the dying away of the strong winds and the appearance of swell from a distant source. Currents powerful enough to sweep away anchored instruments arise in submarine canyons during storms (Shepard and Marshall, 1973a, 1973b; Shepard et al., 1974). Svendsen and Thompson (1978) have measured wind-induced currents in a fjord. ~

COMPLEX MODELS OF WIND EFFECTS

The preceding two-dimensional models give many valuable insights into the nature of wind surges and currents, yet because of the restricted conditions assumed are generally too inaccurate for many purposes. For the

484

complete understanding of sediment transport in shallow waters, as well as for the design of coastal protection works and offshore installations, models that incorporate more realistic conditions are essential. Although covering only the earlier stages in their development, the reviews of Weylander (1961), Heaps (1965), and Bretschneider (1967) indicate the essentials of these models, of which there are three kinds: empirical, analytical and, with the advent of high-speed computing, numerical. Many early models for surge prediction are empirical. Representative of those based on two-dimensional considerations is that of Keulegan ( 1951, 1952, 1953), in which appear factors to account for such features as the irregular shape of a water-body. The model for surge prediction proposed by Conner et al. (1957) is typical of several used for open coasts. Essentially, it relates the surge to the pressure field in the controlling depression. Although three-dimensional analytical models appeared at an early stage (e.g. Proudman and Doodson, 1926), that based on the bathystrophic approximation (horizontal water-motions only) was the first to achieve practical success (Freeman et al., 1957; Bretschneider, 1966a, 1966b; Bodine, 1971). Subsequent analytical models are capable of describing the circulation and set-up in water-bodies of simple shape (rectangular, circular or elliptical basins) under either steady or unsteady conditions, and with the influence of Coriolis force partly included (Goldstein and Gedney, 1971, 1973; Liu and Perez, 1971; Birchfield, 1972; Noye, 1973; Bennett, 1974; S.J. Jacobs, 1974; Witten and Thomas, 1976). Most of these models use simplified forms of the equations of motion and simple assumptions about eddy viscosity. Numerical models for circulation and set-up dependent on finite-difference techniques now abound (Liggett, 1969a, 1969b; Liggett and Hadjitheodorou, 1969; Gedney and Lick, 1971, 1972; Das, 1972; Flier1 and Robinson, 1972; Gedney et al., 1972; Bonham-Carter and Thomas, 1973; Gallagher et al., 1973; J.E. Banks, 1974; Bennett, 1974; D.J. Clarke, 1974; Das et al., 1974; Forristall, 1974; Prandle, 1975; A.M. Davies, 1977; Sheng et al., 1978; Johns and Ali, 1980). They are capable of handling the equations of motion in non-linear form, water-bodies of irregular as well as regular shape, stratified as well as unstratified systems, and Coriolis effects. Surge predictions of remarkably high accuracy are obtainable from such models. They yield the circulation less satisfactorily, however, chiefly because of the difficulty of realistically treating the turbulent resistance of the water. Many workers have used a constant eddy-viscosity model, but Witten and Thomas (1976) find a depth-dependent relationship to be better. Crawford (1979) and Yeh and Chou (1979) have published the most recent models for storm surges. The model described by Koutitas and O’Connor (1980) requires some parameters to be introduced on the basis of experimental work. Fox and Davis ( 1979b) recently described an interesting model capable of predicting for three-dimensional storms, the characteristics of the wind, the development of surface waves, and the longshore currents. See also Pearce and Cooper ( 1981).

485

DEPENDENCE OF WIND STRESS ON WIND SPEED

However one proposes to model the surge and circulation, it is necessary to provide a value for the wind stress on the water surface, for insertion into such as eqs. (12.10), (12.15), (12.18) and (12.21). Direct measurement is rarely possible, reliance being instead placed on either theoretical or empirical relationships which permit the shear stress to be estimated. Because turbulent conditions dominate in the field, most workers have sought to establish an empirical relationship connecting a friction coefficient, with a suitably defined wind speed. A measurement height of 10 m above the mean water surface has become standard for the reference wind. The friction coefficient used here is the Darcy-Weisbach form, defined by T~ = ( fiO/8)paU& in which pa is the density of the air, and the subscript denotes the reference height. In the laboratory, the mean wind speed is commonly used in calculating the coefficient. There are four main ways of estimating the wind stress and of obtaining the friction coefficient (Francis, 1959; Wieringa, 1974; Garratt, 1977). The first, applicable in the laboratory and under restricted field conditions, depends on the measurement of water-surface slope and water depth. The application of eq. (12.7) with a suitable value for k , then yields the stress. The second lies in measuring the velocity profile of the wind, which is approximately logarithmic (Plate, 197la). This technique also is appropriate to both field and laboratory conditions. The third method, restricted to field use, depends on the measurement of the geostrophic departure of the wind vector, and does not readily yield good results. The fourth method can be employed in both the field and laboratory and rests on knowing the turbulent components of the wind velocity. Many have attempted to establish experimentally the dependence of the friction coefficient on wind speed (Francis, 1951; Johnson and Rice, 1952; Sibul, 1955a; Fitzgerald, 1963; Hidy et al., 1966; Wu, 1968). Apparently, the coefficient increases linearly with wind speed at sufficiently high speeds, indicating the variation of the shear stress with the cube of the wind velocity, in accordance with the theoretical suggestions of Munk (1955) and Charnak ( 1955). At low speeds, however, different relationships seem to prevail. Fitzgerald saw the friction coefficient as a constant. Wu found the coefficient to vary with the wind velocity to the power minus one-half, and noticed that the change to the linear law occurred at wind speeds sufficient to cause wave-breaking. Representative field studies of the friction coefficient are described by Hellstrom (1953), Keulegan (1953), Hay (1955), Charnock et al. (1956), Deacon et al. (1956), Hsu (1973), Wieringa (1974), Whitaker et al. (1975), and Meshal (1977), the latter comparing friction coefficients measured directly with these obtained from the wind velocity profile. Francis (1954, 1959) and B.W. Wilson (1960) published important early reviews of the

486 486

dependence of the coefficient on wind speed. A masterly review by Garratt (1977) treats the voluminous data of recent years. He analysed 791 individual measurements of the coefficient from a total of 27 sources for winds between about 3 and 2 1 m s I , determining means over successive 1 m s - I intervals. Similarly, 65 estimates for the winds associated with actual or simulated hurricanes from 6 sources were treated in successive intervals of 5 m s - I . Figure 12-6 shows Garratt's mean values, the dashed lines being the approximate envelope of the standard deviations about the means. The coefficient increases approximately as the square root of the wind speed at 10m between speeds of about 3 and 50m s - ' . The friction coefficient given in Fig. 12-6 is for a neutrally stable atmosphere, the value in practice varying slightly according to the stability of the air over the water and on the extent of wave-breaking (Sethuraman and Raynor, 1975; Melville, 1977). At high wind speeds, the coefficient may also be weakly influenced by the foam on the water surface and spray in the wind (Kraus, 1967b). Van Dorn (1953) found that the shear stress due to heavy rain, such as often accompanies storms, .amounted to about 20 percent of the total stress (see also Caldwell and Elliott, 1971). Figure 12-6 may be confidently used for most practical purposes, however, as these additional sources of variation are often smaller than the measurement and other errors. ~

-

c; 0

.-c Q

5 r

-

0.030

0

c .c

._ c L

0.020 0

9 .D

.-

: 2.

g

n

0.010

-

-

n l 0

I

10

20

I

I

30

I

40

I

I

50

60

Wind velocity at IOm height, U, (m .-I)

Fig. 12-6. Empirical relationship between the friction coefficient of a wind-affected water surface and the wind speed at a height if 10m above the surface. The points represent the averages, in bands of either 1 m s - I or 5 m s - ' , of numbers of individual estimates of the friction coefficient. For data and full explanation of sources and treatment see Garratt (1977). The dashed lines are the approximate envelope of the standard deviations about the individual mean values.

487 A MODEL OF STORM SEDIMENTATION IN SHALLOW WATERS

Qualitative description The material summarized above, combined with earlier data, provides the basis for the development of a simple model for storm sedimentation in shallow offshore waters.

Fig. 12-7. A speculative physical model for storm sedimentation. a. Definition diagram for a shelf with sandy shore affected by a storm travelling across the shelf from deeper water. b, c, d. Variation of wave-related currents with time and with distance across the shelf, as illustrated by inner shelf, mid shelf, and outer shelf stations. In (c) the change in wave properties with time is also sketched. e. The movement of the margins of the storm and of the leading edge of the zone of storm-mobilized sand. The graph also summarizes the sedimentation effects of the storm. The potential limit of sand movement on the shelf is indicated, but thresholds related to the deposition of mud and to its erosion have been ignored owing to their relatively uncertain nature.

488

The specific setting of the model is a shelf richly supplied with mud and sand by rivers (Fig. 12-7), but the scheme is equally applicable to a shelf bordered by shoals and barriers of autochthonous carbonate sediments. In developing the model qualitatively, it is recognized that a storm is a moving, localized disturbance with transient effects at each station. These effects can be related at any site to five gradational stages of storm development. The pre-storm stage sees gentle winds and small surface waves, that is, fair weather (Hobday and Reading, 1972). The stage of storm growth witnesses a rapid increase in wind strength and consequently in wave size and period. During the next stage, that of fuff storm, wind and wave conditions remain substantially constant for a significant interval. There follows a long stage of storm decay during which the wind speed and sea are gradually restored to something like their pre-storm state. The post-storm stage resembles that of the pre-storm. The sedimentological consequences of a storm crossing a shelf toward a sandy coast are best analysed in terms of events at representative outer-shelf, mid-shelf and inner-shelf stations (Fig. 12-7). Since abundant mud is considered to be available, it may be further assumed that during fair weather a blanket of mud accumulates over the bed, except in the extreme shallows, where wave-action is invariably powerful enough to sustain sand movement. The shore would therefore seem to be the major if not sole (linear) source of sand-grade sediment redistributed during the storm. The centre of a storm should take several to many hours to cross a shelf in the order of 50-100 km wide. At a station in its path, one would observe a rapid increase during the growth stage in the characteristic wave period and wave height, a steadying of the period and height during the full-storm stage, and their gradual decline during the decay stage (Fig. 12-7c). We consequently see from Vol. I, eq. (1.49) that U,,, the maximum horizontal orbital velocity of a near-bed water particle, will first increase rapidly with time, become relatively steady for a period, and then decline more slowly during the passage of the storm. Two factors contribute to the comparatively rapid local changes in U,,, firstly, its linear dependence on wave height and, secondly, its inverse relationship to the wave period. Because U,, is also inversely related to water depth, (Vol. I, eq. 1.49), the post powerful waverelated bottom currents will arise on the inner shelf as compared with the mid-shelf, and on the mid-shelf as compared with the outer shelf (Fig. 12-7b-d). However, the finite storm transit-time means that the changes in U,, are out of phase at these various stations. Indeed, since the stage of storm-growth has a duration of the same order as the transit-time over a shelf of the width indicated, fair weather conditions may persist over the inner shelf virtually up to the time when the storm is at full force at the shelf edge. Therefore for a short while after the leading edge of the storm has passed the shelf-edge, Urn, may decline shoreward from the shelf-edge and with decreasing water depth. Only when the storm lashes the inner shelf will

489

Urn, begin to decrease with increasing depth, which condition will persist until the storm has everywhere decayed. It is again not until the storm attacks the inner shelf that terrigenous or carbonate sand will be released by wave-action inshore for outward transport into deeper waters by the wind-induced bottom currents, by eq. (12.21). The seaward edge of the belt of moving sand particles maintained as a dispersed load through the action of Urn,, (Vol. I, eq. 2.43), will travel outward at a rate comparable with U,, the velocity (offshore) of the wind-induced current at the bed, and to a distance determined either by the temporal development of U, over the duration of the storm, or by advance for the into the depth at which Urn, is less than the critical value, ( entrainment of the sand supplied. Since U, would seem to be smaller than the speed of the storm centre, storm duration is probably the main control on the seaward spreading of sand (Fig. 12-7b-d). Clearly, sand arrivals will be out of phase at the various stations, appearing later with increasing distance from shore and water depth. As sketched in Fig. 12-7e, this phase effect acts in the opposite direction to that deriving from storm movement. Moreover, the phase changes related to sand movement are delayed with respect to those connected with wind and wave conditions. A further point to note is that, by the time sand has begun to be mobilized, Urn,,(t ) is everywhere probably increasing or constant while Urn=(x ) is at most instants an increasing function. We can now describe the sedimentary regimes likely to operate at different times and places during the storm (Fig. 12-7e). Under the assumed sediment supply, the pre-storm stage sees mud deposition over the entire shelf except for a ribbon inshore. The path of the leading edge of the storm-mobilized sand gives the lower bound to a regime of sand deposition, on account of the mode of variation of Urn,(x,t) just noted. Rewriting Vol. I, eq. (2.24) for sediment transport using Vol. I, eq. (2.43) for the load supported through wave action and U, as given by eq. (12.21) for the transport velocity, we obtain in outline for the .rate of sediment transfer: (12.22) for two-dimensional conditions. Noting from Vol. I, eq. (2.43) that m , the sediment load, increases as a large power of Urn,,we find that the transfer rate A is positive, indicating deposition. A second storm-related regime is defined by the path of the belt of mobilized sand, and the paths of the leading and trailing edges of the storm. Under this regime, either mud already deposited on the shelf is eroded, or the supplied mud remains dispersed. The control is the magnitude of Urn=.Where relatively low values prevail, as on the muddy outer shelf, non-deposition may be expected. Erosion should dominate on the inner shelf and mid-shelf, where the values reached are likely to exceed the critical for fluid-stressing, and where

490

autochthonous coarse debris such as shells can be mobilized for corrasion. Any sediment accumulated on the outer shelf during the storm is expected to be mud, such lamination as may be found reflecting the cessation of deposition during storms. As sedimentation rates are likely to be relatively low, however, subsequent bioturbation could lead to complete destratification. The mid-shelf deposits are likely to be thin allochthonous sands interbedded with thicker autochthonous muds. The storm sand-layers should have sharp and often erosional bases, reflecting the moderate values of U,,, prevailing. The beds should be relatively thin, because the regime of sand deposition exists for comparatively short periods at mid-shelf stations, and they should ordinarily be normally graded, since the regime is operative mainly during the storm-decay stage. We should expect to find wave-current ripples on the tops of the sand beds and, internally, a related climbing-ripple cross-lamination (Vol. I, Figs. 11-18, 11-20). The inner-shelf deposits should be thick allochthonous sands alternating with thinner autochthonous muds. Most sand beds should have a sharp and erosional base, and in many instances channelling, rilling, and fluting (offshore-directed) may be detectable. The coarse beds are expected to be relatively thick because the regime of sand deposition endures for relatively

2

5

b

.s 3

erosional bases

Increasing depth and distance

Storm

duration

* $

KEY

t

@ Wave ripples

d

and cross-lammatian

Parallel lamination

BShells

and mud clasts

Storm duration

Fig. 12-8. Three-dimensional graph suggesting the character of storm sand-layers as a function of storm duration, characteristic wind speed, and increasing water depth and distance from land.

49 1

long periods at inshore stations and, moreover, the rate of change of U,,, with x is here at its greatest. Normal grading should typify the upper parts of the sand beds, formed during the storm-decay stage, but the middle and lower portions may show a sand texture constant with height, reflecting accumulation during the relatively stable full-storm stage. Because of the preceding relatively intense erosion of the mud, however, sand beds may reveal basal lags of shell and other biogenic debris, partly derived locally and partly introduced from elsewhere on the shelf floor. Since U,,, attains relatively large values at inner-shelf stations, we should expect from Vol. I, Figs. 11-18 and 11-20 to observe parallel lamination followed upward by wave-related cross-lamination within the sand beds and perhaps a wavecurrent rippled top. The ripples and cross-lamination formed on the inner and mid shelves should have an asymmetry indicating transport in the same direction as the wind-induced bottom current. Figure 12-8 summarizes the trends and characteristics expected above and indicates the likely effects of storm intensity, as expressed by the wind speed, controlling both wave characteristics and the strength of the wind-induced currents, and the storm duration. Aspects of a quantitative model Clearly, Vol. I, eqs. ( 1.49), (2.43), this Vol., eqs. (12.2 1) and ( 12.22), together with Figs. 1 1-18 and 11-20, of Vol. I, afford some basis for the quantitative estimation of the characteristics of storm sand-layers, provided that the storms themselves, together with the boundary conditions, can be specified. These calculations, proceeding in suitably small time-steps, are too involved to be described here, but it is useful to explore an abbreviated model, particularly in order to establish the order of magnitude of the horizontal and vertical dimensions characteristic of storm sand layers. Equation (12.15) may be used to calculate the water-surface profile and set-up, if so desired, whence an impression may be gained of the likely simultaneous effects of the storm at the shore. In these simplified calculations, it is assumed for the boundary conditions that water depth decreases linearly with increasing distance shoreward from the shelf-edge. The storm is characterized by a wind of constant speed and direction (normal to shore) and by waves of a single significant height and period, taken for each wind speed from Darbyshire and Draper’s (1963) graphs for coastal waters. The friction coefficient necessary to calculate the wind-induced bottom current comes from Fig. 12-6, and in eqs. ( 12.15) and ( 12.2l), k , = 1.1 and fo = 0.04. Under this specification, the amount of deposit formed at a station is proportional to the product of the duration of the regime of sand deposition at that station and the deposition rate afforded by the first term of eq. (12.22). A bulk density for the deposited sediment of 2000 kg m-3 is assumed in calculating final bed thicknesses. It is finally assumed that deposition begins

TABLE 12-1 Principal conditions and results for storm sand-layers deposited on a uniformly sloping shelf Wind speed

40

Wave period T

(m s - ' )

6)

Wave height H (m)

Friction coefficient of sea surface fI0

Velocity of near-bed offshore currents

Reach of sand away from shore Sand transported offshore distance depth during storm (km) (4 (kg m-')

UO (m s-I)

30 20 15 10

9.5 7.7 6.7 5.4

9.95 3.58 2.34 1.30

2.16X l o p 2 1.68X 1.44x 1 0 - 2 1.12x

0.0865 0.0508 0.0353 0.0207

20.45 10.94 7.53 4.38

54.54 29.18 20.09 11.69

3.43 x 10' 8.02X lo6 2.85 X lo6 105 9.74~

493

t 10-61

0

4 I

2

4

6

8

10

12

14

16

18

PO

22

Perpendicular distance outward from shore (km)

Fig. 12-9. Calculated variation in storm sand-layer thickness with distance from shore and wind speed on a uniformly sloping shelf of width 75 km and shelf-edge depth 200 m. Sand transported is of diameter 0.000125 m, solids density 2650 km mp3, and bulk density when deposited 2000 kg m-3. Storm duration 48 h. See also Table 12-1.

immediately seaward of the depth in which the waves appropriate to the wind speed break. Table 12-1 and Fig. 12-9 summarize the calculations made for four different wind speeds, under the supposition that the wind and its effects endure for 48 hours at any site. The results indicate that considerable volumes of sand can be transported offshore during storms, and that storm sand-layers may accumulate many kilometres from shore, in depths of several tens of metres, and to thicknesses in the order of centimetres or decimetres. For sand particles of the size and density assumed, Fig. 11-18 (Vol. I) affords a critical value of U,,, = 0.6 m s - for the occurrence of a plane bed. Reference to this threshold in Fig. 12-9 suggests that parallel lamination succeeded by cross-lamination is restricted to the thick proximal parts of storm sand layers. Cross-lamination is the only structure preserved distally.

'

STORM SAND-LAYERS IN MODERN SEDIMENTARY ENVIRONMENTS

Hayes (1967) gives from his work on the continental shelf off Padre Island in the Gulf of Mexico an account of the sand layer that can with most confidence be regarded as a storm deposit.

494

He sampled the shelf sediments prior to the appearance in the area of hurricane Carla in September, 1961, and again the following spring and summer, no other hurricanes having occurred in the interval. The sea bed before the hurricane comprised homogeneous sandy mud with uniformly dispersed foraminifera. The bed was afterwards found to consist of a layer of well-sorted sand approximately 0.0 1-0.03 m thick in depths up to 20 m and, in water as deep as 36m (the outer limit of sampling), a layer of very fine sand or coarse silt approximately 0.01 m thick that passed rapidly into silty mud and then clayey mud. This deeper layer, with a maximum thickness of 0.09m, is described by Hayes (1967) as graded. Its base is invariably very sharp, and the overlying very fine sand or coarse silt, locally laminated, is rich in abraded foraminifera. The graded bed was shown to be developed over a distance of almost 65 km parallel with the shore, and the exposed sand bed to landward over a frontage of about half this length. A water depth of 36m is attained 25 km from shore. Largely because of a spatial relationship between the thickest parts of his graded bed and hurricane channels in the neighbouring barrier island, Hayes (1967) attributed both the sand layer and the entire graded bed to deposition from a turbidity current created by the eventual ebbing of the storm surge. However, sand dunes at the coast were cut back in the order of 50-100m during the storm, whence it is plausible that the sand layer, fining out into the sandy basal portion of the graded bed, was deposited by offshore-flowing currents during the main part of the hurricane. Other workers describe from the Gulf of Mexico shelf what may be storm deposits. Bernard et al. (1959, 1962) and Bernard and LeBlanc (1965) report an investigation by boring and coring into the sediments of the Galveston Island barrier to the northeast of Padre Island. The deposits found at depths greater than about 10m are interbedded muds and sands, the latter characteristically several centimetres thick, well laminated, and often sharp-based and graded, with shell-rich lower parts. Possible storm sand-layers are described from the German Bight in the eastern North Sea (Reineck et al., 1967, 1968; Gadow and Reineck, 1969; Reineck and Singh, 1972; Reineck, 1974d). Much of the sea bed between the mouths of the Weser and Elbe, and Helgoland some 40 km offshore, is underlain by sand beds a few centimetres thick interbedded with generally thicker muds. Depths characterized by this association range from 6 m close to shore to nearly 40m near Helgoland. The sand layers (Fig. 12-10) have sharp bases, with some preserving what may be erosional furrows, and typically are normally graded. Texturally, the layers range from fine sand to coarse silt. Many appear to be parallel-laminated throughout, whereas others seem to show only cross-lamination and a sharp rippled top. Parallel lamination in some underlies cross-lamination. To judge from the long cores examined by Reineck et al. (1968), the sand layers become thinner on the average and less frequent toward deeper water. Gadow and Reineck (1969)

495

(a) (b) Fig. 12-10. Possible storm sand layers, German Bight, North Sea. a. Water depth 27 m, sample thickness 0.2 m (see Reineck et al., 1967). b. Water depth 15 m, sample thickness approximately 0.3 m, the two uppermost sand layers being attributed to the winter of 1966-1967 (see Reineck et al., 1968). Photographs courtesy of H.-E. Reineck.

claim that some individual layers are continuously distributed over horizontal distances in the order of 10 km, on the basis of their close association with intensely bioturbated muds. Individual layers may well have an extensive distribution, but the particular correlations proposed by Reineck et al. (1967, 1968) are not convincing, intense bioturbation being rather local in its distribution. The suggestion by Reineck et al. (1967) that these North Sea sand-layers are storm deposits is appealing. The German Bight experiences frequent storm surges, during which tidal currents out to sea are significantly enhanced by wind-induced flows. Moreover, the sand layers are mineralogically similar to the sands that form barrier islands and sand flats along the nearby coast, and often contained when deposited living organisms whose normal habitat was an intertidal flat. Finally, the character of the sand layers, and their spatial variations in thickness and frequency, are consistent with the models outlined above. Interbedded sands, clean silts, and muds not unlike those reported from the North Sea occur in depths as great as about 60m and at distances from shore as great as 40 km on the muddy continental shelf off the Niger Delta (Allen, 1965e, 1970e). Few of the layers resemble compositionally the relict shelf sands, and most must have been derived, perhaps through storm-action,

496

from the extensive coastal sand barriers of the delta. What may also be storm sand-layers occur in water depths of 10-20m in the Baltic Sea (Werner, 1968), and at depths of about 10 m off the sandy shores of the Gulf of Gaeta in the Tyrrhenian Sea (Reineck and Singh, 1971; Reineck, 1974d). Kumar and Sanders ( 1976) attribute to storm-action thick, sharp-based, graded sand units with gravelly bases found amongst continuous sands in water depths of 5-21 m off Long Island. Much of each unit consists of parallel-laminated fine sand, indicating accumulation beneath powerful waves. As the result of work in the North Sea and Gulf of Gaeta, Reineck and Singh (1972) proposed a model of storm sedimentation which differs significantly from that sketched above. They suggest that sand accumulates only when wave action is decaying and, like Hayes (1967), associate the offshore movement of sand with storm-surge ebb. There must undoubtedly be deposition of dispersed material during the stage of storm-decay, but in terms of the present model, the bulk of the deposit could be formed during the full-storm stage, on the supposition, justified in most real cases, that depth increases with increasing distance from land. For example, in the calculations summarized in Fig. 12-9, the sediment left dispersed in the water column at the end of the period of storm action is in thickness generally much less than that deposited during the storm.

STORM SAND-LAYERS IN THE STRATIGRAPHIC RECORD

Description of examples

There have come from the stratigraphic record many descriptions of deposits that are increasingly being interpreted as storm sand-layers formed at a substantial distance from land in mainly marine waters perhaps several tens of metres deep. Goldring (1966) was the first clearly to isolate such layers as a distinct facies,.though he did not at the time propose a storm origin. Deposits with possible storm sand-layers occur in the Precambrian (Goldring and Curnow, 1967, Unit B, Wilpena Group; Hobday and Reading, 1972, Facies A, Skallsneset Sandstone; Banks, 1973b, Facies 2 and 3 Innerelv Member; Anderton, 1975, Craignish Phyllites, 1976, Jura Quartzite; Andrews and Laird, 1976, wavy-bedded sandstones, Bowers Group), and many are recorded from rocks of Lower Palaeozoic age (Martinsson, 1965, Paradoxissimus Siltstone; Reading, 1965, Quartzite and Shale Member, Kistedal Formation; Goldring, 1966; Anstey and Fowler, 1969, Eden Shale; Curtis, 1972, Damery Beds; A.M. Thompson, 1972, Reedsville Formation; Goldring and Bridges, 1973; Bridges, 1975, Upper Llandovery sandstones; Brenchley et al., 1979, Brenchley and Pickerill, 1980, Ordovician sandstones

497

and limestones; Hurst, 1979a, 1979b, Alternata Limestone; Cant, 1980). Fine examples are seen after winter storms in the Wenlock rocks of Freshwater East and Freshwater West, South Wales (Dixon, 1921; Bassett, 1974). Upper Palaeozoic strata are also rich in storm layers (De Raaf et al., 1965, Facies H, Abbotsham and Northam Formations; Jux and Strauch, 1965, “Hians”-Schille; Goldring, 1966, 1971, Reynard and Diplocraterion yoyo Facies, Baggy Beds; Hobday, 1973, Facies 2, Ecca Group; Dzulynski and Kubicz, 1975, Muschelkalk; Kelling and Mullin, 1975; Vos and Hobday, 1977, Ecca Group; Poole, 1977, -sandstone-shale facies, Holt Farm Group; Vos, 1977; Aigner, 1979, Muschelkalk; Goldring and Langenstrassen, 1979, Pilton Beds, Sonyea Group). The facies is widely known from Mesozoic sediments, particularly the Jurassic and Upper Cretaceous shallow-marine rocks of the Western Interior of the U S A . and Canada (J.D. Howard, 1966a, Panther Sandstone Tongue; Masters, 1967, Mesaverde Formation; Hiintzschel and Reineck, 1968; Michaelis and Dixon, 1969, Facies B1, Cardium Sand; Sellwood et al., 1970, Thorncornbe Sand; Campbell, 1971, Gallup Sandstone; Hubert, 1972, Hubert et al., 1972, upper part Cody Shale; Brenner and Davies, 1973, Sundance Formation; Goldring and Bridges, 1973; Cotter, 1975, Washboard Unit, Ferron Sandstone; Hamblin and Walker, 1979, Fernie-Kootenay sediments; Bourgeois, 1980, Cape Sebastian Sandstone). See also D.W. Lewis (1980), Vos (1981), and Wright and Walker (1981). Although most of the cited examples involve only terrigenous sediments, a few include or are dominated by carbonate deposits. Many of these examples of storm sand-layers are recorded from just below thick sandstones seemingly of littoral, tidal or fluvial origin. The characteristics of storm sand-layers change with setting and age, but a number of distinctive features, represented in most examples of such sediments, can be isolated. Figure 12-1 1, from Devonian-Carboniferous shallow-marine rocks of Morocco (Vos, 1977), is typical of storm deposits as seen in substantial exposures. Facies containing storm sand-layers, to judge from the cited examples, generally consist of alternations of mudstone or shale with coarser beds, either quartz sandstones typically of fine -sand, very fine sand, or coarse silt grade, or bioclastic sandstones or even rudites of granule or coarser sizes. The mudstone content and the thickness of the coarse beds tend to vary inversely, and it is very rare to find individual sandstones more than 1 m thick. Coarse beds ranging in thickness between a few millimetres and several centimetres are generally associated with mudstones in the order of 5- 10 times thicker. Terrigenous or bioclastic sandstones ranging between a few centimetres to perhaps 0.3 m thick occur with about equally abundant mudstones. In sequences with even less mudstone, individual coarse beds commonly reach 0.5m in thickness, and some of decimetre scale may lie amalgamated in thick groups. The thinner coarse beds are typically of an impressive lateral extent, though not necessarily of a uniform thickness.

498

Fig. 12-1 1 . General view of sandstones (? storm layers) interbedded with siltstones and shales, Tournasian rocks, Ersane, Tindouf Basin, Morocco. Photograph courtesy of R.G. Vos (see vos, 1977).

Martinsson (1965) could trace layers only a few centimetres thick over horizontal distances at least as great as 400 m. Brenchley et al. (1979) could trace beds no more than a few centimetres thick for as much as 50m or so along their strike. Anderton (1976) recorded from the Jura Quartzite that beds extended laterally for distances more than lo4 times their thickness. The thicker coarse beds, however, are more often visibly lenticular, and some are seen to occupy channel-like features. The bases of the coarse beds are invariably reported as sharp and in most cases as either planar, gently undulose, or irregular and clearly erosional. Some bases are quite smooth, except in some instances for animal tracks (e.g. Martinsson, 1965), whereas others show small tool marks and in places flute marks or small erosional furrows. Occasionally, the thicker coarse beds preserve large corrasional furrows beneath (e.g. Aigner, 1979), called Rinnen (Hantzschel and Reineck, 1968) or gutter casts (Whitaker, 1973) (Chapter 1).

499

Fig. 12-12. Schematic representation of vertical sequences reported from beds thought to be storm sand-layers.

Fig. 12-13. Topmost 0.08 m of a 0.15 m sharp-based sandstone bed (? storm layer) in which parallel laminations are succeeded by wave ripple marks, Sandstone Series, Middle Silurian, Dyfed, Wales. Photograph courtesy of R. Goldring (see Goldring and Bridges, 1973).

500

The tops of beds usually are less sharp than the bases, some units exhibiting a perceptible upward transition from sandstone, through sand and mud laminae, into mudstone. Figure 12-12 illustrates the more important sequences recorded from what are here suggested to be storm sand-layers formed of terrigenous sand. Many of these resemble sequences known in turbidites. Their resemblance to turbidites is further strengthened by the presence in most of the sand-layers of normal textural grading, if not throughout the whole bed then in its upper part. Beds of type A contain parallel lamination as the only internal structure (e.g. Goldring and Bridges, 1973; Anderton, 1975), thus resembling

Fig. 12-14. Bands of mainly wave and wave-current ripple laminated sandstones alternating with mudstones, Abbotsham Formation (Westphalian), Devon, England. Photograph courtesy of R.G. Walker (see De Raaf et al., 1965). Note sharp uneven bases to sandstones and local development of parallel lamination just above bases.

50I

Fig. 12-15. Part (0.15 m) of a storm sand layer showing climbing-ripple cross-lamination with upward increasing and reversing angle of climb, Tournasian rocks, Aftes, Tindouf Basin, Morocco. Parent ripples probably wave-current to wave in type. Photograph courtesy of R.G. Vos (see Vos, 1977).

some inferred storm sand-layers from modern environments. Wave ripples and wave-current ripples, occasionally strongly three-dimensional, are frequently reported from facies believed to be of storm origin. In type B beds (Fig. 12-13) a wave-rippled top overlies parallel lamination (e.g. Goldring and Bridges, 1973; Hamblin and Walker, 1979). Beds of type C abound, revealing a substantial development of wave-current or current-ripple crosslamination above parallel lamination (Goldring and Curnow, 1967; Hubert et al., 1972; Banks, 1973b; Hobday, 1973; Cotter, 1975; Anderton, 1976; Vos, 1977). Type D beds (Figs. 12-14, 12-15) consist only of wave-current to current-ripple cross-laminated deposits, often showing small or moderate angles of climb (De Raaf et al., 1965; Goldring and Curnow, 1967; Michaelis and Dixon, 1969; Sellwood et al., 1970; Hubert et al., 1972; A.M. Thompson, 1972; Anderton, 1976; Vos, 1977). Beds of type E are truncated erosively and overlain mainly by mudstone, whereas beds of type F are sandstones amalgamated at erosion surfaces. The parallel lamination recorded from storm sand-layers is often rolling, with slight internal discontinuities (hummocky cross-stratification of Hamblin and Walker, 1979). The biological features of terrigenous storm sand-layers are significant. In Phanerozoic cases, for example, Llandovery and Wenlock deposits in South

502

Fig. 12-16. A storm sandstone layer approximately 0.1 m thick showing concentration of coarse bioclastic material immediately above uneven erosional base, grading up into crosslaminated sandstone with indications of wave ripple marks, Tournasian rocks, between Aftes and Messeied, Tindouf Basin, Morocco. Photograph courtesy of R.G. Vos (see Vos, 1977).

Wales and adjacent areas (Dixon, 1921; Curtis, 1972; Bassett, 1974; Bridges, 1975), and the Devonian-Carboniferous of Morocco (Vos, 1977), a mainly suspension-feeding fauna (brachiopods, bivalves, crinoids, bryozoans, corals and in places tribolites) occurs in the lower parts of beds as transported, often broken and disarticulated, remains (Fig. 12-12, types, G, H). These shelly layers usually contribute toward the grading visible in the sandstones, the debris being coarsest and most plentiful toward the base (Fig. 12-16). The mudstones immediately below, however, may yield a much more restricted though partly identical fauna. Goldring and Bridges ( 1973) indicate that the mudstone faunas seem to have been smothered in life-position, whereas faunas in the sandstones represent organic remains swept together from a wide area. Another pointer to relatively rapid sandstone deposition and the displaced nature of the sandstone fauna lies in the preservation of delicate tracks on occasional sandstone soles (e.g. Martinsson, 1965). The mudstones between sand layers are often described as bioturbated, and trace fossils, occasionally associated with complete destratification, are frequently reported (Fig. 12-12, type J) from the upper parts of the sand beds (Martinsson, 1965; Goldring and Bridges, 1973; Cotter, 1965; Vos and Hobday, 1977). The trace fossil assemblages reported from facies with inferred storm sand-layers mainly belong to Seilacher’s ( 1963, 1964) shallow-marine

503

TERRIGENOUS

ELEMENT

BlOCLASTlC

ELEMENT

Cross-lamination

Cross-bedding

Parollel lamination

Parallel tamination

0

Mossive

Massive

Fig. 12-17. Varieties of sequence in supposed storm sand-layers of mixed bioclastic and terngenous elements, Carboniferous, Morocco. After Kelling and Mullin ( 1975).

Fig. 12- 18. Limestone-sandstone couplet in Carboniferous rocks, Oued Cherrat, Morocco. The lower portion consists of parallel-laminated and poorly graded limestone with an irregular and erosional base. The upper part is of cross-laminated quartzite. Photograph courtesy of G. Kelling.

504

Cruziana association (Martinsson, 1965; Howard, 1966b, 1972; Frey and Howard, 1970; Campbell, 1971 ; Goldring, 1971). Much less is known of possible storm sand-layers from sequences where the coarser clastic material is wholly or predominantly biogenic (Anstey and Fowler, 1969; Brenner and Davies, 1973; Dzulynski and Kubicz, 1975; Kelling and Mullin, 1975; Aigner, 1979). Sharp-based and graded limestones and six types of limestone-quartzite couplets were distinguished by Kelling and Mullin in the shallow-marine Lower Carboniferous rocks of central Morocco (Figs. 12-17, 12-18). The graded limestones range from 0.04 to 1.1 m in thickness, are often lenticular and occasionally channel-filling, and range in grade at the base from coarse sand to small cobbles. Many units have a massive, graded lower part succeeded by either parallel lamination, cross-lamination or, rarely, cross-bedding. Couplets of type A lack visible signs of internal bedding, consisting of an ungraded lower bioclastic portion overlain by fine quartz sandstone. Type B couplets are similar in the absence of internal bedding but are normally graded. Types C and D couplets show a massive then graded and parallel-laminated bioclastic portion sharply overlain by quartz sandstone, in some instances cross-laminated. Couplets of type E comprise massive and ungraded bioclastic sediment succeeded erosively by either parallel-laminated or cross-laminated quartz sandstone. In type F, the bioclastic portion is cross-bedded and the top, concealed by quartz sandstone, shaped into large ripples. Vos and Hobday ( 1977) have described cross-bedding from terrigenous storm sand-layers as coarse as these carbonate-dominated sediments. Comparison with the model

Figures 12-7 and 12-9 summarize a model of storm sand-layers which has a quantitative basis, expressing the idea that these deposits depend on the simultaneous action during storms of wave-generated oscillatory currents, entraining grains and dispersing them as a sustained load above the bed, with wind-induced unidirectional currents that effect net offshore transport. The coarse layers reported from the stratigraphic record conform closely to this model in their generally small thickness, great lateral extent, the prevalence of normal grading, the frequent indications of wave action, and the presence in examples of suitable age of allochthonous faunal assemblages. What are here attributed to storms in many respects resemble turbidites. Goldring (1966) noted this similarity but rejected turbidity currents as the depositional agent, in favour of the combined action of waves with currents, though an association with storms was not made explicit. This view was later adopted by Vos ( 1977) and vigorously supported, with elaborations, by Kelling and Mullin (1975). In a further discussion (Goldring and Bridges, 1973), three possible storm-related processes were favoured: (1) storm waves operating alone, (2) storm waves combined with ebbing tidal currents, and

505

(3) storm surges. The second of these, also advanced by Anderton (1976), partly resembles the present model, but can only be significant in restricted waters, such as an estuary or gulf. Banks (1973b), following Hayes (1967) and Gadow and Reineck (1969), attributed his coarse layers to the decay of the surge itself, as also did Brenchley et al. (1979). Offshore flow must obviously accompany the return of the water surface to horizontality, but other than immediately inshore the currents due solely to this cause are extremely weak, due to the smallness of the set-up in comparison with shelf depths. Vos (1977) explained his storm layers by wave-action alone. The insurmountable problem presented by this explanation is that storm sandlayers have a thickness much greater than can be provided for by the collapse of an un translated wave-supported sediment load. There seems to be no realistic alternative to Goldring's original proposal. The similarity between turbidites and storm sand-layers records not merely parallel trends of flow power and sedimentary regime, but in some instances perhaps a significant direct connection (Hamblin and Walker, 1979). De Raaf et al. (1965), Walker (1969, 1970b), and Hobday (1973) record a close spatial relationship between what seem to be storm sand-layers and thin-bedded turbidites, either interspersed with the storm sands or in thin bundles. We saw in Vol. I, Chapter2 that the sediment dispersed above the bed through wave-action is concentrated close to the bed, whence an effectively stratified system is created. If the bed sloped sufficiently steeply, and the bulk density of the mixture was large enough, the dispersion could under its own weight flow swiftly into deeper waters still within the bounds of the shelf. In depths where wave-induced currents were small, the resulting deposits would afford no evidence for wave-action, and would closely resemble conventional turbidites. That the wave-related currents rapidly decline with increasing depth is shown by calculating U,,, for a depth of l00m (mid-shelf) using the data of Table 12-1, the largest value obtained being 0.076 m s - I .

SUMMARY

Most storms are associated with atmospheric depressions (cyclones) and amongst the most important of their effects on bodies of shallow water are the creation of a positive set-up (storm tide) at the shore toward which they move, an onshore near-surface current, and an offshore bottom current. The magnitudes of the set-up and currents are now calculable under a variety of circumstances. The simultaneous action of the offshore bottom current with the storm-enhanced wave-related currents at the bed can be shown by means of a simple quantitative model to result in the transport toward the offshore of large volumes of coarse sediment derived from the coast, and to the deposition of sharp-based graded layers of displaced sand in depths where

506

the fair-weather accumulate is mud. These layers bear an additional resemblance to conventional turbidites in showing Bouma-like sequences of internal structures. They are distinguished from turbidites, however, by the preservation of wave-related ripple marks and/or cross-lamination. The grain dispersions produced through storm action may under some circumstances escape downslope into shelf depths where wave-action is reduced, and so form turbidity currents from which result graded beds closely resembling deep-water turbidites of the thin-bedded variety.

507

Chapter 13

MISCELLANEOUS SEDIMENTARY STRUCTURES

INTRODUCTION

There are many sedimentary structures which, not fitting comfortably into the categories indicated in the preceding chapters and Volume, are considered here in a wide-ranging miscellany. Rill marks are miniature stream systems, varying from an origin on sand beds by erosion, to one of differential deposition when formed on surfaces of sticky mud. Tool marks are single grooves made in a stationary bed by an object impelled by a transporting agent. Drifting ice masses, debris propelled by turbidity currents, and stones caught up by glaciers are the main natural tools. A stationary tool, free in a current only to rotate about its anchor-point, makes a scratch circle on a deformable bed. The action of densely arrayed fluid-driven tools is to corrade a deformable bed, producing ripples, grooves or sastrugi. Swash and foam marks are features restricted to sand beaches. Vesicular structure is common in high intertidal sands but can also be found in the soils of hot, dry regions. Adhesion ripples, shaped from wind-blown sand, and mud waves, accumulated on the ocean floor beneath mud-bearing currents, record an instability between a fluid stream and a wavy bed capable of permanently capturing particles in transport. Desiccation and synaeresis cracks record the effects of tensile stresses in layers of sediment possessed of defects internally and/or on their boundaries. The injection of mobilised grains into strata under tension results in sedimentary intrusions. Infilled shrinkage cracks and penecontemporaneously formed sedimentary intrusions often during consolidation become buckled into ptygmatic folds, the shape and scale of which, as with their tectonic counterparts, partly depends on the viscosity of the layers involved.

RILL MARKS

These are systems of small, arborescent furrows equivalent to ordinary river networks but which drain small amounts of water from intermittently exposed surfaces of fresh sediment. They appear in the stratigraphic record chiefly as rill moulds, in early days regarded as organic. Rill marks (Fig. 13-1) are chiefly found on muds and sands in the intertidal zone, where they were described by Williamson ( 1887) and Dawson (1890), who attributed them to erosion by the drainage from the exposed sediment. Cepek and Reineck (1970) have documented a wide variety of these marks, which occur on mild to steep slopes and consist of up to three

508

Fig. 13-1. Rill marks on an intertidal sandbank of well-sorted fine sand, Wells-next-the-Sea, Norfolk, England. Trowel 0.28 m long points downslope.

509

orders of practically straight to moderately sinuous furrows. Size of furrow increases steeply with ascending order. The water shaping rills comes from three possible sources: (1) groundwater stored within the body of the sediment (e.g. beach or bar), in some instances channeled by pre-existing organism burrows (e.g. B.W. Flemming, 1977), (2) wave swash, and (3) from within the most recent layer of sediment as it coagulates and consolidates. The predominance of the first source is gradually replaced by that of the second and third as the sediment changes from permeable sand, through low-permeability muddy sand and sandy mud, to impermeable mud. Rill marks (described as surge marks) in mud occur on steep banks in the channels of ephemeral streams (High and Picard, 1968; Picard and High, 1973), on tidal flats (Reineck, 1974a), and in cave passages (P.A. Bull, 1976, 1978). Small rill marks ornament the terraces that Picard and High (1973) called fluted steps. Jaggar (1908) made rill marks experimentally by allowing water to seep out of a deposit of sand with a sloping surface. He also made them when a thick soup of mud coated on to an inclined glass plate coagulated further and dewatered, the excess water and some of the sediment draining off through small dendritic channels. This mechanism of differential deposition explains better than any other the surge marks of constructional type described by P.A. Bull (1978). Rill moulds are common in the stratigraphic record, where their significance is primarily as indicators of exposure. Dawson (1890) illustrates fine examples from Carboniferous rocks in Nova Scotia, and later workers (Boyd and Ore, 1963a, 1963b; Diesel et al., 1967; Gall, 1971) describe similar forms. H.C. Beasley (see Cummins, 1958) assembled a large collection of photographs of slabs from the English Trias, now in the Department of Geology, University of Liverpool, amongst which are further excellent examples, which he interpreted as the “natural casts of stream courses”. The tassel marks of Hantzschel and Reineck (1968) are rill moulds. High and Picard (1968) and Cepek and Reineck (1970) list other occurrences. Stear (1979) illustrated rill marks from the side of a sand bar in a Karoo-age stream, South Africa.

TOOL MARKS

General

Dzulynski and Sanders (1962b) proposed this name “as a general term for all marks which were made by the contact of some object (the tool) with the bottom”. Their context is an analysis of the structures shaped on mud beds and preserved as moulds by turbidity currents, but no fundamental mechanical distinction is possible between any of the agents of sediment transport as

510

regards the markings on solid boundaries, where those markings are attributable to an object propelled by the agent. Hence the bed-rock striae chiselled by debris held on a glacier base, and the grooves cut into the sea bed by drifting ice, are equally tool marks with what these authors had in mind. Our knowledge of tool marks extends back many years. Agassiz (1838) and Chamberlin (1888) were amongst the earliest workers to describe and explain glacial striae. James Hall (1843) gave the first account of tool marks in turbidites, assigning the structures to the gouging of the bottom by objects larger than the sand grains present in a current. Opinion for a time veered to a less general mechanical origin, in the intertidal zone (J.M. Clarke, 1917; S. Powers, 1921), and even toward an organic explanation (Fuchs, 1895), but has now returned to the view expressed by Hall. Dzulynski and Sanders (1962b), Dzulynski and Walton (1965), and RicciLucchi (1969a) gave a classification of tool marks based essentially on mark morphology and inferred tool motion. These ideas are followed here with but slight modification, chiefly a somewhat greater emphasis on tool motion. Tool marks are flow-parallel structures and express the action of objects that either approach sufficiently close to or actually cut into a bed. Hence a fundamental distinction is at once possible between structures resulting from near-approaches and those due to actual contacts. A tool in the first case acts indirectly, the bed receiving a mark either by the action of eddies shed from

I-PROTRACTED

CONTACT

II- BRIEF

-

CONTACT

/----...__ _

I- Tumbles (e.g. cube)

A- DRAG

x 3

I-

!

9 -

?

\ >

Ploughinps. smooth, pinnate froctures

B-ROLLS (e.g. ammonite)

x&fy

Motion of

centre of tool

Motion of Doint on surface

Fig. 13-2. A classification of .tool marks in terms of tool kinematics.

of

tool

----.

51 I

the tool, or because of waves generated at the deformable boundary by the passage of the object. In the second instance, the marks express the direct disruption of the bed of rock or unconsolidated sediment by the tool. Marks made in this way are the most numerous and varied (Fig. 13-2). Contact between bed and tool may be either protracted, in which case the mark will be very long compared to width, or brief, in which case the mark will be similar in width and length or long but with visible terminations. Whether protracted or brief, however, tool marks as compared with flute marks, their common associates, express essentially the instantaneous properties of the current. Brief contacts can be either single or repeated. A single contact marks the surface but once, whereas repeated contact yields a train of essentially identical marks. Further distinctions result from considering the paths followed respectively by the centre of the tool and a point on its surface. The tool rotates little or not at all when it is dragged, skims, or saltates over the surface. A rolling tool, however, maintains a substantially continuous contact with the bed, the centre remaining at a constant distance, while a point on its surface describes a cycloid. In tumbling, confined to relatively angular objects, there is a repeated, momentary loss of contact with the bed as the tool turns from one edge to another. Prod marks are attributable to elongated tools that pierce the bed, are held there briefly, and then, after a more or less small rotation in the plane of flow, are plucked out. Drag marks These record protracted contact between the moving tool and bed, and are by far the largest group. Some are attributable to ice drifting in a current or wind, others to objects propelled by turbidity currents, and yet others to stones transported over the surfaces of playas. Glacial striae also belong to this class. The drifting and grounding of ice masses in rivers, lakes and seas in areas of cold climate creates in the bottom sediments often spectacularly large and dense groove-shaped drag marks. These structures are known from a number of rivers (Kindle, 1918; Collinson, 1971a) and lakes (Weber, 1958; Berkson and Clay, 1973; Dionne, 1979), and also from sandy or muddy tidal flats (Reineck, 1956, 1976; Gripp, 1963; Dionne, 1968a, 1968b, 1968c, 1969a, 1969b, 1971a, 1973b, 1974a, 1974b; Wunderlich, 1973). Carsola (1954) and Rex ( 1955) attributed bottom-irregularities revealed by echo-sounding in arctic seas to drifting ice. The application of side-scan sonar to these waters has confirmed their work, revealing that large areas of the sea bed are extensively grooved each year by drifting ice masses (Shearer et al., 1971; Kovacs, 1972; Pelletier and Shearer, 1972; Reimnitz et al., 1972, 1973, 1977, 1978; Barnes and Reimnitz, 1974; I. McK. Harris, 1974; Harris and Jollymore, 1974; Reimnitz and Barnes, 1974; Barnes et al., 1978). Belderson et al. (1972, 1973) found off the west coast of the British Isles what are probably

512

late Pleistocene iceberg drag-marks, to judge from their softened relief, due to subsequent deposition and erosion, and the water-depth at which they occur relative to the inferred scale of North Atlantic icebergs (E.H. Smith, 1931). Other fossil examples appear off Norway (Belderson and Wilson, 1973) and Newfoundland (L.H. King, 1976). They may be some on the now-exposed floor of Pleistocene Lake Agassiz (Clayton et al., 1965). The only pre-Quaternary drag marks explicable by ice-movement occur on a wave-rippled bedding surface in the South African Fish River Series (Halbich, 1964; Pettijohn and Potter, 1964). See also Martini (1981). Drag marks due to drifting and grounding ice are parallel to criss-crossing, straight, curved or zig-zag grooves up to a few metres deep, a few tens of metres wide, and hundreds of metres to several kilometres long (Fig. 13-3).

Fig. 13-3. Iceberg drag marks. a. Side-scan sonar record of crossing marks with marginal ploughed-up sediment, floor of Beaufort Sea, North American Arctic. Photograph courtesy of E. Reimnitz (see Barnes et al., 1978). b. Schematic fish-eye view of drag marks in process of formation, adopted from Reimnitz et al. (1973).

513

Fig. 13-4. Crossing drag marks in the order of 0.1- 1.0m wide on the sole of a turbidite, Marnosa-arenacea romagnola, Roman Appennines, Italy. Photograph courtesy of G. Piacentini and R. Ricci-Lucchi.

Irregularities on the surface of the ice are reflected within each groove by precisely parallel longitudinal striae. Within some grooves are transverse furrows, called “jigger” marks by Reimnitz and Barnes (1974), that record the varying depths to which the keel of the ice-mass pierced the sediment as it rose and fell in the tide or waves. Many grooves are flanked by irregular heaps of debris gouged up by the ice, and adjacent to some are oblique to almost perpendicular pinnate fractures. The sediment not gouged up may become strongly deformed (Wunderlich, 1973). The gouging of the bottom by drifting ice is an important process on the intertidal flats of the St. Lawrence River (Dionne, 1974a, 1974b), and again on the continental shelf of the Beaufort Sea (Reimnitz et al., 1977, 1978), where 1-2% of the surface

514

is grooved annually and sediment equivalent to a continuous thickness of 0.2 m is completely reworked within the order of 100 years. Figure 13-4 shows the underside of a sandstone with the moulds of drag marks typical of those preserved in turbidites (J.M. Clarke, 1917; S. Powers, 1921 ; Dzulynski and Radomski, 1955; Walton, 1955; Kuenen and Sanders, 1956; Kuenen, 1957; Ten Haaf, 1959; Wood and Smith, 1959; McBride, 1962, 1966; Dzulynski, 1963; Spotts and Weser, 1964; Dzulynski and Walton, 1965; Sanders, 1965; Enos, 1969a; Ricci-Lucchi, 1969a, 1970; Tanaka, 1970). Similar structures are occasionally preserved in non-turbidite facies (Cummins, 1958; Prentice, 1962b). The marks, cut into mud, resemble these formed by ice, but are normally just a few centimetres deep and seldom wider than 1 m. They are parallel to criss-crossing usually rectilinear grooves with precisely parallel longitudinal striae internally and, in some cases, unevenly raised rims formed from ploughed-up or pinnately fractured mud. Occasionally, the tool-a fragment of mud or billet of wood-is found at the downcurrent end (Dzulynski and Radomski, 1955; Dzulynski and Slaczka, 1958; Wood and Smith, 1959; Enos, 1969a). These drag marks range in frequency from dense swarms, when the whole surface is covered (Fig. 13-4), to isolated structures, the greater part of the mud surface remaining smooth or showing other features. There has been much debate, ably summarized by Ricci-Lucchi (1969a), as to whether criss-crossing drag marks could be made by a single turbidity current, or whether more than one movement of debris must be invoked, with only the last introducing a preserving deposit. A careful scrutiny of a surface large enough to constitute a valid sample, however, generally fails to reveal a consistent relationship between mark age and orientation, whence such marks need not be attributed to more than one current. That a single turbidity current could impress many different directions of tool motion as it passed a fixed point on the bed should hardly occasion surprise. From what has already been said (Vol.1, Chapter 1; this Vol., Chapter 10) it seems certain that the heads of these currents are highly turbulent and filled with large-scale secondary flows. Only when the marks fall rigorously into two or more directional sets, each of a distinct age, it is necessary to invoke the action of more than one movement of debris. The drag marks that decorate many playa floors have provoked much study, though somewhat of a curiosity (McAllister and Agnew, 1948; Clements, 1952; L.G. Kirk, 1952; Shelton, 1953; G.M. Stanley, 1955; Schumm, 1956b; W.E. Sharp, 1960; Sharp and Carey, 1976). Similar structures are reported from a Canadian lake (Weber, 1958). These marks are shallow, often longitudinally striated grooves, generally with a stone or cob of burro dung at the end. In plan they are straight, curvilinear, meandering to zig-zag or, rarely, looped. Occasionally, as Stanley demonstrated, a small number of closely spaced marks take on an identical plan shape. McAllister and Agnew (1948), Clements (1952), and Kirk (1952) all

515

Fig. 13-5. Glacial striae on gneiss, Fondalen, Nordland, Norway. Scale 0.15 m long. Ice flowed from right to left. Photograph courtesy P. Worsley.

suggested that the wind had propelled the stones found at the ends of the marks. This idea was widely opposed, as many of the tools weighed more than 100 kg. Shelton (1953) experimented with a wind-machine on an artificially wetted playa, but in gale-force winds (18 m s - ’ ) succeeded only in entraining small stones. The theoretical calculations of Schumm ( 1956b), Weber (1958), and W.E. Sharp (1960) also strongly discount the wind hypothesis. Stanley ( 1955) likewise rejected the wind-propulsion of the stones, pointing out that the climate of the playas, and the sets of identical tracks, were consistent with the grooving of the mud by stones trapped in drifting sheets of ice. Sharp and Carey (1976), reinvestigating the question, conclude that most stones are propelled by the wind on a lubricating film of slippery mud as the playa dries out, with but few travelling frozen in ice. However, their inference implies that the stones indent the playa surface hardly at all, and that the coefficient of sliding friction is extremely small, to both of which there seem grave physical objections. Only small stones have so far been seen to move beneath a strong wind and groove a surface, and only when attached to an extensive “sail” (e.g. kelp) (Sainsbury, 1956). Glacial striae (Fig. 13-5) are fine, generally rectilinear, parallel to nearparallel scratches to be found covering smooth, undulating bed-rock surfaces in glaciated terrain (Chamberlin, 1888; Pettijohn and Potter, 1964; Embleton and King, 1975; Sugden and John, 1976). The smallest, no doubt chiselled by sand and small stones trapped in the ice, are no more than a millimetre

516

wide and deep and a decimetre or so long. The largest measure several metres in length, a centimetre or so across, and several millimetres in depth, presumably recording the gouging action of cobbles and boulders. Though generally showing little local variation in direction, the trend of glacial striae is sensitive to quite small changes in the attitude of the bed-rock surface (Virkkala, 1960), and shows large variations where change is abrupt and substantial (Demorest, 1938). Striated bed-rock occurs widely in the fossil record in association with glacial deposits of Precambrian (Schenk, 1965a, 1965b; Spjeldnaes, 1965; Bjpfrlykke, 1968; Conybeare and Crook, 1968; Perry and Roberts, 1968; Ojakangas and Matsch, 1980), Ordovician (Biju-Duval and Gariel, 1969; Beuf et al., 1971; P. Allen, 1975; Rapp, 1975a; McClure, 1978), and Permo-Carboniferous ages (A.J. Smith, 1963; Halbich, 1964; Dow, 1965; Bigarella et al., 1967; Hamilton and Krinsley, 1967; Frakes and Crowell, 1969, 1970; Crowell and Frakes, 1971a, 1971b, 1972; Frakes et al., 1971). Caution is needed in the identification of glacial striae, however, since agencies other than glaciers on occasions produce similar marks (Hovey, 1909; Blackwelder, 1930; Dyson, 1937; Harrington, 1971). Roll marks

Roll marks (Krejci-Graf, 1932) are made by essentially cylindrical or discoidal tools that roll over the bed with their axis of symmetry perpendicular to flow, remaining in substantially continuous contact with the surface (Fig. 13-2, Class IB). The best known, preserved in Alpine and Carpathian turbidites, are the moulds of ladder-like marks due to fish vertebrae bowled along on their rims (Pavoni, 1959; Dzulynski and Slaczka, 1960; Dzulynski and Sanders, 1962b; Dzulynski, 1963; Dzulynski and Walton, 1965), as Pavoni (1959) showed experimentally. Roll marks can also be made by ammonite shells (Dzulynski and Sanders, 1962b), and by straight, orthocone cephalopods acting as tools (Kelling and Whitaker, 1970; D.E.B. Bates, 1974).

Prod marks Prod marks (Dzulynski and Slaczka, 1958) are fairly common structures due to a brief contact between the bed and an elongated tool approaching the surface in a downcurrent-dipping attitude (Fig. 13-2, Class IIAI). Moulds (Fig. 13-6) preserved chiefly in turbidites (Cummins, 1958, 1965; Dzulynski and Slaczka, 1958; Allen, 1960; Craig and Walton, 1962; Dzulynski and Sanders, 1962b; Dzulynski, 1963; Dzulynski and Walton, 1965; Enos, 1969a; Ricci-Lucchi, 1969a, 1970; Jawarowski, 1971; Ghibaudo et al., 1974) show that the marks generally lack transverse symmetry, the upstream slope being gentle and often longitudinally striated, reflecting irregularities or orna-

517

Fig. 13-6. Prod marks (approximately 0.02 m long, current from left to right) preserved on the sole of a Carboniferous turbidite, Mam Tor Sandstone, Derbyshire, England.

mentation on the tool, while the downstream surface is steep and uneven, consistent with the more or less abrupt withdrawal of the object. Occasional marks are close to being transversely symmetrical, suggesting the even approach and release of the tool. Flat or pointed mud fragments, graptolites, orthocone cephalopod shells, and plant stems, particularly the equisitiform, have according to circumstances been proposed as the tools. Tumble marks

This is a new term proposed for marks, previously assigned to skipping or saltation, which appear to have been made by a relatively equant tool that somersaulted over the bed (Fig. 13-2, Class IIBI). Where the tool is transversely as well as axially symmetrical, the mark consists of a line of evenly spaced identical to closely similar impressions, separated by not much more than the inferred length of the tool. Objects that lack transverse symmetry yield a row of two kinds of impression in alternation, representing opposite faces of the tool. Examples preserved in turbidites are attributable to fish vertebrae tumbling with their axis of symmetry in the flow-plane (Dzulynski and Slaczka, 1958, 1960; Pavoni, 1959; Dzulynski and Sanders, 1962b; Dzulynski, 1963, 1965; Dzulynski and Walton, 1965), to orthocone

518

cephalopod shells travelling likewise (D.E.B. Bates, 1974), and to somersaulting angular mud clasts (Dzulynski and Walton, 1965). To call these structures skip marks (Dzulynski and Walton, 1965; D.E.B. Bates, 1974) seems inappropriate, for skipping with translation is a more complex motion than the objects appear actually to have described. Some of the structures have been called saltation marks (Dzulynski and Walton, 1965), but this term is most useful for when there is no evidence that a repeated contact involved significant rotation (e.g. Dzulynski and Walton, 1965, fig. 78). Skim marks These are gouged by objects that just grazed the bed while at the bottom of a gently curved, concave-up trajectory. Examples appear in many turbidite formations (e.g. Allen, 1960; Dzulynski, 1963; Dzulynski and Walton, 1965; Jawarowski, 1971) and can be found beneath sandstones in a wide range of shallow-water deposits. The marks, often carrying parallel internal striations, are much longer than wide and are distinguished by their transverse as well as longitudinal symmetry. They are seldom longer than 3m, wider than 0.05m and deeper than a few millimetres. Many are extremely delicate, being no more than a few millimetres or centimetres in length, and could be due to sand grains whirled about in the current. Trewin (1979) has recently described marks apparently due to graptolites skimming over a mud surface. Marks related to near-approaches Turbidite formations yield many examples of chevron marks (Dunbar and Rodgers, 1957) which, as recognized independently by Craig and Walton (1962) and by Dzulynski and Sanders (1962b), form a continuous morphological series (Figs. 13-7, 13-8) between drag or skim marks associated laterally with symmetrical rows of oblique ridges (interrupted chevrons), through axially severed rows of V-shaped furrows and crests (cut chevrons), to rows of nested V-shaped or U-shaped ridges (uninterrupted chevrons) (Kuenen, 1957; Dzulynski and Slaczka, 1958; Ten Haaf, 1959; Craig and Walton, 1962; Dzulynski and Sanders, 1962b; Dzulynski, 1963; Dzulynski and Walton, 1965; Enos, 1969a; Ricci-Lucchi, 1970). Independent evidence shows that the chevrons close in the direction of travel of the object. As sketched in Fig. 13-7, the chevrons consist of downcurrent-facing overfolds of the mud surface. Since interrupted chevrons grade downstream into cut chevrons (Craig and Walton, 1962), or into uninterrupted ones (Dzulynski and Sanders, 1962a), and drag marks occasionally pass downcurrent into uninterrupted chevrons (Kuenen, 1957), it is evident that the series represents the range of extents to which a tool following a concave-up trajectory penetrated (or failed to penetrate) the bed. As Craig and Walton explain,

519 Interrupted chevrons

cut chevrons

Uninterrupted chevrons

j

I: ....... ..

... ..... ... ...i,.: ....:.... ...... ... .... ......,. .. .:... . . ... ...... ... .. . ....., :...:.. .:.:... ..... :.. ...:: :: .: ...... .,:: .,

t

t

B

~

Fig. 13-7. Classification of chevron marks. Adapted from Craig and Walton (1962).

Fig. 13-8. Interrupted to cut chevrons preserved as mould on sole of Silurian turbidite, Kirkcudbright, Southern Uplands, Scotland. Groove approximately 0.2 m long formed by current from lower left to upper right. Photograph courtesy of E.K. Walton (see Dzulynski and Walton, 1965).

520

maximum cut is recorded by interrupted chevrons, whereas complete chevrons suggest that the object was positioned just above the bed without actually touching it. Mechanics of tool marks Broad ideas only can be advanced under this head, until the behaviour of mud and rock under the cutting action or near-approach of tools is better understood. The phenomena represented appear to be wide-ranging. Tool marks due to near-approaches give particular difficulty, for they seem to record effects ranging from the purely hydrodynamic, when the tool acts indirectly on the mud bed, to the partially mechanical, when a part of the structure arises from the cutting of the deposit. Craig and Walton (1962), as well as Dzulynski and Sanders (1962b), likened chevron marks to the symmetrically arranged, oblique waves made by a travelling ship or, we may add, a submerged obstacle. The geometrical parallels are undeniably strong (Havelock, 1908; Lamb, 1932), but insufficient is known of these waves to allow a quantitative test. Later, Dzulynski and Walton (1965) suggested that chevron marks are formed by the action of eddies shed into the wake of an object gliding just above the bed, giving a diagram showing the eddies upstream of the tool. This idea seems to be in error. Firstly, as the tool is drawn along by the fluid, the tool has the lower speed, which means that its wake lies on the downstream side. Secondly, since the fluid in the axis of the wake is the most retarded relative to the ground, any waves shaped on the bed by eddies in the wake should close upcurrent, which is not the observed orientation of chevron marks. Finally, using the cylinder as model (Roshko, 1954a, 1954b, 1955a, 1961), the wavelength of chevrons is one to two orders of magnitude smaller than is expected if the structures were due to shed eddies. A complicated set of three-dimensional forces arises whenever an object forms a tool mark by directly cutting into a bed. These are: (1) the cutting force, proportional to the drag of the transporting medium on the tool, (2) the resisting force, related to the bed-material strength and depth of tool penetration, (3) the weight of the tool immersed in the bed and the transporting medium (water and air in the case of drifting ice), (4) the weight of the ice lying above the tool (glacial striae only), and (5) appropriate reactions. Mechanically, the process is identical with the cutting of metals on a lathe (e.g. Merchant, 1945a, 1945b; Finnie, 1956; Wallace and Boothroyd, 1964; Fenton and Oxley, 1969, 1970; Lin and Oxley, 1972), though at present we are far from being able to analyse natural cases, except in regard to the mode of deformation of the affected material (Klemm and Smekal, 1941; Smekal and Klemm, 1951; M.C. Shaw, 1954; Engelder and Scholz, 1976; Scholz and Engelder, 1976). A given material cut by a lightly loaded tool deforms by plastic flow (ductile mode), but by fracture (brittle mode) when the load is

52 1

sufficiently great. The tool marks of turbidites seem overwhelmingly to represent the first mode. Drifting ice masses, no doubt because of the great weight, seem at times to cause brittle fracture in bottom sediments. Boulton’s (1974, 1975) observations and reasoning suggest that the production of glacial striae involves mainly brittle failure, except where relatively soft bed-rocks are concerned.

SCRATCH CIRCLES

The term scratch circles (Scharrkreise),introduced by R. Richter (1926), is applied to sets of concentric grooves cut generally in sand or mud by the action of sharp objects anchored at the centre of curvature of the set, but otherwise free to swing or rotate horizontally about that centre. The most familiar examples come from sandy coasts. Here the bent-over leaves and sometimes the toppled but incompletely ruptured stems of grasses such as marram cut grooves into the sand in the shape of circular arcs, almost complete circles, or full circles, as they sway from side to side with the gusty wind (Barthel, 1966; Gerharz, 1966; Koerfer and Schwarzbach, 1971; Seppala, 1972). These arcs rarely exceed a diameter of 0.4m but Kukal and Al-Naqash (1970) observed that spiny desert bushes cut circles with a diameter of 1.1 m into flat surfaces of friable sandstone. Scratch circles are also to be found in aqueous environments, as Twenhofel(l932) appreciated. R. Richter (1926) and Prentice (1962b) mentioned them as occurring on intertidal mud flats. Langerfeldt ( 1935) described impressive examples that had been shaped on tidal muds by the rotation of halophytes and seaweeds about their roots or holdfasts. Heezen and Hollister (1964) illustrate scratch circles cut by a sea pen or bryozoan at a water depth of 3800m off Cape Horn! Prentice ( 1962b) described fine examples of scratch circles preserved as moulds on the underside of a Cretaceous lacustrine sandstone, the only instances reported from the stratigraphic record. Figure 13-9 shows a case. The grooves, with a maximum diameter of 0.125m, are arranged concentrically around a shallow conical depression, from the centre of which there seems to have risen a stout plant-stem, now represented by an upright sand-filled tube 0.01 1 m across. None of the grooves makes a complete circle and some define arcs of no more than 20’ or so. The grooves are deepest in diametrically opposite zones. Several carry an oblique pattern of finer grooves (Fig. 13-9b), a fretting which in modern examples arises when a leaf or stem jerks rapidly up-and-down during a swing. Prentice (1962b) interprets the marks in a slightly different and less appealing way, suggesting that they are “the centres of hollows cut by swirling twigs” that had been “caught by one end in the mud or by other vegetation”. The orientation of scratch circles is only weakly influenced by current

522

Fig. 13-9. Mould in very fine grained sandstone of scratch circles cut into mud, probably by a plant, Weald Clay (Cretaceous), Warnham Brickworks, near Horsham, Sussex, England. a. General view. Rock surface measures approximately 0.12 by 0.16 m. b. Detail of fretting seen in upper left of second circle outward from centre.

direction but is strongly dependent on plant architecture and the torsional strength of their stems. For example, the pattern seen in Fig. 13-9 is explicable either by current reversal or by the positioning of leaves on opposite sides of a plant.

523

CORRASION BENEATH THE WIND

Winds carrying abrasive silt and sand over hard surfaces cut structures that differ significantly in shape from the flute marks formed on mud beds by sand-laden aqueous currents (Chapter 7). This is because the inertia of all but the finest mineral grains in the wind is too great for flow separation and turbulence to exert much of an influence on the sculpturing by corrasion of rock surfaces. At a density-contrast of three orders of magnitude, most wind-borne particles take paths influenced only by the largest and most powerful of the vortices and eddies that are present. Corrasion ripples or rills, the smallest of wind-scoured structures, are widely known from the smooth, polished surfaces of ventifacts and windabraded rock exposures in cold as well as hot deserts (Hobbs, 1917; Hume, 1925; Bourcart, 1928; L.C. King, 1936; Maxson, 1940; Whitney and Brewer, 1968; Whitney and Dietrich, 1973; Whitney, 1978). The ripples are parallel, rather regular, transverse ridges and furrows (Fig. 13-10) that much resemble the more round-crested wave-current ripple marks. The wavelength of corrasion ripples rarely exceeds several millimetres, however, and is commonly much smaller. In cross-section they vary from almost symmetrical, showing equally well-rounded ridges and troughs, to downstream-facing and moderately asymmetrical, with troughs and crests of intermediate roundness. Examples temporarily removed from wind influence occasionally become modified by solution. Tiny square-section furrows appear in the troughs and their crests can become sharp and symmetrical.

Fig. 13-10. Corrasion ripples (wavelength approximately 0.0015 m) cut by silt-laden wind (top to bottom of photograph) on surface of halite. Photograph courtesy of M.I. Whitney.

524

The ripples form on a wide variety of materials, including agate, basalt, bone, glass, granite, obsidian, pitch, porphyry, quartzite, vein-quartz, and wood, but are commonest on surfaces underlain by finely and evenly textured limestone or dolomite. The structures shown in Fig. 13-10 resulted from the bombardment of a cleavage surface of halite by wind-blown silt (Whitney and Dietrich, 1973). Transverse ripples identical in all essential respects to the natural structures have been produced by engineers interested in wear in chemical plant and in sand-blasting as a finishing process (Bitter, 1963; Finnie and Kabil, 1965; Sheldon and Finnie, 1966; Raask, 1969; Mills and Mason, 1977a; Carter et al., 1980). Pure aluminium, silver, hard aluminium alloys, mild steel, and glass will all under appropriate conditions take the structures when corraded. Laudermilk and Woodford ( 1932) assigned naturally occurring corrasion ripples to solution, because sand-blasting would remove them, and Maxson (1940) also offered this interpretation. But the fact that the ripples can form on normally insoluble rocks, and on heterogeneous materials, signifies another cause. Their association with ventifacts, and close similarity to experimental corrasion structures (Bitter, 1963; Finnie and Kabil, 1965; Sheldon and Finnie, 1966; Whitney and Brewer, 1968; Whitney and Dietrich, 1973; Whitney, 1978; Carter et al., 1980), points to an origin through wear by wind-blown silt or sand. Finnie and Kabil emphasized that corrasion ripples form when the substance bombarded yields to the bombarding grains in the ductile or cutting mode (Vol. I, Fig. 2-8). This mode of wear is restricted to small low-speed particles that approach the target at a shallow to moderate angle. Laudermilk and Woodford’s results are for this reason alone not a disproof of the corrasional origin of ripples on ventifacts, for their experiments may have been made under unsuitable conditions. Also, Finnie and Kabil developed a theory of the ripples, predicting their downstream migration, downstream facing, and dependence for wavelength on the average length of cut made by impacting grains. The instability of a rippled surface was shown to depend on the way in which the local curvature controls the quantity of material that can be removed at each cut. Experimentally, ripple wavelength turns out to be approximately six times the average length of cut. Carter et al. (1980) indicate that the local workhardening of the material being scoured by the tools responsible for the erosion may be the cause of ripples, at least as observed on ductile metals. There is much less evidence for Whitney’s (1978) idea that vorticity is paramount in shaping the ripples. Solitary to gregarious wind-parallel grooves are frequently reported from boulders and rock surfaces known or inferred to have been scoured by air-borne mineral grains (Blackwelder, 1929; W.E. Powers, 1936; Maxson, 1940; Denny, 1941; Sharp, 1949, 1964; Fristrup, 1952; Tremblay, 1961; Minard, 1966; Mainguet, 1972a; Selby, 1977). They are smooth, roundbottomed channels up to 0.05 m wide and 0.45 m long separated by gener-

525

ally sharp crests. Some grooves turn up at the downwind end to make a long, scoop-like feature. Hence their steeper slopes face the wind. Grooves are occasionally seen to extend downwind from defects within the rock, such as small cavities or resistant phenocrysts. Their origin is unknown, other than that they record scour by air-borne particles. Wear by relatively large, high-speed grains in the brittle or deformation mode (Vol. I, Fig. 2-8) may be recorded, since the grooves lack corrasion ripples. Further examples of grooved boulders are described by Johnson (1980). Even dreikanter can show what appear to be sand-blasted grooves (Svensson, 1980). The corrasional structures named sustrugi (Wright and Priestley, 1922; Kotlyakov, 1966) or skuvler (Seligman, 1936) are best known from surfaces of partly hardened snow or ice in polar regions (Cornish, 1902, 1914; Wright and Priestley, 1922; Seligman, 1936; R. Moss, 1938; Mather and Goodspeed, 1959; Vickers, 1959; Mather, 1962; Mellor, 1965; Kotlyakov, 1966). Only in the McMurdo Oasis, Antarctica, are they known to mark any other substrate (friable sandstone) (Selby, 1977). Sustrugi are very variable but are characterized by an asymmetry in which the steeper slopes, constructed from flat intersecting facets, face upwind. The structures range from short and almost straight transverse ridges, through oblique or upwind-pointing V-shaped crests with subsidiary streamwise spines to lee, to narrow sharp-crested features lying parallel with the wind. Examples of each of these forms can generally be found together in any one field of sustrugi. The ridges vary in maximum height between a few millimetres and 1.3 m with values of about 0.1 m being most common. They range up to 10 m in length and several metres in distance apart. The corrasional origin of sustrugi under the action of airborne snow is clearly established by the discordantly stratified snow exposed within them (Cornish, 1902; Wright and Priestley, 1922), their tendency to form or strengthen when old and hard granular snow is redistributed under strong winds (Mellor, 1965), and the sharpness of their facet-determined crests and subsidiary spines. Sustrugi bear a remarkable similarity to forms produced in steel and plastic pipes by the scouring action of air-borne alumina sand (Mason and Smith, 1972; Mills and Mason, 1977a, 1977b). It is possible that sustrugi also represent a mainly brittle type of wear (Vol. I, Fig. 2-8).

SWASH AND FOAM MARKS

The forward momentum of a surface wave approaching and breaking on the shore carries some of the water up the beach as the swash, that part not absorbed into the beach returning in due course as the backwash. On the upper parts of beaches of very-fine sand, above the minimum level of the water-table, the landward limit of the swash is generally marked under

526

Fig. 13-1 1. Swash marks on beach of fine sand, coast near Burnham Overy Staithe, Norfolk, England. Trowel 0.28 m long points toward sea.

conditions of light to moderate wind by grains heaped into an irregularly curved, thread-like ridge arranged convexly to the land. Figure 13-11 illustrates a set. These ridges-D.W. Johnson’s (1919) swash mark-are well known from modern beaches (Kindle, 1917a; D.W. Johnson, 1919; Twenhofel, 1932; Emery and Gale, 1951; Martins, 1967; Reineck and Singh, 1973). Each ridge consists of sand grains mixed with such light or angular debris as mica flakes, tiny pieces of shell, and fragments of seaweed or salt-marsh plants. A band of this debris can sometimes be found on the seaward side of each ridge. Since the waves arrive frequently, and the swashes come up along an uneven front owing to their three-dimensionality, later swash marks partly obliterate earlier ones, to create over the surface an eventually net-like pattern of connected ridges (Fig. 13-11). These increase in spacing with decreasing beach slope (Emery and Gale, 1951) and, presumably, with increasing wave size. Much of the upper part of a beach can acquire these patterns. Careful observations by O.F. Evans (1938b), Emery (1945a), Emery and Gale (1951) showed that the ridges consist of grains trapped in the surfacetension film on the surface of the swash and concentrated at its nose. The flotation transport of thoroughly wetted grains is impossible, however, which

527

is one reason why swash marks are confined to the upper beach. In contrast, swash marks on beaches of coarse sand are made from grains transported in the normal way (Sallenger, 1981). Swash marks are typically accompanied by upper-stage plane beds with parting lineation. Each interstice within the net-like pattern of ridges is part of the area affected by a single swash and may contain a lamina related to that swash, partly overlying laminae formed by earlier swashes. I have often noticed that the lineations associated with each swash mark are related to it like the rays of a fan to its edge (Fig. 13-12) and, moreover, that their wavelength commonly increases downbeach (Figs. 13-12, 13-13). This pattern clearly shows that many swashes spread out slightly while ascending the beach, as can often be directly observed. The wavelength change is less easily explained, but may reflect either a decrease in bed shear stress from the edge (shallow depth) to the inner parts (greater depth) of the swash (or backwash), or the formation of some lineations by secondary flows unrelated to boundary-layer streaks (Vol. I, Chapter 6; this Vol., Chapter 1). Swash marks form on sand beaches neither during moderate to heavy rain nor at times of strong onshore wind. Such winds blow foam patches produced by wave-breaking over the surface of the swash and up onto the beach itself, to which the patches firmly adhere while migrating beneath the forceful air-flow. The patches, arranged transversely to the wind and as much as 0.6 m long, moisten the surface as they gradually diminish. Bubbles

Fig. 13- 12. Schematic swash marks, to show general form and the variation in scale of parting lineations between marks.

528

Fig. 13-13. Variation in scale of parting lineations to seaward of a single swash mark (emphasized by line of ink dots) in fine sand, coast near Burnham Overy Staithe, Norfolk, England. Trowel 0.28 m long points in direction of swash.

within them move as though on the surface of a highly compressible cylinder rolling beneath a heavy beam. As each bubble on the windward side of the patch is jerked upward, it leaves behind a small depression on the sand surface. But as each patch contains many hundreds of bubbles, and the patches travel in close array, large parts of the beach assume these delicate markings (Fig. 13-14). They were first described by Hantzschel (1935b) and independently recorded by Allen (1967). Hantzschel's marks show a dominant element that is parallel with the wind, whereas in Allen's there is a dominant transverse element, a difference that remains unexplained. The marks made by stationary foam, however, lack linear elements and possess sharp, bold rims (Twenhofel, 1921; Hantzschel, 1935b). Swash marks are rare in the stratigraphic record (H.L. Fairchild, 1901; W.O. Thompson, 1949), and foam marks have yet to be recorded. More common are parallel-laminated sandstones in which the parting lineations vary by 20-40" from one lamina to the next, as if formed by overlapping swashes (Fig. 13-12). This may be an indication of a beach origin, either by the sea or on the edge of a large river or lake.

529

Fig. 13-14. Foam marks on beach of fine sand, Wells-next-the-Sea, Norfolk, England. Lens cap 0.055 m across. Wind from right to left.

ADHESION AND RAIN-IMPACT RIPPLE MARKS

When the wind blows dry sand grains on to a sufficiently wet surface, deposition of sand takes place generally under the form of closely spaced transverse ridges to which the names anti-ripplets (Van Straaten, 1953b), Haftrippeln (Reineck, 1955), aeolian microridges (Hunter, 1969), and adhesion ripples (Glennie, 1970) have been applied. The last of these terms expresses well the origin of the structures and is widely used. Blown snow also creates adhesion ripples (Cornish, 1914; Van. Straaten, 1953b), the finest appearing where the underlying surface is formed of ice. ‘Typical adhesion ripples in sand (Fig. 13-15) are irregular to regular transverse ridges, with a wavelength between 0.005 and 0.025 m and a height of a few millimetres or less. Crests in plan range from straight to slightly sinuous and 5-10 times longer than the ripple wavelength, to strongly curved and rather irregular, with button-shaped protuberances, and only 2- 5 times longer than the spacing. The upwind slopes invariably are steep and commonly near-vertical or even overhanging, some taking a frayed appearance from the presence of outward-leaning spike-like clusters of grains. Leeward slopes are gentle. Structures answering to this description are familiar from sandy beaches and intertidal flats (Van Straaten, 1953b; Reineck, 1955; Gripp and Martens, 1963; Bajard, 1966; Hunter, 1969;

530

Fig. 13-15. Adhesion ripples form by the drifting of fine sand over a beach. Trowel 0.28 m long points with wind. a. Moderately two-dimensional adhesion ripples on plane portion of beach. b. Adhesion ripples varying systematically in dimensionality and scale with slope of surface, where sand is being plastered over current ripples oblique to the wind. Coast near Burnham Overy Staithe, Norfolk, England.

53 1

Borowka, 1980), where they are found on low-lying wet areas lying downwind from sources of dry grains, such as the upper parts of the beach or the crests of bars. Adhesion ripples in these settings form a coating, occasionally more than 0.1 m thick (Hunter, 1973, 1980a), on beds previously rippled or made plane by wave or tidal currents. Wet or hygroscopic surfaces also occur in desert sabkhas, but the adhesion ripples found here are generally much less regular and also larger than those in Fig. 13-15 (Glennie, 1970, 1972). The ripples figures by Soleilvahoup and Bertouille (1976) were found in a desert wadi after a flood. Rust (1972) described an unusual form from the alluvium of the Donjek River, arctic Canada. These ripples are flat, spatulate, wind-aligned structures up to 0.05 m wide and 0.07 m long, each topped by a plumose to dendritic pattern of small furrows. Instead of forming transverse rows, they lay irregularly or en echelon. Excellent examples of adhesion ripples, called “current ridges”, were described by Lorenz ( 1974) from the top of a layer of vesiculated ash of presumed base-surge origin. Adhesion ripples, with a facing opposite to that of ballistic and current ripples, are seen on beaches and intertidal flats to climb upward into the wind with continuing deposition. Vertical internal sections parallel with the wind (Reineck, 1955; Bajard, 1966; Hunter, 1973) show irregular, interconnected laminations inclined downwind at angles of 20-60” (Fig. 13-16). These evidently record the upwind climb of laterally adjacent ripples which, as individuals, varied in wavelength, height, and crestal extent throughout life. Stratification representing time-planes, however, is faint or lacking. In contrast, under some circumstances, however, the lamination expressing tWind

Fig. 13-16. Schematic three-dimensional representation of bedding due to sand accretion on a wet adhesion-rippled sand surface.

532

climb is almost horizontal, an almost planar stratification being produced (Hunter, 1980b). Adhesion ripples in sabkhas are associated with often muddy and blotchy to irregular or wavy lamination (Glennie, 1970, 1972). Internal structures due to adhesion ripples are claimed from several ancient sabkha sequences (Glennie, 1970, 1972; Burgess and Holliday, 1974). De Vries (1973) illustrates a fairly convincing set of adhesion ripples from amongst current-rippled sandstones of the Waterberg System in South Africa. Clemmey (1978) saw possible adhesion ripples in Proterozoic lacustrine deposit. Gradzinski et al. (1979) found examples in Triassic aeolian dune and inter-dune sediments. The rock structures discussed by Hunter (1969) and Bergstrom ( 1976) are possibly wrinkle marks (Teichert, 1970). That adhesion ripples form when dry grains are trapped by a surface kept permanently moist by the capillary rise of water from below has been understood since Van Straaten (1953b) first described these structures. How surface tension creates the observed effect has not hitherto been explained. The mechanism is here suggested to involve an instability between the local slope of the wetted surface and its capacity to retain particles blown over it. Consider in Fig. 13-17 dry sand grains incident on a surface of the same sand kept wet through capillary rise. The entire surface consists of water, albeit in an exceedingly thin film over the summit areas of the grains. A dry grain A, approaching on a glancing trajectory, merely touches the summit of a surface grain, and thus is wetted effectively at a point. Since the surfacetension force causing grain capture is proportional to the linear contact between incident grain and surface-tension film, the elastic force causing the grain to rebound will easily be the greater, whence grain A will escape downwind. The dry grain B approaches on a slightly steeper path but, in clearing surface grains, takes but a slight dip into the water. Again the elastic

\

Particle path

Surface tension

Fig. 13-17. The influence of approach angle on the ability of a surface of water-saturatedsand to capture fresh wind-blown grains.

533

force exceeds the surface-tension force, but not to as large an extent as in the first case. Grain B also escapes from the surface. Grain D, however, arrives on such a steep path that in just clearing other grains it intersects a significant part of the surface-tension film. The extent of contact is now sufficiently large that the restraining surface-tension force exceeds the elastic rebound. Grain D is therefore trapped. But there is some intermediate angle of approach, followed by grain C, when sufficient of the film can be intersected as to equalise the two forces, whence only grains on this and steeper paths can be captured. But only some of the particles approaching at these angles are actually trapped, for those that happen to strike the summits of surface grains must immediately rebound, for the same reason that particle A rebounds. In contrast, all grains arriving on trajectories as shallow as those of A and B are returned to the sand-flow. Since grains driven by a steady wind descend at a statistically uniform angle, it follows that the local rate at which they are captured by a wetted surface is proportional to its local slope. Any part of the surface which by chance faces upwind will capture grains at a greater rate than segments of gentler or downwind slope. Downwind-dipping parts will therefore experience little or no change. Upwind-dipping segments will rapidly grow taller and steeper, because they capture a proportion of the directly arriving grains and a proportion of the grains deflected off slopes that dip downwind. But the growth of upwind slopes will not proceed indefinitely. An upward limit relative to depressions on the bed may be imposed by the ability of the wetting front to ascend through the bed. It is readily shown experimentally that this front is highly irregular, revealing a deep interpenetration of wet and still-dry sand. Now the height of adhesion ripples seems to be of the same order as the depth of this front and may, on these grounds, be controlled by the front, for growth is impossible beyond the level of wetted sand. The height being determined in this way, the wavelength follows as the response of the bed to the mean angle of arrival of dry grains. In the case of ripples formed in blown snow, there is some evidence that the wavelength increases with wind speed. Hence we may see in adhesion ripples the effect of an instability mechanism in which the influence of local slope on the rate of grain-capture is moderated by the ability of a wetting front to ascend, so that a limiting wavelength and height appear. The ability of falling raindrops to mark an exposed surface of mud or sand is well known (e.g. Shrock, 1948). Less generally appreciated is the fact that heavy rain driven by a strong wind can shape a sandy surface into orderly ridges, in some respects similar to adhesion ripples. The ridging of sand under raindrop-impact was noticed by Wasmund (1930) and by Gripp and Martens (1963), but without comment on the attitude of the ridges relative to the wind. Clifton (1977) recently pointed out that the structures lie transversely to the wind, giving them the name rain-impact ripples (Fig. 13-18). They occur on beaches and intertidal flats formed of relatively fine

534

Fig. 13-18. Rain impact ripples due to wind from left to right, superimposed on current ripples, Willapa Bay, Washington, U.S.A. Photograph courtesy of H.E. Clifton (see Clifton, 1977).

sand, and I have seen excellent examples on tidal points bars in the upper Severn Estuary. The ripples have a wavelength of about 0.01 m and a height of a few millimetres. The crests are long, sinuous to irregular, and strongly asymmetrical, the lee sides being steep to overhanging. The ripples migrate slowly before the wind. The existence of rain-impact ripples points to the occurrence of yet another unstable mode of sediment transport. Does the wind or the rain effect grain movement, and what is the mechanism of instability? The wind would certainly entrain the sand if it acted on a dry bed. Yet it is ineffective because the accompanying rain makes the grains cohere. That raindropimpact exerts an entraining force can be established from the work of Caldwell and Elliott (1971), who showed that the mean tangential stress due to rainfall is: r=pUR (13.1) where p is the density of rainwater, U is the horizontal speed of the raindrops at impact, and R is the rainfall rate. Plausible values for heavy rain in a strong wind are U = 1 0 m s - ’ and R = 1 X 1 0 - 5 m s - ’ (0.036m hr-I). The resulting stress, equal to 0.01 N mP2, exceeds the critical for very fine and fine sands in water, whence transport should occur. The regular ripple spacing results, according to Clifton (1977), from “absence of impact in the shadow created by the ridges”. This statement implies that the wavelength depends on the ridge height and the angle of raindrop attack (note the correspondence with adhesion ripples) but does

535

not identify the crucial factor that controls the height. This could be raindrop size. The maximum elevation of the rim of a raindrop impact crater above the surrounding bed should vary with the angle of attack, from zero for a tangential approach, a maximum at an intermediate angle, and a small value at normal incidence, much as in ductile wear (Vol. I, Fig. 2-8). The repeated impact of drops following identically the same oblique trajectory would tend to amplify the ridge created by the first, but upward growth could not continue indefinitely. Once the ridge attained a height comparable with the drop diameter, the tendency to growth would be replaced by a tendency to flatten, as drops falling on parallel paths attacked its crest. The ridges are repeated over the bed because there would seem to be a relationship between the local slope and the maximum rise of a randrop crater-rim. Rain-impact ripples have probably little chance of preservation but are thought to be present in a Proterozoic deposit (Clemmey, 1978).

CAVERNOUS SAND, SAND HOLES, AND SAND DOMES

Air becomes trapped within any layer of initially dry or damp sand or granular soil suddenly flooded from above, provided that: (1) the material is sufficiently fine grained, and (2) the layer is sealed below by either a continuous water surface or an impermeable horizon. The invariable product

Fig. 13-19. Vertical section through cavernous beach sand (cavities typically several millimetres across), Bull Island, Dublin Bay, Ireland. Photograph courtesy of C.R.Harris (see Harris, 1974).

536

is a cavernous or vesicular structure within the layer, in which three phases may be distinguished. These are air bubbles shaped by surface-tension, generally a few millimetres across, but reaching up to 0.0 1-0.0 15 m, and a matrix composed of sand or soil particles and interstitial water. This cavernous structure is strong enough to remain should the layer dry out and to be distinguishable at depths of burial as great as 1 m. Cavernous structure (Fig. 13-19) is widely developed on the upper parts of beaches and on the crests of intertidal beach bars, where the sand, which must be fine or very fine grained, drains well at low tide (Kindle, 1936b; Emery, 1945b; Baudoin, 1949, 1951; H.B. Stewart, 1956; Hoyt and Henry, 1964; C.R. Harris, 1974; Jago, 1980). As Kindle and Emery suggest, and Stewart confirmed experimentally, the structure forms when the air ingested into the beach during the tidal ebb becomes trapped on the subsequent flood between the water-table rising from below and the water seeping unevenly down from the swash above (Fig. 13-20). The cavernous layer is generally between 0.1 and 0.15 m thick but exceptionally reaches a thickness of 0.45 m. Repeated drowning and drying out causes the bubbles gradually to increase in size, but only the largest achieve the buoyancy necessary to overcome the strength of the surficial sand, and so float to the surface. Sections cut into the beach may show more than one layer of cavernous sand, down to depths of 1 m or so. Whereas the bubbles in the topmost layer vary from spherical to irregular or vertically elongated, those below are invariably flattened in the plane of the beach, a sign of partial consolidation. Initially, the bubbles may make up more than one-third of the volume of the sediment, whence substantial reductions in thickness can be achieved. Cavernous sand as such stands in beaches little chance of preservation into the stratigraphic record. However, its formation in this setting may explain some sandstones with a relatively disordered grain fabric and poor or no lamination (Hoyt and Henry, 1964). /Sand

domes

. . . . . .. .. . . . .. .. . . . . . .. .. .. . .. .. .. .. . . . . ... . .. . ... ... . :..:

. . . .. . .. .. .. . .. . ... .. .. .. .. . .. .

. . . . .

Fig. 13-20. Schematic representation of the development of cavernous sand in a tidally influenced sand beach, together with the formation of sand domes and sand holes.

537

Fig. 13-21. Sand domes and sand holes in beach of fine sand, Marloes, Dyfed, Wales. a. Sand domes varying from scarcely perceptible to pronounced blister-like forms, with some lying seaward of the swash mark having a central vent. b. Close-up of sand domes and sand holes seaward of a prominent swash mark. Photographs courtesy of J.H. McD. Whitaker.

538

Granular soils in places where rainfall is infrequent but heavy often reveal cavernous structure (Volk and Geyger, 1970; D.E. Miller, 1971; Evenari et al., 1974). Bull (1964) noticed it frequently in alluvial-fan debris-flows, the air either being engorged at the advancing snout, or rising into the flow from the dry ground beneath. Steiglitz and Inden (1969) found cavernous structure in fluvial sediments flooded by heavy rains. Like H.B. Stewart (1956), several of these workers showed experimentally that cavernous structure depended on the repeated flooding and drying of sand. Some of the air driven out of beaches by the tide escapes through the upper saturated layer to form in the swash-zone what Palmer (1928) and Emery (1945b) have distinguished as sand holes (Figs. 13-20, 13-21). These are upright, cylindrical to irregular tubes several millimetres across that reach to the surface of the sand, and from which streams of bubbles are released into any covering water. Palmer found these holes to extend commonly as deep as 0.1 m below the surface. Where fine and coarse laminae alternate, the escaping air accumulates in the coarse layers just below the surface as laccolith-like blisters or sand domes, sometimes called air-heave structures (D.W. Johnson, 1919; Palmer, 1928; Emery, 1945b). These domes (Fig. 13-21) are circular to oval in plan and up to 0.1 m across. Typically sand domes form just ahead of and within the zone affected by the swash, releasing their air once drowned. Some domes are fed by sand holes. W.O. Thompson (1949) claimed to find sand domes in the Lyons Sandstone.

MUD WAVES ON THE DEEP-OCEAN FLOOR

Distribution and character The precision depth-recorder and continuous seismic-profiler reveal in detail both the surface form and immediate subsurface structure of the deep-ocean floor. Their widespread use has shown that substantial parts of the ocean bed carry long-crested sediment waves on a scale generally much larger than any of the transverse bedforms so far described. These structures began to be recorded at an early date (Ewing and Ewing, 1962; Savit et al., 1964; Bunce and Hersey, 1966; E.L. Hamilton, 1967; Schneider et al., 1967; Ewing et al., 1968), but gained little notice until Heezen et al. (1966b) pointed to the significance of contour-following thermohaline currents in the shaping of the continental rise and its outlying accretionary sediment ridges, on which the waves commonly lie. The term mud wave or sediment wave is generally applied to the structures, with some authors preferring antidune (Fox et al., 1968) or dune (Ewing et al., 1971; Bouma and Treadwell, 1975), on the basis of the inferred relative migration of some examples. The largest are sufficiently big as to have been classified amongst abyssal hills (Asquith, 1979; Lonsdale and Smith, 1980). Within the waves hemipelagic mud

539

predominates (Damuth, 1975, 1978; Johnson and Lonsdale, 1976; Damuth and Hayes, 1977; Embley and Langseth, 1977). Accompanying it are thin bands of current-reworked terrigenous silt or biogenic debris and, in places, thin turbidite sands. Mud waves are widely distributed in the Atlantic Ocean, particularly along its western borders (Ewing and Ewing, 1962; Savit et al., 1964; Ballard, 1966; Bunce and Hersey, 1966; Schneider et al., 1967; Fox et al., 1968; Rona, 1969; Mark1 et al,, 1970; Ewing et al., 1971; Egloff, 1972; Tucholke and Ewing, 1974; Bouma and Treadwell, 1975; Damuth, 1975, 1978, 1980; Jacobi et al., 1975; Johnson and Lonsdale, 1976; Damuth and Hayes, 1977; Embley and Langseth, 1977; Lonsdale and Spiess, 1977; Hollister et al., 1978; Asquith, 1979; Roberts and Kidd, 1979; Tucholke, 1979; Embley et al., 1980). They occur chiefly on the middle and lower continental rise, in depths between 2500 and 5000 m, and on abyssal sedimentary ridges like the Blake- Bahama Outer Ridge, the Greater Antilles Outer Ridge, and the Feni Ridge. Some cover the broad levees of large distributary channels on active or recently active deep-sea turbidity-current dispersal cones, whereas others are restricted to the upcurrent sides of seamounts. Similarly set mud waves occur locally in the Indian (Ewing et al., 1968; Kolla et al., 1976, 1980; Johnson and Bunce, 1977; Johnson and Damuth, 1979) and Pacific Oceans (E.L. Hamilton, 1967; Shepard et al., 1976; Tucholke, 1977; Damuth, 1979; Jacobi and Mrozowski, 1979; Normark et al., 1980), and more examples should emerge as these waters become better known. Two classes of mud wave-small-scale and large-scale- are clearly distinguishable, and within the second of these three further divisions are tentatively suggested. It must be remembered that the orientation of mud waves relative to ship’s tracks is in most cases unknown. Small-scale mud waves are so far known only from the upcurrent side of Mytilus Seamount, off New England, where they underlie a layer of relatively turbid bottom water (Johnson and Lonsdale, 1976; Lonsdale and Spiess, 1977). The structures have long, comparatively straight crests, and are locally arranged en enchelon. Their wavelength is between 10 and 20 m and their height from 1-2 m. The forms lie transverse to the prevailing bottom current, but of their symmetry nothing is known. Large-scale mud waves are of three related kinds. Those distinguished as steep and irregular (Fig. 13-22a,b) appear as discrete to slightly overlapping echo-traces of symmetrical to weakly asymmetrical shape and with an apparent wavelength generally between 0.5 and 2 km (e.g. Damuth, 1975; Shepard et al., 1976). Their height is in the order of 10-50m, occasionally reaching more than 100m. A feature possibly attributable to the nature of the acoustic return is that crests appear to be much less curved than troughs. Sub-bottom reflectors concordant with the surface can be traced to depths of 50-100m beneath the waves. On the basis of echo-sounder and profiler

540

-

I

-

I

I km

2 km

r

I km

I

I km

I km

I

I I

Fig. 13-22. Slightly simplified reconstructions of seismic profiler records across different types of mud wave, to show the form of the sea bed and principal internal reflectors. a, b. Steep irregular waves, equatorial Atlantic Ocean (after Damuth, 1975). c, d. Steep regular mud waves, equatorial and southeast Atlantic Oceans (after Embley and Langseth, 1977, and Damuth and Hayes, 1977). e, f. Flat regular mud waves, equatorial Atlantic Ocean (after Damuth, 1975).

traces uncorrected for vertical exaggeration, it might be inferred that the waves are stationary, but restoration to true scale accords with moderate to steep angles of climb. Mud waves distinguished as steep and regular (Fig.

54 1

13-22c,d) have apparent wavelengths of 0.5-3 km and heights in the order of 10-50m (Bouma and Treadwell, 1975; Damuth, 1975, 1978; Jacobi et a]., 1975; Kolla et al., 1976; Damuth and Hayes, 1977; Embley and Langseth, 1977). The waves have long, parallel to subparallel crests and a weak cross-sectional asymmetry. In the subsurface are large numbers of concordant reflectors whose offset points to wave translation on true paths inclined between about 4" and 10". The third type of large-scale mud wave, distinguished as flat and regular (Fig. 13-22e, f), has an apparent wavelength generally between 3 and 10 km and a height rarely more than 10m (Bouma and Treadwell, 1975; Damuth, 1975; Kolla et al., 1976; Embley and Langseth, 1977). Concordant to locally discordant internal reflectors point to their rapid translation on true paths inclined upward at only 2-4". The waves are weakly asymmetrical, the reflectors being spaced furthest apart beneath the steepest slopes. The close relationship between these three forms is suggested by traces showing large variations in angle of climb, and some variation in wave height, through time (e.g. Damuth, 1975; Tucholke, 1977).

Origins of mud waves Only in their broadest aspects are the origins of abyssal mud waves understood. Ewing and Ewing (1962) favoured a tectonic cause, though allowing that the forms could be sedimentary. Ballard (1966) thought that they might be folds resulting from mass-flow on the continental margin. Features in some respects like mud waves were ascribed by K.B. Lewis ( 1971) to thrusting associated within large slumps. Structures resembling mud waves were seen in profile by Carlson (1978) on a slump off the Alaskan coast. Since the work of Savit et al. (1964) and Bunce and Hersey (1966), however, mud waves have generally been treated as sedimentary in origin, and particularly since their marked association with turbidity-current dispersal cones and the sites of strong, turbid, contour-currents was established (e.g. Damuth, 1975; Eittreim et al., 1976; Kolla et al., 1976; Biscaye and Eittreim, 1977; Embley and Langseth,. 1977). The main noncircumstantial evidence for their primarily depositional origin is provided by their smooth slopes and parallel internal layering, though the occasionally discordant internal reflectors, and the superimposed scoured furrows observed by Hollister et al. (1974), show that erosion plays a role at times. But what precisely are the currents and depositional mechanisms involved in the building of the waves? Because of their large scale, and the apparent lack of continuous bottom currents, Bouma and Treadwell (1975) interpreted the mud waves they described as lobes of sediment deposited from individual turbidity currents or debris flows. This idea is difficult to accept, because (1) mud waves are common on accretionary ridges of extremely low slope, and (2) their orderliness is inconsistent with the random variations in size and mobility to be

542

expected of a debris-flow or turbidity-current sequence. That some mud waves may be turbidity-current formed, though not as envisaged by Bouma and Treadwell, is suggested by Damuth (1979) and is implied by Embley and Langseth (1977), who reported a train of mud waves lying on and parallel with the levee of a large channel on the Amazon Deep-sea Cone. E.L. Hamilton ( 1967) had earlier described a similar association, which Damuth (1975) also had noticed. But the apparent restriction of waves to only one of the levees casts some doubt on the turbidity-current origin of the structures in this setting; a symmetrical distribution would be expected. It is not known, unfortunately, if the wavy levee is invariably, say, on the leeward side of the channel with respect to some contour-current. On balance turbidity currents seem unlikely to be the general cause of mud waves. Mud waves may be due to either (1) an unstable interaction between a deformable (primarily by differential deposition) bed and a turbid oceanbottom current, or (2) differential deposition under the influence of a largescale wave motion imposed on such a current. Both modes of origin are favoured by the relative persistence of oceanic thermohaline currents, and by the observation that mud waves extend through thicknesses of sediment that represent in the order of 105-106 years and in places more (e.g. Roberts and Kidd, 1979; Tucholke, 1979). There is as yet no formal mathematical theory of mud waves as instability phenomena, though certain observations described in connection with transverse bedforms on cohesionless substrates (Vol. I, Chapter 7) make this idea attractive. It was pointed out that, during turbulent flow over a wavy bed, the maximum of bed shear stress occurs on the upstream face of each bed wave. Now McCave (1969, 1970), Odd and Owen (1972), and McCave and Swift (1976) have proposed a plausible model for the deposition of cohesive sediments (Vol. I, Chapter 2), in which the deposition rate is an inverse function of the bed shear stress, at each sediment falling velocity and near-bed concentration. When this model is applied to turbid ocean-bottom currents, then an initial perturbation on the ocean floor, creating a streamwise fluctuation of bed shear stress, should continue to grow in amplitude through differential deposition and so form mud waves. As with cohesionless beds, the deposition-rate maximum on a mud wave should occur on.the downstream slope, where the stress is a minimum, whence the forms should migrate only downcurrent. This prediction is supported by the inferences of Ewing et al. (1971) and of Roberts and Kidd (1979), but not by the observations of Fox et al. (1968), Asquith (1979), and Embley et al. (1980). The question of the sense of translation of mud waves cannot therefore be regarded as solved. The second idea implies that mud waves depend on the stationary lee waves that can arise in stratified ocean currents where these flow over suitable bottom irregularities. An everyday example is afforded by the standing surface waves generated where a river flows over an isolated and

543

shallowly submerged stone. Theoretical and experimental studies of lee waves are described by Queney (1948), Scorer (1949), Long (1953a, 1953b, 1954, 1955, 1956, 1958), Yih (1960), and Baines (1979). The following discussion is based on Yih's (1965, 1969a) useful reviews. It can be shown that lee waves exist only if the densiometric Froude number is smaller than IT (approximately 0.318), a result that must exclude many turbidity currents as causes of lee waves. There are N lee-wave components if: 1 1
Fig. 13-23. Lee waves in a stratified flow downstream of a low mound, as calculated by Long (1955) for Fr'=O.2.

544

sediment existed in the flow, we should, by the previous argument, expect a mud wave to grow beneath the crest of each lee wave. But deposition means that the boundary is no longer rigid, whence the mud waves may travel slowly downstream, as the lag between bottom shape and bed stress takes effect, and so modifies or even overwhelms the influence of the barrier. It may even be possible for mud waves in a stratified flow to act as their own generators, since the spatial lag of bed shear stress provides a mechanism for growth, and the water waves would at all times be stationary relative to the bed waves. Does the lee-wave model yield wavelengths of the correct order? The Froude number of ocean currents is generally less than the critical value of 0.3 18, on the basis of observed thicknesses, densities, and density differences. For example, with h = 1000 m, q = 200 m3m- s - I , and Ap = 0.5 kgm-3, we find that Fr' = 0.092 and N = 3. By eq. (13.4) the wavelengths of the lee-wave components range between approximately 600 and 1 140 m, which is consistent with observation. The apparently one-sided development of mud waves on the levees of deep-sea channels, and the upslope migration of those waves, may give support to this.mode1, for the edge of a channel is an ideal generator. Another model was proposed by Kolla et al. (1980), who suggest that mud waves are bed features locked to stationary internal waves on a current whose densiometric Froude number is approximately critical. A closely related interpretation is proposed by Normark et al. (1980). The implications of mud waves for the stratigraphic record are uncertain. The smaller ones may be detectable in sufficiently large exposures, and the presence of the waves generally should be a source of variation within and between deep-sea silt-sand layers and in the ratio of mud to silt-sand. The only morphologically comparable structures so far described from the stratigraphic record are certain Cretaceous carbonate-mud mounds (Kennedy and Juignet, 1974; Thomsen, 1976). These formed in relatively shallow water, however, and trapping and binding organisms probably played a decisive role in their growth. It is interesting to note that the mounds described by Thomsen are steepest on the upcurrent side and grew upcurrent.

'

SHRINKAGE CRACKS

Character and distribution

Shrinkage cracks are incompletely to completely connected polygonal fractures that form perpendicular to the surface of a layer undergoing volume reduction as the result of cooling, dewatering, or a change of mineralogical composition. They occur in ceramic glazes, paint films, ill-made concrete, frozen ground, lava flows, and igneous dykes and sills. Additionally, and of interest here, are the fissures developed in layers of muddy

545

sediment that lost water either through an increase while still submerged in the strength of attractive inter-particle forces (synaeresis cracks), or through drying directly beneath the atmosphere (desiccation cracks). Shrinkage cracks wherever found express the action of tensile stresses in materials of limited tensile strength. Lachenbruch ( 1962, 1963) gives a morphogenetic classification of cracks in frozen ground which, with slight amplification, applies to desiccation and synaeresis cracks (Fig. 13-24). Fracture systems as seen in plan are divided between nonorthogonal and orthogonal, on the basis of the angles made where cracks or their projections intersect. Nonorthogonal cracks are either complete or incomplete, depending on whether the fissures are joined. Orthogonal cracks are subdivided first on their degree of preferred orientation. Whereas random cracks are unoriented, in oriented systerns two orthogonally related directions are strongly preferred. Oriented and random cracks may be either incomplete or complete. There are three kinds of incomplete oriented orthogonal fissures: ( 1 ) fractures that are elongated in a single predominant direction, (2) similarly oriented rosette-like arrangements of cracks, each rosette consisting of two or more cross-shaped groups of fractures, and

CRACK INFILLING Bridged

Unbridged

Simple

Fig. 13-24. A classification of shrinkage cracks and their infillings.

Compound

546

(3) sets of four radiating fissures making an orthogonal cross. Lachenbruch ( 1963) distinguished smoothly rectilinear or curvilinear cracks, which he called regular, from irregular ones (Fig. 13-24). In places, up to three orders of cracks are developed. Nonorthogonal shrinkage cracks are comparatively rare in muddy sediments. Complete systems defining predominantly six-sided polygons in the order of 0.1 m across occur on playas (Longwell, 1928; Neal et al., 1968; Krinsley, 1970; Sharp and Carey, 1976), tidal mud flats and salt-marsh pans (Van Straaten, 1954a; Dionne, 1974c; Gebelein, 1977), and dried-up stream beds (Soleilvahoup and Bertouille, 1976). Incomplete forms, often accompanying incomplete orthogonal cracks, have a similar distribution (Kindle, 1926; Soleilvahoup and Bertouille, 1976; Mason and Von Brunn, 1978). Fenton and Fenton (1937), Picard (1966), and Donovan and Foster (1972) report examples from lacustrine beds in the fossil record. Incomplete random orthogonal cracks are even rarer. Van Straaten (1954a) saw some accompanying complete fractures on the bottom of a channel empty at low tide. The forms illustrated by Soleilvahoup and Bertouille (1976) from a desert stream bed include semicircular to nearly circular fissures. Donovan and Foster (1972) figured from Devonian lacustrine rocks a bedding surface showing incomplete fractures. Complete random orthogonal cracks defining mainly four-sided polygons (Fig. 13-25b, c) are by far the commonest in muddy sediments. Fine examples abound in dried-up river channels, pools and lakes (W.H. Bradley, 1933; Keller and Foley, 1949; Fagerstrom, 1967; Conybeare and Crooke, 1968; Picard and High, 1969; Glennie, 1970; Minter, 1970; G.E. Williams, 1970; Donovan and Archer, 1975; Soleilvahoup and Bertouille, 1976), playas (Kindle, 1926; Willden and Mabey, 1961; Neal et al., 1968), and on both clay-mineral and carbonate tidal mud flats (Kindle, 1923; Van Straaten, 1954a; Mathieu, 1966; Dionne, 1974c; Gebelein, 1977; Kues and Siemers, 1977). W.B. Bull (1964) reported them on an alluvial fan. In most systems, the polygons are in the order of 0.1- 1 m across and the cracks seldom more than 0.05 m wide and 0.25 m deep. The playa fissures described by Lang (1943), Willden and Mabey (1961), Neal et al. (1968), and Schreiber et al. (1972) occur on a giant scale, however, the polygons measuring 15- 100 m across and the cracks 0.5- 1 m in width and 5 m or more in depth. Examples of the smaller fissures abound in the stratigraphic record (e.g. McKee, 1954; Van Houten, 1964). D.B. Smith (personal communication, 1978) has shown me photographs of infilled polygonal fractures in possible muddy gravel-rich debris-flow deposits of Permian age in southwest England. There are few examples of incomplete oriented orthogonal cracks. The rosette type is based on a single report, from a playa (Kindle, 1926). Radiating fractures making orthogonal crosses were seen by Corte and Higashi (1964) in one of their experimental tanks, and by Mason and Von Brunn (1978) in a desiccated pool. Rectilinear-parallel cracks were found by

547

Picard and High (1969, 1973) on a dried-up stream bed, and similar patterns are known from the stratigraphic record (Picard, 1966; Picard and High, 1969; Donovan and Foster, 1972). Complete oriented orthogonal fracture systems (Fig. 13-25a, d) dominated by four-sided polygons are reported from the dried-up beds of rivers (Picard and High, 1973), lakes (Donovan and Archer, 1975), and tidal mud flats (Bajard, 1966; Mathieu, 1966). Some giant playa cracks are of this type (Willden and Mabey, 1961; Neal et al., 1968). Examples of remarkable regularity were described by Shrock (1940, 1948) from the Silurian Byron Limestone of Wisconsin. Those of the Green River Formation are less regular (Picard, 1966). Shrinkage cracks are much simpler in vertical view than plan, tapering gradually downward from the surface, either to nothing or to a minimum width at the top of some layer that was not involved in the volume reduction. Superficially, the surfaces of the fissures are smooth, but a careful scrutiny will usually reveal plume (or plumose) markings (N.J. Price, 1966; Hobbs et al., 1976), as noted by Corte and Higashi (1964) and by Cegla and Dzulynski (1967). Fissures width and depth, and the diameter or area of the polygons they define, all increase in harmony in systems of shrinkagecracks. Generally, the polygons between cracks are mildly concave-up, but under some circumstances are convex-up, and occasionally are of mixed shape (e.g. Kindle, 1923; Ward, 1923; Longwell, 1928; Minter, 1970; Picard and High, 1973). Very thin layers of mud roll up tightly as they dry, to form mud curls resembling the brims of bicorn or tricorn hats (Longwell, 1928; Fagerstrom, 1967; Karcz and Goldberg, 1967; Picard and High, 1969, 1973; Glennie, 1970; Soleilvahoup and Bertouille, 1976). We therefore see that shrinkage cracks occur in many continental and shore-related environments, but there are very few if any detectable geometrical differences between the fractures developed in these various settings. The fissures of carbonate tidal mud flats are very similar to those of clay-mineral tidal flats, which in turn are indistinguishable from shrinkage cracks developed on river floodplains and dried-up river beds. The faint suggestion that incomplete and nonorthogonal fractures may be more prevalent in saline than fresh water environments is explicable by inadequate sampling as much as by environmental differences. Shrinkage cracks in muddy deposits become preserved into the stratigraphic record through being infilled with fresh sediment, normally silt or sand, and as often wind-laid as water-borne. Infilling and burial of the fissured surface occurs often as the result of a single depositional act, when a simple bridged filling is produced (Fig. 13-24). Burial is otherwise episodic. In the simpler of these cases,.on incomplete filling of silt or sand is followed by further mud, to give an unbridged compound fill. When the first and last depositional episodes involve sand or silt, the fracture filling is compound and bridged. Occasionally, the filling and its host rock are both erosively truncated (Wells, 1969).

548

Fig. 13-25. Desiccation cracks in mud. a. Large partly oriented orthogonal fractures, upper tidal flat, Lydney, Gloucestershire. England. Hammer 0.33 m long. b. Random orthogonal irregular cracks, upper tidal flat Lydney, Gloucestershire,England. Hammer 0.33 m long.

549

c. Random orthogonal cracks, amongst which secondary cracks of a smaller size have begun to form, aided by defects provided by ice-crystal moulds. Tidal flat, Barmouth Estuary, Wales. Notebook 0.20 m long. d. Locally oriented cracks formed above buried vehicle tracks on quarry floor. Hammer 0.35 m long.

550

Mechanics and controls

The tensile stresses promoting shrinkage cracks are caused differently in desiccation as compared with synaeresis. During desiccation- the loss of water by a muddy sediment directly to the atmosphere- the stress is created by surface tension on the films of water that bridge the mineral grains at bulk water-contents lower than the sediment dry porosity (Pearce and Donald, 1959). The stress due to this cause is a maximum at a water-content intermediate between full saturation, when the force is zero, and complete dryness, when it is again zero. The maximum stress increases steeply with decreasing grain size, for it is closely related to the number of bridging films that can form and, therefore, to pore-space density. Tensile stresses due to surface tension are consequently small in sand but typically very large in muddy sediments. During synaeresis, in which a muddy sediment loses water directly to a superincumbent aqueous layer, tensile stress is created by an increase in the strength of inter-particle surface forces (Van Olphen, 1963; Gillott, 1968). These forces are comparatively very weak, for they create in poorly cohesive sediments generally less shrinkage than do the stresses associated with the desiccation of muddy sediments orders of magnitude stronger at the drying stage. The context in which these forces act is created partly by the sediment itself and partly by its setting. Twenhofel (1932) at an early stage listed the controls on the scale and character of sedimentary shrinkage cracks as: (1) character (mineralogy and texture) of the sediment, (2) rate of water-loss, (3) thickness of the affected layer, (4) character (temperature, chemical composition) of the water in which the muddy sediment was deposited, ( 5 ) nature of the undkrlying material, and (6) the presence of foreign matter. Many workers in analysing shrinkage cracks state or imply that the affected layer should tend to be divided by fissures which at the surface define regular six-sided polygons (Mallet, 1875; James, 1920; Hewes, 1948; Spry, 1962; Smalley, 1966a; Bertouille, 1974). While it is true that this pattern represents the maximum release of strain energy per unit crack area (principle of least work), the Occurrence of hexagonal cracks, in practice rarely found in muddy sediments, implies the start of fissuring at many points simultaneously and the subsequent very rapid development of fractures. Shrinkage cracks in muddy sediments in fact are predominantly orthogonal, having developed from very few points and rather slowly. A more satisfactory model of shrinkage cracks is Lachenbruch’s (1961, 1962, 1963), in which attention is focussed on the development of single fractures. A real layer of muddy sediment is not homogeneous, but includes a distribution of defects of many sizes and shapes and, as well, defects in the sense that its thickness varies spatially even when nominally uniform. As Lachenbruch explains, these kinds of defect, which may not be distributed randomly, play a crucial role in the development of cracks. Tensile stresses

55 I

build up in the upper parts of a dewatering layer as it shrinks, declining downward from a maximum at the surface until, at a certain depth, they are replaced by compression related to the lithostatic force. Eventually a water content is reached at which the surface stress exceeds the tensile strength of the sediment in the layer overall, and a crack is initiated. This will invariably occur at some large defect of a widely spaced kind (a long piece of wire is always weaker than a short length cut from the same piece). But that defect can cause no further cracks, and the layer is left stronger than before. Hence a further water-loss is necessary before new fractures can appear at other defects situated in or on the layer. The development of the initial crack also has the effect of releasing the stress in its vicinity, to a much greater degree normal than parallel with itself. The crack may branch at its tip as it grows, but no further fractures can arise within the bordering zones of stress-release, though fissures initiated elsewhere may cross those zones. Because of the layer-parallel anisotropy in the stress-release, and the tendency of cracks to form normal to the direction of greatest tensile stress, a fissure travelling toward an existing fracture will tend to do so orthogonally. In these ways, as water-loss proceeds, predominantly orthogonal cracks will arise, the more closely spaced internal defects controlling in some degree their characteristic spacing, and the more sparsely distributed the uniformity of the pattern. The system of shrinkage cracks appearing in, for example, Fig. 13-25a, is clearly consistent with this model. That most of shrinkage cracks in muddy sediments conform to this model of slow orthogonal growth from a relatively few centres was amply demonstrated by Corte and Higashi (1964), who studied the desiccation of muds by time-lapse photography and by mapping crack growth-directions from plumose markings (Fig. 13-26). It appears that nonorthogonal cracking is restricted to materials that are highly homogeneous, relatively brittle, and shrunk uniformly, a set of conditions rarely met in natural muddy sediments. Evidence for the role attributed by Lachenbruch to defects has long been available. In describing organic structures preserved in an episodically accumulated and later desiccated mud, Hughes (1884) remarked that “if anything begins a groove in the top layer, any subsequent-cracking would be likely to follow that line”. Shrinkage cracks have been initiated at such internal defects as stones or bivalves (Corte and Higashi, 1964; Kues and Siemers, 1977), and at such boundary defects as ripple marks (Picard, 1966; Picard and High, 1969, 1973; Donovan and Foster, 1972), gastropod trails (Baldwin, 1974), worm tracks (Soleilvahoup and Bertouille, 1976), the impressions of bird’s feet (Wuest, 1934; Schafer, 1953; Mason and Von Brunn, 1978), and the tracks of beetle larvae (Metz, 1980). Small and densely arrayed defects, such as sand grains, lead to irregular fractures (e.g. Corte and Higashi, 1964), apparently formed by the fusion of many small en echelon tension gashes. Because zones of stress-release about a crack grow in width with crack

552

Fig. 13-26. Propagation directions of desiccation cracks as given by plumose markings on the walls of cracks produced experimentally. After Corte and Higashi (1964).

depth (Lachenbruch, 1961), and layer thickness sets a downward limit to the fissures, the size of the polygons enclosed by shrinkage cracks should increase with fracture depth and with layer thickness. Twenhofel (1932) showed an early qualitative awareness of this correlation. Depending on the boundary conditions, the polygons in Corte and Higashi's (1964) experiments varied in diameter approximately as the square-root or first power of the layer thickness. Donovan and Archer (1975) found a steeper relationship between maximum polygon width and maximum crack depth in a dried-up lake bed (Fig. 13-27). A useful rule of thumb is that polygons size is 3-8 times the crack depth or layer thickness. Only nominally uniform layers subject to uniform external conditions are expected by Lachenbruch ( 1962) to yield random orthogonal fractures. Should the layer thicken in a particular direction, or be subject to a body-force because it lies on a slope, or experience a horizontally varying drying rate, then because of layer-parallel anisotropy oriented fissures will instead result. The combined effects of slope and thickness-change are well illustrated by Donovan and Archer (1975), who found that complete oriented orthogonal cracks were restricted to the edge of a former lake-bed, where the slope exceeded about 5'. The effect of a local anisotropy in dewatering rate is shown by the ring-fissures surrounding clusters of phreatophytes in playas (Neal et al., 1968), and the linear cracks deliberately induced under certain crop irrigation schemes (Swartz, 1966a, 1966b).

553 0.16

0.14

042

E

f

0.10

0

x

e g 008 -.-

.-VeU 0

-E s

0'06

0.04

0.02

0 0.10

0.20

0.30

0.40

0.50

0.60

Moximum desiccation polygon width (ml

Fig. 13-27. Depth of desiccation cracks as a measured function of polygon width, dried bed of Haweswater, English Lake District. After Donovan and Archer (1975).

A vexed question since Moore (1914) reported seeing open fractures in mud covered by water for a long period has been the extent to which shrinkage cracks in muddy sediments are attributable to synaeresis, a possibility to which Jungst (1934) laid vigorous claim. However, whether synaeresis occurs naturally has never been proved and, should this deficiency ever be remedied, there is no mechanical reason to expect any intrinsic difference between synaeresis and desiccation cracks. The data assembled by Moore (1914) and Van Straaten (1954a) are inadequate to show that the fissures they described were not due to normal desiccation. W.A. White (1961) found experimentally that clays allowed to settle in electrolytes tended to crack on consolidation, but the initial concentrations of each were higher than would ordinarily be found naturally. Kindle (1917c), Kindle and Cole (1938), and Baria (1977) found that the sedimentation of muds in electrolytes tended to suppress fracturing as comparing to fresh water. Also in experimental studies, Burst (1965) and Donovan and Foster (1972) found that clays settled in fresh water cracked when leached with strong electrolytes. This could

554

occur frequently in playas and on sabkhas, perhaps very occasionally on tidal mud flats, but virtually never in lakes and rivers. Synaeresis should not therefore be a common geological phenomenon.

SHEET-LIKE SEDIMENTARY INTRUSIONS

The infilled shrinkage cracks discussed above exemplify a type of sedimentary structure which has also been called a Neptunian dyke, a beddingdiscordant system of generally planar fissures filled under gravity with sediment from above, more or less gradually and often episodically. There are other sheet-like sedimentary bodies that appear to have been emplaced more or less forcefully, while the material composing them (sand, gravel, rarely mud) was readily deformable, either liquidized or plastic. These are generally classed as intrusive clustic or sedimentary dykes, but many of them are bedding-parallel (i.e. sills), while others cut the host strata obliquely. Surveys and reviews of intrusive sedimentary sheets are given by Shock (1948), Hayashi (1966), Strauch (1966), and Dionne and Shilts (1974). Most authors agree that sedimentary intrusions arise only when three conditions are met: (1) a state of horizontal tension, (2) the presence nearby of suitable source materials (e.g. plastic clays, or ill-cemented sands or gravels), and (3) in the case of a sand or gravel source, a pore-water pressure temporarily in excess of lithostatic so that liquefaction can occur. These conditions are satisfied under two broad and only partially separable circumstances: ( 1) penecontemporaneously with deposition, often in association with sediment slumping and sliding, seismically induced liquefactions, or with movement on growth-faults, and (2) during tectonic events that occur significantly after sediment deposition, but before lithification is completed. Sedimentary intrusions for which a penecontemporaneous origin is claimed or seems likely are widely described (Bailey and Weir, 1932; Waterston, 1950; Dzulynski and Radomski, 1956; Greensmith, 1957; Rutten and Schonberger, 1957; Smith and Rast, 1958; Wood and Smith, 1958; Ten Haaf, 1959; Shelton, 1962; A.D. Stewart, 1962a; Marschalko, 1965; Hayashi, 1966; Oomkens, 1966; Teisseyre, 1967; A.G. Smith, 1968; Gregory, 1969; Powell, 1969, 1973; Cook and Johnson, 1970; Eisbacher, 1970; Dunbar and McCall, 1971; Heron et al., 1971; Moors and Schleiger, 1971; D.W. Lewis, 1973; Boulter, 1974; J.D. Roberts, 1974; Dionne and Shilts, 1974; Bates, 1975; Elson, 1975; Larsson, 1975; Sturt and Furnes, 1976; D.M. Williams, 1976; Hesse and Reading, 1978; Hiscott, 1979; Snavely et al., 1980). They range from shrinkage cracks filled from below (Oomkens, 1966), to fractures plugged with sand apparently in association with the developing instability of sediments rapidly accumulated on submarine slopes (Dzulynski and Radomski, 1956; Snavely et al., 1980), to infilled growth-faults and early joints that reached up practically to the depositional surface (Cook and

555

Johnson, 1970). Included amongst penecontemporaneous intrusions are the large dykes emplaced into recent sediments during the great Alaskan earthquake of 1964 (Reimnitz and Marshall, 1965). The most telling evidence in favour of a penecontemporaneous origin for intrusive sedimentary dykes and sills is their close spatial association with mobilized strata (slumps, slides, soft-sediment deformations), a preferred orientation perpendicularly to the currents that deposited the host sediment (i.e., slope-parallel), and a lack of a directional relationship to tectonic structures. The last criterion of course fails with intrusions related to growth-faults. There are several examples of sedimentary intrusions for which a tectonic origin is claimed or seems plausible (Diller, 1889; Newsom, 1903; Jenkins, 1925a; Vitanage, 1954; Harms, 1965; Peterson, 1966, 1968; Marschalko, 1965; Spencer, 1971; Brandon, 1972; Truswell, 1972). These intrusions have a spatial association with faults and an orientation that is closely related to that of joints, folds or faults. Some in addition are accompanied by bedding offsets or cut large clasts. In detail, sedimentary intrusions are concordant to discordant, planar to irregular sheets that commonly branch or send out short apophyses. The majority are between 0.1 and 1 m in width (e.g. Hayashi, 1966; Peterson, 1966), but some are in the order of 100 m across (Newsom, 1906; Harms, 1965). They commonly occur en echelon in swarms and, in well-exposed ground, can be traced individually along strike for distances from a few hundred metres to many kilometres. The walls are generally smooth but can be striated or slickensided (Peterson, 1968; Brandon, 1972), or erosively fluted and grooved (Dott, 1966b). Occasionally, the bedding immediately adjacent to the dyke is bent or sheared out downward or upward. Most intrusions are described as structureless internally, though some reveal a wall-parallel preferred orientation of mica flakes, quartz grains, gravel fragments, and pieces of included wall-rock (Harms, 1965; Peterson, 1966, 1968; Gregory, 1969; Moors and Schleiger, 1971; Brandon, 1972; D.W. Lewis, 1973; Sturt and Furnes, 1976; D.M. Williams, 1976; Lewis et al., 1979). Some dykes show a wall-parallel layering on a millimetre to centimetre scale (Reimnitz and Marshall, 1965; Hayashi, 1966; Peterson, 1968; D.W. Lewis, 1973; Lewis et al., 1979). In the dykes he described, Peterson found the layers to have a transverse textural grading. Rarely, the intrusions are graded overall, the coarsest debris occurring along the centre (Diller, 1889; Peterson, 1968; Eisbacher, 1970). Vitanage ( 1954) described a layering that resembled deep menisci, a possible expression of the profile of particle velocity developed during intrusion (see Coward, 1980). The intrusive origin of a sedimentary dyke is not easily established. It is strongly suggested for sheets of irregular form with apophyses and upward branches, and for dykes or sills that extend up from sand or gravel bodies identical in texture and composition to themselves. A wall-parallel grain

556

fabric also strongly suggests intrusion, as do striated or fluted walls, and deformed wall-rocks. Ten Haaf (1959) found plumose markings on the wall of one upward-intruded sand dyke. Wall-parallel layering that involves clay laminae points to infilling by partly plastic strata (Jenkins, 1925b), or in the case of sand or gravel layers to episodic infilling by liquidized material. Where there are graded sand or gravel layers, however, forceful intrusion may confidently be inferred, as such grading is explicable, as has been shown (Chapter 4), in terms of Bagnoldian dispersive pressures acting between intensely sheared, densely arrayed particles. Graded layers are best known from the dykes ascribed by Peterson (1966, 1968) to the infilling of tension gashes produced during faulting some millions of years following deposition of the affected strata. Since after the elapse of this time the rocks would have become somewhat brittle, and the faulting took place beneath an overburden, the gashes could have propagated at speeds of tens or even hundreds of metres per second (N.J. Price, 1966), and would have been simultaneously filled to the accompaniment of intense shearing of the fill. Episodic growth of the gashes in response to stick-slip on the faults may explain the multiple layering.

PTYGMATIC FOLDS IN DESICCATION-CRACK INFILLS AND SEDIMENTARY DYKES

Kuenen (1966~)gave the best available definition of ptygmatic folds, characterizing them as “multiple tortuosities in a sheet of rock embedded in a host showing a simpler pattern (or none at all)”. As reviewers make plain (Kuenen, 1938, 1966c; G. Wilson, 1952; Godfrey, 1954; Mitra and Datta, 1978), ptygmatically folded dykes, sills and veins are familiar features in highly folded and metamorphosed terrain. Similar structures, again on a relatively small scale, abound in some sedimentary sequences, but under conditions such that tectonism could not possibly be held to account for them. Within sedimentary sequences that are little or not at all deformed tectonically, ptygmatic folds occur almost exclusively in desiccation-crack infills and in sedimentary dykes. Here they are often called molar-tooth structures (e.g. A.G. Smith, 1968), after their strong resemblance to the intricate folds of enamel seen on herbivore teeth, although the name merits no general currency. Fine examples of ptygmatically folded desication-crack infills were described by W.H. Bradley (1930) from the Green River Series, the folded sand-sheets tapering downward into mud and creating polygonal or triradiate patterns on bedding surfaces. Figure 13-28 shows examples from the Middle Devonian lacustrine shales of Scotland, where the folds were also found by Burollet et al. (1969) an&by Donovan and Foster (1972). The short infill on the left forms two relatively large folds, whereas the longer on the

557

Fig. 13-28. Ptygmatically folded sand wedges infilling desiccation cracks in silty shale, Stromness Flagstone (Devonian), Orkney, Scotland. Specimen 0.15 m wide.

right is strongly distorted only near the top. Each toward its lower end reveals a fine-scale, external corrugation, indicative of concentric folding. Locally the infills are obliquely ruptured. Other ptygmatically folded desiccation-crack infills were described by Teichmuller (1955) and by Young and Jefferson (1975). Some of Boulter’s (1974) folded sandstone sheets appear to have formed penecontemporaneously with sedimentation, and may therefore be desiccation-crack infills. Ptygmatically folded sedimentary dykes (Shelton, 1962; A.G. Smith, 1968; Truswell, 1972; Boulter, 1974; Hiscott, 1979) are identifiable by their in places upward as well as typically downward extension from coarse-grained beds, their generally extreme length compared to thickness, their commonly oblique attitude to bedding, and their frequently parallel sides. Because sedimentary dykes are often large, the folds range more widely in size than in the case of deformed desiccation-crack infills. There are, however, no geometrical differences between the folds in the two cases. Provided that the dykes are nearly perpendicular to bedding, the folds are flat-lying, generally with long limbs and sharply curved hinges. But oblique dykes become deformed into asymmetrical folds (Fig. 13-29), the vertical limbs being usually short and thick. Ptygmatic folding occurs under a wide range of geological conditions and has several possible explanations (Kuenen, 1966b). Only two are of interest here, for either the sediment sheets were folded during emplacement, or were emplaced passively and then deformed. G . Wilson ( 1952) vigorously espoused

558

Fig. 13-29. Ptygmatically folded oblique sandstone dyke penetrating shales, Ecca Series (Permian), Coffee Bay, near Durban, South Africa. After Truswell (1972).

the first, hypothesis to explain certain igneous and metamorphic dykes. He argued that the folding occurred when the dyke-material, while penetrating a less competent country-rock, met a relatively resistant horizon against which it was forced to buckle. This idea was supported by experiments in which ribbons of glazier’s putty injected into solidified gelatine of various consistencies proceeded to fold on meeting a resistant layer. The same effect arises when stiff paint or cream is poured from a height into a wide bowl, when buckle after buckle will be observed to form as liquid in the descending ribbon nears the level accumulated in the vessel. According to the second explanation, championed by Kuenen ( 1938), partly on experimental grounds, the structures as seen in igneous and metamorphic terrain are buckle folds produced when the layer containing each deformed sheet was reduced in thickness. Only consolidation (compaction) could effect this in a sedimentary sequence but little or not at all influenced by tectonism. The two hypotheses are largely interchangeable from a purely physical standpoint, but have quite different practical implications. Wilson’s is not applicable to folded desiccation-crack infills, which were passively emplaced, but may be appropriate for some sedimentary dykes. One would look not only for indications of forceful emplacement, such as internal grading or wall-parallel layering, but also for evidence- two orders of folds, for example-that deformation occurred in more than one stage, one of which antedated consolidation. Folding during consolidation provides a ready explanation for ptygmatically folded desiccation-crack infills and many deformed sedimentary dykes. With dykes it is generally only necessary to establish a single phase of deformation. W.H. Bradley ( 1930) qualitatively interpreted ptygmatically folded desiccation-crack infills in terms of consolidation. A quantitative analysis based on thickness variation around folds (Ramsay, 1967) was advanced by

559

!-

Fig. 13-30. Definition diagrams for (a) the consolidation of a shale containing an oblique sand sheet, and (b) the buckling of a single stiff layer embedded in a viscous medium.

Donovan and Foster (1972). Shelton (1962), A.G. Smith (1968), .Boulter (1974), and Hiscott (1979) calculated from the fold sinuosity the consolidation of sediments containing ptygmatically folded dykes. If we assume that (1) the initial porosity of the host sediment is just zero by the end of the period of folding, (2) one order of folds is present, (3) the folded layer experienced no layer-parallel shortening, and (4) the direction of maximum compressive stress is normal to bedding, then the initial fractional porosity Po of the host is (Fig. 13-30a): (13.5) in which h , is the fold arc-length between A and B, h , is the straight-line distance between these points, and a is the inclination of the folded zone relative to bedding. Under these assumptions, P, is of course also the fraction by which the host layer was reduced in thickness during consolidation. Shelton, Smith, Boulter and Hiscott all obtained realistic estimates for the degree of consolidation, although some of the assumptions listed are severe. Ptygmatic folding occurs experimentally whenever a sheet of viscous material is compressed parallel with its length while embedded in a medium of lower viscosity (Escher and Kuenen, 1928; Erdmannsdorffer, 1938; Kuenen, 1938; G. Wilson, 1952; Ramberg, 1959; Biot et al., 1961; Agostino, 1971; Hudleston, 1973). The theory of the process is given by Biot (1957, 1959a, 1959b, 1961) and Biot and Ode (1962), and by Ramberg (1959, 1960, 1961, 1962, 1963a, 1970a, 1970b), in two important series of papers, with recently Fletcher (1974, 1977) and R.B. Smith (1975, 1977) contributing

560

significant advances. Fletcher gives an exact solution for folds of infinitesimally small amplitude (Fig. 13-30b) which, to an excellent approximation, may be stated as: L27 (13.6) - (6qm/qsh)1/3 - ( q m / 2 q s h ) for frictionless contacts between deformed sheet and medium, and (13.7) when the two are welded together. In these equations, L is the fold wavelength, H the thickness of the deformed sheet, Vsh the dynamic viscosity of the sheet, and q m the viscosity of the medium. In each case the relative wavelength increases as the viscosity ratio decreases below unity. This result supercedes those of Goguel (1948), Biot (1957), and Ramberg (1959, 1960), and may be used to estimate viscosity ratios from measured ptygmatic folds. The best developed in Fig. 13-28, for example, point to approximately equal viscosities. These estimates must be treated cautiously, however, as layerparallel shortening is almost certain to have occurred in real cases of ptygmatic folding (Sherwin and Chapple, 1968; Hudleston, 1973; Hudleston and Stephansson, 1973). Equation (13.5) is similarly suspect.

56 I

REFERENCES

Aario, R., 1971. Bull. Geol. SOC.Finl., 43: 163-172. Aario, R., 1972. Ann. Acad. Sci. Fenn., Ser. A3, 1 1 1: 1-55. Aario, R., 1977a. Boreas, 6: 87-100. Aario, R., 1977b. Nordia, 2: 5-14. Abad, G.N. and Machemehl, J.L., 1974. An experimental study of scour around marine foundations due to oscillatory waves and unidirectional currents. N.C. State Univ., Cent. Mar. Coastal Stud., Rep. No. 74-5. Abbott, B.M., 1974. Palaeogeogr. Palaeoclimatol. Palaeoecol., 15: 1-27. Abbott, D.E. and Kline, S.J., 1962. Trans. ASME, D84: 317-325. Abdel-Rahman, N.M., 1963. The Effect of Flowing Water on Cohesive Beds. Swiss Federal University of Technology, Zurich. Abele, R.W., 1977. U.S. Coastal Eng. Res. Cent., Misc. Rep., No. MR 77-5. Abramovich, G.N., 1963. The Theory of Turbulent Jets. Massachusetts Institute of Technology Press, Cambridge, Mass., 671 pp. Achenbach, E., 1968. J. Fluid Mech., 34: 624-639. Ackeret, J., 1967. In: G. Sovran (Editor), Fluid Mechanics of Internal Flow. Elsevier, Amsterdam, pp. 1-24. Ackers, P., 1964. J. Hydraul. Div. ASCE, 90 (HY4): 1-37. Ackers, P. and Charlton, F.G., 1970a. J. Hydraul. Res., 8: 287-314. Ackers, P. and Charlton, F.G., 1970b. J. Hydrol., 1 I : 230-252. Ackers, P. and Charlton, F.G., 1970~.Proc. Inst. Civ. Eng., S12: 289-317. Ackers, P. and Charlton, F.G., 1970d. Proc. Inst. Civ. Eng., S15: 349-370. Acrivos, A. and Herbolzheimer, E., 1979. J. Fluid Mech., 92: 435-457. Acrivos, A., Snowden, D.D., Groves, S. and Petersen, E.E., 1965, J. Fluid Mech., 21: 737-760. Acrivos, A,, Leal, L.G., Snowden, D.D. and Pan, F., 1968. J. Fluid Mech., 34: 25-48. Acton, E.A., 1980. J. Fluid Mech., 98: 1-31. Adams, A.E. and Cossey, P.J., 1978. Geol. J., 13: 47-60. Adams, R.D., 1976. Earthquake Eng. Struct. Dyn., 4: 423-437. Adler, I.L. and Happel, J., 1962. Chem. Eng. Prog., Symp. Ser., No. 38: 98-105. Agassiz, L., 1838. Proc. Geol. SOC.,No. 3: 321-322. Ager, D.V. and Wallace, P., 1966. Proc. Geol. Assoc., 77: 385-417. Aghassy, J., 1978. Z. Geomorphol., 22: 129-147. Agostino, P.N., 1971. Geol. SOC.Am. Bull., 82: 2651-2660. Agrawal, Y., Talbot, L. and Gong, K., 1978. J. Fluid Mech., 85: 497-518. Ahlbrandt, T.S. and Andrews, S., 1978. Palaeogeogr. Palaeoclimatol. Palaeoecol., 25: 327-35 1. Ahlmann, H.W., 1924. Sver. Geol. Unders., Ser.Ca, 12: 119 pp. Ahmad, K. and Smalley, I.J., 1973. Powder Technol., 8: 69-75. Ahmad, M. and Pilpel, N., 1969. Rheol. Acta, 8: 448-456. Ahmad, M. and Pilpel, N., 1970. Rheol. Acta. 9: 585-594. Ahnert, F., 1960. Geogr. Rev., 50: 390-401. Aigner, T., 1979. Neues Jahrb. Mineral., Geol. Palaontol., Abh., 157: 326-343. Aigner, T. and Futterer, E., 1978. Neues Jahrb. Mineral., Geol. Palaontol., Abh., 156: 285-304. Aihara, Y., 1976. Phys. Fluids, 19: 1655-1660. Ajbulatov, N., Griesseier, H. and Shadrin, I., 1962. Acta Hydrophys., 7: 105-150.

562 Ala, M.A., 1974. Bull. Am. Assoc. Pet. Geol., 58: 1758-1770. Albertson, M.L., Dai, Y.B., Jensen, R.A. and Rouse, H., 1950. Trans. ASCE, 115: 639-664. Alexander, C.S. and Nunnally, N.R., 1972. Ann. Assoc. Am. Geogr., 62: 41 1-417. Alexander, H.S., 1932. J. Geol., 40: 305-337. Alexander, L.G., Baron, T. and Comings, E.W., 1953. Bull. Ill. Univ. Eng. Exploit. Stn., No. 413. Alexandersson, T., 1969. Sedimentology, 12: 47-6 I . Alexandersson, T., 1973. In: D.J.Stanley (Editor), The Mediterranean Sea: a Natural Sedimentation Laboratory. Dowden, Hutchinson and Ross, Stroudsburg, Penn., pp. 203-223. Alexandre-Pyre, S., 1971. Mem. Inst. R. Colon. Belge, Sect. Sci. Nat. Med., NS18, No. 3: 151 PP. Allen, J.R.L., 1960. J. Sediment. Petrol., 30: 193-208. Allen, J.R.L., 1962. Nature (London), 194: 167-169. Allen, J.R.L., 1963a. Geol. Mijnbouw, 42: 223-238. Allen, J.R.L., 1963b. Sedimentology, 2: 93-1 14. Allen, J.R.L., 1964. Sedimentology, 3: 163-198. Allen, J.R.L.. 1965a. Proc. Yorks. Geol. SOC.,35: 139-185. Allen. J.R.L., 1965b. Sedimentology, 5: 89-191. Allen, J.R.L., 1965~.Geol. Mijnbouw, 44: 1-21. Allen, J.R.L., 1965d. J. Sediment. Petrol., 35: 331-338. Allen, J.R.L., 1965e. Bull. Am. Assoc. Pet. Geol., 49: 547-600. Allen, J.R.L., 1965f. J. Geol., 73: 95-116. Allen. J.R.L., 1966a. J. Fluid Mech., 25: 331-335. Allen, J.R.L., 1966b. J. Sediment. Petrol., 36: 806-811. Allen, J.R.L., 1966~.Sedimentology. 6: 153- 190. Allen, J.R.L., 1967. J. Sediment. Petrol., 37: 691-692. Allen, J.R.L., 1968a. Geol. Mijnbouw, 47: 173- 185. Allen, J.R.L., 1968b. Sedimentology, 10: 161-182. Allen,.J.R.L., 1968~.J. Sediment. Petrol., 38: 1379-1381. Allen, J.R.L., 1968d. Nature (London), 219: 602-604. Allen, J.R.L., 1968e. Geol. Mag., 105: 166-176. Allen, J.R.L., 1968f. J. Sediment. Petrol., 38: 621-633. Allen, J.R.L., 1968g. Current Ripples. North-Holland, Amsterdam. Allen, J.R.L., 1968h. Geol. Mijnbouw, 47: 3-16. Allen, J.R.L., 1969a. J. Sediment. Petrol., 39: 607-623. Allen, J.R.L., 1969b. Geogr. Ann. A51: 61-96. Allen, J.R.L.. 1969c. Proc. Geol. Assoc., 80: 1-42. Allen, J.R.L., 1970a. J. Geol., 78: 326-351. Allen, J.R.L., 1970b. Geol. J., 7: 129-146. Allen, J.R.L., 1970~.J. Sediment. Petrol., 40: 298-323. Allen, J.R.L., 1970d. Scott. J. Geol., 6: 146-161. Allen, J.R.L., 1970e. In: J.P. Morgan (Editor), Deltaic Sedimentation, Modem and Ancient. SOC.Econ. Paleontol. Mineral., Spec. Publ., 15: 138-151. Allen, J.R.L., 1970f. Physical Processes of Sedimentation. Allen and Unwin, London. Allen, J.R.L., 1971a. Sci. Prog., Oxford, 59: 109-122. Allen, J.R.L., I971b. J. Sediment. Petrol., 41 : 97- 1 13. Allen, J.R.L., 1971~.Sediment. Geol., 5: 167-384. Allen. J.R.L., 1971d. J. Fluid Mech., 49: 49-63. Allen, J.R.L., 1971e. J. Geol. SOC.,London, 127: 553-561. Allen, J.R.L., 1972. Rass. Speleol. Ital., 24: 3-23. Allen. J.R.L., 1973. Sediment. Geol., 10: 157-177. Allen, J.R.L., 1974a. Sediment. Geol., 12: 73-167.

563 Allen, J.R.L., 1974b. Earth-Sci. Rev., 10: 263-342. Allen, J.R.L., 1975. Sediment. Geol., 13: 1-26. Allen, J.R.L., 1977a. In: K.J. Gregory (Editor), River Channel Changes. Wiley, London, pp. 15-45. Allen, J.R.L., 1977b. Sedimentology, 24: 53-62. Allen, J.R.L., 1977~.J. Geol. Soc., London, 134: 19-31. Allen, J.R.L., 1978. In: A.D. Miall (Editor), Fluvial Sedimentology. Mem. Can. SOC.Pet. Geol., 5: 199-209. Allen, J.R.L., 1981. Proc. Geol. Assoc., 92: 75-76. Allen, J.R.L. and Banks, N.L., 1972. Sedimentology. 19: 257-283. Allen, J.R.L. and Friend, P.F., 1968. Geol. SOC.Am., Spec. Pap., 106: 21-74. Allen, J.R.L. and Kaye, P., 1973. Geol. Mag., 110: 153-163. Allen, J.R.L. and Narayan, J., 1964. Geol. Mijnbouw, 43: 451-461. Allen, P., 1959. Philos. Trans. R. SOC.London, Ser. B, 242: 282-346. Allen, P., 1962. Proc. Geol. Assoc., 73: 219-243. Allen, P., 1975. In: A.E. Wright and F. Moseley (Editors), Ice Ages: Ancient and Modern. See1 House Press, Liverpool, pp. 275-286. Allen, S.J. and Kline, K.A., 1968. Trans. SOC.Rheol., 12: 457-468. Alvarez, W.. Gordon, A. and Rashak, E.D., 1975. Geol. Rom., 14: 141-154. Amaranth, T. and Rajappa, N.R., 1976. Acta Mech. 24: 87-97. Ambraseys, N. and Sarma, S., 1969. Bull. Seismol. SOC.Am., 59: 651-664. Ananyan, A.K., 1965. Fluid Flow in Bends of Conduits. Israel Program for Scientific Translations, Jerusalem. Anderson, A.G., 1967. Proc. 12th Conf. Int. Assoc. Hydraul. Res., 1: 370-378. Anderson, A.M., 1976. Trans. Geol. SOC.S. Afr., 78: 265-273. Anderson, C.A. and Russell, R.D., 1939. Calif. J. Mines Geol., 35: 219-253. Anderson, T. and Flett, J.S., 1903. Philos. Trans. R. Soc. London, Ser. A., 200: 353-553. Anderson, T.B. and Jackson, R., 1968. Ind. Eng. Chem. Fund., 7: 12-21. Andersson, K.E.B., 1961. Svensk Kem. Tidskr., 73: 334-345. Anderton, R., 1975. Geol. Mag., 112: 337-348. Anderton, R., 1976. Sedimentology, 23: 429-458. Andresen, A. and Bjerrum, L., 1967. In: A.F. Richards (Editor), Marine Geotechnique. University of Chicago Press, Urbana, Ill., pp. 221-239. Andrews, J.T. and King, C.A.M., 1968. Proc. Yorks. Geol. SOC.,36: 435-461. Andrews, P.B. and Laird, M.G., 1976. Sediment. Geol., 16: 21-44. Angeby, O., 1951. Lund. Stud. Geogr., Ser. A, No. 2: 1-34. Angeby, O., 1952. Lund. Stud. Geogr., Ser. A, No. 3: 14-24. Angell, J.K., 1971. J. Atmos. Sci., 28: 135-138. Angell, J.K., 1972. J. Atmos. Sci., 29: 1252-1261. Angell, J.K., Pack, D.H., Holzworth, G.C. and Dickson, C.R., 1966. J. Appl. Meteorol., 5: 565-572. Angell, J.K., Pack, D.H. and Dickson, C.R., 1968. J. Atmos. Sci., 25: 707-717. Angell, J.K., Pack, D.H., Machta, L., Dickson, C.R. and Hoecker, W.H., 1972. J. Appl. Meterol., 1 1 : 45 1-47 I . Angelucci, A,. De Rosa, E., Fierro, G., Gnaccolini, M., La Monica, G.B., Martinis, B., Parea, G.C., Pescatore, T., Rizzini, A. and Wezel, F.C., 1967. Geol. Rom. 6: 345-420. Anketell, J.M. and Dzulynski, S., 1968a. Ann. SOC.Geol. Pol., 38: 401-409. Anketell, J.M. and Dzulynski, S., 1968b. Ann. SOC.Geol. Pol., 38: 41 1-416. Anketell, J.M., Cegla, J. and Dzulynski, S., 1970. Ann. SOC.Geol. Pol., 40: 3-30. Anstey, R.L. and Fowler, M.L., 1969. J. Geol., 77: 668-682. Apmann, R.P., 1972. J. Hydraul. Div. ASCE, 98 (HY5): 795-810. Aref, H. and Siggia, E.D., 1980. J. Fluid Mech., 100: 705-737.

564 Arie, M. and Rouse. H., 1956. J. Fluid Mech., 1: 129-141. Arnborg, L., 1957. Geogr. An., 39: 132-147. Arnborg, L., 1958. Publ. Geogr. Inst. Univ. Uppsala, Phys. Geogr., No. 1 : 181-247. Arrhenius, S.. 1887. Z. Phys. Chem., I : 285-298. Artyushkov, Y.V., 1963a. Dokl. Akad. Nauk SSSR, 153: 162-165. Artyushkov, Y.V., 1963b. Dokl. Akad. Nauk SSSR, 153: 412-415. Artyushkov, Y.V., 1971. J. Geophys. Res., 75: 1397-1415. Asai, T., 1970a. J. Meteorol. SOC.Jpn., 48: 18-29. Asai, T., 1970b. J. Meteorol. SOC.Jpn., 48: 129-139. Ashida, K. and Narai, S., 1969. Bull. Disaster Prev. Res. Inst., Kyoto Univ., 19: 15-30. Ashton, G.D., 1972a. Proc. 1972 Heat Transfer and Fluid Mechanics Institute, Stanford Univ., pp. 200-213. Ashton, G.D., 1972b. Int. Assoc. Hydraul. Res. Ice Symp., Leningrad, pp. 123-129. Ashton, G.D., 1978. Annu. Rev. Fluid Mech., 10: 369-392. Ashton, G.D., 1979. In: H.W. Shen (Editor), Modeling of Rivers. Wiley, New York. pp. 14-1- 14-26. Ashton, G.D. and Kennedy, J.F., 1972. J. Hydraul. Div. ASCE, 98(HY9): 1603-1624. Ashton. G.D., Uzuner, M.S. and Kennedy, J.F., 1970. Two investigations of river ice. Iowa Inst. Hydraul. Res., Rep. No. 129. Ashwell, I.Y. and Hannell, F.G., 1966. J. Glaciol., 6: 135-143. Asquith, S.M.. 1979. Mar. Geol., 32: 165-190. Assaf, G., Gordon, R. and Gordon, A.L., 1971. J. Geophys. Res., 76: 6550-6572. Atkinson, B. and Taylor, B.N., 1963. Trans. Inst. Chem. Eng., 41: 140-145. Aufdermauer, A.N. and Joss, J.A., 1967. Z. Angew. Math. Mech., 18: 852-866. Auffret, G.A., Berthois, L., Cabioch, L., Douville, J.L. and Kenyon, N.L., 1972. Ann. Inst. Oceanogr., Monaco, 48: 157- 172. Aufrtre, L., 1928. Proc. 12th Int. Geogr. Congr., pp. 220-231. Aufrere, L., 1935. Geogr. Ann., 17: 481-498. Augenstein. D.A. and Hogg, R., 1978. Powder Technol., 19: 205-215. Augustinus, P.G.E.F., 1978. The changing shoreline of Surinam (South America). Natuunvetenschappelijke Studiekring voor Suriname en de Nederlandse Antillen, Utrecht, No. 95, 232 pp. Augustinus, P.G.E.F., 1980. Sediment. Geol., 26: 91-1 13. Avias, J., 1972. In: M. Merak and V.T. Springfield (Editors), Karst. Elsevier, Amsterdam, pp. 129- 188. Axelsson, V., 1967. Geogr. Ann. A49: 3-127. Back, L.H. and Roschke, E.J., 1972. Trans. ASME, E39: 677-681. Back, L.H., Massier, P.F. and Gier, H.L., 1964. Int. J. Heat Mass Transfer, 7: 549-568. Back, L.H., Massier, P.F. and Roschke, E.J., 1972. Trans. ASME, C39: 119-127. Backhaus, E., 1967. Jahresber. Mitt. Oberrhein. Geol. Ver., NF49: 157-171. Bagnold, R.A.. 1931. Geogr. J., 78: 13-33. Bagnold, R.A., 1933. Geogr. J., 82: 106-126. Bagnold. R.A., 1937. Geogr. J.. 89: 409-438. Bagnold, R.A., 1940. J. Inst. Civ. Eng., 15: 27-52. Bagnold, R.A., 1947. J. Inst. Civ. Eng., 27: 447-469. Bagnold, R.A., 1951. Geogr. J., 117: 78-86. Bagnold, R.A., 1953. Spec. Publ. Res. Counc. Isr., No. 2: 89-93. Bagnold, R.A., 1954a. Proc. R. SOC.London, Ser. A, 225: 49-63. Bagnold, R.A., 1954b. The Physics of Blown Sand and Desert Dunes. Methuen, London, 2nd ed., 265 pp. Bagnold, R.A., 1956. Philos. Trans. R. SOC.London, Ser. A, 259: 235-297. Bagnold, R.A., 1960. U.S. Geol. Surv., Prof. Pap., 282-E: 135-144.

565 Bagnold, R.A., 1962. Proc. R. SOC.London, Ser. A, 265: 315-319. Bagnold, R.A., 1966. U.S. Geol. Sum., Prof. Pap., 422-1. Bagnold, R.A., 1973. Proc. R. SOC.London, Ser. A, 332: 473-504. Bailey, E.B. and Weir, J., 1932. Trans. R. SOC.Edinburgh, 57: 429-467. Bailey, R.J., 1966. Sedimentology, 7: 131-136. Baines, P.G., 1979. Tellus, 3 1 : 35 1-371. Baines, W.D. and Knapp, D.J., 1965. J. Hydraul. Div. ASCE, 91(HY2): 205-221. Baird, M.H.I., Senior, M.G. and Thompson, R.J., 1967. Chem. Eng. Sci.. 22: 551-558. Bajard, J., 1966. Rev. Geogr. Phys. Geol. Dyn., (2)8: 39-1 11. Bajorunas, L. and Duane, D.B., 1967. J. Geophys. Res., 72: 6195-6205. Baker, C.J., 1979. J. Fluid Mech., 95: 347-367. Baker, G., 1956. Mem. Natl. Mus. Victoria, No. 20: 59-172. Baker, G., 1958. Am. J. Sci., 256: 369-383. Baker, G., 1959. Mem. Natl. Mus. Victoria, No. 23: 1-313. Baker, G., 1961. Proc. R. SOC.Victoria, 74: 47-54. Baker, G., 1963. In: J.A. O’Keefe, Tektites. University of Chicago Press, Urbana, Ill., pp. 1-24. Baker, V.R., 1973a. Geol. SOC.Am., Spec. Pap., 144. Baker, V.R., 1973b. Water Resour. Res., 9: 695-706. Baker, V.R., 1974. In: M. Morisawa (Editor), Fluvial Geomorphology. State University of New York, Binghamton, N.Y., pp. 123-148. Baker, V.R. and Milton, D.J., 1974. Icarus, 23: 27-41. Balks, D., 1962. Karszt-es barlang-kutaths, 2: 3-82. Baldwin, C.J. and Johnson, H.D., 1977. Sedimentology, 24: 801 -818. Baldwin, C.T., 1974. J. Sediment. Petrol., 44: 695-697. Ball, F.K., 1954. Weather, 9: 322-323. Ball, M.M., 1967. J. Sediment. Petrol., 37: 556-591. Ballance, P.F., 1964a. J. Sediment. Petrol., 34: 91-101. Ballance, P.F., 1964b. N.Z.J. Geol. Geophys., 7: 466-499. Ballard, J.A., 1966. Geophysics, 3 1 : 506-523. Balsillie, J.H., 1975. U.S. Coastal Eng. Res. Cent., Tech. Mem., No. 49. Bandrowski, J. and Rybski, W., 1976. Int. J. Heat Mass Transfer, 19: 827-838. Banejee, I., 1973a. Bull. Geol. Sum. Can., No. 226: 1-44. Banerjee, I., 1973b. Bull. Geol. Sum. Can., No. 226: 45-60. Banerjee, I., 1977. J. Sediment. Petrol., 47: 771-783. Banks, J.E., 1974. Philos. Trans. R. SOC.London, Ser. A, 275: 567-609. Banks, N.L., 1973a. J. Sediment. Petrol., 43: 423-427. Banks, N.L., 197313. Norg. Geol. Unders.. No. 288: 7-25. Banks, N.L., Edwards, M.B., Geddes, W.P., Hobday, D.A. and Reading, H.G., 1971. Norg. Geol. Unders., No. 269: 197-236. Baragar, W.R.A., 1960. Bull. Geol. SOC.Am., 71: 1589-1644. Baranowski, S., 1970. Geogr. Ann., A52: 68-75. Barberi, F., Innocenti, F., Lirer, L., Munno, R., Pescatore, T. and Santacroce, R., 1978. Bull. Volcanol., 41: 10-31. Barcilon, A.I. and Lau, J.P., 1973. J. Geophys. Res., 78: 2656-2664. Bareis, C.J., 1964. Am. Antiq., 30: 88-91. Barela, D.A., 1972. Supercritical flow in curved channels. U.S. Army Corps Eng., Waterw. Ekp. St., Vicksburg, Rep. No. 1- 109. Baria, L.R., 1977. J. Sediment. Petrol., 47: 908-914. Barnes, C.R., 1965. J. Sediment. Petrol., 35: 257-261. Barnes, H.L., 1956. Am. J. Sci., 254: 493-505. Barnes, P.W. and Reimnitz, E., 1974. In: J.C. Reed and J.E. Slater (Editors), The Coast and

566 Shelf of the Arctic Beaufort Sea. Arctic Institute of North America, Arlington, Va., pp.

439-476. Barnes, P.W., McDowell, D. and Reimnitz, E., 1978.U.S. Geol. Surv., Open-file Rep. No.

78-370. Barrett, P.J. and Kohn, B.P., 1975. In: K.S.W. Campbell (Editor), Gondwana Geology. Australian National University Press, Canberra, pp. 15-35. Barrows, J.F., 1963.Trans. ASME, E85: 505-508. Barthel, K.W., 1966.J. Sediment. Petrol., 36: 1156-1162. Bartrum, J.A. and Mason, A.P., 1948.N.Z.J. Sci. Technol.. B30: 166-172. Barwis, J.H., 1976.In: M.O. Hayes and T.W. Kana (Editors), Terrigenous Clastic Environments. Univ. South Caroline, Dep. Geol., Coastal Res. Div.. Techn. Rep., No. 1 I-CRD: 11-115-11-125. Barwis, J.H., 1978.Mem. Can. SOC.Pet. Geol., 5: 129-160. Bascom, W.J., 1951.Trans. Am. Geophys. Union, 32:866-874. Bascom, W.J., 1960.Sci. Am., August 1960: 12 pp. Bassett, D.A.and Walton, E.K., 1960.Q.J. Geol. SOC.London, 116:85-105. Bassett, M.G., 1974.Palaeontology, 17:745-777. Basu, A. and Guha, P.K.S., 1972.Proc. Ind. Acad. Sci., A37:408-410. Basumallick, S., 1966.Sedimentology, 6:35-68. Bata, G.L., 1959.Proc. 8th Congr. Int. Assoc. Hydraul. Res., pp. 12-C-1-12-C-15. Batchelor, G.K., 1956.J. Fluid Mech., 1 : 177-190. Batchelor, G.K., 1967.An Introduction to Fluid Dynamics. Cambridge University Press, London. Bates, D.E.B., 1974.Geol. Mag., 1 1 1 : 31-34. Bates, D.E.B.. 1975.Geol. J., 10: 167-175. Bates, D.E.B. and Kirkaldy, J.F., 1976.Field Geology in Colour. Blandford Press, Poole, Dorset. Bates, R.A., 1939.Bull. Geol. SOC.Am., 50: 819-880. Bathurst,.J.C., Thorne, C.R. and Hey, R.D.. 1977.Nature (London). 269:504-506. Baturin, W.W.. 1959.Luftungsanlagen fur Industriebauten. Vils Verlag Technik, Berlin. Baudoin. R.. 1949.Bull. SOC.Geol. Fr., (6)19: 189-194. Baudoin, R., 1951.Bull. SOC.Geol. Fr., (7)l:213-220. Bauer, F.. 1962.Actes 2nd Congr. Int. Speleol.. 1: 299-328. Bauer, F. and Zotl. J., 1972.In: M. Herak and V.T. Springfield (Editors). Karst. Elsevier, Amsterdam, pp. 224-265. Baum, E., 1964.AIAA J., 2: 128-131. Bayley, F.J., Owen, M.J. and Turner, A.B., 1972.Heat Transfer. Nelson, London. Beadnell, H.J.L., 1910.Geogr. J., 35: 379-392. Beaudoin, B., 1968.Sediment. Geol., 4:135-151. Beavers, G.S. and Wilson, T.A., 1970.J. Fluid Mech., 44:97-1 1 2. Beck, M.S., Lee, K.T. and Stanley-Wood, N.G., 1973.Powder Technol., 8:85-90. Becker, H.A. and Massaro, T.A., 1968.J. Fluid Mech., 31: 435-448. Begin, Z.B., 1975.Sediment. Geol., 14: 191-218. Beheiry, S.A., 1967.Ann. Assoc. Am. Geogr., 57:25-48. Behr, S.H., 1965.Mem. Geol. Surv. Union S. Afr., No. 56: 116 p. Behrens, M.. 1973.Jahrb. Geol. Bundesanst., Wien, 116:51-83. Beiersdorf, H., Kudrass, H.-R. and Von Stackelberg, U.,1980.Geol. Jahrb., D36: 5-85. Belderson, R.H., 1964.Mar. Geol.. 2: 147-163. Belderson, R.H. and Laughton, AS., 1966.Sedimentology. 7: 103-1 16. Belderson, R.H. and Stride, A.H., 1966.Mar. Geol., 4:237-257. Belderson, R.H. and Wilson, J.B., 1973.Nor. Geol. Tidsskr., 53: 323-328. Belderson, R.H., Kenyon, N.H. and Stride, A.H., 1971.Rep. Inst. Geol. Sci., No. 70/14: 15 1 - 170.

567 Belderson, R.H., Kenyon, N.H., Stride, A.H. and Stubbs, A.R., 1972. Sonographs of the Sea Floor. Elsevier, Amsterdam. Belderson, R.H., Kenyon, N.H. and Wilson, J.B., 1973. Palaeogeogr. Palaeoclimatol. Palaeoecol., 13: 215-224. Belik, L., 1973. Aeronaut. Q.. 24: 47-54. Bell, H.S., 1942. J. Geol., 50: 512-547. Bellman, R. and Pennington, R.H., 1954. Q. Appl. Math., 12: 15 I - 162. Belt, E.S., 1968. Geol. SOC.Am., Spec. Pap., 106: 127-176. Bennett, J.R., 1974. J. Phys. Oceanogr., 4: 400-414. Bennetts, K.R.W. and Pilkey, O.H., 1976. Geol. SOC.Am. Bull., 87: 1291-1300. Berg, J.C., Boudart, M. and Acrivos, A., 1966. J. Fluid Mech., 24: 721-735. Bergsten, F., 1955. Geogr. Ann., 37: 119-140. Bergstrdm, J., 1976. Can. J. Earth Sci., 13: 1613-1633. Berkson, J.M. and Clay, C.S., 1973. Geol. Soc. Am. Bull., 84: 1315-1328. Bernard, C., 1971a. Rev. Geogr. Montreal, 25: 1 I I - 127. Bernard, C., 1971b. Rev. Geogr. Montreal, 25: 265-279. Bernard, H.C. and LeBlanc, R.J., 1965. In: H.E. Wright and D.G. Frey (Editors), The Quaternary of the United States. Princeton University Press, Princeton, N.J., pp. 137- 185. Bernard, H.A. and Major, C.F., 1963. Bull. Am. Assoc. Pet. Geol., 47: 350 (abstr.). Bernard, H.A., LeBlanc, R.J. and Major, C.F., 1962. In: Geology of the Gulf Coast and Central Texas and Guidebook of Excursion. Houston Geological Society, Houston, Calif., pp. 175-224. Bernard, H.A., Major, C.F. and Parrott, B.S., 1959. Trans. Gulf-Coast Assoc. Geol. SOC.,9: 22 1-224. Bernard, H.A., Major, C.F., Parrott, B.S. and LeBlanc, R.J., 1970. Recent Sediments of Southeast Texas. Univ. Tex., Bur. Econ. Geol. Guideb., No. 11. Berner, H., Ramberg, H. and Stephansson, O., 1972. Tectonophysics, 15: 197-218. Berry, F.G., 1961. Proc. Geol. Assoc., 72: 33-39. Berry, R.W., 1973. J. Sediment. Petrol., 43: 205-206. Bertouille, H., 1974. Rev. Geomorphol. Dyn., 22: 1-18. Betchov, R. and Szewnyk, A., 1963. Phys. Fluids, 6: 1391-1396. Bethe, H.A. and Adams, M.C., 1959. J. Aerospace Sci., 26: 321-328. Beuf, S., Debyser, J., Gariel, 0. and Montadert, L., 1966. Rev. Inst. Fr. Pet., 21: 1769-1782. Beuf, S., Biju-Duval, B., De Charpal, O., Rognon, P.. Gariel, 0. and Bennacef. A., 1971. Les Grks du Paleozolque Inferieure au Sahara. Editions Technip. Paris. Beutner, E.C., 1975. J. Sediment. Petrol., 45: 212-214. Beutner, E.C., Flueckinger, L.A. and Gard, T.M., 1967. Geol. SOC.Am. Bull., 78: 91 1-916. Bhatnagar, P.L. and Wong, H.C., 1974. Proc. Indian Acad. Sci., A79: 173-194. Bhattacharji, S., 1967. J. Geol., 74: 101-1 12. Bhattacharji, S. and Smith, C.H., 1964. Science, 145: 150- 153. Bialik, A., Trammer, J. and Zapasnik, T., 1972. Acta Geol. Pol., 22: 265-274. Bigarella, J.J., Salamuni, R. and Fuck, R.A., 1967. Palaeogeogr. Palaeoclim. Palaeoecol., 3: 265-276. Bigarella, J.J., Becker, R.D. and Duarte, G.M., 1969. Mar. Geol., 7: 5-55. Biju-Duval, N.B. and Gariel, O., 1969. Palaeogeogr. Palaeoclimatol. Palaeoecol., 6: 283-3 15. Biot, M.A., 1957. Proc. R. SOC.London, Ser. A, 242: 444-454. Biot, M.A., 1959a. Q. Appl. Math., 17: 185-204. Biot, M.A., 1959b. Appl. Mech., 26: 393-400. Biot, M.A., 1961. Geol. SOC.Am. Bull., 72: 1595-1620. Biot, M.A. and Ode, H., 1962. Q. Appl. Math., 19: 351-353. Biot, M.A., Ode, H. and Roever, W.C., 1961. Geol. SOC.Am. Bull.. 72: 1621-1632. Bippes, H., 1977. Acta Mech., 26: 223-245.

568

Bippes, H. and Gortler. H., 1972. Acta Mech., 14: 239-250. Birchfield, G.E., 1972. Arch. Meteorol., Geophys., Bioklimatol., Ser. A, 21 : 419-430. Bird, E.C.F., 1971. Aust. Geogr. Stud., 9: 107-115. Birkemeier, W.A., 1979. Shore Beach, January 1979: 7- 15. Birkemeier, W.A., 1981. Misc. Rep. U.S.Army Eng. Coastal Eng. Rcs. Cent., No. XI-2. Birkenmajer, K., 1979. Stud. Geol. Pol., 60: 45-55. Biscaye, P.E. and Eittreim, S.L., 1977. Mar. Geol., 23: 155-172. Bishop, A.W., 1973. Q.J. Eng. Geol., 6: 335-376. Bishop, A.W. and Skinner, A.E., 1976. Philos. Trans. R. SOC.London, Ser. A. 284: 91-130. Bitter, J.G.A., 1963. Wear, 6: 5-21. Bjerrum. L., 1971. Nom. Geotech. Inst., Publ. No. 88. Bjerrum, L.. Kringstad, S. and Kummeneje, O., 1961. Proc. 5th Int. Conf. Soil Mech. Found. Eng., 1: 29-37. BjHrIykke, K., 1968. Norg. Geol. Unders., No. 25 1 : 18-44. Black. M.. 1928. Geol. Mag., 65: 301-307. Blackburn, G.. Bond, R.D. and Clarke, A.R.P., 1965. Soils Land Use Ser.. C.S.I.R.O., Aust., No. 22. Blackwelder. E., 1929. J. Geol., 37: 256-260. Blackwelder. E., 1930. J. Geol., 41: 154. Blackwelder, E.. 1934. Bull. Geol. SOC.Am., 45: 159-166. Blake, D.H. and Ollier, C.D., 1971. Z. Geomorphol., S12: 1-17. Blanford, W.T., 1876. J. Asiat. SOC.Bengal., 45(2): 86-103. Blay, P., Cosgrove, J.W. and Summers, J.M., 1977. J. Geol. SOC.,London, 133: 329-342. Blench, T., 1957. Regime Behaviour of Canals and Rivers. Butterworths, London. Blench, T., 1969. Mobile-bed Fluviology. University of Alberta Press, Edmonton, Aha. Blinco, P.H. and Partheniades, E., 1971. J. Hydraul. Res., 9: 43-71. Blinco, P.H. and Simons, D.B., 1975. J. Eng. Mech. Div. ASCE, lOl(EM3): 241-255. Bloom, M.H. and Pallone, A.. 1957. Proc. 1957 Heat Transfer Fluid Mech. Inst., Stanford U ~ V .pp. , 249-278. Bluck, B.J.. 1971. Scott. J. Geol., 7: 93-138. Bluck, B.J., 1976. Trans. R. SOC.Edinburgh, 69: 425-456. Blue, F.L., Herbert, J.K. and Lancefield, R.J., 1934: Civ. Eng., 4: 258-260. Blumberg, P.N. and Curl. R.L.. 1974. J. Fluid Mech., 65: 735-751. Bonar-Karakiewin, B., 1975. Bull. Acad. Pol. Sci., Ser. Sci. Terre, 22: 127-134. Bodine, B.R., 1971. U.S.Coastal Eng. Res. Cent., Tech. Mem., No. 35: 55 pp. Boersma, J.R., 1967. Geol. Mijnbouw, 46: 217-235. Boersma. J.R., Van de Meene, E.A. and Tjalsma. R.C., 1968. Sedimentology, 1 I : 147- 162. Bogan, K., Dzulynski, S., Gradsinski, R. and Kostecka, A., 1968. Ann. Soc. Geol. Pol., 38: 385-394.

Bogdonoff, S.M. and Kepler, C.E., 1955. J. Aeronaut. Sci., 22: 414-425. Bdgli, A., 1951. Geogr. Helv., 6: 191-204. Bogli. A.. 1960. Z. Geomorphol., S2: 4-21. Bogli, A,, 1961. Z. Geomorphol., 5: 185-193. Bogli. A., 1978. Karsthydrographie und Physische Spelaologie. Springer, Berlin. Bokman, J., 1953. J. Geol., 61: 152-170. Boll, F.-C., Kullmann, J. and Schonenberg, R., 1976. Neues Jahrb. Geol. Palaontol., Abh., 152: 357-379.

Bonasoundas, M., 1973. Ber. Versuchanst. Wasserbau, Tech. Univ. Miinchen, Oskar V. Miller Inst.. No. 28: 108 pp. Bond, A. and Sparks, R.S.J., 1976. J. Geol. SOC.London, 132: 1-16. Bondesen, E., 1966. Medd. Dan. Geol. Foren.. 16: 195-198. Bonham-Carter, G.F. and Sutherland, A.J.. 1967. Trans. Gulf-Coast Assoc. Geol. SOC.,197: 326-338.

569 Bonham-Carter, G.F. and Surtherland, A.J., 1968. Comput. Contrib., No. 24: 56 pp. Bonham-Carter, G.F. and Thomas, J.H., 1973. Proc. 16th Conf. Great Lakes Res., pp. 640-66 I . Bonnefille, R. and Goddet, J., 1959. Proc. 8th Congr. Int. Assoc. Hydraul. Res., pp. 14-C-1- 14-C-29. Booth, B., 1973. Proc. Geol. Assoc., 84: 353-370. Bornhold, B.D. and Pilkey, O.H., 1971. Geol. SOC.Am. Bull., 82: 1341-1354. Borowka, R.K., 1979. Quastiones Geogr., 5: 5-22. Borowka, R.K., 1980. Poznan. Tow. Przyj. Nauk, Pr. Kom. Geogr.-Geol., Wydz. Mat.-Przyr., 20: 1-126. Borradaile, G.J. and Johnson, H.D., 1973. Tectonophysics, 18: 249-259. Bosworth, T.O., 1922. Geology of the Tertiary and Quaternary Periods in the Northwestern Part of Peru. Macmillan, London. Botterill, J.S.M. and Abdul Halim, B.H., 1978. In: J.F. Davidson and D.L. Keairns (Editors), Fluidization. Cambridge University Press, Cambridge, pp. 122- 127. Botterill, J.S.M. and Bessant, D.J., 1973. Powder Technol., 8: 213-222. Botterill, J.S.M. and Van der Kolk, M., 1971. AIChE, Symp. Ser., No. 16: 70-76. Botterill, J.S.M., Chandrasekhar, R. and Van der Kolk, M., 1970. Chem. Eng. Prog. Symp. Ser., No. 66: 61-69. Botterill, J.S.M., Van der Kolk, M., Elliott, D.E. and McGuigan, S., 1972. Powder Technol., 6: 343-351. Botvinkina, L.N., Feofilova, A.P. and Jablokov, V.C., 1954. Trud. Inst. Geol. Nauk Mosk., No. 151: 30-89 (in Russian). Boulter, C.A., 1974. Geol. SOC.Am., Bull., 85: 1413-1420. Boulton, G.S., 1974. In: D.R. Coates (Editor), Glacial Geomorphology. State University of New York, Binghamton, N.Y., pp. 41-87. Boulton, G.S., 1975. In: A.E. Wright and F. Moseley (Editors), Ice Ages: Ancient and Modern. See1 House Press, Liverpool, pp. 7-42. Boulton, G.S., 1976. J. Glaciol., 17: 287-309. Bouma, A.H., 1962. Sedimentology of Some Flysch Deposits. Elsevier, Amsterdam. Bouma, A.H. and Treadwell, T.K., 1975. Mar. Geol., 19: M53-M59. Bouma, A.H., Hampton, M.A. and Orlando, R.C., 1977a. Mar. Geotech. 2: 291-308. Bouma, A.H., Hampton, M.A., Wennekens, M.P. and Dygas, J.A., 1977b. Proc. 9th Offshore Technol. Conf., pp. 79-84. Bouma, A.H., Hampton, M.A., Rappeport. M.L., Whitney, J.L., Teleki, P.G., Orlando, R.C. and Torresan, M.E., 1978. Proc. Offshore Technol. Conf. 1978. Pap. OTC 331 1: 2271-2284. Bourcart, J., 1928. Rev. Geogr. Phys. Geol. Dyn., 1: 26-54, 195-265. Bourgeois, J., 1980. J. Sediment Petrol., 50: 681-702. Bourque, C. and Newman, B.G., 1960. Aeronaut. Q., 11: 201-232. Bouvard, M., 1951. Houille Blanche, 6: 862-864. Bouvard, M. and Petkovic, S., 1973. Houille Blanche, 28: 35-52. Bowen, A.J., 1969a. J. Mar. Res., 27: 206-215. Bowen, A.J., 1969b. J. Geophys. Res.. 74: 5467-5478. Bowen, A.J., 1973. Proc. 13th Conf. Coastal Eng. 2: 1313-1320. Bowen, A.J., 1975. EOS, Trans. Am. Geophys. Union, 56: 83 (abstr.). Bowen, A.J. and Inman, D.L., 1969. J. Geophys. Res., 74: 5479-5490. Bowen, A.J. and Inman, D.L., 1971. J. Geophys. Res., 76: 8662-8671. Bowler, J.M., 1966. Mem. Natl. Mus. Victoria, No. 27: 19-67. Boyd, D.W. and Ore, H.T., i963a. J. Sediment. Petrol., 33: 438-451. Boyd, D.W. and Ore, T.H., 1963b. Wyoming Contrib. Geol., 2: 63-68. Boye, M., 1954. Rev. Geomorphol. Dyn., 15: 241 -27 1. Braden, G.E., 1947. Proc. Okla. Acad. Sci., 27: 1-92.

570 Bradley, J.S.. 1957. J. Sediment. Petrol., 27: 116-125. Bradley, W.H.. 1930. Am. J. Sci., 20: 136- 144. Bradley, W.H., 1933. Am. J. Sci.. 26: 55-71. Bradshaw. J.D.. 1966. Sedimentology, 7: 149- 154. Bradshaw, P. and Galea, P.V., 1967. J. Fluid Mech.. 27: 1 1 1 - 130. Bradshaw, P. and Wong, F.Y.E., 1972. J. Fluid Mech., 52: 113-135. Brand, G., 1955. Meyniana, 4: 84- 1 I I . Brandon, A,, 1972. Geol. Mag., 109: 36 1-367. Branner, J.C.. 1900. J. Geol., 8: 481-484. Branner J.C., 1913. Proc. Am. Philos. SOC.,52: 163-174. Bray, D.I.. 1973. In: Fluvial Processes and Sedimentation. Inland Waterways Directorate, Department of Environment, Canada, pp. 440-452. Brekken, R.A., Lancaster. E.B. and Wheelock, T.D., 1970. Chem. Eng. Prog. Symp. Ser., No. 101: 81-90. Brenchley, P.J. and Pickerill, R.K., 1980. Proc. Geol. Assoc., 91 : 177- 194. Brenchley. P.J. and Newall, G., 1977. J. Sediment. Petrol., 47: 819-833. Brenchley, P.J., Newall, G. and Stanistreet, I.G., 1979. Sediment. Geol., 22: 185-217. Brenner, H., 1958. Phys. Fluids, I : 338-346. Brenner, R.L. and Davies, D.K., 1973. Geol. SOC.Am. Bull., 84: 1685-1697. Brenninkmeyer, B.M., 1973. Surf zone sedimentation patterns. Univ. Southern Calif. (Los Angeles). Dep. Geol. Sci., Rep. No. USC Geol. 73-1. Bretschneider, C.L., 1966a. Shore Beach, 34: 8- I I . Bretschneider, C.L., 1966b. On wind tides and longshore currents over the continental shelf due to waves blowing at an angle to the coast. Natl. Eng. Sci. Comp. Pasadena, Rep. SN- 134- 17. Bretschneider, C.L., 1967. Adv. Hydrosci., 4: 341 -418. Bretz, J.H., 1942. J. Geol., 50: 675-81 I . Breusers, H.N.C., 1965. Bull. Int. Assoc. Hydraul. Res., 19: 276. Breusers, H.N.C., I97 I . In: M.W.C. Oosterveld (Editor), Offshore Hydrodynamics. Neth. Ship Model Basin, Wageningen, Publ. No. 375: X. 1 -X. 16. Breusers. H.N.C., Nicollet, G. and Shen, H.W., 1977. J. Hydraul. Res., 15: 21 1-252. Brice, J.C., 1964. U.S. Geol. Sum., Prof. Pap., 422-D. Brice, J.C., 1974a. In: M. Morisawa (Editor), Fluvial Geomorphology. State University of New York, Binghamton, N.Y., pp. 179-200. Brice, J.C., 1974b. Geol. Soc. Am. Bull., 85: 581-586. Bridge, J.S., 1975a. Sedimentology, 22: 3-43. Bridge, J.S., 1975b. Comput. Appl., 2: 217-266. Bridge, J.S., 1976. Sedimentology, 23: 407-414. Bridge, J.S., 1977. Earth Surf. Processes, 2: 401-416. Bridge, J.S., 1978. Mem. Can. SOC.Pet. Geol., 5: 723-742. Bridge, J.A. and Jarvis, J., 1976. Earth Surf. Processes, 1: 303-336. Bridge, J.S. and Jarvis, J., 1977. Earth Surf. Processes, 2: 281-294. Bridges, P.H., 1972. Geol. Mag., 109: 405-410. Bridges, P.H., 1975. J. Sediment. Petrol., 45: 79-94. Bridges, P.H. and Leeder, M.R., 1976. Sedimentology, 23: 533-562. Bridgewater, J., 1980. Powder Techno]., 25: 129- I3 I . Bridgewater, J. and Ingram, N.D., 1971. Trans. Inst. Chem. Eng., 49: 163-170. Bridgewater, J. and Scott, A.M., 1974. Trans. Inst. Chem. Eng., 52: 317-324. Bridgewater, J., Sharpe, N.W. and Stocker, D.C., 1969. Trans. Inst. Chem. Eng., 47: TI 14-TI 19. Brindley, J.C., McArdle. P. and Schiener, E.J., 1973. Sci. Proc. R. Dublin SOC.,Ser. A, 14: 43 1-438.

57 I Brinkman, H., 1949. Research, 2: 190- 194. Britter, R.E. and Simpson, J.E., 1978. J. Fluid Mech., 88: 223-240. Broadhurst, F.M., 1954. Liverpool Manchester Geol. J., 1 : 240-245. Broadhurst, T.E. and Becker, H.A., 1975. AIChE J., 21: 238-247. Brodnyan, J.G., 1959. Trans. SOC.Rheol., 3: 61-68. Broekman, J.A., 1974. Proc. K. Ned. Akad. Wet., B77: 303-318. Brogger, W.C. and Reusch, H.M., 1874. Q. J. Geol. SOC.London, 30: 750-771. Brookfield, M., 1970. Z. Geomorphol., SIO: 121-153. Brosset, D., 1939. Bull. Inst. Fr. Afr. Noire, 1: 657-690. Browand, F.K., 1966. J. Fluid Mech., 26: 281-307. Browand, F.K. and Weidman, P.D., 1976. J. Fluid Mech., 76: 127-144. Brown, F.R., 1963. J. Hydraul. Div. ASCE, 90(HY I ) : 99- 1 15. Brown, G.L. and Roshko, A,, 1974. J. Fluid Mech., 64: 775-816. Brown, M.C., 1962. Am. J. Sci., 260: 469-470. Brown, R.A., 1970. J. Atmos. Sci., 27: 742-757. Brown, R.A., 1972. J. Atmos. Sci., 29: 850-859. Brown, R.G., 1969. Publ. Geol. SOC.Aust., No. 2: 237-242. Brown, R.L., 1939. J. Inst. Fuel, 13: 15-19. Brown, S.N. and Stewartson, K., 1969. Annu. Rev. Fluid Mech., 1: 45-72. Briick, P.M. and Reeves, T.J., 1976. Proc. R. Ir. Acad., Ser. B, 76: 53-77. Brundrett, E. and Baines, W.D., 1964. J. Fluid Mech., 19: 375-394. Brunt, D., 1937. Q. J. R. Meteorol. Soc.,63: 277-288. Brush, L.M.. 1961. U.S. Geol. Surv., Prof. Pap., 282-F: 145-181. Brush, L.M., 1962. J. Geophys. Res.. 67: 1427-1433. Brush, L.M., 1965a. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation. SOC.Econ. Paleontol. Mineral., Spec. Publ., 12: 25-33. Brush, L.M., 1965b. In: G.V. Middleton (Editor), SOC.Econ. Paleontol. Mineral., Spec. Publ., 12: 17-24. Brush, L.M., Ho, H.W. and Singamsetti, S.R., 1962. Publ. Int. Assoc. Sci. Hydrol., No. 59: 293-310. Brutsaert, W., 1975. Water Resour. Res., 1 1 : 543-550. Bruun, P., 1955. Proc. 5th Conf. Coastal Eng., pp. 269-294. Bruun, H.H., 1979. Proc. R. SOC.London, Ser. A, 367: 193-218. Bryant, P.J., 1973. J. Fluid Mech., 59: 625-644. Buckle, C., 1978. Landforms in Africa. Longman. London. Bull, P.A., 1976. Trans. Br. Cave Res. Assoc., 3: 1-5. Bull, P.A., 1978. Sedimentology, 25: 877-886. Bull, W.B., 1964. U.S. Geol. Surv., Prof. Pap., 437-A. Bunce, E.T. and Hersey, J.B., 1966. Geol. SOC.Am. Bull., 77: 803-812. Burgess, I.C. and Holliday, D.W., 1974. Bull. Geol. Surv. G.B., No. 46: 1-34. Burggraf, O.R., 1966a. J. Fluid Mech., 24: 1 13-151. Burggraf, O.R., 1966b. Proc. 1965 Heat Transfer and Fluid Mechanics Institute, Stanford University, pp. 190-229. Burke, W.H., 1935. Trans. Inst. Min. Metall., 114: 53-61. Burne, R.V., 1970. Sedimentology, 15: 21 1-228. Burollet, P.F., Byramjee, R. and Couppey, C.. 1969. Notes Mem. Cie. Fr. Pet., No. 9. Burst, J.F., 1965. J. Sediment. Petrol., 35: 348-353. Burt, W.V., Crew, H. and Poole, S.L., 1975. J. Mar. Res., S33: 61-68. Burt, W.V., Cummings, T. and Paulson, C.A., 1974. J. Geophys. Res., 79: 5625-5632. Businger, J.A., 1965. J. Geophys. Res., 70: 3307-3313. Butte, J.-N. and Pichon, J., 1970. Houille Blanche, 25: 331-336. Button, A., 1976. Trans. Geol. SOC.S. Afr., 78: 173-183.

572 Button, A. and Vos, R.G., 1977. Sediment. Geol., 18: 175-200. Butzer, K.W., 1971. Recent history of an Ethiopean delta. Univ. Chicago, Dep. Geogr. Res. Pap., No. 136. Bye, J.A.T., 1967. J. Mar. Res., 25: 95-102. Cairns, E.J. and Prausnitz, J.M., 1960. AIChE J., 6: 400-405. Calder, N., 1972. Restless Earth. British Broadcasting Corporation, London. Caldwell, D.R. and Elliott, W.P., 1971. J. Phys. Oceanogr., 1 : 145-148. Caldwell, D.R. and Van Atta, C.W., 1970. J. Fluid Mech.. 44: 79-95. Callander, R.A., 1969. J. Fluid Mech., 36: 465-480. Callander, R.A., 1978. Annu. Rev. Fluid Mech.. 10: 129-158. Campbell, C.V., 1971. J. Sediment. Petrol., 41: 395-409. Canning, T.W., Wilkins, M.E. and Tauner, M.E., 1968. A I M J., 6: 174-175. Cant, D.J., 1980. Can. J. Earth Sci., 17: 120-131. Capes, C.E., 1974. Powder Technol., 10: 303-306. Capot-Rey, R., 1943. Trav. Inst. Rech. Sahariennes, 2: 69-102. Capot-Rey, R., 1957a. Trav. Inst. Rech. Sahariennes, 15: 149- 157. Capot-Rey, R., I957b. Tijdschr. K. Ned. Aardrijksk. Genoot., 74: 242-247. Capot-Rey, R. and Capot-Rey, F., 1948. Trav. Inst. Rech. Sahariennes, 5: 47-80. Carey, K.L., 1966. U.S. Geol. Surv., Prof. Pap., 550-B: 192-198. Carey, K.L., 1967. US. Geol. Surv., Prof. Pap., 575-C: 195-199. Carey, W.C., 1969. J. Hydraul. Div. ASME, 94(HY3): 981-994. Carlson, P.R.. 1978. Bull. Am. Assoc. Pet. Geol., 62: 2412-2426. Carlson, W.O., 1959. Proc. 1959 Heat Transfer and Fluid Mechanics Institute, Stanford Univ.. pp. 140-155. Carlston, C.W., 1965. Am. J. Sci., 263: 864-885. Caroui, A.V., 1962. J. Geol., 70: 246-252. Carr, D.D., 1973. Bull. Indiana Div. Geol., No. 48. Carsola, A.J., 1954. Bull. Am. Assoc. Pet. Geol., 38: 1552-1586. Carstens, M.R. and Sharma, H.R., 1975. Proc. 16th Congr. Int. Assoc. Hydraul. Res., 2: 25 1-262. Carter, G., Collignon, J.S. and Nobes, M.J., 1977. Radiation Effects, 3 1 : 65-87. Carter, G., Nobes, M.J. and Arshak, K.I., 1980. Wear, 65: 151-174. Carter, R.W.G., 1978a. J. Earth Sci. R. Dublin SOC.,1: 205-209. Carter, R.W.G., 1978b. Geol. Mag., 115: 379-383. Carter, T.G., 1972. Proc. Inst. Civ. Eng., 53: 661-665. Carter, T.G., Liu, P.L.F. and Mei, C.C., 1973. ASCE J. Watenv., Harbors Coastal Eng. Div., 99(WW2): 165-184. Cas, R., 1979. J. Sediment. Petrol., 49: 29-44. Cassagrande, A,, 1936. J. Boston SOC.Civ. Eng., 23: 13-32. Casey, H.J., 1935. Mitt. Preuss. Versuchsanst. Wasserbau Schiffbau. 19: 1-87. Caston, G.F.. 1975. Mar. Geol., 18: M77-M85. Caston, G.F., 1976. Rep. Inst. Geol. Sci., No. 76/7: 16 pp. Caston, G.F., 1979. Mar. Geol., 33: 193-204. Caston, V.N.D., 1972. Sedimentology, 18: 63-78. Caston, V.N.D., 1976. Estuarine Coastal Mar. Sci., 4: 23-32. Caston, V.N.D. and Stride, A.H., 1970. Mar. Geol., 9: M38-M42. Castro, G., 1969. Harv. Soil Mech. Ser., No. 81. Castro, G., 1975. J. Geotech. Eng. Div. ASCE, lOl(GT6): 551-569. Castro, G. and Poulos, S.J., 1977. J. Geotech. Eng. Div. ASCE, 103(GT6): 501-506. Castro, I.P., 1971. J. Fluid Mech., 46: 599-609. Castro, I.P. and Bradshaw, P., 1977. J. Fluid Mech., 73: 265-304. Castro, I.P. and Robins, A.G., 1977. J. Fluid Mech., 79: 307-335.

573 Cegla, J. and Dzulynski, S., 1967. Ann. SOC.Geol. Pol., 37: 489-497. Cepek, P. and Reineck, H.-E., 1970. Senckenbergiana Marit., 2: 3-30. Chacinski, T.M. and Francis, J.R.D., 1952. Trans. Am. Geophys. Union, 33: 771-773. Chadwick, G.H., 1931. Bull. Geol. SOC.Am., 42: 242 (abstr.). Chaix, E., 1894. Globe, Geneve, 34: 67- 108. Chaix, E., 1904. Globe, Geneve, 44: 49-60. Chaix, E. and Chaix, A., 1907. Globe, Geneve, 46: 17-53. Chakrabarti, A., 1977. Senckenbergiana Marit., 9: 285-305. Chamberlin, T.C., 1888. Rep. U.S. Geol. Sum., 1885-1886, pp. 155-248. Chandler, P.L. and Sorensen, R.M., 1973. Proc. 10th Conf. Coastal Eng. 1: 385-404. Chandra, K., 1938. Proc. R. SOC.London, Ser. A, 164: 231-242. Chandrasekhar, S., 1955. Proc. Camb. Philos. SOC.Math. Phys. Sci., 51: 162-178. Chandrasekhar, S., 1961. Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford. Chandrsuda, C., Mehta, R.D., Weir, A.D. and Bradshaw, P., 1978. J. Fluid Mech., 85: 693-704. Chang, H.C., 1979. J. Hydrol., 41: 303-327. Chang, H.Y., Simons, D.B. and Woohiser, D.A., 1971. ASCE J. Waterw., Harbors Coastal Eng. Div., 97(WWl): 155-165. Chang, P.K., 1970. Separation of Flow. Pergamon, Oxford. Chang, T.P. and Toebes, G.H., 1970. Water Resour. Res., 6: 557-578. Chao, B.T., 1964. Oesterr. 1ng.-Arch., 18: 7-21. Chapman, D.R., 1956. Natl. Advis. Comm. Aeronaut., Tech. Notes, No. 3792. Chapman, D.R. and Larson, H.K., 1963. Natl. Adv. Comm. Aeronaut., Tech. Notes, No. D- 1556. Chapman, D.R., Kuehn, D.M. and Larson, H.K., 1956. NACA Res. Memor., No. A55L14. Chapman, D.R., Larson, H.K. and Anderson, L.A., 1962. NACA Tech. Rep., No. R-134. Chapman, V.J., 1960. Salt Marshes and Salt Deserts of the World. Leonard Hill, London. Charnock, H., 1955. Q. J. R. Meteorol. SOC.,81: 639. Charnock, H., Francis, J.R.D. and Sheppard, P.A., 1956. Philos. Trans. R. SOC. London, Ser. A, 249: 179-234. Charwat, A.F., Roos, J.N., Dewey, F.C. and Hitz, J.A., 1961a. J. Aerospace Sci., 28: 457-470. Charwat, A.F., Dewey, C.F., Roos, J.N. and Hitz, J.A., 1961b. J. Aerospace Sci., 28: 513-527. Chatley, H., 1931. Engineering (London), 131 : 196- 197, 260-26 1. Chatley, H., 1940. Engineering (London), 149: 628-629. Chaturvedi, M.C., 1963. J. Hydraul. Div. ASCE, 89(HY3): 61-92. Chen, C.J. and Ostarch, S., 1971. AIAA J., 9: 1 120- 1 125. Cheng, K.C. and Wu, R.S., 1976. Appl. Sci. Res., 31: 465-479. Cheng, P.Y. and Schachman, H.K., 1955. J. Polym. Sci., 16: -19-30. Cherdron, W., Durst, F. and Whitelaw, J.H.. 1978. J. Fluid Mech., 84: 13-31. Cherkauer, D.S., 1973. Water Resour. Res., 9: 1613-1628. Chiba, S., Chiba, I., Nienow, A.W. and Kobayashi, H., 1979. Powder Techno]., 22: 255-269. Chilton, T.H. and Colburn, A.P., 1934. Ind. Eng. Chem., 26: 1183-1 187. Chin, D.T. and Litt, M., 1972. J. Fluid Mech., 54: 613-625. Chinese Academy of Sciences, 1970. Karst in China. Institute of Hydrology and Geological Sciences, Chinese Academy of Sciences, Shanghai People’s Publishing House. Chipping, D.H., 1972. J. Sediment. Petrol., 42: 587-595. Chitale, S.V., 1970. J. Hydraul. Div. ASCE, 96(HYl): 201-221. Chitale, S.V., 1973. J. Hydrol., 19: 285-308. Chiu, C.L., 1967. J. Eng. Mech. Div. ASCE, 93(EM4): 69-77. Chiu, C.L. and Lee, T.S., 1971. Water Resour. Res., 7: 834-844. Chorley, R.G., 1962. U.S.Geol. Surv., Prof. Pap., 500-B.

574 Choudhary, U.K. and Narasimhan. S., 1977. J. Hydraul. Div. ASCE, 103(HY6): 651-657. Chough, S. and Hesse, R.. 1976. Geology, 4: 529-533. Christensen, D. and Buhler, R.D., 1959. J. Aerospace Sci., 26: 54. Christian, J.T. and Swiger, W.F., 1975. J. Geotech. Eng. Div. ASCE. IOI(GTI I): 1135-1 150. Chung, P.M. and Viegas. J.R., 1961. NASA Tech. Note, No. TN-D-1071. Clapp, F.G., 1926. Geogr. Rev., 16: 206-231. Clark, J.A. and Markland, E., 1972. J. Hydraul. Div. ASCE, 99(HYI I ) : 1897-1913. Clarke, B., 1967. Trans. Inst. Chem. Eng., 45: T251-T256. Clarke, D.J., 1974. Geophys. J. R. Astron. SOC.,39: 195-199. Clarke, J.M., 1917. Bull. N.Y. State Mus., No. 196: 199-238. Clayton, L., Laird, W.M., Klassen, R.W. and Kupsch, W.O., 1965. J. Geol., 73: 652-656. Cleary, W.J. and Conolly, J.R., 1974. Mar. Geol., 17: 263-279. Cleavinger, H.B., 1974. Geol. Stud. Brigham Young Univ., 2 1 : 247-274. Clements. M.S., 1966. Proc. Inst. Civ. Eng., 34: 171-200. Clements, T.. 1952. J. Sediment. Petrol., 22: 182-186. Clemmey, H., 1978. Spec. Publ. Int. Assoc. Sedimentol., 2: 259-278. Clever, R.M. and Busse, F.H., 1977. J. Fluid Mech., 81: 107- 127. Clifton, H.E., 1969. Mar. Geol., 7: 553-559. Clifton, H.E., 1977. J. Sediment. Petrol., 47: 678-679. Clifton, J.V. and Chapman, A.I., 1969. Int. J. Heat Mass Transfer, 12: 1573-1583. Cloet, R.L., 1954. Geogr. J.. 120: 203-215. Clos-Arceduc, A., 1962. Bull. SOC.Photogramm. Fr., 4: 13-21. Clos-Arceduc. A., 1964. La photographie aeriennes et l’etude des depBts prelittoreaux. Institut Geographique National, Paris, Etude de Photo-interpretation, No. 1. Clos-Arceduc, A., 1972. Trav. Inst. Geogr. Reims, 6: 63-72. Cloud, P.E.. 1959. U.S. Geol. Sum., Prof. Pap., 280-K: 361-445. Cloud. P.E., 1966. Science, 154: 890-891. Coddington, E.A. and Levinson, N., 1955. Theory of Ordinary Differential Equations. McGraw-Hill, New York. Coe, H.S. and Clevenger, G.H., 1916. Trans. Am. Inst. Min., Metall. Pet. Eng., 55: 356-384. Coetzee, F., 1975. Trans. Geol. SOC.S. Afr., 78: 323-333. Coleman, J.C., 1945. Geol. Mag., 82: 138-139. Coleman, J.C.. 1947. Proc. Speleol. SOC.,6: 57-67. Coleman, J.C., 1965. The Caves of Ireland. Anvil Books, Tralee (Republic of Ireland). Coleman, J.M., 1969. Sediment. Geol., 3: 129-239. Coleman, J.M. and Gagliano, S.M., 1965. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation, SOC.Econ. Paleontol. Mineral., Spec. Publ., 12: 133-248. Coleman, J.M., Gagliano, S.M. and Smith, W.G., 1970. In: J.P. Morgan (Editor), Deltaic Sedimentation. Modem and Ancient. Soc. Econ. Paleontol. Mineral., Spec. Publ., 15: 185- 197. Coleman, J.M., Suhayoa, J.N., Whelan, T. and Wright, C.D., 1974. Trans Gulf-Coast Assoc., Geol. Soc.. 24: 49-68. Coles, D., 1965. J. Fluid Mech., 21: 385-425. Colingridge, B.R., 1962. Proc. Speleol. SOC.,9: 212-271. Collins, R., 1979. J. Fluid Mech., 91 : 493-495. Collins, W.M. and Dennis, S.C.R., 1976. Proc. R. SOC.London, Ser. A, 352: 189-21 1. Collinson, J.D.. 1971a. J. Sediment. Petrol., 41: 557-564. Collinson, J.D., 1971b. Geol. Mijnbouw, 50: 671-678. Collinson, J.D., 1972. Medd. Grdnl., No. 192(6). Colton, G.W., 1967. J. Geol., 75: 11-22. Common, R., 1955. Ann. Geogr., 64: 126-128.

575 Conner, W.C., Kraft, R.H. and Harris, D.L., 1957. Mon. Weather. Rev., 85: 113-116. Conybrare, C.E.B. and Crooke, K.A.W., 1968. Manual of Sedimentary Structures. Aust., Bur. Miner. Resour., Geol. Geophys., Bull., No. 102. Cook, A.C. and Johnson, A.R., 1970. Geol. Mag., 107: 361-368. Cooke, H.J., 1973. Z. Geomorphol., 17: 443-459. Cooke, J.C. and Brebner, G.C., 1961. In: G.V. Lachmann (Editor), Boundary Layers and Flow Control, vol. I . Pergamon, Oxford, pp. 144-185. Cooke, M.H., Bridgewater, J. and Scott, A.M., 1978. Powder Technol., 21: 183-193. Cooke, R.U. and Warren, A., 1973. Geomorphology in Deserts. Batsford, London. Cooper, J.R., 1943. J. Geol., 51: 190-203. Cooper, W.S., 1958. Mem. Geol. SOC.Am., No. 72. Corbel, J., 1957. Les Karsts du Nord-ouest de 1’Europe. Mem. Docs. Inst. Etud. Rhodan.. 524 PP. Corbel, J. and Muxart, R., 1970. Z. Geomorphol., 14: 41 1-474. Corbett, K.D., 1972. Sedimentology, 19: 99- 114. Corbett, K.D., 1973. J. Sediment. Petrol., 43: 147-159. Corcos, G.M. and Sherman, F.S., 1976. J. Fluid Mech., 73: 241-264. Cornish, V., 1897. Geogr. J., 9: 278-302. Cornish, V., 1898. Geogr. J., 1 1 : 528-543, 628-647. Cornish, V., 1900. Geogr. J., 15: 1-30. Cornish, V., 1901. Geogr. J., 18: 170-200. Cornish, V., 1902. Geogr. J., 20: 137-175. Cornish, V., 1908. Geogr. J., 3 1 : 400-402. Cornish, V., 1914. Waves of Sand and Snow. Fisher Unwin, London. Cornish, V., 1934. Ocean Waves. Cambridge University Press, Cambridge. Corrsin, S. and Lumley, J., 1965. Appl. Sci. Res., A6: 114- 1 16. Corte, A.E. and Higashi, A., 1964. Experimental research on desiccation cracks in soil. U.S. Army Snow, Ice and Permafrost Establishment, Rep., No. 66. Cotter, E., 1971. J. Sediment. Petrol., 41: 129-138. Cotter, E., 1975. J. Sediment. Petrol., 45: 669-685. Coulson, J.M. and Richardson, J.F., 1962. Chemical Engineering, vol. 2. Pergamon, Oxford. Coulson, J.M. and Richardson, J.F., 1965. Chemical Engineering, vol. 1. Pergamon, Oxford, 2nd ed. Coutenceau, M. and Bouard, R., 1977a. J. Fluid Mech., 79: 23 1-256. Coutenceau, M. and Bouard, R., 1977b. J. Fluid Mech., 79: 257-272. Coward, M.P., 1980. J. Geol. SOC.,London, 137: 605-614. Craig, G.Y. and Walton, W.K., 1962. Trans. Edinburgh Geol. SOC.,19: 100- 1 19. Craik, A.D.D., 1970. J. Fluid Mech., 41: 801-821. Craik, A.D.D., 1976. Phys. Fluids, 19: 479-480. Craik, A.D.D., 1977. J. Fluid Mech., 81: 209-223. Craik, A.D.D. and Leibovich, S., 1976. J. Fluid Mech.. 72: 401-426. Crawford, K.C., 1979. Bull. Am. Meteorol. SOC.,60: 422-429. Crickmay, C.H., 1960. J. Geol., 68: 377-391. Crimes, T.P., 1973. Sedimentology, 20: 105-131. Crimes, T.P., 1975. Palaeogeogr. Palaeoclimatol. Palaeoecol., 19: 1 - 15. Crimes, T.P., 1977. In: T.P. Crimes and J.C. Harper (Editors), Trace Fossils, 2. See1 House Press, Liverpool, pp. 7 1-90. Crimes, T.P., Marcos, A. and Perez-Estuan, A., 1974. Palaeogeogr. Palaeoclimatol. Palaeoecol., 15: 169-184. Crofts, R.A., 1975. Scott. Geogr. Mag., 91: 52-64. Crook, K.A.W., 1961. J. Proc. R. SOC.N.S.W., 94: 189-207. Crossland, C., 1922. J. Linn. SOC.London, 36: 577-620.

576

Crow, S.C. and Champagne, F.H., 1971. J. Fluid Mech., 48: 547-591. Crowe, B.M. and Fisher, R.V., 1973. Geol. Soc. Am. Bull.. 84: 663-682. Crowell, J.C., 1955. Bull. Geol. SOC.Am., 66: 1351-1384. Crowell, J.C. and Frakes, L.A., 1971a. Geol. SOC.Am. Bull., 82: 2515-2540. Crowell, J.C. and Frakes, L.A., 1971b. J. Geol. SOC.Aust., 17: 115-155. Crowell. J.C. and Frakes, L.A., 1972. Geol. SOC.Am. Bull., 83: 2887-2912. Crowell, J.C., Hope, R.A.. Kahle, J.E., Ovenshine, A.T. and Sams, R.H., 1966. Spec. Rep. Calif. Div. Mines Geol., No. 89. Crowther, M.E. and Whitehead, J.C., 1978. In: J.F. Davidson and D.L. Keairns (Editors), Fluidization. Cambridge University Press, Cambridge, pp. 65-70. Cruff, R.W., 1965. Water-Supply Irrig. Pap., Wash., 1592-B. Culbertson. J.K., 1967. U.S. Geol. Surv., Prof. Pap., 575-D: 214-216. Cummins, W.A., 1958. Liverpool Manchester Geol. J., 2: 37-43. Cumrnins, W.A., 1965. Geol. J., 4: 299-300. Cummins, W.A. and Rundle, A.J., 1969. Mercian Geol., 3: 177- 188. Curl, R.L., 1959. Natl. Speleol. SOC.Am., News, No. 17: 94. Curl, R.L., 1966a. Trans. Cave Res. Group G.B., 7: 120-160. Curl, R.L., 1966b. Cave Notes, 8: 1-16. Curl, R.L., 1968. Proc. 4th Int. Congr. Speleol., 3: 61-66. Curray, J.R., 1956. Bull. Am. Assoc. Pet. Geol,, 40: 2440-2456. Curtis, M.L.K., 1972. Proc. Geol. Assoc., 83: 1-35. Cutts, J.A.. 1973. J. Geophys. Res., 78: 421 1-4221. Cvijic, J., 1924. Geogr. Rev., 14: 26-49. Daboll, J.M., 1969. Holocene sediments of the Parker River Estuary, Massachusetts. Univ. Mass. Dep. Geol., Contrib. No. 3-CRG. Dahl. R.. 1965. Geogr. Ann., A47: 83-140. Daley. B., 1968. J. Sediment. Petrol., 38: 114-127. Daley. B., 1972. Sediment. Geol., 7: 35-46. Dalrymple, R.A., 1975. J. Geophys. Res., 80: 3485-3487. Dalrymple. R.A. and Lanan, G.E., 1976. Geol. SOC.Am. Bull., 87: 57-60. Dalrymple, R.A. and Lozano, C.J.. 1978. J. Geophys. Res., 83: 6063-6071. Dalrymple, R.W., 1979. Sedimentology, 26: 835-844. Dalrymple, R.W., Knight, R.J. and Middleton, G.V., 1975. In: L.E. Cronin (Editor), Estuarine Research, vol. 2. Academic Press, New York. N.Y., pp. 293-307. Daly, R.A., 1936. Am. J. Sci.,(5)31: 401-420. Damms, S.M. and Kiichemann, D., 1974. Proc. R. SOC.London, Ser. A, 339: 451-461. Damuth, J.E., 1975. Mar. Geol., 18: 17-45. Damuth, J.E., 1978. Mar. Geol., 28: 1-36. Damuth, J.E., 1979. Geology, 7: 520-523. Damuth, J.E., 1980. Mar. Geol., 38: 51-75. Damuth, J.E. and Hayes, D.E., 1977. Mar. Geol., 24: 73-95. Dangeard, L. and Giresse, P., 1965. Cah. Oceanogr., 17: 255-269. Dangeard, L., Dore. F. and Juignet, P., 1961. Rev. Geogr. Phys. Geol. Dyn., (2)4: 251-259. Dangeard, L., Migniot, C., Larsonneur, C. and Baudet, C., 1964. C.R. Acad. Sci.. Ser. D, 258: 5935-5938. Daniel, J.F., 1971. U.S. Geol. Surv., Prof. Pap., 732-A. Danilov, I.D.. 1973. Bid. Peryglac., 22: 329-337. Darbyshire, J., 1977. In: M.V. Angel (Editor), A Voyage of Discovery: George Deacon 70th Anniversary Volume. Pergamon, Oxford, pp. 405-427. Darbyshire, J. and Pritchard, E., 1978. Riv. Ital. Geofis. Sci. Aff., 5(Bossulasco-Anniversq): 73-80. Darbyshire, M. and Draper, L., 1963. Engineering, 5 April: 482-484.

577 Das, P.K., 1972. Nature (London), 239: 211-213. Das, P.K., Sinha, M.C. and Balasubramanyam, V., 1974. Q. J. R. Meteorol. SOC., 100: 437-449. Davey, A., 1961. J. Fluid Mech., 10: 593-610. Davey, R.F. and Roshko, A., 1972. J. Fluid Mech., 53: 523-543. Davidson, J.F. and Harrison, D., 1963. Fluidized Particles. Cambridge University Press, Cambridge. Davidson, J.F. and Harrison, D., 1971. Fluidization. Academic Press, London. Davidson, J.F. and Keairns, D.L., 1978. Fluidization. Cambridge University Press, Cambridge. Davidson, J.F., Harrison, D. and Guedes de Carvalho, J.R.F., 1977. Annu. Rev. Fluid Mech., 9: 55-86. Davidson-Arnott, R.G.D. and Greenwood, B., 1974. J. Sediment. Petrol., 44: 698-704. Davidson-Arnott, R.G.D. and Greenwood, B., 1976. In: R.A. Davis and R.L. Ethington (Editors), Beach and Nearshore Sedimentation. SOC. Econ. Paleontol. Mineral., Spec. Publ., 24: 149-168. Davidsson, J., 1963. Lund Stud. Geogr., A23: 232 pp. Davies, A.M., 1977. In: J.C.J. Nihoul (Editor), Bottom Turbulence. Elsevier, Amsterdam, pp. 27-47. Davies, D.K., 1966. J. Geol., 74: 234-239. Davies, D.K., Quearry, M.W. and Bonis, S.B., 1978. Geol. SOC.Am. Bull., 89: 369-384. Davies, E.B. and Young, A.D., 1963. Rep. Mem. Aeronaut. Res. Comm. (Counc.), No. 3367. Davies, G.R., 1970a. In: B.W. Logan (Editor), Carbonate Sedimentation and Environments, Shark Bay, Western Australia. Mem. Am. Assoc. Pet. Geol., 13: 85-168. Davies, G.R., 1970b. In: B.W. Logan (Editor), Carbonate Sedimentation and Environments, Shark Bay, Western Australia. Mem. Am. Assoc. Pet. Geol., 13: 169-205. Davies, H.G., 1965. Sedimentology, 5: 305-325. Davies, J.T., 1972. Turbulence Phenomena. Academic Press, New York, NY. Davies, L. and Richardson, J.F., 1966. Trans. Inst. Chem. Eng., 44:T293-T305. Davies, L., Dollimore, D. and Sharp, J.H.. 1976. Powder Technol., 13: 123-132. Davies, P.A., 1972. J. Fluid Mech., 54: 691-718. Davies, R., 1968. Powder Technol., 2: 43-51. Davies, R. and Kaye, B.H., 1972. Powder Technol., 5 : 61-68. Davies, T.A. and Laughton, A.S., 1972. In: A.S. Laughton and W.A. Berggren (Editors), Initial Results of the Deep Sea Drilling Project. Washington, 12: 905-934. Davies, W.E., 1957. Bull. Natl. Speleol. SOC.,19: 40-46. Davis, E.J. and Choi, C.K., 1977. J. Fluid Mech., 81: 565-592. Davis, R.A. and Fox, W.T., 1971. Beach and nearshore dynamics in eastern Lake Michigan. Western Mich. Univ., Off. Nav. Res., Tech. Rep., No. 4; ONR Contract No. NONR-388092. Davis, R.A. and Fox, W.T., 1972a. J. Geol.. 80: 484-493. Davis, R.A. and Fox, W.T., 1972b. J. Sediment. Petrol., 42: 401-412. Davis, R.A. and Fox, W.T., 1975. J. Sediment. Petrol., 45: 852-865. Davis, R.A., Fox, W.T., Hayes, M.O. and Boothroyd, J.C., 1972. J. Sediment. Petrol., 42: 4 13-42 I . Davis, R.A., Fingleton, W.G. and Pritchett, P.C., 1975. U.S. Coastal Eng. Res. Cent., Misc. Pap., No. 10-75. Davis, W.M., 1902. Bull. Mus. Comp. Zool. (Harv. Univ.), (V)38: 281-346. Dawson, D.A. and TraSs, O., 1972. Int. J. Heat Mass Transfer, 15: 1317- 1336. Dawson, J.B. and Hawthorne, J.B., 1973. J. Geol. SOC.,London, 129: 61-84. Dawson, J.W., 1890. Q. J. Geol. SOC.,London, 46: 595-612. De Alba, P., Seed, H.B. and Chan, C.K., 1976. J. Geotech. Eng. Div. ASCE, 102(GT9): 909-927.

578 De Boer, P.L., 1979. Sedimentology. 26: 283-294. De Geer, S., 191 I . Arsb. Sver. Geol. Unders., 4: 198 pp. De Haller, P., 1933. Schweiz. Bauz., lOl(22): 243-264. De Omenaca. J.S., 1974. Bol. R. SOC.Esp. Hist. Nat. (Geol), 72: 191-201. De Raaf, J.F.M. and Boersma, J.R., 1971. Geol. Mijnbouw, 50: 479-504. De Raaf, J.F.M., Reading, H.G. and Walker, R.G., 1965. Sedimentology, 4: 1-52. De Raaf, J.F.M., Boersma, J.R. and Van Gelder, A., 1977. Sedimentology, 24: 451-483. De Vaumas, E., 1970. Mediterranee, 7: 151 - 188. De Vriend, H.J., 1972. Theory of viscous flow in curved shallow channels. Delft Univ. Techno]., Dep. Civ. Eng., Commun. Hydraul., No. 72- I . De Vriend, H.J., 1981. J. Fluid Mech., 107: 423-439. De Vries, W.C.P., 1973. Geol. Mijnbouw, 52: 133-140. De Wall, A.E., Pritchett, P.C. and Galvin, C.J., 1977. U.S. Coastal Eng. Res. Cent., Tech. Pap., No. 77-1. Deacon, E.L., Sheppard, P.A. and Webb, E.K.. 1956. Aust. J. Phys., 9: 511-533. Dean, W.E. and Anderson, R.Y., 1967. J. Geol., 75: 59-75. Deike, G.H. and White, W.B., 1969. Am. J. Sci., 267: 230-241. Demorest, M., 1938. J. Geol., 46: 700-725. Denham, M.K. and Patrick, M.A., 1974. Trans. Inst. Chem. Eng., 52: 361-367. Dennis, S.C.R. and Chang, G.Z., 1970. J. Fluid Mech., 42: 471-489. Dennis, S.C.R. and Smith, F.T. 1980. Proc. R. SOC.London, Ser. A, 372: 393-414. Denny, C.S.. 1941. J. Geol., 49: 225-260. Depuydt. F., 1972. Verh. K. Vlaam. Acad. Wet., 34: 1-229. Deresiewin, H., 1958. Adv. Appl. Mech., 5: 233-306. Derr. M.E., 1974. Brigham Young Univ. Geol. Stud., 21(3): 3-39. Deslauniers, G. and Frenette, M., 1972. In: H.W. Shen (Editor), Sedimentation. Colorado State Univ., Fort Collins, Colo., pp. 10.1-10.19. Diessel, C.F.K., Driver, R.C. and Moelle. K.H.R.. 1967. Proc. Australas. Inst. Min. Metall., No. 22 1 : 19-37. Dietrich, W.E., Smith, J.D. and Dunne, T., 1979. J. Geol., 87: 305-315. Dietz, J.W., 1972. Mitt. Bundanst. Wasserbau, Karlsruhe, No. 31: 96-109. Dietz. R.A., 1952. Ann. Mo. Bot. Gard.. 39: 249-254. Diller, J.S., 1889. Bull. Geol. SOC.Am., I : 41 1-442. Dimotakis. P.E. and Brown, G.L., 1976. J. Fluid Mech., 78: 535-560. Dinga. C.F.A., 1970. Bull. Geogr. SOC.Ill., 12(2): 1-28. Dionne, J.-C., 1968a. Am. J. Sci., 266: 380-388. Dionne, J.-C., 1968b. Marit. Sediments, 4: 113-1 15. Dionne, J.-C., 1968~.Z. Geomorphol., S7: 56-84. Dionne, J.-C., 1969a. Rev. Geogr. Montreal, 23: 5-20. Dionne, J.-C., 1969b. J. Sediment. Petrol., 39: 1174- 1181. Dionne, J.-C., 1971a. Rev. Geomorphol. Dyn., 20: 5-21. Dionne, J.-C.. 1971b. Rev. Geogr. Montreal, 25: 5-33. Dionne, J.-C., 1973a. J. Sediment. Petrol., 43: 848-856. Dionne. J.-C., 1973b. Rev. Geogr. Montreal, 27: 185-21 3. Dionne, J.-C., 1974a. Can. Geogr. J., 88: 4-9. Dionne, J.-C., 1974b. Can. J. Earth Sci., 1 I : 860-866. Dionne, J.-C., 1974~.Can. J. Earth Sci., 1 1 : 489-494. Dionne, J.-C., 1979. Earth-Sci. Rev., 15: 185-212. Dionne, J.-C. and Shilts, W.W., 1974. Can. J. Earth Sci., 1 1 : 1594-1605. Dixon, D.C.. Souter, P. and Buchanan, J.E., 1976. Chem. Eng. Sci., 31: 737-740. Dixon, E.E.L., 1921. Geology of the South Wales Coalfield. The country around Pembroke and Tenby. Mem. Geol. Surv. U.K., 220 pp.

579 Dixon, S.J. and Burke, J.W., 1973. J. Soil Mech. Found, Div., ASCE, 99(SMI I): 921-937. Dobrin, M.B., 1939. J. Appl. Phys., 10: 360-371. Dobrin, M.B., 1941. Trans. Am. Geophys. Union, 22: 528-542. Dobrowolski, L., 1924. Geogr. Ann., 6: 300-367. Dobry, R. and Alvarez, L., 1967. J. Soil Mech. Found, Div., ASCE, 93(SM6): 237-260. Dobson, M.R., Evans, W.E. and James, K.H., 1971. Mar. Geol., 1 I : 27-69. Dodson, P., 1971. Palaeogeogr. Palaeoclimatol. Palaeoecol., 10: 21 -74. Doe, T.W. and Dott, R.H., 1980. J. Sediment. Petrol., 50: 793-812. Doeglas, D.J., 1955. Leidse Geol. Meded., 20: 34-47. Doeglas, D.J., 1962. Sedimentology, 1 : 167- 190. Doichev, K., 1974. Chem. Eng. Sci., 29: 1205-1210. Doichev, K., Todorov, S. and Dimitrov, V., 1975. Chem. Eng. Sci., 30: 419-424. Dolan, R., 1965. Shore Beach, 33: 22-26. Dolan, R., 1971. Geol. SOC.Am. Bull., 82: 177-180. Dolan, R. and Ferm, J.C., 1966. Prof. Geogr., 18: 210-213. Dolan, R., Vincent, L. and Hayden. B., 1974. Z. Geomorphol., 18: 1-12. Dolan, R., Hayden, B. and Felder, W., 1979. J. Geol., 87: 175-185. Dolling, R.K., 1968. Ont. Geogr., 2: 3-1 1. Dominick, T.F., Wilkins, B. and Roberts, H., 1971. Water Resour. Res., 7: 1626-1635. Donald, M.B. and Roseman, B., 1962. Br. Chem. Eng., 7: 749-753. Donner, J.J. and West, R.G., 1957. Skr. Nor. Polarinst., No. 109. Donovan, D.T. and Stride, A.H., 1961. Geol. Mag., 98: 393-398. Donovan, L.F., 1970a. AIAA J., 8: 524-529. Donovan, L.F., 1970b. NASA Tech. Mem., X-52767. Donovan, R.N. and Archer, R., 1975. Proc. Yorks Geol. SOC.,40: 547-562. Donovan, R.N. and Foster, R.J., 1972. J. Sediment. Petrol., 42: 309-317. Dore, B.D., 1976. Pure Appl. Geophys., 114: 629-637. Dore, B.D., 1977. Q. J. Mech. Appl. Math., 30: 157-173. Dorjes, J. and Reineck, R.-E., 1977. Senckenbergiana Marit., 9: 19-45. Dorr, J.A. and Kauffman, E.G., 1963. J. Sediment. Petrol., 33: 751-758. Dorrepaal, J.M., O’Neill, M.E. and Ranger, K.B., 1976. J. Fluid Mech., 75: 273-286. Dott, R.H., 1963. Bull. Am. Assoc. Pet. Geol., 47: 104-128. Dott, R.H., 1966a. J. Geol., 74: 373-420. Dott, R.H., 1966b. Bull. Am. Assoc. Pet. Geol., 50: 610-611 (abstr.). Dott, R.H. and Howard, J.K., 1962. J. Geol., 70: 114-121. Doty, M.S. and Morrison, J.P.E., 1954. Atoll Res. Bull., No. 35: 61 pp. Doubiansky, V., 1928. Bull. Appl. Bot. Genet. Plant Breed., 19: 225-285. Douglas, E. and Sayles, C.P., 1971. AIChE, Symp. Ser., No. 116, 67: 201-209. Douglas, E. and Walsh, T., 1966. Trans. Inst h4in. Metall., 75: C226-C232. Douglas, E., Walsh, T. and Whitehead, A., 1967. The development of equipment for the dry concentration of minerals. Warren Springs Laboratory Paper. DOW,D.B., 1965. Geol. Mag., 102: 407-414. Dozier, J., 1970. Res. Pap. Arct. Inst. North America, No. 57: 69-1 17. Dragovich, D., 1968. Rev. Geomorphol. Dyn., 18: 8-16. Dresch, J., 1975. Bull. Assoc. Geogr. Fr., No. 430: 337-351. Dresch, M.J., 1968. Bull. Assoc. Geogr. Fr., Nos. 362/363: 143-153. Drever, H.L. and Johnston, R., 1958. Trans. R. SOC.Edinburgh, 63: 459-499. Drew, T.B., 1931. Trans. Am. Inst. Chem. Eng., 26: 26-80. Dubieff, J., 1943. Trav. Inst. Rech. Sahariennes, 2: 11-35. Dubieff, J., 1952. Trav. Inst. Rech. Sahariennes, 8: 123-162. Dubois, R.N., 1978. Geol. SOC.Am. Bull., 89: 1133- 1139. Duff, P.Mc1.D. and Walton, E.K., 1973. Congr. Av. Etud. Stratigr. Carb., Krefeld, 1971, 2: 365-379.

580

Duke, C.M. and Leeds, D.J., 1963. Bull. Seismol. SOC.Am., 53: 309-357. Dunbar, (2.0.and Rodgers, J., 1957. Principles of Stratigraphy. Wiley, New York, N.Y. Dunbar, G.J. and McCall, G.J.H., 1971. Sediment. Geol., 5: 93-133. Duncan, J.R., 1964. Mar. Geol., 2: 186-197. Duncanson, H.H., 1909. Science, 29: 869-871. Dunkerley, D.L., 1979. Z. Geomorphol., 23: 332-348. Durst, C.S., 1924. Q. J. R. Meteorol. SOC.,59: 113-1 19. Durst, F., Melling, A. and Whitelaw, J.H., 1972. In: D.J. Cockrell (Editor), Fluid Dynamic Measurements, vol. I . Leicester University Press, Leicester, pp. 81-87. Durst. F., Melling, A. and Whitelaw, J.H., 1974. J. Fluid Mech., 64: 1 1 1-128. Dury, G.H.. 1958. Inst. Br. Geogr. Publ., No. 25: 105-118. Dury, G.H., 1964a. US. Geol. Surv.,Prof. Pap., 452-A: 67 pp. Dury, G.H.. 1964b. U.S. Geol.. Surv., Prof. Pap., 452-B: 56 pp. Dury, G.H., 1965. U.S. Geol. Surv., Prof. Pap., 452-C: 43 pp. Dury, G.H., 1967. Aust. Geogr. Stud., 5 : 135-149. Dury, G.H.. 1969. In: R.J. Chorley (Editor), Water, Earth and Man. Methuen, London, pp. 419-430. Dury, G.H., 1972. Geogr. Ann., A53: 188-197. Dury, G.H.. 1976. J. Hydrol., 30: 219-245. Dury, G.H., Sinker, C.A. and Pannett, D.J., 1972. Area, 4: 81-85. Dussan, E.B., 1975. Arch. Ration. Mech. Anal., 57: '363-379. Dyer, K.R., 1970. Nature (London), 225: 56-58. Dyhr-Nielsen, M. and Sorensen, T., 1970. Proc. 12th Conf. Coastal Eng. 2: 855-866. Dyson, J.L., 1937. J. Geol., 45: 549-557. Dyson, J.L., 1952. Am. J. Sci., 250: 204-21 1. Dzulynski, S., 1963. Stud. Geol. Pol., 12: 1-136. Dzulynski, S., 1965. J. Sediment. Petrol., 35: 196-212. Dzulynski, S., 1966. Ann. SOC.Geol. Pol., 36: 1-21. Dzulynski, S. and Kotarba, A., 1979. Z. Geomorphol., 23: 172-191. Dzulynski, S. and Kotlarczyk, J., 1962. Ann. SOC.Geol. Pol., 32: 147-160. Dzulynski, S. and Kubin, A., 1975. Ann. Soc.Geol. Pol., 45: 157-169. Dzulynski, S. and Radomski. A., 1955. Acta Geol. Pol., 5 : 47-66. Dzulynski, S. and Radomski, A., 1956. Ann. SOC.Geol. Pol., 26: 225-264. Dzulynski. S. and Sanders, J.E., 1962a. Ann. SOC.Geol. Pol., 32: 143-146. Dzulynski. S. and Sanders, J.E., 1962b. Trans. Conn. Acad. Arts Sci., 42: 57-96. Dzulynski, S. and Simpson, F., 1966a. Geol. Rom., 5 : 197-214. Dzulynski, S. and Simpson, F., 1966b. Ann. SOC.Geol. Pol., 36: 285-294. Dzulynski, S. and Slanka, A., 1958. Ann. Soc. Geol. Pol., 28: 205-259. Dzulynski, S. and Slaczka, A., 1960. Ann. Soc. Geol. Pol., 30: 249-255. Dzulynski, S. and Smith, A.J., 1963. J. Sediment. Petrol., 33: 616-627. Dzulynski. S. and Walton, E.K., 1963. Trans. Edinburgh Geol. SOC.,19: 279-305. Dzulynski, S. and Walton, E.K., 1965. Sedimentary Features of Flysch and Graywackes. Elsevier, Amsterdam. Dzulynski, S., Ksiazkiewicz, M. and Kuenen, P.H., 1959. Bull. Geol. Soc.Am., 70: 1089- 1 118. Eakin, H.M., 1914. J. Geol., 18: 435-447. Eakin, H.M., 1935. Trans. Am. Geophys. Union, 16: 467-472. Eardley, A.J., 1938a. Bull. Am. Assoc. Pet. Geol., 22: 1305-141 I . Eardley, A.J., 1938b. Bull. Geol. SOC.Am., 49: 343-358. Earp, J.R., 1938. Q. J. Geol. Soc. London, 94: 125-157. Ebers, E., 1926. Neues Jahrb. Miner. Geol. Palaontol., Beilagebkde 53, Abt. B, pp. 153-270. Eckert, E.R.C. and Soehngen, E., 1952. Trans. ASME, 74: 343-347. Eckert, M., 1900. Wiss. Erghzh. Z. Dtsch.-Oesterr. Alpenver., 31: 52-60.

58 1 Ede, A.J., Hislop, C.T. and Morris, R., 1956. Proc. Inst. Mech. Eng., 170: 1 113- 1 126. Edwards, M.B., 1976. Arb. Nor. Polarinst., 1974: 35-50. Egloff, J., 1972. Bull. Am. Assoc. Pet. Geol., 56: 694-706. Egloff, J. and Johnson, G.L., 1975. Can. J. Earth Sci., 12: 2111-2133. Egolf, C.B. and McCabe, W.L., 1937. Trans. AIChE, 33: 620-640. Ehlers, J. and Stephan, H.J., 1979. J. Glaciol., 22: 345-355. Eichelbrenner, E.A., 1957. Publ. Off. Natl. Etude Rech. Aeronaut., No. 89: 375. Eichelbrenner, E.A. and Michel, R., 1958. In: H. Gortler (Editor), Boundary Layer Research. Springer, Berlin, pp. 161 - 172. Eichelbrenner, E.A. and Oudart, A., 1954. Rech. Aeronaut., No. 40. Eichelbrenner, E.A. and Oudart, A., 1955. Rech. Aeronaut., No. 47. Eichelbrenner, E.A. and Preston, J.H., 1971. J. Mec., 10: 91- 1 12. Einsele, G., 1963. Neues Jahrb. Geol. Piilaontol., Abh., 116: 162-198. Einstein, A., 1905. Ann, Phys., 17: 549-560. Einstein, A., 1906. Ann. Phys., 19: 289-306, 371-381. Einstein, A., 1911. Ann. Phys., 24: 591-592. Einstein, H.A. and Harder, J.A., 1954. Trans. Am. Geophys. Union, 35: 114-120. Einstein, H.A. and Li, H., 1958. Trans. Am. Geophys. Union, 39: 1085-1088. Einstein, H.A. and Shen, H.W., 1964. J. Geophys. Res., 69: 5239-5247. Eirich, F., Bunzl, M. and Margaretha, H., 1936a. Kolloidzeitschrift, 74: 276-285. Eirich, F.R., Margaretha, H. and Bunzl, M., 1936b. Kolloidzeitschrift, 75: 20-37. Eisbacher, G.H., 1970. Can. J. Earth Sci., 7: 215-225. Eisbacher, G.H., 1976. Can. J. Earth Sci., 13: 1495-1513. Eisenlohr, W.S., 1972. U.S. Geol. SUIT., Prof. Pap., 585-A. Eisenschitz, R., 1932. Z. Phys. Chem., A158: 78-90. Eittreim, S.L., Thorndike, E.M. and Sullivan, L., 1976. Deep-sea Res., 23: I 1 15-1 127. Elder, J.W., 1959. J. Fluid Mech., 5 : 355-368. Elder, J.W., 1960. J. Fluid Mech., 9: 133-153. Elliott, R.E., 1961. Proc. Yorks. Geol. Soc.,33: 197-234. Elliott, R.E., 1965. Sedimentology, 5 : 193-209. Elliott, T., 1976a. J. Sediment. Petrol., 46: 70-76. Elliott, T., 1976b. Scott. J. Geol., 12: 115-124. Ellison, T.H. and Turner, J.S., 1959. J. Fluid Mech., 6: 423-448. Ellison, T.H. and Turner, J.S., 1960a. J. Fluid Mech., 8: 514-528. Ellison, T.H. and Turner, J.S., 1960b. J. Fluid Mech., 8: 529-544. Elmore, R.D., Pilkey, O.H., Cleary, W.J. and Curran, H.A., 1979. Geol. Soc. Am. Bull., 90: 1165-1 176. Elson, J.A., 1975. Can. J. Earth Sci., 12: 1048-1053. Elston, E.D., 1917. Sci. Mon., 5 : 557-567, 6: 37-51. Embleton, C. and King, C.A.M., 1975. Glacial and Penglacial Geomorphology. I . Glacial Geomorphology. Arnold, London, 2nd ed. Embley, R.W. and Langseth, M.G., 1977. Mar. Geol.. 25: 279-297. Embley, R.W., Hoose, P.J., Lonsdale, P., Mayer, L. and Tucholke, B.E., 1980. Geol. SOC.Am. Bull., 91: 731-740. Emeleus, C.H., 1963. Mineral. Soc.Am., Spec. Pap., 1 : 22-29. Emery, K.O., 1945a. J. Sediment. Petrol., 15: 84-87. Emery, K.O., 1945b. J. Sediment. Petrol., 15: 39-49. Emery, K.O., 1946. J. Geol., 54: 209-228. Emery, K.O., 1950. J. Sediment. Petrol., 20: 1 1 1 - 115. Emery, K.O. and Cox, D.C., 1956. Pac. Sci., 10: 382-402. Emery, K.O. and Foster, J.F., 1948. J. Mar. Res., 7: 644-654. Emery, K.O. and Gale, J.F., 1951. Trans. Am. Geophys. Union, 32: 31-36.

582

Emery, K.O., Tracey, J.I. and Ladd, H.S., 1954. U.S. Geol. Surv., Prof. Pap., 260-A. Engel, W., 1970. Ver. Geol. Bundestanst., Wien, 4: 570-582. Engel, W., 1974. Gottinger Arb. Geol. Palaontol., No. 16: 65 pp. Engelder, J.T. and Scholz, C.H., 1976. Int. J. Rock Mech. Min. Sci., 13: 155-163. Engels, H., 1905. Z. Bauw., 55: 663-680. Engelund. F., 1971. Tech. Univ. Den., Inst. Hydrodyn. Hydraul. Eng., Prog. Rep., No. 23: 27-3 1.

Engelund, F., 1973. Tech. Univ. Den. Inst. Hydrodyn. Hydraul. Eng., Prog. Rep., No. 28: 3 1-38.

Engelund, F., 1974. J. Hydraul. Div. ASCE, 100(HY1 I ) : 1631-1648. Engelund, F., 1975. J. Fluid Mech., 72: 145-160. Engelund, F. and Skovgaard, O., 1973. J. Fluid Mech., 57: 289-302. Enos, P., 1969a. J. Sediment. Petrol., 39: 680-723. Enos, P., 1969b. Geol. SOC.Am., Spec. Pap., 117. Erdmannsddrffer. O.H., 1938. Zentrbl. Mineral. Geol. Palaontol., Abt. A, No. 9: 257-261. Ergun, S., 1952. Chem. Eng. Prog., 48: 89-94. Eriksson, K.A., 1977. Sediment. Geol., 18: 257-28 1. Eriksson, K.A. and Vos, R.G., 1979. Precambrian Res., 9: 169-188. Erkek, C., 1973. Proc. 15th Congr. Inst. Assoc. Hydraul. Res., 1 : 411-416. Esch, R.E., 1957. J. Fluid Mech., 3: 289-303. Esch, R.E., 1962. J. Fluid Mech., 12: 192-208. Escher, B.G., 1937. Leidse Geol. Meded., 9: 79-104. Escher, B.G. and Kuenen, P.H., 1928. Leidse Geol. Meded., 3: 151-182. Espinosa, A.F., 1976. U S . Geol. Surv., Prof. Pap., 1002. Etheridge, D.W. and Kemp. P.H., 1978. J. Fluid Mech., 86: 545-566. Euteneuer, G.A., 1969. Acta Mech., 7: 161-168. Euteneuer, G.A., 1972. Acta Mech., 13: 215-223. Euteneuer, G.A. and Reimann, J., 1971. Acta Mech., 12: 89-97. Evans, A.M. and Whitaker, J.H.McD., 1964. Trans. Leicester Lit. Philos. SOC.,48: 55-57. Evans, G., 1965. Q. J. Geol. SOC.London, 121: 209-241. Evans, O.F., 1938a. J. Geol., 46: 615-627. Evans, O.F., 1938b. J. Sediment. Petrol., 8: 71. Evans, O.F., 1939. J. Geol., 47: 324-334. Evans, O.F., 1940. J. Geol., 48: 476-51 1. Evenari, M., Yaalon, D.H. and Gutterman, Y., 1974. Z. Geomorphol., 18: 167-172. Everts, C.H., 1973. In: D.R. Coates (Editor), Coastal Geomorphology. State University of New York, Binghamton, N.Y., pp. 279-301. Eveson, G.F.. 1957. J. Oil Colour Chem. Assoc., 40: 456-477. Eveson. G.F., 1958. J. Oil Colour Chem. Assoc., 41 : 150- 155. Eveson, G.F., 1959. In: C.C. Mill (Editor), Rheology of Disperse Systems. Pergamon, London, pp. 61-80. Eveson, G.F., Ward, S.G. and Whitmore, R.L., 1951. Discuss. Farady SOC.,11: 11-14. Ewart, A,, 1965. N.Z. J. Geol. Geophys., 8: 611-677. Ewers, R.O., 1966. Bull. Natl. Speleol. Soc.,28: 133-140. Ewing, J.A. and Ewing, M., 1962. J. Geophys. Res., 67: 4729-4739. Ewing, M., Aitken. T. and Eittreim, S., 1968. Trans. Am. Geophys. Union, 49: 218. Ewing, M., Eittreim, S., Ewing, J. and Le Pichon, X., 1971. Phys. Chem. Earth, 8: 49-78. Exley, J.T. and Brighton, J.A., 1971. Trans. ASME, D93: 192-198. Exner, F.M., 1919. Sitzungsber. Akad. Wiss. Wien, Abt. IIa, 128: 1453-1473. Exner, F.M., 1921. Geogr. Ann., 3: 327-335. Exon, N.F., 1975. Mar. Geol., 18: 197-212. Eyre, J., 1963. Newslett. Cave Res. Group G.B., No. 88: 23-24.

583 Faegri, K.. 1952. J. Glaciol., 2: 24-25. Fagan, J.J., 1962. Geol. SOC.Am. Bull., 73: 595-612. Fage, A. and Falkner, V.M., 1931. Rep. Mem. Aeronaut. Res. Comm. (Counc.), No. 1408. Fagerstrom, J.A., 1967. J. Sediment. Petrol., 37: 73-79. Fahnestock, R.K. and Haushild, W.L., 1962. Geol. SOC.Am. Bull., 72: 1431-1436. Fahnestock, R.K. and Maddock, T., 1964. U.S. Geol. Surv.,Prof. Pap., 501-B: 140-142. Fahrig, W.F., 1961. Bull. Geol. Surv. Can., No. 68. Fairbridge, R.W., 1947. J. Proc. R. SOC.N.S.W.. 81: 99-121. Fairchild, H.L., 1901. Am. Geok., 28: 9-14. Faller, A.J., 1963. J. Fluid Mech., 15: 560-576. Faller, A.J., 1965. J. Atmos. Sci., 22: 176-184. Faller, A.J., 1971. Annu. Rev. Ecol. Syst., 2: 201-236. Faller, A.J., 1978. Science, 201: 618-620. Faller, A.J. and Caponi, E.A., 1978. J. Geophys. Res., 83: 3617-3633. Faller, A.J. and Kaylor, R.E.. 1966. J. Atmos. Sci., 23: 466-480. Faller, A.J. and Woodcock, A.H., 1964. J. Mar. Res., 22: 22-29. Famularo, J. and Happel, J., 1965. AIChE J, 1 I : 981-988. Fan, T.Y.T., 1955. Astrophys. J.. 121: 508-520. Fargue, L., 1908. Hydraulique Fluviale. La Forme du Lit des Rivieres a Fond Mobiles. Gauthiers-Villars, Paris. Farrell, S.C., 1970. Sediment distributions and hydrodynamics: Sacco River and Scarboro Estuaries. Univ. Mass., Dep. Geol., Contrib. No. 6-CRG. Faure, G. and MontAggioni, L., 1976. Mar. Geol., 21: M9-MI6. Feldman, S., 1959. J. Fluid Mech., 6: 131 - 155. Fenech, E.J. and Tobias, C.W., 1960. Electrochim. Acta, 2: 311-325. Fenner, C.N., 1923. The origin and mode of emplacement of the great tuff deposit in the Valley of Ten Thousand Smokes. Natl. Geogr. SOC.,Contrib. Tech. Pap., Katmai Ser., No. I. Fenton, C.L. and Fenton, M.A., 1937. Bull. Geol. SOC.Am., 48: 1873-1970. Fenton, D.L. and White, R.A., 1971. Trans. ASME, D93: 455-457. Fenton, R.G. and Oxley, P.L.B., 1969. Proc. Inst. Mech. Eng., 183: 417-428. Fenton, R.G. and Oxley, P.L.B., 1970. Proc. Inst. Mech. Eng.. 184: 927-937. Ferguson, R.I., 1973a. Water Resour. Res. 9: 1079-1086. Ferguson, R.I., 1973b. Geol. SOC.Am. Bull., 84: 251-256. Ferguson, R.I., 1973c. Area, 5: 38-41. Ferguson, R.I., 1975. J. Hydrol., 26: 315-333. Ferguson, R.I., 1977a. In: K.J. Gregory (Editor), River Channel Changes. Wiley, London, pp. 235-248. Ferguson, R.I., 1977b. Geol. SOC.Am. Bull., 88: 212-214. Field, W.G., 1968. J. Hydraul. Div. ASCE, 94(HY3): 705-719. Figge, K., 1976. Dtsch. Hydrogr. Z., 29: 32-40. Figueiredo, A.G., 1980. Mar. Geol., 35: 367-376. Filetti, E.G. and Kays, W.M., 1966. Trans. ASME, C90: 163-173. Finch, T.F., 1977. Sci. Proc. R. Dublin SOC.,A6: 1-7. Finch, T.F. and Walsh, M., 1973. Proc. R. Ir. Acad., B73: 405-413. Finn, W.D.L., 1966. J. Soil Mech. Found Div. ASCE, 92(SMI): 1-1 1. Finn, W.D.L., Bransby, P.L. and Pickering, D.J., 1970a. J. Soil. Mech. Found. Div., ASCE, 96(SM6): 1917- 1934. Finn, W.D.L., Emery, J.J. and Gupta, Y.P., 1970b. A shaking table study of the liquefaction of saturated sands during earthquakes. Univ. B.C., Dep. Civ. Eng., Soil Mech. Ser., No. 17. Finn, W.D.L., Byme, P.M. and Martin, G.R., 1976. J. Geotech. Eng. Div., ASCE, 102(GT8): 84 1-856.

584 Finn, W.D.L.. Lee, K.W. and Martin, G.R., 1977. J. Geotech. Eng. Div., ASCE, 103(GT6): 517-533. Finn, W.D.L., Pickering, D.J. and Bransby, P.L., 1969. Sand liquefaction in triaxial and simple shear tests. Univ. B.C., Dep. Civ. Eng., Soil Mech. Ser., No. 11. Finney, E.A., 1934. Bull. Mich. Eng. Exp. Stn., No. 57. Finnie, I., 1956. Mech. Eng.. 78: 715-721. Finnie, I. and Kabil, Y.H.. 1965. Wear, 8: 60-69. Fisher, R.V., 1966. Am. J. Sci., 264: 350-363. Fisher, R.V.. 1977. Geol. SOC.Am. Bull., 88: 1287-1297. Fisher, R.V. and Waters, A.C., 1969. Science, 165: 1349-1352. Fisher, R.V. and Waters, A.C.. 1970. Am. J. Sci., 268: 157-180. Fisk, H.N., 1944. Geological investigation of the alluvial valley of the Lower Mississippi River. Mississippi River Commission, Vicksburg, Miss. Fisk, H.N., 1947. Fine grained alluvial deposits and their effects on Mississippi River activity. Mississippi River Commission, Vicksburg, Miss. Fisk, H.N., 1952a. Geological investigation of the Atchafalaya Basin and the problem of Mississippi River diversion. Mississippi River Commission, Vickburg, Miss. Fisk, H.N., 1952b. Trans. ASCE, 1 17: 667-682. Fisk, H.N., 1959. Proc. 2nd Coastal Geogr. Conf., Nat. Acad. Sci., Wash., pp. 103-151. Fitzgerald, L.M., 1963. Aust. J. Phys., 16: 475-489. Fleming, C.A. and Hunt, J.N., 1976. Proc. Inst. Civ. Eng., (2)61: 297-310. Flemming, B.W., 1977. Sediment. Geol., 18: 61-95. Flemming, B.W., 1978. Mar. Geol.. 26: 177-198. Flemming, B.W., 1980. Sediment. Geol., 26: 179-205. Flemming, N.C.. 1964. J. Sediment. Petrol., 34: 1 12- 122. Flemming, N.C., 1965. Rep. Challenger SOC.,3: 42-43. Fletcher, R.C., 1974. Am. J. Sci., 274: 1029-1043. Fletcher, R.C., 1977. Tectonophysics, 39: 593-606. Fleury, E., 1919. C.R. Acad. Sci., 168: 896-899. Fleuty, M.J., 1964. Proc. Geol. Assoc., 75: 461-492. Flierl, G.R. and Robinson, A.R., 1972. Nature (London), 239: 213-215. Flint, R.F. and Bond, G., 1968. Geol. SOC.Am. Bull., 79: 299-314. Florin, V.A. and Ivanov, P.L., 1961. Proc. 5th Int. Conf. Soil. Mech. Found. Eng., 1: 107- 1 1 1. Folk, R.L., 1971a. Sedimentology, 16: 5-54. Folk, R.L., 1971b. Geol. SOC.Am. Bull., 82: 3461-3468. Folk, R.L., 1976. Sedimentology, 23: 649-669. Folk, R.L., 1977. Sedimentology, 24: 864-874. Ford, T.D., 1964. Newslett. Cave Res. Group G.B., No. 90/91: 1 1-13. Ford, T.D.. 1971. Isle Man Nat. Hist. Antiq. J.. 7: 440-448. Ford, T.F., 1960. J. Phys. Chem., 64: I 168- I 174. Forristall, G.Z., 1974. J. Geophys. Res., 79: 2721-2729. Forristall, G.Z., Hamilton, R.C. and Cardone. V.J., 1977. J. Phys. Oceanogr., 7: 532-546. Forssblad. L., 1947. Acta Polytech. Scand., 15: 1-74. Forstail, W. and Gaylord, E.W., 1955. Trans. ASME, E76: 161-164. Foster, H.L. and Karlstrom, T.N.V., 1967. U.S. Geol. Surv., Prof. Pap., 543-F. Fowler, R.T., 1960. Aust. J. Chem. Eng., 1 : 9- 15. Fowler, R.T., 1961. Aust. J. Chem. Eng., 2: 17-20. Fox, J., 1960. NASA Tech. Note, D-2501. Fox, J.A. and Ball, D.J., 1968. Proc. Inst. Civ. Eng., 39: 467-475. Fox, P.J., Heezen, B.C. and Harian. A.M., 1968. Nature (London), 220: 470-472. Fox, W.T. and Davis, R.A., 1970. Proc. 13th Conf. Great Lakes Res., pp. 233-241.

585 Fox, W.T. and Davis, R.A., 1978. Geol. SOC.Am. Bull., 89: 1541-1549. Fox, W.T. and Davis, R.A., 1979a. Estuarine Coastal Mar. Sci., 9: 683-697. Fox, W.T. and Davis, R.A., 1979b. Math. Geol., 1 1 : 143-164. Fox, W.T., Ladd, J.W. and Martin, M.K., 1966. J. Sediment. Petrol., 36: 1126-1130. Frakes, L.A. and Crowell, J.C., 1969. Geol. SOC.Am. Bull.. 80: 1007-1042. Frakes, L.A. and Crowell, J.C., 1970. Geol. SOC.Am. Bull., 81: 2261-2286. Frakes, L.A., Matthews, J.L. and Crowell, J.C., 1971. Geol. SOC.Am. Bull., 82: 1581-1604. Francis, E.H. and Howells, M.F., 1973.J. Geol. SOC.,London, 129: 621-641. Francis, G.P. and Pierce, F.J., 1967.Trans. ASME, D89: 597-607. Francis, J.R.D., 1951.Proc. R. SOC.London, Ser A, 206: 387-406. Francis, J.R.D., 1953.J. Mar. Res., 12: 93-98. Francis, J.R.D., 1954. Q. J. R. Meteorol. SOC.,80: 438-443. Francis, J.R.D., 1959. Proc. Inst. Civ. Eng., 12: 197-216. Francis, J.R.D., 1975. Fluid Mechanics for Engineering Students. Arnold, London, 4th ed. Francis, J.R.D. and Asfari, A.F., 1970.Nature (London), 225: 725-728. Francis, J.R.D. and Asfari, A.F., 1971. J. Hydraul. Res., 9: 73-90. Francis, J.R.D., Pattanaik, A.B. and Wearne, S.H., 1968. Proc. Inst. Civ. Eng., 41: 829-837. Francis, P.J., 1976.Volcanoes. Penguin Books, Harmondsworth. Francis, P.W., 1970. Geogr. Mag., 42: 795-803. Francis, P.W. and Baker, M.C.W., 1977.Nature (London), 270: 164-165. Frankel, N.A. and Acrivos, A., 1967. Chem. Eng. Sci., 22: 847-853. Frazier, D.E. and Osanik, A., 1961.Trans. Gulf-Coast Assoc. Geol. SOC.,1 I : 121 -'137. Freeman, J.F., Baer, L. and Jung, G.H., 1957.J. Mar. Res., 16: 12-22. Freeman, W.E. and Visher, G.S., 1975. J. Sediment. Petrol., 45: 651-668. Frey, F.R. and Howard, J.D., 1970. In: T.P. Crimes and J.C. Harper (Editors), Trace Fossils. See1 House Press, Liverpool, pp. 146-166. Freymuth, P., 1966. J. Fluid Mech., 25: 683-704. Friedkin, J.F., 1945. A laboratory study of the meandering of alluvial rivers. United States Waterways Experiment Station, Vicksburg, Miss. Friend, P.F., 1965. Sedimentology, 5: 39-68. Friend, P.F., Alexander-Marrack, P.D., Nicholson, J. and Yeats. A.K., 1976. Medd. Grdnl., No. 206: 91 pp. Frisch, A.S., Miller, L.J. and Strauch, R.G., 1975. J. Geophys. Res., 80: 5051-5060. Fristrup, B., 1952. Proc. 19th Int. Geol. Congr., Algiers, Sect. 7,pp. 91-99. Froehlich, W., Klimek, K. and Starkel, L., 1972. Stud. Geomorphol. Carpatho-Balcanica, 6: 63-83. Frost, B.A., 1966. Sci. Pap. Meteorol. Off., London, No. 25. Frye, J.C. and Swineford, A., 1947. Am. J. Sci., 245: 366-379. Fuchs, T.,1895. Denkschr. Akad. Wiss., Wien, 62: 369-448. Fiihrbdter, A., Koster, R., Kramer, J., Schwitters, J. and Sindern, J., 1972. Die Kiiste, 23: 1-62. Fujiyoshi, Y., 1950. Jpn. Sci. Rev., l(3): 29-34. Fuller, J.O., 1955. Bull. Geol. SOC.Am., 66: 159-176. Fuller, M.B., 1925.J. Geol., 33: 224-235. Fuller, M.L., 1912. Bull. U.S. Geol. Surv., No. 494. Furuya, Y. and Miyata, M., 1972. Mem. Fac. Eng. Nagoya Univ., 24: 278-293. Futterer, E., 1977. Einregelung, Transport und Ablagerung biozener Hartteile im Stromungskanal. Geological Institute, Eberhard-Karls-University, Tiibingen. Gabriel, A., 1938. Geogr. J., 92: 193-208. Gadd, G.E., Cope, W.E. and Attridge, J.L., 1958. Rep. Mem. Aeronaut. Res. Comm. (Counc.), No. 3 148. Gadow, S. and Reineck, H.-E., 1968.Natur Mus., 98: 195-200.

586 Gadow, S. and Reineck, H.-E., 1969. Senckenbergiana Marit., I : 63-78. Gage, K.S. and Reid, W.H., 1968. J. Fluid Mech., 33: 21-32. Galay, V.J., Kellerhals, R. and Bray, D.I., 1973. In: Fluvial Processes and Sedimentation. Department of Environment, Canada, Inland Waterways Directorate, pp. 2 17-250. Gall, J.C., 1971. Mem. Sew. Carte Geol. Alsace Lorraine, No. 34: 318 pp. Gallagher. R.H., Liggett, J.A. and Chan, S.T.K., 1973. J. Hydraul. Div. ASCE, 99(HY7): 1083-1096. Galloway, J.R. and Sage, B.H., 1968. Int. J. Heat Mass Transfer, 11 : 539-549. Galvin. C.J., 1968. J. Geophys. Res., 73: 3651-3659. Gammelsrdd, T., 1975. J. Geophys. Res., 80: 5069-5075. Garde, R.J. and Ranga Raju, K.G., 1966. J. Hydraul. Div. ASCE, 92(HY4): 77-100. Gamer, F.H. and Grafton, R.W., 1954. Proc. R. SOC.London, Ser. A, 224: 64-82. Garner, F.H. and Keey, R.B., 1959. Chem. Eng. Sci.. 9: 218-224. Gamer, F.H. and Suckling, R.D., 1958. AIChE J., 4: 1 14- 124. Garner, F.H., Jenson, V.G. and Keey, R.B., 1959. Trans. Inst. Chem. Eng., 37: 191-197. Garodz. L.J., 1971. In: J.H. Olson, A. Goldburg and M. Rogers (Editors), Aircraft Wake Turbulence and its Detection. Plenum Press, New York, N.Y., pp. 265-285. Garratt, J.R., 1977. Mon. Weather Rev., 105: 915-929. Garrett, C., 1976. J. Mar. Res., 34: 117- 130. Garside, J. and Al-Dibouni, M., 1974. In: H. Angelino, J.P. Couderc, H. Gilbert and C. Laguerie (Editors), La Fluidization et ses Applications. Cepadues-Editions, Toulouse, pp. 53-62. Gaster, M., 1969. Rep. Mem. Aeronaut. Res. Comm. (Counc.), No. 3595. Gauri. K.L. and Kalterherberg, J., 1966. Sedimentology, 6: 115-133. Gavelin, S. and Russell, R.V., 1967. Geol. For. Stockholm Forh., 89: 74-104. Gavrilovic, D., 1972. Z. Geomorphol., 16: 315-331. Gay, E.C., Nelson, P.A. and Armstrong, W.P., 1969. AIChE J., 15: 815-822. Gebelein, C.D., 1977. Dynamics of Recent Carbonate Sedimentation and Ecology, Cape Sable, Florida. Brill, Leiden, 120 pp. Gedney, R.T. and Lick, W., 1971. Proc. 14th Conf. Great lakes Res., pp. 454-466. Gedney, R.T. and Lick, W., 1972. J. Geophys. Res., 77: 2714-2723. Gedney, R.T., Lick, W. and Mills, F.B., 1972. NASA Tech. Note, TN D-6841. Gedzelman, S.D., 1974. Pure Appl. Geophys., 112: 265-273. Gee, E.R., 1934. Mem. Geol. Sum. India, No. 95. Gellatly, D.C., 1970. Sediment. Geol.. 4: 185-191. Gennessaux, M., 1966. Rev. Geogr. Phys. Geol. Dyn., (2)8: 3-38. Geology Extra-Mural Group, 1968. Proc. Geol. Soc. Glasgow, No. 109: 3 pp. Gerard, R., 1978. J. Hydraul. Div. ASCE, 104(HY5): 755-773. Gerber, E. and Scheidegger, A.E., 1966. Geogr. Helv., 21: 2-31. Gerber, E. and Scheidegger, A.E., 1973. Z. Geomorphol., S18: 37-49. Gerhan, R., 1966. Neues Jahrb. Geol. Palaontol., Monatsh., 1966(9): 550-553. Gerwin, R.A., 1968. Rev. Mod. Phys., 40: 652-658. Gessner, F.B., 1973. J. Fluid Mech., 58: 1-25. Gessner, F.B. and Jones, J.B., 1965. J. Fluid Mech.. 23: 689-713. Geuze, E.C.W.A., 1948. Proc. 2nd Int. Conf. Soil Mech. Found. Eng., 3: 125-130. Gevers, T.W., 1936. S. Afr. Geogr. J., 19: 61-79. Geze. B., 1965. La Speleologie Scientifique. Edition du Seuil, Paris. Ghibaudo, G., Mutti, E. and Rosell, J., 1974. Mem. SOC.Geol. Ital., 13: 497-537. Ghisler, M., 1970. Mineral. Deposita, 5 : 233-236. Gibb, F.G.F., 1968. J. Petrol., 9: 41 1-443. Gibilaro, K.G. and Rowe, P.N., 1974. Chem. Eng. Sci., 29: 1403-1412. Gibson, I.L., 1970. Contrib. Mineral. Petrol., 28: 89-1 1 I .

587 Gibson, I.L. and Tazieff, H., 1967. Nature (London), 215: 1473-1474. Giedt, W.H.. 1949. Trans. ASME, 71: 375-381. Gienapp, H., 1973. Senckenbergiana Marit., 5: 135-151. Gietelink, G., 1973. Leidse Geol. Meded., 49: 125-144. Gifford, F.A., 1953. Mon. Weather Rev., 81: 179-192. Gilbert, G.K., 1885. Rep. U.S. Geol. Surv., pp. 75- 123. Gilbert, G.K., 1905. Bull. Geogr. SOC.Am., 17: 317-320. Gilbert, G.K., 1914. U S . Geol. Surv., Prof. Pap., 86. Gilbert, P.A., 1976. Case histories of liquefaction failures. U.S. Army Waterw. Exp. Stn., Vicksburg, Misc. Pap., No. S-76-4. Gill, D., 1972. Spec. Publ. Trans. Inst. Br. Geogr., No. 4: 123-138. Gill, M.A., 1972. J. Hydraul. Div. ASCE, 98(HY9): 158771602, Gill, W.D., 1957. Proc. Geol. SOC.London, No. 1552: 105. Gill, W.D., 1979. Spec. Pap. Geol. Surv. Ireland, No. 4. Gill, W.D. and Kuenen, P.H., 1958. Q. J. Geol. SOC.London, 113: 441-457. Gillott, J.E., 1968. Clay in Engineering Geology. Elsevier, Amsterdam. Gilpin, R.R., Hirata, T. and Cheng, K.C., 1980. J. Fluid Mech.. 99: 619-640. Ginoux, J.J., 1965. Effects of Mach number on streamwise vortices in laminar reattaching flows. Von Karman Inst. Fluid Dyn., Rhode-Saint-Genese, Belgium, Tech. Note, No. 26. Ginoux, J.J., 1967. Z. Flugwiss., 15: 302-305. Ginoux, J.J., 1969. Von K a r m h Inst. Fluid Dyn., Rhode-Saint-Genese, Belgium, Tech. Note, No. 53. Ginoux, J.J., 1971. A I M J., 9: 759-760. Gitterman, M. and Steinberg, V., 1980. Phys. Fluids, 23: 2154-2160. Gizejewski, J., 1978. Bull. Acad. Sci. Pol., Ser. Sci. Terre, 26: 2 1-27, Gjessing, J., 1965. Nor. Geogr. Tidsskr., 20: 1-37. Gjessing, J., 1967. Geogr. Ann., A49: 178-187. Gjevik, B. and Rded, L.P., 1976. Tellus, 28: 166-182. Glennie, E.A., 1963. Newslett. Cave Res. Group G.B., No. 87: p. 9. Glennie, K.W., 1970. Desert Sedimentary Environments. Elsevier, Amsterdam. Glennie, K.W., 1972. Bull. Am. SOC.Pet. Geol., 56: 1048-1071. Glew, J.R. and Ford, D.C., 1980. Earth Surf. Processes, 5: 25-36. Gliese, J., 1973. Meded. Rijks Geol. Dienst., N. S., 23: 9-23. Gluckert, G., 1973. Fennia, No. 120. Godard, K. and Richardson, J.F., 1968. Inst. Chem. Eng. Symp. Ser., No. 30: 126-135. Godard, K. and Richardson, J.F., 1969. Chem. Eng. Sci., 24: 663-670. Godfrey, J.D., 1954. J. Geol., 62: 378-387. Goguel, J., 1948. Introduction a I’Etude Mechanique des Deformations de I’Ecorce Terrestre. Mem. Sew. Carte Geol. Fr., Paris, 2nd ed., 530 pp. Gohren, H., 1971. Hamb. Kustenforsch., No. 19. Gold, H., Probstein, R.F. and Scullen, R.S., 1971. AIAA J., 9: 1904-1910. Goldie, H., 1973. Trans. Cave Res. Group G.B., 15: 175-190. Goldring, R., 1966. Nature (London), 210: 1248- 1249. Goldring, R., 1971. Mem. Geol. SOC.London, No. 5. Goldring, R. and Bridges, P., 1973. J. Sediment. Petrol., 43: 736-747. Goldring, R. and Curnow, C.W., 1967. J. Geol. SOC.Aust., 14: 195-214. Goldring, R. and Langenstrassen, F., 1979. Spec. Pap. Palaeontol., 23: 81-97. Goldschmidt, V. and Eskinazi, S., 1966. Trans. ASME, E33: 735-747. Goldsmith, V., 1969. In: Coastal Environments of Northeastern Massachusetts and New Hampshire. Univ. Mass., Dep. Geol., Contrib., No. I-CRG: 28 1-289. Goldstein, M. and Gedney, R.T., 1971. NASA Tech. Mem.. No. TMX-67952. Goldstein, M. and Gedney, R.T., 1973. Q. J. Mech. Appl. Math., 26: 321-337.

588 Goldstein, R.J., Erikson, V.L., Olson, R.M. and Eckert, E.R.G., 1970. Trans. ASME, D92: 732-739. Goldstein, R.J., Sparrow, E.M. and Jones, D.C., 1973. Int. J. Heat Mass Transfer, 16: 1025-1035. Golia. C. and Evans, N.A., 1973.Exp. Mech., 13: 157-162. Gonzalez-Bonorino. G. and Middleton, G.V., 1976.J. Sediment. Petrol.. 46: 56-69. Good, M.C. and Joubert, P.N., 1968.J. Fluid Mech., 3 1 : 547-582. Goodchild. M.F. and Ford, D.C., 1971.J. Geol., 79: 52-62. Goode, A.D.T., 1976.J. Petrol., 17: 546-558. Goodman, R.E. and Appuhn, R.A., 1966.Geol. SOC.Am. Bull., 77: 1315-1326. Goodman, R.A. and Seed, H.B., 1966.J. Soil Mech. Found. Div. ASCE, 92(SM2): 125-146. Gordon, R.B., 1972.Physics of the Earth. Holt, Rhinehart and Winston, New York, N.Y. Goreau, T.F., 1959. Ecology, 40: 67-90. Gorsline, D.S., 1966.Mar. Geol., 4: 187-206. Gortler, H., 1940a.Nachr. Gess. Wiss. Gottingen. Math. Phys. KI., (2)l: 1-26. Gortler, H.. 1940b.Z. Angew. Math. Mech., 20: 138-147. Gortler, H., 1941.Z. Angew. Math. Mech., 21: 250-252. Gortler, H.. 1955.In: H. Gortler and W. Tollmien (Editors), 50 Jahre Grenzschichtforschung. Vieweg, Braunschweig, pp. 304-3 14. Gortler, H. and Witting, H., 1958. In: H. Gortler (Editor), Boundary Layer Research. Springer, Berlin, pp. I 10- 126. Gorycki, M.A., 1973a.Geol. SOC.Am. Bull., 84: 175-186. Gorycki, M.A., 1973b.J. Geol., 81 : 109- 1 17. Gottlieb, L., 1974. Tech. Univ. Den., Inst. Hydrodyn. Hydraul. Eng., Prog. Rep., No. 33: 3-13. Gottlieb, L., 1976.Tech. Univ. Den., Inst. Hydrodyn. Hydraul. Eng., Ser. Pap., No. 11: 79 pp. Goudie. AS., 1969. Geogr. J., 135: 404-406. Goudie. AS., 1970.S. Afr. Geogr. J., 52: 93-101. Goudie, AS., Allchin, B. and Hegde, K.T.M., 1973.Geogr. J., 139: 243-257. Grace, J.R., 1970.Can. J. Chem. Eng.. 48: 30-33. Gradowczyk, M.H., Maggiolo, O.J. and Folguera, H.C., 1968.J. Hydraul. Res., 6: 289-326. Gradzinski, R., 1970. Palaeontol. Pol., No. 21: 147-229. Gradzinski, R. and Jerzykiewicz, T., 1974.Palaeontol. Pol., No. 30: 11 1-146. Gradzinski, R., Gagol, J. and Slaczka, A,, 1979.Acta Geol. Pol., 29: 151-175. Graetz, L., 1885.Ann. Phys. Chem., 25: 337-357. Graham, A., 1934. Philos. Trans. R. Soc.London, Ser A, 232: 285-296. Graham, R.W. and Deissler, R.G., 1967.Trans. ASME, C89: 371-372. Grange, L.I., 1937. Bull. N.Z. Geol. Surv., N. S., No. 37. Grant, A.P., 1948.Proc. N.Z. Inst. Civ. Eng., 34: 231-279. Grant, A.P., 1950. Proc. N.Z. Inst. Civ. Eng., 36: 269-301. Grant, US.,1948.J. Mar. Res., 7: 655-660. Grant-Mackie, J.A. and Lowry, D.C., 1964.Sedimentology, 3: 296-3 17. Gravenor, C.P., 1953.Am. J. Sci.. 251: 674-681. Gravenor, C.P.. 1974.J. Glaciol., 13: 45-54. Gravenor, C.P. and Meneley, W.A., 1958.Am. J. Sci., 256: 715-728. Gray, M.J., 1981.Scott. J. Geol., 17: 39-47. Greely, R., Iversen, J.D., Pollack, J.D., Udovich, N. and White, B., 1974. Proc. R. SOC. London, Ser. A, 341:331-360. Greenberg, S.A., Jarnutowski, R. and Chang, T.N., 1965.J. Colloid Sci., 20: 20-43. Greensmith, J.T., 1956.J. Sediment. Petrol., 26: 343-355. Greensmith, J.T., 1957.Trans. Edinburgh Geol. SOC., 17: 54-59. Greensmith, J.T., 1965.J. Sediment. Petrol., 35: 223-242.

589 Greensmith, J.T. and Tucker, E.V., 1966. Proc. Geol. Assoc., 77: 329-346. Greensmith, J.T., Rawson, P.F. and Shalaby, S.E., 1980. Proc. Yorks. Geol. SOC., 42: 525-533. Greenspan, D., 1973. J. Fluid Mech., 57: 167-176. Greenspan, H.P., 1968. The Theory of Rotating Fluids. Cambridge University Press, Cambridge. Greenwald, G.F., 1972. AIAA J., 10: 349-350. Greenwood, B. and Davidson-Amott, R.G.D., 1972. Can. J. Earth Sci., 9: 679-688. Greenwood, B. and Davidson-Arnott, R.G.D., 1975. In: J. Hails and A. Carr (Editors), Nearshore Sediment Dynamics and Sedimentation. Wiley, London, pp. 123- 150. Greenwood, B. and Davidson-Amott, R.G.D., 1979. Can. J. Earth Sci., 16: 312-332. Greenwood, B. and Mittler, P.R., 1979. Mar. Geol., 32: 191-203. Gregory, M.R., 1969. N.Z. J. Geol. Geophys., 12: 248-282. Gregory, N. and Walker, W.S., 1951. Rep. Mem. Aeronaut. Res. Comm. (Counc.), No. 2779. Gregory, N., Stuart, J.T. and Walker, W.S., 1955. Philos. Trans. R. SOC.London, Ser. A, 248: 155- 199. Gripp, K., 1961. Z. Geomorphol., 5: 24-36. Gripp, K., 1963. Z. Geomorphol.. 7: 326-331. Gripp, K., 1968. Die Kiiste, 16: 76-117. Gripp, K. and Martens, L., 1963. Wenn die Natur im Sande Spielt. Verlag der Gesellschaft der Freunde des vaterlbdischen Schul- und Erziehungswesens, Hamburg. Groba, E., 1959. Acta Hydrophys., 5: 163-200. Grove, A.S., Shair, F.H., Petersen, E.E. and Acrivos, A., 1964. J. Fluid Mech., 19: 60-80. Grove, A.T., 1960. Geogr. J., 126: 18-31. Grove, A.T., 1969. Geogr. J., 135: 191-212. Grove, A.T. and Pullan, R.A., 1963. In: H.C. Howell and F. Bourliere (Editors), African Ecology and Human Evolution. Publ. Anthrop. Viking Fund, No. 36: 230-245. Grove, A.T. and Warren, A., 1968. Geogr. J., 134: 194-208. Grumbt, E., 1966. Ber. Dtsch. Ges. Geol. Wiss., A l l : 217-234. Guest, J.E., 1969. Geol. SOC.Am. Bull., 80: 337-362. Guilcher, A., 1949. Bull. SOC.Geol. Fr., (5)19: 15-29. Guilcher, A., 1953. Ann. Geogr., 62: 161-179. Guilcher, A., 1956. Ann. Inst. Oceanogr., Monaco, 33: 65-136. Guilcher, A., 1957. Tijdskr. K. Ned. Aardrijksk. Genoot., 74: 26-269. Guilcher, A., 1958a. Coastal and Submarine Morphology. Methuen, London. Guilcher, A., 1958b. Scott. Geogr. Mag., 74: 137-149. Gurel, S., Ward, S.G. and Whitmore, R.L., 1955. Br. J. Appl. Phys., 6: 83-87. Guth, E. and Simha, R., 1936. Kolloidzeitschrift, 74: 266-275. Gutsche, H., 1961. Mitt. Franzius Inst., 20: 74-21 1. Guy, H.P., Simons,D.B. and Richardson, E.V., 1966. U.S. Geol. Surv., Prof. Pap., 462-1. Guza, R.T. and Bowen, A.J., 1975. J. Geophys. Res., 80: 4529-4534. Guza, R.T. and Bowen, A.J., 1976. J. Mar. Res., 34: 269-293. Guza, R.T. and Bowen, A.J., 1981. J. Geophys. Res., 86: 4125-4132. Guza, R.T. and Davis, R.E., 1974. J. Geophys. Res., 79: 1285-1291. Guza, R.T. and Inman, D.L., 1975. J. Geophys. Res., 80, 2997-301 1. Gwyn, J.E., 1969. AIChE J, 15: 35-38. Hack, J.T., 1941. Geogr. Rev., 3 1 : 240-263. Hack, J.T., 1965. U.S.Geol. Surv., Prof. Pap., 504-B. Hackett, J.E. and Cox, D.K., 1970. J. Fluid Mech., 43: 77-96. Haczewski, G., 1976. Acta Geol. Pol., 26: 331-353. Hadding, A., 1931. Geol. For. Stockholm Forh., 53: 378-393. Hagerdorn, H., 1968. Erdkunde, 22: 257-269.

590 Hagerdorn, H., 1971. Z. Geomorphol., SI 1 : 1-25 1. Hagyard, T. and Sacerdote, A.M., 1966. Ind. Eng. Chem. Fund., 5: 500-508. Hahn. M., 1969. AIAA J.. 7: 1092-1098. Hikanson, L., 1973. Nordic Hydrol., 4: 119- 128. Hdbich, I.W., 1964. Trans. Proc. Geol. SOC.S. Afr., 67: 95-109. Hall, B.A., 1973. Geol. SOC.Am., Abstr. Progr., 5: 648. Hall, C.C. and Crumley, P., 1952. J. Appl. Chem., Suppl. Issue I. 2: 47-55. Hall, J., 1843. Geology of New York, part IV. Geology of the Fourth District, Carol1 and Cook, Albany, N.Y. Hallanger, N.L., Herd, G.R., Shortley, G. and Stearman, R.L., 1962. J. Atmos. Sci., 19: 99- 106. Halliday, W.R. and Anderson, C.H., 1970. Stud. Speleol., 2: 53-59. Hallier, U.W., 1976. Z. Geomorphol., 20: 108-120. Halprin, R.W., 1965. AIAA J., 3: 357-359. Hama, F.R., 1968. AIAA J., 6: 212-219. Hamblin, A.P. and Walker, R.G., 1979. Can. J. Earth Sci., 16: 1673-1690. Hamielec, A.E. and Raal, J.D., 1969. Phys. Fluids, 12: 1 1- 17. Hamilton, D.. Channon, R.D., Griffiths, E.C. and Sommerville, J.H., 1974. Mem. Inst. Geol. Bassin Aquitaine, No. 7: 259-265. Hamilton, E.L.. 1967. J. Geophys. Res., 72: 4189-4213. Hamilton, W. and Krinsley, D., 1967. Geol. SOC.Am. Bull., 78: 783-800. Hammerlin, G., 1955a. J. Ration. Mech. Anal., 4: 279-321. Hammerlin, G., 1955b. In: H. Gortler and W. Tollmien (Editors), 50 Jahre Grenzschichtforschung. Vieweg, Braunschweig, pp. 3 15-327. Han, T. and Patel, V.C., 1979. J. Fluid Mech., 92: 643-657. Hancock, R.T., 1937. Trans. Inst. Min. Eng., 94: 114-121. Hands, E.B., 1976. U.S. Coastal Eng. Res. Cent., Tech. Rep., No. 76-1. Handy, R.L., 1972. Geol. SOC.Am. Bull., 83: 475-480. Hanesian, D. and Rankell, A,, 1968. Ind. Eng. Chem. Fund., 7: 452-458. Hanlon, J., 1972. New Sci., 54: 732-734. Hanna, S.R.. 1969. J. Appl. Meteorol., 8: 874-883. Hanratty, T.J., 1956. J. AIChE, 2: 359-362. Hanratty, T.J., 1981. Annu. Rev. Fluid Mech., 13: 231-252. Hanratty, T.J. and Bandukwala, A., 1957. AIChE J., 3: 293-296. Hansen, D., 1970. Deep-sea Res., 17: 495-511. Hansen, E., 1965. Yearb. Carnegie Inst. Wash., 65: 387-405. Hansen, E., 1967. Tech. Univ. Den., Coastal Eng. Lab., Basic Res. Prog. Rep., No. 13: 9-13. Hansen, W.R., 1965. U.S. Geol. Surv., Prof. Pap., 542-A. Hhtzschel. W., 1935a. Senckenbergiana, 17: 167- 177. Hantzschel, W., 1935b. Natur Volk, 65: 461-465. Hantzschel, W., 1936. Senckenbergiana, 18: 3 16-356. Hhtzschel, W., 1938. Senckenbergiana, 20: 1-42. Hhtzschel, W., 1939. Natur Volk, 69: 40-48. Hantzschel, W. and Reineck, H.-E., 1968. Mitt. Geol. Staatsinst. Hamburg, 37: 5-39. Happel, J., 1957. J. Appl. Phys., 28: 1288-1292. Happel, J., 1958. AIChE J., 4: 197-201. Happel, J. and Brenner, H., 1965. Low Reynolds Number Hydrodynamics. Prentice-Hall, Englewood Cliffs, N.J. Harding, J. and Binding, A.A., 1978. Meteorol. Mag., 107: 164-181. Harms, J.C., 1965. Geol. SOC.Am. Bull., 76: 981-1002. Harms, J.C. and Fahnestock, R.K., 1965. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation. SOC.Econ. Paleontol. Mineral., Spec. Publ., 12: 84-1 15.

59 1 Harms, J.C., MacKenzie, D.B. and McCubbin, D.G., 1963. J. Geol., 71: 566-580. Harms, J.C., MacKenzie, D.B. and McCubbin, D.G., 1965. Wyo. Geol. Assoc. Guideb., 19th Field Conf. 1965, pp. 113-130. Harrington, H.J., 1971. Bull. Am. Assoc. Pet. Geol., 5 5 : 1344-1347. Harris, C.C., 1959a. Nature (London), 183: 530-53 I . Harris, C.C., 1959b. Nature (London), 184: 716. Harris, C.C., Somasundaran, P. and Jensen, R.R., 1975. Powder Technol., 1 1 : 75-84. Harris, C.R., 1974. J. Sediment. Petrol., 44: 1024-1028. Harris, G.P. and Lott, J.N.A., 1973. Limnol. Oceanogr., 18: 584-589. Harris, I.McK., 1974. Res. Pap. Geol. Surv. Can., 74-30: 97-101. Harris, I.McK. and Jollymore, P.G., 1974. Can. J. Earth Sci., 11: 43-52. Harrison, D., 1974. Sci. Progr. Oxford, 61: 191-217. Harrison, D., Davidson, J.F. and de Kock, J.W., 1961. Trans. Inst. Chem. Eng., 29: 202-21 1. Harrison, S.C., 1972. The sediments and sedimentary processes of the Holocene tidal flat complex, Delmarva Peninsula, Virginia. La. State Univ., Baton Rouge, Coastal Stud. Inst., Tech. Rep., No. 112. Harrison, S.S., 1970. Geol. SOC.Am. Bull., 81: 3407-3410. Harrison, W., 1969. Mar. Geol., 7: 529-551. Harrison, W., 1970. Prog. Geogr., 2: 207-235. Hartwell, A.D., 1970. Hydrography and Holocene sedimentation of the Merrimack River Estuary, Massachusetts. Univ. Mass., Dep. Geol., Contrib. No. 5-CRG. Harvey, A.M., 1975. Am. J. Sci.. 275: 470-478. Harvey, L.D.D., 1980. J. Sediment. Petrol., 50: 787-792. Harwood, C.F., 1977. Powder Technol., 16: 51-57. Hassett, N.J., 1961. Br. Chem. Eng.. 6: 777-780. Hatschek, E., 1910. Kolloidzeitschrift, 7: 301. Hattin, D.E., 1958. J. Glaciol., 3: 315-319. Haugen, R.L. and Dhanak, A.M., 1966. Trans. ASME, E33: 641-646. Hauser, E.A. and Le Beau, D.S., 1939. Kolloidzeitschrift, 86: 105-107. Haussling, H.J., 1977. J. Atmos. Sci., 34: 589-602. Havelock, T.H., 1908. Proc. R. SOC.London, Ser. A, 81: 38-51. Hawkes, D.D., 1962. Nature (London), 196: 128- 130. Hawksley, P.G.W., 1951. Some Aspects of Fluid Flow. Arnold, London. Hawthorne, W.R., 1954a. Proc. R. SOC.London, Ser. A, 206: 374-387. Hawthorne, W.R., 1954b. J. Aeronaut. Sci., 21: 588-606. Hay, J.S., 1955. Q. J. R. Meteorol. SOC.,81: 307-319. Hayakawa, N. and Unny, T.E., 1974. Phys. Fluids, 17: 879-882. Hayashi, T., 1960. Trans. J. Jpn. Geol. Geogr.. 3 1 : 1 - 17. Hayashi, T., 1966. Trans. J. Jpn. Geol. Geogr., 37: 1-20. Hayashi, T., 1974. Symposium on River Mechanics, Int. Assoc. Hydraul. Res.. Bangkok, 1 ; 667-668. Hayashi, T. and Iwai, T., 1959. Trans. J. Jpn. Geol. Geogr., 30: 195-200. Hayes, M.O., 1967. Rep. Invest. Bur. Econ. Geol. Univ. Tex., No. 61. Hayes, M.O., 1972. In: R.E. Meyer (Editor), Waves on Beaches and Resulting Sediment Transport. Academic Press, New York, N.Y., pp. 297-356. Hayes, M.O. and Boothroyd, J.C., 1969. Storms as modifying agents in the coastal environment. In: Coastal Environments of northeastern Massachusetts and New Hampshire. Univ. Mass., Dep. Geol., Contrib. No. 1-CRG, pp. 290-315. Hayes, M.O., Owens, E.H., Hubbard, D.K. and Abele, R.W., 1973. In: D.R. Coates (Editor), Coastal Geomorphology. State University of New York, Binghamton, N.Y., pp. 11-41. Heaps, N.S., 1965. Proc. Roy. SOC. London, Ser. A, 257: 351-383. Heaps, N.S., 1967. Annu. Rev. Oceanogr. Mar. Biol., 5 : 11-47.

592 Hedman, E.R., 1970. Water-Supply Irrig. Pap., Wash., 1999-E. Heezen, B.C., 1956. Sci. Am., 195: 36-41. Heezen, B.C. and Ewing, M., 1952. Am. J. Sci., 250: 849-873. Heezen, B.C. and Ewing, M., 1955. Bull. Am. Assoc. Pet. Geol., 39: 2506-2514. Heezen, B.C. and Hollister, C., 1964. Mar. Geol.. 1 : 141- 174. Heezen, B.C. and Hollister, C., 1971. The Face of the Deep. Oxford University Press, New York, N.Y. Heezen, B.C. and Johnson, G.L., 1963. Dtsch. Hydrogr. Z., 16: 269-272. Heezen, B.C. and Johnson, G.L., 1969. Bull. Inst. Oceanogr., Monaco, No. 1382. Heezen, B.C. and Rawson, M., 1977. Mar. Geol., 23: 173-196. Heezen, B.C., Ericson, D.B. and Ewing, M., 1954. Deep-sea Res., 1: 193-202. Heezen, B.C., Ewing, M. and Johnson, G.L.. 1966a. Deep-sea Res., 13: 381-41 1. Heezen, B.C.. Hollister, C.D. and Ruddiman, W.F., 1966b. Science, 152: 502-508. Heiken, G.H., 1971. J. Geophys. Res., 76: 5615-5626. Heikkinen, 0. and Tikkanen, M., 1979. Fennia, 157: 1-12. Heim, A,, 1878. Jahrb. Schweiz. Alp. Klub, 13: 421-433. Heimlich, R.A. and Manzer, G.K., 1973. Earth Planet. Sci. Lett., 17: 350-356. HellstrBm, B., 1941. Ingenioervetenskapsakad.,Handl., No. 158. Hellstram, B., 1953. Trans. Am. Geophys. Union, 34: 194-198. Helwig, J., 1970. J. Geol., 78: 172-187. Henderson, E.P. and Perry, S.H., 1958. Proc. U.S. Natl. Mus., 107: 339-403. Henderson, F.M., 1966. Open Channel Flow. Macmillan, New York, N.Y. Henderson, S.M.K., 1935. Trans. R. SOC.Edinburgh, (II)58: 487-509. Hendry, H.E., 1973. J. Sediment. Petrol., 43: 125-136. Hendry, H.E., 1978. Can. J. Earth Sci., 15: 1472-1488. Hendry, H.E. and Stauffer. M.R., 1975. J. Sediment. Petrol., 45: 932-943. Hendry, H.E. and Stauffer, M.R., 1977. Geol. Soc. Am. Bull., 88: 809-812. Henkel, D.J., 1970. Geotechnique, 20: 75-80. Henry, H.R., Laursen, E.M., Adams, J.R.. Hwang, L.J. and Chen, C.L., 1964. Pressure and shear distribution on schematic dunes. Natl. Sci. Found. Wash., Final Rep. NSF G-7409. Hensen, W., 1943. Bautechnik, 21: 79-96. Hensen, W., 1957. Mitt. Franzius Inst., 10: 86-1 19. Herbich, J.B., 1970. Proc. 12th Conf. Coastal Eng., 2: 1281-1300. Heron, S.D., Judd, J.B. and Johnson, H.S., 1971. Geol. SOC.Am. Bull., 82: 1801- I8 10. Herringe, R.A., 1976. Chem. Eng. J., 11: 89-99. Hervieu, J., 1968. Contribution a I’etude de l’alluvionnement en milieux tropical. Off. Rech. Sci. Tech. Outre-Mer, Mem., No. 24. Heskestad, G., 1966. Trans. ASME, D88: 539-549. Hesp, P.A., 1981. J. Sediment. Petrol., 51: 101-112. Hess, H.H., 1960. Mem. Geol. Soc. Am., No. 80. Hesse, R., 1965. Z. Dtsch. Geol. Ges., 116: 403-426. Hesse, R., 1974. Geol. SOC.Am. Bull., 85: 859-870. Hesse, R. and Reading, H.G., 1978. Spec. Publ. Int. Assoc. Sedimentol., 2: 241-257. Hetsroni, G. and Sokolov, M., 1971. Trans. ASME, E38: 315-327. Heu, H.A., 1967. J. Hydraul. Div. ASCE, 93(HY5): 149-165. Hewes, L.I., 1948. Am. J. Sci., 246: 138-149. Hey, R.D. and Thorne, C.R., 1975. Area, 7: 191-195. Hickin, E.J., 1974. Am. J. Sci., 274: 414-442. Hickin, E.J., 1978. Can. J. Earth Sci., 15: 1833-1849. Hickin, E.J. and Nanson, G.C., 1975. Geol. SOC.Am. Bull., 86: 487-494. Hide, R., 1955. Proc. Camb. Philos. SOC.Math. Phys. Sci., 51: 279-301. Hidy, G.M., Plate, E.J. and Lilly, D.K., 1966. J. Fluid Mech., 26: 651-687.

593 Hieu, H.M. and Hebrard, P., 1977. J. Hydraul. Res., 15: 1-18. Higginbotham, G.H., Oliver, D.R. and Ward, D.R., 1958. Br. J. Appl. Phys., 9: 372-377. Higgins, C.G., 1956. Bull. Geol. SOC.Am., 67: 671-674. Higgins, C.G., 1957. J. Glaciol., 3: 11-12. Higgins, G.M., Baig, S. and Brinkman, R., 1974. Z. Geomorphol., 18: 272-290. High, L.R. and Picard, M.D., 1968. Wyo. Contrib. Geol.. 7: 1-6. Hill, A.R., 1971. Geogr. Ann., A53: 14-31. Hill, A.R., 1973a. Ann. Assoc. Am. Geogr., 63: 226-240. Hill, A.R., 1973b. Z. Geomorphol., 17: 428-442. Hill, H.M., 1966. J. Hydraul. Div. ASCE, 92(HY2): 127-143. Hill, H.M., Srinivasan, V.S. and Unny, T.E., 1969. J. Hydraul. Div. ASCE, 95(HY5): 1545- 1558. Hill, R.D., 1966. J. Trop. Geogr., 23: 19-27. Hills, E.S., 1941. Proc. R. SOC.Victoria, 53: 167-191. Hine, A.C., 1979. Sedimentology, 26: 333-351. Hino, M., 1974. Coastal Eng. Jpn., 17: 23-37. Hino, M. and Hayashi, T., 1973. Coastal Eng. Jpn., 16: 55-60. Hinze, J.O., 1959. Turbulence. McGraw-Hill, New York. Hinze, J.O., 1973. Appl. Sci. Res., 28: 453-465. Hinze, J.O. and Van der Hegge Zijnen, J., 1949. Appl. Sci. Res., 1: 435-461. Hirayama, J. and Nakajima, T., 1977. Sedimentology, 24: 747-779. Hirschfelder, J.O., Parker, D.B., Kramish, A., Smith, R.C. and Glasstone, S., '1950. The Effects of Atomic Weapons. McGraw-Hill, New York, N.Y. Hiscott, R.N., 1979. J. Sediment. Petrol., 49: 1-10. Hjorth, P., 1975. Studies on the nature of local scour. Lund Inst. Technol., Univ. Lund, Dep. Water Resour. Eng., Bull. Ser. A, No. 46. Hjulstrom, F., 1935. Bull. Geol. Inst. Univ. Uppsala. 25: 221-527. Hjulstrdm, F., 1942. Geogr. Ann., B24: 45-97. Hjulstrom, F., 1949. Geogr. Ann., 31 (Glaciers and Climate): 83-89. Hjulstrom, F., 1957. K. Vetensk. SOC.Arsb., 1957: 1-42. Hobbs, B.E., Means, W.D. and Williams, P.F., 1976. An Outline of Structural Geology. Wiley, New York, N.Y. Hobbs, W.H., 1917. Ann. Assoc. Am. Geogr., 7: 25-60. Hobday, D.K., 1973. Trans. Geol. SOC.S. Afr., 76: 309-318. Hobday, D.K., 1974. Nor. Geol. Unders., No. 303: 39-56. Hobday, D.K. and Horne, J.C., 1977. Sediment. Geol., 18: 97-122. Hobday, D.K. and Mathew, D., 1975. In: M.L. Broussard (Editor), Deltas. Models for Exploration. Houston Geological Society, Houston, Tex., pp:457-469. Hobday, D.K. and Reading, H.G., 1972. J. Sediment. Petrol., 42: 318-324. Hobday, D.K. and Von Bruun, V., 1979. Palaeogeogr. Palaeoclimatol. Palaeoeocol., 28: 169- 184. Hobday, D.K., Brauteseth, S.V. and Mathew, D., 1971. Petros, 3: 51-56. Hodgson, J.W., 1970. AIAA J., 8: 2291-2293. Hoedemaker, P.J., 1973. Scr. Geol. Univ. Utrecht, No. 19: 207 pp. Hoerner, S.F., 1950. J. Aeronaut. Sci., 17: 622-628. Hoffman, P., 1967. Science, 157: 1177-1 180. Hoffman, P., 1973. Philos. Trans. R. SOC.London, Ser. A, 273: 547-581. Hoffman, P., 1974. Bull. Am. Assoc. Pet. Geol., 58: 856-867. Hoffmann, R.L., 1972. Trans. SOC.Rheol., 16: 155-173. Hoffmann, R.L., 1974. J. Colloid Interface Sci., 46: 491-506. Hofmann, H.J., 1973. Earth-Sci. Rev., 9: 339-373. Hogg, N.G., 1973. J. Fluid Mech., 58: 517-537.

594 Holland, C.H., 1959. Geol. Mag., 96: 230-236. Holland, C.H., 1960. Bull. Geol. SOC.Am., 71: 633-634. Hollister, C.D. and Heezen, B.C., 1972. Stud. Phys. Oceanogr., 2: 37-66. Hollister, C.D., Flood. R.D., Johnson, D.A., Lonsdale. P. and Southard, J.B., 1974. Geology, 2: 395-404. Hollister, C.D., Southard, J.B., Flood, R.D. and Lonsdale, P.F., 1976. In: I.N. McCave (Editor), The Benthic Boundary Layer. Plenum Press, New York, N.Y., 183-204. Hollister, C.D., Flood. R. and McCave, I.N., 1978. Oceanus, 21: 5-13. Holm, D.A., 1960. Science, 132: 1369-1379. Holmes, P.S., 1974. N.Z. Eng., 29: 313-320. Holtedahl, H., 1965. In: W.F. Whittard and R. Bradshaw (Editors), Submarine Geology and Geophysics. Buttenvorths, London, pp. 107- 140. Holtedahl, H., 1967. Geogr. Ann., A49: 188-203. Homewood, P., 1976. Eclog. Geol. Helv., 69: 281-295. Horn-Ma, M. and Sonu, C.J., 1963. Proc. 7th Conf. Coastal Eng., pp. 248-278. Honji, H., 1975. J. Fluid Mech., 69: 229-240. Hooke, J.M., 1977. In: K.J. Gregory (Editor), River Channel Changes. Wiley, London, pp. 265-280. Hooke, R.LeB., 1974. Shear-stress and sediment distribution in a meander bend. Univ. Uppsala, UNGI Rep. No. 30. Hooke, R.LeB., 1975. J. Geol., 83: 543-565. Hopkins, E.J., Keating. S.J. and Bandettini, A., 1960. NASA Tech. Note, No. TN D-328. Hopley, D., 1974a. Aust. Geogr., 12: 462-468. Hopley. D.. 1974b. Aust. Geogr. Stud., 12: 90-106. Hoppe, G., 1951. Geogr. Ann., 33: 157-165. Hoppe, G. and Schytt, V., 1953. Geogr. Ann., 35: 105-115. Horikawa, K. and Shen. H.W., 1960. Tech. Mem. U.S. Beach Erosion Bd., No. 119. Home, G.S., 1970. Geol. SOC.Am. Bull., 81 : 1767- 1788. H0rnung;H.G. and Joubert, P.N., 1963. J. Fluid Mech., 15: 368-384. Horsfield, H.T., 1934. J. SOC.Chem. Ind., 53: T107-TI15. Houboult, J.J.H.C., 1968. Geol. Mijnbouw, 47: 245-273. Houghton, G., 1963. Proc. R. Soc. London, Ser. A, 272: 33-43. Houtz, R.E. and Wellman, H.W., 1962. Geol. Mag., 99: 57-62. Hovey, E.O., 1909. Bull. Geol. SOC.Am., 20: 409-416. Howard, A.D., 1963. Bull. Natl. Speleol. Soc.,25: 45-65. Howard. A.D., 1977. Geol. SOC.Am. Bull., 88: 853-856. Howard, J.C., 1971. Bull. Am. Assoc. Pet. Geol., 5 5 : 495-513. Howard, J.D.. 1966a. Bull. Utah Geol. Mineral. Surv., No. 80: 23-33. Howard, J.D., 1966b. Bull. Utah Geol. Mineral. Surv., No. 80: 35-53. Howard, J.D., 1972. In: J.K. Rigby and W.K. Hamblin (Editors), Recognition of Ancient Sedimentary Environments. SOC.Econ. Paleontol. Mineral., Spec. Publ., 16: 2 15-225. Howard, J.D. and Lohrengel, C.F., 1969. J. Sediment. Petrol., 39: 1032-1039. Howard, J.D. and Reineck, H.-E., 1981. Bull. Am. Assoc. Pet. Geol., 65: 807-830. Howard, J.D., Elders, C.A. and Heinbokel, J.F., 1975. Senckenbergiana Marit., 7: 181-203. Howarth, L., 1938. Proc. Cambridge Philos. SOC.,Math. Phys. Sci., 34: 335-344. Hoyt, J.H., 1962. J. Sediment. Petrol., 32: 309-31 I . Hoyt, J.H., 1967. Sedimentology, 8: 229-238. Hoyt, J.H. and Henry, V.J., 1964. Sedimentology, 3: 44-51. Hoyt, J.H. and Henry, V.J., 1971. Geol. SOC.Am. Bull., 82: 59-66. Hsu, K.J., 1959. Am. J. Sci., 257: 529-536. Hsu, N.T. and Sage, B.H., 1957. AIChE J., 3: 405-410. Hsu, S.A., 1973. Proc. 13th Conf. Coastal Eng., 3: 2531-2541.

595 Hubert, C., Lajoie, J. and Leonard, M.A., 1970. Geol. Assoc. Can., Spec. Pap., No. 7: 103- 125. Hubert, J.F., 1966a. J. Sediment. Petrol., 36: 677-699. Hubert, J.F., 1966b. Nature (London), 21 I : 614-615. Hubert, J.F., 1967. J. Sediment. Petrol., 37: 885-907. Hubert, J.F., 1972. Proc. 24th Int. Geol. Congr. Sect. 6, pp. 107-1 14. Hubert, J.F., Butera, J.G. and Rice, R.F., 1972. Geol. SOC.Am. Bull., 83: 1649-1670. Hubert, J.F., Reed, A.A. and Carey, P.J., 1976. Am. J. Sci., 276: 1183- 1207. Hudleston, P.J., 1973. Tectonophysics, 16: 189-214. Hudleston, P.J. and Stephansson, O., 1973. Tectonophysics, 17: 299-321. Hudson, G.H., 1910. Bull. N.Y. State Mus., 140: 161-196. Hughes, D.J., 1977. In: K.J. Gregory (Editor), River Channel Changes. Wiley, London, pp. 193-205. Hughes, P., 1956. Q. J. R. Meteorol. SOC.,82: 494-502. Hughes, T.H. and Reid, W.H., 1965. J. Fluid Mech., 23: 727-747. Hughes, T.J., 1976. J. Glaciol., 16: 41-69. Hughes, T. M’K., 1884. Q. J. Geol. SOC.London, 40: 178-185. Hume, W.F., 1925. Geology of Egypt, vol. 1. Government Press, Cairo. Humphrey, J.A.C., Taylor, A.M.K. and Whitelaw. J.H., 1977. J. Fluid Mech., 83: 509-527. Humphreys, M. and Friedman, G.M., 1975. In: M.L. Broussard (Editor), Deltas. Models for Exploration. Houston Geological Society, Houston, Tex., pp. 369-379. Humphries, D.W., 1966. Sedimentology, 6: 135- 152. Hung, T.K. and Macagno, E.O., 1966. Houille Blanche, 21: 391-400. Hunsche, U., 1978. Geol. Jahrb., E12: 53-107. Hunt, J.C.R., 1971. Philos. Trans. R. SOC.London, Ser. A, 269: 457-467. Hunt, J.C.R., Abell, C.J., Peterka, J.A. and Woo, H., 1978. J. Fluid Mech., 86: 179-200. Hunt, J.N. and Johns, B., 1963. Tellus, 15: 343-351. Hunt, R.E., Swift, D.J.P. and Palmer, H., 1977. Geol. SOC.Am. Bull., 88: 299-31 I. Hunter, R.E., 1969. J. Sediment. Petrol., 39: 1573- 1578. Hunter, R.E., 1973. J. Sediment. Petrol., 43: 1125-1127. Hunter, R.E., 1976. Bull. Am. Assoc. Pet. Geol., 60: 683-684. Hunter, R.E., 1977. Sedimentology, 24: 361-387. Hunter, R.E., 1980a. Sediment. Geol., 27: 241-262. Hunter, R.E., 1980b. J. Sediment. Petrol., 50: 263-266. Hunter, R.E. and Hill, G.W., 1980. Remote Sensing of Environment, 10: 115-134. Hunter, R.E., Watson, R.L., Hill, G.W. and Dickinson, K.A., 1972. In: R.F. Travis, R.N. Tench and W.D. Hodgson (Editors), Padre Island, National Sea Shore Field Guide. Gulf Coast Association of Geological Societies, pp. 1-27. Hunter, R.E., Clifton, H.E. and Phillips, R.L., 1979. J. Sediment. Petrol., 49: 711-726. Huntley, D.A. and Bowen, A.J., 1973. Nature (London), 243: 160-161. Huntley, D.A. and Bowen, A.J., 1974. J. Geol. Soc. London, 131: 69-81. Huntley, D.A. and Bowen, A.J., 1975. In: J. Hails and A. Carr (Editors), Nearshore Sediment Dynamics and Sedimentation. Wiley, London, pp. 69- 109. Hurd, A.C. and Peters, A.R., 1970. Trans. ASME, D92: 908-914. Hurst, J.M., 1979a. Geol. J., 14: 15-40. Hurst, J.M., 1979b. Palaeogeogr. Palaeoclimatol. Palaeoecol., 27: 189-246. Husar, R.B. and Sparrow, E.M., 1968. Int. J. Heat Mass Transfer, 1 1 : 1206-1208. Hussain, A.K.M.F. and Clark, A.R., 1981. J. Fluid Mech., 104: 263-294. Huthnance, J.M., 1973. Estuarine Coastal Mar. Sci., 1 : 89-99. Ichiye, T., 1967. Phys. Fluids, SIO: 270-277. Idrac, M.P., 1920. C. R. Acad. Sci., 171: 42-44. Idriss, I.M. and Seed, H.B., 1967. J. Soil Mech. Found. Div. ASCE. 93(SM3): 61-82.

596 Ikeda, S., 1974. Proc. Jpn. SOC.Civ. Eng., No. 229: 55-65. Ikeda, S., 1975. Proc. 16th Conf. Inst. Assoc. Hydraul. Res., 2: 105-1 12. Ikeda, S., 1981. J. Hydraul. Div. ASCE, 107(HY4): 389-406. Illing, L.V., 1954. Bull. Am. SOC.Pet. Geol., 38: 1-95. Imbrie, J. and Buchanan, H., 1965. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation. SOC.Econ. Paleontol. Mineral., Spec. Publ., 12: 149-172. Immamura, G., 1935. Jpn. J. Geol. Geogr., 12: 33-38. Inger, G.R., 1969. AIAA J., 7: 763-764. Inger, G.R., 1972. A I M J., 10: 1641-1646. Inger, G.R. and Williams, E.P., 1972. AIAA J., 10: 636-642. Ingle, J.C., 1966. The Movement of Beach Sand. Elsevier, Amsterdam. Inglis, C.C., 1947. Meanders and their bearing on river training. Inst. Civ. Eng., Marit. Waterw. Eng. Div., Sess. 1946-47, 54 pp. Inglis, C.C., 1949. Res. Publ. Cent. Water. Powr. Irrig. Navig. Res. Stn., Poona, 13(I): 143-157. Inglis, C.C. and Kestner, F.J.T., 1958. Proc. Inst. Civ. Eng., 1 1 : 435-466. Ingraham, R.L.. 1954. Proc. Phys. SOC.,London, Ser. B, 67: 748-752. Inman, D.L., 1953. Tech. Mem., U.S.Beach Erosion Board., No. 39. Inman, D.L. and Filloux, J., 1960. J. Geol., 68: 225-231. Inman, D.L.. Ewing, G.C. and Corliss. J.B., 1966. Geol. SOC.Am. Bull., 77: 787-802. Inman, D.L., Tait, R.J. and Nordstrom, C.E., 1971. J. Geophys. Res., 76: 3493-3514. Institute of Geological Sciences, 1981. Annual Report for 1979. I.G.S., London. Ippen, A.T. and Drinker, P.A., 1962. J. Hydraul. Div. ASCE. 88(HY5): 143-179. Irvine, T.N., 1965. In: G.V. Middleton (Editor), Primary Sedimentary structures and their Hydrodynamic Interpretation. SOC.Econ. Paleontol. Mineral., Spec. Publ., 12: 220-232. Irving, E., 1958. Philos. Trans. R. SOC.London, Ser. A, 250: 100-110. Jackson, E.D., 1971. Fortschr. Mineral., 48: 128- 174. Jackson, R., 1963a. Trans. Inst. Chem. Eng., 41: 13-28. Jackson, R., 1963b. Trans. Inst. Chem. Eng., 41: 22-28. Jackson, R., 1971. In: J.F. Davidson and D. Harrison (Editors), Fluidization. Academic Press, London, 847 pp. Jackson, R.G., 1975. Geol. SOC.Am. Bull., 86: 151 1-1522. Jackson, R.G., 1976. J. Sediment. Petrol., 46: 579-594. Jacobi, R. and Mrozowski, C.L., 1979. Mar. Geol., 29: MI-M9. Jacobi, R.D., Rabinowitz, P.D. and Embley, R.W., 1975. Mar. Geol., 19: M61-M67. Jacobs, S.J., 1974. J. Phys. Oceanogr., 4: 392-399. Jacobs, W., 1938. 1ng.-Arch., 9: 343-355. Jaggar, T., 1908. Bull. Mus. Comp. Zool., Harv. UNv., Geol. Ser., 8(6): 285-305. Jago, C.F., 1980. Sediment. Geol., 26: 21-49. Jahn, A. and Klappa, M., 1968. J. Glaciol., 7: 299-3 12. Jahns, R.H., 1947. Water-Supply Irrig. Pap., Wash., 996. Jain, S.C., 1981. J. Hydraul. Div. ASCE, 107(HY5): 611-626. Jain, S.C. and Fischer, E.E., 1980. J. Hydraul. Div. ASCE, 106(HYll): 1827-1842. Jakobsen, B., 1962. Geogr. Tidsskr., 61: 1 19- 135. Jakucs, L., 1977. Morphogenetics of Karst Regions. Hilger, Bristol. James, A.V.G., 1920. J. Geol., 28: 458-470. James, D.M.D., 1975. Geol. Mag., 1 12: 195-204. Jardine, W.G., 1965. Scott. J. Geol., 1: 221-224. Jardine, W.G., 1973. Scott. J. Geol., 9: 213-218. Jarocki, W., 1949. Proc. 3rd Congr. Inst. Assoc. Hydraul. Res., Pap. 11-2, 17 pp. Jarrett, E.L. and Sweeney, T.L., 1967. AIChE J., 13: 797-800.

597 Jawarowski, K., 1971. Acta Geol. Pol., 21: 519-571. Jefferson, M.S.W., 1899. J. Geol., 7: 237-246. Jefferson, M.S.W., 1902. Natl. Geogr. Mag., 13: 373-384. Jeffrey, D.J. and Acrivos, A., 1976. AIChE J., 22: 417-432. Jeffreys, H., 1926. Philos. Mag. (7)2: 833-844. Jeffreys, H., 1928. Proc. R. Soc. London, Ser. A, 118: 195-208. Jenkins, O.P., 1925a. Am. J. Sci., 10: 234-246. Jenkins, O.P., 1925b. Eng. Min. J.-Press, 120: 12. Jennings, J.N., 1967. In: J.N. Jennings and J.A. Mabbutt (Editors), Land Form Studies in Australia and New Guinea. Cambridge University Press, Cambridge, pp. 256-292. Jennings, J.N., 1968. Aust. Geogr., 10: 408-409. Jennings, J.N., 1971. Karst. Massachusetts Institute of Technology Press, Cambridge, Mass. Jennings, J.N. and Sweeting, M.M., 1963. Bonn. Geogr. Abh.. 32: 1-60. Jensen, M., 1954. Shelter Effect. Danish Technical Press, Copenhagen. Jimenez, J., 1980. J. Fluid Mech., 96: 447-460, Jindrich, V., 1969. J. Sediment. Petrol., 39: 531-553. Johannesen, N.H., 1955. Philos. Mag., (7)46: 3 1-39. Johansson, C.-E., 1960. Svensk Geogr. Arsb., 36: 13-144. Johansson, C.-E., 1963. Geogr. Ann., 45: 85-112. Johansson, C.-E., 1965. Geol. For. Stockholm Forh., 87: 3-61. Johansson, C.-E., 1975. Svensk Geogr. Arsb., 51: 87-99. Johansson, C.-E., 1976. Geogr. Ann., A58: 201-300. Johns, B. and Ali, M.A., 1980. Q. J. R. Meteorol. Soc., 106: 1-18. Johnson, D.A. and Bunce, E.T., 1977. Abyssal sediment waves in the Amirante Passage, western Indian Ocean. Woods Hole Oceanogr. Inst., Woods Hole, Mass., Tech. Rep., No. 77-7. Johnson, D.A. and Damuth, J.E., 1979. Mar. Geol., 33: 1-44. Johnson, D.A. and Johnson, T.C., 1970. Deep-sea Res., 17: 157-169. Johnson, D.A. and Lonsdale, P.F., 1976. Deep-sea Res., 23: 429-440. Johnson, D.W., 1910. Bull. Geol. SOC.Am., 21: 599-624. Johnson, D.W., 1919. Shore Processes and Shoreline Development. Wiley, New York, N.Y. Johnson, E., 1950. Trans. Inst. Gas Eng., 100: 302-386. Johnson, E.W., 1981. Geol. J., 16: 93-110. Johnson, G.L., Vogt, P.R. and Schneider. E.D., 1971. Dtsch. Hydrogr. Z.. 24: 49-73. Johnson, H.D., 1977a. Sedimentology, 24: 245-270. Johnson, H.D., 1977b. Sedimentology, 24: 389-41 1. Johnson, H.D., 1978. Nor. Geol. Tidsskr., 58: 175-190. Johnson, J.W. and Rice, E.K., 1952. Trans. Am. Geophys. Union, 33: 845-854. Johnson, K.G. and Friedman, G.M., 1969. J. Sediment. Petrol., 39: 451-485. Johnson, R.B., 1967. U.S. Geol. Surv., Prof. Pap., 575-C: 177-183. Johnson, V,E., 1963. J. Hydraul. Div. ASCE, 89(HY3): 25 1-275. Johnson, G . , 1956. Glacialmorfologiska Studier i S a r a Sverige. University of Lund, Geographical Institute. Johnsson, G., 1980. Svensk. Geogr. Arsb., 56: 13-22. Johnston, J.P., 1960a. Trans. ASME, D82: 233-248. Johnston, J.P., 1960b. Trans. ASME, D82: 622-628. Jones, B.G., 1969. N.Z.J. Geol. Geophys., 12: 215-217. Jones, B.G., 1972a. J. Geol. SOC.Aust., 19: 229-249. Jones, B.G., 1972b. J. Sediment. Petrol., 42: 935-940. Jones, G.P., 1961. Rec. Geol. Surv. Nigeria, 1959: 5-14. Jones, G.P., 1962. J. Sediment. Petrol., 32: 231-239. Jones, O.T., 1937. Q. J. Geol. SOC.London, 93: 241-282.

598 Jones, O.T., 1940. Q. J. Geol. SOC.London, 95: 335-382. Jones, R.J., 1965. Proc. Geol. Assoc., 76: 421-433. Jonker, R.K., 1972. Leidse Geol. Meded., 48: 275-379. Jopling, A.V., 1961. U.S. Geol. Surv., Prof. Pap., 424-D: 15-17. Jopling, A.V., 1962. Proc. 1st Natl. Shallow Water Res. Conf., pp. 291-295. Jopling, A.V., 1963. Sedimentology, 2: 1 15- 12 1. Jopling, A.V., 1964a. J. Geophys. Res., 69: 3403-3418. Jopling, A.V., 1964b. J. Sediment. Petrol., 34: 165-172. Jopling, A.V., 1965a. J. Sediment. Petrol., 35: 777-791. Jopling, A.V., 1965b. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation. Soc. Econ. Paleontol. Mineral., Spec. Publ., 12: 53-65. Jopling, A.V., 1966a. J. Geophys. Res., 71: 1123-1133. Jopling, A.V., 1966b. J. Sediment. Petrol., 36: 5-49. Jopling, A.V., 1966~.J. Sediment. Petrol.. 36: 880-887. Jopling, A.V., 1967. J. Geol.. 75: 287-305. Jordan, G.F., 1962. Science, 136: 839-848. Joseph, D.D., 1976a. Stability of Fluid Motions, vol. 1. Springer, Berlin. Joseph, D.D., 1976b. Stability of Fluid Motions, vol. 2. Springer, Berlin. Jottrand, R.,'1954. Chem. Eng. Sci., 3: 12-16. Juma, A.K.A. and Richardson, J.F., 1979. Chem. Eng. Sci., 34: 137-143. Jiingst, H., 1934. Geol. Rundsch., 25: 321-325. Jutson, J.T., 1939. J. Geomorphol., 2: 237-250. Jux. U. and Strauch, F., 1965. Fortschr. Geol. Rheinl. Westfalen, 9: 51-86. Kabelac, O.W., 1957. ASCE J. Waterw., Harbors Coastal Eng., 83 (WWI), Paper 1208. Kada, H. and Hanratty, T.J., 1960. AIChE J., 6: 624-630. Kadar, L., 1934. Geogr. J., 83: 470-478. Kadiu, L., 1966. Foldrajzi Ert., 15: 413-448. Kader, B.A. and Yaglom, A.M., 1972. Int. J. Heat Mass Transfer, 15: 2329-2351. Kader, B.A. and Yaglom, A.M., 1977. Int. J. Heat Mass Transfer, 20: 345-357. Kahawita, R.A. and Meroney, R.N., 1974. Phys. Fluids, 17: 1661-1666. Kaiser, K., 1971. Koln. Geogr. Arb. Supplementb. Kaiser, pp. 65-71. Kamoi, A. and Tanaka, H., 1972. In: D.J. Cockrell (Editor), Fluid Dynamic Measurements, Vol. 1. Leicester University Press, Leicester, pp. 217-227. Kana, T.W., 1977. ASCE J. Waterw., Harbors Coastal Eng., 103(WW4): 505-518. Kaplan, W.. 1958. Advanced Calculus. Addison-Wesley, Reading, Mass. Kapur, A.D. and Reynolds, A.J., 1967. J. Hydraul. Res., 5: 1-14. Karashima, K., Kubota, H. and Sato, H., 1968. Univ. Tokyo, Inst. Space Aeronaut. Sci.. Rep. NO. 425: 157-191. Karcz, I.. 1966. J. Geophys. Res., 71 : 3 109-3 1 12. Karcz, I., 1967. J. Geol., 75: 113-121. Karcz, I., 1968. J. Sediment. Petrol., 38: IOOO-1012. Karcz, I., 1971. J. Geol., 79: 234-240. Karcz, I., 1972. Sediment. Geol., 7: 161-182. Karcz, I., 1974. In: M. Morisawa (Editor), Fluvial Geomorphology. State University of New York, Bingharnton, N.Y., pp. 149-173. Karcz, I. and Goldberg, M., 1967. J. Sediment. Petrol., 37: 1244-1245. Karcz. I., Enos, P. and Langville, G., 1974. Geology, 2: 289-290. Karl, H.A., 1976. J. Sediment. Petrol., 46: 124-131. Karl, H.A., 1980. Mar. Geol., 34: M9-MI8. Katz, B., Gerard, R. and Costin, M., 1965. J. Geophys. Res., 70: 5505-5513. Kawakarni, F. and Asada, A., 1966. Soil Found., 6: 18-23. Kawamura, R., 1964. Study of sand movement by wind. Univ. Calif., Berkeley Hydraul. Eng. Lab., Tech. Rep. HEL-2-8.

599 Kay, J.M., 1963. Fluid Mechanics and Heat Transfer, 2nd ed. Cambridge University Press, Cambridge. Kaye, C.A., 1959. U.S. Geol. Sum., Prof. Pap. 317-B: 49-140. Kaye, C.A. and Power, W.R., 1954. Am. J. Sci., 252: 309-310. Kays, W.M., 1966. Convective Heat and Mass Transfer. McGraw-Hill, New York, N.Y. Kearsey, H.A., 1962. Trans. Inst. Chem. Eng., 50: 149-145. Keeley, J.R., 1977. Can. J. Earth Sci., 14: 1906-1915. Keffer, J.F. and Baines, W.D., 1963. J. Fluid Mech., 15: 481-496. Keller, E.A., 1971. Geol. SOC.Am. Bull., 82: 279-280. Keller, E.A., 1972. Geol. SOC.Am. Bull., 83: 1531- 1536. Keller, E.A. and Melhorn, W.N., 1974. In: M. Morisawa (Editor), Fluvial Geomorphology. State University of New York, Binghamton, N.Y., pp. 253-283. Keller, E.A. and Melhorn, W.N., 1978. Geol. SOC.Am. Bull., 89: 723-730. Keller, W.D. and Foley, R., 1949. J. Sediment. Petrol., 19: 78-81. Kelletat, D., 1974. Z. Geomorphol., S19: 1-161. Kelling, G. and Mullin, P.R., 1975. Sediment. Geol., 13: 161-190. Kelling, G. and Stanley, D.J., 1972. In: D.J. Stanley (Editor), The Mediterranean Sea. Dowden, Hutchinson and Ross, Stroudsburg, Penn., pp. 489-5 19. Kelling, G. and Walton, E.K., 1957. Geol. Mag., 94: 481-490. Kelling, G. and Walton, E.K., 1961. J. Geol., 69: 224-225. Kelling, G. and Whitaker, J.H.McD., 1970. J. Geol., 78: 371-374. Kelling, G. and Williams, B.P.J., 1966. J. Sediment. Petrol., 36: 927-939. Kemper, E., 1968. Geol. Jahrb., 86: 49-106. Kendall, C.G.St.C. and Skipwith, Sir P.A. d’E., 1969. Geol. SOC.Am. Bull., 80: 865-892. Kenn, M.J., 1966. Civ. Eng. Publ. Works Rev., November 1966. Kenn, M.J., 1968. Tech. Note Constr. Ind. Res. Inf. Serv., No. 1. Kenn, M.J. and Minton, P., 1968. Nature (London), 217: 633-634. Kennedy, J.F., 1963. J. Fluid Mech., 16: 521-544. Kennedy, J.F., 1966. J. Hydraul. Div. ASCE, 92(HY3): 51-64. Kennedy, J.F., 1969. Annu. Rev. Fluid Mech., 1: 147-168. Kennedy, W.J. and Juignet, P., 1974. Sedimentology, 21: 1-42. Kent, P.E., 1966. J. Geol., 74: 79-83. Kenyon, N.H., 1970a. Mar. Geol., 9: 25-39. Kenyon, N.H., 1970b. Geol. Mag., 107: 389-394. Kenyon, N.H. and Belderson, R.H., 1973. Sediment. Geol., 9: 77-99. Kenyon, N.H. and Stride, A.H., 1970. Sedimentology, 14: 159-173. Kepferle, R.C., 1977. U.S. Geol. Surv., Prof. Pap., 1007. Kersey, D.G. and Hsu, K.J., 1976. Sedimentology, 23: 761-789. Kesel, R.H., Dunne, K.C., McDonald, R.C. and Allison, K.R., 1974. Geology, 2: 461-464. Kestin, J. and Wood, R.T., 1970. J. Fluid Mech., 44: 461-479. Kestner, F.J.T., 1962. Geogr. J., 457-471. Kestner, F.J.T., 1975. Geogr. J., 141: 388-414. Keulegan, G.H., 1948. Tech. Rep. U.S. Beach Erosion Board, No. 3: 42 pp. Keulegan, G.H., 1951. J. Res. Natl. Bur. Stand., 46: 358-381. Keulegan, G.H., 1952. Rep. Natl. Bur. Stand., No. 1835. Keulegan, G.H., 1953. J. Res. Natl. Bur. Stand., 50: 99-109. Keutner, C., 1932. Bautechnik, 10: 161-170. Kezdi, A., 1979. Soil Physics. Selected Topics. Elsevier, Amsterdam. Khanna, S.D., 1970. J. Hydraul. Div. ASCE, 96(HY10): 2029-2040. Kidson, C. and Manton, M.M.M., 1973. Estuarine Coastal Mar. Sci., 1: 271-283. Kiersch, G.S., 1950. Bull. Am. Assoc. Pet. Geol., 34: 923-942. Kikkawa, H., Ikeda, S., Ohkawa, J.H. and Kawamura, Y., 1973. Proc. Jpn. S&. Civ. Eng., No. 219: 107-1 14.

600 Kimura, R.. Tsu, H. and Yagashima, A,, 1971. J. Meteorol. SOC.Jpn., 49: 249-260. Kindle, E.M.. 1916. Geol. Mag., (6)3: 542-547. Kindle, E.M., 1917a. Bull. Geol. Surv. Can., No. 25. Kindle, E.M.. 1917b. Bull. Geol. SOC.Am., 28: 323-334. Kindle, E.M., 1917~.J. Geol., 25: 135-144. Kindle, E.M., 1918. J. Geol., 26: 341-360. Kindle, E.M., 1923. J. Geol., 31: 138-145. Kindle, E.M., 1926. Proc. Trans. R. Soc. Can., (3)20: 71-75. Kindle, E.M., 1936a. J. Geol., 44: 861-869. Kindle, E.M., 1936b. J. Sediment. Petrol., 6: 16-22. Kindle, E.M. and Cole, L.H.. 1938. Geol. Meere Binnengewasser, 2: 278-283. King, C.A.M., 1951. J. Sediment. Petrol., 21: 131-140. King, C.A.M., 1953. Publ. Inst. Br. Geogr., No. 19: 13-23. King, C.A.M., 1959. Beaches and Coasts. Arnold, London. King, C.A.M., 1965. Ir. Geogr., 5: 46-50. King, C.A.M., 1972. Beaches and Coasts. Arnold, London, 2nd ed. King, C.A.M., 1973. In: D.R. Coates (Editor), Coastal Geomorphology. State University of New York, Binghamton, N.Y., pp. 73-98. King. C.A.M. and Barnes, F.A., 1964. Z. Geomorphol., 8: 105-126. King, C.A.M. and Williams, W.W., 1949. Geogr. J., 113: 70-85. King, D., 1956. Trans. R. Soc.S.Aust., 79: 931103. King, D., 1960. Trans. R. SOC.S.Aust., 83: 99-109. King, L.C., 1936. J. Geol., 44: 201-213. King, L.H., 1976. Can. J. Earth Sci., 13: 1082-1092. King, P.B., 1927. J. Geol., 35: 631-638. Kingma, J.T., 1958. N.Z.J. Geol. Geophys., 1: 1-30. Kinoshita, R., 1957. Trans. Jpn. SOC.Civ. Eng., No. 42: 1-21. Kirk, L.G., 1952. J. Sediment. Petrol., 22: 173-181. Kirk, R.M., 1969. N. Z. Geogr., 25: 23-35. Kirk, R.M., 1975. Geogr. Ann., A57: 117-133. Kirkby, M.J., 1972. Area, 4: 284-288. Kirkby, M.J. and Statham, I., 1975. J. Geol., 83: 349-362. Kishida, H., 1966. Soil Found., 6: 71-88. Kistler, A.L. and Tan, F.C., 1967. Phys. Fluids, SIO: 165-173. Kiya, M. and Arie, M., 1972. J. Fluid Mech., 56: 201-219. Klaer, W., 1956. Petermanns Geogr. Mitt., Erganzh., No. 261: 146 pp. Klein, G. deV., 1965. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation. SOC.Econ. Paleontol. Mineral., Spec. Publ., 12: 173- 191. Klein, G. deV., 1970. J. Sediment. Petrol., 40: 1095-1127. Klein, G. deV., DeMelo, U. and Favera, J.C.D., 1972. Geol. Soc. Am. Bull., 83: 1469-1492. Kleist. J.R., 1974. Geology, 2: 501-504. Klemm, W. and Smekal, A,, 1941. Naturwissenschaften, 29: 688-689. Klimek, K., 1972. Pol. Acad. Sci., Geogr. Ser., No. 94. Kline, S.J., 1959. Trans. ASME, D81: 305-319. Knapp, R.T., 1938. Trans. Am. Geophys. Union, 19: 501-505. Knapp, R.T., 1943. Proc. 2nd Iowa Conf. Hydraul., pp. 289-306. Knight, D.W., 1975. Proc. 16th Congr. Int. Assoc. Hydraul. Res., 2: 243-250. Knight, R.J. and Dalrymple, R.W., 1975. In: R.N. Ginsburg (Editor), Tidal Deposits. Springer, New York, N.Y.. 47-55. Knight, S.H., 1929. Univ. Wyo. Publ. Sci., Geol., 1: 1-82. Knighton, A.D., 1972a. Geol. Soc. Am. Bull., 83: 3813-3822. Knighton, A.D., 1972b. Geol. Soc. Am. Bull., 83: 201-204.

60 1 Knighton, A.D., 1974. Geol. SOC.Am. Bull., 85: 1069-1076. Knox, G.J., 1976. Geol. Mag., 1 13: 341-348. Knudsen, J.G. and Katz, D.L., 1958. Fluid Dynamics and Heat Transfer. McGraw-Hill, New York, N.Y. Koch, A.J. and McLean, H., 1975. Geol. SOC.Am. Bull., 86: 529-541. Koerfer, L.E. and Schwarzbach, M., 1971. Z. Geomorphol., 15: 348-349. Kolar, V., 1965. Int. J. Heat Mass Transfer, 8: 639-653. Kolla, V., Moore, D.G. and Curray, J.R., 1976. Mar. Geol., 21: 255-270. Kolla, V., Eittreim, S., Sullivan, L., Kostecki, J.A. and Burckle, L.H., 1980. Mar. Geol., 34: 171-206. Komar, P.D., 1969. J. Geophys. Res., 74: 4544-4558. Komar, P.D., 1971. Geol. SOC.Am. Bull., 82: 2643-2650. Komar, P.D., 1972a. Geol. SOC.Am. Bull., 83: 973-988. Komar, P.D., 1972b. Geol. SOC.Am. Bull., 83: 3443-3448. Komar, P.D., 1973. Geol. SOC.Am. Bull., 84: 3593-3600. Komar, P.D., 1976a. Beach Processes and Sedimentation. Prentice-Hall, Englewood Cliffs, N.J. Komar, P.D., 1976b. Geol. SOC.Am. Bull., 87: 1336-1342. Komura, S. and Shen, H.W., 1970. Proc. Jpn. SOC.Civ. Eng.. No. 184: 129-141. Kondrat’yev, N.Y., 1969. Sov. Hydrol. Select. Pap. 1968, No. 4: 309-335. Konrad, T.G., 1968. Proc. Int. Conf. Cloud Phys. Toronto, pp. 539-543. Koo, J.-K. and James, D.F., 1973. J. Fluid Mech., 60: 513-538. Koppejan, A.W., Van Wamelen, B.M. and Weinberg, L.J.H., 1948. Proc. 2nd Int. Conf. Soil Mech. Found. Eng., 5: 89-96. Koster, E.H., 1977. Prog. Abstr. 1st Int. Symp. on Fluvial Sedimentation, Calgary, Alta., p. 17. Kotlyakov, V.M., 1966. The Snow Cover of the Antarctic and its Role in the Present-day Glaciation of the Continent. Israel Program for Scientific Translations, Jerusalem. Kotsovinos, N.E., 1976. J. Fluid Mech., 77: 305-31 I . Koutaniemi, L., 1979. Fennia, 157(1): 13-73. Koutitas, C. and O’Connor, B., 1980. J. Hydraul. Div. ASCE, 106(HYI I): 1843-1865. Koutsoftas, D., 1978. J. Geotech. Eng. Div. ASCE, 104(GT5): 609-620. Kovacs, A., 1972. Oil Gas J., October 23, 1972: 92-106. Krall, K.M. and Sparrow, E.M., 1966. Trans. ASME, C88: 131-136. Kramers, H. and Kreyger, P.J., 1956. Chem. Eng. Sci., 6: 42-48. Kramers, H., Westermann, M.D., De Groot, J.H. and Dupont, F.A.A., 1962. Proc. 3rd Congr. Europ. Fed. Chem. Eng., 114. Kraus, E.B., 1967a. Phys. Fluids, S10: 294-297. Kraus, E.B., 1967b. Adv. Geophys., 12: 213-256. Krause, D.C., White, W.C., Piper, D.J.W. and Heezen, B.C., 1970. Geol. SOC. Am. Bull., 81: 21 53-2160. Kreiger, M.H., 1979. U.S. Geol. Surv.,Prof. Pap., 1 104. Kreith, F., 1965. Principles of Heat Transfer. International Textbook Co., Scranton, Pa., 2nd ed. Kreith, F., Taylor, J.H. and Chong, J.P., 1959. Trans. ASME, C81: 95-105. Krejci-Graf, K., 1932. Senckenbergiana Lethaea, 14: 19-39. Krinov, E.L., 1960. Principles of Meteoritics. Pergamon, Oxford. Krinsley, D., 1970. A geomorphological and paleoclimatological study of the playas of Iran. U.S. Geol. Surv., Rep., No. AFCRL-70-0503. Krinsley, D.H. and Doornkamp, J.C., 1973. Atlas of Quartz Sand Surface Textures. Cambridge University Press, Cambridge. Krishnamurti, R., 1970a. J. Fluid Mech., 42: 295-307.

602 Krishnamurti, R., 1970b. J. Fluid Mech., 42: 309-320. Krishnamurti, R., 1973. J. Fluid Mech., 60: 285-303. Krishnarnurti, R., 1975a. J. Atmos. Sci., 32: 1353-1363. Krishnamurti, R., 1975b. J. Atmos. Sci., 32: 1364-1372. Krishnamurti, R., 1975c. J. Atmos. Sci., 32: 1373-1383. Krishnappan, B.G. and Lau. Y.L., 1977. J. Hydraul. Res., 15: 351-371. Krizek, R.J., 1971a. Trans. Soc. Rheol., 15: 433-489. Knzek. R.J., 1971b. Trans. Soc. Rheol., 15: 491-540. Kruit, C., Brouwer, J. and Ealey, P.. 1972. Nature (London), Phys. Sci., 240: 59-61. Kruit, C., Brouwer, J., Knox, G., Schollnberger, W. and Van Vliet, A,, 1975. Une excursion aux canes d’alluvions en eau profonde d’Lge Tertiaire pres de San Sebastian. Guide to Excursion 2-23, 9th Int. Congr. Sedimentology, Nice. Ksiazkiewicz, M., 1954. Ann. SOC.Geol. Pol., 22: 399-449. Ksiazkiewicz, M., 1958. Ann. SOC.Geol. Pol., 28: 123-150. Kuboi, R.. Murasawa, I. and Otake, T., 1972. J. Chem. SOC.Jpn., 5: 349-355. Kubota, T., 1960. ARS J., 30: 1164-1 169. Kiichemann, D., 1953. J. R. Aeronaut. SOC.,57: 683-699. Kiichemann, D. and Weber, J., 1965. Z. Angew. Math. Mech.. 45: 457-474. Kudrass, H.R., 1967. Ber. Naturf. Ges. Freiburg im Breisgau, 57: 203-206. Kuenen, P.H., 1937. Leidse Geol. Meded., 8: 327-335. Kuenen, P.H., 1938. Bull. Comm. Geol. Finl., No. 123: 11-28, Kuenen, P.H., 1948a. J. Geol., 56: 34-40. Kuenen, P.H., 1948b. Q. J. Geol. SOC.London, 104: 365-380. Kuenen. P.H., 1950. Proc. 18th Int. Geol. Congr., Part 8: 44-51. Kuenen, P.H., I95 la. In: J.L. Hough (Editor), Turbidity Currents. SOC.Econ. Paleontol. Mineral., Spec. Publ., 2: 14-33. Kuenen, P.H., 1951b. Geol. For. Stockholm Forh., 73: 69-84. Kuenen, P.H., 1952. Am. J. Sci., 250: 874-884. Kuenen, P.H., 1953a. Bull. Am. Assoc. Pet. Geol., 37: 1044-1066. Kuenen, P.H., 1953b. Verh. K. Ned. Akad. Wet., (1)20(3): 1-47. Kuenen, P.H., 1956. Geol. Mijnbouw, 18: 277-283. Kuenen, P.H., 1957. J. Geol., 65: 231-258. Kuenen, P.H., 1958. Trans. Geol. SOC.Glasgow, 23: 1-28. Kuenen, P.H., 1963. Natuurk. Voordrachten, N. S., No. 41: 83-91. Kuenen, P.H., 1965a. In: W.F. Whittard and R. Bradshaw (Editors), Submarine Geology and Geophysics. Buttenvorths, London, pp. 47-74. Kuenen. P.H., 1965b. Geol. Mijnbouw, 44: 22-36. Kuenen, P.H., 1966a. J. Geol., 74: 523-545. Kuenen, P.H., 1966b. Sedimentology, 7: 267-297. Kuenen, P.H., 1966~.Tectonophysics, 6: 143- 158. Kuenen, P.H., 1967. Sedimentology, 9: 203-243. Kuenen, P.H., 1968. J. Sediment. Petrol., 38: 817-831. Kuenen, P.H. and Carozzi, A., 1953. J. Geol., 61: 363-373. Kuenen, P.H. and Menard, H.W., 1952. J. Sediment. Petrol., 22: 83-96. Kuenen, P.H. and Miglionni, C.I., 1950. J. Geol., 58: 91-127. Kuenen, P.H. and Prentice, J.E., 1957. Geol. Mag., 97: 173-174. Kuenen, P.H. and Sanders, J.E., 1956. Am. J. Sci., 254: 649-671. Kues, B.S. and Siemers, C.T., 1977. J. Sediment. Petrol., 47: 844-848. Kuethe, A.M., 1958. J. Aeronaut. Sci., 25: 338-339. Kuettner, J.P., 1959. Tellus, 11: 267-294. Kuettner, J.P., 1967. Aeronaut. Rev., 42: 52-56, 109-1 12. Kuettner, J.P., 1971. Tellus. 23: 404-426.

603 Kuettner, J.P. and Soules, S.D., 1966. Bull. Am. Meteorol. SOC.,47: 364-370. Kuhn, W., 1932. Z. Phys. Chem., A161: 1-32. Kuhn, W. and Kuhn, H., 1945. Helv. Chim. Acta, 28: 97-127. Kiihn-Velten, H., 1955. Geol. Rundsch., 44: 1-25. Kukal, Z. and Al-Naqash, A., 1970. Z. Geomorphol., 14: 329-334. Kukuk, P., 1920. Gliickauf, 56: 805-810, 829-835. Kulemina, N.M., 1975. Sov. Hydrol.. Select. Pap., 1973 (6): 518-534. Kumar, N. and Sanders, J.E., 1976. J. Sediment. Petrol., 46: 145-162. Kunii, D. and Levenspiel, O., 1969. Fluidization Engineering. Wiley, New York, N.Y. Kuno, H., Ishikawa, T., Katsui, Y., Yagi, K.. Yamasaki, M. and Taneda, A., 1964. Trans. Jpn. J. Geol. Geogr., 35: 223-238. Kunz, R.G., 1971. Powder Technol., 4: 156-162. Kuo, H.L., 1963. Phys. Fluids, 6: 195-21 I . Kurzeme, M., 1970. In: Foundations on Interbedded Sands. Division of Applied Geomechanics C.S.I.R.O. and Western Australia Group of Australian Geomechanics Society, Perth, pp. 52-60. Kuzyk, W. and Chen, C.J., 1972. AIAA J., 10: 1505-1508. Kynch, G.J., 1952. Trans. Faraday SOC..48: 166-176. Kynch, G.J., 1954. Brit. J. Appl. Phys., Suppl. No. 3: S5-SIO. Kynch, G.J., 1956. Proc. R. SOC.,London, Ser. A, 237: 90-116. Lachenbruch, A.H., 1961. J. Geophys. Res., 66: 4273-4292. Lachenbruch, A.H., 1962. Geol. Soc. Am., Spec. Pap., No. 70. Lachenbruch, A.H., 1963. Contraction theory of ice-wedge polygons: a qualitative discussion. Nat. Acad. Sci., Natl. Res. Counc. Publ., No. 1287: 63-71. Laczay, LA., 1977. In: K.J. Gregory (Editor), River Channel Changes. Wiley, London, pp. 185- 192. Ladd, R.S., 1977. J. Geotech. Eng. Div. ASCE, 103(GT6): 535-547. Laganelli, A.L. and Nestler, D.E., 1969. AIAA J., 7: 1319-1325. Laird, M.G., 1972. N.Z. J. Geol. Geophys., 15: 372-393. Lajoie, J., 1972. J. Sediment. Petrol., 42: 584-586. Lamb, H., 1932. Hydrodynamics. Cambridge University Press, Cambridge, 6th ed. Lamb, J.P., 1967. Trans. ASME, D89: 633-640. Lamb, J.P. and Hood, G.G., 1972. Trans. ASME, C94: 87-94. Lambe, T.W. and Whitman, R.V., 1969. Soil Mechanics. Wiley, New York, N.Y. Lamont, A., 1938. Proc. R. Ir. Acad., B45: 1-32. Lamont, A., 1965. Scott. J. Sci., 1: 13-18. Lancaster, N., 1980. Z. Geomorphol., 24: 160-167. Lancaster, N., 1981. Palaeogeogr. Palaeoclimatol. Palaeoecol,, 33: 327-346. Land, L.S. and Hoyt, J.H., 1966. Sedimentology, 6: 191-207. Lane, E.W., 1955. Trans. ASCE, 120: 1234-1279. Lane, E.W., 1957. A study of the shape of channels formed by natural streams flowing in erodible materials. U S . Army Corps of Engineers, Omaha, Nebr. Lang, W.B., 1943. Science, 98: 583-584. Langbein, W.B., 1963. Bull. Int. Assoc. Sci. Hydrol., 8(3): 84-94. Langbein, W.B., 1964. U.S. Geol. Surv.,Prof. Pap., 501-B. Langbein, W.B. and Leopold, L.B., 1966. U.S. Geol. Surv., Prof. Pap., 422-H. Langerfeldt, J., 1935. Natur Volk, 65: 458-461. Langhaar, H.L., 1951. Proc. 1st Midwestern Conf. Fluid Dyn., pp. 278-296. Langmuir, I., 1938. Science, 87: 119-123. Lanteaume, M., Beaudoin, B. and Campredon, R., 1967. Figures sedimentaires du flysch “Grks d’Annot” du synclinal Peira Cava. Centre National Recherche Scientifique, Paris. Lapidus, L. and Elgin, J.C., 1957. AIChE J., 3: 63-68.

604 Lapierre, F., 1975. Philos. Trans. R. SOC.London, Ser. A, 279: 177-187. Larras, J., 1963. Ann. Ponts Chauss., 133: 41 1-424. Larsen, P.A., 1969. J. Boston SOC. Civ. Eng., 56: 45-67. Larsen, P.A., 1973. J. Hydraul. Div. ASCE, 99(HYI): 1 1 1 - 1 19. Larson, H.K., 1959. J. Aero/Space Sci., 26: 731-738. Larsonneur. C., 1975. In: 'R.N. Ginsburg (Editor), Tidal Deposits. Springer, Berlin, pp. 21-30. Larsson, K., 1975. Geol. For. Stockholm Forh., 97: 125-134. Lathrap, D.W., 1968. Am. Antiq., 33: 62-79. Lattman, L.H. and Olive, W.H., 1955. Bull. Am. Assoc. Pet. Geol., 39: 2084-2087. Lau, J. and Travis, B., 1973. J. Geophys. Res.. 78: 4489-4497. Lau, J.C. and Fisher, M.J., 1975. J. Fluid Mech., 67: 299-337. Laudermilk. J.D. and Woodford, A.O., 1932. Am. J. Sci., 23: 135-154. Laufer. J., 1951. NACA Rep. 1053. Laufer, J., 1954. NACA Rep. 1 174. Launder, B.E. and Ying. W.M., 1972. J. Fluid Mech., 54: 289-295. Laursen, E.M., 1963. J. Hydraul. Div. ASCE, 89(HY3): 93-118. Laursen, E.M. and Toch, A., 1953. Proc. Mnn. Int. Hydraul. Conv., pp. 123-131. Laursen, E.M. and Toch, A., 1956. Bull. Iowa Highw. Res. Board, No. 4. Laursen, E.M. and Toch, A., 1959. In: H. Rouse (Editor), Advanced Mechanics of Fluids. Wiley, New York, N.Y., pp. 359-406. Law, C.H., 1974. AIAA J., 12: 794-797. Lawn, C.J., 1969. Trans. ASME, C92: 532-536. Lawrence, L.R. and Beddow, J.K., 1969. Powder Technol., 2: 253-259. Lawson, A. and Hassett, N.J., 1967. In: A.A.H. Drinkenberg (Editor), Proceedings of the International Symposium on Fluidization, Eindhoven. Netherlands University Press, Amsterdam, pp. 113-122. Lawther? K.R. and Berglin, C.L.W., 1957. Rep. U.K. Atom. Energy Auth., AERE CE/R 2360. Le Gall, J. and Larsonneur, C., 1972. Rev. Geogr. Phys. Geol. Dyn., (2)14: 189-204. Le Mone, M.A., 1973. J. Atmos. Sci., 30: 1077-1091. Leatherman, S.P., 1979. Q. J. Eng. Geol., 12: 281-290. LeBlond, P.H. and Tang, C.L., 1974. J. Geophys. Res., 79: 81 1-816. Lee, C.A., 1981. J. Geol. Soc.,London, 138: 327-341. Lee, D.I., 1969. Trans. Soc. Rheol., 13: 272-288. Lee, K.L. and Albaisa, A., 1974. J. Geotech. Eng. Div. ASCE, 100(GT4): 387-406. Lee, K.L. and Focht, J.A., 1975. J. Geotech. Eng. Div. ASCE, IOI(GT1): 1-18. Lee, K.L. and Seed, H.B., 1967a. J. Soil Mech. Found. Div. ASCE, 93(SMl): 47-70. Lee, K.L. and Seed, H.B., 1967b. J. Soil Mech. Found. Div. ASCE, 93(SM5): 169-190. Leeder, M.R., 1973. Geol. Mag., 110: 265-276. Leeder, M.R. and Bridges, P.H., 1975. Nature (London), 253: 338-339. Legendre, R., 1956. La Recherche Aeronautique, No. 54: 3-8. Leibovich, S., 1976. J. Fluid Mech., 79: 715-743. Leibovich, S., 1977. J. Fluid Mech., 82: 561-581. Leibovich, S., 1980. J. Fluid Mech., 99: 715-724. Leibovich, S. and Radhakrishnan, K., 1977. J. Fluid Mech., 80: 481-507. Leibovich, S. and Ulrich, D., 1972. J. Geophys. Res., 77: 1683-1688. Leighly, J., 1948. Geogr. Rev., 38: 300-306. Leighly, J.B., 1932. Univ. Calif. Publ. Geogr., 6: 1-22. Leliavsky, S., 1955. An Introduction to Fluvial Hydraulics. Constable, London. Lemke, R.W., 1958. Am. J. Sci., 256: 270-284. Le Mone, M.A., 1973. J. Atmosph. Sci., 30: 1077-1091.

605 Lennon, G.W., 1963a. Proc. Inst. Civ. Eng., 25: 451-484. Lennon, G.W., 1963b. Q. J. R. Meteorol. Soc.,89: 381-394. Leopold, L.B., 1973. Geol. SOC.Am. Bull., 1845-1860. Leopold, L.B. and Langbein, W.B., 1962. U.S. Geol. Surv., Prof. Pap., 500-A. Leopold, L.B. and Langbein, W.B., 1966. Sci. Am., 214: 60-70. Leopold, L.B. and Maddock, J.T., 1953. U.S. Geol. Surv., Prof. Pap., 252. Leopold, L.B. and Miller, J.P., 1956. U.S. Geol. Surv., Prof. Pap., 282-A. Leopold, L.B. and Wolman, M.G., 1957. U.S. Geol. Surv., Prof. Pap., 282-B. Leopold, L.B. and Wolman, M.G., 1960. Bull. Geol. SOC.Am., 71: 769-794. Leopold, L.B., Bagnold, R.A:, Wolman. M.G. and Brush, L.M.. 1960. U.S. Geol. Surv., Prof. Pap., 282-D. Leopold, L.B., Wolman, M.G. and Miller, J.P.. 1964. Fluvial Processes in Geomorphology. Freeman, San Francisco, Calif. Lessen, M., Fox, J.A. and Zien, H.M., 1965. J. Fluid Mech., 23: 355-367. Lessen, M. and KO, S.-H., 1966. Phys. Fluids, 9: 1 179- 1183. Lettau, H., 1932. Ann. Hydrogr. Berlin, 60: 385. Leva, M., 1959. Fluidization. McGraw-Hill, New York, N.Y. Leva, M. and Wen, C.Y., 1971. In: J.F. Davidson and D. Harrison (Editors), Fluidization. Academic Press, London. Leva, M., Weintraub, M., Grummer, M., Pollchik, M. and Storch, H., 1951. Bull. U.S. Bur. Mines, No. 504. Levich, V.G., 1962. Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs, N.J. Lewin, J., 1972. Nature (London), Phys. Sci., 240: 116. Lewin, J., 1976. Geol. Soc.Am. Bull., 87: 281-285. Lewis, A.D., 1936. S. Afr. Geogr. J., 19: 33-49. Lewis, D.J., 1950. Proc. R. Soc.London, Ser. A, 202: 81-96. Lewis, D.W., 1973. J. Sediment. Petrol., 43: 1031-1045. Lewis, D.W., 1980. N.Z.J. Geol. Geophys., 23: 353-369. Lewis, D.W., Smale, D. and Van der Lingen, J., 1979. N. Z. J. Geol. Geophys., 22: 295-305. Lewis, E.W. and Bowerman, E.W., 1952. Chem. Eng. Prog., 48: 603-609. Lewis, J.B., 1969. Proc. Geol. Soc. London, No. 1655: 106-108. Lewis, J.S., 1971. Int. J. Heat Mass Transfer, 14: 325-329. Lewis, K.B., 1971. Sedimentology, 16: 97-1 10. Lewis, K.B., 1979. Mar. Geol., 3 1 : 32-43. Lewis, T.B. and Nielsen, L.E., 1968. Trans. Soc. Rheol., 12: 421-443. Lewis, W.K., Gillilan, E.R. and Bauer, W.C., 1949. Ind. Eng. Chem., 41 : 1104- 1 1 17. Ley, R.G., 1979. Z. Geomorphol., S32: 75-89. Li, R.M. and Shen, H.W., 1973. J. Hydraul. Div. ASCE, 99(HY5): 793-814. Liepmann, H.W. and Laufer, J., 1947. NACA Tech. Note 1257. Liggett, J.A., 1969a. J. Hydraul. Div. ASCE, 95(HY4): 1273- 1288. Liggett, J.A., 1969b. Proc. 13th Congr. Int. Assoc. Hydraul. Res., 3: 103-1 12. Liggett, J.R. and Hadjitheodorou, C., 1969. J. Hydraul. Div. ASCE, 95(HY2): 609-620. Liggett, J.A., Chiu, C.L. and Maiao, L.S., 1965. J. Hydraul. Div. ASCE, 91(HY6): 99-117. Lighthill, M.J., 1953. Proc. R. Soc.London, Ser. A, 217: 344-357. Lighthill, M.J., 1956. J. Fluid Mech., 1: 31-56. Lighthill, M.J., 1957. J. Fluid Mech., 2: 311-312. Lilly, D.K., 1966. J. Atmos. Sci., 23: 481-494. Lin, C.C., 1955. The Theory of Hydrodynamic Stability. Cambridge University Press, Cambridge. Lin, G.C.I. and Oxley, P.L.B., 1972. Proc. Inst. Mech. Eng., 186: 813-820. Lindner, H.G., 1930. Petermanns Geogr. Mitt., Ergbzh., No. 208. Lindsey, D.A., 1971. Palaeogeogr. Palaeoclimatol. Palaeoecol., 9: 7-25.

606 Lindstrom, M., 1960. Geol. For. Stockholm Forh., 82: 319-341. Linger, D.A., 1963. Highw. Res. Rec., No. 22. Linton, M. and Sutherland, K.L., 1960. Chem. Eng. Sci., 12: 214-229. Linton, M. and Sherwood, T.K., 1950. Chem. Eng. Prog., 46: 258-264. Lipfert. F. and Genovese, J., 1971. AIAA J., 9: 1330-1337. Lipman, P.W., 1967. Contrib. Mineral. Petrol., 16: 300-327. Lipman, P.W., Chnstiansen, R.L. and O’Connor. J.T., 1966. U.S. Geol. Surv., Prof. Pap., 524-F. Liu, H.K. and Perez, H.J., 1971. J. Hydraul. Div. ASCE, 97(HY7): 923-935. Liu, J.T.C., 1974. J. Fluid Mech., 62: 437-464. Liu, P.L. and Lennon, G.P., 1978. ASCE J. Waterw., Harbors Coastal Eng., 104(WW2): 175- 189. Ljungner, E., 1930. Bull. Geol. Inst. Univ. Uppsala, 21: 255-478. Lliboutry, L., 1964. Traite de Glaciologie, vol. 1. Masson, Pans. Lliboutry, L., 1965. Traite de Glaciologie. vol. 2. Masson, Pans. Lloyd, E.F.. 1972. N. Z. Geol. Surv. Bull., 85. Lloyd, J.R. and Moran, W.R., 1974. Trans. ASME, C96: 443-447. Lloyd, J.R. and Sparrow, E.M., 1970. J. Fluid Mech., 42: 465-470. Lobeck. A.K., 1939. Geomorphology. McGraw-Hill, New York, N.Y. Lockett, M.J. and Al-Habbooby, H.M., 1973. Trans. Inst. Chem. Eng., 51: 281-292. Lockett, M.J. and Al-Habbooby, H.M., 1974. Powder Technol., 10: 67-71. Lofquist, K., 1960. Phys. Fluids, 3: 158-175. Logan, B.W., Hoffman, P. and Gebelein, C.D., 1974. In: B.W. Logan (Editor), Evolution and Diagenesis of Quaternary Carbonate Sequences, Shark Bay, Australia. Mem. Am. Assoc. Pet. Geol., 22: 140-194. Logan, R.F., 1960. The Central Namib Desert, South West Africa. Natl. Acad. Sci., Natl. Res. Counc., Publ. No. 758. Long, D.G.F., 1978. Mem. Can. SOC.Pet. Geol., 5: 313-341. Long, R.R., 1953a. Bull. Am. Meteorol. SOC.,34: 205-21 1. Long, R.R., 1953b. Tellus, 5: 42-58. Long, R.R., 1954. Tellus, 6: 97- 1 15. Long, R.R., 1955. Tellus, 7: 342-357. Long, R.R., 1956. In: R.R. Long (Editor), Fluid Models in Geophysics. US. Government Printing Office, Washington, D.C., pp. 135- 147. Long, R.R., 1958. Q. J. R. Meteorol. SOC.,84: 159-161. Long, R.R., 1976. J. Fluid Mech., 73: 445-451. Longman, M.W. and Brownlee, D.N., 1980. Z. Geomorphol., 24: 299-317. Longuet-Higgins, M.S., 1953. Philos. Trans. R. Soc. London, Ser. A, 245: 535-581. Longuet-Higgins, M.S., 1981. J. Fluid Mech., 107: 1-35. Longuet-Higgins. M.S. and Parkin. D.W., 1962. Geogr. J., 128: 194-201. Longwell, C.R., 1928. Am. J. Sci., (5)5: 136-145. Lonsdale, P., 1976. J. Geophys. Res., 81: 1 163-1 176. Lonsdale, P. and Hollister, C.D., 1979. Geology, 7: 597-601. Lonsdale, P. and Malfait, B., 1974. Geol. SOC.Am. Bull., 8 5 : 1697-1712. Lonsdale, P. and Smith, S.M., 1980. Mar. Geol., 34: M19-M25. Lonsdale, P. and Spiess, F.N., 1977. Mar. Geol., 23: 57-75. Lonsdale, F.,Spiess, F.N. and Mudie, J.D., 1973. EOS, Trans. Am. Geophys. Union, 54: I 1 10 (abstr.). Loreau, J.P. and Purser, B.H., 1973. In: B.H. Purser (Editor), The Persian Gulf. Springer, Berlin, pp. 278-328. Lorenz, V., 1970. Geol. SOC.Am. Bull., 81: 1823-1830. Lorenz, V., 1974. Sedimentology, 21: 273-291.

607 Losacco, U. and Parea, G.C., 1969. Atti. SOC.Nat. Mat., 94. Lovell, J.P.B., 1969. J. Sediment. Petrol., 39: 935-953. Lovell, J.P.B., 1970. Geol. Mag., 107: 147-158. Lovell, J.P.B., 1971. Sedimentology, 17: 81-88. Lovell, J.P.B., 1974. Scott. J. Geol., 10: 161-162. Low, A., 1929. Proc. R. SOC.London, Ser. A, 125: 180-195. Lowe, D.R., 1972. J. Sediment. Petrol., 42: 89-101. Lowe, D.R., 1975. Sedimentology, 22: 157-204. Lowe, D.R., 1976. Sedimentology, 23: 285-308. Lowe, D.R. and LoPiccolo, R.D., 1974. J. Sediment. Petrol., 44:484-501. Lowrie, A. and Heezen, B.C., 1967. Science, 157: 1552-1553. Lowrie, A., Egloff, J. and Jahn, W.H., 1978. Mar. Geol., 26: M29-M35. Lowry, D.C. and Jennings, J.N., 1974. Z. Geomorphol., 18: 35-81. Luders, K., 1929. Senckenbergiana, 11: 123- 142. Ludwick, J.C., 1970. Va. J. Sci., 21: 178-184. Ludwick, J.C., 1973. Tidal Currents and zig-zag sand shoals in a wide estuary entrance. Inst. Oceanogr., Old Domin. Univ., Norfolk, Va., Tech. Rep., No. 7. Lugeon, M., 1915. Ann. Geogr., 24: 385-393. Mabbutt, J.A., 1968. Aust. Geogr. Stud., 6: 139-150. Mabbutt, J.A., 1971. In: D.J. Mulvaney and J. Gobson, Aboriginal Man and Environment in Australia. Australian National University Press, Canberra, pp. 66-79. Mabbutt, J.A., 1977. Desert Landforms. Australian National University Press, Canberra. Mabbutt, J.A. and Sullivan, M.E., 1968. Aust. Geogr.. 6: 483-487. Mabbutt, J.A., Wooding, R.A. and Jennings, J.N., 1969. Aust. J. Sci., 32: 159-160. Maberry, J.O., 1971. U.S. Geol. Surv., Prof. Pap., 688. Macagno, E.O. and Hung, T.K., 1967a. Phys. Fluids, 10: 78-82. Macagno, E.O. and Hung, T.K., 1967b. J. Fluid Mech., 28: 43-64. Macagno, E.O. and Rouse, H., 1962. Trans. ASCE, 127: 102-128. Macar, P., 1948. Ann. SOC.Geol. Belg., 72: 47-74. Macar, P., 1951. Ann. Soc. Geol. Belg., 75: 11 1- 115. Macar, P. and Antun, P., 1950. Ann. SOC.Geol. Belg., 73: I2 1 - 149. Macar, P. and Ek, C., 1965. Sedimentology, 4: 53-64. MacDonald, G.A., 1972. Volcanoes. Prentic-Hall, Englewood Cliffs, N.J. MacDonald, G.A. and Alcaraz, A., 1956. Bull. Volcanol., (2)18: 169-178. Mackay, J.R., 1974. h4isc. Rep. Geol. Surv. Can., No. 23. MacNae, W., 1966. Aust. J. Bot., 14: 67-104. MacNae, W., 1968. Adv. Mar. Biol., 6: 73-270. Maddock, T., 1969. U.S. Geol. Surv., Prof. Pap., 622-A. Madigan, C.T., 1936. Geogr. Rev., 26: 205-227. Madigan, C.T., 1938. J. Proc. R. Soc. N.S.W., 71: 503-535. Madigan, C.T., 1946. Trans. R. Soc. Aust., 70: 45-63. Madjirsky, Y.,1969. Houille Blanche, 24: 6 1 1-6 13. Madsen, O.S., 1978. Geotechnique, 28: 377-393. Mahato, B.K. and Shemilt, L.W., 1968. Chem. Fag. Sci., 23: 183-185. Maiklem, W.R., 1968. J. Sediment. Petrol., 38: 785-798. Mainguet, M., 1968. Ann. Geogr., 77: 296-322. Mainguet, M., 1972a. Le Modele des Gres. Institut Geographique National, Paris, 2 vols. Mainguet, M., 1972b. C.R. Acad. Sci., D274: 1633-1636. Mainguet, M. and Canon, L., 1976. Rev. Geogr. Phys. Geol. Dyn., 18: 241-250. Mal, S., 1931. Beitr. Phys. Atmos., 17: 40-70. Malkus, J.S. and Ronne, C., 1960. Am. Geophys. Union, Monogr., No. 5: 45-60. Mallet, R., 1875. Philos. Mag., 50: 122-134, 201-226.

608 Mandelbaum, H., 1955. Trans. Am. Geophys. Union, 36: 72-86. Manegold, E., Hofman, R. and %If, K., 1931. Kolloidzeitschrift, 56: 142-159. Mansikkaniemi, H., 1972. Fennia, No. 118. Marangozis, J., Trass, 0. and Johnson, A.I., 1963. Can. J. Chem. Eng., 41: 195-202. Margarvey. R.H.and McLatchy, C.S., 1968. AIChE J., 14: 260-265. Markl, R.G., Bryan, G.M. and Ewing, J.I., 1970. J. Geophys. Res., 75: 4534-4555. Markson, R., 1975. Science, 188: 1 171- 1177. Marr, J.E., 1926. Geol. Mag., 63: 338-341. Marschalko, R.,1963. Geol. Pr., 28: 161-168. Marschalko, R., 1964. In: R. Bouma and A.H. Brouwer (Editors), Turbidites. Elsevier, Amsterdam, pp. 106-126. Marschalko, R., 1965. Geol. Pr., 36: 139-148. Marshal, J.R., 1962. Scott. Geogr. Mag., 78: 81-99. Martin, J.C. and Moyse, W.J., 1952a. Philos. Trans. R. SOC.London, Ser. A, 244: 312-324. Martin, J.C. and Moyse, W.J., 1952b. Philos. Trans. R. SOC.London, Ser. A, 244: 325-334. Martin, R.C., 1965. N.Z. J. Geol. Geophys., 8: 680-701. Martinez, J.F., 1977. Sedimentation Triasica en el borde sureste de la Meseta. University of Granada. Martini, I.P., 1977. Sedimentology, 24: 603-622. Martini, I.P., 1981. Z. Geomorphol., 25: 1-16. Martins, L.R., 1967. Aspectos texturais e deposicionais dos sedimentos praiais e eolicos da planicie costeira d o Rio Grande d o Sul. Esc. Geol. Porto Alegre, Publ. No. 13. Martinsson, A., 1965. Geol. Far. Stockholm Forh., 87: 181-230. Martvall, S. and Nilsson, G., 1972. Experimental studies of meandering. University of Uppsala, UNGI Rep. No. 20. Masch, F.D., 1963. Int. J. Air Water Pollut., 7: 697-720. Masch, F.D. and Moore, W.L., 1960. J. Hydraul. Div. ASCE, 86(HY7): 1-1 1. Maskell, E.C., 1955. Rep. Mem. Aeronaut. Res. Comm. (Counc.), No. 2565. Masliyah, J.H., 1972. Phys. Fluids, 15: 1144-1 146. Masliyah, J.H., 1980. J. Fluid Mech., 99: 469-479. Masliyah, J. and Bridgewater, J., 1974. Trans. Inst. Chem. Eng., 52: 31-42. Masliyah, J. and Epstein, N., 1970. J. Fluid Mech., 44: 493-512. Mason, B., 1962. Meteorites. Wiley, New York, N.Y. Mason, J.S. and Smith, B.V., 1972. Powder Technol., 6: 323-335. Mason, P.J. and Sykes, R.I., 1979. J. Fluid Mech., 91: 433-450. Mason, T.R. and Von Brunn, V., 1978. S. Afr. J. Sci., 74: 224-225. Masson, M.H., 1973. Bull. SOC. Belg. Geol. Paleontol. Hydrol., 82: 469-480. Masters, C.D., 1967. Bull. Am. Assoc. Pet. Geol., 51: 2033-2043. Mather, K.B., 1962. Polar Rec., 11: 158-171. Mather, K.B. and Goodspeed, M.J., 1959. Polar Rec., 9: 436-445. Matheson, E.L., Herbst, W.A. and Holt, P.H., 1949. Ind. Eng. Chem., 41: 1099-1104. Mathieu, R., 1966. Rev. Giogr. Phys. Geol. Dyn., (2)8: 113-122. Mathur, K.B. and Epstein, N., 1974. Spouted Beds. Academic Press, New York, N.Y. Matschinski, M., 1966. C.R. Acad. Sci., D262: 2001-2004. Matthee, H., 1967. Powder Technol., 1: 265-271. Matthes, G.H., 1941. Trans. Am. Geophys. Union, 22: 632-636. Matthews, P.E., 1961. Trans. Geol. Soc. S. Afr., 64: 55-69. Matthews, R.J. and Liggett, J.A., 1967. J. Hydraul. Div. ASCE, 93(HY6): 387-407. Mattson, P.H. and Alvara, W., 1973. Boll. Volcanol., (2)37: 553-572. Maude, A.D. and Whitmore, R.L., 1958. Br. J. Appl. Phys., 9: 477-482. Maull, D.J. and East, L.F., 1963. J. Fluid Mech., 16: 620-632. Maurin, V. and Zotl, J., 1966. Erdkunde, 20: 204-208.

609 Maxson, J.H., 1940. J. Geol., 48: 717-751. Maxson, J.H. and Campbell, I., 1935. J. Geol., 43: 729-744. McAllister, J.F. and Agnew, A.F., 1948. Bull. Geol. Soc. Am., 59: 1377 (abstr.). McArthur, D.S. and Onesti, L.J., 1970. Geogr. Ann., A52: 186-193. McBirney, A.R. and Noyes, R.M., 1979. J. Petrol., 20: 487-554. McBride, E.F., 1962. J. Sediment. Petrol., 32: 39-91. McBride, E.F., 1966. Univ. Tex., Bur. Econ Geol., Rep. Invest., No. 57. McBride, E.F., 1970. Geol. Assoc. Can., Spec. Pap., 7: 67-83. McBride, E.F. and Kimberley, J.E., 1963. Bull. Am. Assoc. Pet. Geol., 47: 1840-1854. McBride, E.F., Shepherd, R.G. and Crawley, R.A., 1975a. J. Sediment. Petrol., 45: 132-139. McBride, E.F., Weidie, A.E. and Wolleben, J.A., 1975b. In: M.L. Broussard (Editor), Deltas. Models for Exploration. Houston Geological Society, Houston, Tex., pp. 485-522. McCabe, P.J., 1977. Sedimentology, 24: 271 -290. McCabe, P.J. and Waugh, B., 1973. Proc. Yorks Geol. Soc.,39: 445-470. McCallien, W.J., Ruxton, B.P. and Walton, B.J., 1964. Overseas Geol. Mineral Resour., 9: 257-294. McCauley, J.F., 1973. J. Geophys. Res., 78: 4123-4137. McCauley, J.F., Grollier, M.J. and Breed, C.S., 1977. Yardangs of Peru and other desert regions. U.S. Geol. SUIT.,Inter-Agency Rep., Astrogeol., No. 81. McCave, I.N., 1969. Nature (London), 224: 1288- 1289. McCave, I.N., 1970. J. Geophys. Res., 75: 4151-4159. McCave,I.N., 1979. Mar. Geol.,31: 101-114. McCave, I.N. and Swift, D.J.P., 1976. Geol. SOC.Am. Bull., 87: 541-546. McClure, H.A., 1978. Palaeogeogr. Palaeoclimatol. Palaeoecol., 25: 3 15-326. McCormack, P.D., Welker, H. and Kelleher, M., 1970. Trans. ASME, C92: 101-1 12. McCormick, B.W., 1962. Trans. ASME, D84: 369-379. McCormick, C.D. and Picard, M.D., 1969. J. Sediment. Petrol., 39: 1484-1508. McCracken, W.A., 1969. Bull. Am. Soc.Pet. Geol., 53: 463. McCullough, G.B., Nitzberg, G.E. and Kelly, J.A., 1951. NACA Res. Mem., A50L12. McDevitt, J.B. and Mellenthin, J.A., 1969. NASA Tech. Note TN D-5346. McDonald, R.C., 1976. Z. Geomorphol., S26: 79-91. McEwan, A.D. and Taylor, G.I., 1966. J. Fluid Mech., 26: 1-15. McFarland, B.L. and Harmon, D.B., 1961. Proc. 1961 Heat Transfer Fluid Mech. Inst. Stanford Univ., pp. 208-219. McGowen, J.H., 1971. Univ. Texas, Bureau Econ. Geol., Rep. Invest., No. 71. McGregor, D.R., Pendery, E.C. and McGregor, D.L., 1963. J. Geol., 7 1 : 108- 1 15. McGregor, O.W. and White, R.A., 1970. AIAA J., 8: 1959-1964. McHone, J.F., 1972. Morphologic time series from a submarine sand ridge on the south Virginia coast. Institute of Oceanography, Old Dominion University, Norfolk, Va. McIntire, W.G. and Walker, H.J., 1964. Ann. Assoc. Am. Geogr., 54: 582-596. McIntyre, R.J., 1979. Appl. Math. Modelling, 3: 89-98. McKee, E.D., 1933. Publ. Carnegie Inst. Wash., No. 440: 79-1 15. McKee, E.D., 1938. J. Sediment. Petrol., 8: 77-83. McKee, E.D., 1945. J. Geol., 53: 313-325. McKee, E.D., 1954. Mem. Geol. Soc.Am., No. 61. McKee, E.D., 1957a. Bull. Am. Assoc. Pet. Geol., 41: 1704-1747. McKee, E.D., 1957b. J. Sediment. Petrol., 27: 129-134. McKee, E.D., 1962. Geol. Rundsch., 52: 551-587. McKee, E.D., 1966a. U.S. Geol. Surv., Prof. Pap., 550-D: 94-103. McKee, E.D., 1966b. Sedimentology, 7: 1-69. McKee, E.D. and Bigarella, J.J., 1972. J. Sediment. Petrol., 42: 670-68 I . McKee, E.D. and Goldberg, M., 1969. Geol. Soc. Am. Bull., 80: 231-244.

610 McKee, E.D. and Sterrett, T.S., 1961. In: J.A. Peterson and J.C. Osmond (Editors), Geometry of Sandstone Bodies. American Association of Petroleum Geologists, Tulsa, Okla., pp. 13-28. McKee, E.D. and Tibbitts, G.C., 1964. J. Sediment. Petrol., 34: 5-17. McKee. E.D., Crosby, E.J. and Berryhill, H.L., 1967. J. Sediment. Petrol., 37: 829-851. McKee, E.D., Douglass, J.R. and Rittenhouse, S., 1971. Geol. SOC.Am. Bull., 82: 359-378. McKee, E.D., Reynolds, M.A. and Baker, C.H., 1962a. U.S. Geol. Surv., Prof. Pap., 450-D: 151- 155. McKee, E.D., Reynolds, M.A. and Baker, C.H., 1962b. U.S.Geol. Surv., Prof. Pap., 450-D: 155-160. McKee, R.F. and Murfitt, R.F.A., 1967. Sierra Leone Geogr. J., No. 1 1 : 4-10. McKellar, P., 1890. Geol. Soc. Am. Bull.. 1: 568-570. McKenzie, P., 1958. J. Geol., 66: 103-113. McKinney, T.F., Stubblefield, W.C. and Swift, D.J.P., 1974. Mar. Geol., 17: 79-102. McLaughlin, R.T., 1959. J. Hydraul. Div. ASCE, 85(HY 12): 9-41. McLean, R.F., 1967. Mar. Geol., 5: 181-193. McLeish, W., 1968. Deep-sea Res., 15: 461-469. McNair, E. and Sorensen. R.M., 1971. Proc. 12th Conf. Coastal Eng., 1: 415-434. McPherson. H.J., 1969. In: J.G. Nelson and M.J. Chambers (Editors), Geomorphology. Methuen, Toronto, Ont., pp. 257-279. McTaggart, K.C., 1960. Am. J. Sci., 258: 369-381. McTaggart. K.C., 1962. Am. J. Sci.. 260: 470-476. Medway, (Lord), Wall, J.R.D. and Wilford, G.E., 1967. Z. Geomorphol., 1 1 : 161-168. Meek, C.C. and Jones, B.G., 1973. J. Atmos. Sci.. 30: 239-244. Mehta. P.R., 1979. J. Hydraul. Div. ASCE, 105(HY5): 501-516. Mehta, P.R., 1981. J. Hydraul. Div. ASCE, 107(HY4): 451-460. Mehta, U.B. and Lavan, Z.. 1969. Trans. ASME, E36: 897-901. Mei, C.C. and Liu, P.L.F., 1977. Estuarine Coastal Mar. Sci., 5: 25-37. Mei, C.C., Liu, P.L.F. and Carter, T.G., 1972. Mass transport in water waves. Mass. Inst. Techno]., Dep. Civ. Eng., Rep. No. 146. Meischner, K.D., 1964. In: A. Bouma and A. Brouwer (Editors), Turbidites. Elsevier. Amsterdam, pp. 156- 19I . Meksyn. D., 1950. Proc. R. SOC.London, Ser. A, 203: 253-265. Melcher, J.R. and Hunvitz. M., 1967. J. Spacecraft Rockets, 4: 864-871. Melieres, F., Nesteroff. W.D. and Lancelot, Y., 1970. Cah. Oceanogr., 22: 63-72. Mellor, M., 1965. Blowing snow. U.S. Army Cold Reg. Res. Eng. Lab., Report IILA3c. Melton, F.A., 1936. Geogr. Rev., 26: 593-609. Melton, F.A., 1940. J. Geol., 48: 113-145. Melton, M.A., 1961. Am. J. Sci., 259: 231-233. Melville, B.W., 1975. Local scour at bridge sites. Univ. Auckland, School Eng., Rep. No. 117. Melville, B.W. and Raudkivi, A.J., 1977. J. Hydraul. Res., 15: 373-380. Melville, W.K.. 1977. J. Phys. Oceanogr., 7: 702-710. Melville, W.K. and Bray, K.N.C., 1979. Int. J. Heat Mass Transfer, 22: 279-287. Menard, H.W. and Ludwick, J.C., 1951. In: J.L. Hough (Editor), Turbidity Currents. SOC. Econ. Paleontol. Mineral., Spec. Publ., 2: 2- 13. Menkes, J.. 1959. J. Fluid Mech., 6: 518-522. Menzies, J., 1979a. J. Glaciol., 22: 373-384. Menzies, J., 1979b. Earth-Sci. Rev., 14: 315-359. Merchant, M.E., 1945a. J. Appl. Phys., 16: 267-275. Merchant, M.E., 1945b. J. Appl. Phys., 16: 318-324. Meshal, A.H.. 1977. Atmosphere, 15: 166-177. Metz, R., 1980. J. Sediment. Petrol., 50: 841-842.

61 1 Metzner, A.B. and Whitlock, M., 1958. Trans. SOC.Rheol., 2: 239-254. Meyer, W., Stets, J. and Wurster, P., 1974. Geol. Rundsch., 63: 1 1 13-1 132. Meyer-Peter, E., Hoeck, E. and Muller, R., 1937. Schweiz. Bauztg., 109: 199-202. Miall, A.D., 1979. Mem. Geol. Surv. Can., No. 387. Michaelis, E.R. and Dixon, G., 1969. Bull. Can. Pet. Geol., 17: 410-443. Michaels, AS. and Bolger, J.C., 1962. Ind. Eng. Chem. Fund., 1: 24-33. Michalke, A., 1965a. J. Fluid Mech., 22: 371-383. Michalke, A., 1965b. J. Fluid Mech., 23: 521-544. Michalke, A., 1969. J. Fluid Mech., 38: 765-767. Michalke, A. and Timme, A,, 1967. J. Fluid Mech., 29: 647-666. Michalke, A. and Wille, R., 1966. In: H. Gortler (Editor), Boundary Layer Research. Springer, Berlin, pp. 962-972. Michon, S., Godet, J. and Bonnefille, R., 1955. Etude theorique et experimentale des courants de densite. Laboratoire Nationale d’Hydraulique, Chatou, 2 vols. Middleton. G.V., 1966a. J. Sediment. Petrol., 36: 202-208. Middleton, G.V., 1966b. Can. J. Earth Sci., 3: 523-546. Middleton, G.V., 1966~.Can. J. Earth Sci., 3: 627-637. Middleton, G.V., 1967a. Can. J. Earth Sci., 4: 475-504. Middleton, G.V., 1967b. J. Sediment. Petrol., 37: 229-232. Middleton, G.V., 1970. Geol. Assoc. Can., Spec. Pap., 7: 253-272. Middleton, G.V. and Hampton, M.A., 1973. In: G.V. Middleton and A.H. Bouma (Editors), Short Course, Turbidites and Deep Water Sedimentation. SEPM Pacific Section, Anaheim, pp. 1-38. Middleton, G.V. and Hampton, M.A., 1976. In: D.J. Stanley and D.J.P. Swift (Editors), Marine Sediment Transport and Environmental Management, Wiley, New York, N.Y., pp. 197-218. Migliorini, C.I., 1950. Mem. SOC.Tosc. Sci. Nat., A57: 3-15. Migniot, C., 1968. Houille Blanche, 23: 591-620. Mii, H., 1958. Sci. Rep. Tohoku Univ., (2)29: 77-107. Miksad, R.W., 1972. J. Fluid Mech., 56: 695-719. Miksad, R.W., 1973. J. Fluid Mech., 59: 1-21. Miller, C. and Barcillon, A., 1978. J. Geophys. Res., 83: 4107-41 16. Miller, C.D., 1978. J. Res. U.S. Geol. Surv., 6: 61 1-624. Miller, D.E., 1971. Soil Sci. SOC.Am. Proc., 35: 635-637. Miller, R.L., 1976. In: R.A. Davis and R.L. Ethington (Editors), Beach and Nearshore Sedimentation. Soc. Econ. Paleont. Mineral., Spec. Publ., 24: 92-1 19. Miller, R.L. and Kahn, J.V., 1962. Statistical Analysis in the Geological Sciences. Wiley, New York, N.Y., 483 pp. Miller, R.L. and Zeigler, J.M., 1958. J. Geol., 66: 417-441. Miller, T.P. and Smith, R.L., 1977. Geology, 5: 173-176. Miller, W.J., 1922. J. Geol., 30: 587-610. Milling, M.E. and Behrens, E.W., 1966. Publ. Inst. Mar. Sci. Univ. Tex. 11: 135-148. Mills, D. and Mason, J.S., 1977a. Wear, 44: 31 1-328. Mills, D. and Mason, J.S., 1977b. Powder Techno]., 17: 37-53. Mills, R.D., 1965a. J. R. Aeronaut. SOC.,69: 116-120. Mills, R.D., 1965b. J. R. Aeronaut. SOC.,69: 714-718. Minard, J.P., 1966. U.S.Geol. Surv., Prof. Pap., 550-B. Minter, W.E.L., 1970. J. Sediment. Petrol., 40: 755-764. Minzoni, AS. and Whitman, G.B., 1977. J. Fluid Mech., 79: 273-287. Miotke, F.D., 1968. Jahresber. Geogr. Ges. Hannover, No. 4. Mirza, S. and Richardson, J.F., 1979. Chem. Eng. Sci., 35: 447-454. Mishra, P.N., Severson, D.E. and Owens, J.C., 1970. Chem. Eng. Sci., 25: 653-663.

612 Misra, R.C. and Awashthi, N., 1962. J. Sediment. Petrol., 32: 764-775. Mitchell, D.R., 1938. Trans. Am. Inst. Min., Metall. Eng., 130: 107-128. Mitchell, G.F., 1976. The Irish Landscape. Collins, London. Mitchell, R.J. and Markell, A.R., 1974. Can. Geotech., 1 1 : 11-31. Mitchell, R.J., Tsui, K.K. and Sangrey, D.A., 1973. Proc. 13th Conf. Coastal Eng., 2: 15 15- 1541. Mitra, S. and Datta, J., 1978. Geol. Rundsch., 67: 880-895. Mizushina, T., Ogino, F., Oka, Y. and Fukuda. H., 1971. Int. J. Heat Mass Transfer, 14: 1 705- 1716. Mochizuki, M., 1961. J. Phys. SOC.Jpn., 16: 995-1008. Mockmore, C.A., 1944. Trans. ASCE, 109: 593-628. Moffatt, H.K., 1964. J. Fluid Mech., 18: 1-18. Molerus, O., 1967. In: A.A.H. Drinkenberg (Editor), Proc. Int. Symposium on Fluidization, Eindhoven. Netherlands Universities Press, Amsterdam, pp. 134- 143. Mollard, J.D., 1973. In: Fluvial Processes and Sedimentation. Inland Waterways Directorate, Department of Environment, Canada, pp. 341-380. Monod, T., 1958. Mem. Int. Fr. Afr. Noire, No. 52. Montenat, C., 1980. Bull. SOC.Geol. Fr., (7)22: 501-509. Moody-Stuart, M., 1966. J. Sediment. Petrol., 36: 1102- 1 1 17. Mooney. M., 1951. J. Colloid. Sci., 6: 162-170. Moore, D.G., Curray, J.R. and Emmel, F.J., 1976. Mar. Geol., 21 : 21 1-226. Moore, D.W. and Saffman, P.G.. 1975. J. Fluid Mech., 69: 465-473. Moore, E.S., 1914. Am. J. Sci.. 38: 101-102. Moore, G.W. and Nicholas, G., 1964. Speleology. Heath, Boston, Mass. Moore, J.G., 1967. Bull. Volcanol., (2)30: 337-363. Moore, J.G. and Melson, W.G., 1969. Bull. Volcanol., (2)33: 600-620. Moore, J.G., Nakamura. K. and Alcaraz, A., 1966. Science, 151: 955-960. Moore, T.W.F., 1960. J. R. Aeronaut. SOC.,64: 668-672. Moore, W.L. and Masch, F.D., 1965. U.S. Dept. Agric., Misc. Publ., No. 970: 314-320. Moors, H.T. and Schleiger, N.W., 1971. J. Geol. SOC.Aust., 17: 157-169. Moran, S., Clayton, L., Hooke, LeB., Fenton, M.M. and Andriashek. L.D., 1980. J. Glaciol., 457-476. Moreland, C., 1963. Can. J. Chem. Eng., 41 : 24-28. Moretti, P.M. and Kays, W.M., 1965. Int. J. Heat Mass Transfer, 8: 1187-1202. Morgan, A.V., 1970. J. Glaciol., 9: 125-133. Morgan, J.P. and Andersen, H.V., 1961. Bull. La. Geol. SUIT.,No. 35. Morgan, J.P., Coleman, J.M. and Gagliano, S.M., 1968. In: Diapers and Diaperism. Mem. Am. Assoc. Pet. Geol., 8: 145-161. Morgenstern, N.R., 1967. In: A.F. Richards (Editor), Marine Geotechnique. University of Illinois Press, Urbana, Ill., pp. 189-220. Morkovin, M.V., 1972. Forsch. Ber. Dtsch. Luft-Raumfahrt, No. 72-77: 270-301. Morris, E.M. and Morland, L.W.. 1976. J. Glaciol., 17: 3 11-323. Morris, R.C., 1971. J. Sediment. Petrol., 41: 410-424. Moshagen, H. and Tdrum, A,, 1975. ASCE J. Watenv., Harbors Coastal Eng. Div.. IOI(WWI): 49-57. Mosley. M.P., 1973. J. Sediment. Petrol., 43: 795-798. Mosonyi, E., Meckel, H. and Meder, G., 1975. Proc. 16th Congr. Int. Assoc. Hydraul. Res., 2: 347-355. Moss, R., 1938. Geogr. J.. 92: 21 1-227. Moss, W.D., 1972. J. Fluid Mech., 52: 307-320. Mothersill, J.S., 1969. J. Sediment. Petrol., 39: 1317- 1324. Mountain, E.D., 1964. Trans. Proc. Geol. Soc. S. Afr., 67: 203-209.

613 Moussa, Z.M., Trischka, J.W. and Eskinazi, S., 1977. J. Fluid Mech., 80: 49-80. Mrakovich, J.V. and Cougan, A.H., 1974. J. Sediment. Petrol., 44: 1 186- 1 199. Mueller, J.E., 1968. Ann. Am. Assoc. Geogr., 58: 371-385. Mueller, T.J. and O’Leary, R.A., 1970. Proc. AIAA 3rd Fluid and Plasma Dyn. Conf., Pap. NO. 70-763. Mueller, T.J., Korst, H.H. and Chow, W.L., 1964. Trans. ASME, D86: 221-225. Muir-Wood, A.M., 1969. Coastal Hydraulics, Macmillan, London. Mukejee, T., Farshi, A. and Martin, B.W., 1971. J. Fluid Mech., 46: 293-297. Mulhearn, P.J., 1973. Nature (London), Phys. Sci., 241: 165- 167. Mulhearn, P.J. and Bradley, E.F., 1977. Boundary-layer Meteorol., 12: 75-92. Miiller, G., 1964. Beitr. Mineral. Petrogr., 10: 125-131. Munk, W.H., 1955. Q. J. R. Meteorol. SOC.,81: 320-332. Munk, W.H. and Sargent, M.C., 1948. Trans. Am. Geophys. Union, 29: 855-860. Munk, W.H. and Sargent, M.C., 1954. U.S. Geol. Surv., Prof. Pap., 260-C. Murai, I., 1961. Bull. Earthquake Res. Inst. Tokyo Univ., 39: 133-248. Muramoto, Y., 1967. Proc. 12th Congr. Inst. Assoc. Hydraul. Res., pp. 429-437. Murata, S., Miyake. Y. and Inaba, T., 1976. J. Fluid Mech., 73: 735-752. Murphy, M.A. and Schlanger, S.O., 1962. Bull. Am. Assoc. Pet. Geol., 46: 457-477. Murray, J.D., 1965. J. Fluid Mech., 2 I : 465-493. Murray, S.P., 1970a. J. Geophys. Res., 75: 1647-1654. Murray, S.P., 1970b. J. Geophys. Res.. 75: 4579-4582. Murray, S.P., 1972. In: D.J.P. Swift, D.B. Duane and O.H. Pilkey (Editors), Shelf Sediment Transport: Process and Pattern. Dowden, Hutchinson and Ross, Stroudsburg, Penn., pp. 127- 142. Mutch, T.A., Binder, A.D., Huck, F.O., Levinthal, E.C., Liebes, S., Morris, E.C.. Patterson, W.R., Pollack, J.B., Sagan, C. and Taylor, G.R., 1976a. Science, 192: 791-801. Mutch, T.A., Arvidson, R.E., Binder, A.B., Huck, F.O., Levinthal, E.C., Liebes, S., Nummedal, D., Pollack, J.B. and Sagan, C., 1976b. Science, 194: 87-91. Mutti, E. and Ricci-Lucchi, F., 1972. Mem. SOC.Geol. Ital.. 1 1 : I6 1 - 199. Mutti, E. and Sanuy, J.R., 1968. Acta Geol. Hisp., 3: 120-123. Myrick, R.M. and Leopold, L.B., 1963. U.S. Geol. Surv., Prof. Pap., 422-B. Nachtsheim, P.R., 1970. Phys. Fluids, 13: 2432-2447. Nachtsheim, P.R. and Hagen, J.R., 1972. AIAA J., 10: 1637-1640. Nachtsheim, P.R. and Larson, H.K., 1971. AIAA J., 9: 1608-1614. Nagabhushanaiah, H.S., 1967. Bull. Inst. Assoc. Sci. Hydrol., 17: 28-43. Nageli, W., 1941. Mitt. Schweiz. Anst. Forst. Versuchsw., 23: 221-276. Nagtegaal, P.J.C., 1963. Geol. Mijnbouw, 42: 363-374. Nagtegaal, P.J.C., 1965. Geol. Mijnbouw, 44: 347-352. Nagtegaal, P.J.C., 1966. Geol. Mijnbouw, 45: 342-354. Nagtegaal, P.J.C., 1969. Leidse Geol. Meded., 42: 143-238. Naib, S.K.A., 1966. J. Inst. Water Eng., 20: 199-206. Nairn, LA., 1979. N.Z. J. Geol. Geophys., 22: 363-378. Nakamura, K. and Kriher, F., 1970. Neues Jahrb. Geol. Palaontol., Monatsh., pp. 491-501. Nallasamy, M. and Prasad, K.K., 1977. J. Fluid Mech., 79: 391-414. Nami, M., 1976. Geol. Mag., 113: 47-52. Nami, M. and Leeder, M.R., 1978. Mem. Can. Soc. Petrol. Geol., 5 : 431-440. Nanson, G.C., 1980. Sedimentology, 27: 3-29. Nanz, R.H., 1954. Bull. Am. Assoc. Pet. Geol., 38: 96-117. Narasimhan, S., 1967. J. Eng. Mech. Div. ASCE, 93(EM5): 1 1 1- 135. Narayan, J., 1971. Sediment. Geol., 6: 73-109. Narayanan, R., 1972. J. Hydraul. Div. ASCE, 98(HY6): 993-101 I. Narayanan, R. and Reynolds, A.J., 1968. J. Hydraul. Div. ASCE, 9qHY6): 1383-1398.

614 Narayanan, R. and Reynolds, A.J., 1972. J. Hydraul. Div. ASCE, 98(HY5): 913-934. Nash, J.F., Quincey, V.G. and Callinan, J., 1963. Rep. Aero. Div. Natl. Phys. Lab., No. 1070. Nasner. H. and Partenscky, H.W., 1975. Die Kiiste, No. 28: 97-113. Natland, M.L. and Kuenen, P.H.. 1951. In: J.L. Hough (Editor), Turbidity Currents. SOC. Econ. Palaeontol. Mineral., Spec. Publ., 2: 76- 107. Nayak, I.V., 1970. Equilibrium profiles of model beaches. Univ. Calif. Berkeley, Hydraul. Eng. Lab., Rep. HEL-2-25. Nayfeh, A.H. and Saric, W.S., 1971. AIAA J., 9: 750-752. Naysmith, A., 1958. Tech. Note R. Aircr. Establ., No. Aero 2558. Naysmith, A., 1961. Tech. Mem. Royal Aircr. Establ., No. Aero 709. Neal, J.T., Langer, A.M. and Kerr, P.F., 1968. Geol. SOC.Am. Bull., 79: 69-90. NEDECO (Netherlands Engineering Consultants), 1959. River Studies and Recommendations on Improvement of Niger and Benue. North-Holland, Amsterdam. Nederlof, H.M., 1959. Leidse Geol. Meded., 24: 603-703. Needham, R.S., 1978. Sedimentology, 25: 285-295. Neev, D. and Emery, K.O., 1967. Bull. Geol. Surv. Isr., No. 41. Negendank, J.F.W., 1970. Abh. Hess. Landesamt. Bodenforsch., 56: 151- 162. Negendank, J.F.W., 1972. Neues Jahrb. Geol. Palaontol., Monatsh., No. 9: 561 -572. Neill. C.R., 1964. Trans. Eng. Inst. Can., 7(A-3): 3-8. Neill, C.R., 1965. Proc. Inst. Civ. Eng., 30: 415-436. Neill, C.R., 1967. Proc. 12th Congr. Int. Assoc. Hydraul. Res., 3: 46-64. Neill, C.R., 1973a. In: Fluvial Processes and Sedimentation. Inland Waterways Directorate, Department of Environment, Canada, pp. 453-46 1. Neill, C.R., 1973b. Guide to Bridge Hydraulics. University of Toronto Press, Toronto, Ont. Nemenyi, P., 1946. Trans. ASCE, 1 1 1 : 1 16- 125. Nesteroff, W.D., 1961. Rev. Geogr. Phys. Geol. Dyn., (2)4: 263-268. Nestler, D.E.. Saydah, A.R. and Auxer, W.L., 1969. AIAA J., 7: 1368-1370. Nettleton, L.L., 1934. Bull. Am. Assoc. Pet. Geol., 18: 1175-1204. Neu, H.A., 1967. J. Hydraul. Div. ASCE, 93(HY5): 149-165. Neumann, A.C. and Ball, M.M., 1970. Geol. SOC.Am. Bull., 81: 2861-2874. Neumann-Mahlkau, P., 1976. Sedimentology, 23: 421 -425. Nevill. W.E., 1957. Sci. Proc. R. Dublin SOC.,27: 313-324. Nevin, C.M. and Trainer, D.W., 1927. Bull. Geol. SOC.Am., 38: 451-458. Newell, N.D., 1956. Bull. Am. Nat. Hist., 109: 31 1-372. Newell, N.D. and Rigby. J., 1957. In: R.J. LeBlanc and J.G. Breeding (Editors), Regional Aspects of Carbonate Deposition. SOC.Econ. Paleontol. Mineral., Spec. Publ., 5 : 15-72. Newell, N.D., Imbrie, J., Purdy, E. and Thurber, D.L., 1959. Bull. Am. Mus. Nat. Hist., 117: 183-228. Newell, N.D., Rigby, J.K., Whiteman, A.J. and Bradley, J.S., 195I . Bull. Am. Mus. Nat. Hist., 97: 1-29. Newell, N.D., Rigby. J.K., Whiteman, A.J., Fisher, A.G., Hickox, J.E. and Bradley, J.S., 1953. The Permian Reef Complex of the Guadeloupe Mountains Region, Texas and New Mexico. Freeman, San Francisco, Calif. Newman, B.G., 1961. In: G.V. Lachmann (Editor), Boundary Layer and Flow Control, vol. 1. Pergamon, Oxford, pp. 232-264. Newsom, J.F., 1903. Bull. Geol. SOC.Am., 14: 227-268. Newton, R.S., 1968a. Mar. Geol., 6: 73-75. Newton, R.S., 1968b. Sedimentology, 1 1 : 275-292. Newton, R.S., Seibold, E. and Werner, F., 1973. “Meteor” Forschungsergeb., Reihe C, 15: 55-77. Nicholls, S., 1978. Q. J. R. Meteorol. SOC.,104: 653-676. Nicks, O.W., 1970. This Island Earth. NASA, Washington, D.C.

615 Nicollet, G., 1975. Proc. 16th Congr. Inst. Assoc. Hydraul. Res., 2: 478-484. Niedoroda, A.W. and Tanner, F.W., 1970. Mar. Geol., 9: 41-62. Niedoroda, A.W., 1973a. Trans. Gulf-Coast Assoc. Geol. SOC.,22: 229-240. Niedoroda, A.W., 1973b. In: D.R. Coates (Editor), Coastal Geomorphology. State University of New York, Binghamton, N.Y., pp. 103-1 13. Niehoff, W., 1958. Geol. Rundsch., 47: 252-321. Niem, A.R., 1977. Geol. SOC.Am. Bull., 88: 49-61. Nienow, A.W., Rowe, P.N. and Cheung, L.Y.L., 1978. In: J.F. Davidson and D.L. Keairns (Editors), Fluidization. Cambridge University Press, Cambridge, pp. 146- 150. Nieuwstadt, F. and Keller, H.B., 1973. Comput. Fluids, 1: 59-71. Nikuradse, J., 1930. 1ng.-Arch., 1 : 306-332. Nilsen, T.H., 1965. J. Sediment. Petrol., 35: 805-817. Nilsen, T.H., 1968. Norg. Geol. Unders., No. 259. Nilsen, T.H. and Clarke, S.H., 1975. U.S. Geol. Surv., Prof. Pap., 925. Nilsen, T.H., Bartow, J.A., Stump, E. and Link, M.H., 1977. J. Sediment. Petrol., 47: 1299- 1304. Nilsson, G. and Martvall, S . , 1972. The Ore River and its meanders. Univ. Uppsala, UNGI Rep. No. 19. Nilsson, H.D., 1973. In: D.R. Coates (Editors), Coastal Geomorphology. State University of New York, Binghamton, N.Y. Nininger, H.H., 1936a. Am. J. Sci., (5)31: 209-222. Nininger, H.H., 1936b. Am. J. Sci., (5)32: 1-20, Nininger, H.H., 1959. Out of the Sky. Dover Publications, New York, N.Y. Niyogi, D., 1970. Bull. Geol. Min. Metall. SOC.India, No. 43: 1-36. Noble, C.A. and Palmquist, R.C., 1968. Proc. Iowa Acad. Sci., 75: 234-242. Noble, D.C., 1965. U.S. Geol. Surv., Prof. Pap., 525-B: 85-90. Noda, H., 1969. Proc. 11th Conf. Coastal Eng., 1 : 227-247. Noda, E.K., 1973. Rip-currents. Proc. 13th Conf. Coastal Eng., 1: 653-667. Nomitsu, R., 1943. Geophysics, 7: 61-79. Noorthoorn van der Kruijff, J.F. and Lagaaij, R., 1960. Geol. Mijnbouw, 39: 71 1-723. Nordstrom, C.E. and Inman, D.L., 1975. U.S. Coastal Eng. Res. Cent., Misc. Pap., No. 1 1-75. Normark, W.R. and Spiess, F.N., 1976. Geol. SOC.Am. Bull., 87: 286-296. Normark, W.R., Hess, G.R., Stow, D.A.V. and Bowen, A.J., 1980. Mar. Geol., 37: 1-18. Norris, R.M., 1956. Bull. Am. Assoc. Pet. Geol., 40: 1681-1686. Norman, J.O., 1964. Geogr. Ann., 46: 3-238. Norman, J.O., 1972. Surtsey Prog. Rep., No. 6. Notter, R.H. and Sleicher, C.A.. 1971a. Chem. Eng. Sci., 26: 161-171. Notter, R.H. and Sleicher, C.A., 1971b. Chem. Eng. Sci., 26: 559-565. Notter, R.H. and Sleicher, C.A., 1972. Chem. Eng. Sci., 27: 2073-2093. Noye, B.J., 1973. Bull. Aust. Math. SOC.,8: 423-433. Nwachukwu, B.A., 1973. Proc. 1st Can. Hydraul. Conf., Edmonton, Alta., pp. 144-164. Obiakor, E.K. and Whitmore, R.L., 1967. Rheol. Acta, 6: 353-359. O’Brien, V., 1972. Phys. Fluids, 15: 2089-2097. Odd, N.V.M. and Owen, M.V., 1972. Proc. Inst. Civ. Eng. Suppl., No. 9: 175-205. Off, T., 1963. Bull. Am. Assoc. Pet. Geol., 47: 324-341. Ojakangas, R.W., 1968. Geol. Soc.Am. Bull., 1979: 973-1008. Ojakangas, R.W. and Matsch, C.L., 1980. Geol. SOC.Am. Bull., 91: 495-501. Ojha, S.K., 1969. J. Aeronaut. SOC.India, 21: 275-303. Okabe, J. and Inoue, S . , 1960. Rep. Res. Inst. Appl. Mech., Kyushu Univ., 8: 91-101. Okabe, J. and Inoue, S., 1961. Rep. Res. Inst. Appl. Mech., Kyushu Univ., 9: 147-161. Okada, H. and Whitaker, J.H.McD., 1979. J. Geol. SOC.Jpn., 85: 187-196.

616 O’Keefe, J.A., 1963. In: J.A. O’Keefe (Editor), Tektites. University of Chicago Press, Chicago, Ill., pp. 167-188. O’Keefe, J.A. and Adams, E.W., 1965. J. Geophys. Res., 70: 3819-3829. Okko, M., 1967. C. R. SOC.Geol. Finl., 39: 123-131. Oldershaw, W., 1960. J. Geol. Soc. Aust., 6: 197-199. Oldham, R.D., 1899. Mem. Geol. Surv. India, 29: 1-379. Oliver, D.R., 1961. Chem. Eng. Sci., 15: 230-242. Oliver, D.R. and Atherinos, T.E., 1968. Chem. Eng. Sci., 23: 525-536. Oliver, D.R. and Ward, S.G., 1953. Nature (London), 171: 396-397. Ollier, C.D., 1974. In: L. Civetta, P. Gasperini, G. Luongo and A. Rapolla (Editors), Physical Volcanology. Elsevier, Amsterdam, pp. 289-3 1 1. Ollier, C.D., 1975. Z. Geomorphol., 19: 164-190. Ollier, C.D. and Trattman, E.K., 1969. In: E.K. Trattman (Editor), The Caves of Northwest Ireland. David and Charles, Newton Abbot, Devon, pp. 59-95. Olson, M.D. and Tuann, S.Y.. 1979. Comput. Fluids. 7: 123-135. Ongley, E.D., 1968. J. Hydro]., 6: 15-32. Onishi, Y., Jain, S.C. and Kennedy, J.F.. 1972. Effects of meandering on sediment discharges and friction factors of alluvial streams. Iowa Inst. Hydraul. Res. Rep. No. 141. Oomkens, E., 1966. Sedimentology. 7: 145- 148. Oomkens, E. and Terwindt, J.H.J., 1960. Geol. Mijnbouw, 30: 701-710. Orford, J.D. and Wright, P., 1978. Mar. Geol., 28: MI-M8. Osberg, G.L. and Charlesworth, D.H., 1951. Chem. Eng. Prog., 47: 566-570. Oswatitsch, K.. 1958. In: H. Gbrtler (Editor), Boundary Layer Research. Springer, Berlin, pp. 357-367. Otto, T., 1911. Jahresber. Geogr. Ges. Greigswald, 13: 235-485. Otvos, E.G., 1964. J. Sediment. Petrol., 34: 554-560. Otvos, E.G., 1965. J. Sediment. Petrol., 35: 604-609. Otvos, G.. 1966.’Bull. Am. Assoc. Pet. Geol., 50: 159-165. Owen, D.M. and Emery, K.O., 1967. In: J.B. Hersey (Editor), Deep-sea Photography. Johns Hopkins Press, Baltimore, Md., pp. 167- 172. Owen, M.W., 1971. Proc. 14th Congr. Int. Assoc. Hydraul. Res., 4: 27-32. Owen, P.R., 1970. Aeronaut. Q., 61: 69-78. Owen, P.R., 1973. Aeronaut. J., 77: 383-405. Owens, E.H., 1977. J. Sediment. Petrol., 47: 168-190. Owens, E.H. and Bowen, A.J., 1978. Marit. Sediments, 13: 1-31. Owens, E.H. and Frobel, D.H., 1977. J. Sediment. Petrol., 47: 191-198. 1965. Can. Geogr., 9: 138-143. Packer, R.W., Padgett, G.V. and Ehrlich, R., 1976. Geol. SOC.Am. Bull., 87: 1101-1104. Pai, S.I., 1954. Fluid Dynamics of Jets. Van Nostrand, Princeton, N.J. Pai, S.I., 1957. Viscous Flow Theory, 11. Turbulent Flow. Van Nostrand, Princeton, N.J. Pai, S.I., 1972. J. Math. Phys. Sci., 6: 137-161. Pai, S.I., Hsieh, T. and OKeefe, J.A.. 1972. J. Geophys. Res., 77: 3631-3649. Palmer, H.S., 1927. Geogr. Rev., 17: 627-631. Palmer, J.R., 1834. Philos. Trans. R. Soc. London, 124: 567-576. Palmer, R.H., 1928. J. Geol., 36: 176-180. Paltz, S.,Drew, T.B. and Ryan, W.P., 1931. Trans. Am. Inst. Chem. Eng., 26: 1 18-146. Pan, F. and Acrivos, A.. 1967. J. Fluid Mech., 28: 643-655. Panin, N., 1967. Mar. Geol., 5: 207-219. Pannekoek, A.J., 1960. Bol. Inf., Asoc. Venez. Geol., Miner. Pet., 3: 221-229. Pantin, H.M., 1979. Mar. Geol., 31: 59-99. Parea, G.C., 1965. Atti Mem. Acad. Sci. Lett. Modena, 7: 5-97. Parent, J.D., Yagol, N. and Steiner, C.S., 1947. Chem. Eng. Progr.. 43: 429-436.

617 Park, C.C., 1977. J. Hydrol., 33: 133-146. Park, C.C., 1981. Rev. Geomorphol. Dyn., 30: 1-9. Park, Y.A., 1974. Meyniana, 24: 73-89. Parkash, B., 1970. J. Sediment. Petrol., 40: 572-590. Parkash, B. and Middleton, G.V., 1970. Sedimentology, 14: 259-293. Parker, G., 1975. Water Resour. Res., 1 1 : 551-552. Parker, G., 1976. J. Fluid Mech., 76: 457-480. Parker, T.J. and McDowell, A.N., 1955. Bull. Am. Assoc. Pet. Geol., 39: 2384-2470. Parker, W.R., 1973. Sedimentology, 20: 615-623. Parker, W.R., 1975. In: J. Hails and A. Carr (Editors), Nearshore Sediment Dynamics and Sedimentation. Wiley, London, pp. 150- 178. Parkin, J., 1976. Proc. R. Ir. Acad., Sect. B, 76: 577-606. Parry, J.T., 1960. Can. Geogr., No. 1: 14-21. Parsons, D.A., 1960. J. Hydraul. Div. ASCE, 86(HY4): 21-34. Parsons, I. and Butterfield, A.W., 1981. J. Geol. SOC.,London, 138: 289-306. Passarge, S., 1904. Die Kalahari, 2 vols. Reimer, Berlin. Patankar, S.V. and Spalding, D.B., 1970. Heat and Mass Transfer in Boundary Layers. Intertext Books, London, 2nd ed. Patel, R.P., 1973. AIAA J., I 1 : 67-71. Patnaik, P.C., Sherman, F.S. and Corcos, G.M., 1977. J. Fluid Mech., 73: 215-240. Paulissen, E., 1973. Verh. K. Vlaam. Acad. Wet., No. 35. Pavoni, N., 1959. Eclog. Geol. Helv.. 52: 941-949. Payne, R., Connolly, J.R. and Abbott, W.H., 1972. Geol. SOC.Am. Bull., 83: 481-486. Peabody, F.E., 1947. J. Sediment. Petrol., 17: 73-76. Peacock, J.D., 1966. Bull. Geol. Surv. G.B., No. 24: 157-162. Peacock, W.H. and Seed, H.B., 1968. J. Soil Mech. Found. Div. ASCE. 94(SM3): 689-708. Peake, D.J. and Galway, R.D., 1965. In: Recent Developments in Boundary Layer Research. AGARDograph 97, vol. 2: 1049-1080. Pearce, B.R. and Cooper, C.K., 1981. J. Hydraul. Div. ASCE. 107(HY3): 285-302. Pearce, K.W. and Donald, M.B., 1959. Chem. Eng. Sci., 10: 212-214. Peck, R.B. and Kaun, W.V., 1948. Proc. 2nd Int. Conf. Soil Mech. Found. Eng., 2: 31-33. Pedersen, G.K. and Surlyk, F., 1977. Sedimentology, 24: 581-590. Pedgley, D.E., 1967. Weather, 22: 42-48. Peel, R.F., 1966. Trans. Inst. Br. Geogr., No. 38: 1-23. Pelevin, V.S., 1965. In: Soviet Antarctic Expedition. Information Bulletin. vol. 111. Elsevier, Amsterdam, pp. 156-161. Pelletier, B.R. and Shearer, J.M., 1972. Proc. 24th Int. Geol. Congr., Sect. 8: 251-261. Pellew, A. and Southwell, R.V., 1940. Proc. R. SOC.London, Ser. A, 176: 312-343. Pendlebury, D.C. and Dobson, M.R., 1976. Scott. J. Geol., 1 1 : 315-332. Penny, W.G. and Thornhill, C.K., 1951. Philos. Trans. R. SOC.London, Ser. A, 244: 285-3 1 I. Pepper, J.F., De Witt, W. and Demarest, D.F., 1954. U.S. Geol. Surv., Prof. Pap., 259. Perkins, H.J., 1970. J. Fluid Mech., 44: 721-740. Perret, F.A., 1924. Publ. Carnegie Inst. Wash., No. 339. Perret, F.A., 1935. Publ. Carnegie Inst. Wash., No. 458. Perry, A.E. and Fairlie, B.D., 1974. Adv. Geophys., B18: 299-315. Perry, A.E. and Fairlie, B.D., 1975. J. Fluid Mech., 69: 657-672. Perry, A.E. and Hoffmann, P.H., 1976. J. Fluid Mech., 77: 355-368. Perry, A.E. and Joubert, P.N., 1965. J. Fluid Mech., 22: 285-304. Perry, W.J. and Roberts, H.G., 1968. J. Geol. SOC.Aust., 15: 51-56. Persen, L.N., 1971. Z. Flugwiss., 19: 116-119. Pescatore, T., 1966. Geol. Rom., 5: 99-116. Pestrong, R., 1965. Publ. Earth Sci. Stanford Univ., lO(2): 1-87.

618 Pestrong, R., 1972a. Sediment. Geol., 8: 251 -288. Pestrong, R., 1972b. Calif. Geology, 25(2): 27-40. Peterlin, A., 1938. Z. Phys., 1 1 I: 232-263. Petersen, R.A., 1978. J. Fluid Mech., 89: 469-495. Peterson, D.W., 1970. J. Geol. Educ., 18: 66-76. Peterson, G.L., 1966. Geol. Soc.Am. Bull., 77: 833-842. Peterson, G.L., 1968. Sediment. Geol., 2: 177-190. Pett, J.W. and Walker, R.G., 1971. J. Sediment. Petrol., 41: 114-128. Pettijohn, F.J., 1957. Sedimentary Rocks. Harper, New York, N.Y., 2nd ed. Pettijohn, F.J. and Potter, P.E., 1964. Atlas and Glossary of Primary Sedimentary Structures. Springer, Berlin. Pfeffer, K.H., 1976. Z. Geomorphol., S26: 6-34. Phillips, A.C. and Walker, G.T., 1932. Q. J. R. Meteorol. SOC.,58: 23-30. Phillips, C.R. and Smith, T.N., 1969. Chem. Eng. Sci., 24: 1321-1335. Phillips, C.R. and Smith, T.N.. 1971. Ind. Eng. Chem. Fund., 10: 581-587. Phillips, O.M. and Banner, M.L., 1974. J. Fluid Mech., 66: 625-640. Picard, M.D., 1966. J. Sediment. Petrol., 36: 1050- 1057. Picard, M.D. and High, L.R., 1969. Bull. Geol. Surv. Utah, 82: 175-190. Picard, M.D. and High, L.R., 1970. Spec. Stud. Utah Geol. Miner. SUN., No. 33. Picard, M.D. and High, L.R., 1973. Sedimentary Structures of Ephemeral Streams. Elsevier, Amsterdam. Picha, F. and Niem. A.R., 1974. J. Sediment. Petrol., 44: 328-335. Pierce, D., 1961. J. Fluid Mech., 1 1 : 460-464. Piercy, N.A.V. and Richardson, E.G., 1928. Philos. Mag., (7)6: 970-977. Piercy, N.A.V. and Richardson, E.G.. 1930. Philos. Mag., (7)9: 1038-1041. Piest, R.F., Bradford, J.M. and Wyatt, G.M., 1975. J. Hydraul. Div. ASCE, IOI(HY1): 65-79. Pigford, R.L. and Baron, T., 1965. Ind. Eng. Chem. Fund., 4: 81-87. Pinchbeck, P.H. and Popper, F., 1956. Chem. Eng. Sci., 6: 57-64. Pinczewski, W.V. and Sideman, S., 1974. Chem. Eng. Sci., 29: 1969-1976. Pise, J., Pribyl, J., Stelcl, 0. and Vlcek, K., 1975. Petermanns Geogr. Mitt., 119: 123-128. Plank, V.G., 1966. Tellus, 18: 1-12. Plate, E.J., 1970. J. Eng. Mech. Div. ASCE, 96(EM3): 295-312. Plate, E.J., I971 a. Aerodynamic characteristics of atmospheric boundary layers. U.S. Atomic Energy Commission, Oak Ridge, Tenn. Plate, E.J., 1971b. Agric. Meteorol., 8: 203-222. Plate, E.J., Chang, P.C. and Hidy, G.M., 1969. J. Fluid Mech., 35: 625-656. Plesset, M.S. and Whipple, C.G., 1974. Phys. Fluids, 17: 1-17. Plessman, W., 1961. Geol. Jahrb., 78: 503-566. Pluhar, A. and Ford, D.C., 1970. Z. Geomorphol., 14: 392-410. Poddar, M.C., 1952. Bull. Geol. Surv. India, Ser. B, No. 2. Poole, E.G., 1977. Bull. Geol. Surv. G.B., No. 57. Popov, I.V., 1965. Sov. Hydrol. Select. Pap. 1964, No. 2: 188-195. Postma, H., 1967. In: G.H. Lauff (Editor), Estuaries. American Association for the Advancement of Science, Washington, D.C., pp. 158-180. Potter, P.E., 1963. Geol. Sum. Ill., Rep. Invest., No. 217. Potter, P.E. and Glass, H.D., 1958. Geol. SUN. Ill., Rep. Invest., No. 204. Potter, P.E. and Pettijohn, F.J., 1963. Palaeocurrents and Basin Analysis. Springer, Berlin. Potter, P.E. and Scheidegger, A.E., 1966. Sedimentology, 7: 233-240. Powell, C.McA., 1969. Geol. Soc. Am. Bull., 80: 2585-2594. Powell, C.McA., 1973. Geol. Soc. Am. Bull., 84: 3045-3050. Powers, S., 1921. J. Geol., 29: 66-80. Powers, W.E., 1936. J. Geol., 44:213-219.

619 Prakash, S. and Gupta, M.K., 1971. In: D.A. Howells, I.P. Haigh and C. Taylor (Editors), Dynamic Waves in Civil Engineers. Wiley-Interscience, London, pp. 228-244. Prandle, D., 1975. Proc. R. SOC.London, Ser. A, 344: 509-539. Prandtl, L., 1927a. Proc. 2nd Int. Conf. Appl. Mech., Zurich, pp. 62-75. Prandtl, L., 1927b. The generation of vortices in fluids of small viscosity. J. R. Aeronaut. SOC., 31: 720-741. Prandtl, L., 1952. Essentials of Fluid Dynamics. Blackie, London. Pratt, R.M., 1968. US. Geol. Surv., Prof. Pap., 529-B. Prentice, J.E., 1956. Geol. Mag., 93: 393-400. Prentice, J.E., 1960. J. Geol., 68: 217-225. Prentice, J.E., 1962a. In: K. Coe (Editor), Some Aspects of the Variscan Fold Belt. Manchester University Press, Manchester, pp. 93- 108. Prentice, J.E., 1962b. Proc. Geol. Assoc., 73: 171 - 185. Price, G.A. and Clements, M.S., 1974. J. Inst. Water Pollut. Control, No. 1: 3-14. Price, N.J., 1966. Fault and Joint Development. Pergamon, New York, N.Y. Price, R.J., 1972. Geogr. Mag., 44: 687-691. Price, W.H., 1947. J. Am. Concr. Inst., 19: 1009-1023. Pringle, J. and Eckford, R., 1945. Trans. Edinburgh Geol. SOC.,14: 5-7. Prior, D.B. and Coleman, J.M., 1980a. Mar. Geol., 36: 227-239. Prior, D.B. and Coleman, J.M., 1980b. Mar. Geotech., 3: 37-60. Probstein, R.F. and Gold, H., 1970. AIAA J., 8: 364-366. Proudman, J. and Doodson, A.T., 1926. Proc. Math. SOC.London, (2)24: 140-149. Pruden, B.B. and Epstein, N., 1964. Chem. Eng. Sci., 19: 696-700. Prudhoe, J. and Whitmore, R.L., 1964. Br. Chem. Eng., 9: 371-375. Pruppacher, H.R., Le Clair, B.P. and Hamielec. A.E., 1970. J. Fluid Mech., 44: 781-790. Prus-Chacinski, T.M., 1954. Publ. Int. Assoc. Sci. Hydrol., No. 38: 311-318. Pryor, W.A., 1971. Sediment. Geol., 6: 221-254. Psuty, N.P., 1965. Ann. Assoc. Am. Geogr., 5 5 : 112-124. Psuty, N.P., 1966. The geomorphology of beach ridges in Tabasco, Mexico. La. State Univ., Coastal Stud. Inst., Tech. Rep., No. 30. Pugh, H.Ll.D., 1950. Snow fences. Tech. Pap. Road Res., Lab., No. 19. Pugh, H.Ll.D. and Price, W.I.J., 1954. Polar Rec., 7: 4-23. Pugh, J.C., 1953. Bull. Inf. Com. Cent. Oceanogr. Etude Cbtes, 5(6): 245-276. Puigdefabrigas, C., 1973. Sedimentology, 20: 133- 144. Puigdefabrigas, C., 1974. Bull. Cent. Rech. Pau, 8: 305-325. Puigdefabrigas, C. and Van Vliet, A,, 1978. Mem. Can. SOC.Pet. Geol., 5 : 469-485. Pullan, R.A., 1964. J.W. Afr. Sci. Assoc., 9: 115-139. Pumpelly, R.W., 1908. In: R. Pumpelly (Editor), Explorations in Turkestan. Publ. Carnegie Inst. Wash., No. 2, Vol. 73, Pt. V: 243-337. Purdy, E.G., 1974. In: L.F. Laporte (Editor), Reefs in Time and Space. SOC.E o n . Paleontol. Mineral., Spec. Publ., 18: 9-76. Purdy, E.G., Pusey, W.C. and Wantland, K.F., 1975. In: K.F. Wantland and W.C. Pusey (Editors), Belize Shelf-Carbonate Sediments, Clastic Sediments and Ecology. Studies in Geology, No. 2. American Association of Petrolium Geologists, Tulsa, Okla., pp. 1-52. Putzer, H., 1971. Z. Geomorphol., 15: 330-338. Queney, P., 1948. Bull. Am. Meteorol. SOC.,29: 16-26. Queney, P. and Dubief, J., 1943. Trav. Inst. Rech. Sahariennes, 2: 169-176. Quick, M.C., 1974. J. Hydraul. Div. ASCE, 100(HY6): 741-752. Quirke, T.T., 1930. J. Geol., 38: 88-91. Quraishy, M.S., 1944. Current Sci. (India), 13: 36-39. Quraishy, M., 1973. J. Res. Sind Univ., Sci. Ser., 7: 95-152. Raask, E., 1969. Wear, 13: 301-315.

620 Rabien, A., 1956. Abh. Hess. Landesamt. Bodenforsch., 16: 1-83. Radomski, A., 1958. Acta Geol. Pol., 8: 335-409. Radwanski. A., 1960. Acta Geol. Pol., 10: 221-246. Radwanski, A. and Roniewicz, P., 1962. Acta Geol. Pol., 12: 296-305. Raisz, E.. 1955. Photogrammetric Eng., 21: 738. Raithby, G.D., Hallett, W.L., Crawford, T.L. and Slawson, P.R., 1978. Boundary-Layer Meteorol., 15: 181-194. Rajagopal, E.S., 1960. Z. Phys. Chem., 23: 342-347. Rajappa, N.R., 1970. Acta Mech.. 10: 193-205. Rajappa, N.R. and Amaranth, T., 1977. Q. J. Mech. Appl. Math., 30: 13I - 141. Rajaratnam, N., 1976. Turbulent Jets. Elsevier, Amsterdam. Rajaratnam, N. and Subramanya, K., 1968. J. Hydraul. Div. ASCE, 94(HYl): 95-1 12. Ramberg, H., 1959. Norsk. Geol. Tidsskr., 29: 99-151. Ramberg, H., 1960. Am. J. Sci., 258: 36-46. Ramberg, H., 1961. Am. J. Sci., 259: 382-390. Ramberg, H.. 1962. Geol. Rundsch., 51: 405-439. Ramberg, H., 1963a. Bull. Am. Assoc. Pet. Geol., 47: 484-505. Ramberg, H., 1963b. Bull. Geol. Inst. Univ. Uppsala, 42: 1-96. Ramberg, H., 1964. Tectonophysics, 4: 307-34 I . Ramberg, H., 1966. Proc. 3rd Symp. on Salt, pp. 261-270. Ramberg, H., 1967. Gravity, Deformation and the Earth’s Crust. Academic Press, London. Ramberg, H., 1968a. Phys. Earth Planet. Inter., 1 : 63-87. Ramberg, H., 1968b. Phys. Earth Planet. Inter., 1 : 427-474. Ramberg. H., 1970a. Phys. Earth Planet. Inter., 2: 203-232. Ramberg, H., 1970b. Phys. Earth Planet. Inter., 4: 83-120. Ramberg, H., 1972a. Phys. Earth Planet. Inter., 5 : 45-60. Ramberg, H., 1972b. J. Geophys. Res., 77: 877-889. Ramberg, H., 1973. In: K.A. De Jay and R. Scholten (Editors), Gravity and Tectonics. Wiley, New York, N.Y., pp. 49-66. Ramsay. J.G., 1967. Folding and Fracturing of Rocks. McGraw-Hill, New York, N.Y. Rao, N.S.G. and Thiruvengadam, A,, 1961. J. Hydraul. Div. ASCE, 87(HY5): 37-62. Rapp, A., 1975a. Geol. For. Stockholm Forh., 97: 142-150. Rapp, A., 1975b. Svensk Naturvetensk., 1975: 74-82. Rascoe, B., 1975. Bull. Am. Assoc. Pet. Geol., 59: 1626-1638. Ratkowsky, D.A. and Rotem, Z., 1968. Phys. Fluids, 1 1 : 2761-2763. Ratte, J.C. and Steven, T.A., 1967. U.S.Geol. Surv., Prof. Pap., 524-H. Rattigan, J.H., 1967. J. Geol. SOC.Aust., 14: 5-18. Raudkivi, A.J., 1963. J. Hydraul. Div. ASCE, 89(HY6): 15-36. Raudkivi, A.J., 1966a. J. Fluid Mech., 26: 507-514. Raudkivi, A.J., 1966b. Proc. 2nd Australas. Conf. Hydraul. Fluid Mech., A135-Al42. Raustein, E., 1972. Met. Ann., 6(6): 125-139. Rautman, C.A. and Dott. R.H., 1977. J. Sediment. Petrol., 47: 101-106. Ray, P.K., 1976. J. Sediment. Petrol., 46: 788-801. Rayleigh, Lord, 1880. Proc. Math. SOC.London, 1 1 : 57-70. Rayleigh, Lord, 1883. Proc. Math. SOC.London, 14: 170-177. Rayleigh, Lord, 1916a. Proc. R. SOC.London, Ser. A, 93: 148-154. Rayleigh, Lord, 1916b. Philos. Mag., (6)32: 529-546. Reade, T.M., 1884. Geol. Mag., 21: 20-22. Reading, H.G., 1965. Norg. Geol. Unders., No. 234: 167-191. Reboux, P., 1954. Phenomenes de Fluidisation. Association Frangaise de Fluidisation, Paris. Rector, R.L., 1954. Tech. Mem. U.S. Beach Erosion Board, No. 41. Reed, B., Galvin, C.J. and Miller, J.P., 1962. Am. J. Sci., 260: 200-210.

62 1 Rehbock, T., 1930. Z. Dtsch. Geol. Ges., 81: 497-534. Reid, R.O.,1957. Tech. Mem. U.S. Beach Erosion Board, No. 93. Reiman, T.C. and Sabersky, R.H., 1968. Int. J. Heat Mass Transfer, 1 1 : 1083- 1085. Reimnitz, E. and Barnes, P.W., 1974. In: J.C. Reed and J.E. Sater (Editors), The Coast and Shelf of the Beaufort Sea. Arctic Institute of North America, Arlington, Va., pp. 301-353. Reimnitz, E. and Marshall, N.F., 1965. J. Geophys. Res., 70: 2363-2376. Reimnitz, E., Barnes, P., Forgatsch, T. and Rodeick, C., 1972. Mar. Geol., 13: 323-334. Reimnitz, E., Barnes, P.W. and Alpha, T.R., 1973. Misc. Field Stud. U.S. Geol. Surv., Map MF-532. Reimnitz, E., Toimil, L.J., Shepard, F.P. and Gutierrez-Estrada, M., 1976. Geology, 4: 395-400. Reimnitz, E., Barnes, P., Toimil, L.J. and Melchior, J., 1977. Geology, 5: 405-408. Reimnitz, E., Toimil, L. and Barnes, P., 1978. Mar. Geol., 28: 179-210. Reineck, H.-E., 1955. Senckenbergiana Lethaea, 36: 347-357. Reineck, H.-E., 1956. Senckenbergiana Lethaea, 37: 129- 146. Reineck, H.-E., 1958a. Geol. Rundsch., 47: 73-82. Reineck, H.-E., 1958b. Natur Volk, 88: 81-84. Reineck, H.-E., 1960. Jahresber. Forschungsanst. Norderney, 1 1 : 21 -38. Reineck, H.-E., 1961. Senckenbergiana Lethaea, 42: 5 1-67. Reineck, H.-E., 1962. Natur Mus., 92: 151-172. Reineck, H.-E., 1963. Abh. Senckenb. Naturforsch. Ges.. No. 505. Reineck, H.-E., 1970a. Natur Mus., 100: 105-111. Reineck, H.-E., 1970b. Rinnen. In: H.-E. Reineck (Editor), Das Watt. Kramer, Frankfurt, pp. 56-60. Reineck, H.-E., 1974a. Senckenbergiana Marit., 6: 47-63. Reineck, H.-E., 1974b. Senckenbergiana Marit., 6: 65-73. Reineck, H.-E., 1974~.Senckenbergiana Marit., 6: 145- 147. Reineck, H.-E., 1974d. Geol. Rundsch., 63: 1087-1 101. Reineck, H.-E., 1976. Rev. Geogr. Montreal, 30: 197-200. Reineck, H.-E. and Singh, I.B., 1971. Senckenbergiana Marit., 3: 185-201. Reineck, H.-E. and Singh, I.B., 1972. Sedimentology, 18: 123- 128. Reineck, H.-E. and Singh, I.B., 1973. Depositional Sedimentary Environments. Springer, Berlin. Reineck, H.-E. and Wunderlich, F., 1969. Senckenbergiana Marit., 50: 79-84. Reineck, H.-E., Gutmann, W.F. and Hertweck, G., 1967. Senckenbergiana Lethaea, 48: 219-275. Reineck, H.-E., Ddjes, J., Gadow, S. and Hertweck, G., 1968. Senckenbergiana Lethaea, 49: 26 1-309. Reinhardt, J. and Cleaves, E.T., 1978. Geol. Soc. Am. Bull., 89: 307-313. Reinson, G.E., 1979. Mar. Geol., 3 I : 279-296. Reiter, E.R., 1963. Jet-Stream Meteorology. University of Chicago Press, Chicago, Ill. Renault, P.,1963. Proc. 3rd Congr. Speleol., 2: 105-1 14. Rettger, R.E., 1935. Bull. Am. Assoc. Pet. Geol., 19: 271-292. Reuter, H., 1966. Chem. Eng. Progr. Symp., Ser. No. 62: 92-99. Revelle, R. and Emery, K.O., 1957. U.S.Geol. Surv., Prof. Pap., 260-T: 699-709. Rex, R.W., 1955. Arctic, 8: 177-186. Reynolds, A.J., 1962. J. Fluid Mech., 14: 552-556. Reynolds, A.J., 1965. J. Fluid Mech., 22: 113-133. Reynolds, D.L., 1954. Am. J. Sci., 252: 577-614. Reynolds, D.L., 1961. J. Geol., 69: 110-117. Reynolds, D.L., 1969. Proc. Geol. Soc. London, No. 1655: 110-1 13. Reynolds, O., 1874. Proc. Manchester Lit. Philos. SOC.,14: 7-12.

622 Reynolds, O., 1883. Philos. Trans. R. SOC.London, Ser. A, 174: 935-982. Reynolds, O., 1885. Philos. Mag., (5)20: 469-489. Reynolds, O., 1886. Proc. R. Inst. G.B., 1 1 : 354-363. Ricci-Lucchi, F., 1969a. G. Geol.. (2a)36: 363-438. Ricci-Lucchi, F., 1969b. G. Geol., (2a)35: 168-198. Ricci-Lucchi, F., 1969~.G. Geol., (2a)36: 203-282. Ricci-Lucchi, F., 1970. Sedimentografia. Zanichelli, Bologna. Ricci-Lucchi, F. and Valmori, E., 1980. Sedimentology, 27: 241 -270. Rice, R.C.. 1939a. Proc. Liverpool Geol. SOC.,17: 349-355. Rice, R.C., 1939b. Proc. Liverpool Geol. SOC.,17: 361-370. Rice, W.J. and Wilhelm, R.H., 1958. AIChE J, 4: 423-429. Rich, J.L., 1942. Spec. Publ. Am. Geogr. SOC.,No. 26. Rich, J.L., 1950. Bull. Am. Assoc. Pet. Geol.. 34: 717-741. Rich, J.L., 1951. Bull. Geol. SOC.Am., 62: 1-20. Richards, A.F., 1959. Bull. Volcanol., (2)22: 73-123. Richards, A.F., 1965. Bull. Volcanol., (2)27: 1-23. Richards, K.S., 1973. Am. J. Sci., 273: 877-896. Richards, K.S., 1976a. Earth Surface Process., 1: 71-88. Richards, K.S., 1976b. Geol. Soc. Am. Bull., 87: 199-206. Richards, K.S., 1976~.Geol. SOC.Am. Bull., 87: 883-890. Richardson, H., 1903. Rep. Yorks Philos. Soc. 1902, p. 43-58. Richardson, J.F., 1971. In: J.F. Davidson and D. Harrison (Editors), Fluidization. Academic Press, London, pp. 26-64. Richardson, J.F. and Meikle, R.A., 1961a. Trans. Inst. Chem. Eng., 39: 348-356. Richardson, J.F. and Meikle, R.A., 1961b. Trans. Inst. Chem. Eng., 39: 356-362. Richardson, J.F. and Zaki, W.N., 1954a. Trans. Inst. Chem. Eng., 32: 35-53. Richardson, J.F. and Zaki, W.N., 1954b. Chem. Eng. Sci., 3: 65-73. Richardson, P.D., 1968. J. Sediment. Petrol., 38: 965-970. Richardson, W.E., 1951. Weather, 6: 383. Richardson, W.E., 1954. Weather, 9: 117-121. Richardson, W.E. and Harper, R.D.M., 1957. J. Glaciol.. 3: 25-27. Richter, C.F., 1958. Elementary Seismology. Freeman, San Francisco, Calif. Richter, D., 1965. Geol. Mitt., 4: 153-210. Richter, D., 1967. Geol. Rundsch., 56: 543-561. Richter. R., 1926. Natur Mus., 56: 389-407. Riddell, J.F., 1969. Can. J. Earth Sci., 6: 231-246. Rider, M.H., 1974. Proc. R. Ir. Acad., B74: 125-142. Rider, N.E., 1952. Q. J. R. Meteorol. Soc.. 78: 97-101. Ridgway. K. and Rupp, R., 1970. Chem. Process. Eng. (Bombay), May 1970: 82-85. Ridgway, K. and Rupp, R., 1971. Powder Technol., 4: 195-202. Ridgway, K., Rupp, R. and Sanchez, A., 1968. J. Pharm. Pharmacol., 20: S185-SI93. Rietema, K. and Mutsers, S.M.P., 1978. In: J.F. Davidson and D.L. Keairns (Editors), Fluidization. Cambridge University Press, Cambridge, pp. 8 1-86. Rigby, G.R., Van Blockland, G.P., Parks, W.H. and Capes, C.E., 1970. Chem. Eng. Sci., 25: 1729- 1741. Rigby, J.K., 1958. J. Sediment. Petrol., 28: 298-315. Rigby, J.K. and Roberts, H.H., 1976. Spec. Pap. Brigham Young Univ. Geol. Stud., No. 4: 1-95. Riley, C., 1943. J. Geol., 5 1: 270-275. Riley, S.J., 1975. Sediment. Geol., 14: 253-258. Ringleb, F.O., 1961. In: G.V. Lachmann (Editor), Boundary Layer and Flow Control, vol. 2. Pergamon, London, pp. 265-294.

623 Ripley, H.C., 1927. Trans. ASCE, 5 1 : 1907- 1938. Riviere, A., Arbey, F. and Vernhet, S., 1961. C. R. Acad. Sci., D252: 767-769. Roache, P.J. and Mueller, T.J., 1970. AIAA J., 8: 530-538. Roberts, D., 1972. Geol. Mag., 109: 235-242. Roberts, D.G. and Kidd, R.B., 1979. Mar. Geol., 33: 175-191. Roberts, D.G., Hogg, N.G., Bishop, D.G. and Flewellen, C.G., 1974. Deep-sea Res., 21: 175- 184. Roberts, H.H., Murray, S.P. and Suhayda, J.N., 1975. J. Mar. Res., 33: 233-260. Roberts, J.D., 1974. Norg. Geol. Unders., No. 303: 57-1 18. Robertson, J.M. and Huang, W.H., 1969. J. Appl. Math. Phys., 18: 621-642. Robinson, A.H.W., 1956. J. Inst. Navig., 9: 20-46. Robinson, A.H.W., 1960. Geography, 45: 183-199. Robinson, A.R., Tomasin, A. and Artegiani, A., 1973. Q. J. R. Meteorol. SOC.,99: 688-692. Robinson, A.R., Luyten, J.R. and Fuglister, F.C., 1974. J. Phys. Oceanogr., 4: 237-255. Robinson, J.L., 1974. J. Fluid Mech., 63: 723-752. Robinson, J.V., 1949. J. Phys. Chem., 53: 1042-1056. Robinson, J.V., 1951. J. Phys. Chem., 5 5 : 455-464. Robson, D.A., 1956. Q. J. Geol. SOC.London, 116: 241-258. Rocheleau, M. and Lajoie, J., 1974. J. Sediment. Petrol., 44: 826-836. Rockwell, D. and Knisely, C., 1979. J. Hydraul. Div. ASCE, 105(HY8): 959-979. Roep, T.B., Beets, D.J., Dronkert, H. and Pagnier, H., 1979. Sediment. Geol., 22: 135-163. Roland, N.W., 1976. Geol. Jahrb., A33: 1 17- 131. Roll, H.U., 1965. Physics of the Marine Atmosphere. Academic Press, New York, N.Y. Rona, P.A., 1969. J. Sediment. Petrol., 39: 1132-1141. Roobol, M.J., 1972. Geol. Mag., 109: 393-404. Roots, E.F. and Swithinbank, C.W.M., 1955. Polar Rec., 7: 380-387. Roques, H., 1969. Trans. Cave Res. Group G.B., 1 1 : 139-163. Rosberg, J.E., 1925. Fennia, 46(2): 1-103. Rose, J. and Letzer, J.M., 1977. J. Glaciol., 18: 471-480. Rose, W.I., Pearson, T. and Bonis, S., 1977. Bull. Volcanol., 40: 23-38. Rosenhead, L., 1931. Proc. R. SOC.London, Ser. A, 134: 170-192. Rosenhead, L., 1963. Laminar Boundary Layers. Clarendon Press, Oxford. Roshko, A., 1954a. NACA Rep., No. 1 191. Roshko, A., 1954b. NACA Tech. Note, No. 3169. Roshko, A., 1955a. J. Aeronaut. Sci., 22: 124-132. Roshko, A., 1955b. NACA Tech. Note, No. 3488. Roshko, A., 1961. J. Fluid Mech., 10: 345-356. Roshko, A., 1976. AIAA J., 14: 1349-1357. Roshko, A. and Thomke, G.J., 1966. AIAA J., 4: 975-980. Ross, C.S. and Smith, R.L., 1961. U.S. Geol. SUIV.Prof. Pap., 366. Rossi, G., 1976. Z. Geomorphol., S26: 124-152. Rossiter, J.R., 1954. Philos. Trans. R. SOC.London, Ser. A, 246: 371-400. Rotem, Z., Ratkowsky, D.A. and Neilston, J.E., 1970. Phys. Fluids, 13: 2650-2656. Rouse, H. and Jezdinksy, V., 1966. J. Hydraul. Div. ASCE, 92(HY3): 1-12. Rowe, M., 1970. J. Fluid Mech., 43: 771-783. Rowe, P.N., 1971. In: J.F. Davidson and D. Harrison (Editors), Fluidization. Academic Press, London, pp. 121-191. Rowe, P.N., Nienow, A.W. and Agbim, A.J., 1972a. Trans. Inst. Chem. Eng., 50: 310-323. Rowe, P.N., Nienow, A.W. and Agbim, A.J., 1972b. Trans. Inst. Chem. Eng., 50: 324-333. Rowe, P.N. and Partridge, B.A., 1965. Trans. Inst. Chem. Eng., 43: T157-TI75. Roy, M., 1952. C. R. Acad. Sci., 234: 2501-2504. Rozovskii, I.L., 1961. Flow of Water in Bends of Open Channels. Israel Program for Scientific Translations, Jerusalem.

624 Rubey, W.W., 1933. Am. J. Sci., 225: 325-338. Rucklin, H., 1938. Senckenbergiana, 20: 94-1 14. Ruddiman, W.F., 1972. Geol. SOC.Am. Bull., 83: 2039-2062. Rudnicki, J., 1960. Speleol. Bid. Speleoklubu Warsz., 2( I): 17-30. Rudnicki, J., 1962. Proc. 2nd Int. Congr. Speleol., 1: 344-345. Rudowski, S., 1964. Acta Geol. Pol., 14: 131-150. Rudowski, S., 1970. Acta Geol. Pol., 20: 45 1-483. Ruegg, G.H.J., 1975. Meded. Rijks Geol. Dienst., N. S., 26(1): 17-37. Rupke, N.A., 1976. Sedimentology, 23: 43-65. Rusnak, G.A., 1957. J. Sediment. Petrol., 27: 41-55. Russell, R.J., 1932. Univ. Calif. Publ. Geogr., 6: 23-121. Russell, R.J., 1954. Ann. Assoc. Am. Geogr., 44: 363-391. Russell, R.J., 1959. Z. Geomorphol., 3: 227-236. Russell, R.J. and McIntire, W.G., 1965. Geol. SOC.Am. Bull., 76: 307-320. Rust, B.R., 1965. Scott. J. Geol., 1: 231-246. Rust, B.R., 1968. J. Sediment. Petrol., 38: 87-91. Rust, B.R., 1972. Sedimentology, 18: 221-245. Rust, B.R., 1976. Can. J. Earth Sci., 14: 175-184. Rust, B.R., 1978. In: A.B. Miall (Editor), Fluvial Sedimentology. Mem. Can. SOC.Pet. Geol., 5 : 187-198. Rust, I.C.. 1961. Trans. Geol. SOC.S. Afr., 64: 99. 'Rutgers, R., 1962a. Rheol. Acta, 2: 202-210. 3: 118-122. Rutgers, R., 1962b. Rheol. Acta, 2: 305-348. Ruth, D.W., Hollands, K.G.T. and Raithby, G.D., 1980. J. Fluid Mech., 96: 461-479. Rutten, M.G. and Schanberger, H.J.M., 1957. Geol. Mijnbouw, 19: 214-220. Ryan, W.B.F., Workum, F. and Hersey, J.B., 1965. Geol. SOC.Am. Bull., 76: 1261-1282. Sachs, P., 1972. Wind Forces in Engineering. Pergamon, Oxford. Sadeh, W.Z. and Brauer, H.J., 1980. J. Fluid Mech., 99: 53-64. Sadeh, W.Z., Sutera, S.P. and Maeder, P.F., 1970a. Z. Angew. Math. Phys., 21: 699-716. Sadeh, W.Z., Sutera, S.P. and Maeder, P.F., 1970b. Z. Angew. Math. Phys., 21: 717-742. Sainsbury, C.L., 1956. Bull. Geol. Soc. Am., 67: 1659-1660. Sakalowsky, P.P., 1975a. Z. Geomorphol., 19: 460-478. Sakalowsky, P.P., 1975b. Mar. Geol., 18: M35-M43. Sallenger, A.H., 1979a. J. Sediment. Petrol., 49: 553-562. Sallenger, A.H.. 1979b. Mar. Geol., 29: 23-37. Sallenger, A.H., 1981. J. Sediment. Petrol., 51: 261-264. Sanders, J.E., 1960. Geol. Mag., 97: 409-421. Sanders, J.E., 1965. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation. Soc. Econ. Paleontol. Mineral., Spec. Publ., 12: 192-21 7. Sanderson, I.D., 1974. Geol. Stud. Brigham Young Univ., 21: 215-246. Sandford, J. and Ginoux, J.J., 1968. Laminar, transitional and turbulent heat transfer behind a backward facing step in supersonic flow. Van K k m h Inst. Fluid Dyn., Tech. Note, No. 38. Sandmayr, G., 1966. Forschber. Dtsch. Luft-Raumfahrt, No. 66-41. Sani, R.L., 1965. AIChE J., 1 I : 971-980. Saplyukov, F.V., 1973. Sov. Hydro]. Select. Pap., 1971 (5): 465-468. Sarkar, S.K. and Basumallick, S., 1968. J. Sediment. Petrol., 38: 747-754. Sather, N.F. and Lee, K.J., 1972. Progr. Heat Mass Transfer, 6: 575-589. Sato, H., 1959a. J. Phys. Soc. Jpn., 14: 1797-1810. Sato, H., 1959b. J. Fluid Mech., 7: 53-80. Saville, T., 1952. Tech. Mem. U.S. Beach Erosion Board, No. 27. Savit, C.H., Knox, W.A., Blue, D.M. and Paitson, L., 1964. J. Geophys. Res., 69: 701-719.

625 Sawyer, R.A., 1960. J. Fluid Mech., 9: 543-560. Sawyer, R.A., 1963. J. Fluid Mech., 17: 481-498. Saylor, J.H. and Hands, E.B., 1971. Proc. 12th Conf. Coastal Eng., 2: 839-853. Scarlett, B. and Blogg, M.J., 1967. In: A.A.H. Drinkenburg (Editor), Proc. International Symposium on Fluidization, Eindhoven. Netherlands Universities Press, Amsterdam, pp. 82-89. Schlfer, W., 1953. Natur Volk, 83: 355-357. Schattner, I., 1962. Scr. Hierosoloymitana, No. 1 1 . Scheidegger, A.E., 1960. The Physics of Flow through Porous Media. University of Toronto Press, Toronto, Ont. Scheidegger, A.E. and Langbein, W.B., 1966. U.S. Geol. Surv., Prof. Pap., 500-C. Scheidegger, A.E. and Potter, P.E., 1965. Sedimentology, 5 : 289-304. Scheidegger, A.E. and Potter, P.E., 1971. Sedimentology, 17: 41 -49. Schenk, P.E., 1965a. J. Sediment. Petrol., 35: 309-318. Schenk, P.E., 1965b. Science, 159: 309-319. Scherberg, M.G. and Smith, H.E., 1966. Isr. J. Technol., 4: 55-62. Schiener, E.J., 1970. Geol. J., 7: 25-46. Schiffman, A., 1965. Limnol. Oceanogr., 10: 255-260. Schlager, W., Hooke. R.L. and James, N.P., 1976. Geol. SOC.Am. Bull., 87: 1 1 15- 1 I 18. Schlichting, H., 1936. 1ng.-Arch., 7: 1-34. Schlichting. H., 1960. Boundary Layer Theory. McGraw-Hill, New York, N.Y., 4th ed. Schlichting, H., 1971. Trans. ASME. E38: 289-300. Schmidt, E. and Wenner, K., 1941. Forsch. Ges. Ingenieunves., 12: 65-73. Schmincke, H.-U. and Swanson, D.A., 1967. J. Geol., 75: 641-664. Schmincke, H.-U., Fisher, R.V. and Water, A.C., 1973. Sedimentology. 20: 553-574. Schmudde, T.H., 1963. Ann. Assoc. Am. Geogr., 53: 60-73. Schneider, E.D., Fox, P.J., Hollister, D.C., Needham, H.D. and Heezen, B.C., 1967. Earth Planet. Sci. Lett., 2: 351-359. Schofield, R.K. and Keen, B.A., 1929. Nature (London), 123: 492-493. Scholle, P.A., 1971. Geol. SOC.Am. Bull., 82: 629-658. Scholz, C.H. and Engelder, J.T., 1976. Int. J. Rock Mech. Min. Sci., Geomech. Abstr., 13: 149-154. Schou, A., 1967. In: G.H. Lauff (Editor), Estuaries. American Association for the Advancement of Science, Washington, D.C., pp. 129-145. Schreiber, J.F., Pine, G.L., Pipkin, B.W., Robinson, R.C. and Wilt, J.C., 1972. In: C.C. Reeves (Editor), Playa Lake Symposium. Lubbock, Tex. ICASALS Publ. No. 4: 133-184. Schroder, L., 1965. Geol. Jahrb., 82: 655-704. Schroter, H., 1933. Z. Ver. Dtsch. Ing., 77: 865-869. Schugerl, K., 1971. In: J.F. Davidson and D. Harrison (Editors), Fluidization, Adacemic Press, London, pp. 26 1-292. Schugerl, K., Men, M. and Fetting, F., 1961. Chem. Eng. Sci., 15: 1-38. Schultz-Grunow, F., 1956. Z. Angew. Math. Mech., 36: 309. Schumm, S.A., 1956a. Geol. SOC.Am. Bull., 67: 597-646. Schumm, S.A., 1956b. J. Sediment. Petrol., 26: 284-286. Schumm, S.A., 1960a. U.S. Geol. Surv., Prof. Pap., 352-B. Schumm, S.A., 1960b. Am. J. Sci., 258: 177-184. Schumm, S.A., 1963a. Geol. SOC.Am. Bull., 74: 1089-1100. Schumm, S.A., 1963b. Circ. U.S. Geol. Surv., 477. Schumm, S.A., 1967. Science, 157: 1549- 1550. Schumm, S.A., 1968a. US.Geol. Surv., Prof. Pap., 598. Schumm, S.A., 1968b. Geol. SOC.Am. Bull., 79: 1573-1588. Schumm, S.A., 1969. J. Hydraul. Div. ASCE, 95(HY1): 255-273.

626 Schumm, S.A., 1970. Geol. SOC.Am. Bull., 81: 2539-2552. Schumm, S.A., 1971. In: H.W. Shen (Editor), River Mechanics. Colorado State University, Fort Collins, Colo., pp. 5- 1-5-22. Schumm, S.A., 1972. In: J.K. Rigby and W.K. Hamblin (Editors), Recognition of Ancient Sedimentary Environments. SOC.Econ. Paleontol. Mineral., Spec. Publ., 16: 98- 107. Schumm, S.A. and Khan, H.R., 1971. Nature (London), 233: 407-409. Schumm, S.A. and Khan, H.R., 1972. Geol. SOC.Am. Bull., 83: 1755-1770. Schumm, S.A., Khan, H.R., Winkley, B.R. and Robbins, L.G., 1972. Nature (London), 237: 75-76. Schunke, E., 1976. Z. Geomorphol., S26: 65-78. Schwartz, M.L., 1967. J. Sediment. Petrol., 37: 677-683. Schwartz, M.L., 1968. J. Geol., 76: 508-517. Schwartz, M.L.. 1972. Geol. SOC.Am. Bull., 83: 1 1 15-1 116. Schwenk, T., 1965. Sensitive Chaos. Steiner, London. Schwind, R.G., 1962. The three-dimensional boundary layer near a strut. Mass. Inst. Techno]., Gas Turbine Lab., Rep. No. 67. Scorer, R.S., 1949. Q. J. R. Meteorol. Soc.,76: 41-56. Scorer, R.S., 1955. Q. J. R. Meteorol. SOC.,81: 340-350. Scorer, R.S., 1969. Radio Sci., 4: 1299-1308. Scorer, R.S., 1972. Clouds of the World. Lothian, Melbourne. Scorer, R.S., 1978. Environmental Aerodynamics. Horwood, Chichester. Scott, A.M. and Bridgewater, J., 1975. Ind. Eng. Chem. Fund., 14: 22-33. Scott, G.D., 1960. Nature (London), 188: 908-909. Scott, J.T., Myer, G.E., Stewart, R. and Waltham, E.G., 1969. Limnol. Oceanogr., 14: 493-503. Scott, K.M., 1966. Bull. Am. Assoc. Pet. Geol., 50: 72-107. Scott, W.H. and Hansen, E., 1967. Yearb. Carnegie Inst. Wash., 67: 254-258. Seban, R.A., 1964. Trans. ASME, C86: 259-264. Seban, R.A. and Caldwell, G.L., 1968. Trans. ASME, C90: 408-412. Seban, R.A. and Dougherty, D., 1956. Trans. ASME, C78: 217-223. Seban, R.A. and Fox, J., 1963. In: International Developments in Heat Transfer. American Society of Mechanical Engineers, New York, N.Y., pp. 426-43 1. Sedimentation Seminar, 1966. Sedimentology, 6: 95- 1 14. Sedney, R., 1972. Phys. Fluids, 15: 2439-2441. Sedney, R., 1973. AIAA J., 11 : 782-792. Seed, H.B., 1967. J. Soil Mech. Found. Div. ASCE, 93(SM3): 299-323. Seed, H.B., 1968. J. Soil Mech. Found. Div. ASCE, 94 (SM5): 1055-1 122. Seed, H.B. and Goodman, R.E., 1964. J. Soil Mech. Found. Div. ASCE, 90(SM6): 43-73. Seed, H.B. and Idriss, I.M., 1967. J. Soil Mech. Found. Div. ASCE, 93(SM3): 83-108. Seed, H.B. and Idriss, I.M., 1970. A simplified procedure for evaluating soil liquefaction potential. Univ. Calif., Berkeley, Earthquake Eng. Res. Cent., Rep. No. EERC 70-9. Seed, H.B. and Idriss, I.M., 1971. J. Soil Mech. Found. Div. ASCE, 97(SM9): 1249-1273. Seed, H.B. and Lee, K.L., 1965. Studies of the liquefaction potential of sands under cyclic loading conditions. Univ. Calif., Berkeley, Dep. Civ. Eng., Rep. No. TE-65-5. Seed, H.B. and Lee, K.L., 1966. J. Soil Mech. Found. Div. ASCE, 92(SM6): 105- 134. Seed, H.B. and Peacock, W.H., 1970. Application of laboratory test procedures for measuring soil liquefaction characteristics under cyclic loading. University of Calif., Berkeley, Earthquake Eng. Res. Cent., Rep. No. EERC 70-8. Seed, H.B. and Silver, M.L., 1972. J. Soil Mech. Found. Div. ASCE, 98(SM4): 381-397. Seed, H.B. and Wilson, S.D., 1967. J. Soil Mech. Found. Div. ASCE, 93(SM4): 325-353. Seed, H.B., Arango, I. and Chan, C., 1975. Evaluation of liquefaction potential during earthquakes. Univ. Calif., Berkeley, Earthquake Eng. Res. Cent., Rep. EERC 75-28.

627 Seed, H.B., Mori, K. and Chan, C.K., 1977. J. Geotech. Eng. Div. ASCE, 103(GT4): 257-270. Seed, H.B., Arango, I., Chan, C.K., Gomez-Masso, A. and Ascoli, R.G., 1981. J. Geotech. Eng. Div. ASCE, 107(GT4): 501-518. Segerstrom, K., 1950. Bull. US.Geol. Surv., 965-A. Seibold, E., 1963. Prog. Oceanogr., 1 : 3-70. Seibold, E., 1964. Neues Jahrb. Geol. Palaontol., Abh., 120: 233-252. Seiglie, G.A., Froelich, P.N. and Pilkey, O.H., 1976. Deep-sea Res., 23: 89-101. Seilacher, A., 1953. Natur Volk, 83: 263-272. Seilacher, A., 1962. J. Geol., 70: 227-234. Seilacher, A., 1963. Fortschr. Geol. Rheinl. Westf., 10: 81-94. Seilacher, A., 1964. In: J. Imbrie and N.D. Newell (Editors), Approaches to Paleoecology. Wiley, New York, N.Y., pp. 296-316. Seilacher, A. and Meischner, D., 1965. Geol. Rundsch., 54: 596-619. Selby, M.J., 1977. N. Z. J. Geol. Geophys., 20: 949-969. Self, S., 1972. Comun. Serv. Geol. Port., 55: 165-180. Seligman, G., 1936. Snow Structure and Ski Fields. Macmillan, London. Sellars, J.R., Tribus, M. and Klein, J.S., 1956. Trans. ASME, 78: 44-448. Selley, R.C., 1964. In: L.M.J.U. Van Straaten (Editor), Deltaic and Shallow Marine Deposits. Elsevier, Amsterdam, pp. 362-367. Selley, R.C., 1969. Scott. J. Geol., 5 : 328-346. Selley, R.C., 1972. J. Geol. Soc. London, 128: 135-150. Selley, R.C. and Shearman, D.J., 1962. Proc. Geol. SOC.London, No. 1599: 101-102. Selley, R.C., Shearman, D.J., Sutton, J. and Watson, J., 1963. Geol. Mag., 100: 224-243. Sellwood, B.W., Durkin, M.K. and Kennedy, W.J., 1970. Proc. Geol. Assoc., 81: 715-732. Sengupta, S., 1966. J. Sediment. Petrol., 36: 362-369. Seppda, M., 1972. Bull. Geol. Soc. Finl., 44: 131 - 132. Servant, M. and Servant, S., 1970. Rev. Geogr. Phys. Geol. Dyn., 12: 63-76. Sestini, G. and Curcio, M., 1965. Boll. SOC.Geol. Ital., 84: 1-26. Sethuraman, S., 1979. Mon. Weather Rev., 107: 314-321. Sethuraman, S. and Raynor, G.S., 1975. J. Geophys. Res., 80: 4983-4988. Shahjahan, M., 1970. Bull. Int. Assoc. Sci. Hydrol., 15(3): 13-24. Shamov, G.I., 1959. Alluvial Rivers. Gidrometeorizdat, Leningrad, 2nd ed. (in Russian). Shannon, P.T., De Haas, R.D., Stroupe, E.P. and Tory, E., 1964. Ind. Eng. Chem. Fund., 3: 250-260. Shantzer, E.V., 1951. Tr. Inst. Geol. Nauk. Akad. Nauk SSSR, Geol. Ser., No. 135: 1-271 (in Russian). Sharp, R.P., 1947. Geogr. Rev., 37: 26-52. Sharp, R.P., 1949. J. Geol., 57: 175-195. Sharp, R.P., 1963. J. Geol., 71: 617-636. Sharp, R.P., 1964. Geol. Soc.Am. Bull., 75: 785-804. Sharp, R.P., 1966. Geol. SOC.Am. Bull., 77: 1045-1074. Sharp, R.P., 1973. J. Geophys. Res., 78: 4222-4230. Sharp, R.P. and Carey, D.L., 1976. Geol. SOC.Am. Bull., 87: 1704-1717. Sharp, W.E., 1960. J. Geol., 68: 567-572. Shaw, J., 1975. In: R.P. Suggate and M.M. Creswell (Editors), Quaternary Studies. Royal Society of New Zealand, pp. 253-258. Shaw, J., 1977. Boreas, 6: 189-201. Shaw, J. and Freschauf, R.C., 1973. Can. Geogr., 17: 19-35. Shaw, M.C., 1954. Proc. Natl. Acad. Sci., 40: 394-401. Shaw, M.S., Hopkins, J.S. and Caton, P.G.F., 1976. Weather, 31: 172-183. Shaw, W.B.K., 1936. Geogr. J., 87: 193-217. Shearer, J.M., MacNab, R.F., Pelletier, B.R. and Smith, T.B., 1971. Science, 174: 816-818.

628 Sheldon, G.L. and Finnie, I., 1966. Trans. ASME, B88: 387-392. Sheldon, P.G., 1928. Am. J. Sci., (5)15: 243-252. Sheldon, P.G., 1929. Am. J. Sci., 5(17): 525-533. Shelton, J.S., 1953. Science, 117: 438-439. Shelton, J.W., 1962. J. Sediment. Petrol., 32: 873-877. Shelton, J.W., 1965. Bull. Am. Assoc. Pet. Geol., 49: 1385-1397. Shemdin, O.H., 1973. J. Hydraul. Res., 1 1 : 281-297. Shen, H.W.. 1961. A study on meandering and other bed patterns in straight alluvial channels. Univ. Calif., Berkeley, Water Resour. Cent., Hydraul. Lab., Contrib. No. 33. Shen, H.W., 1971a. In: H.W. Shen (Editor), River Mechanics, vol. 1. Colorado State University, Fort Collins, Colo., pp. 16-1-16-33. Shen, H.W., 1971b. In: H.W. Shen (Editor), River Mechanics, vol. 2. Colorado State University, Fort Collins, Colo., pp. 23-1-23-25. Shen, H.W. and Komura, S., 1968. J. Hydraul. Div. ASCE, 94(HY4): 997-1016. Shen, H.W., Schneider, V.R. and Araki, S., 1969. J. Hydraul. Div. ASCE, 95(HY6): 1919- 1940. Sheng, Y.P., Lick, W., Gedney, R.T. and Molls, F.B.. 1978. J. Geophys. Res., 8: 713-727. Shepard, F.P., 1935. Science, 82: 25 1-253. Shepard, F.P., 1950. Tech. Mem. U.S. Beach Erosion Board, No. 15. Shepard, F.P., 1'960. In: F.P. Shepard and F.B. Phleger (Editors), Recent Sediment, Northwest Gulf of Mexico. American Association of Petroleum Geologists, Tulsa, Okla., pp. 197-220. Shepard, F.P., 1963. Submarine Geology. Harper and Row, New York, N.Y., 2nd ed. Shepard, F.P. and Einsele. G., 1962. Sedimentology, 1 : 8 1 - 133. Shepard, F.P. and Marshall, N.F., 1973a. Mar. Geol., 15: M19-M24. Shepard, F.P. and Marshall, N.F.. 1973b. Bull. Am. Assoc. Pet. Geol., 57: 244-264. Shepard, F.P. and Moore, D.G., 1960. In: F.P. Shepard and F.B. Phleger (Editors), Recent Sediments, Northwest Gulf of Mexico. American Association of Petroleum Geologists, Tulsa, Oklahoma, pp. 1 17- 152. Shepard, F.P., Marshall, N.F. and McLoughlin, P.A., 1974. Deep-sea Res. 21: 691-706. Shepard, F.P., Marshall, N.F., McLoughlin, P.A. and Fisher, R.L., 1976. Mar. Geol., 20: 1-6. Shepherd, R.G., 1972. Science, 178: 409-41 I . Shepherd, R.G. and Schumm, S.A., 1974. Geol. Soc.Am. Bull., 85: 257-268. Sheridan, M.F. and Updike, R.G., 1975. Geol. SOC. Am. Bull., 86: 571-581. Sherman, R.A. and Kaiser, E.R., 1937. Combustion, 9: 25-28. Sherwin, J.A. and Chapple, W.M., 1968. Am. J. Sci., 266: 167-179. Sherwood, T.K., 1940. Trans. Inst. Chem. Eng., 36: 817-840. Sherwood, T.K. and Ryan, J.M., 1959. Chem. Eng. Sci., 1 1 : 81-91. Shiells, K.A.G., 1963. Geol. Mag., 100: 498-502. Shiki, T., 1961. Mem. Coll. Sci. Univ. Kyoto, B27: 293-308. Shinn, E.A., 1963. J. Sediment. Petrol., 33: 291-303. Shirai, T. and Tsuchiya, Y., 1974. Coastal Eng. Jpn., 17: 141-154. Shirley, J., 1955. Q. J. Geol. Soc. London, 1 1 1 : 265-279. Short, A.D., 1975a. J. Geol., 83: 209-221. Short, A.D., 1975b. J. Geophys. Res., 80: 3838-3840. Shreve, R.L., 1966. Science, 154: 1639-1643. Shreve, R.L., 1968a. Geol. Soc. Am., Spec. Pap., No. 108. Shreve, R.L., 1968b. Geol. SOC.Am. Bull., 79: 653-658. Shrock, R.R., 1940. Trans. Wisc. Acad. Sci., 32: 229-232. Shrock, R.R., 1948. Sequence in Layered Rocks. McGraw-Hill. New York, N.Y. Shukry, A., 1950. Trans. ASCE, 1 15: 751-779. Shurcliff, W.A., 1947. Bombs at Bikini. Wise, New York, N.Y. Sibul, O., 1955a. Tech. Mem. U.S. Beach Erosion Board, No. 74.

629 Sibul, O., 1955b. Tech. Mem. U.S. Beach Erosion Board, No. 61. Sibul, 0. and Johnson, J.W., 1957. ASCE J. Waterw., Harbors Div. Coastal Eng., 83(WWI), Pap. 1210, 32 pp. Siebert, W. and Gotz, W., 1975. Proc. 16th Congr. Int. Assoc. Hydraul. Res., 2: 141-149. Siemes, W. and Hellmer, L., 1962. Chem. Eng. Sci., 17: 555-571. Silver. M.L. and Seed, H.B., 1971a. J. Soil Mech. Found. Div. ASCE. 97(SM9): 1171-1 182. Silver, M.L. and Seed, H.B., 1971b. J. Soil Mech. Found. Div. ASCE, 97: 1081-1098. Simha, R., 1952. J. Appl. Phys., 23: 1010-1024. Simha, R. and Somcynsky, T., 1965. J. Colloid Sci., 20: 278-281. Simkin, T., 1967. In: P.J. Wyllie (Editor), Ultramafic and Related Rocks. Wiley, New York, N.Y., pp. 64-69. Simon, J.A. and Hopkins, M.C., 1966. Guideb. Ser. Ill. State Geol. Surv.. No. 7. Simons, D.B., 1971. In: H.W. Shen (Editor), River Mechanics, vol. 2. Colorado State University, Fort Collins, Colo., pp. 20- 1-20-60. Simons, D.B. and Richardson, E.V., 1961. J. Hydraul. Div. ASCE, 87(HY3): 87-105. Simons, D.B., Richardson, E.V. and Nordin, C.F., 1965. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation. Soc. Econ. Paleontol. Mineral., Spec. Publ., 12: 34-52. Simons, F.S. and Erickson, G.E., 1953. Bol. SOC.Geol. Peru, 26: 229-246. Simpkins, P.G., 1963. J. Fluid Mech., 15: 119-132. Simpson, H.C. and Rodger, B.W., 1961. Chem. Eng. Sci., 16: 153-180. Simpson, J.E. 1969. Q. J. R. Meteorol. SOC.,95: 758-765. Simpson, J.E., 1972. J. Fluid Mech., 53: 759-768. Simpson, J.E. and Britter, R.E., 1979. J. Fluid Mech., 94: 477-495. Simpson, J.E. and Britter, R.E., 1980. Q. J. R. Meteorol. Soc.,106: 485-500. Sims, J.D., 1973. Science, 182: 161-163. Sims, J.D., 1975. Tectonophysics, 29: 141-152. Singamsetti, S.R., 1966. J. Hydraul. Div. ASCE, 92(HY2): 153-168. Singh, A.N. and Sen Gupta, P., 1980. Can. J. Chem. Eng., 58: 116-1 18. Singh, B. and Shah, C.R., 1971. Houille Blanche, 26: 59-64. Singh, B., Calcott, T.G.C. and Rigby, G.R., 1978. Powder Technol., 20: 99- I 13. Singh, I.B., 1969. Nor. Geol. Tiddskr., 49: 1-33. Singh, I.B. and Kumar, S., 1974. Sediment. Geol., 12: 53-66. Sirkar, K.K. and Hanratty, T.J., 1970. J. Fluid Mech., 44: 589-603. Skipper, K., 1971. Sedimentology, 17: 51-68. Skipper, K. and Middleton, G.V., 1975. Can. J. Earth Sci., 12: 1934-1952. Slanka, A. and Unrug, R., 1976. Ann. SOC.Geol. Pol., 46: 55-75. Slatt, R.M. and Hoskin, C., 1968. J. Sediment. Petrol., 38: 434-456. Sleicher, C.A., Notter, R.H. and Cnppen, M.D., 1970. Chem. Eng. Sci., 25: 845-857. Slis, P.L., Willemse, T.H. and Kramers, H., 1959. Appl. Sci. Res., A8: 209-218. Small, J., 1935. Philos. Mag., (7)49: 251-260. Smalley, I.J., 1966a. Geol. Mag., 103: 110-1 14. Smalley, I.J., 1966b. Science, 151: 1379-1380. Smalley, I.J. and Unwin, D.J., 1968. J. Glaciol., 7: 377-390. Smalley, I.J., Bentley, S.P. and Moon, C.F., 1975. Can. Mineral., 13: 364-369. Smekal, A. and Klem, W., 1951. Monatsh. Chem., 82: 41 1-421. Smiles, D.E., 1976. Chem. Eng. Sci., 31: 273-275. Smith, A.G., 1968. J. Geol., 76: 426-443. Smith, A.J., 1959. J. Sediment. Petrol., 29: 447-453. Smith, A.J., 1963. J. Sediment. Petrol., 33: 739-750. Smith, A.J. and Rast, N., 1958. Geol. Mag., 95: 234-240. Smith, A.L., 1909. Bull. Am. Geogr. SOC.,41: 729-742.

630 Smith, A.M.O., 1955. Q. Appl. Math., 13: 233-262. Smith, B.. 1916. Geol. Mag., (6)3: 146-156. Smith, E.H.. 1931. Bull. U.S. Coast Guard, 19: 1-221. Smith, F.T.. 1979. J. Fluid Mech., 90: 725-754. Smith, F.T.. Sykes, R.I. and Brighton, P.W.M., 1977. J. Fluid Mech., 83: 163-176. Smith, H.T.U., 1946. Trans. N.Y. Acad. Sci., (2)8: 197-199. Smith, H.T.U., 1948. Am. J. Sci., 246: 503-514. Smith, H.T.U., 1963. Eolian geomorphology, wind direction, and climatic change in North Africa. U.S. Air Force, Cambridge Res. Lab., Rep. 63-443. Smith, H.T.U., 1967. Past versus present wind action in the Mojave Desert region, California. U.S. Air Force, Cambridge Res. Lab., Rep. 67-0683. Smith, J.D. and Hopkins, T.S., 1972. In: D.J.P. Swift, D.B. Duane and O.H. Pilkey (Editors), Shelf Sediment Transport: Process and Pattern. Dowden, Hutchinson and Ross, Stroudsburg, Pa., pp. 143-180. Smith, J.F. and Albritton, C.C., 1941. Bull. Geol. SOC.Am., 52: 61-78. Smith, N.D., 1970. Geol. SOC.Am. Bull., 81: 2993-3014. Smith, R.B., 1975. Geol. Soc. Am. Bull., 86: 1601-1609. Smith, R.B.. 1977. Geol. Soc. Am. Bull., 88: 312-320. Smith, R.B.. 1979. Am. J. Sci., 279: 272-287. Smith, R.L., 1960. Bull. Geol. SOC.Am., 71: 795-841. Smith, R.L.. 1963. Bull. Volcanol., (2)25: 109-120. Smith, R.L. and Bailey, R.A., 1966. Bull. Volcanol., (2)29: 83-104. Smith, T.E., 1967. Scott. J. Geol., 3: 282-305. Smith, T.N., 1965. Trans. Inst. Chem. Eng., 43: T69-T73. Smith, T.N., 1966. Trans. Inst. Chem. Eng., 44: T153-TI57. Smith. T.N., 1967. Trans. Inst. Chem. Eng., 45: T311LT313. Smith, T.R., 1974. J. Geol., 82: 98-104. Smits. A.J., Young, S.T.B. and Bradshaw, P., 1979. J. Fluid Mech., 94: 209-242. Smits, B.J., 1971. Palaeogeogr. Palaeoclimatol. Palaeoecol., 9: 123-131. Snavely, P.D., Niem, A.R., Macleod, N.S., Pearle, J.E. and Rau, W.W., 1980. U.S. Geol. Surv., Prof. Pap., 1162-B. Sneh, A. and Friedman, G.M., 1980. J. Sediment. Petrol., 50: 981-986. So, C.L., Pierce, J.W. and Siegel, F.R., 1974. Geogr. Ann., A56: 227-235. Soares de Carvalho, G., 1975. Mem. Inst. Invest. Cient. Mopmbique, Ser. B, BIO: 51-71. Soleilvahoup, F. and Bertouille, J., 1976. Rev. Geomorphol. Dyn., 24(3): 81-98. Soliman, M.M. and Tinney, E.R., 1968. J. Hydraul. Div. ASCE. 94(HY4): 893-908. Soliman. S.M.. 1964. In: L.M.J.U. Van Straaten (Editor), Deltaic and Shallow Marine Deposits. Elsevier, Amsterdam. pp. 379-387. Sommer. M.A., 1977. J. Geol., 85: 423-432. Sonneville, P., 1976. Bull. Dir. Etud. Rech., Electr. Fr., Ser. A, No. 3. Sonu, C.J., 1969. Proc. 1 Ith Conf. Coastal Eng., 1: 373-400. Sonu, C.J., 1972. J. Geophys. Res., 77: 3232-3247. Sonu, C.J., 1973. J. Geol., 81: 42-64. Sonu, C.J. and Russell, R.J., 1967. Proc. 10th Conf. Coastal Eng., 1: 502-524. Sonu, C.J., McCloy, J.M. and McArthur, D.S., 1967. Proc. 10th Conf. Coastal Eng., 1: 525-549. Sorauf, J.E., 1965. J. Sediment. Petrol., 35: 553-563. Sorby, H.C., 1908. Q. J. Geol. Soc. London, 64: 171-233. Southard, J.B. and Mackintosh, M.E., 1981. Earth Surface Processes and Landforms, 6: 103-111. South African National Building Research Institute, 1969. Wind-breaks. Tech. Note S. Afr., C.S.I.R.O., X/BOU 123, Build. Ser., D15-123.

63 1 Sowerby, L., 1965. J. Fluid Mech., 22: 587-598. Spain, R.W., 1955. Ceram. Ind., 65: 67-68, 103-105. Spalding, D.B., 1961. Aeronaut. Q., 12: 237-274. Spalding, D.B., 1967. J. Fluid Mech., 27: 97-109. Spangenberg, W.B. and Rowland, W.R., 1961. Phys. Fluids, 4: 743-750. Sparks, R.S.J., 1975. Geol. Rundsch., 64: 497-523. Sparks, R.S.J., 1976. Sedimentology, 23: 147- 188. Sparks, R.S.J. and Walker, G.P.L., 1973. Nature (London), Phys. Sci., 241 : 62-64. Sparks, R.S.J. and Wilson, L., 1976. J. Geol. SOC. London, 132: 441-451. Sparks, R.S.J., Self, S. and Walker, G.P.L., 1973. Geology, 1: 115-1 18. Sparks, R.S.J., Wilson, L. and Hulme, G., 1978. J. Geophys. Res., 83: 1727-1739. Sparks, R.S.J., Wilson, L. and Sigurdsson, H., 1981. Philos. Trans. R. SOC.,London, Ser. A, 299: 241 -273. Sparrow, E.M. and Husar, R.B., 1969. J. Fluid Mech., 37: 251-255. Speight, J.G., 1965a. J. Hydrol., 3: 1 - 15. Speight, J.G., 1965b. J. Hydrol., 3: 16-36. Speight, J.G., 1967. In: J.N. Jennings and J.A. Mabbutt (Editors), Landform Studies from Australia and New Ginea. Cambridge University Press, Cambridge, pp. 48-63. Spencer, A.M., 1971. Mem. Geol. SOC.London, No. 6. Spjeldnaes, N., 1965. Geol. Rundsch., 54: 24-45. Spotts, J.H. and Wezer, O.E., 1964. In: A.H. Bouma and A. Brouwer (Editors), Turbidites. Elsevier, Amsterdam, pp. 199-22 1. Spreng, A.C., 1967. J. Sediment. Petrol., 37: 804-817. Spry, A., 1962. J. Geol. SOC.Aust., 8: 191-216. Squire, H.B., 1956. J. R. Aeronaut. SOC.,60: 203-205. Stall, J.B. and Yang, C.T., 1972. Univ. Ill., Water Resour. Cent., Rep. B-051-ILL. Stanley, D.J., 1968. Geol. SOC.Am., Spec. Pap., No. 106: 211-239. Stanley, D.J., 1974. Bull. Cent. Rech. Pau, 8: 351-371. Stanley, G.M., 1955. Bull. Geol. Soc. Am., 66: 1329-1350. Stanley, K.O., 1974. J. Sediment. Petrol., 44: 472-483. Stanley, K.O. and Surdam, R.C., 1978. J. Sediment. Petrol., 48: 557-573. Stanley, S.M., 1975. Annu. Rev. Earth Planet. Sci., 3: 360-385. Stapor, F.W., 1975. Z. Geomorphol., S22: 116-144. Statham, I., 1976. Earth Surf. Processes, 1: 173-180. Stauffer, P.H., 1967. J. Sediment. Petrol., 37: 487-508. Stear, W.M., 1979. Trans. Geol. SOC.S. Afr., 81: 393-399. Stebbings, J., 1963. Proc. Inst. Civ. Eng., 25: 485-510. Steele, J.H., 1976. Philos. Trans. R. SOC.London, Ser. B, 274: 401-415. Steers, J.A., 1934. Scolt Head Island. Heffer, Cambridge. Steers, J.A., 1946. The Coastline of England and Wales. Cambridge University Press, Cambridge. Steers, J.A., 1960. The Coast of England and Wales in Pictures. Cambridge University Press, Cambridge. Steidtmann, J.R., 1969. Wyo. Contrib. Geol., 8: 168-170. Steidtmann, J.R., 1974. Geol. Soc. Am. Bull., 85: 1835-1842. Steiglitz, R.D. and Inden, R.F., 1969. J. Sediment. Petrol., 39: 342-344. Stein, A., 1920. Geogr. Rev., 9: 1-34. Stein, R.A., 1965. J. Geophys. Res., 70: 1831-1842. Steinbrugge, K.V. and Flores, R., 1963. Bull. Seismol. Soc. Am., 53: 225-307. Steinour, H.H., 1944. Ind. Eng. Chem., 36: 618-624, 840-847, 90-907. Stephansson, O., 1975. Precambrian Res., 2: 189-214. Stephansson, 0. and Johnson, K., 1976. Precambrian Res., 3: 159-181.

632 Stevenson, J.F., 1973. Trans. ASME, E40: 355-361. Stewart, A.D., 1962a. Liverpool Manchester Geol. J., 3: 121-155. Stewart, A.D., 1962b. Geol. Mag., 99: 399-419. Stewart, A.D., 1963. Geol. Mag., 100: 205-218. Stewart, H.B., 1956. Bull. Am. Assoc. Pet. Geol., 40: 153-161. Stewart, J.H., 1961. U.S. Geol. Surv., Prof. Pap., 424-B: 127-129. Stewart, J.H., Poole, F.G. and Wilson, R.F., 1972. U.S. Geol. Surv., Prof. Pap., 690. Stewart, P.S.B. and Davidson, J.F.. 1967. Powder Technol., 1: 61-80. Stewart, R. and Schmitt, R.K., 1968. Proc. 1 Ith Conf. Great Lakes Res., pp. 496-499. Stock, A.J., 1944. Mech. Eng., 66: 523-528. Stock, H.W., 1975a. AIAA J., 13: 1217-1223. Stock, H.W., 1975b. Phys. Fluids, 18: 1652-1659. Stock, H.W. and Ginoux, J.J., 1971a. AIAA J., 9: 971-973. Stock, H.W. and Ginoux, J.J., 1971b. Von Karmhn Inst. Fluid Dyn., Tech. Note, 64. Stock, H.W. and Ginoux, J.J., 1972. AIAA J.. 10: 557-558. Stoddart, D.R., 1971. Geogr. Mag., 43: 610-615. Stoertz, G.E. and Erickson, G.E., 1974. U.S. Geol. Surv., Prof. Pap., 8 I 1. Stommel, H., 1947. Ann. N.Y. Acad. Sci., 48: 715-726. Stone, R.O., 1967. Earth-Sci. Rev., 3: 211-268. Stone, R.O., Carter, L.D. and von der Haar, S.P., 1973. Z. Geomorphol., S18: 156-174. Strahler, A.N., 1966. J. Geol., 74: 247-268. Strauch, F., 1966. Neues Jahrb. Geol. Palaontol., Abh., 124: 259-288. Straw, S.H., 1937. Q. J. Geol. Soc. London, 93: 406-456. Streiff-Becker, R., 1951a. J. Glaciol., 1 : 488-490. Streiff-Becker, R., 1951b. J. Glaciol., 1: 582. Stride, A.H., 1959a. J. Mar. Biol. Assoc. U.K., 38: 313-318. Stride, A.H., 1959b. Dock Harbor Auth., 40: 145-147. Stride, A.H., 1961. New Sci., 10: 304-306. Stride, A.H., 1963. Q. J. Geol. Soc. London, 119: 175-197. Stride, A.H., 1973. In: E.D. Goldberg (Editor), North Sea Science. Massachusetts Institute of Technology Press, Cambridge, Mass., pp. 10I - 130. Stride, A.H.. 1974. Estuarine Coastal Mar. Sci., 2: 27-36. Stride, A.H., Belderson, R.H. and Kenyon, N.H., 1972. Mem. Bur. Rech. Geol. Min., No. 79: 233-240. Striem, H.L., 1954. Bull. Res. Counc. Isr., 4: 195-198. Striem, H.L., 1974. Int. Hydro]. Rev., 51: 59-70. Sturt, B.A. and Fumes, H., 1976. J. Sediment. Petrol., 46: 555-562. Suga, K., 1967. Proc. 12th Cong. Int. Assoc. Hydraul. Res., 1 : 487-495. Sugden, D.E. and John, B.S., 1976. Glaciers and Landscape. Amold, London. Sukegawa, N., 1970. J. Fac. Eng. UNv. Tokyo, 30: 289-306. Sullwold, H.H., 1959. Bull. Geol. SOC. Am., 70: 1247-1248. Sun, W.Y., 1978. J. Atmos. Sci., 35: 466-483. Sundborg, A., 1956. Geogr. Ann., 38: 127-316. Sundborg, A. and Norrman, J., 1963. Sver. Geol. Unders., Ser. Ca, No. 4. Surkan, A.J. and Van Kan, J., 1969. Water Resour. Res., 5: 1343-1352. Sutcliffe, W.H., Sheldon, R.W., Prakash. A. and Gordon, D.C., 1971. Deep-sea Res., 18: 639-643. Sutera, S.P., 1965. J. Fluid Mech., 21: 513-534. Sutherland, A.J., 1967. J. Geophys. Res., 72: 6183-6194. Suthons, C.T., 1963. Proc. Inst. Civ. Eng., 25: 433-450. Sutton, G.W., 1958. J. Aeronaut. Sci., 25: 29-32, 36. Sutton, G.W., 1959. J. Aerospace Sci., 26: 681-682.

633 Sutton, J. and Watson, J., 1956. Proc. Geol. Assoc., 66: 101-133. Sutton, J. and Watson, J., 1960. Geol. Mag., 97: 102-122. Sutton, R.G. and Lewis, T.L., 1966. J. Sediment. Petrol., 36: 225-228. Svendsen, H. and Thompson, R.O.R.Y., 1978. J. Geophys. Res., 83: 703-712. Svensson, H., 1980. Svensk. Geogr. Arsb., 56: 5-12. Swanson, D.A. and Christiansen, R.J., 1973. Geology, I : 83-86. Swarbrick, E.E., 1968. Sediment. Geol., 2: 161-175. Swartz, G.L., 1966a. Q. J. Agric. Sci., 23: 279-285. Swartz, G.L., 1966b. Q. J. Agric. Sci., 23: 407-422. Sweeney, R.H. and Geckler, R.D., 1954. J. Appl. Phys., 25: 1 135-1 144. Sweeting, M.M., 1966.. In: G.H. Dury (Editor), Essays in Geomorphology. Heinemann, London. Sweeting, M.M., 1972. Karst Landforms. Macmillan, London. Sweeting, M.M., 1974. In: A.C. Waltham (Editor), Limestones and Caves of North-West England. David and Charles, Newton Abbot, Devon, pp. 46-78. Sweeting, M.M., 1979. Geogr. Mag., 51: 271-277. Swenson, F.A., 1970. U.S. Geol. Surv., Prof. Pap., 700-B. Swift, D.J.P., 1975. Mar. Geol., 18: 105-134. Swift, D.J.P. and Ludwick, J.C., 1976. In: D.J. Stanley and D.J.P. Swift (Editors), Marine Sediment Transport and Environmental Management. Wiley, New York, N.Y., pp. 159196. Swift, D.J.P., Molnia, B.F. and Jackson, R.G., 1978. J. Sediment. Petrol., 48: 897-900. Swift, E., 1962. U.S. Naval Ordnance Lab., Tech. Rep., 62- I9 I . Swigart, R.J., 1974. AIAA J., 12: 1301-1318. Swinnerton, A.C., 1927. J. Geol., 35: 171-179. Sykes, D.M., 1962. J. Fluid Mech.. 12: 367-387. Sykes, R.I., 1980. Proc. R. SOC.London, Ser. A, 373: 311-329. Synge, J.L., 1933. Trans. R. Soc. Can., (3)27: 1-18. Synge, J.L., 1938. Proc. R. SOC.London, Ser. A, 167: 250-256. Szodruch, J., 1978. AIAA J., 16: 1306-1309. Tabler, R.D. and Veal, D.L., 1971. Bull. Int. Assoc. Sci. Hydrol., 16(4): 49-56. Takaki, R. and Kovasznay, L.S.G., 1978. Phys. Fluids, 21: 153-156. Tanaka, K., 1970. Rep. Geol. Surv. Jpn., No. 236. Taneda, S., 1956a. J. Phys. SOC.Jpn., 1 1 : 302-307. Taneda, S., 1956b. Rep. Res. Inst. Appl. Mech., Kyushu Univ., 4: 99-105. Taneda, S., 1972. In: E.A. Eichelbrenner (Editor), Recent Research on Unsteady Boundary Layers, vol. 2. University of Lava1 Press, Quebec, pp. 1165- 1215. Taneda, S., 1979. Mem. Fac. Sci. Kyushu Univ., D24: 109-154. Taneda, S. and Honji, H., 1971. J. Phys. Soc.Jpn., 30: 262-272. Tani, I., 1958. In: H. Gortler (Editor), Boundary Layer Res., Springer, Berlin, pp. 377-386. Tani, I., 1962. J. Geophys. Res., 67: 3075-3080. Tani, I., 1964. Prog. Aeronaut. Sci., 5: 70-104. Tani, I., Iuchi, M. and Komoda, H., 1961. Rep. Aeronaut. Res. Inst. Univ. Tokyo, No. 364: 119-137. Tankard, A.J. and Hobday, D.K., 1977. Sediment Geol., 18: 135-159. Tanner, W.F., 1960. J. Geophys. Res., 65: 993-995. Tanner, W.F., 1962. J. Geol. Educ., 10: 116-118. Tanner, W.F., 1963. Science, 139: 41-42. Tasse, N., Lajoie, J. and Dimroth, E., 1978. Can. J. Earth Sci., 15: 874-888. Tatro, P.R. and Mollo-Christensen, E.I., 1967. J. Fluid Mech., 28: 531-544. Taulbee, D.B. and Robertson, J.M., 1972. Trans. ASME, D94: 544-560. Tavenas, F., Chagnon, J.Y. and La Rochelle, P., 1971. Can. Geotech., 8: 463-478.

634 Taylor, E.S., 1959. Trans. ASME, D81: 297-304. Taylor, E.S., 1967. In: G. Sovran (Editor), Fluid Mechanics of Internal Flow. Elsevier, Amsterdam, pp. 320-325. Taylor, G., Crook, K.A.W. and Woodyer, K.D., 1971. J. Sediment. Petrol., 41: 578-581. Taylor, G.A., 1958. Aust., Bur. Miner. Res., Geol. Geophys., Bull., No. 38. Taylor, G.I., 1923. Philos. Trans. R. SOC.London, Ser. A, 223: 289-243. Taylor, G.I., 1950. Proc. R. SOC.London, Ser. A, 201: 192-196. Taylor, G.I. and Batchelor, G.K., 1949. Q. J. Mech. Appl. Math., 2: 1-28. Taylor, P.T., Stanley, D.J. and Jahn, W., 1975. Mar. Geol., 19: 139-157. Taylor, R.K. and Morrell, G.R.. 1979. Eng. Geol., 14: 219-229. Teichert, C., 1970. J. Sediment. Petrol., 40: 1056. Teichert, C. and Fairbridge, R.W., 1948. Geogr. Rev., 38: 222-249. Teichmuller, R., 1955. Neues Jahrb. Geol. Palaontol., Monatsh., No. 2: 146- 168. Teisseyre, A.K., 1967. Bull. Acad. Sci. Pol., %r. Geol. Geogr., 15: 15-22. Teisseyre, A.K., 1977. Geol. Sudetica, 12: 79-89. Teisseyre, A.K., 1978. Geol. Sudetica, 13: 7-20. Teisseyre, A.K., 1980. Geol. Sudetica, 15: 67-1 12. Ten Haaf. E., 1956. Geol. Mijnbouw, 18: 188-194. Ten Haaf, E., 1959. Graded Beds of the Northern Apennines. University of Groningen, Groningen. Teraoka. Y.,1970. Rep. Geol. Surv. Jpn., No. 237: Terwindt, J.H.J., 1970. Geol. Mijnbouw, 49: 489-501. Terzaghi, K., 1925. Erdbaumechanik auf Bodenphysikalischer Grundlage. Deuticke, Wien. Tenaghi, K., 1957. Publ. Norw. Geotech. Inst., No. 25. Tesaker, E., 1969a. Proc. 12th Congr. Inst. Assoc. Hydraul. Res., 2: 1-8. Tesaker, E., I969b. Uniform turbidity current experiments. Technical University of Norway. Thakur, T.R. and Scheidegger, A.E., 1968. Water Resour. Res., 4: 317-329. Thakur, T.R. and Scheidegger, A.E., 1970. J. Hydrol., 12: 25-47. Thandveswara, B.S. and Seetharamiah, K.. 1971. Houille Blanche, 26: 43-47. Thomann, H., 1959. Rep. Aeronaut. Res. Inst. Swed., No. 82. Thomas, C.E., Morgan, K. and Taylor, C., 1981. Computers and Fluids, 9: 265-278. Thomas, D.G., 1965. J. Colloid Sci., 20: 267-277. Thomas, G., 1958. Q. J. Geol. SOC.London, 113: 457-458. Thomas, R.M., 1979. Nature (London), 277: 281-283. Thomas, R.N. and Whipple, F.L., 1951. J. Aeronaut. Sci., 18: 636-637. Thomas, T.M., 1970. Trans. Inst. Br. Geogr., No. 50: 87-105. Thomas, W.J., Grey, P.J. and Watkins, S.B., 1961. Br. J. Chem. Eng., 6: 176-181. Thompson, A.F. and Thomasson, M.R., 1969. In: G.M. Friedman (Editor), Depositional Environment in Carbonate Rocks. Soc. Econ. Paleontol. Mineral., Spec. Publ., 14: 57-78. Thompson, A.M., 1972. Proc. 24th Int. Geol. Congr., Sect. 6, pp. 89-99. Thompson, R.N. and Patrick, D.J., 1968. Geol. J., 139-146. Thompson, W.C. and Harlett, J.C.. 1969. Proc. 1 1 th Conf. Coastal Eng., 1: 352-372. Thompson, W.O., 1937. Bull. Geol. SOC.Am., 48: 723-752. Thompson, W.O., 1949. Bull. Am. Ass. Pet. Geol., 33: 52-72. Thomsen, E., 1976. Sedimentology, 23: 485-509. Thomson, J., 1876. Proc. R. SOC.London, 25: 5-8. Thomson, J., 1877. Proc. R. SOC.London, 26: 356-357. Thomson, J., 1879. Proc. Inst. Mech. Eng., 9 August 1879: 456-460. Thomson, J.J. and Newall, H.F., 1886. Proc. R. SOC.London, 39: 417-436. Thorarinsson, S., Einarsson, T., Sigvaldason. G. and Elisson, G., 1964. Bull. Volcanol., (2)27: 434-445. Thoren, R., 1969. Picture Atlas of the Arctic. Elsevier, Amsterdam.

635 Thornes, J.B., 1970. Geogr. J., 136: 376-382. Thorpe, S.A., 1968. J. Fluid Mech., 32: 693-704. Thorpe, S.A., 1969a. Radio Sci., 4: 1327-1331. Thorpe, S.A., 1969b. J. Fluid Mech., 36: 673-683. Thorpe, S.A., 1969~.J. Fluid Mech., 39: 25-48. Thorpe, S.A., 1971. J. Fluid Mech., 46: 299-319. Thorpe, S.A.. 1973a. Boundary-Layer Meteorol., 5 : 95- 119. Thorpe, S.A., 1973b. J. Fluid Mech., 61: 731-751. Thorpe, S.A., 1973~.Weather, 28: .471-475. Thorpe, S.A., Hall, A.J. and Taylor, C., 1977. Deep-sea Res., 24: 371-379. Thwaites, B., 1960. Incompressible Aerodynamics. Clarendon Press, Oxford. Thy, P. and Wilson, J.R., 1980. Geol. Mag., 117: 363-371. Tickner, E.G., 1960. Tech. Mem. U.S. Beach Erosion Board, No. 122. Tietze, K.W., 1975. Geol. Rundsch., 64: 100-1 18. Tiffany, J.B. and Nelson, G.A., 1939. Trans. Am. Geophys. Union, 20: 644-649. Timmermans, P.D., 1935. Leidse Geol. Meded., 6: 231-386. Tinkler. K.J., 1970. Geol. SOC.Am. Bull., 81: 547-552. Tinkler, K.J.. 1971. Geol. Soc.Am. Bull., 1783- 1800. Tison, L.J., 1940. Ann. Trav. Publ. Belg., 41(6): 813-868. Tison, L.J., 1961. J. Geophys. Res., 66: 4227-4232. Tobak, M., 1970. AIAA J., 8: 330-334. Tobak, M., 1971. Z. Angew. Math. Mech., 22: 130-143. Tobak, M., 1973. Z. Angew. Math. Phys., 24: 330-354. Tobisch, O.T., 1965. J. Sediment. Petrol., 35: 415-419. Toebes, G.H. and Chang, T.P., 1967. Proc. 12th Congr. Int. Assoc. Hydraul. Res., 1 : 362-369. Toimil, L.J. and Reimnitz, E., 1979. Sediment. Geol., 22: 219-228. Tokuhashi, S., 1979. Mem. Fac. Sci. Kyoto Univ., Ser. Geol. Mineral, 46: 1-60. Toomre, A,, 1960. J. Fluid Mech., 7: 145-155. Toor, H.L. and Marchello, J.M., 1958. AIChE J., 4: 97-101. Towl, R.N., 1935. Eng. News-Rec., 1 15: 262-264. Townsend, A.A., 1976. The Structure of Turbulent Shear Flow. Cambridge University Press, Cambridge, 2nd ed. Townsend, I.J., 1974. Q. Geol. Notes, Geol. Surv. S. Aust., No. 49: 8-1 1. Tracey, J.I., Ladd, H.S. and Hoffmeister, J.E., 1948. Bull. Geol. SOC.Am., 59: 861-878. Tracey, J.I., Schlanger, S.O., Stark, J.T., Doan, D.B. and May, H.G., 1964. U.S. Geol. Surv., Prof. Pap., 403-A. Tremblay, L.P., 1961. Bull. Geol. SOC.Am., 72: 1561-1564. Trenhaile, A.S., 1971. Can. Geogr., 15: 113-126. Trenhaile, A.S., 1976. Ann. Assoc. Am. Geogr., 65: 297-312. Trettin, H.P., 1970. Geol. Assoc. Can., Spec. Pap., No. 7: 13-35. Trewin, N.H., 1979. Scott. J. Geol., 15: 287-292. Trewin, N.H. and Holdsworth, B.K., 1973. Proc. Yorks Geol. Soc., 39: 371-408. Tricart, J.L.F., 1977. Ann. Geogr., 86: 1-54. Tritton, D.J., 1950. J. Fluid Mech., 6: 547-567. Trusheim, F., 1929. Senckenbergiana, 1 I : 47-55. Trusheim, F., 1935. Senckenbergiana, 17: 62-72. Truswell, J.F., 1972. J. Sediment. Petrol., 42: 578-583. Tsoar, H., 1974. Z. Geomorphol., S20: 41-61. Tsuchiya, Y. and Kawata, Y., 1971. Annu. Disaster Prev. Res. Inst., Kyoto Univ., No. 14B: 3 1 1-325. Tucholke, B.E., 1977. Mar. Geol., 25: 209-230. Tucholke, B.E., 1979. Mar. Geol., 31: M13-M20.

636

Tucholke, B.E. and Ewing, J.I., 1974. Geol. Soc. Am. Bull., 85: 1789-1802. Tucker, M.E., 1973. Geol. Mijnbouw, 52: 203-215. Tucker, M.E., 1977. Geol. J., 12: 169-188. Tunstall, M.J. and Harvey, J.K., 1968. J. Fluid Mech., 34: 595-608. Turcotte, D.L., 1960. J. Fluid Mech., 8: 123-129. Turnbull, W.J., Krinitzky, E.L. and Weaver, F.J., 1966. J. Soil Mech. Found. Div. ASCE, 92(SMI): 121- 136. Turner, J.S., 1973. Buoyancy Effects in Fluids. Cambridge University Press, Cambridge. Twenhofel, W.H., 1921. Bull. Geol. SOC.Am., 32: 559-572. Twenhofel, W.H., 1932. Treatise on Sedimentation. Williams and Wilkins, Baltimore, Md., 2nd ed. Twidale, C.R., 1964. Z. Geomorphol., 8: 189-21 1. Twidale, C.R., 1966. Geomorphology of the Leichardt-Gilbert area of northwest Queensland. C.S.I.R.O., Land Res. Ser., No. 16. Twidale, C.R., 1968. Trans. R. SOC.S. Aust., 92: 1 15-123. Twidale, C.R., 1972a. Geogr. Rev., 62: 40-70. Twidale, C.R., 1972b. Trans. Inst. Br. Geogr., No. 56: 77-109. Twidale, C.R. and Bourne, J.A., 1976a. J. Geol. SOC.Aust., 23: 371-381. Twidale, C.R. and Bourne, J.A., 1976b. Z. Geomorphol., 20: 405-416. Twidale, C.R. and Corbin, E.M., 1963. Rev. Geomorphol. Dyn., 14: 1-20. Tyler, J.H., 1972. J. Sediment. Petrol., 537-557. Udden, J.A., 1925. Univ. Tex. Bull., 2509: 3-9. Umeji, A.C.. 1975. Geol. J., 10: 107-130. Umeya, K., Osoda, T., Ishii, T. and Sawamura, K., 1969. Powder Techno]., 3: 259-266. Underwood, J.R. and Lambert, W., 1974. J. Sediment. Petrol., 44: 11 1 1 - 1 113. Unrug, R., 1963. Ann. Soc. Geol. Pol., 33: 49-92. Upham, W., 1900. Bull. Geol. Soc. Am., 12: 25-44. Upton, B.G.J., 1960. Medd. Grdnl., 123: 1-145. Ursell, F., 1956. In: G.K. Bachelor and R.M. Davies (Editors), Surveys in Mechanics. Cambridge University Press, Cambridge, pp. 216-249. USACERC ( U S Army Coastal Engineering Research Center), 1977. Shore Protection Manual, 3 vols. 3rd ed. U S . Coastal Engineering Research Center, Fort Belvoir, Va. Van Bendegom, L., 1947. Die Ingenieur, 59(4): 1-1 I . Van de Kamp, P.C., Harper, J.D., Conniff, J.J. and Morris, D.A., 1974. J. Geol. SOC.London, 130: 545-565. Van Denberg, J.F. and Bauer, W.C., 1964. Chem. Eng., 71: 135-140, 142. Van den Berg, J.H., 1977. Geol. Mijnbouw, 56: 185-202. Van der Knaap, W. and Eijpe, R., 1968. Sedimentology, 11: 115-124. Van der Linden, W.J.M., 1963. Geol. Ultraiectina, No. 12. Van Dom, W.G., 1953. J. Mar. Res., 12: 249-276. Van Eden, J.G., 1970. Geol. Mijnbouw. 49: 145-197. Van Gelder, A., 1974. Sedimentation in the marine margin of the Old Red continent, south of Cork, Ireland. University of Utrecht, Utrecht. Van Houten, F.B., 1954. Bull. Geol. Soc. Am., 65: 813-818. Van Houten, F.B., 1964. Bull. Geol. Surv. K.ans., No. 169: 497-531. Van Loon, A.J. and Wiggers, A.J., 1975. Sediment. Geol., 13: 253-265. Van Loon, A.J. and Wiggers, A.J., 1976. Sediment. Geol., 16: 237-254. Van Olphen, H., 1963. An Introduction to Clay Colloid Chemistry. Interscience, New York,

N.Y. Van Straaten, L.M.J.U., 1949. C. R. SOC.Geol. Finl., 25(22): 9-18. Van Straaten, L.M.J.U., 1950a. Proc. K. Ned. Akad. Wet., 53(8): 1217-1227. Van Straaten. L.M.J.U., 1950b. Tijdschr. K. Ned. Aardrijksk. Genoot., 67: 94-108.

637 Van Straaten, L.M.J.U., 1953a. Geol. Mijnbouw, 15: 1 - 1 1 . Van Straaten, L.M.J.U., 1953b. Geol. Mijnbouw, 15: 3 1-43. Van Straaten, L.M.J.U., 1954a. Leidse Geol. Meded., 19: 1 - 1 10. Van Straaten, L.M.J.U., 1954b. Geol. Mijnbouw, 16: 25-47. Van Straaten, L.M.J.U., 1965. Meded. Geol. Sticht., N. Ser., No. 17: 41-75. Van Straaten, L.M.J.U., 1967. Rev. Geogr. Phys. Geol. Dyn., 9: 219-240. Van Straaten, P. and Tucker, M.E., 1972. Palaeontology, 15: 430-438. Van Tassel], J., 1981. J. Geol., 89: 317-333. Van Til, K. and Tops, J.W., 1953. Proc. 18th Int. Navig. Congr., Sect. I, Question Id, pp. 15-25. Van Veen, J., 1935. Hydrogr. Rev., 12: 21-29. Van Veen, J., 1936. Ondelzoekingen in De Hoofden. Algemeene Landsdrukkerij, 'sGravenhage. Van Veen, J., 1938. Geol. Meere Binnengewass., 2: 62-86. Van Veen, J., 1950. Tijdschr. K. Ned. Aardrijksk. Genoot., 67: 43-65. Vand, V., 1948. J. Phys. Colloid Chem., 52: 277-299, 200-314. Vanecek. V., Markvart, M. and Drbohlav, R., 1966. Fluidized Bed Drying. Leonard Hill, London. Vanoni, V.A., 1946. Trans. ASCE, 1 1 1 : 67- 102. Vanoni, V.A. and Hwang, L.S., 1967. J. Hydraul. Div. ASCE. 93(HY3): 121-144. Varjo, U., 1969. Die Kiiste, 17: 51-80. Varshney, D.V. and Garde, R.J., 1975. J. Hydraul. Div. ASCE, I O I ( H Y 8 ) : 1053-1066. Vasiliu, J., 1962. J. Aerospace Sci., 29: 596-601. Verger, F., 1968. Marais et Wadden du Littoral Francais. Biscaye, Bordeaux, France. Verlaque, C., 1958. Trav. Inst. Rech. Sahariennes, 17: 13-57. Verloop. J. and Heertjes, P.M., 1973. Powder Technol., 7: 161-168. Verma, S.B. and Cermak, J.E., 1974a. Int. J. Heat Mass Transfer, 17: 567-579. Verma, S.B. and Cermak, J.E., 1974b. J. Appl. Meteorol., 13: 578-587. Vernon, P., 1966. J. Glaciol., 6: 401-408. Verschoor, H., 1950. Appl. Sci. Res., A2: 155-161. Verstappen, H.T., 1968. Z. Geomofphol., 12: 200-220. Verstappen, H.T., 1970. Z. Geomorphol., SIO: 104-120. Verstappen, H.T., 1977. Remote Sensing in Geomorphology. Elsevier, Amsterdam. Verstappen, H.T. and Van Zuidam, R.A., 1970. Geoforum, 2: 33-47. Vickers, W.W., 1959. Trans. Am. Geophys. Union, 40: 162-167. Vincent, L., 1973. Quantification of shoreline meandering. Univ. Va., Dep. Environ. Sci., Tech. Rep. No. 7. Vinje, J.J., 1969. On the flow-Characteristics of vortices in three-dimensional local scour. Delft Hydraul. Lab., Publ. No. 48. Virkkala, K., 1960. Bull. Comm. Geol. Finl., No. 188: 161-176. Visher, G.S., 1965a. Bull. Am. Assoc. Petrol. Gel., 49: 41-61. Visher, G.S., 1965b. In: G.V. Middleton (Editor), Primary Sedimentary Structures and their Hydrodynamic Interpretation. Soc. Econ. Palaeontol. Mineral., Spec. Publ., 12: 1 16- 132. Visher, G.S., 1971. Geol. SOC.Am. Bull., 82: 1421-1424. Visher, G.S., 1972. In: J.K. Rigby and W.K. Hamblin (Editors), Recognition of Ancient Sedimentary Environments. SOC. Econ. Palaeontol. Mineral., Spec. Publ., 16: 84-97. Vitanage, P.W., 1954. J. Geol., 62: 493-500. Viviand, H. and Berger, S.A., 1965a. J. Fluid Mech., 23: 417-438. Viviand, H. and Berger, S.A., 1965b. J. Fluid Mech., 23: 439-458. Vogel, H.D. and Thompson, P.W., 1933. Civ. Eng., May 1933: 266-268. Volk, O.H. and Geyger, E., 1970. Z. Geomorphol., 14: 79-95. Von Karmh, T., 1934. Proc. 4th Int. Congr. Appl. Mech., pp. 54-91.

638 Von Rad, U., 1968. J. Sediment. Petrol., 38: 1120-1 154. Von Schelling, H., 1951. Trans. Am. Geophys. Union, 32: 222-226. Von Seifert, G., 1954. Meyniana, 2: 126-189. Von Stackelberg, U., Von Rad, U. and Zobel. B., 1976. Meteorol. Forsch.-Ergeb., C25: 1-46. Von Stackelberg, U., Von Rad, U. and Zobel, B., 1979. Mar. Geol., 33: 117-132. Vortisch, W., 1973. Geol. Rundsch., 62: 491-506. Vos, R.G., 1977. J. Sediment. Petrol., 47: 1242-1260. Vos, R.G., 1981. Sediment. Geol., 29: 67-88. Vos, R.G. and Hobday. D.K.. 1977. Sediment. Geol., 19: 217-232. Waddell, E., 1976. In: R.A. Davis and R.L. Ethington (Editors), Beach and Nearshore Sedimentation. SOC.Econ. Paleontol. Mineral., Spec. Publ., 24: 115-125. Wadsworth. W.J., 1961. Philos. Trans. R. SOC.London, Ser. B, 244: 21-64. Wadsworth, W.J., 1973. Miner. Sci. Eng., 5: 25-35. Wager, L.R. and Brown, G.M., 1968. Layered Igneous Rocks. Oliver and Boyd, Edinburgh. Wager, L.R. and Deer, W.A., 1939. Medd. Grdnl., No. 105: 1-352. Wagner, R.H. and Varker, V.J., 1971. Trab. Geol. Univ. Oviedo, 4: 533-601. Wahrhaftig, C., 1965. US. Geol. Surv., Prof. Pap., 482. Wakeman, R.J. and Stopp, B.W., 1976. Powder Technol., 13: 261-268. Walker, G.P.L., 1962. Q. J. Geol. Soc. London, 118: 275-293. Walker, G.P.L., 1971. J. Geol., 79: 696-714. Walker, G.P.L., 1972. Contrib. Mineral. Petrol., 36: 135-146. Walker, G.P.L., 1973. Geol. Rundsch.. 62: 43 1-446. Walker, G.P.L. and Croasdale, R., 1971. J. Geol. SOC.London, 127: 17-55. Walker, J.R. and Massingill, J.V.. 1970. Geol. SOC.Am. Bull., 81: 3103-3108. Walker, M.J.C., 1973. Can. J. Earth Sci., 10: 1340-1346. Walker, R.G., 1965. Proc. Yorks. Geol. Soc.. 35: 1-32. Walker, R.G., 1967a. J. Sediment. Petrol., 37: 1052-1058. Walker, R.G., 1967b. J. Sediment. Petrol., 37: 25-43. Walker, R.G., 1969. J. Geol., 77: 125-143. Walker, R.G., 1970a. Geol. Assoc. Can., Spec. Pap., 7: 219-250. Walker, R.G., 1970b. Proc. Geol. Assoc., 81: 43-67. Walker, R.G., 1973. In: R.N. Ginsburg (Editor), Evolving concepts in Sedimentology. John Hopkins University Press, Baltimore, Md., pp. 1-37. Walker, R.G., 1978. Bull. Am. Assoc. Pet. Geol., 62: 932-966. Walker, R.G. and Sutton, R.G., 1967. J. Sediment. Petrol., 37: 1012-1022. Wall, J.R.D. and Wilford, G.E., 1966a. Z. Geomorphol., 10: 91-94. Wall, J.R.D. and Wilford, G.E., 1966b. Z. Geomorphol., 10: 462-468. Wallace, P.W. and Boothroyd, G., 1964. J. Mech. Eng. Sci., 6: 74-87. Wallis, G.B., 1962, Proc. Symp. Interaction between Fluids and Particles. Institution of Chemical Engineers, London, pp. 9- 16. Wallis, G.B., 1969. One-dimensional Two-phase Flow. McGraw-Hill, New York, N.Y. Walter, M.R., 1972. J. Geol. Soc. Aust., 18: 395-399. Waltham, A.C., 1974. The Limestones and Caves of North-west England. David and Charles, Newton Abbot, Devon. Waltham, A.C. and Ede, D.P., 1973. Trans. Cave Res. Group G.B., 15: 27-40. Walter, B.A., 1981. Mon. Weather Rev., U.S. Dep. Agric., 108: 2024-2031. Walton, E.K., 1955. Proc. R. SOC.Edinburgh, B64: 327-357. Walton, E.K., 1967. Scott. J. Geol., 3: 306-317. Wang, K.C., 1972. AIAA J., 10: 1044-1050. Ward, F., 1923. Am. J. Sci., (5)6: 308-309. Ward, S.G., 1955. J. Oil Color Chem. Assoc., 38: 9-31. Ward, S.G. and Whitmore, R.L., 1950a. Br. J. Appl. Phys., 1: 286-290.

639 Ward, S.G. and Whitmore, R.L., 1950b. Br. J. Appl. Phys., 1: 325-328. Warnke, D.A., 1969. Southeastern Geol., 4: 189-200. Warnke, D.A., Goldsmith, V., Grose, P. and Holt. J.J., 1966. J. Geophys. Res., 71: 2013-2016. Warren, A., 1970. Z. Geomorphol., SIO: 154-180. Warren, A., 1971. Geogr. J., 137: 458-461. Warren, A,, 1972. Sedimentology, 19: 37-44. Warren, A., 1976. Nature (London), 259: 653-654. Warren, P.T., 1963. Trans. Edinburgh Geol. SOC.,19: 225-255. Wasmund, E., 1930. Senckenbergiana. 12: 139- 15 I . Waterhouse, J.B. and Bradley, J., 1957. Trans. R. SOC.N. Z., 84: 519-549. Waters, A.C. and Fisher, R.V., 1970. Proc. 2nd Columbia River Basalt Symp., pp. 157-170. Waters, A.C. and Fisher, R.V., 1971. J. Geophys. Res., 76: 5596-5614. Waterston, C.D., 1950. Geol. Mag., 87: 133-139. Watson, T.N., 1974. J. Pet. Techno]., 26: 289-293. Watts, G.M. and Dearduff, R.F., 1954. Tech. Mem. U S . Beach Erosion Board, 52. Watts, I.E.M., 1959. Hong Kong R. Obs., Tidal Monogr., 8. Wazzan, A.R., Okamura, T.T. and Smith, A.M.O., 1967. Phys. Fluids, 10: 2540-2545. Weaver, J.D., 1976. Geol. Mag., 113: 535-543. Weaver, J.D. and Jeffcoat, R.E., 1978. Geol. Mag., 115: 245-253. Webby, B.D., 1959. N.Z. J. Geol. Geophys., 2: 461-478. Weber, J.N., 1958. J. Sediment. Petrol., 28: 333-341. Weiss, R.F. and Florsheim, B.H., 1965. Phys. Fluids, 8: 1631-1635. Wellander, P., 1964. Tellus, 16: 347-358. Wells, D.R. and Sorensen, R.M., 1970. Scour around a circular pile due to oscillatory wave motion. Texas A. and M. Univ., Sea Grant Publ. No. 208. Wells, D.R. and Sorensen, R.M., 1971. Proc. 12th Conf. Coastal Eng., 2: 1263-1280. Wells, M.K., 1962. Overseas Geol. Miner. Resour., Suppl. Ser., No. 4. Wells, R.B., 1969. Proc. Pa. Acad. Sci., 43: 187-190. Welsh, W.E., 1970. AIAA J., 8: 1983-1989. Wen, C.Y. and Yu, Y.H., 1966a. AIChE J., 12: 610-612. Wen, C.Y. and Yu, Y.H., 1966b. Symp. Ser. Chem. Eng. Prog., No. 62: 100-1 1 I . Wentworth, C.K., 1944. J. Geol., 52: 117- 130. Wentworth, C.M., 1967. Bull. Am. Assoc. Pet. Geol., 51: 485 (abstr.). Werle, H., 1961. Publ. O.N.E.R.A., No. 103. Werner, F., 1963. Meyniana, 13: 108-121. Werner, F., 1968. Meyniana, 18: 79-105. Werner, F. and Newton, R.A., 1975a. In: L.E. Cronin (Editor), Estuarine Res., vol. 2. Academic Press, New York, N.Y. Werner, F. and Newton, R.S., 1975b. Mar. Geol., 19: 29-59. Werner, F., Unsold, G., Koopmann, B. and Stefanon, A., 1980. Sediment. Geol., 26: 233-262. Werner, P.W., 1951. Trans. Am. Geophys. Union, 32: 898-902. Westman, A.E.R. and Hugill, H.R., 1930. J. Am. Ceram. SOC.,9: 767-779. Weston, K.J., 1980. Tellus, 32: 433-438. Weylander, P., 1961. Adv. Geophys., 8: 316-379. Wezel, F.C., 1970. Mem. Geol. SOC.Ital., 9: 225-280. Whitaker, J.H. McD., 1965. Nature (London), 207: 709-71 I . Whitaker, J.H. McD., 1973. Nor. Geol. Tidsskr., 53: 403-417. Whitaker, R.E., Reid, R.O. and Vastano, A.C., 1975. Tech. Mem. U.S.Coastal Eng. Res. Cent., 56. White, B.R. and Schulz, J.C., 1977. J. Fluid Mech., 81: 497-512. White, C.O. and Grabow, R.M., 1973. A I M J., 1 1 : 1316-1322. White, H.E. and Walton, S.F., 1937. J. Am. Ceram. SOC.,20: 155-166.

640 White, R.A., 1971. Trans ASME, D93: 537-542. White, W.A., 1961. J. Sediment. Petrol., 31: 560-570. White, W.B. and White, E.L., 1970. Caves Karst, 12(6): 41-48. Whitehead, A.H. and Keyes, J.W., 1968. AIAA J., 6: 2380-2387. Whitmore, R.L., 1955. Br. J. Appl. Phys., 6: 239-295. Whitmore, R.L., 1957. J. Inst. Fuel, May 1957: 238-242. Whitney, M.I., 1978. Geol. SOC.Am. Bull., 89: 1-18. Whitney, M.I. and Brewer, H.B., 1968. Proc. Mich. Acad. Sci. Arts Lett., 53: 91-104. Whitney. M.I. and Dietrich, R.V., 1973. Geol. SOC.Am. Bull., 84: 2561-2582. Whittecar, G.R. and Mickelson, D.M., 1979. J. Glaciol., 22: 357-371. Wiegel, R.L., 1964. Oceanographical Engineering. Prentice-Hall, Englewood Cliffs, N.J. Wiegel, R.L. and Fuchs, R.A., 1955. Trans. Am. Geophys. Union, 36: 975-984. Wiegel, R.L., Patrick, D.A. and Kimberley, H.K., 1954. Trans. Am. Geophys. Union, 35: 887-896. Wieghardt, K., 1953. Forschungsh. Schiffstech., No. 2: 68-81. Wiens, H.J., 1959. Ann. Assoc. Am. Geogr., 49: 31-54. Wieringa, J., 1974. Boundary-Layer Meteorol., 7: 3-19. Wiethe, J.D.. 1970. Compass of Sigma Gamma Epsilon, 47: 110-1 18. Wilcox, D.C., 1975. AIAA J., 13: 555-556. Wilford, C.E., 1966. Bull. Natl. Speleol. SOC.,28: 179-182. Wilford, C.E. and Wall, J.R.D., 1965. J. Trop. Geogr., 21: 44-70. Wilhelm, R.H. and Kwauk, M., 1948. Chem. Eng. Prog.,3: 201-218. Willden, R. and Mabey, D.R., 1961. Science, 133: 1359-1360. Williams, A.T., 1971a. J. Trop. Geogr., 32: 62-68. Williams, A.T., 1971b. Mar. Geol., 11: 145-158. Williams, A.T., 1973a. J. Sediment. Petrol., 43: 857-866. Williams, A.T., 1973b. J. Trop. Geogr., 36: 66-77. Williams, A.T., 1974. Z. Geomorphol., 18: 13-34. Williams, B.J. and Prentice, J.E., 1957. Proc. Geol. Assoc., 68: 286-293. Williams, D.M., 1976. Geol. Mag., 1 13: 169-176. Williams, D.T., 1959. Smithsonian Contrib. Astrophys., 3(6): 47-67. Williams, D.T., 1963a. AIAA J., 1: 494-496. Williams, D.T., 1963b. AIAA J., 1: 2384-2385. Williams, D.T., 1966. Eng. Prog. Univ. Fla., 20: 1-20. Williams. E., 1959. Pap. Proc. E. Soc.Tasmania, 93: 29-32. Williams, E., 1960. Geol. Mag., 97: 208-219. Williams, E., 1961. Geol. Mag., 98: 168-170. Williams, E., 1963. In: Syntaphral Tectonics and Diagenesis. University of Tasmania Press, Hobart, Tasmania, pp. 11-16. Williams, E.P., 1971. AIAA J., 9: 1315-1321. Williams, G.E., 1970. Z. Geomorphol., SIO: 40-63. Williams, H., 1942. Publ. Carnegie Inst. Wash., 540. Williams, H.S., 1881. Am. J. Sci., (4)21: 318-320. Williams, J.C., 1963. J. Fuel Soc. Univ. Sheffield, 14: 29-34. Williams, J.C., 1968. Powder Techno]., 2: 13-20. Williams, J.C., 1976. Powder Technol., 15: 245-25 I . Williams, J.C. and Shields, G., 1967. Powder Techno]., I : 134-142. Williams, P.F., 1969. Geol. Mag., 106: 395-411. Williams, P.S., 1953. J. Appl. Chem., 3: 120-128. Williams, P.W., 1966. Trans. Inst. Br. Geogr., No. 40: 155-172. Williams, W.W., 1947. Geogr. J., 109: 76-90. Williamson, I.A., 1960. Proc. Geol. Assoc., 7 1 : 3 12-3 15.

64 1 Williamson, W.C., 1887. Mem. Proc. Manchester Lit. Philos. SOC.,(3)lO: 19-29. Willmarth, W.W., 1975. Annu. Rev. Fluid Mech., 7: 13-38. Wilson, B.W., 1960. J. Geophys. Res., 65: 3377-3382. Wilson, G., 1952. Geol. Mag., 89: 1-21. Wilson, I.G., 1971. Geogr. J., 137: 180-199. Wilson, I.G., 1972a. New Sci., 53: 634-637. Wilson. I.G., 1972b. J. Sediment. Petrol., 42: 667-669. Wilson, I.G., 1972c. Sedimentology, 19: 173-210. Wilson, I.G., 1973. Nature (London), 241: 393-394. Winant, C.D. and Browand, F.K., 1974. J. Fluid Mech., 63: 237-255. Winant, C.D., Inman, D.L. and Nordstrom, C.E., 1975. J. Geophys. Res., 80: 1979-1986. Wincierz, J., 1973. Neues Jahrb. Geol. Palaontol., Abh., 144: 104-141. Winkley, B.R., 1973. Metamorphosis of a River. Mississippi Water Resources Council, Vicksburg, Miss. Winn, R.D. and Dott, R.H., 1979. Sedimentology, 26: 203-228. Winterer, E.L., 1964. In: A.E.M. Nairn (Editor), Problems in Palaeoclimatology. Interscience, London, pp. 159- 187. Wipperman, F., 1969. Beitr. Phys. Atmos., 42: 225-244. Wirth, K., 1978. Z. Geomorphol., 22: 297-309. Wise, A.F.E., 1971. Philos. Trans. R. Soc. London, Ser. A, 269: 469-485. Wisniewski, E., 1973. Fennia, No. 122. Witten, A.J. and Thomas, J.H., 1976. J. Phys. Oceanogr., 6: 85-92. Wittman, H. and Boss, P., 1938. Wasser und Geschiebebewegung in Gekriimmten Flusstrecken. Springer, Berlin. Wohlenberg, E., 1954. Die Kiiste, 2: 33-94. Wolman, M.G., 1955. U.S. Geol. Surv.,Prof. Pap., 271. Wolman, M.G., 1959. Am. J. Sci., 257: 204-216. Wolman, M.G. and Brush, L.M., 1961. U.S. Geol. Surv., Prof. Pap., 282-G: 183-210. Wolman, M.G. and Leopold, L.B., 1957. U.S. Geol. Surv., Prof. Pap., 282-C: 87-107. Wong, R.T., Seed, H.B. and Chan, C.K., 1975. J. Geotech. Div. ASCE, lOl(GT6): 571-583. Wood, A. and Smith, A.J., 1958. J. Sediment. Petrol., 28: 97-101. Wood, A. and Smith, A.J., 1959. Q. J. Geol. Soc. London, 114: 163-190. Woodcock, A.H., 1940. J. Mar. Res., 3: 248-253. Woodcock, A.H., 1941. Sci. Mon., N.Y., 25: 226-232. Woodcock, A.H. and Wyman, J., 1947. Ann. N.Y. Acad. Sci., 48: 749-777. Woodcock, N.H., 1976a. J. Geol. SOC.London, 132: 399-415. Woodcock, N.H., 1976b. Proc. Geol. Assoc., 87: 169-182. Woodcock, N.H., 1979. J. Struct. Geol., 1: 137-142. Woodrow, D.L., 1968. Gen. Geol. Rep. Pa. Geol. Surv., No. G54. Woods, J.D., 1968. Weather, 23: 225-235. Wopfner, H. and Twidale, C.R., 1967. In: J.N. Jennings and J.A. Mabbutt (Editors), Land Form Studies from Australia and New Zealand. Cambridge University Press, Cambridge, pp. 119-143. Worrall, G.A., 1969. J. Geol., 77: 484-487. Worrall, G.A., 1974. Z. Geomorphol., 18: 291-302. Wortmann, F.X., 1969. J. Fluid Mech., 38: 473-480. Wragg, A.A., 1968. Electrochim. Acta, 13: 2159-2165. Wragg, A.A. and Loomba, R.P., 1970. Int. J. Heat Mass Transfer, 13: 439-442. Wright, C.S. and Priestley, R.E., 1922. Glaciology. Harrison, London. Wright, H.E., 1957. Geogr. Ann., 39: 19-31. Wright, J.A., 1964. Trans. Proc. Geol. SOC.S. Afr., 67: 163-171. Wright, L.D., Chappell, J., Thom, B.G., Bradshaw, M.P. and Cowell, P., 1979. Mar. Geol., 32: 105-140.

642 Wright, M.E. and Walker, R.G., 1981. Can. J. Earth Sci., 18: 795-809. Wright, P., 1976. Sedimentology, 23: 705-712. Wu, J., 1968. J. Fluid Mech., 34: 91- 1 1 I . Wu, J., 1975a. J. Fluid Mech., 68: 49-70. Wu, J., 1975b. J. Hydraul. Res., 13: 405-423. Wu, R.S. and Cheng, K.C., 1976. Int. J. Heat Mass Transfer, 19: 907-913. Wuest, W., 1934. Natur Volk, 64: 73-74. Wulf, G.R., 1963. Bull. Am. Assoc. Pet. Geol., 47: 691-695. Wunderlich, F., 1967. Senckenbergiana Lethaea, 48: 345-349. Wunderlich. F., 1970. J. Sediment. Petrol., 40: 102- 130. Wunderlich, F., 1971. Senckenbergiana Marit.. 3: 103-133. Wunderlich, F., 1972. Senckenbergiana Marit., 4: 47-79. Wunderlich. F., 1973. Senckenbergiana Marit., 5 : 153- 159. Wygnanski, I. and Fiedler, H.E., 1970. J. Fluid Mech., 41: 327-361. Yagashita, K., 1971. J. Geol. Soc. Jpn., 77: 779-790. Yaglom. A.M. and Kader, B.A., 1974. J. Fluid Mech., 62: 601-623. Yair. A., 1973. Z. Geomorphol., S18: 1-9. Yalin, M.S., 1964. J. Hydraul. Div. ASCE, 90(HY5): 105-1 19. Yalin, M.S., 1971. Proc. 14th Congr. Int. Assoc. Hydraul. Res., 3: 101-108. Yalin, M.S., 1972. Mechanics of Sediment Transport. Pergamon, Oxford. Yamada, G., 1966. Soil Found., 6: 1-13. Yang, C.T., 1971a. Water Resour. Res., 7: 311-322. Yang, C.T., 1971b. J. Hydrol., 13: 231-253. Yang, C.T.. 1971~.Water Resour. Res., 7: 156771574, Yang, C.T. and Stall, J.B., 1974. Unit stream power for sediment transport in natural rivers. Univ. 111. Water Resour. Cent., Res. Rep., No. 88. Yarnell, D.L. and Woodward, S.M., 1936. Tech. Bull. U.S. Dep. Agric., No. 526. Yeh, G.T. and Chou, F.K., 1979. ASCE J. Waterw., Harbors coastal Eng., 105(WW2): 247-263. Yen, B.C., 1965. Characteristics of subcritical flow in a meandering channel. University of Iowa Institute of Hydraulic Research, Iowa City, Iowa. Yen, B.C., 1972. In: H.W. Shen (Editor), Sedimentation. Colo. State Univ., Fort Collins, Colo., pp. 22.1-22.33. Yen, C.L., 1970. J. Hydraul. Div. ASCE, 96(HYl): 57-73. Yen, C.L. and Yen, B.C., 1971. J. Hydraul. Div. ASCE, 97(HY2): 303-321. Yih, C.S., 1960. J. Fluid Mech., 9: 161-174. Yih. C.S., 1965. Dynamics of Nonhomogeneous Fluids. Macmillan, New York, N.Y. Yih, C.S., 1969a. Annu. Rev. Fluid Mech., 1: 73-1 10. Yih, C.S., 1969b. Fluid Mechanics. McGraw-Hill, New York. N.Y. Yokoyama, S., 1974. Sci. Rep. Tokyo Kyoiku Daigaku, C12: 17-62. Yoshimi, Y., 1967. Soil Found., 7: 20-32. Yoshimi, Y. and Kuwabara, F., 1973. Soil Found., 13: 67-81. Young, G.A., 1965. The physics of the base surge. U.S. Nav. Ordnance Lab., Tech. Rep. NOL TR 64-103. Young, G.M., 1968. Palaeogeogr. Palaeoclimatol. Palaeoecol., 4: 125- 153. Young, G.M., 1970. Palaeogeogr. Palaeoclimatol. Palaeoecol., 7: 85- 101. Young, G.M., 1974. Precambrian Res., 1: 13-41. Young, G.M. and Jefferson, C.W., 1975. Can. J. Earth Sci., 12: 1734-1748. Young, G.M. and Long, D.G.F., 1976. Palaeogeogr. Palaeoclimatol. Palaeoecol., 19: 303-3 18. Young, G.M. and Long, D.G.F., 1977. Can. J. Earth Sci., 14: 2246-2261. Yule, A.J., 1978. J. Fluid Mech., 89: 413-432. Zeigler, J.M., Hayes, C.R. and Tuttle, S.D., 1959. J. Geol., 67: 318-336.

643 Zeigler, J.M. and Tuttler, S.D., 1961. J. Geol., 69: 583-599. Zeller, J., 1967a. Geogr. Helv., 22: 57-95. Zeller, J., 1967b. Int. Assoc. Sci. Hydrol., Publ. No. 75: 174-186. Zemanick, P.P. and Dougall, R.S., 1970. Trans. ASME, C92: 53-60. Zenkovitch, V.P., 1967. Processes of Coastal Development. Wiley, New York, N.Y. Zenz, F.A., 1971. In: J.F. Davidson and D. Harrison (Editors), Fluidization. Academic Press, London, pp. 1-23. Zenz, F.A. and Othmer, D.F., 1960. Fluidization and Fluid-Particle Systems. Reinhold, New York, N.Y. Zimmerman, C., 1977. J. Hydraul. Res., 15: 73-85. Zimmerman, C. and Kennedy, J.F., 1978. J. Hydraul. Div. ASCE, 104(HYI): 33-48. Zotov, V.D., 1941. J. Geomorphol., 4: 71-73. Zukoski, E.E., 1967. A I M J., 5: 1746-1753.

This Page Intentionally Left Blank

645

SUBJECT INDEX Ablation, (11): 207, 208, 249, 250, 279 Accretionary lapilli, (11): 430 Adhesion ripples, (I): 504: (11): 430, 431 -, beaches, river beds and sabkhas, (11): 530-53 1 -, bedding, (11): 53 I -, character and occurrence, (11): 529-532 -, genesis, (11): 532-533 -, pyroclastic-surge deposits, (11): 53 I -, wavelength, (11): 529 Aeolian deposits, (I): 217, 314, 364-365, 368, 372, 426, 514; (11): 154, 166, 386, 532 Aeolian dunes -, control on size, (I): 275 -, equant, (I): 466-469 -, initiation, (I): 273 -, longitudinal. (11): 3 1-36 -, transverse types, (I): 3 19-326 Aggregate (turbostratic) fabric, (I): 23 I , 232, 233 Aggregative fluidization, (11): 307, 308, 3 14 Air -, density, (I): 1 dynamic viscosity, (I): 1 AkIC., (I): 321-324 Algal reefs and bioherms, (11): 48 Alternate depths, (I): 385-387 Angle of initial yield, (I): 61, 282: (11): 149 Antidune bedforms -, character and occurrence, (I): 4 1 I -4 14, 416 -, internal structure, (I): 414 An tidunes -, as consequence of lag, (I): 288-290 -, character and occurrence, (I): 409-41 1 -, cyclic growth, (I): 41 I -, deposition on, (I): 274 -, existence field, (I): 409 -, flow over, (I): 274 -, potential flow models, (I): 293, 295 -, reflecting “chaos”, (I): 275 -, rooster-tail, (I): 414 rotational-flow models, (I): 295 -, textural control, (I): 295 theory, (I): 405-408 -, wavelength, (I): 407, 410

-.

-. -.

Antidunes (pyroclastic surges), (11): 422. 430 Antiripplets, (I): 504 Apparent viscosity, (I): 4; (11): 321-327 Armouring, (I): 342; (11): 158 Atmosphere, (I): 2 -, mesoscale pressure systems, (I): 28 zonal circulation, (I): 27 Atomic weapons, (11): 396 Attachment -, line, (11): 102. 104 point, (11), 102, 104 Auto-suspension, (11): 398 Avalanche deposits -, bedding, (11): 171 -, fabric, (I): 217 Avalanches -, bulk self-fluidizing, (11): 3 15-317 -, continuous and discontinuous, (11): 149 grading in, (11): 152-158 -, lubrication by air, (11): 295-298 -, on ripples and dunes, (11): 150 -, period, (11): 148-150, 151 -, speed, (11): 156

-.

-.

-.

Backwash ripples, (I): 412 Badland drainage, (11): 235 Bagnold number, (I): 22 Ball-and-pillow -, character, (11): 359, 360-363 -, genesis, (11): 363 Ballistic ripples, (I): 271, 280 -, character &d occurrence, (I): 310-314 on obstacle marks, (11): 189. 199 -, response to changing wind, (I): 5 12 Barkhans -, character and occurrence, (I): 319-321 -, genesis, (I): 274, 320 -, in rivers, (I): 321 -, in seas and oceans, (I): 321 Barred coasts, (11): 434 Bars, (I): 279 -, cross-bedding, (I): 373 Base surges, (I): 49; (11): 396, 418 Beach antidunes, (I): 41 I Beach cusps -, character and occurrence, (11): 453-455

-.

646 -, control by grain size, (11): 455

-, control by swash length, (11): 456 -, due to edge waves, (11): 458-459 due to intersecting waves, (11): 458 -, due to instability, (11): 460 -, internal structure, (11): 461 -, secondary flows, (11): 457 Beach deposits, (I): 261, 265. 403, 416. 505; (11): 468-469, 528 Beach lamination -, attitude, (11): 461 hierarchy, (11): 462 -, scale of the tide, (11): 464-466 -, scale of waves, (11): 462-463 -, storm/seasonal scale, (11): 466-468 -, stratigraphic record, (11): 468-469 Beach profile -, change due to storms, (11): 466-467 change on tidal scale, (11): 465-466 Beach slope and grain size, (11): 461 Beaches -, on emerging bedforms, (I): 496 Bedform existence fields, (I): 336-343, 444-446 -, applied to turbidites, (11): 413-416 Bedform lag -, dunes in rivers, (I): 474-476 -, dunes under tidal influence, (I): 476-479 -, dynamical systems theory, (I): 482-491 effect on classification, (I): 335 -, mechanisms, (I): 484 phase difference, (I): 485-488 -, reactivation, (I): 496-499 Bed forms -, concept of population, (I): 473 -, in river meanders, (11): 93 Benthic boundary layer, (11): 28, 182 Bivalve shells -, attitude after settling, (I): 189 -, attitude during traction, (I): 189 attitude in turbidites, (I): 190 -, attitude on rippled beds, (I): 190 attitude while settling, (I): 186-188 -, current crescents at, (11): 194, 203 edgewise fabric, (I): 229 -, fabric, (I): 179 -, orientation beneath current, (I): 222, 226-227 -, packing, (I): 156, 165 -, stable attitude beneath currents, (I): 227 Bluff-body flows -, heat transfer, (11): 218, 230, 279

-.

-.

-.

-. -.

-. -. -I

-, oscillatory and rotary currents, (11): 181 -, permeable obstacles, (11): 180 -, planetary boundary layers, (11): 182 -, turbulence and shear stress, (11): 179I88 -, sedimentation, (11): 183- 186 -, surface-mounted cylinder, (11): 174- 180 -, two-dimensional, (11): 174- 182 Bomb sags, (I): 113; (11): 431 Bottomsets, (11): 147, 158, 166, 168-171 Bouma sequence -, grading, (11): 404-405 -, vertical patterns, (11): 401-404 Boundary layer streaks, (I): 252-256, 262, 269 -, and current ripples, (I): 272 Boundary layers -, laminar, (I): 10, 12, 242: (11): 6, 7 -, oscillatory, (I): 16, 68 rotating, (I): 10 transitional, (I): 242 -, turbulent, (I): 10, 12, 243; (11): 6, 7, 8 Box folds, (11): 350, 379, 382, 389 Breakout floods, (I): 330; (11): 25, 31 Bubbling bed, (11): 307 Buckles (pyroclastic-flow deposits), (11):43 I Buffer layer, (I): 243 Buildings in the wind, (11): 180, I97 Bulk self-fluidization, (11): 305, 3 15-3 17

-. -.

Cabbage-leaf (plumose) markings, (I): 70 Cardhouse fabric, (I): 23 1 Cave conduits, (11): 239 Cave deposits, (11): 509 Cave flutes and scallops, (11): 242-245 Cavernous sand, (11): 535-538 Cavitation, (I): 73-74; (11): 289 Cavities heat transfer, (11): 218, 219 Changing flows implications for bed roughness, (I): 481 -482 -, implications for bedforms, (I): 471-473 -, wave-action during (I): 496 -, wind-action during, (I): 496 Channel bends -, flow processes, (11): 71-79 -, sedimentation, (11): 91-94 Channeling bed, (11): 307 Channels -, beaded, (11): 62, 239 -, braided, (11): 69

-. -.

647

-, dendritic, (11): 59 -, meandering, (11): 54-59 -, parallel-sided, (11): 62

-, reticulate, (11): 59 -, straight, (11): 64 -, tidal, (11): 55, 62, 65 Chevron marks, (11): 518-520 Chutes and pools, (11): 429, 430 Clastic dykes association with soft-sediment deformation, (11): 554 -, character and occurrence, (11): 554-556 -, fabric, (11): 555 -, grading in, (11): 154, 555 internal layering, (11): 555 -, ptygmatically folded, (11): 557 Clay dunes (lunettes), (I): 325 Clay minerals, (I): 230; 23 I Clay minerals and synaeresis, (11): 553-554 Cliffs and clifflets -, on emerging bedforms, (I): 496, 503 Cloud streets, (11): 14 Coarse-tail grading, (11): 405, 417 Coastal morphology, (11): 433-434 Cockling, (11): 229, 241 Coefficient of dynamic friction, (I): 21 Co-flowing streams, (11): 121 Cohesive sediments, (11): 429, 430 Collective settling, (11): 337 Comet marks. (11): 194 Compound cross-stratification, (I): 353356, 371-373, 498 Concentration -, effects of void-filling, (I): 148 -, effect on viscosity of particle dispersions, (11): 321-325 -, haphazard and random packings, (I): 163-165, 167-173 -, sphere packings, (I): 140, 144, 145, 146. 158, 159, 160, 163-165 -, spheroid packings, (I): 152- I55 Conductivities, (11): 21 1 Conjugate depths, (I): 397 Consolidation and ptygmatic folds, (11): 558-559 Convection, (11): 13-14, 36, 51, 208, 221, 232 Convolute lamination -, genesis, (11): 352-354 -, geometry, (11): 349 -, metadepositional, (11): 352 -, post-depositional, (11): 35 1

-.

-.

-, syndepositional, (11): 352 Coordination -, defined, (I): 139 -, sand, (I): 172 -, sphere packings, (I): 140. 144. 145, 146, 159, 165-166 -, spheroid packings, (I): 152-155 Coral reefs, (11): 47 Corrasion. (I): 71; (11): 24, 25. 27. 28, 30, 31,43, 185, 193, 200, 241, 278, 281, 285, 289. 524, 525 Corrasion grooves, (11): 524-525 Corrasion ripples, (11): 523-524 Couette flow -, particle fabric due to, (I): 191-205 Crack growth, (11): 550-55 I Cratering, (I): 133. (11): 431 Crinoids, (I): 221 Critical flow, (I): 385 Crookedness, (11): 64 Cross-bedded deposits -, fabric, (I): 217-218 Cross-bedding -, compound, (I): 371 -373. 498 -, deformed, (11): 385-393 -, dune, (I): 364-366 -, in Bouma sequences, (11): 403-404 -, with reactivation surfaces, (I): 496-499, 509 storm deposits, (11): 504 Cross-hatching -, character, (11): 249 -, due to instability, (11): 220 -, theories, (11): 250 Cross-lamination -, and parallel lamination, (I): 376 -, due to counter-current ripples, (11): 166 -, in Bouma sequences, (11): 402-404 -, storm deposits, (11): 490-491, 493, 494, 500-50 I , 504 -, subcritical, (I): 362-364, 366 -, supercritical, (I): 367-371 -, vertical patterns of climb, (I): 373-376, 378-380 -, wave ripple, (I): 427 Cross-s tratification -, and grain size, (I): 381 -, angle of climb, (I): 352 -, centroclinal, (11): 193 -, compaction of, (I): 357 compound, (I): 353-356, 371-373.498 description and classificatian, (I): 346349

-.

-. -.

648

-. equant dunes, (I):

468 experimental, (I): 359. 366, 370 -, form sets, (I): 353 -, genesis, (I): 345 grading, (11): 154-158 -, herring-bone, (I): 462 -, hierarchical erosion surfaces, (I): 356 longitudinal dunes, (11): 32 models, (I): 350-357, 360, 367 -, sand waves, (I): 459-463 -, set thickness, (I): 377-380 -, small-scale features, (11): 168- 171 subcritical sets, (I): 353 -, supercritical sets, (I): 353 -, tidal dunes, (I): 506-5 10 Current crescents -, aeolian environments, (11): 189- 191 -, shallow-water environments, (11): 191194 varieties. (11): 185 Current ripples -, and lee-side eddy, (I): 276 -, and viscous sublayer instability, (I): 280 -, as consequence of lag, (I): 288-290 -, at obstacle marks, (11): 194, 200 birth and death, (I): 305 character and occurrence, (I): 3 14-3 19 -, climbing. (I): 351,363,366,368,373-380 -, controls on size, (I): 3 14 -, counter-current, (11): 166 cross-lamination, (I): 362, 367-370 -, distinction from wave ripples, (I): 424, 429 -, due to instability, (I): 279-280 -, existence field, (I): 338-343 in hurkhun form, (I): 321 initiation, (I): 272-273 -, lag deposits on, (11): 158 lagging tidal currents, (I): 505 -, morphologicaP’analysis, (I): 307-3 10 -, on sand waves: (I): 458 -, potential flow models, (I): 293 -, sediment diffusion and deposition to lee, (11): 141-148 -, superimposed on dunes, (I): 501 -, superimposed on wave ripples, (I): 503 textural limit, (I): 283 -, three-dimensionality, (I): 3 16-319 wavelength, (I): 303 -, wavelength/height ratio, (I): 303 Current shadows -, aeolian environments, (11): 197- 199 -I

-.

-.

-.

-.

-.

-. -.

-.

-.-. -.

-. -.

-, aqueous environments, (11): 200 -, internal structure, (11): 200 -, varieties, (11): 185 Currents -, classification on basis of components, (I): 419-422 Cutting (ductile) wear, (I): 71; (11): 520, 524 Cyclic liquefaction -, controls, (11): 302-304 -, due to earthquakes, (11): 298-300 -, due to storm waves, (11): 300, 385 -, laboratory experiments, (11): 300-302 Cylinders attitude in shear flows, (I): 194, 197, 198 -, flow separation, (11): 106. 174- 179 -, lodging on a bed, (I): 221-224, 225 -, mass and heat transfer, (11): 217 -, settling. (I): 188

-.

Dam-break waves, (I): 53 Debris flows, (I): 20 fabric, (I): 199-205 Dicollement, (11): 349, 363. 389 Deep-sea floor dunes, (I): 330, (11): 161 -, erosional grooves and ridges, (11): 28 -, mud waves, (11): 538-544 -, obstacle marks, (11): 195-197, 203 ripples, (I): 318, 426 sand ribbons, (11): 20 Defects in desiccation and synaeresis, (11): 550-55 1 Defects and flute marks, (11): 267, 269, 270-272, 274, 277, 281 Deflation, (I): 496. 504; (11): 203 Deformation (brittle) wear, (I): 71; (11): 520. 525 Deformed cross-bedding -, complex (due to drag), (11): 388, 392 -, complex (due to slumping), (11): 385-386 -, simple (due to drag), (11): 386-388, 389 -392 Delta wings, (11): 115 Deltaic deposits, (11): 139, 351, 355, 359, 361, 380, 388 Deltas -, in dune troughs, (I): 503 Dense haphazard packing, (I): 139, 163 Deposition rate -, from cross-lamination, (I): 380 Depth of disturbance (sand beaches), (11): 465

-.

-.

-. -.

649

Desiccation cracks, (11): 545 -, fluvial, (11): 546, 547 intertidal, (I): 504; (11); 546, 547 -, lacustrine, (11): 546 -, see shrinkage cracks Dewatering -, expressed by sand volcanoes, (11): 137141 Diffusion sediment in jets, (11): 135-137 sediment in separated flows (half-jets), (11): 141-148 Diffusivities, (11): 21 1 Dirt polygons, (11): 249 Discs, (I): 212, 222 -, attitude in shear flows, (I): 194, 197, 198 -, settling, (I): 188 Dish structures -, character and occurrence, (11): 367-370 -, genesis, (11): 371-374 relation to other sedimentary structures, (11): 370 roofing deposits, (11): 371 Dissipation of gravity currents, (11): 396400 Dissolution, (11): 208 Distribution grading, (11): 405 Drag coefficient -, natural grains, (I): 81 spherical particles, (I): 77 Drag marks, (11): 51 1-516 Drop-stones, (I): 189; (11): 194 Drumlins, (11): 49 Dunes -, abandoned, (I): 495,499-501 -, analytical models of lag, (I): 496 -, and lee-side eddy, (I): 276 -, and streak bursting, (I): 276 -, as consequence of lag, (I): 288-290 -, avalanches on, (11): 150 -, bimodal populations, (I): 493 birth and death, (I): 305 -, character and occurrence, (I): 326-33 I -, controls on size, (I): 275, 280, 296, 331334 -, cross-bedding, (I): 364-366, 372 -, drainage across crests, (I): 495 -, drainage along troughs, (1):'50l -, excursion, (I): 490 existence field, (I): 338-343 -, in erosional grooves, (11): 28, 29 -, internal structure in tidal environments,

-.

-.

-.

-.

-.

-.

-.

-.

(I): 506-510 -, lag, (I): 473-479,491-495 lag deposits on, (11): 158 -, lifespan, (I): 490 -, loading mud, (11): 379 morphological analysis, (I): 307-3 10 -, numerical models of lag, (I): 491-495 -, oblique, (I): 300, 329 -, on sand waves, (I): 457 -, polymodal populations, (I): 479-480, 493 -, potential flow models, (I): 293 relation to bars, (I): 334-336 relative height, (I): 336-340 -, ripple-forms on, (11): 159-168 -, rotational flow models, (I): 295-298 -, sediment diffusion and deposition to lee, (11): 141-148 superimposed, (I): 474, 475, 479 -, superimposed on dunes, (I): 503 -, unimodal populations, (I): 493 -, wavelength/height ratio, (I): 303 wave-rounded, (I): 503 Dynamic friction, (I): 213, 282, 289

-.

-.

-. -.

-.

-.

Earthquake effects, (11): 293, 384, 395 Ebb-flood evasion, (11): 38 Edge waves, (I): 44;(11): 445 Edgewise fabric, (I): 229 Electrolytes -, effect on clay-mineral fabric, (I): 231, 232, 233 Elu triation during fluidization, (11): 315 -, during sedimentation, (11): 355, 341, 347 Entrainment threshold, (I): 94, 338-343 Equant dunes -, character and distribution, (I): 466-468 -, controls, (I): 468 Equilibrium scour depth, (11): 187 Erosion (cohesive beds) -, by cavitation, (I): 73 -, by corrasion, (I): 71 -, by fluid-stressing, (I): 69, 268-269 Erosional grooves and ridges -, deep-sea floor, (11): 28 -, in deserts, (11): 29-3 I -, on river beds, (11): 24 -, shallow-marine environments, (11): 2528 Excursion, (I): 489, 490 Experiments

-.

-, antidunes, (I): 440

-, apparent viscosity of dispersions, (11): 32 1-337 -, avalanching, (11): 150, 151, 153, 154. 156 -, ballastic ripples, (I): 3 10 -, beach cusps, (11): 458, 460 - * bedform lag, (I): 481 -, boundary layer flow configuration. (I): 252-259 -, cavitation erosion, (I): 79 -, concentration in particle mixtures, (I): 171- 173 -, controls on packing, (I): 174-175 corrasion. (I): 73 -, corrasion ripples, (11): 524 -, cross-lamination, (I): 366-367. 370-371 -, current-ripple shape in plan, (I): 316317 cyclic liquefaction, (11): 300-303 -, dune shape, (I): 335 -, erosion of mud beds, (I): 70, 268-269 -, flow-fluidization, (11): 305 -, flute marks, (11): 267, 272-284 -, gravity currents, (I): 50-5 I , 54, 55 -, haphazard particle packing, (I): 163I65 -, heat and mass transfer, (11): 214, 215, 216, 217, 218, 225, 235, 242-245, 246, 250, 251 heavy mineral sags and drops, (11): 365 -, hydraulic jumps, (I): 395 load casts, (11): 356, 359 -, longshore bars and troughs, (11): 44044 I , 442-443,445 mass-transport due to waves, (I): 39 - * meandering, (11): 70, 72, 75, 78, 82 -, modes of particle transport, (I): 90,93 -, mud ripples, (11): 286-288 obstacle marks, (11): 176, 179, 180, 186189, 191, 203 -, particle coordination, (I): 165- 166 -, particle fabric, (I): 186-188, 190-191, 198-199, 219, 225-227, 232 -, particle radial distribution function, (I): 162- 163, 166- I67 -, particle settling, (I): 77. 79, 80-81, 82 -, passively deformed beds, (11): 367 potholes, (11): 264, 288 - , pseudo-nodules and ball-and-pillow, (11): 363 -, ptygmatic folds, (11): 559 -, repose of sand, (I): 61-62

-.

-.

-.

-.

-.

-.

-.

-, rhomboid ripples, (I): 401 -, rill marks, (11): 509

-. roll marks, (11): 516 -. secondary flows, (11): 6, 8, 14, 16, 17, 41 -, sediment entrainment, (I): 64, 68 -. sediment transport by waves, (I): 106107 -, sedimentation (s.s), (11): 328, 334, 337 -, sedimentation in jets, (11): 135. 140

-. sedimentation in separated

flows, (11): 143, 143-148 -, separated flows, (11): 106, 107, 109, 1 1 1, 112, 115, 117. 119. 120, 123, 126 -, shrinkage cracks, (11): 551-552, 553 -, surface waves, (I): 37 -, suspension transport, (I): I00 -, transcurrent laminations, (I): 359 -, transition to turbulence, (I): 243-250 -, transverse bars (coasts), (11): 452 -, transverse ribs, (I): 394 wave-related ripples. (I): 438, 439, 440442,445.448.451 -, wind set-up, (11): 476-477 wind-related currents, (11): 480-481 Exposure indicators, (I): 496,498, 501 -505; (11): 509, 544-549 External flow, (11): 101

-. -.

Fabric -, appositional, (I): 179 -, changes during liquefaction, (11): 297 -, controls on strength, (I): 199, 208, 209 -, creeping soils, (I): 199. 203 -, crystals in igneous and metamorphic rocks, (I): 205 -, debris flows, (I): 199-205. deformational, (I): 180 -, due to granular shear, (I): 212-220 -, due to settling, (I): 183-191 -, effects of consolidation, (I): 233, 234235 -, experiments on particles in sheared fluids, (I): 198 -, magnetic, (I): 180 -, measurement and representation, (I): 180- 183 -, models for till. (I): 211-212 muddy sediments, (I): 230-235 -, particle lodgement, (I): 221 -229 -, particles in shear flows, (I): I9 1- 199 -, parting lineation, (I): 261 -, rheotactic, (I): 179

-.

-.

-, solifluction deposits, (I): 199, 203 -, stones in ice, (I): 210 -, symmetry, (I): 182 -, theory for particles in a sheared fluid, (I): 192-197 tills, (I): 199, 204, 208-212; (11): 50 Fair weather deposits, (11): 488 Fissility, (I): 234 Fluchkurren, (11): 224, 226, 230, 238 Fluserschichren, (I): 423, 428, 510-51 1 Flat-topped ripples, (I): 503, 505 Floccules, (I): 57, 231, 232 Flow configurations relation to sedimentary structures, (I): 250-251, 209 transitional boundary layers, (I): 243250 -, turbulent boundary layers, (I): 251-259 Flow differentiation, (11): 153 Flow regimes (open channel), (I): 24 Flow regimes (settling particles), (I): 77 Flow separation -, and bedforms, (I): 276-277 -, and cavitation erosion, (11): 289 at bluff bodies, (11): 176-179 at cylinders, (11): 186 -, at high speeds, (11): 127 -, axisymmetric, (11): 114, 126 -, backflow speed, (11): 106, 118 -, cavities, (11): 107-109, I15 delta wings, (11): 115 -, downstream-facing steps, (11): 110-1 13, 117-119, 119-120, 121, 126 -, flute marks, (11): 281-284 -, heat and mass transfer, (11): 217-219 -, in channel bends, (11): 78 in erosion, (I): 73 -, in meteorite pits, (11): 251 -, mathematical models, (11): 109 mud ripples, (11): 287 -, on cave flutes and scallops, (11): 244 o n sand waves, (I): 461 -, o n wave ripples, (I): 441 -, pressure (fluctuating) distribution, (11): 120 -, pressure (mean) distribution, (11): I19 -, revealed by ripple fans, (11): 159-168 -, rollers and vortices, (11): 105, 117 -, spheroids, (11): 114 -, shown by counter-current ripples, (11): 166 streamline mapping, (11): 102-105

-.

-. -.

-. -.

-. -.

-. -.

-.

-. streamwise plate, (11): 106 -, three-dimensional, (11): 102, 114-1 19 -, transverse walls, (11): 109, 116, 119 -, topological rules, (11): 104 turbulence production, (11): 121- 127 two-dimensional, (I): 18; (11): 102. 106I I4 -, upstream-facing steps, (11): 109 Flow slides, (11): 294, 298 Fluidization -, and volcanic phenomena, (11): 294. 3 10 -, after liquefaction, (11): 340, 347 -, defined, (11): 294, 295 -, grain sorting, (11): 314 -, particle rounding, (11): 308 stationary, (11): 306-315 -, varieties, (11): 305 Fluids -, Newtonian, (I): 3 -, non-Newtonian, (I): 3-5, 17, 199 Fluid-stressing, (I): 69; (11): 278 Flute marks and flow separation, (11): 281-284 -, asymmetrical, (11): 259 classification, (11): 254 -, comet-shaped, (11): 258, 278 -, enlargement by corrasion, (11): 281 -, enlargement by fluid-stressing, (11): 278 -, experiments with mud beds, (11): 27728 1 genesis, (11): 267 -, local erosion rate, (11): 284 morphology, (11): 253 -, parabolic, (11): 255-257, 272, 281 -, patterns, (11): 259 Plaster of Paris beds (mass transfer analogy), (11): 272-277 -, size, (11): 269 -, spindle shaped, (11): 257, 277, 278 -, theory of evolution, (11): 268-272 Fluvial deposits, (I): 193, 200, 219, 229. 26 I , 265, 330, 358, 362, 363, 369. 372. 375. 376. 416, 426, 427, 429, 434. 496, 498; (11): 100, 154, 261, 351, 355, 359, 380, 386-388, 509 Foam marks, (11): 527-528 Foam on beaches, (I): 505 Folds due to migrating loads, (11): 378-379 Forced convection, (11): 208, 214-216 Form sets current ripples, (I): 346 dunes, (I): 330, 346

-. -.

-?

-. -.

-. -.

-?

-.-.

652

-, wave ripples, (I): 427 Free convection, (11): 208, 216, 240, 245 Free shear-layers sediment diffusion in, (11): 144-148 -, transition to turbulence, (11): 124 -, turbulence properties, (11): 125- 127 -, vortex production, (11): 121-125 Froude number, (I): 24, 385, 397, 399. 407. 408; (11): 543

Gravel -, fabric, (I): 217-219, 228-229 Gravel stripes, (11): 46 Gravity currents -, classes, (I): 47 -, dissipation, (11): 396-400 -, secondary flow, (11): 12 Guinness, (11): 307 Gutter casts, (11): 27

Galileo number, (11): 309, 327 Gastropod shells, -, models, (I): 221 -, orientation in currents, (I): 225-226 Gelifluction, (I): 7 Glacial deposits, (I): 208-212; (11): 48 Glacial flutings, (11): 48-51 Glacial striae, (11): 290, 515-516 Glacier moulins. (11): 288 Glaciers. (I): 9, 21 1 ; (11): 290 meltwater, (I): 26 -, secondary flow, (11): 51 Glaciomarine deposits, (I): 189 Gradient current -, defined, (11): 471 -, theory, (11): 477 Grading coarse-tail. (11): 405, 417 -, controls, (11): 155-158 -, distribution, (11): 405 -, normal, (11): 154, 155 -, perpendicular, (11): 154, 155 -, pyroclastic-fall deposits, (I): 117-122 -, pyroclastic-flow deposits, (11): 418 -, reverse, (11): 154. 155, 158 -, tangential, (11): 154, 156, 158 -, turbidites, (11): 404-405. 416, 417 Grain self-fluidization. (11): 305, 3 17-320 Grain shape, (I): 57-61 -, effect on viscosity of dispersions, (11): 325 Grain size -, beach slope, (11): 461 -, effect on liquefaction, (11): 302 -, effect on viscosity of dispersions, (11): 324 -, longshore bars and troughs, (11): 452 Grain-fall stratification, (11): 17I Granular shearing, (I): 21, 85; (11): 156, 327, 556 -, fabric, (I): 212 Grashof number, (11): 2 I3

Huhooh (and chuhusio), (I): 48; (11): 12 Hairpin vortices, (I): 245, 258, 260, 275 Haphazard packing, (I): 139, 163- 173 Harrow marks, (11): 19 Heat transfer -, analogy with momentum transfer, (11): 213 -, bluff bodies, (11): 217, 218 -, free convection, (11): 216 -, general theory, (11): 21 1-213 -, high-speed flows, (11): 218 instability, (11): 219 separated flows, (11): 217-218, 251 Heat-with-mass-transfer, (11): 207, 208, 21 8 Heavy mineral sags and drops, (11): 364366 Height -, dunes, (I): 333 -, sand waves, (I): 465 Hierarchies of sedimentary structures, (I): 372 Hierarchy of erosion surfaces, (I): 356, 371. 46 1 Honeycombe fabric, (I): 23 I Horizontal form-index -, ballistic ripples, (I): 313 -, defined, (I): 310 -, dunes, (I): 328 -, transverse dunes, (I): 322 -, wave ripples, (I): 422 Hydraulic jumps -, and beach antidunes, (I): 412 -, and transverse ribs, (I): 390. 394 -, oblique, (I): 398-399 -, theory, (I): 397 -, varieties, (I): 395-396 Hydromorphological relationships in rivers, (11): 65-70 Hydrosphere, (I): 2

-.

-.

-.

-. -I

Ice, (I): 4 -, ablation forms, (11): 228

653 -, sustrugi, (11): 525 Ice ripples -, character, (11): 246 -, due to instability, (11): 220, 247 Ice waves, (11): 245, 249 Iceberg drag marks, (11): 5 11-514 Ice-melting, (11): 207, 210 Imbrication, (I): 182, 203, 204, 209, 216. 217, 218, 224, 261; (11): 189 Incipient fluidization, (11): 307 Interference (Brick-and-tile) ripples, (I): 434-436 Internal flow, (11): 102 Instability accompanying heat and mass transfer, (11): 219-222, 240, 244 -, ball-and-pillow, (11): 363 -, convolute lamination, (11): 359 -, dish structures, (11): 373-374 gravity-current head, (11): 12 -, heavy mineral sags and drops, (11): 365 -, load casts, (11): 357 -, plane bed, (I): 281-284 -, pseudo-nodules, (11): 363 -, sedimenting systems, (11): 340 Internal waves, (I): 30, 40, 43, 109, 426; (11): 544 Inviscid flows -, over wavy beds, (I): 285

-.

-.

Jets -, and sand volcanoes, (11): 137 attaching, (11): I12 -, in cross-streams, (11): 130 -, sedimentation from, (11): 135- 137 -, turbulent, (11): 128-131 Junctures, (I): 309, 3 13, 328, 422, 432, 454; (11): 26, 32, 41

-.

Kurren -, cave flutes and scallops, (11): 242-245,

246-248 -, classification, (11): 222-224 -, cockling, (11): 241 -, first order, (11): 224-230 -, on gypsum, (11): 235, 242 -, on halite, (11): 229 -, second order, (11): 230-241 Kelvin-Helmholtz instability, (I): 275, 279; (11): 121 Kinematic sieving, (11): 157 Kinematic waves, (I): 277-279; (11): 150

Khjlkurren, (11): 226-228, 229, 234. 238, 24 1

Lacustrine deposits, (I): 368, 373, 375, 426, 429; (11): 359, 380, 388, 521 Lag -, flow over wavy beds, (I): 286; (11): 219220 -, of dunes, (I): 335,473-483 in meanders, (11): 91, 220 -, in sediment transport, (I): 287-290; (11): I44 -, influence on bed stability, (I): 288-290, 292, 294, 295, 299; (11): 219-220 Lag deposits channel bends, (11): 94, 96 -, on ripples and dunes, (11): 158 -, storm sequences, (11): 491 Lamb-Taylor instability, (11): 222 Laminar flow -, mass and heat transfer, (11): 211, 214, 215 Laminar-turbulent transition, (I): 237 Lateral accretion, (11): 53 -, in river meanders, (11): 95-100 -, in tidal meanders, (11): 94 Lattice point, (I): 138 -, unit, (I): 138 Lee side, (I): 309 Lee waves, (I): 30; (11): 542-544 Lee-side eddy, (I): 276-277 Lifespan, (I): 484, 490 Lift on transported particles, (I): 86-88. 191 Limestone -, dissolution, (11): 208, 209 Kurren; (11): 222-245 Limit cycle, (I): 492 Linsenschichten, (I): 428, 432, 510-51 I Liquefaction -, and earthquakes, (11): 293, 295, 298-300 -, changes in fabric during (11): 297 -, cyclic, (11): 295, 298-305 defined, (11): 293, 295 -, dynamic, (11): 295, 300 -, pore-fluid pressure, (11): 297 spontaneous, (11): 294 static, (11): 295, 296-298 Liquefaction potential, (11): 303 Liquidization -, defined, (11): 293, 295

-.

-.

-.

-.

-.

-. -.

654

-. -.

role of pore fluid, (11): 294 Liquidized sand fabric, (I): 220 Liquidized sediments, (11): 293. 295 -, apparent viscosity, (11): 321-327 Load casts character, (11): 354-357 -, genesis, (11): 357-358 Load-casted ripple marks, (11): 375-378 Lobes and clefts, (I): 50; (11): 12, 41-43, 399,421 Longitudinal bedforms and secondary flows, (11): 1 -, desert dunes ( s e i f ) , (11): 31-36 -, erosional grooves and ridges, (11): 24-3 1 glacial flutings, (11): 48-51 meandering grooves, (I): 266-269 -, rectilinear grooves, (I): 266-269 -, ridge-and-furrow moulds, (11) 40-43 -, sand ribbons (aeolian), (11): 23-24 sand ribbons, (aqueous currents). (11): 17-23 -, spur-and-groove, (11): 47-48 -, tidal current ridges, (11): 36-40 -, trough banding, (11): 51-52 -, wave-related furrow and ridges, (11): 43 -46 -, wave-related gravel stripes, (11):46 Longitudinal dunes -, character and occurrence, (11): 3 1-33 genesis, (11): 33-36 -, internal structure, (11): 32 Longitudinal grooves (mud beds), (I): 266269 Longshore bars and troughs -, character and occurrence, (11): 435-440 genesis of three-dimensional forms, (11): 444-445 patterns of flow and sediment transport, (11): 446-450 related to wave reflection, (11): 442-444 -, related to wave breaking, (11): 441 -, related to wave shoaling, (11): 442 seasonal and storm variation, (11): 440 -, sedimentary structures (intertidal), (11): 448-450 -, sedimentary structures (subtidal), (11): 450-452 Loose haphazard packing. (I): 139. 163 Lunettes, (I): 325

-.

-.

-.

-.

-.

-.

-. -.

-.

-.

Muanderkarren, (11): 238-240

M a w volcanoes. (11): 396 Magma -, viscosity of, (I): 2 Magmatic sedimentary structures, (I): 3. 133. 205, 319; (11): 51, 154, 355, 380 Magnus effect, (I): 86 Mars -, dunes, (I): 324 -, obstacle marks, (11): 197. 199 wind ridges-and-furrows, (11): 30 Mass flows, (I): 6, 8, 19-22 Mass-flow deposits, (I): 199-205, 220 Mass transfer, (11): 207, 208 -, analogy with momentum transfer, (11): 213 -, experimental flute marks, (11): 284 -, free convection, (11): 216 -, general theory, (11): 210-213 -, instability, (11): 219-220 laminar flow (conduit), (11): 215 laminar flow (flat surface), (11): 214, 227 - * separated flows, (11): 217-218 -, turbulent flow (conduit), (11): 215 -, turbulent flow (flat surface), (11): 214, 227 Mass transport -, over wavy bed, (I): 42, 438-441 -, surface waves, (I): 38-42 -, tide, (I): 47 Meander scrolls, (11): 60, 89, 100 Meander-belt, (11): 59 Meandering grooves, (I): 266 Meanders -, analysis and description, (11): 59-64 classification, (II):54 cross-sectional profile, (11): 83-86 -, discharge effects on secondary flow, (11): 71 -, evolution, (11): 88-91 -, flow processes, (11): 71-79 -, flow separation in, (11): 78 -, general occurrence, (11): 53 -, ice, (11): 220, 240 -, lateral accretion, (11): 94-100 limestone, (11): 238-240 -, migration processes, (11): 86 -, migration rates, (11): 87 -, models for planimetric form, (11): 90 patterns, (11) 54-59 -, radius, (11): 69 -, rivers, (11): 54-55, 61 -, secondary flow, (11): 72-79

-.

-. -.

-.

-.

-. -.

655

-, sediment equilibrium in, (11): 80-83 -, sediment influences, (11): 70

-. superelevation, sinuosity, (11): 69 (11): 71 -, -, tidal, (11): 55

-. wavelength and channel width, (11): 67-

Oceanic currents, (I): 8 Ordered packing, (I): 138, 140-156 Organisms, (11): 5 , 48 Orientation of fossils, (I): 227 Orthorhombic fabric, (I): 182. 189 Oscillatory currents, (I): 419-422; (11): 183

69 -, wavelength and discharge, (11): 66

-, wavelength and drainage-basin area (11): 66 Meandering theories of, (11): 79 Mechanical sedimentary structures, defined, (I): 1 Melting, (11): 208 Meltwater, (11): 289 Meteorites, (11): 208, 218, 250 Minerals - * density of, (I): 2, 3 Moats at sea-mounts, (11): 195 Monoclinic fabric, (I): 182, 204, 209, 219. 228 Mud deposition of, (I): 105, 51 I ; (11): 542 Mud beds -, grooves on, (I): 266-269 Mud drapes, (I): 461,495, 501. 509, 514 Mud plastering, (11): 430 Mud ripples -, character and occurrence, (11): 259-261 -, genesis, (11): 286 -, wavelength, (11): 287 Mud waves as turbidity-current deposits, (11): 541 character and occurrence, (11): 538-541 -, due to internal waves, (11): 544 -, due to lee waves, (11): 541-544 Muddy sediments fabric, (I): 230-235

-.

-.

-. -. -.

Nodal point, (11): 104 Non-barred coasts, (11): 434 Normal grading, (I): 117, 118; (11): 154, 155, 404, 490, 491, 494,496, 500 Nuees urdentes, (I): 49: (11): 396, 418 Nusselt number, (11): 212 Obstacle marks classification, (11): 185 -, controls on size, (11): 186-189 -, general, (11): 173 -, related to current pattern, (11): 183-186

-.

Packing -, binary systems, (I): 168, 171 -, bivalve shells, (I): 156 -, continuous size-distributions, (I): 172173 -, defined, (I): 137 distribution function, (I): 162, 166 -, effect of deposition rate, (I): 174-177 -, effect of depositional medium, (I): 174175 effects of particle roughness, (I): 165 -, effect of material properties, (I): 175, 177 -, effect of mode of deposition, (I): 163165, 173 -, effect on liquefaction, (11): 302 -, effects of particle size, (I): 160 effects of particle sorting, (I): 148, 172 -, geometrical (polyhedral) models, (I): 159 -, kinds, (I): 138, 139 -, muds, (I): 173 -, non-spherical regular shapes, (I): 156 -, poiydisperse systems, (I): 167- I73 -, sand, (I): 165, 172, 174 -, significance, (I): 137 - * spheres (haphazard), (I): 163-167 -, spheres (non-simple ordered), (I): 144I47 -, spheres (random), (I): 156-160 spheres (simple ordered), (I): 140-144 spheroids (non-simple ordered), (I): 154 - 155 spheroids (simple ordered), (I): 144-154 statistical models, (I): 157-160 symmetry in, (I): 140 -, ternary systems, (I): 168-171 -, voids, (I): 147-149 -, wall effects, (I): 160-163 Parabolic dunes, (I): 324-326 Parallel lamination, (I): 265 -, and cross-lamination, (I): 376 in Bouma sequences, (11): 402-404 possible genesis, (I): 357-360 storm deposits, (11): 491, 493, 494, 500501, 504

-.

-.

-.

-. -. -. -. -.

-. -. -.

656

Parallel-laminated deposits -, fabric, (I): 219 Particle concentration -, defined, (I): 139 Particulate fluidization, (11): 307, 308, 3 14 Parting lineation -, character, (I): 259-261 -, due to boundary layer streaks, (I): 262265 -, environmental distribution, (I): 265-266 -, fabric, (I): 261 -, pattern within swash marks, (11): 527, 528 Parvoids, (11): 307 Passively deformed bedding, (11): 366-367 Penitentes, (11): 228 Percolation, (11): 157 Perpendicular grading, (11): 154 Phase diagrams, (I): 483 Phase difference, (I): 485-488 Pipe flow, (I): 26 Pitching, (I): 188 Plane beds, (I): 265, 298, 357-360: (11): 527 -, existence fields, (I): 338-343, 344 -* instability, (I): 281-284 Plastic deformation of mud beds, (11): 42, 28 1 Plateau’s instability, (11): 459 Plates flow separation, (11): 106 Playa stone-tracks, (11): 5 14-5 I5 Plumes (fresh water over salt), (I): 49 (volcanic debris), (I): 1 1 1 Plumose markings, (I): 70: (11): 551, 556 Point, bars, (11): 60. 62 -, equilibrium of sediment, (11): 80-83 -, model for bedform and grain size, (11): 91-94 -, transverse profile, (11): 83-86 Pools, (11): 62 Pore-fluid pressure, (11): 384 Porosity -, defined, (I): 139 mud, (I): 230 Potholes -, character and occurrence, (11): 261-264 -, genesis, (11): 288 Powder-snow avalanches, (I): 49 Prandtl number, (11): 212 Pressure -, in separated flows, (11): I19 Pseudo-nodules

-.

-.

-.

-, character, (11): 359

-, genesis, (11): 363 Pseudokarren, (11): 222, 228, 230, 232, 235 Ptygmatic folds, -, character and occurrence, (11): 556-557 consolidation, (11): 558-559 -, genesis, (11): 557-560 Pure shear -, particle fabric due to, (I): 205-212 Pyramidal dunes, (I): 466-468 Pyroclastic debris, (I): I12 Pyroclastic-fall deposits -, bombs in. (I): 121 -, bomb sags, (I): 133 -, lateral grading in, (I): 119-122 -, models (bombs), (I): 123-125 - * models (vertical and lateral grading), (I): 125-132 -, thickness patterns, (I): 114-1 17 vertical grading in, (I): I 17- 1 I8 Pyroclastic flows, (11): 294, 317, 320, 396 Pyroclastic-flow deposits -, buckles, (11): 321 -, textural and compositional grading, (11): 418 -, thickness changes, (11): 418 Pyroclastic-surge deposits -, accretionary lapilli, (11): 430 -, adhesion ripples, (11): 430. 43 I bomb sags, (11): 431 -, cross-bedding, (11): 424-430 -, parallel stratification, (11): 422 sand waves, (11): 422-423 soft-sediment deformations, (11): 43043 1 -, vesicular structure, (11): 428-430

-.

-.

-.

-.-.

Radial distribution function, (I): 162, 166 Radial grooves on volcanoes accretionary, (11): 421 attributed to base-surge lobes and clefts, (11): 422 erosional, (11): 419-421 Rain -, effect on limestone, (11): 225 -, effect on sand beds, (11): 533-535 -, stress due to, (11): 534 Rain-impact ripples, (11): 533-535 Random currents, (I): 419 Random packing, (I): 139, 156-160 Rayleigh-Taylor instability, (11): 1 I , 22 I , 317, 354, 357-358, 363, 365

-.

-. -.

657

Reactivation structures -, origins, (I): 498, 509, 513 Regmaglypts. (11): 250 Relaxation time, (I): 484, 488-491 Residual angle after shearing, (I): 61; (11): I49 Reverse grading, (11): 154, 155, 404, 418. 422 Reynolds analogy, (11): 2 13 Reynolds number, (I): 13: (11): 212 Rhomboid dunes -, and oblique jumps, (I): 404 -, character and occurrence, (I): 403 Rhomboid rill marks -, character and occurrence, (I): 400 -, oblique jumps, (I): 404 Rhomboid ripple marks -, and oblique jumps, (I): 404 -, character and occurrence, (I): 400-402 Richardson-Zaki equation, (11): 3 13 Ridge-and-furrow moulds, (11): 26 I , 28 I , 287 -, character and occurrence, (11): 40-41 hierarchical patterns, (11): 42 Ridges and runnels, (11): 435 Riffles (crossings), (11): 62 Rill marks, (I): 504, 507-509 Rillenkarren, (11): 226, 229, 232, 233-235 Ring dunes, (11): 422 Ring-waves, (11): 250 Ritznenkarren, (11): 235 Ripple fans, (11): 159-168, 189, 194, 199 Ripple marks -, terraced, (I): 503 Rippled toroids, (11): 204 Rivers, (I): 7 -, channel pattern, (I): 25 -, flow in ideal channel, (I): 22 hydrological regime, (I): 25 Roll marks, (11): 516 Roll waves, (I): 408 Rolling, (I): 90, 228, 229 Roof pendants, (11): 240 Rotary currents, (I): 419-422, (11): 183 Rundkurren, (11): 225, 226, 229, 235-238

-.

-.

Sabkha deposits, (11): 525 Saddle point, (11): 104 Salt domes, (11): 357 Saltation -, and obstacle marks, (11): 203 -, in air, (I): 90, 280 in water, (I): 91

-.

Sand -, angles of repose, (I): 61 -, avalanches, (I): 212 -, fabric, (I): 228, 229, 261 packing, (I): 165, 172, 174 Sand domes, (11): 538 Sand holes, (11): 538 Sand ribbons due to centifugal instability, (11): 21 -, due to transverse roughness variatioiis, (11): 19, 20 -, in aeolian environments, (11): 23 -, in tidal seas, (11): 19-21 -, on continuous beds, (11): 21 -, on rough beds, (11): 17- I9 -, on smooth beds, (11): 17 Sand shadows, (11): 185 Sand volcanoes, (11): 138-141, 293 Sand waves character and occurrence, (I): 454-459 genesis, (I): 465 -, internal structure and flow asymmetry, (I): 459-462 -, internal structures, (I): 459-463 -, mud drapes in, (I): 461, 462 -, range in symmetry, (I): 454 relation to dunes, (I): 335 -, shape and flow asymmetry, (I): 463 shapes in profile, (I): 457 -, superimposed dunes, (I): 457 Sand waves (pyroclastic flows), -, cross-bedding, (11): 424-430 -, shape and size, 01): 422-423 Sand-flow stratification, (11): 171 Sand-flows grading in, (11): 155-158 -, on aeolian dunes, (11): 150 Susstrugi. (11): 203, 430, 525 Schmidt number, (11): 212 Scour at bridge piers, (11): 186- I89 Scour-remnant ridges, (11): 185, 190. 200203 Scratch circles, (11): 521-522 Screes, (I): 217; (11): 158 Sea breezes, (I): 48; (11): 12 Seamounts -, flow around, (11): 182 obstacle marks at, (11): 195 Secondary flow -, accompanying Lamb-Taylor instability, (11): 222 -, and organisms, (11): 5

-.

-.

-.-.

-. -.

-.

-.

65X

- , associated

with shoaling/breaking waves, (11): 46, 47 atmosphere, (I): 29 -, beach cusps, (11): 457 -, channel bends, (11): 72-75 -, due to centrifugal instability, (11): 5-7 -, due to edges and corner, (11): 8 -, due to thermal convection, (11): 13 -, due to transverse roughness variations, (11): 9- I 1 -, general character and effects, (11): 2-5 -, glaciers, (11): 51 -, gravity-current heads, (11): 12 -, heads of base surges, (11): 421 Langmuir circulation, (11): 15-17 -, related to density contrasts, (11): I 1 -, response of organisms, (11): 48 -, rippled beds, (I): 318 -, river bends, (11): 75-79 -, rivers, (I): 26 -, three-dimensional boundary layers, (11): 7 -, turbidity-current heads, (11): 41 -43 Sediment diffusion -, during suspension transport, (I): 99 to lee of ripples and dunes, (11): 141- 148 Sediment dispersions, (I): 83-85, 104 Sediment entrainment -, air compared with water, (I): 64 - * in wave boundary layers, (I): 66-68 problem of motion threshold, (I): 64 steady flows, (I): 62-66 Sediment load, (I): 83 Sediment transport -, and energetics, (I): 97, 101 -, as bedload, (I): 88, 287 -, bedload formulae, (I): 95-98 -, concentration profile during, (I): 98, 99, 107; (11): 42 -, creeping mode, (I): 92 -, criterion for, (I): 94. 338-343 -, differential, (I): 95, 280, 321 -, flotation, (11): 526 -, forces responsible for. (I): 85 -, general concepts, (I): 82-85 -, in suspension, (I): 87. 93-94, 287 -, in varying flows (continuity), (I): 102 -, in varying flows (tidal), (I): 104 -, in varying flows (undirectional), (I): 103 -, in varying flows (wind waves), (I): 106107 -, lag during, (I): 104, 105. 287-290

-.

-.

-. -. -.

-, longshore (wind waves), (I): 107-109 -, particle speed during, (I): 95 relation to transport stage, (I): 93 -, rolling mode, (I): 90, 228 -, saltating mode, (I): 90-92 -, sliding mode, (I): 89 -, suspended load formula, (I): 101 -, unusual modes, (I): 109 Sedimentary environments -, deep-marine, (I):8-9 shallow-marine, (I): 8 shore-related, (I): 7-8 -, terrestrial. (I): 6-7 Sedimentary particles -, biogenic, (I): 59 -, shape and size, (I): 57-60 Sedimentation ( s . s ) -, and deformed cross-bedding, (11): 392 -, continuously graded systems, (11): 339 -, defined, (11): 293, 327 -, duration, (11): 345 -, discontinuously graded systems, (11): 337-339 -, general principles, (11): 327-330 -, monodisperse systems, (11): 330-333 polydisperse systems, (11): 333-337, 417 Sediments -, cohesionless, (I): 60 -, cohesive, (I): 61, 69-79 segregation, (11): 153 Sensitive clays, (I): 232; (11): 294 Separated flows -, erosion in, (11): 285 sediment diffusion and deposition in half-jets, (11): 141-148 -, sediment diffusion in jets, (11): 135-137 Separation -, line, (11): 102, 104 -, point, (11): 102, 104 Separation bubble length, (11): 106, I 1 I Settling -, at high concentrations, (11): 327-340 -, attitude of non-spherical particles. (I): 183- 188 -, biogenic particles, (I): 80 effects due to neighbouring particles, (I): 82 -, effects of boundaries, (I): 78 -, effects of particle roughness, (I): 81 -, effects of turbulence, (11): 134 -, in non-Newtonian fluids, (I): 78

-.

-.

-?

-. -. -.

-.

-.

659

-, mineral grains, (I): 80 -, non-spherical particles, (I): 79-8 1 -, particle stability, (I): 188 -, spherical particles, (I): 75-78 Shallow-marine deposits, (I): 190, 227-228. 265, 330, 364-365, 372, 426, 428; (11): 27, 46, 161, 261, 355, 359, 361, 366, 368, 388, 452, 496-504 Shape fabrics, (I): 179 Sheet slumps, (11): 380-384 Shelf environments -, storm deposits, (11): 493-504 Sherwood number, (11): 212, 214, 215, 216 Ship waves, (11): 250 Shrinkage cracks -, character and occurrence, (11): 546-547 -, classification, (11): 544-546, 547 -, mechanics, (11): 550-554 -, ptygmatically folded, (11): 556-557 -, size and spacing, (11): 552 Sichelwunnen -, character and occurrence, (11): 264-266 -, genesis, (11): 289 Sigmoidal sand banks, (11): 37 Simple shear -, particle fabric due to, (I): 191-205 Sinter terraces, (11): 233 Sinuosity, (11): 64 Skim marks, (11): 518 Slides, (I): 8 Slip face, (I): 310 Slugging bed, (11): 307 Slumps, (I): 8 Snow -, ballistic ripples, (I): 3 14 -, hurkhuns, (I): 321 -, corrasion by, (11): 525 -, dirt polygons, (11): 249 -, obstacle marks, (11): 189, 197, 200 -, slumped, (11): 384 -, transport, (I): 98 -, transverse dunes, (I): 324 Soft-sediment deformations -, ball-and-pillow, (11): 359-364 -, change of state, (11): 343 -, classification, (11): 348 convolute lamination, (11): 349-354. -, deformed cross-bedding, (11): 385-393 -, dish structures, (11): 367-374 -, fabric, (I): 220 -, folds, due to migrating loads, (11): 378379

-.

-, heavy mineral sags and drops, (11): 364-

366

-. kinematics and dynamics, (11): 344-348 -. load casts, (11): 354-358 -, load-casted ripple marks, (11): 375-378 -, passively deformed bedding, (11): 366 -, pseudo-nodules, (11): 359-364

-, related to earthquakes, (11): 293 -, sheet slumps, (11): 380-384 Soil creep, (I): 19 -, fabric, (I): 199, 203 Solifluction, (I): 7 Solifluction deposits -, fabric, (I): 199, 203 Solitary bed wave, (I): 299 Solution basins, (11): 229, 230-232, 239 Solution ripples, (11): 234, 246-249 Space vehicles, (11): 220 Specific energy, (I): 383-387 Specific force, (I): 397 Spheres -, in shear flows, (I): 191, 198 -, mass and heat transfer, (11): 217 -, settling, (I): 75-78 Spheroids -, attitude in shear flows, (I): 192-197, 198, 205-212 -, flow separation, (11): I14 packing, (I): 149-155 -, settling, (I): 186, 188 Spitzkurren. (11): 228-230, 234, 241 Spouting bed, (11): 307 Spring-neap cycle -, effect on drape-spacing in sand waves, (I): 462 -, effect on dune internal structure, (I): 510 -, effect on dune movement, (I): 478 Spur-and-groove, (11): 47-48 Stanton number, (11): 212 Star-shaped dunes, (I): 466-468 Static friction, (I): 281 Stationary fluidization -, bed expansion, (11): 3 12-3 14 -, bed stability, (11): 308-3 10, 3 12 -, defined, (11): 305 -, elutriation, (11): 315 -, gas compared to liquid, (11): 308 -, grain sorting, (11): 314 -, minimum velocity. (11): 310-312 -, pressure drop, (11): 310 -, regimes, (11): 306-310

-.

Steps flow separation, (11): 109-1 13, 117-1 19,

-.

119-120 -, heat transfer, (11): 218. 219

Stokes law, (I): 76 Stone cells, (I): 390 Stone clusters, (I): 390 Stoping, (11): 373 Storm deposits bioclastic sediments, (11): 504 -, body and trace fossils, (11): 501-504 compared to model, (11): 504-505 -, general, (11): 472 general model, (11): 487-491 -, modern shelf environments, (11): 493-

-.

-. -.

496 -, quantitative aspects, (11): 491 -493

-, resemblance to turbidites, (11): 500, 504 -, stratigraphic record, (11): 496-505 -, vertical and lateral sequences, (11): 48949 1, 494. 500, 504 Storm rollers, (11): 363 Storm surges -, advanced mathematical models, (11): 483-485 -, changes in water level, (11): 472-477 -, currents measured in the field. (11): 482 -483 -, dependence of wind stress on wind speed, (11): 485-486 -, general, (11): 471 -, magnitude and frequency, (11): 481-482 -, theory of currents, (11): 477-481 Storms, (I): 425, 426, 465; (11): 367, 440, 47 1,483 Stoss side, (I): 309 Stranded ice, (11): 192 Streak bursting -, and boundary roughness, (I): 258 -, and dunes, (I): 276 -, and turbulence production, (I): 259 -, general, (I): 256-259 -, periodicity, (I): 258 Streak lifting, (I): 258 Stream power and structures, (I): 338, 381 Subcritical flow, (I): 24, 385 Sublimation, (11): 208 Supercritical flow, (I): 24, 385, 405-408; (11): 240 Superelevation in channel bends, (11): 71 Suspension transport

-.

-.

diffusion model, (I): 99 Surge marks, (11): 509 Swash marks, (11): 525-527 Swash zone, (I): 265 Synaeresis cracks, (11): 545, 563 Tadpole nests, (I): 436 Tangential grading, (11): 159 Taylor-Gdrtler vortices, (11): 6-7, 52, 232 Tektites, (11): 208, 218, 250 Thalweg, (11): 63 Thatching, (I): 245 Thrust faults, (11): 379, 382 Thunderstorm downwashes, (I): 48; (11): 12 Tidal asymmetry -, effect on dunes, (1): 506 -, effect on sand waves, (I): 459-463 Tidal current ridges character and occurrence, (11): 36-38 -, in fossil record, (11): 39 -, internal structure, (11): 38 -, relation to tidal flows, (11): 38-39 Tidal deposits, (I): 358, 365, 368, 372, 426, 428-429, 462, 505. 509. 51 I ; (11): 39-40,

-.

46. 100

Tides, (I): 8 -, effect at obstacles, (11): 181 -, general character, (I): 44 -, mass-transport due to, (I): 47 -, rotary, (I): 45 Till -, fabric, (I): 179. 199. 204, 208-212; (11): 50 -, fluted, (11): 48-50

Tip and spoil heaps, (11): 294, 298 Tollmien-Schlichting waves, (I): 243, 245 Tool marks -, chevron marks, (11): 518-520 -, classification, (11): 509-51 I -, drag marks, (11): 51 1-516 mechanics, (11): 520 -, prod marks, (11): 516-517 -, roll marks, (11): 516 -, skim marks, (11): 518 -, tumble marks, (11): 5 17-5 18 Tortuosity, (11): 64 Transcurrent lamination, (I): 357-360 Transfer processes, (11): 207 Transition bedforms, (I): 335 Transition to turbulence -, non-linear and three-dimensional effects, (I): 240-250

-.

66 I

-, theoretical models, (I): 239-241 -, transverse changes in velocity, (I): 249250 transverse variations in turbulence, (I): 246-249 velocity-profile changes, (I): 241 -243 -, visualization, (I): 243-246 Translational fluidization, (11): 305 Transverse bars (coasts), (11): 452 Transverse bedforms -, adhesion ripples, (I): 529-535 antidunes, (I): 41 1-416 as kinematic waves, (I): 277-279, 301 -, as stochastic phenomena, (I): 304-305 -, ballistic ripples, (I): 310-314, 512 -, harkhans, (I): 319-321 birth and death, (I): 305. 484 cave flutes and scallops, (11): 242-245 -, classification, (I): 310 corrasion ripples, (11): 523-525 -, cross-hatching, (11): 249-250 -, current ripples, (I): 314-319, 505 -, deposition on (I): 274 -, dunes (aqueous environments), (I): 326336, 473-480,495, 499-501 existence fields, (I): 336-343, 444-446 flow over, (I): 274 -, foam marks, (11): 527-528 -, flute marks, (11): 253-259, 267-286 -, general features of mathematical models, .(I): 290-292 -, hydraulic models. (I): 298-299 ice ripples, (11): 245-246 -, in curved flows, (I): 301 -, initiation, (I): 272-274 -, internal structures, (I): 380 -, kinds, (I): 271 -, morphological analysis, (I): 307-3 10 -, movement, (I): 274 -, movement of grains through, (I): 301 -, mud ripples, (11): 259-261, 286-288 -, mud waves, (11): 538-544 -, parabolic dunes and lunettes, (I): 324326 -, potential flow models, (I): 292-295, 299 -, related to flow configurations, (I): 275277, 279 -, relation to lag, (I): 284-290 -, rhomboid structures, ( I ) 400-405 -, ring waves, (11): 250 -, rotational flow models, (I): 295-298 -, sand waves, (I): 454-466

-. -.

-. -.

-. -.

-.

-. -. -.

-, sand waves (pyroclastic surges), (11) 422

-430

-. shape in profile, (I): 302 -, Sichelwunnen, (11): 264-266, 289-290 -, solution ripples, (11): 246-248

-, spectral analysis. (I): 304 -, theoretical height, (I): 302-303 -, three-dimensional, (I): 299-30 1 -, transverse dunes (aklk), (I): 321-324, 512 -, transverse ribs, (I): 387-390 Trittkorren, (11): 233 -, wave-related ripples, (I): 422-454 -, zibur, (I): 324 Transverse dunes -, response to changing winds, (I): 512-514 Transverse dunes ( u k K ) -, character and occurrence, (I): 321-324 Transverse ribs -, as antidunes, (I): 390 and Trittkarren, (11): 233 -, character and occurrence, (I): 387-390 -, model of, (I): 390-395 -, related to hydraulic jumps, (I): 394 Trees -, orientation beneath current, (I): 222 -, as obstacles, (11): 193 Trittkarren, (11): 233 Trochoidal ripples, (I): 422 Trough banding, (11): 51 Tsuticrmi, (11): 300 Tumble marks, (11): 5 17-5 18 Tumbling, (I): 188 Turbidites, (9: 190. 265; (11): 40 -, antidune bedforms, (I): 416 -, bivalve shells in, (I): 190 -, Bouma sequence, (11): 401-407.413-417 -, correlation, (11): 409-412 downcurrent changes (Bouma sequence), (11): 404-408, 41 1-412 -, downcurrent changes (grain size) (11): 412, 417 -, downcurrent changes, (sole marks) (11): 408 drag marks, (11): 5 14, 5 16. 5 17, 5 18 -, interpretation of vertical and lateral changes, (11): 412-417 -, sand fabrics, (I): 219-220 -, sand volcanoes amongst, (11): 138 Turbidity currents, (I): 9; (11): 395 -, general occurrence, (I): 49 -, head billows, (I): 51; (11): 400

-.

-.

-. -.

662

lobes and clefts, (I): 50; (11): 12, 41-43 -, models, (I): 53-56 related to storm-action, (11): 505 Turbulence, (I): 13 -, above ripple and dune beds, (11): 127 due to flow separation, (11): 121-127 -, effect on particle settling, (11): 134, 135 -, effect on transfer processes, (11): 210, 21 1 in erosion, (I): 73 -, techniques for study, (I): 238-239 transition to, (I): 13, 17, 24, 239-250 Turbulent flow -, mass and heat transfer. (11): 211, 214, 215 Turbulent spots, (I): 245, 246, 250 -I

-.

-.

-. -.

Unidirectional currents, (I): 419-422; (11): 183 Unit cell, (I): 138 Vegetation -, and sediment transport, (11): 197-200 -, cause of scratch circles, (11): 520 Ventifacts, (11): 523, 524, 525 Vertical form-index -, ballistic ripples, (I): 313 current ripples, (I): 315 -, defined; (I): 310 dunes, (I): 328 -, sand waves, (I): 454 -, sand waves (pyroclastic surges), (11): 423 -, wave ripples, (I): 424, 446 Vesicular structure -, beach sands, (11): 535-538 pyroclastic-surge deposits, (11): 428, 430 -, soils, (11): 538 Viscosity, air, (I): I -, fluidized beds, (11): 325-327 -, magma, (I): 2 -, measurement, (11): 321 -, sediment dispersions (high concentration), (11): 322-325 -, sediment dispersions (low concentration), (11): 321 -, water, (I): 2 Viscous sublayer. (I): 243, 252 -, model of streak bursting, (I): 256-259 -, streaky structure, (I): 246, 252-256 Voids -, in sphere packing, (I): 147-149

-.

-.

-.

-.

Volcanic bombs, (I): 121, 133: (11): 431 Volcanic eruptions, (11): 395 -, classification, (I): 112, 117 -, explosive, (I): 113 -, general, (I): I 1 1 Voronoi polyhedra, (I): 159, 166 Vortices -, in free shear-layers, (11): 121-125 Wake downstream of cylinder, (11): 178I80 Wakes, (11): 520 Wall effects -, on particle packing, (I): 160-163 Water -, density, (I): 2 -, dynamic viscosity, (I): 2 Water table in beach, (11): 464, 536 Water-escape structures. (11): 343 Wave base, (I): 36 Wave overwash. (11): 446, 448 Wave reflection and longshore bars and troughs, (11): 442-444 Wave ripples -, and mass transport, (I): 438-441 -, character and occurrence, (I): 422-427 -, climbing, (I): 427 existence field, (I): 444 -, experimental, (I): 435, 438, 441, 452 -, flow separation, (I): 441; (11): 11 1 general controls, (I): 436-442 multi-crested, (I): 433, 451 -, in palaeohydraulic reconstruction, (I): 452-454 -, initiation of vortex-type, (I): 442 -, interference type, (I): 434-436. 452 -, internal structure, (I): 427-429 -, response to changing wave climate, (I): 506 rolling-grain type, (I): 438-441 -, superimposed on current ripples, (I): 496, 503 -, superimposed on dunes, (I): 503 -, vertical form-index and orbital diameter, (I): 446 vortex type, (I): 441 wavelength and grain size, (I): 448 -, wavelength and orbital diameter, (I): 446 Wave swash and backwash, (I): 43: (11): 462-463,464-465 Wave-current ripples, (I): 429-432, 44845 1

-.

-.

-.

-.

-. -.

663

-, and flow asymmetry, (I): 450 -, relation to other forms, (I): 319

Wavelength -, adhesion ripples, (11): 529 -, antidunes, (I): 407 - , atmospheric secondary flows (cloud streets), (11): 14, 35 -, ballistic ripples, (I): 3 13 -, beach cusps, (11): 453, 456,458 -, cave flutes and scallops, (11): 245 -, cave-conduit meanders, (11): 240 -, convection, (11): 14 -, current ripples, (I): 303. 314 -, dunes, (I): 298, 303, 331 -, Ekman-layer instabilities, (11): 8 -, erosional grooves and ridges, (11): 24, 25, 26, 29 -, ice ripples, (11): 245 -, lagging dunes, (I): 474-479 -, Langmuir circulation, (11): I7 -, load casts, (11): 357 -, longitudinal dunes, (11): 32 -, Muanderkarren, (9): 239 meanders, (11): 60, 66-70 -, mud ripples, (11): 287 -, mud waves, (11): 539, 541, 544 -, ridge-and-furrow moulds, (11): 41 -, rhomboid structures, (I): 405 -, Rillenkarren, (11): 234 -, Rinnenkarren, (11): 235 -, sand ribbons, (11): 17, 21. 23, 28 -, spur-and-groove, (11): 48 -, sand waves, (I): 454 -, sand waves (pyroclastic surges), (11): 423 -, solution ripples, (11): 247 -, Taylor-Gortler vortices, (11): 6 -, tidal current ridges, (11): 37 -, transverse dunes (akle), (I): 322 -, transverse ribs, (I): 388 -, Trittkarren, (11): 233 -, wave ripples, (I): 424, 426 wave-related furrows and ridges, (11): 44, 46 -, zihar, (I): 324 Wave-related furrows and ridges, (11): 4346

-.

-.

Wave-related ripples -, in storm deposits, (11): 490, 491, 493 -, superimposed, (I): 503, 506 Waves (surface), (I): 8 -, breaker types, (I): 43 -, effect at obstacles, (11): 181, 203-204 -, fabric due to, (I): 229 -, general categories, (I): 30 -, ideal, (I): 32 -, mass transport due to, (I): 38-42; (11): 442-444 -, near to shore, (I): 42 -, orientation of shells beneath, (I): 226, 227 -, real, (I): 31 -, relation to wind speed, (I): 32 role in liquidization, (11): 300, 385 -, swash and backwash, (I): 43 -, swash marks (11): 525-527 Wavy beds -, inviscid flow over, (I): 285 Wind, (I): 7 -, geostrophic, (I): 29 Wind ridges-and-furrows, (11): 29-3 1 Wind set-up -, associated currents, (11): 477-48 1 basin with shelf, (11): 476 closed basin, (11): 475 defined, (11): 471 -, laboratory studies, (11): 476-477 -, laminar case, (11): 472-479 turbulent case, (11): 474-475 Wind stress and wind speed, (11): 485-486 Wind-breaks, (11): I81 Wind-drift current -, defined, (11): 471 -, theory, (-11): 477 Wind-related currents, -, dependence on wind speed, (11): 481 -, laboratory studies, (11): 480 -, theory, (11): 477-480 Wreck marks, (11): 194

-.

-. -. -. -.

Yurdungs, (11): 30 Yield stress, (I): 4, 70 Zzhar, (I): 324

This Page Intentionally Left Blank

Sedimentary structures, their character and physical basis Volume 1

Sedimentary structures, their character and physical basis Volume 1

Desert Sedimentary Environments (Developments in Sedimentology 14)

Desert Sedimentary Environments (Developments in Sedimentology 14)

Diagenesis in Sediments and Sedimentary Rocks (Developments in Sedimentology, 25a) (v. 1)

Diagenesis in Sediments and Sedimentary Rocks (Developments in Sedimentology, 25a) (v. 1)

The techniques of sedimentary Mineralogy (Developments in Sedimentology 4)

The techniques of sedimentary Mineralogy (Developments in Sedimentology 4)

Carbonate rocks: Physical and Chemical Aspects (Developments in Sedimentology 9B)

Carbonate rocks: Physical and Chemical Aspects (Developments in Sedimentology 9B)

Carbonate Reservoirs (Developments in Sedimentology)

Carbonate Reservoirs (Developments in Sedimentology)

Diagenesis, IV (Developments in Sedimentology)

Diagenesis, IV (Developments in Sedimentology)

Diagenesis, IV (Developments in Sedimentology)

Diagenesis, IV (Developments in Sedimentology)

Developments in sedimentology, Volume 19

Developments in sedimentology, Volume 19

Developments in sedimentary provenance studies

Developments in sedimentary provenance studies

Tsunamiites - Features and Implications (Developments in Sedimentology)

Tsunamiites - Features and Implications (Developments in Sedimentology)

Green Marine Clays (Developments in Sedimentology)

Green Marine Clays (Developments in Sedimentology)

Cyclic Sedimentation (Developments in Sedimentology 10)

Cyclic Sedimentation (Developments in Sedimentology 10)

Continental Red Beds (Developments in Sedimentology)

Continental Red Beds (Developments in Sedimentology)

Diagenesis in Sediments & Sedimentary Rocks (v. 2)

Diagenesis in Sediments & Sedimentary Rocks (v. 2)

Sedimentary structures of ephemeral streams

Sedimentary structures of ephemeral streams

Physical basis of chemistry

Physical basis of chemistry

Palygorskite-Sepiolite: Occurrences, Genesis and Uses (Developments in Sedimentology)

Palygorskite-Sepiolite: Occurrences, Genesis and Uses (Developments in Sedimentology)

Developments in Sedimentology, Volume 52: Cyclostratigraphy and the Milankovitch Theory

Developments in Sedimentology, Volume 52: Cyclostratigraphy and the Milankovitch Theory

Deltaic and Shallow Marine Deposits (Developments in Sedimentology, Volume 1)

Deltaic and Shallow Marine Deposits (Developments in Sedimentology, Volume 1)

Bentonites: Geology, Mineralogy, Properties and Uses (Developments in sedimentology)

Bentonites: Geology, Mineralogy, Properties and Uses (Developments in sedimentology)

Carbonate Rocks: Origin, Occurrence and Classification (Developments in Sedimentology 9A)

Carbonate Rocks: Origin, Occurrence and Classification (Developments in Sedimentology 9A)

Siliceous Deposits in the Pacific Region (Developments in Sedimentology 36)

Siliceous Deposits in the Pacific Region (Developments in Sedimentology 36)

Hypersaline Brine and Evaporitic Environments: Seminar Proceedings (Developments in sedimentology)

Hypersaline Brine and Evaporitic Environments: Seminar Proceedings (Developments in sedimentology)

Clays and Clay Minerals of Japan, #26 (Developments in Sedimentology)

Clays and Clay Minerals of Japan, #26 (Developments in Sedimentology)

The character of physical law

The character of physical law

Data Structures and Their Algorithms

Data Structures and Their Algorithms

Data Structures and Their Algorithms

Data Structures and Their Algorithms

Data Structures and Their Algorithms

Data Structures and Their Algorithms

The character of physical law

The character of physical law

Our partners will collect data and use cookies for ad personalization and measurement. Learn how we and our ad partner Google, collect and use data. Agree & close