Ocean Hydrodynamics: Ecohydrodynamics 12th: International Colloquium Proceedings

ECOHYDRODYNAMICS

FURTHER TITLES IN THIS SERIES 1 J.L. MERO THE M INE R A L RESOURCES OF THE SEA 2 L.M.FOMlN THEDYNAMIC METHOD IN OCEANOGRAPHY 3 E.J.F.WOOD MICROBIOLOGY OF OCEANS A ND ESTUARIES 4 G.NEUMANN OCEAN CURRENTS 5 N.G. JERLOV OPTICAL OCEANOGRAPHY 6 V.VACQUIER GEOMAGNETISM I N MARINE GEOLOGY 7 W.J. WALLACE THE DEVELOPMENTS OF THE CHLORINITY/SALINITY CONCEPT I N OCEANOGRAPHY 8 E. L lS lTZ l N SEA-LEVEL CHANGES 9 R.H.PARKER THE STUDY OF BENTHIC COMMUNITIES 10 J.C.J. NI H OUL (Editor) MODELLING OF MARINE SYSTEMS 11 0.1. M A MA Y E V TEMPERATURE-SALINITY ANALYSIS OF WORLD OCEAN WATERS 12 E.J. FERGUSON WOOD and R.E. JOHANNES TROPICAL MARINE POLLUTION 13 E. STEEMANN NIELSEN MARINE PHOTOSYNTHESIS 14 N.G. JERLOV MARINE OPTICS 15 G.P. GLASBY MARINE MANGANESE DEPOSITS 16 V.M. KAMENKOVICH FUNDAMENTALS OF OCEAN DYNAMICS 17 R.A.GEYER SUBMERSIBLES AND THEIR USE I N OCEANOGRAPHY AND OCEAN ENGINEERING 18 J.W. CARUTHERS FUNDAMENTALS OF MARINE ACOUSTICS 19 J.C.J. NI H OUL (Editor) BOTTOM TURBULENCE 20 P.H. LEBLOND and L.A. MYSAK WAVES I N THE OCEAN 21 C.C. VON DER BORCH (Editor) SYNTHESIS OF DEEP-SEA DRI L LI NG RESULTS I N THE IN D IAN OCEAN 22 P. DEHLINGER MARINE GRA V I TY 23 J.C.J. NIHOUL (Editor) HYDRODYNAMICS OF ESTUARIES AND FJORDS 24 F.T. BANNER, M.B. COLLlNSand K.S. MASSIE (Editors) THE NORTH-WEST EUROPEAN SHELF SEAS: THE SEA BED AN D THE SEA IN MOTION 25 J.C.J.NIHOUL (Editor) MAR I N E FORECAST ING 26 H.G. RAMMING and Z. KOWALIK NUMERICAL MODELLING MARINE HYDRODYNAMICS 27 R.A. GEYER (Editor) MARINE ENVIRONMENTAL POLLUTION 28 J.C.J. NIHOUL (Editor) MARINE TURBULENCE 29 M. WALDICHUK. G.B. KULLENBERG and M.J. ORREN (Editors) MARINE POLLUTANT T ~ A N S F E RPROCESSES 30 A . VOlPlO (Editor) THE BALTIC SEA 3 1 E.K.-DUURSMA and R. DAWSON (Editors) MARINE ORGANIC CHEMISTRY

Elsevier Oceanography Series, 32

ECOHYDRODYNAMlCS PROCEEDINGS OF THE 12th INTERNATIONAL L l i G E COLLOQUIUM ON OCEAN HYDRODYNAMICS

Edited by JACQUES C.J. NIHOUL Professor of Ocean Hydrodynamics, University of LiGge L i$ge, Belgium

ELSEVIER SCIENTIFIC PUBLISHING COMPANY Amsterdam - Oxford - New York

1981

ELSEVIER SCIENTIFIC PUBLISHING COMPANY 1, Molenwerf, 1014 AG Amsterdam P.O. Box 211, 1000 AE Amsterdam, The Netherlands Distributions for the United States and Canada: ELSEVIER/NORTH-HOLLAND INC. 52, Vanderbilt Avenue New York, N.Y. 10017

Lihrary 01

(

o n g w \ \ Catalocing i n P u t i l l c a l l o i l U a l a

I p t e r n a t i o n n l Lihge Colloquiun on Ocean Hydrodynamics, L?tir: 1980. Ecoiiydrodynamics

.

(Elsevier oceano(;rapiiy s e r i e s : 3 2 ) BiSlioy,rapiiy: p . I n c l u d e s index. Conienis : Marine iiydrodynxrics a t e c o l o g i c a l s c a l e s / J . C . J . liiiioul -- F a t e 01 n u t r i e n t enriciinent on continental s h e l v e s as i n d i c a t e d by t h e C/N cnnterit o f bottom sediments / J . J . Walsi-1, F:.T. Prcmuzic, m d T . E . Whitledge -- Cross thermocline ; l o w on c o n t i n e n t a l shelves and tk.e l o c a t i o n s o f s!ielf fronts / A. Stigebrandt, - - [ e t , c . l 1. Marine ccolo~y--ConEresses. 2 . Oceanograpiiy-Cmgresscs. 3. Hydrod~amics--Con&resses. I. N i : i s u l , Jacques C.J.

111. S e r i e s .

11. T i t l e .

(a1541.5.s316 1980 ISBU 0-41d-41969-1

574.5'2636

01-4435 AACH.2

ISBN 044441969-1 (Val. 32) ISBN 0 4 4 4 4 1 6 2 3 4 (Series)

0 Elsevier Scientific Publishing Company, 1981 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 Printed in The Netherlands

V

FOREWORD

The International Liege Colloquia on Ocean Hydrodynamics are organized annually. Their topics differ from one year to another and try to address, as much as possible, recent problems and incentive new subjects in physical oceanography. Assembling a group of active and eminent scientists from different countries and often different disciplines, they provide a forum for discussion and foster a mutually beneficial exchange of information opening on to a survey of major recent discoveries, essential mechanisms, impelling question-marks and valuable suggestions for future research. The subject of the Twelfth Colloquium was initially described as "Marine Hydrodynamics, as a constraint on the dynamics of ecosystems". The emphasis was laid on hydrodynamical processes which had a determinant influence on the life of marine ecosystems by controlling, over appropriate scales of time and space, essential water characteristics such as temperature, salinity, the quantity and the quality of available nutrients, the penetration of light

...

These processes are not necessarily, -and actually rarely are- the most spectacular, from a physical point of view.

In many cases, the kind of information chemists

and biologists require is a small effect, a long term trend hidden somewhere in the results of hydrodynamical studies concerned in more intense, even if more transitory, phenomena. The determination of hydrodynamic constraints on ecosystems calls then for a new skill, learning to look for what one regarded before as minor residues and to parameterize mechanisms formerly regarded as essential. A new form of Hydrodynamics results, defined by distinctive time scales and length

scales, characteristic of the interactions between hydrodynamic and ecological processes. It is to emphasize the importance of such interactions that the word "Ecohydrodynamics" has been introduced and adopted as a title for the proceedings of the Twelfth Colloquium. One should however not be misled by the laconism of the title.

The present book

is not a manual or a textbook in Ecohydrodynamics. Its objective is to provide, with the help of well documented and often circumstantial case studies, illustrative examples of ecohydrodynamic problems, emphasizing the general features such problems have in common and their outstandinq importance for the understanding of hydrodynamic processes at ecological scales. Jacques C.J. NIHOUL.

This Page Intentionally Left Blank

VII

The Scientific Organizing Committee of the Twelfth International LiSge Colloquium on Ocean Hydrodynamics and all the participants wish to express their gratitude to the Belgian Minister of Education, the National Science Foundation of Belgium, the University of Liege, the Intergovernmental Oceanoqraphic Commission and the Office of Naval Research for their most valuable support.

This Page Intentionally Left Blank

IX

LIST OF PARTICIPANTS

ADAM, Y., Dr., Ministere de l'Environnement, Belgium. AITSAM, A., Prof., Academy of Sciences of the Estonian S S R , Tallinn, U.S.S.R. BAYENS, W., Dr., Vrije Universiteit Brussel, Belgium. BAH, A., Prof., Ecole Polytechnique de Conakry, Guinea,and Universite de Liege, Belgium. CLEMENT,

F.,

Mr., Universite de Liege, Belgium.

CREPON, M., Dr., Laboratoire d'oceanographie Physique du Museum, Paris, France. DISTECHE, ,A., Prof., Dr., Universit6 de LiGge, Belgium. DJENIDI, S., Ir., Universite de LiPge, Belgium. du PEUTY, J . , Mrs., CNEXO, Paris, France. ESTRADA, M., Dr., ~nstitutode Investigaciones Pesqueras, Barcelona, Spain. FLOS, J., Mr., Universidad de Barcelona, Spain. FRASSETTO, R., Dr., Laboratorio per lo Studio della Dinamica delle Grandi Masse, Venezia, Italy. GALLARDO, Y., Dr., Centre de Recherches Oceanographiques de Dakar-Thiaroye, Dakar, SBnBgal. GJERP, S.A., IT., Norwegian Hydrodynamic Laboratories, Trondheim, Norway. HAPPEL, J . J . ,

Ir., Universite de Liege, Belqium.

HENROTAY, P., Ir., Universite de Liege, Belgium. KLEIN, P., Dr., Institut de Mecanique Statistique de la Turbulence, Marseille, France.

I

LAGOS, P., Dr., Instituto Geofisico del Peru, Lima, Peru. LARSSON, A.M., Mr.,

University of Giiteborg, Sweden.

LEBON, G., Prof., Dr., Universite de Liege, Belgium. LEGENDRE, L., Prof., Dr., Universite Lava]., Quebec, Canada. LEWALLE, A., Ir., Universitf? de Liege, Belgium. LOFFET, A., Ir., UnivPrsite de Liege, Belgium.

A

MAITREJEAN, E., Mr., Universite de LiPge, Belgium MICHAUX, T., Ir., Universite de Liege, Belgium. NIHOUL, J.C.J.,

Prof., Dr., Universit6 de Liege and Universite de Louvain, Belgium.

O'BRIEN, J.J., Prof., Dr., Florida State University, Tallahassee, U.S.A. OZER, J., Ir., MinistPre de l'Environnement, Belgium. PARKER, R.A., Prof., Dr., Washington State University, Pullman, U.S.A. PICHOT, G., Dr., Ministere de l'Environnement, Belgium. RAMMING, H.G., Dr., Universitat Hamburg, F.R.G. ROMANA, L.A., Dr., CNEXO, COB, Brest, France. RONDAY, F.C.., Dr., Universite de Liege, Belgium. RUNFOLA, Y., Mr., Universite de Liege, Belgium. SALOMON, J.C., Dr., Universite de Bretagne Occidentale, Laboratoire d'oceanographie Physique, Brest, France. SMITH, N.P., Dr., Harbor Branch Foundation, Fort Pierce, F.A., U.S.A. STIGEBRANDT, A., VISSER, M.P., VOIGI,

Dr., University of Goteborg, Sweden.

Ir., K.N.M.I.,

De Bilt, The Netherlands.

K.F., Dr., UNESCO, IOC, Paris, France.

WALSH, J.J.,

Prof., Dr., Brookhaven National Laboratory, Upton, U.S.A.

WILLIAMS, P.J.L., YENTSCH, C.S., U.S.A.

Dr., University of Southampton, Dept. of Oceanography, U.K.

Dr., Bigelow Laboratory for Ocean Sciences, West Boothbay Harbor,

XI

CONTENTS

................................................................ ACKNOWLEDGMENTS ......................................................... LIST OF PARTICIPANTS .................................................... J.C.J. NIHOUL : Marine hydrodynamics at ecological scales ............... FOREWORD

J.J. WALSH, E.T. PREMUZIC and T.E. WHITLEDGE

:

V VI I IX 1

Fate of nutrient enrich-

ment on continental shelves as indicated by the C/N content of bottom sediments A. STIGEBRANDT

:

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

Cross thermocline flow on continental shelves and the

locations of shelf fronts C.S. YENTSCH

:

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

Vertical mixing, a constraint to primary production

an extension of the concept of an optimal mixing zone N.P. SMITH

:

13

51

:

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

67

An investigation of seasonal upwelling along the Atlantic

coast of Florida

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

79

A . BAH : Upwelling in the Gulf of Guinea. Results of a mathematical

model

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

Y. GALLARDO sula

:

On two marine ecosystems of Senegal separated by a penin-

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

141

R.A. PARKER

:

Differential dispersion and nutrient-plankton distributions

A.M. AITSAM

:

Hydrodynamics as a limiting factor in the development of the

Baltic Sea ecosystem L. LEGENDRE

:

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

Hydrodynamic control of marine phytoplankton production

the paradox of stability P.J.L.

155

165 :

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

191

WILLIAMS and L.R. MUIR : Diffusion as a constraint on the biologi-

cal importance of microzones in the sea J.C.J.

99

NIHOUL and Y. RUNFOLA

P. KLEIN and M. COANTIC

:

:

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

The residual circulation in the North Sea

:

219

Modelling the physical mechanisms in the marine

.................. Seine estuary .........

upper layers with a second-order turbulence closure J.C. SALOMON

209

Modelling turbidity maximum in the

W. BAYENS, Y. ADAM, J.P. MOMMAERTS and

G.

PICHOT

:

273

285

Numerical simulations

of salinity, turbidity and sediment accumulation in the Scheldt estuary

319

XI1 Y. ADAM, W. BAYENS, J.P. MOMMAERTS, G. PICHOT

:

Mathematical modelling of

recent sedimentology in the shallow waters along the Belgian Coast SUBJECT INDEX

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

.._

333

351

MARINE HYDRODYNAMICS AT ECOLOGICAL SCALES

Jacques C.J. NLHOUL’ Geophysical Fluid Dynamics. University of Ligge, Belgium. ‘Also at the “Institut d ’Astronomie et de GPophysique”, University of Louvain, Belgium.

INTRODUCTION Marine chemists and marine biologists rely on physical oceanographers to provide information about currents, temperature and salinity distributions

_..

Marine hydrodynamics is often regarded as a constraint on ecosystems because marine ecosystems depend very much on the water characteristics, the quantity and the quality of available nutrients, the concentration of oxygen, the penetration of solar radiation

...

However, despite the enormous progress made in the recent years in understanding the physics of the sea, surprisingly little has been exploited by marine ecologists and most of the existing ecosystem models are still box models with a very crude representation of physical effects. This may be due, to a large extent, to the difficulty for chemists and biologists to determine the parameters of chemical and ecological kinetics as functions of space and time, in the sea, where the situation is often very different from laboratory conditions. It is, however, becoming more and more evident, that hydrodynamicists have also a responsability. They provide indeed very detailed information on the mechanisms which, to them, appear as essential but they often fail to understand the needs of the chemists and the biologists whose main interest lies frequently in phenomena which may be less spectacular but which have time scales and length scales more appropriate to the dynamics of ecosystems. In many cases, the kind of information chemists and biologists require is a small effect, a long term trend hidden somewhere in the results of hydrodynamical studies concerned in more intense, even if more transitory, phenomena. The determination of hydrodynamic constraints on ecosystems may call for a new skill, learning to look for what one regarded before as minor residues and parameterizing mechanisms formely regarded as essential.

2 T h i s may r e s u l t i n a new form of m a r i n e hydrodynamics c h a r a c t e r i z e d by d i f f e r e n t t i m e and l e n g t h s c a l e s , which one might t r y t o i d e n t i f y by t h e v o c a b l e "Ecohydrodynamics". A few examples a r e d i s c u s s e d i n t h e f o l l o w i n g .

SPAWNING AND MIGRATION OF PLAICE I N THE NORTH SEA P l a i c e p o p u l a t i o n s i n t h e N o r t h Sea a r e c h a r a c t e r i z e d by f a i r l y l a r g e s p r e a d i n g and s t r o n g s e a s o n a l v a r i a t i o n s . The s e a s o n a l v a r i a t i o n s a r e t h e r e s u l t o f m i g r a t i o n s from o r t o f e e d i n g g r o u n d s and spawning g r o u n d s . Spawning o c c u r s i n t h e w i n t e r (december - j a n u a r y ) . The r e q u i r e m e n t s f o r spawning a r e a t e m p e r a t u r e h i g h e r t h a n 5OC and a s a l i n i t y above 35

%.

(Oray, 1 9 6 5 ) .

These c o n d i t i o n s l i m i t t h e e x t e n s i o n o f spawning t o t h e N o r t h b u t a r e n o t , o t h e r -

w i s e p a r t i c u l a r l y s e v e r e . S t i l l , spawning a p p e a r s t o o c c u r , i n t h e N o r t h S e a , i n f i v e w e l l d e f i n e d and l i m i t e d r e g i o n s ( D e Veen and Boerema, 1959, D e C l e r c k and C l o e t , 1 9 7 7 ) . These a r e shown of f i g u r e 1 r e p r o d u c e d from D e C l e r c k and C l o e t ( 1 9 7 7 ) .

F i g , 1. Spawning g r o u n d s o f p l a i c e i n t h e N o r t h Sea (from De C l e r c k and C l o e t , 1 9 7 7 ) .

3 Experiments with marked specimens have shown that the fish always return to the same spawning ground. (De Veen and Boerema, 1959, De Veen, 1962, 1970). An extensive study of the plaice spawning in the Southern Bight was carried on with marked specimens from the North-Hinder area by the Belgian "Rijksstation voor Zeevisserij" (De Clerck and Cloet, 1977). Spawning in the Southern Bight takes place between the 7th and the 19th of January. After the spawning period, the fish progressively leave the spawning ground. This migration lasts from February to April and follows well defined directions from North-East to North. The distances covered by the fish vary from a hundred kilometers to six hundred kilometers according to the main direction of migration. The average migration velocity is typically of the order of a few centimeters per second. In trying to interpret these observations, the marine biologist will turn to the physicist €or explanation. It is obvious that migrations are motivated by the search for food and the return to the spawning grounds but the question remains why specific regions roughly the same every year appear to be suitable, exclusive of others. If specific water characteristics are required for spawning or for finding a suitable prey, what are these conditions and, most of all, how can one explain that the same areas, every year, appear to fulfil them. If currents, diffusion or other physical processes are responsible, one should be able to identify the mechanisms by which they operate, determine the areas with suitable ecological characteristics, foresee the changes which might follow modifications of the hydrodynamical regime and repeating the analysis for other species, predict what their preferential grounds will be. Thus, the marine biologist will turn to hydrodynamicists but he will find them engrossed in the study of tides and storm surges which, with current velocities of one m s-l or larger and surface elevations reaching several meters, constitute by far the most intense hydrodynamic processes in the North Sea. What other effect there may be appears as noise in current-meter data and in models; the instruments as well as the models being, since almost a half century, tuned to the dominant mesoscale signals.

However, mesoscale motions like tides and storm surges cannot possibly provide any direct explanation for the type of ecosystem patterns and dynamics which has been described above, The time scales, the length scales and the velocity scales are simply not right. Migration velocities are one or two orders of magnitude smaller than tidal velocities. Tides move the water back and forth some ten kilometers in a half day. The characteristic time of evolution of a typical weather pattern and of the atmospheric forcing on the sea is of the order of a few days. Spawning, on the other hand, lasts several weeks and migration several months

:

the corresponding time scales are one

4 or two orders of magnitude larger. Similarly, the length scales involved (sizes of the spawning grounds, distances covered by migration) are one or two orders of magnitude larger than, say, a typical tidal excursion. If this particular behaviour of a given ecosystem is the result of hydrodynamic constraints, one obviously must look into macroscale hydrodynamic processes such as the residual currents, fronts and eddies in the North Sea. Macroscale effects account for a small percentage of the North Sea kinetic energy at any instant but, in the long run, they survive changing and reversing mesoscale motions which more or less cancel out over periods of time of ecological interest although, through the non-linear terms, they have a determinant influence on the residual circulation pattern. Residual currents have velocities in harmony with the migration velocities quoted before, their length scales and time scales are in the right range and, in the spatial distribution of residual energy exchanges between macroscales and mesoscales, one can see structures which are reminiscent of spawning patchiness or other ecoloqical patterns (Nihoul, 1980). The macroscale hydrodynamics of the North Sea may not be the obvious objective of hydrodynamical investigations and it may be rather difficult to study, embedded as it is in much more energetic mesoscale motions. It is not clear whether it can be obtained, with enough accuracy, by measurements with classical instruments. Modelling may be the best way to approach the problem but models must be designed very carefully to make sure that the small residue one is looking for is indeed sorted out of the much stronger mesoscale effects without being tampered with by numerical or other errors (e.9. Nihoul, 1980).

HYDRODYNAMIC CONSTRAINTS ON ECOSYSTEMS IN THE SOUTHEASTERN BERING SEA A very interesting interdisciplinary study of the Bering Sea was conducted in the recent years under the name of PROBES (Processes and Resources of the Bering Sea). PROBES investigations have shown the existence of distinct ecosystems in the Southeastern Bering Sea, conditioned by hydrodynamic features. Major food webs leading to large stocks of pelagic fauna and benthic fauna are found well separated in space and organized in relation with a series of fronts (Iverson et al, 1979). Figure 2 shows the three fronts which have been observed. The shelf-break front which roughly follows the 200 m isobath along the continental slope near the shelfbreak is persistent for periods of years and marks a transition between oceanic and shelf waters (Kinder and Coachman, 1978). The inner front is located at the 50 m isobath where the water column is well mixed by tide-induced turbulence (Schumacher et al, 1979). Between these two fronts, lies a middle shelf front near the 100 m isobath (Coachman and Charnell, 1979).

5

BERING SEA

Fig. 2 . F r o n t s i n t h e S o u t h e a s t e r n B e r i n g Sea (from I v e r s o n e t a l , 1 9 7 9 ) .

The s h e l f b r e a k f r o n t and t h e middle s h e l f f r o n t a r e s e p a r a t e d by t h e o u t e r s h e l f zone which e x t e n d s o v e r some 100 km. A s d e s c r i b e d by I v e r s o n e t a 1 (19791, Open Bering Sea w a t e r s e x t e n d o n t o t h e s h e l f i n a bottom l a y e r o f a t h i c k n e s s o f some 30 m w h i l e s h e l f w a t e r s f l o w seawards above it.

(figure 3 ) . The u p p e r mixed l a y e r and t h e bottom t u r b u l e n t l a y e r a r e s e p a r a t e d , i n t h e o u t e r

s h e l f zone by a mld-depth r e g i o n where i n t e r l e a v i n g w a t e r l a y e r s produce a v e r t i c a l fine structure. The middle s h e l f f r o n t and t h e i n n e r f r o n t a r e s e p a r a t e d by t h e middle s h e l f zone which h a s a w i d t h o f 200 t o 300 km. The middle s h e l f zone i s c h a r a c t e r i z e d by a s t r o n g s e a s o n a l t h e r m o c l i n e and two d i s t i n c t superposed l a y e r s of f l u i d s w i t h o c c a s i o n a l mixing between t h e two l a y e r s d u r i n g s t o r m s . The bottom l a y e r i s c o l d and r i c h i n nutrients. The s o u r c e o f n u t r i e n t s f o r t h e s h e l f ecosystems i s l i m i t e d t o t h e bottom boundary l a y e r o f t h e m i d d l e s h e l f zone and t o t h e d e e p w a t e r s of t h e o u t e r s h e l f zone.

PHYTOPLANKTON

Y f L F BREAK FRONT OCEANIC ZONE

4

MIDDLE FRONT

OUTER SHELF ZONE

LASKA STREAM /

MlOOLE SHELF Z

INNER F M T

4

M

m T A L ZONf

---

,* '-

; WIND

MIXING

-0

Fig, 3, Cross-shelf hydrographic features and relative primary production in the Southeastern Bering Sea (from Iverson et al, 1979).

The major spring phytoplankton bloom occurs first in the shallow waters of the middle shelf zone. The herbivores can be separated into a shelf group community (confined to the region shoreward of the middle front) and an oceanic community (seaward of the front). The former consists of small animals rather ineffective in grazing the large chainforming diatoms which dominate the phytoplankton in the middle shelf zone. On the contrary, the oceanic zooplankton (composed in particular of large calanoid copepods) is an effective grazer of large phytoplankton. Almost negligible cross-shelf advection and the presence of the middle front acting as a barrier for diffusion restrict the large oceanic herbivores to the outer shelf zone, The small coastal herbivores which inhabit the middle shelf zone cannot graze the large diatoms there and the phytoplankton biomass accumulates and settles to the bottom. This promotes the development of benthic ecosyst-ems and large stocks of benthic infauna, demersal fish and crabs are found I n the middle shelf zone (Bakkala and Smith, 1978).

I n t h e o u t e r s h e l f zone, on t h e c o n t r a r y , t h e g r a z i n g o f t h e p h y t o p l a n k t o n by t h e l a r g e o c e a n i c z o o p l a n k t o n i n i t i a t e s an e f f e c t u a l p e l a g i c food c h a i n and l a r g e s t o c k s of b i r d s , mammals and p e l a g i c f i s h a r e found (Nasu, 1974, Bakkala and S m i t h , 1 9 7 8 ) . The s h o r t d e s c r i p t i o n g i v e n above o f t h e S o u t h e a s t e r n Bering Sea ecosystems f o l l o w s c l o s e l y t h e c o n c l u s i o n s o f I v e r s o n e t a 1 (1979) r e p o r t i n g on t h e r e s u l t s o f PROBES. I t shows c l e a r l y t h a t , f o r t h e a u t h o r s , t h e e c o l o g i c a l p a t t e r n s o b s e r v e d i n t h e

S o u t h e a s t e r n B e r i n g Sea r e s u l t from p h y s i c a l c o n s t r a i n t s on t h e system which l i m i t t h e t r a n s p o r t and t h e d i f f u s i o n o f n u t r i e n t s and p l a n k t o n s p e c i e s . However, a l t h o u g h t h e most i n t e n s i v e p h y s i c a l p r o c e s s e s a r e most c e r t a i n l y a s s o c i a t e d w i t h t i d e s , wind f o r c i n g and s t o r m s , t h e s e phenomena a r e s c a r c e l y mentioned and o n l y c a l l e d upon f o r t h e i r a v e r a g e mixing e f f e c t

:

p r e s e n c e and d e p t h of a wind-mixed

l a y e r , e x i s t e n c e of

a t u r b u l e n t bottom boundary l a y e r i n r e l a t i o n w i t h t i d a l c u r r e n t s and bottom f r i c t i o n , mingling o f t h e two l a y e r s d u r i n g s t o r m s i n t h e middle s h e l f r e g i o n and s u b s e q u e n t transfer'of

n u t r i e n t s i n t h e p h o t i c zone, f o r m a t i o n o f a f i n e s t r u c t u r e i n t h e o u t e r

s h e l f r e g i o n where t h e two mixed l a y e r s a r e s e p a r a t e d and a s s o c i a t e d i n t e r l e a v i n g o f s a l i n i t y and t e m p e r a t u r e enhancing v e r t i c a l d i f f u s i o n and v e r t i c a l t r a n s p o r t o f nut r i e n t s near t h e shel f break f r o n t . For t h e r e s t , t h e p i c t u r e a p p e a r s r a t h e r a s a s t e a d y o n e , i g n o r i n g s h o r t d i s t a n c e mesoscale e x c u r s i o n s and a d d r e s s i n g phenomena w i t h l e n g t h s c a l e s of t h e o r d e r o f 100 km o r more and t i m e s c a l e s r a n g i n g from s e a s o n s t o y e a r s . Very s m a l l r e s i d u a l cross-shelf

o r v e r t i c a l m o t i o n s seem t o matter much more t h a n c l e a r l y more i n t e n s i v e

wind-induced and t i d a l c u r r e n t s . One c a n s e e h e r e a g a i n a c a s e where t h e i n t e r e s t of t h e b i o l o g i s t d o e s n o t l i e p r i m a r i l y i n t h e most i n t e n s e hydrodynamic p r o c e s s e s b u t i n t h e p a r a m e t e r i z a t i o n o f t h e i r e f f e c t i n t h e mean and i n t h e d e t e r m i n a t i o n of t h e l o n g t e r m "ecohydrodynamic" c i r culation patterns.

TIDAL FRONTS ON THE EUROPEAN CONTINENTAL SHELF

Marked f r o n t a l s t r u c t u r e s have been o b s e r v e d on t h e European C o n t i n e n t a l S h e l f d u r i n g t h e summer months. These f r o n t s which s e p a r a t e well-mixed w a t e r s on one s i d e , and v e r t i c a l l y s t r a t i f i e d waters on t h e o t h e r , c a n be d e t e c t e d a t t h e s e a s u r f a c e by a t e m p e r a t u r e d i s c o n t i n u i t y and a r e q u i t e v i s i b l e on i n f r a r e d remote s e n s i n g images ( e . 9 . Simpson e t a l , 1 9 7 8 ) . A l l o b s e r v a t i o n s i n d i c a t e t h a t t h e f r o n t s a r e f a i r l y p e r s i s t e n t and a p p e a r a s a p p r o x i m a t e l y two-dimenslonal v e l o c i t y and d e n s i t y p a t t e r n s o s c i l l a t i n g back and f o r t h w i t h t i d e s . A v e r t i c a l c i r c u l a t i o n seems t o be a s s o c i a t e d w i t h t h e f r o n t a l s t r u c t u r e s a s

sketched i n f i g u r e 4. The e x i s t e n c e of a r e g i o n o f s u r f a c e convergence i s confirmed by t h e o b s e r v a t i o n , i n n e a r calm s u r f a c e c o n d i t i o n s , of a more o r l e s s c o n t i n u o u s s l i c k where j e l l y f i s h , seaweed, e t c . . .

a r e found t o a c c u m u l a t e . F r e q u e n t l y , a l s o , a minimum i s observed i n

t h e sea s u r f a c e t e m p e r a t u r e i n t h e mixed w a t e r j u s t b e f o r e c r o s s i n g t h e f r o n t .

8

Q

Y u R1

L(

8

u Q

:

temperature

w

Y convergence E

divergence distance in the cross-front direction

+J

u a0

aJ

A2

u

P

u

.c

t 7

.r(

2

distance in the cross-front direction

Fig. 4. Schematic vertical circulation at a front (from Simpson et al, 1978) This minimum is consistent with the existence of an upwelling and a region of surface divergence as shown in figure 4. (Simpson et al, 1978).

The fronts axe produced by variations in the level of wind and tidal mixing. The comparison of the different terms in the energy balance equation suggests that fronts are likely to be found in the regions where the Monin-Obhukov length scale is of the same order as the depth (Simpson and Hunter, 1974, Simpson et al, 1978, Garrett et al, 1978). When applied to a limited geographical area and a given period of time, the criterion can be simplified taking into account the relatively small variations of the mean atmospheric inputs. One can show, then, that the formation of a front can be associated with a given critical value of the mean rate of energy dissipation (Pingree and Griffiths, 1978, Nihoul, 1980).

9

Figure 5, reproduced from Nihoul (19801, shows the curves of equal value of

*

s

=

log

where

10 ER

E~

is the mean rate of energy dissipation per unit mass (m2 s - ~ )and

value of reference taken as

*= E

*

E

a

m2 s - ~ .

The havy line corresponds to the value

S = 1.5

which is generally accepted as the

critical value for the formation of fronts on the North European Continental Shelf.

Fig. 5. Curves of equal values of the Simpson-Hunter parameter in the North Sea (from Nihoul, 1980).

S = log10(10-4~~1)

10 I n f r a r e d s a t e l l i t e images and s h i p s u r v e y s c o n f i r m t h e e x i s t e n c e o f t h e c o a s t a l f r o n t s a t t h e N c r t h e r n S c o t t i s h c o a s t , i n t h e German B i g h t and o f f t h e c o a s t o f Denmark a s w e l l a s o f f r o n t a l s t r u c t u r e s c o r r e s p o n d i n g t o t h e Western and E a s t e r n e n d s o f t h e main c r i t i c a l l i n e c r o s s i n g t h e S o u t h e r n N o r t h Sea f r o m t h e E n g l i s h c o a s t t o t h e Dutch c o a s t ( f i g u r e 5). I n p a r t i c u l a r , s t r o n g e v i d e n c e e x i s t s of t h e Flamborough Head f r o n t , e x t e n d i n g seaward o f f t h e B r i t i s h c o a s t , i n v e r y good agreement w i t h t h e s h a p e o f t h e c r i t i c a l c u r v e i n t h a t r e g i o n ( P i n g r e e and G r i f f i t h s , 1 9 7 8 , Nihoul,

1980).

O b s e r v a t i o n s show t h a t f r o n t s a r e o f t e n u n s t a b l e and meanders of i n c r e a s i n g amplit u d e g e n e r a t e c y c l o n i c e d d i e s w i t h a s p a c i a l e x t e n t o f 20-40 km and a l i f e t i m e o f several days.

( P i n g r e e , 1 9 7 8 ) . I n t h e summer, s u c h c y c l o n i c e d d i e s p l a y a n i m p o r t a n t

r o l e i n t h e t r a n s f e r o f h e a t , s a l t and n u t r i e n t s a c c r o s s s t r a t i f i e d r e g i o n s . They p r e s u m a b l y have a c o g e n t i n f l u e n c e on p r i m a r y p r o d u c t i v i t y t h r o u g h t h e t r a n s f e r o f n u t r i e n t s and p h y t o p l a n k t o n a c c r o s s t h e f r o n t a l zone ( P i n g r e e e t a l , 1 9 7 9 ) .

5-50

h

I

5-30 W

i,

/

2 3

F i g . 6 . An example o f s u r f a c e d i s t r i b u t i o n s o f t e m p e r a t u r e , s a l i n i t y and c h l o r o p h y l l a , r e f l e c t i n g a c y c l o n i c eddy s t r u c t u r e .

11 Comparing the phytoplankton's growth rate and the life time of the cyclonic eddies, Pingree et a1 (1979) argued that the growth of the population may actually occur in the eddy transfer process. Figure 6 (reproduced from Pingree et al, 1979) shows a remarkable coherence between the surface distributions of temperature, salinity and chlorophyll a , reflecting the cyclonic eddy structure seen in the infrared image.

These admirable studies by Simpson, Pingree and others illustrate again the constraints which hydrodynamics processes impose on the dynamics of ecosystems. The hydrodynamic constraints result from energetic mesoscale motions such as tides and wind-induced currents but, as before, these processes, however essential they may seem to the hydrodynamicists, are not interesting per se. It is their ability or their inability to mix the water column which is determinant in the formation Of fronts. The data are corrected for tidal excursions which are otherwise disregarded and such phenomena as frontal circulation, frontal instabilities and cyclogenesis are interpreted by means of quasi steady-state pictures obtained by working in axes moving with the front or, as mentioned before, in relation with the residual circulation in the North Sea, by averaging over periods of time large enough to smooth out tidal and other mesoscale oscillations. The critical parameter used in predicting the locations of the fronts is written in terms of similarly average quantities such as the mean rate of energy dissipation (Pingree and Griffiths, 1978, Nihoul, 1980). Typical time scales of interest vary from seasons to a minimum of several days (for the growth of phytoplankton in the eddy like frontal excrescences). The formation and evolution of frontal structures in European shelf seas and their ecological implications, by the time scales, length scales and velocity scales involved, provide another example of these weak but persistent physical processes which deserve the solicitude of Ecohydrodynamics.

REFERENCES Bakkala R.G. and Smith G.B., 1978. Demersal fish resources of the Eastern Bering Sea: Spring 1976. Northwest and Alaska Fisheries Center Processed Report, U.S. Department of Commerce, National Marine Fisheries Service, Seattle, Washington, 234 pp. Coachman L.K. and Charnel1 R.L., 1979. On lateral water mass interaction. A case study. Bristol Bay, Alaska, J. Physical Ocean, 9: 278-297. De Clerck R. and Cloet N., 1977. Merkproeven of schol in de Zuidelijke Bocht. Mede lingen van het Rijksstation voor Zeevisserij, C.L.O. Gent, 124 B, 16. De Veen J.F., 1962. On the sub-populations of plaice in the Southern North Sea, I C E S CM 1962: 94. De Veen J.F., 1970. On the orientation of the plaice. I. Evidence from orientating factors derived from ICES transplantat.lor, experiments in the years 1904-1909, J. Cons. int. Explor. Mer, 33: 2. De Veen J.F. and Boerema L.K., 1959. Distinquishlng Southern North Sea spawning populations of plaice by means of otolith characteristics, ICES C.M. 1959: 91.

12 Garrett C.J.R., Keeley J.R. and Greenberg D.A., 1978. Tidal Mixing versus Thermal Stratification in the Bay of Fundy and the Gulf of Maine, Atmosphere-Ocean 16: 403-423, Iverson RIL., Coachman L.D., Cooney R.T., English T . S . , Goering J.J., Hunt G.L., Macauley M.C., MC Roy C.P., Reeburg W.S. and Whitledge T.E, 1979. Ecological significance of fronts in the Southeastern Bering Sea, in Ecological Processes in Coastal and Marine Systems. Ed by Robert J. Livingston, Plenum Publ., 437-466. Kinder T.H. and Coachman L.K., 1978. The front overlaying the continental slope in the Eastern Bering Sea, J. Geophys. Res.,83: 4551-4559. Nasu T., 1974. Movement of baleen whales in relation to hydrographic conditions in the Northern Part of the North Pacific Ocean and the Bering Sea, in Oceanography of the Bering Sea. Ed by D.W. Hood and E.J. Kelley, Institute of Marine Science, University of Alaska, Fairbanks, 345-361. Nihoul J.C.J., 1980. Residual circulation, long waves and mesoscale eddies in the North Sea. Oceanologica Acta, 3: 309-316. Oray I.K., 1965. Uber die Verbreitung der Fischbrut in der Sudlichen Nordsee. Ber. Dt. Wiss. Komm. Meeresforsch, 18: 1-11. Pingree R.D., 1978. Cyclonic eddies and cross-frontal mixing. J. mar. biol. Ass. U.K. 58: 955-963. Pingree R.D. and Griffiths D.K., 1978. Tidal fronts on the Shelf Seas Around the British Isles, J. Geophys. Res.,83: 4615-4622. Pingree R.D., Holligan P.M. and Mardell G.T., 1979. Phytoplankton growth and cyclonic eddies. Nature, 278: 245-247. Schumacher J.D., Hinder T.H., Pashinski D.J. and Charnel1 R.L., 1979. A structural front over the continental shelf of the Eastern Bering Sea, J. physical Ocean, 9: 79-87. SimpSon J.H. and Hunter J.R., 1974. Fronts in the Irish Sea. Nature, 250: 404-406. Simpson J.H., Allen C.M. and Morris N.C.G., 1978. Fronts on the Continental Shelf, J. Geophys, Res., 83: 4607-4614.

13

FATE OF NUTRIENT ENRICHMENT ON CONTINENTAL SHELVES AS INDICATED BY THE C/N

CONTENT O F BOTTOM SEDIMENTS

J O H N J. WALSH, EUGENE T.

PREMUZIC, AND TERRY E. WHITLEDGE

Brookhaven N a t i o n a l L a b o r a t o r y , Upton, NY, 11973

INTRODUCTION

I met a t r a v e l l e r from an a n t i q u e l a n d Who s a i d : "Two v a s t and t r u n k l e s s l e g s of s t o n e Stand i n t h e d e s e r t . Near them, on t h e s a n d ,

Half sunk, a s h a t t e r e d v i s a g e l i e s , whose frown, And w r i n k l e d l i p , and s n e e r of c o l d command, Tell t h a t i t s sculptor w e l l those passions read Which y e t s u r v i v e , stamped on t h e s e l i f e l e s s t h i n g s , The hand t h a t mocked them and t h e h e a r t t h a t f e d ; And on t h e p e d e s t a l t h e s e works a p p e a r ; 'My name i s Ozymandias, King o f K i n g s ; Look on my works, ye Mighty, and d e s p a i r ! ' Nothing b e s i d e r e m a i n s , Round t h e d e c a y Of t h a t c o l o s s a l wreck, b o u n d l e s s and b a r e The l o n e and l e v e l s a n d s s t r e t c h far away." (P.B.

S h e l l e y , 1817)

P h y t o p l a n k t o n growth p r o c e s s e s a r e r e a s o n a b l y well-known

f u n c t i o n s of l i g h t ,

t e m p e r a t u r e , and n u t r i e n t s : however, t h e i r l o s s p r o c e s s e s a r e c o m p a r a t i v e l y unknown.

For example, t h e l o w p r o d u c t i v i t y and n i t r a t e c o n t e n t o f m o s t o c e a n i c

s u r f a c e w a t e r s ( F i g . 1 ) r e f l e c t t h e slow upward rate of n u t r i e n t i n p u t a c r o s s t h e main t h e r m o c l i n e t o t h e e u p h o t i c zone. e.g.,

A t t h e c o a s t a l b o u n d a r i e s o f t h e ocean,

on t h e c o n t i n e n t a l s h e l v e s , d a i l y f l u x e s of n i t r a t e s u p p l y and e n s u i n g pro-

d u c t i v i t y a r e 1 t o 2 o r d e r s of magnitude l a r g e r (Walsh, 1976) a s a r e s u l t o f l o c a l l y i n t e n s i f i e d p h y s i c a l p r o c e s s e s of u p w e l l i n g , ing.

r i v e r r u n o f f , and t i d a l mix-

15N estimates o f n i t r a t e u p t a k e by p h y t o p l a n k t o n s u g g e s t t h a t o n l y 10% o f

t h e d a i l y n i t r o g e n demand of p h o t o s y n t h e s i s i s m e t by n i t r a t e i n t h e open ocean (Eppley and P e t e r s e n , 1 9 7 9 ) , w h e r e a s n i t r a t e i s 1.50% of t h e d a i l y n i t r o g e n s o u r c e f o r p h y t o p l a n k t o n i n coastal waters o f f P e r u (MacIsaac and Dugdale, 1 9 7 2 ) . N e w York (Conway and W h i t l e d g e , 1 9 7 9 ) , C a l i f o r n i a (R. Eppley, p e r s o n a l c o m u n i c a -

t i o n ) , and A l a s k a (J. G o e r i n g , p e r s o n a l communication).

N i t r a t e u p t a k e i s con-

s i d e r e d an e s t i m a t e of t h e "new" d a i l y p r o d u c t i o n (Dugdale and G o e r i n g , 1967) t h a t i s a v a i l a b l e f o r e x p o r t from an ecosystem and is a s s o c i a t e d w i t h t h e

14

3

NITRATE ( UG - ATOM I LITER) 10 I5 20

5

25

30

0

20

40

60

-

-E

-

ec

I

I-

n W

1oc

I2C

14C

ma

1ec

X

*

NORTH PACIFIC

0

= EASTERN MEDITERRANEAN

A

NORTW CENTRAL ATLANTIC

A

= PERU CURRENT = CALIFORNIA CURRENT = CANARY CURRENT

Fig. 1. The v e r t i c a l d i s t r i b u t i o n of n i t r a t e in t h e open ocean and w i t h i n t h e e a s t e r n boundary c u r r e n t s . o u t b r e a k of blooms of p h y t o p l a n k t o n p o p u l a t i o n s in c o a s t a l waters ( Y e n t s c h e t

al.,

1977).

Annual b u d g e t s , i n f a c t , s u g g e s t t h a t o n l y 1 0 % of t h e p a r t i c u l a t e

n i t r o g e n , f i x e d i n t h e open ocean, s i n k s o u t of t h e e u p h o t i c zone, b u t t h a t a s much as 50% of t h e p a r t i c u l a t e n i t r o g e n , f i x e d on t h e c o n t i n e n t a l s h e l f , may p e r h a p s be e x p o r t e d to t h e slope s e d i m e n t s (Walsh, 1 9 8 0 a ) . The t r a j e c t o r y and f a t e of t h i s p a r t i c u l a t e m a t t e r are p o o r l y u n d e r s t o o d pro-

cesses i n a s p a t i a l l y h e t e r o g e n e o u s c o a s t a l Ocean.

P a r a m e t e r i z a t i o n of a p p r o p r i -

a t e hydrodynamics f o r a q u a n t i t a t i v e d e s c r i p t i o n of t h e s e loss p r o c e s s e s must t h u s a w a i t d e f i n i t i o n of t h e i m p o r t a n t b i o l o g i c a l t i m e and s p a c e scales. t h e bottom s a n d s t e n d to " r e c o r d " t h e h i s t o r y of t h e w a t e r column, we have

Since

15 s e l e c t e d t h e C/N c o n t e c t of s h e l f s e d i m e n t s a s a p o s s i b l e t r a c e r of

1 ) s i t e s of

n u t r i e n t i n t r o d u c t i o n t o t h e s h e l f by v a r i o u s p h y s i c a l mechanisms, o f 2 ) a r e a s of subsequent downstream u t i l i z a t i o n by t h e p h y t o p l a n k t o n , and of 3 ) where loss of p a r t i c u l a t e matter might occur f r m t h e w a t e r column.

An a n a l y s i s i s made of

the

C/N p a t t e r n s of bottom s u r f a c e s e d i m e n t s i n r e l a t i o n to t h e n i t r o g e n s o u r c e s from

upwelling,

r i v e r r u n o f f , and t i d a l mixing on t h e P e r u v i a n , w e s t A f r i c a n ,

Amazonian, Gulf of Mexico, e a s t e r n U.S.,

B e r i n g , and North Sea s h e l v e s i n an

i n i t i a l a t t e m p t t o p r o s c r i b e t h e p a r t i c l e t r a j e c t o r i e s of o r g a n i c m a t t e r on t h e continental shelf. The r a t i o of carbon to n i t r o g e n ( C / N ) c o n t e n t i n most marine organisms i s l e s s than 6 , u n l i k e t h a t of l a n d p l a n t s which use more c a r b o h y d r a t e s f o r t h e i r s u p p o r t s t r u c t u r e s ( P a r s o n s , 1976) and have C/N r a t i o s >15 ( M u l l e r , 1977).

Detrital

p a r t i c l e s i n the sea a l s o have a C/N r a t i o g r e a t e r t h a n 10 a s a r e s u l t of t h e i n c r e a s e d r e c y c l i n g of n i t r o g e n compounds compared to slower decomposition of r e f r a c t o r y c a r b o n compounds (Degens, 1 9 7 0 ) .

For example, d u r i n g blooms of phyto-

plankton t h e C/N c o n t e n t of p a r t i c u l a t e matter i n t h e w a t e r column i s <6 (Banse, 19741, whereas t h e C/N

c o n t e n t of p a r t i c u l a t e m a t t e r i s

c o n c e n t r a t i o n s ( < 0 . 5 ug c h l a L - ' ) ,

> 10 a t low c h l o r o p h y l l

i . e , when mainly d e t r i t u s i s p r e s e n t .

Recent

sediment t r a p d a t a , i n f a c t , i n d i c a t e t h a t h i g h e r C/N r a t i o s are found both a f t e r t h e s p r i n g bloom on t h e s h e l f (Smetacek e t a l . ,

1978) and w i t h i n c r e a s i n g d e p t h

i n t h e open ocean (Honjo, 1 9 8 0 ) . Although C/N r a t i o s o f > 2 0 c a n be induced i n l a b o r a t o r y c u l t u r e s of phytop l a n k t o n under n i t r o g e n s t a r v a t i o n (Caperon and Meyer, 1 9 7 2 ) , i n d i v i d u a l phytop l a n k t o n c e l l s a r e p r o b a b l y n o t n i t r o g e n l i m i t e d i n t h e ocean (Walsh, 1976).

At

c l o s e to maximal growth rates, l a b o r a t o r y c u l t u r e s of p h y t o p l a n k t o n have, i n f a c t , C/N r a t i o s <6, which more c l o s e l y approximate t h e c o n d i t i o n s of i n d i v i d u a l c e l l growth i n b o t h o l i g o t r o p h i c and e u t r o p h i c marine environments (Goldman, 1980).

D i s s o l v e d o r g a n i c m a t t e r h a s a C/N r a t i o of 20-30

in s u r f a c e w a t e r s and

a s l i t t l e as $ 3 i n deep w a t e r s , b u t t h i s l a r g e r carbon p o l has an a v e r a g e residence time o f 3400 y r ( W i l l i a m s e t a l . ,

1969) and i s t h o u g h t t o be a minor i n p u t

t o t h e s e d i m e n t s (Degens, 1 9 7 0 ) . Areas o f l o w C / N

i n s h e l f b o t t m sediments t h u s presumably r e f l e c t r e g i o n s of

" f r e s h " marine d e p o s i t s , above which b o t h t h e p h y t o p l a n k t o n c e l l and i t s p p u l a t i o n had n o t been n i t r o g e n l i m i t e d d u r i n g a r e l a t i v e l y s h o r t t r a v e l t i m e f r a n t h e e u p h o t i c zone t o t h e bottom.

Areas of h i g h C/N r a t i o s c o u l d r e p r e s e n t e i t h e r

marine d e p o s i t s o f " o l d e r " d e t r i t a l p a r t i c u l a t e m a t t e r o r r e l i c t t e r r e s t r i a l d e p o s i t s n o t o v e r l a i n by modern b i o g e n i c s e d i m e n t s d u r i n g t h e Holocene (Walsh, 1980b).

Measurements of n a t u r a l

613C ( H u n t ,

1966) and

615N

( P e t e r s e t al.,

1978) i s o t o p e s of t h e s e d i m e n t a r y o r g a n i c m a t t e r , as w e l l as t h e q u a l i t y of carbon, e.g.

n-alkanes

( F a r r i n g t o n and T r i p p , 19771, l i g n i n (Hedges and P a r k e r ,

1 9 7 6 ) , and f a t t y a c i d s ( M o r r i s and C a l v e r t ,

1 9 8 0 ) , c a n t h e n be used to i n f e r a

16 marine or t e r r e s t r i a l o r i g i n f o r these >10 C/N sediments.

COASTAL UPWELLING A.

Peru River discharge and t i d a l mixing of n u t r i e n t s i n t o t h e Peru upwelling eco-

system are minimal.

A composite (Fig. 2 ) of t h e C/N d i s t r i b u t i o n in these sedi-

ments (Rowe, personal communication;

Suess and Mueller, 1980; ICANE,

1978)

accordingly r e f l e c t s t h e dominant physical mechanism of a supply of 20-30 ug-at NO3

P,-’

by c o a s t a l upwelling (Fig. 3).

Low C/N r a t i o s a r e found i n t h e sediments

near the c o a s t where phytoplankton blooms of 10-20 lJg chl a %-l C/N c o n t e n t of 5.1

(Walsh and Howe, 1976).

contain a mean

The band of higher sediment C/N

r a t i o s of 8-10 between the shelf and the Peru-Chile trench r e f l e c t s t h e very low

Fig. 2 . The r a t i o of carbon/nitroyen within surface sediments off Peru ( a f t e r Suess and Muller, 1980; I C A N E , 1978, and G. ROwe, personal communication).

17

DISTANCE OFFSHORE (km) Fig. 3. C r o s s - s h e l f d i s t r i b u t i o n of n i t r a t e on t h e Peru s h e l f d u r i n g August 1976 ( l o c a t i o n shown i n Fig. 2 ) .

oxygen c o n t e n t o f t h e s e slope waters ( 4 . 1 m l 02 k - ’ ) ,

which does n o t e x t e n d

f u r t h e r o f f s h o r e where t h e b a s i n s e d i m e n t s a g a i n have a lower C/N r a t i o .

Under

very low oxygen c o n d i t i o n s of t h e s l o p e , t h e p r o c e s s of d e n i t r i f i c a t i o n l e a d s t o consumption of G?m o l e s of c a r b o n f o r each m o l e of N 2 produced ( R i c h a r d s , 19651,

i.e.,

an i n c r e a s e i n t h e C/N r a t i o o f t h e remaining p a r t i c u l a t e m a t t e r d u r i n g

early diagenesis.

A f t e r f u r t h e r d i a q e n e s i s and/or as a r e s u l t of t e r r e s t r i a l

i n p u t , P l e i s t o c e n e and o l d e r s e d i m e n t s have C/N r a t i o s o f 20-30 v a l u e s of -25 t o -28 (Degens , 1970

.

as w e l l as

d 3C

i n c o n t r a s t t o -19 t o -21 w i t h i n r e c e n t marine s e d i m e n t s

The s u r f a c e s e d i m e n t s o f f P e r u have an a v e r a g e

6 13C of -20.9

and n-alkane

hydrocarbon f r a c t i o n i n t h e low m o l e c u l a r r a n g e ( < C 2 4 ) , i n d i c a t i n g mainly a non-terrestrial

component of t h e o r g a n i c carbon in t h e s e muds ( I C A N E ,

much a s 50% o f t h e 1000 g C m-2

yr-’

1978).

As

primary p r o d u c t i o n o f f Peru may now be

d e p o s i t e d on the bottom, r e s u l t i n g in marine d e p o s i t s of 1 t o 4% c a r b o n on t h e s h e l f and 5 t o 2 0 % on t h e upper s l o p e (Walsh, 1 9 8 0 ~ ) . A t 2 2 s t a t i o n s a c r o s s t h e Peru s h e l f and s l o p e , t h e mean s u b s u r f a c e C/N v a l u e a t 50 c m d e p t h of c o r e s i s

7 . 7 6 compared t o 7.53

i n s u r f a c e s e d i m e n t s , i.e.,

l i t t l e d i a g e n e t i c change.

In

18 c a r b o n w a s 2.89 a t 50 cm and a l m o s t t w i c e a s much, 4.82 a t t h e

contrast, the

%

s u r f a c e (G.T.

ROwe,

p e r s o n a l communication), s u g g e s t i n g a r e c e n t i n c r e a s e i n

c a r b o n f l u x to t h e s e d i m e n t s t h a t c o u l d have o c c u r r e d w i t h i n j u s t t h e l a s t decade

as a r e s u l t o f o v e r f i s h i n g (Walsh, 1 9 8 0 ~ ) . A t a s e d i m e n t i i t i o n r a t e of 66-140

1 9 7 9 ) , t h e s e s u b s u r f a c e C/N

c m 1000 yr-’

o f f P e r u ( M u l l e r and S u e s s ,

samples a t 50 an d e p t h may b e 500 t o 1000 y r o l d .

Radio-carbon d a t i n g s u g g e s t s a s i m i l a r age d e p t h of r e c e n t sediments with a 6l3C o f -19.5

t o -20.5

o f f Southwest A f r i c a (Morris and C a l v e r t , 1 9 8 0 ) .

m a r i n e i n p u t , a s a l s o i n d i c a t e d by n-alkane

A totally

f r a c t i o n s and f a t t y a c i d s , a s w e l l as

t h e a p p a r e n t l a c k of d i a g e n e s i s w i t h d e p t h o f f Southwest A f r i c a over t h e l a s t 1000 y r a p p e a r t o be analogous t o t h e P e r u u p w e l l i n g s i t u a t i o n .

The 8 t o 14%

c a r b o n muds on t h e a n o x i c s o u t h w e s t A f r i c a n s h e l f , i n c o n t r a s t to t h o s e of 1 t o 4 % on t h e P e r u s h e l f , do n o t d e c l i n e i n amount from 0 t o 5 0 cm d e p t h , however,

i.e.,

no r e c e n t t r a n s i e n t s i n c a r b o n l o a d i n g .

These sediment r e c o r d s s u g g e s t

t h a t u n t i l r e c e n t l y more of t h e p h o t o s y n t h e t i c c a r b o n w a s l o s t t o t h e bottom from t h e p e l a g i c food web on t h e Southwest A f r i c a n s h e l f t h a n o f f Peru.

In f a c t , t h e

maximum y i e l d of t h e f i s h e r y f o r t h e S o u t h A f r i c a n s a r d i n e w a s o n l y 5 x l o 5 t o n s yr-’

i n c o n t r a s t t o 1 x l o 7 t o n s of anchovy h a r v e s t e d o f f Peru i n 1970 (Walsh,

1 9 7 7 ) , b e f o r e t h e r e c e n t d e c l i n e i n y i e l d to 1 x l o 6 t o n s yr-’ d u r i n g 1976-79.

B.

Northwest A f r i c a Upwelling o f f Northwest A f r i c a i s a s e a s o n a l phenomenon of i n c r e a s i n g d u r a t i o n

a s a f u n c t i o n of l a t i t u d e from 15O t o 25O N , u n l i k e t h e more c o n t i n u o u s i n p u t of n u t r i e n t s o v e r t h e same d i s t a n c e o f f Peru and Southwest A f r i c a (Walsh, 1977). The a n n u a l p r i m a r y p r o d u c t i o n o f f Northwest A f r i c a is t h u s 200-500 (Schemainda e t a l . ,

yr-’

1975; Huntsman and B a r b e r , 19771, o n l y 1 t o 4 % carbon i s

found on t h e upper s l o p e (Diester-Haass,

m l 0 2 L-’.

c o n t a i n s 1.5-2.0

g C m-2

1 9 7 8 ) , and t h e oxygen minimum zone s t i l l

F a t t y a c i d , n-alkane,

t h e upper slope ( G a s k e l l e t a l . ,

and 613C c o n t e n t s of a c o r e on

1975) a l l s u g g e s t a m i x t u r e of t e r r e s t r i a l and

m a r i n e c a r b o n i n t h e s e s e d i m e n t s u n l i k e t h e u p w e l l i n g a r e a s o f f Peru and Southwest Africa. The s e d i m e n t a c c u m u l a t i o n r a t e i s much lower w i t h i n t h e less p r o d u c t i v e North-

w e s t Africa u p w e l l i n g ecosystem, w i t h an age of 1 0 0 0 y r a t o n l y 5 c m d e p t h (Gaskell e t a l . ,

1 9 7 5 ) , i.e.,

and C a l v e r t , 1 9 8 0 ) .

t e n f o l d o l d e r t h a n o f f Southwest A f r i c a (Morris

A p p a r e n t l y , t h e d e t r i t u s of marine o r i g i n has t h u s n o t

d i l u t e d e o l i a n t e r r e s t r i a l i n p u t s c o n t a i n i n g as much as 16% c a r b o n (Aston e t a l . , 1973).

For example, t e r r i g e n o u s suspended material is found on t h e i n n e r s h e l f

a t 22%

( M i l l i m a n , 1977) where a t u r b i d i t y maximum o c c u r s i n t h e absence of r i v e r

discharge.

The suspended matter of t h e o u t e r s h e l f o f f Northwest Africa i s of

m a r i n e o r i g i n , b u t i n s m a l l amounts compared t o t h a t on t h e Southwest A f r i c a n (Emery e t a l . ,

1973) o r Amazonian s h e l v e s (Milliman e t a l . ,

19751.

19 The C/N

r a t i o of t h e s u r f a c e s e d i m e n t s r e f l e c t s b o t h t h e t e r r i g e n o u s and

marine o r i g i n o f carbon o f f Northwest A f r i c a w i t h a r a t i o o f >lo-15,

indicating

t e r r e s t r i a l m a t e r i a l ( D i e s t e r - H a a s s and M u l l e r , 1979) and found i n waters less than 50 m d e p t h on t h e s h e l f between 15-25%;

a lower r a t i o o f 5-10 i s o b s e r v e d

i n marine d e p o s i t s on t h e o u t e r s h e l f and upper s l o p e (G.T. munication; D i e s t e r - H a a s s

and M u l l e r , 1 9 7 9 ) .

R D w e , p e r s o n a l com-

The primary p r o d u c t i v i t y and s e d i -

ment C/N r a t i o s do n o t change w i t h l a t i t u d e o f f Northwest A f r i c a , s u g g e s t i n g t h a t weak u p w e l l i n g now p r o v i d e s t h e n u t r i e n t s u p p l y i n t h e n o r t h e r n r e g i o n and r i v e r runoff i n t h e s o u t h e r n area (Schemainda e t a l . , Africa, t h e

%

1975).

S i m i l a r to Southwest

c a r b o n does n o t change much w i t h d e p t h d u r i n g t h e 10,000 y r H o l e

cene (0-70 cm) on t h e Northwest A f r i c a n slope ( G a s k e l l e t a l . ,

1975) or rise

(Muller and S u e s s , 1 9 7 9 ) , and t h e maximum s a r d i n e y i e l d h a s been o n l y %3 x l o 5 t o n s yr-’

(Gulland, 1970).

During P l e i s t o c e n e g l a c i a l p e r i o d s , however, t h e % o r g a n i c carbon of t h e s e d i ments i n c r e a s e d s i g n i f i c a n t l y w i t h d e p t h (70-500 c m ) a t a changing s e d i m e n t a t i o n r a t e on t h e c o n t i n e n t a l rise from o n l y 3.5 t o 23 c m 1000 yr-’ Africa.

o f f Northwest

Presumably, t h e rate of c a r b o n i n p u t a l s o i n c r e a s e d a t t h i s t i m e as a

f u n c t i o n o f e i t h e r g r e a t e r r i v e r r u n o f f or u p w e l l i n g d u r i n g lower sea l e v e l s (Mueller and S u e s s , 1 9 7 9 ) .

An

i n c r e a s e i n t h e a n n u a l u p w e l l i n g r a t e , similar to

t h a t o f f P e r u and Southwest A f r i c a , c o u l d have o c c u r r e d i n r e s p o n s e to s t r o n g e r t r a d e winds ( S a r n t h e i n , 1 9 7 8 ) .

F o r example, d u r i n g t h e l a t e P l e i s t o c e n e , a nega-

t i v e t e m p e r a t u r e anomaly of 6OC h a s been e s t i m a t e d f o r s u r f a c e waters o f f North-

west A f r i c a 18,000 y r ago ( M c I n t y r e e t a l . , sediments a p p e a r e d to have remained t h e same

1976).

The C/N c o n t e n t of t h e rise

(%a) d u r i n g t h e P l e i s t o c e n e as i n

t h e Holocene, t h e r e i s no o t h e r e v i d e n c e t h a t t h i s sediment c a r b o n w a s from a t e r r e s t r i a l s o u r c e d u r i n g g l a c i a t i o n , and r i v e r r a f t i n g of m a t e r i a l a t 20°N off Northwest A f r i c a p r o b a b l y d i d n o t o c c u r ( M u l l e r and S u e s s , 1 9 7 9 ) .

RIVER DISCHARGE A.

Amazon Each second t h e Amazon R i v e r d i s c h a r g e s 2 x l o 8 l i t e r s of f r e s h water ( % l o

times t h e i n p u t of t h e M i s s i s s i p p i R i v e r ) c o n t a i n i n g % l o pg-at 1968; Ryther e t a l . ,

NO3 !?-l ( W i l l i a m s ,

1 9 6 7 ) t o o l i g o t r o p h i c s u r f a c e waters ( 0 . 1 p g - a t NO3 11-l) of The C/N r a t i o of p a r t i c u l a t e m a t t e r i n t h e r i v e r i s

the a d j a c e n t B r a z i l s h e l f .

>10 ( W i l l i a m s , 1 9 6 8 ) , compared to <6 w i t h i n t h e s h e l f e u p h o t i c zone (J. Ryther, p e r s o n a l communication). (Richey e t a l . , column a t t h e

P h y t o p l a n k t o n p r o d u c t i o n i s n e g l i g i b l e in t h e r i v e r

1 9 8 0 ) , and t h e suspended terrestrial l o a d d r o p s o u t of t h e water

3O/Oo

s a l i n i t y region of t h e e s t u a r y (Milliman e t al.,

1975).

Export of t h e r i v e r t h u s c o n s i s t s mainly of d i s s o l v e d o r g a n i c carbon of terres-

t r i a l o r i g i n (Richey e t al., dissolved n u t r i e n t s .

1 9 8 0 ) ‘ w i t h a C/N o f 15-40

(Williams,

1 9 6 8 ) , and

20 A f t e r u p t a k e of n u t r i e n t s by p h y t o p l a n k t o n on t h e a d j a c e n t s h e l f , t h e prime components of suspended m a t t e r i n t h e b r a c k i s h Amazon plume are d i a t m f r u s t u l e s (Millirnan e t a l . ,

1975) from p h y t o p l a n k t o n p o p u l a t i o n s t h a t a r e two o r d e r s of

magnitude l a r g e r t h a n w i t h i n o u t e r s h e l f w a t e r s ( H u l b u r t and Corwin, C/N

c o n t e n t ( B a r r e t o e t al.,

1969).

The

1975) of t h e Amazonian s h e l f s e d i m e n t s ( F i g . 4 )

r e f l e c t s t e r r e s t r i a l d e p o s i t i o n w i t h r a t i o s >10 a t t h e edge of t h e c o a s t and marine b i o g e n i c d e p o s i t i o n w i t h r a t i o s < 6 on t h e middle and o u t e r s h e l f .

Little

a c c u m u l a t i o n of diatom f r u s t u l e s i s found i n t h e s u r f a c e s h e l f s e d i m e n t s (Milliman e t a l . ,

1 9 7 5 ) , however, and d e s p i t e t h e trace amounts of marine c a r b o n ,

much o f t h e s e d e p o s i t s a r e t h o u g h t t o be r e l i c t ( B a r r e t o e t a l . ,

1975).

With t h e

e x c e p t i o n of t h e mud wedge o f f t h e Amazon mouth, which may also be r e l i c t , t h e h i g h e s t c o n c e n t r a t i o n of o r g a n i c m a t t e r i s i n s t e a d found on t h e upper s l o p e .

The

s i n k i n g p h y t o p l a n k t o n p p u l a t i o n s , d e r i v e d f r o m t h e Amazon e f f l u e n t , c o u l d t h u s e i t h e r be t r a n s p o r t e d o f f s h o r e and/or

B.

northward w i t h t h e Guiana C u r r e n t .

Mississippi The a n n u a l M i s s i s s i p p i River d i s c h a r g e i s f i v e f o l d t h a t of t h e t o t a l f r e s h -

water i n f l u x of t h e Mid-Atlantic

B i g h t (Bue, 1 9 7 0 ) , w i t h a n i t r o g e n c o n t e n t a s

-

4" -

2" -

0" -

2" -

4"' 56"

AMAZONIAN SHELF C/N 54"

I

I

52"

f

'

50"

I

'

48"

46"

44"

' "

42"

40"

F i g . 4. The r a t i o of c a r b o n / n i t r o g e n w i t h i n s u r f a c e s e d i m e n t s o f f t h e Amazon River ( a f t e r B a r r e t t o e t a l . , 1 9 7 5 ) .

21

0

5

-

. I

10 /

E

I

I

v

I. I*

I 15

kw

n

20 25 30

I

I ’

J

F

M A M J J A S O N D LOUISIANA SHELF ( MISSISSIPPI INPUT)

J

Fig. 5. A t i m e series of n i t r a t e i n p u t from t h e M i s s i s s i p p i River a s measured -50 km downplume on t h e L o u i s i a n a s h e l f ( a f t e r F u c i k , 1 9 7 4 ) .

much a s 150 ug-at NO3 9.-l

d u r i n g s p r i n g flood ( E v e r e t t , 1971).

After dilution

and p h y t o p l a n k t o n u p t a k e on t h e o t h e r w i s e o l i g o t r o p h i c L o u i s i a n a s h e l f , a seasonal m a x i m u m of o n l y 30 u T a t NO3 P.-l of t h e r i v e r ( F i g . 5 ) . 1.250-350 g C m-’ g C m-2

yr-’

(El-Sayed,

yr-’

i s found -50 km downplume from the mouth

The a n n u a l primary p r o d u c t i o n of the M i s s i s s i p p i D e l t a i s (Thomas and Simmons, 1960; F u c i k , 1974) i n c o n t r a s t t o -25

f o r t h e open Gulf of Mexico and t h e W e s t F l o r i d a and Texas s h e l v e s 1972).

input of a l l U . S .

The suspended l o a d of t h e M i s s i s s i p p i i s a b o u t 10 t i m e s t h e

e a s t c o a s t r i v e r s (Emery and Uchupi, 19721, such t h a t a t u r -

b i d i t y maximum is found w i t h i n 10 km of t h e c o a s t (Manheim e t a l . , carbon i m p o r t o f (Happ e t a l . ,

0.5

1977).

g C m-2

day-’

19721, where a

i s r e c e i v e d f r a n a d j a c e n t bays and marshes

Over 9 0 % of t h e c a r b o n e x p o r t f r o m t h e Mississippi is in

t h e form o f d i s s o l v e d o r g a n i c c a r b o n (Hoffman, 1974) w i t h a g e n e r a l seaward d e c l i n e in c o n c e n t r a t i o n o b s e r v e d a f t e r i n p u t to the s h e l f (Maurer and P a r k e r , 1972). A p a r t i c u l a t e d e p o s i t i o n r a t e of

1.6 g C

day-l

t o t h e s e d i m e n t s i s esti-

mated f o r t h e n e a r s h o r e t u r b i d area w i t h a bottom c a r b o n c o n t e n t o f 0.42%, a d e l t a s e d i m e n t a t i o n rate of 30,000 c m 1 0 0 0 yr-’ production o f o n l y 0.3 g C m-2

day-’

( S c r u t o n , 1 9 6 0 ) , and a primary

(Thomas and Simmons, 1 9 6 0 ) .

In contrast,

22 a d e p o s i t i o n r a t e of o n l y 0 . 4

g C m-2

day-’

may o c c u r 2 0 km o f f t h e c o a s t w i t h

bottom s e d i m e n t s of l e s s c a r b o n ( 0 . 2 7 % ) , b u t where a g r e a t e r d a i l y p r i m a r y prod u c t i o n of 1.5 g C m-2

day-’

occurs.

L i k e t h e Amazon system, t h e r e may a l s o be

seaward e x p o r t o f t h e p h y t o p l a n k t o n c a r b o n , d e r i v e d f r m t h e M i s s i s s i p p i e f f l u e n t , t o t h e upper s l o p e of t h e Gulf of Mexico where 1 t o 2 % o r g a n i c c a r b o n muds

are l o c a t e d ( T r a s k , 1 9 5 3 ) .

In c o n t r a s t t o P e r u , however, t h e n e a r bottmn oxygen

c o n t e n t of t h e s e d i m e n t a r y o r g a n i c c a r b o n maximum i s s t i l l 2-3 m l O 2 L-l

a t

d e p t h s o f 150-850 m ( R i c h a r d s and R e d f i e l d , 1 9 5 4 ) . The C/N

r a t i o of p a r t i c u l a t e matter i n t h e M i s s i s s i p p i River is > 1 0 i n con-

t r a s t t o <6 w i t h i n t h e e u p h o t i c zone of t h e L o u i s i a n a s h e l f (Armstrong, 1 9 7 4 ) . I n t h e s u r f a c e s e d i m e n t s , t h e C/N

r a t i o r e f l e c t s t h e above m u r c e and d e p o s i t i o n

p a t t e r n s w i t h >10 r a t i o s found n e a r t h e c o a s t ( F i g . 6 ) and <6 o b s e r v a t i o n s found under t h e M i s s i s s i p p i R i v e r plume ( T r a s k , 1953; Armstrong, 1 9 7 4 ) . of p a r t i c u l a t e m a t t e r i n t h e M i s s i s s i p p i River i s -25.6

t o -25.9

w h e r e a s 10-20 km o f f t h e mouth, p a r t i c u l a t e v a l u e s of -19.6 a r e r e p r e s e n t a t i v e of warm w a t e r p l a n k t o n ( S a c k e t t e t a l . ,

The 6 1 3 C v a l u e (Hoffman, 1 9 7 4 ) ,

a r e found; t h e l a t t e r 1971 )

.

The 6 3C

31

29

27

......:. .. ‘

98

96

94

92

90

88

86

84

82

80

F i g . 6. The r a t i o o f c a r b o n / n i t r o g e n w i t h i n s u r f a c e s e d i m e n t s of t h e Gulf of Mexico and t h e S o u t h A t l a n t i c B i g h t ( a f t e r T r a s k , 1954; Armstrong, 1974; P o l g e r , 1972; Hathaway, 1971; and R. I v e r s o n , p e r s o n a l communication).

23 v a l u e s of t h e s u r f a c e s e d i m e n t s of t h e M i s s i s s i p p i R i v e r , of a d j o i n i n g b a y s , and of t h e s a l t m a r s h e s a r e s i m i l a r l y -22.4

t o -23.6,

ments i n t h e f r e s h w a t e r swamps and -19.0 tinental shelf

i n c o n t r a s t t o -25.0

t o -20.8

of s e d i -

o f s e d i m e n t s of t h e o u t e r con-

(50-100 m ) between t h e M i s s i s s i p p i D e l t a and t h e Rio Grande

(Hedges and P a r k e r ,

1976).

The Holocene s e d i m e n t s (%0-60 cm) of t h e upper s l o p e ( P a r k e r e t a l . , a l s o have 613C v a l u e s of m a r i n e o r i g i n (-18.0

t o -20.0),

P l e i s t o c e n e s e d i m e n t s (%60 t o 1000 c m ) have 6 13C ( - 2 2 . 0

t o -26.0)

( % 1 0 - 1 2 ) v a l u e s t h a t may be of t e r r e s t r i a l o r i g i n (Newman e t a l . , than j u s t r e f l e c t i o n s of d i a g e n e s i s (Degens, 1 9 7 0 ) . the P l e i s t o c e n e , b o t h t h e M i s s i s s i p p i

( M i l l i m a n e t al.,

1972)

whereas t h e deeper and C/N 1973) r a t h e r

During lower s e a l e v e l s of

( D a v i e s and Moore, 1970) and t h e Amazon

1975) i n s t e a d d i s c h a r g e d i n t o t h e a b y s s a l p l a i n s , presumably

d e p o s i t i n g t e r r e s t r i a l m a t t e r on the upper s l o p e ( S a c k e t t , 1 9 6 4 ) .

After glacial

r e c e s s i o n s , t h e s e d i m e n t a r y r a t e of i n p u t t o t h e bottom i s t h o u g h t t o d e c l i n e by

1 t o 2 o r d e r s of magnitude ( M u e l l e r and S u e s s , 1 9 7 9 ) , s u c h t h a t modern s e d i m e n t s a r e now o n l y found u n d e r n e a t h t h e M i s s i s s i p p i Plume on t h e e a s t Texas-Louisiana s h e l f w i t h t h e rest of t h e s h e l f s e d i m e n t s c o n s i d e r e d to be r e l i c t (Emery and Uchupi,

1972).

The p r e s e n t e x p o r t t o t h e slope of t h e Gulf of Mexico may t h u s be

mainly o r g a n i c m a t t e r f i x e d on t h e c o n t i n e n t a l s h e l f (Walsh, 1 9 8 0 a ) .

C.

Hudson A t p r e s e n t , o v e r 90% of t h e suspended t e r r e s t r i a l m a t t e r i s t r a p p e d w i t h i n t h e

e s t u a r i e s a d j a c e n t t o t h e n o r t h e a s t c o n t i n e n t a l s h e l f (Meade e t a l . ,

1 9 7 5 ) , where

twice a s much r i v e r r u n o f f o c c u r s a s i n t h e South A t l a n t i c B i g h t (Bue, 1 9 7 0 ) . The s e s t o n and n u t r i e n t c o n t e n t of t h e w a t e r column b o t h d e c l i n e by an o r d e r of magnitude between t h e Hudson River and t h e New York B i g h t (P. communication).

Falkowski, p e r s o n a l

A g r a d i e n t i n n i t r a t e c o n c e n t r a t i o n from % 4 0 t o 5

1.19-at NO3 L-l

i s o b s e r v e d and a g a i n t h e m a j o r c a r b o n e x p o r t from t h i s e s t u a r y i s i n t h e form of dissolved o r g a n i c carbon (Falkowski e t a l . ,

1980).

The s u s p e n d e d m a t t e r a t t h e mouth o f t h e e s t u a r i e s i s n e a r l y a l l o r g a n i c and on t h e s h e l f it s e a s o n a l l y c o v a r i e s (Manheim e t a l . ,

1970; Meade e t a l . ,

1975)

with c h a n g i n g c h l o r o p h y l l d i s t r i b u t i o n s a s a f u n c t i o n of t h e n u t r i e n t s u p p l y r a t e mediated by t h e s t r a t i f i c a t i o n of t h e water column (Walsh e t a l . ,

1978).

During

summer when t h e n u t r i e n t s u p p l y from l o c a l u p w e l l i n g ( F i g . 7 ) and r i v e r r u n o f f i s c o n f i n e d t o w i t h i n 10 km of t h e c o a s t , t h e C/N

c o n t e n t of h i g h c h l o r o p h y l l ( > l o

119 c h l R - l ) p a t c h e s of t h e Hudson River plume i s <6.

t-’ i s found above t h e p y c n o c l i n e ,

C/N

O f f s h o r e , where < 1 pq c h l

v a l u e s of summer p a r t i c u l a t e m a t t e r i n t h e

New York B i g h t a r e i n s t e a d > l o . Most of t h e s e d i m e n t on t h e M i d - A t l a n t j r

shejf i s r e l i c t sand w i t h < 0 . 5 % c a r -

bon (F2nery and Uchupi, 1 9 7 2 ) , d e p o s i t e d d u r i n g o r soon a f t e r t h e l a s t Wisconsin g l a c i a t i o n , when t h e she1.f was d r y l a n d 15,000 y e a r s ago.

Seaward of t h e 6 0 m

24

C

6(

I2(

-E 18( h

I

I-

n

i -20'

W

0

30(

-25-

4a

OCTOBER 1978 NITRATE (,ug at {-I) NEW YORK SHELF

I

I

54(

3 1

I00 I50 DISTANCE OFFSHORE (km)

50

I

200

F i g . 7. C r o s s - s h e l f d i s t r i b u t i o n of n i t r a t e on t h e N e w York s h e l f d u r i n g October 1978 ( l o c a t i o n shown i n F i g . 8 ) .

i s o b a t h , t h e s e d i m e n t s c o n t a i n more s i l t ( F r e e l a n d a n d S w i f t , 19781, and, beyond t h e s h e l f b r e a k , t h e o r g a n i c c o n t e n t f i n a l l y i n c r e a s e s t o 1 t o 2% c a r b o n on t h e upper s l o p e , b u t s t i l l l o w e r t h a n t h e 5 t o 20% c a r b o n muds o f f t h e P e r u coast (Walsh, 1 9 8 0 ~ ) . The Hudson Canyon, areas of Georges Bank (Hathaway e t a l . , 19791, and t h e "mud h o l e " a r e g i o n o f 4x103 km2 s o u t h w e s t of M a r t h a ' s Vineyard between t h e 50-100

m i s o b a t h s , are t h e e x c e p t i o n s where 1 t o 2 % c a r b o n muds are

found on t h e M i d - A t l a n t i c

shelf.

I n t h e s e a r e a s , 14C a n d 210Pb d a t i n g s u g g e s t

modern d e p o s i t s w i t h an a c c u m u l a t i o n rate of a t least 50-100

e t al.,

1978; Bothner e t a l . ,

(Hathaway e t a l . ,

cm 1000 yr-'

1980) and p e r h a p s 363 c m 1000 yr-l

1 9 7 9 ) , i n c o n t r a s t to a b o u t 15 c m 1000 y r - l

( M a c I l v a i n e , 1973) a n d 3 c m 1000 yr-'

on t h e rise ( M i l l i m a n ,

(Drake

o n Georges Bank

on t h e slope 1973).

25

Fig. 8. The r a t i o of c a r b o n - n i t r o g e n w i t h i n s u r f a c e s e d i m e n t s of t h e Mid-Atlantic B i g h t ( a f t e r Hathaway, 1971 and G. R o w e , p e r s o n a l communication).

The C/N

r a t i o ( F i g . 8 ) of Mid-Atlantic

s h e l f s e d i m e n t s ( M i l l i m a n , 1973) can be

used a s an i n d e x o f a r e a s of modern carbon d e p o s i t i o n and p o s s i b l y a l s o of t h e f a t e of p a r t i c l e s d u r i n g t r a n s p o r t i n t h i s system.

A t t h e head of Chesapeake

Bay, f o r example, t h e C/N c o n t e n t of t h e sediment i s >30, and 6 13C v a l u e s of -24.0

t o -25.3

( H u n t , 1966) s u g g e s t t e r r e s t r i a l o r i g i n .

Hudson R i v e r a l s o have a 6'3C

v a l u e of -23.3

t o -24.7.

Delaware, and Chesapeake e s t u a r i e s , t h e low C/N

The sediments i n t h e S o u t h e a s t of t h e Hudson,

c o n t e n t of t h e sediments s u g g e s t

seaward t r a n s p o r t of s i n k i n g marine o r g a n i s m s ( w a l s h , 1980b). h o l e , " 6l3C measurements of -20.5

t o -21.0

Within t h e "mud

(Hunt, 1966) a l s o s u g g e s t t h a t t h e

s u r f a c e s e d i m e n t s w i t h a C/N <6 s o u t h of M a r t h a ' s Vineyard ( F i g . 8 ) a r e of marine origin.

S i m i l a r 613C measurements are n o t a v a i l a b l e f o r t h e > I 0 C/N

o f f New York and N e w J e r s e y ( F i g . 81, b u t t h e n-alkane

sediments

hydrocarbon f r a c t i o n of

the sediment c a r b o n pool i n t h i s r e g i o n s u g g e s t s t h a t t h i s material i n s t e a d had both t e r r e s t r i a l and p e t r o c h e m i c a l o r i g i n ( F a r r i n g t o n and T r i p p ,

1977).

26 The h i g h e r C/N r a t i o s of 16-30 i n the s h e l f s e d i m e n t s ( F i g . 8 ) t h u s s u g g e s t t e r r e s t r i a l or vascular

p l a n t carbon d e p o s i t i o n , presumably when r e l i c t s a n d s

w e r e d e p o s i t e d d u r i n g b o t h t h e l a s t Wisconsin and p r e v i o u s g l a c i a t i o n s .

The

d e p t h o f P l e i s t o c e n e s e d i m e n t s on t h e upper s l o p e i s a 3 0 0 m i n c o n t r a s t to o n l y a100 m on t h e s h e l f (Hathaway e t a l . , r e s p e c t i v e l y 15 c m 1000 yr-’

a v e r a g e accumulation r a t e s of

1 9 7 8 ) , i.e.,

a n d 5 c m 1000 yr-’.

A s t h e r i v 6 r mouths and marshes

r e t r e a t e d t o w a r d s t h e p r e s e n t s h o r e l i n e d u r i n g the Holocene t r a n s g r e s s i o n , s e d i ments o f >10 C/N c o n t e n t w e r e c o n t i n u a l l y l a i d down and a r e s t i l l observed a c r o s s t h e s h e l f i n s o m e areas, e.g.,

s o u t h of Montauk P o i n t and east of A t l a n t i c C i t y

( F i g . 8 ) , where t h e a n n u a l primary p r o d u c t i o n i s now a250 9 C m-2

areas, e.g.,

Georges Bank (Hathaway e t a l . ,

yr-’.

In o t h e r

1 9 7 9 ) , Nantucket S h o a l s , t h e “mud

h o l e , ” Hudson Canyon, and downstream of t h e mouth of e s t u a r i e s , a s u r f a c e l a y e r of modern b i o g e n i c <6 C/N s e d i m e n t s may presumably now o v e r l a y t h e r e l i c t s e d i ments w i t h t h e i r >10 C/N r a t i o s .

The primary p r o d u c t i o n of t h e Hudson R i v e r

plume and Georges Bank i s a 5 0 0 g C m-2 mixing,

yr-l,

a r e s u l t of r i v e r r u n o f f and t i d a l

and may r e p r e s e n t some of t h e upstream p r o t e i n s o u r c e s f o r t h e low C/N

s e d i m e n t s and f o r a p a k f i s h y i e l d of a 1 . 4 ~ 1 0t~ o n s yr-l

on this s h e l f .

UFWELLING

EDDY-INDUCED

Florida Current

A.

C l a s s i c a l e x p l a n a t i o n s of w e s t e r n boundary c u r r e n t s ( S t o m e l , 1948; Munk,

1950 ) s u g g e s t t h a t p s i t i v e ( c o u n t e r c l o c k w i s e ) v o r t i c i t y i s developed a t t h e shelf-edge

s i d e s of t h e s e f a s t moving c u r r e n t s to p r o v i d e a f r i c t i o n a l b a l a n c e t o

t h e n e g a t i v e v o r t i c i t y of t h e b a s i n c i r c u l a t i o n induced by t h e c u r l of t h e wind

stress.

Spin-off

c y c l o n i c e d d i e s in t h e F l o r i d a C u r r e n t ( L e e , 1975) do, in f a c t ,

r o t a t e c o u n t e r c l o c k w i s e and t h e i r o c c u r r e n c e is p o s i t i v e l y c o r r e l a t e d w i t h t h e c u r l o f t h e wind stress (Duing e t a l . ,

1977), i.e.,

t h e g r e a t e r t h e c u r l t h e more

i n t e n s e i s t h e p s i t i v e v o r t i c i t y g e n e r a t e d a t t h e edge of t h e Florida-Georgia shelf.

Ekman s u c t i o n i s c r e a t e d i n t h e c e n t e r of t h e s e e d d i e s ( L e e and Mayer,

1977) w i t h an u p w e l l i n g v e l o c i t y of and O ’ B r i e n , 1972) i n c o n t r a s t t o

cm sec-l

a t t h e edge of t h e s h e l f (Hsueh

an sec-’ found n e a r s h o r e d u r i n g c o a s t a l

u p w e l l i n g (Walsh, 1 9 7 5 ) . A s much a s 10 VTat NO3 k-’

can be b r o u g h t i n t o t h e o l i g o t r o p h i c outer s h e l f

e u p h o t i c zone w i t h i n t h e c e n t e r of t h e s e e d d i e s ( L e e e t al., t h a n 1 ug-at

NO3 k-l

found a t t h e i r b o u n d a r i e s ( F i g . 9 ) .

1 9 8 0 ) , w i t h less

Diatom blooms of 5 Vq

Chl Q-l h a v e been found a s s o c i a t e d w i t h t h e n i t r a t e i n p u t from eddy-induced upw e l l i n g a t t h e s h e l f break o f f Florida-Georgia (Atkinson e t a l . ,

1980).

Without

c o n s i d e r a t i o n of n i t r o g e n r e c y c l i n g , a minimal annual p r o d u c t i o n of $40 g C yr-l

a t a C/N r a t i o o f 5/1

gen s o u r c e .

(Lee e t a l . ,

1980) c o u l d be d e r i v e d f r a n such a n i t r o -

T h i s i s , i n f a c t , f i v e f o l d the e s t i m a t e d n i t r o g e n i n p u t from r i v e r

81"

80"

I

0

I80

2 - l80b

I20

60

0

I

50

NITRATE i p g - a t 1-0 C) SPIN-OFF EDDY

APRIL 1977

50

I

NITRATE ( p g - o t I A) GEORGIA SHELF

APRIL 1977

I

I

I00

100

1

r

1

I50

J

(

I

I

I

UW'

50

I

NITRATE ( p g - a t I - ' ) B) SPIN-OFF EDDY

DISTANCE OFFSHORE ( k m )

'i

v

2 6 7 5 2 6 5 5 2 6 3 5 2615 2 5 9 5

I00

I50

N 4

27

F i g . 9. Cross-shelf d i s t r i b u t i o n of nitrate on t h e Georgia-Florida s h e l v e s ( A - I ) ) during A p r i l 1977 ( l o c a t i o n shown in Fig. 6 ) in relation t~ surface temperatures of a s p i n - o f f eddy (after Lee et al., 19801,

28 runoff

( H a i n e s , 1975; Dunstan and A t k i n s o n , 1 9 7 6 ) .

r i v e r i n p u t e v e n t u a l l y y i e l d s %550 g C m-*

yr-'

A f t e r n i t r o g e n r e c y c l i n g , the

(Thomas, 1966) w i t h i n 5-10 kin of

t h e t u r b i d c o a s t a l zone, where a t h r e e f o l d h i g h e r suspended load i s r e c e i v e d i n t h e South A t l a n t i c B i g h t t h a n in t h e Mid-Atlantic

B i g h t (Emery and Uchupi,

1972).

N u t r i e n t s and presumably c h l o r o p h y l l do n o t have a l o n g r e s i d e n c e t i m e on t h e s i n c e t h i s area is f l u s h e d

o u t e r s h e l f o f t h e South A t l a n t i c B i g h t , however,

a f t e r e v e r y u p w e l l i n g e v e n t of 1 t o 3 week d u r a t i o n (Lee and Mayer, 1977). Although f a s t growing g e l a t i n o u s zooplankton a r e found a t t h e s h e l f b r e a k , t h e i r abundance is n o t c o r r e l a t e d w i t h t h e spin-off

e d d i e s (Atkinson e t al.,

1978).

primary p r o d u c t i o n may s i n k to t h e b o t t a n and/or b e

Most o f t h e eddy-induced

f l u s h e d o f f s h o r e r a t h e r than be i n c o r p o r a t e d w i t h i n h i g h e r t r o p h i c l e v e l s .

The

s e a s o n a l o s c i l l a t i o n s o f copepod and l a r v a l f i s h biomass of t h e G e o r g i a - F l o r i d a s h e l f a r e i n s t e a d c o r r e l a t e d w i t h n e a r s h o r e increases of e s t u a r i n e d e r i v e d n u t r i f a l l (Turner e t a l . ,

e n t s d u r i n g l a t e summer-early

1 9 7 9 ) , such t h a t b o t h t h e f i s h

biomass and y i e l d of t h e South A t l a n t i c B i g h t i s % l o %t h a t of t h e Mid-Atlantic Bight (Turner e t a l . ,

0

II-I

1979; Walsh, 1980b).

IT-2

IT-3

69

.

60

I-

--

I20

f

5-

3

E

180

W Q

300

NOVEMBER 1969,1977 NITRATE (pg-at 1-'1 WEST TEXAS SHELF

-

1 0 -

1

420

540

I

50

I

I

I

I00 I50 200 DISTANCE OFFSHORE (km)

I

250

300

Fig. 10. C r o s s - s h e l f d i s t r i b u t i o n o f n i t r a t e on t h e West Texas s h e l f ( l o c a t i o n shown in Fig. 6 ) d u r i n g November 1969, 1977 ( a f t e r F l i n t and G r i f f i n , 1977; NODC

.

29

DISTANCE OFFSHORE (krn)

30 0

)

50

50

100

I00

150

150

0

rn D

-3

2M)x

NOj ( p g o t / j )

-

BAJA CALIFORNIA 250

250

26'40' N

N03(pqot /4) OREGON

/?

38

45'15"

37

36

35

THOMPSON (CUE II) STATIONS

300

300

,350

350

t

THOMPSON (MESCAL

It) STATIONS

Fig. 11. C r o s s - s h e l f d i s t r i b u t i o n o f n i t r a t e on t h e Baja C a l i f o r n i a s h e l f d u r i n g A p r i l 1973 and on t h e Oregon s h e l f d u r i n g J u l y 1973.

The low C/N r a t i o o f t h e s e d i m e n t s (Hathaway, 1971) a t t h e F l o r i d a - G e o r g i a

s h e l f b r e a k ( F i g . 6 ) c o n f i r m s d e p o s i t i o n o f m a r i n e c a r b o n i n t h i s r e g i o n as corroborated by n-alkane

of -19.4

t o -21.3

f r a c t i o n s (Hathaway e t a l , 1979) and & 1 3 C sediment v a l u e s

(Hunt, 1966) on t h e o u t e r s h e l f .

I n c o n t r a s t , t h e s e s t o n has a

613C v a l u e o f -27 i n t h e r i v e r s ( H a i n e s , 1 9 7 9 ) , where t h e s e d i m e n t s are s i m i l a r l y -25.1 t o -26.1

( H u n t , 19661, i m p l y i n g t h a t t h e h i g h n e a r s h o r e s e d i m e n t C/N r a t i o s

r e p r e s e n t t e r r e s t r i a l material t h a t h a s dropped o u t o f t h e e s t u a r i n e water column.

S i m i l a r to t h e L o u i s i a n a swamps, t h e G e o r g i a salt marshes may m a i n l y

export c a r b o n i n t h e form of DOC a t an a n n u a l r a t e o f % 2 2 g C m-' e t al.,

1977).

yr-l

(Pomeroy

The ephemeral p r o d u c t i o n and d e p o s i t i o n of m a r i n e c a r b o n from

eddy-induced u p w e l l i n g is r e s t r i c t e d to t h e edge of t h e s h e l f , however, u n l i k e c o a s t a l u p w e l l i n g o f f P e r u and s o u t h w e s t A f r i c a , s u c h t h a t m o s t of t h e Florida-Georgia

B.

s h e l f d e p o s i t s are r e l i c t s a n d s (Emery and Uchupi,

1972).

Mexican C u r r e n t The p r e s e n c e and s e a s o n a l i n t e n s i f i c a t i o n of a w e s t e r n boundary c u r r e n t o f f

the Mexican-Texas

s h e l f h a s been c o r r e l a t e d w i t h c h a n g e s in t h e wind c u r l

30

I

I-

n W n

TEXAS SHELF (SLOPE INPUT) F i g . 12. A t i m e series of n i t r a t e i n p u t from slope water a s measured a t t h e s h e l f - b r e a k o f t h e West Texas s h e l f ( a f t e r F l i n t and G r i f f i n , 1 9 7 7 ) .

( S t u r g e s and Blaha,

1976) t h a t m i g h t a l s o l e a d t o eddy-induced

upwelling o f f t h i s

I n c o n t r a s t t o c o a s t a l u p w e l l i n g a t t h e S a m e l a t i t u d e o f f Baja

coast (Fig. 10).

C a l i f o r n i a ( F i g . l l ) , however, h i g h n i t r a t e c o n c e n t r a t i o n s are c o n f i n e d to t h e s h e l f e d g e off t h e T e x a s coast.

An annual

t i m e series of n i t r a t e c o n t e n t a t t h i s

s h e l f b r e a k ( F i g . 1 2 ) f u r t h e r s u g g e s t s t h a t eddy-induced u p w e l l i n g m i g h t be i n t e n s i f i e d d u r i n g w i n t e r and summer, i.e., c u r l f o r c i n g ( S t u r g e s and B l a h a , 1 9 7 6 ) . more c o n t i n u o u s F l o r i d a - G e o r g i a

system, a t l e a s t 20 g C m-*

produced on t h e w e s t Texas s h e l f ; t h i s , p r o d u c t i o n (El-Sayed,

1972).

i n phase w i t h changes i n t h e wind

A t a y e a r l y n i t r a t e i n p u t of h a l f t h e

yr-l

might be

i n f a c t , is t h e e s t i m a t e d annual

The o n l y l o w C/N r a t i o s of t h e west Texas s h e l f

s e d i m e n t s are found a t t h e s h e l f b r e a k ( F i g . 6 ) , s u g g e s t i n g t h a t eddy-induced u p w e l l i n g l e a d s t o c a r b o n e x p o r t i n t h i s system, as w e l l .

C.

Guiana C u r r e n t The Guiana C u r r e n t f l o w s n o r t h a t t h e edge o f t h e Amazon S h e l f a s a w e s t e r n

boundary e x t e n s i o n of t h e N o r t h E q u a t o r i a l C u r r e n t ( M e t c a l f , 1 9 6 8 ) . s p e e d s o f 20-200

an sec-'

Varying a t

as a f u n c t i o n o f t h e wind f o r c i n g ( M i l l i m a n e t a l . ,

19751, t h e Guiana C u r r e n t s h o u l d shed s p i n - o f f

e d d i e s on t h e Amazon s h e l f

a n a l o g o u s t o t h o s e on t h e F l o r i d a , G e o r g i a , and Texas s h e l v e s .

Upwelling a t t h e

31

673

674

0

672

67 I

670

I

ia

!

i a

1201

JUNE 1965 V I T RATE GUIANA SHELF

W

4201 a

5400

I

100

I

I

I

50

I

I

1

150 200 250 300 350 400 450 500 DISTANCE OFFSHORE (km)

Fig.

13.

Cross-shelf

d i s t r i b u t i o n of n i t r a t e on t h e Guiana s h e l f ( l o c a t i o n shown 1967).

i n F i g . 4 ) d u r i n g J u n e 1965 ( a f t e r R y t h e r e t a l . ,

s h e l f - b r e a k due t o an unknown mechanism was, i n f a c t , p o s t u l a t e d f o r t h i s s h e l f 1967) on t h e b a s i s of n i t r a t e s e c t i o n s ( F i g . (Ryther e t a l . ;

131, s i m i l a r t o

those shown a c r o s s t h e F l o r i d a and Mexican C u r r e n t s ( F i g s . 9 , 1 0 ) . i n f l u e n c e o f t h e Amazon R i v e r d i s c h a r g e , t h e low C/N shelf-break

Away from t h e

c o n t e n t of s e d i m e n t s a t t h e

( F i g . 4 ) may a l s o r e f l e c t t h e c o n c o m i t t a n t p r o c e s s of eddy-induced

upwelling from t h i s w e s t e r n boundary c u r r e n t .

D.

Loop C u r r e n t N i t r a t e s e c t i o n s a c r o s s t h e Loop C u r r e n t a t t h e edge of t h e W e s t F l o r i d a s h e l f

( O ’ B r i e n and Wroblewski, 1972) s u g g e s t s h e l f - b r e a k u p w e l l i n g ( F i g . eddies have been o b s e r v e d on t h i s s h e l f a s w e l l (Maul, 1 9 7 7 ) . of t h e n u t r i e n t i s o p l e t h s i n t h e o f f s h o r e r e g i o n ( F i g . s y n o p t i c n u t r i e n t s e c t i o n s ( M o r r i s o n and Nowlin,

1977 ) ,

14).

Spin-off

The upward s l o p e

14) i s a l s o t y p i c a l of delineating the anti-

c y c l o n i c Loop C u r r e n t a s it p e n e t r a t e s f a r t h e r i n t o t h e Gulf of Mexico frcm t h e Yucatan S t r a i t .

During 1973-77,

however, t h e Loop C u r r e n t was found due n o r t h of

28ON o n l y 1 0 % o f t h e t i m e , and a g a i n s t t h e s h e l f - b r e a k north of 26ON ( V u k o v i t c h e t a l . ,

1979).

less t h a n 3 0 % of t h e time

Without f r e q u e n t g e n e r a t i o n of p o s i t i v e

v o r t i c i t y a s f r i c t i o n a l d r a g of t h e Loop C u r r e n t a g a i n s t t h e West F l o r i d a s h e l f ,

less eddy-induced u p w e l l i n g would occur i n r e s p o n s e to t h i s w e s t e r n boundary curr e n t a s from t h e E’lorjda, Mexican, and Guiana C u r r e n t s .

The o n l y a r e a of low C/N

32

Fig. 14. Cross-shelf d i s t r i b u t i o n of n i t r a t e on the West Florida shelf ( l o c a t i o n shown i n Fig. 6 ) d u r i n g November 1969, 1971 ( a f t e r O'Brien and Wroblewski, 1972; NODC)

.

r a t i o in the sediments ( F o l g e r , 1977; Hathaway, 1971; R.

Iversen, personal

communication) i s , i n f a c t , found a t t h e Key West shelf-break where t h e Loop Current c o n t i n u a l l y passes through t h e S t r a i t s of Florida (Fig. 6 ) .

Marine

biogenic d e p o s i t i o n has not overlain t h e Mangrove d e t r i t u s of t h e nearshore zone

or the r e l i c t d e p o s i t s on t h e r e s t of t h e West F l o r i d a s h e l f , while the annual f i s h y i e l d kmW2 (Heald, 1969) i s 1/6 t h a t of t h e comparatively impoverished South A t l a n t i c Bight.

TIDAL M I X I N G A.

Georges Bank On some s h e l v e s , t i d a l motion i s an important f a c t o r of n u t r i e n t supply i n

a d d i t i o n to upwelling and r i v e r runoff.

Large t i d a l v e l o c i t i e s of 55 c m sec-l

maximum amplitude, f o r example, can lead to roughly t h e same v e r t i c a l mixing a s a 1 3 m sec-'

wind (Pingree e t a l . ,

1978), with t h e t i d a l mixing energy applied to

t h e water column f r a below a s opposed to t h e wind energy f r a n above. tidal. v e l o c i t i e s a t %30 m depth are b15-25

c m sec-'

Maximal

i n t h e N e w York Bight and

33 $55-110

c m s e c - l on Georges Bank.

The l a t t e r v e l o c i t i e s a r e s i m i l a r to t h o s e of

250 cm sec-’ a t t h e mouth of t h e Amazon ( M i l l i m a n e t a l . , around t h e B r i t i s h Isles (Simpson and P i n g r e e ,

1975) and 150 an sec-’

1 9 7 8 ) , where an index of t h e t i d a l

mixing (Simpson and Hunter, 1974) h a s been f o r m u l a t e d a s t h e r a t i o of t h e d e p t h ( h ) of t h e w a t e r ,column to t h e cube of t h e a m p l i t u d e ( u ) of t h e t i d a l stream, i.e.,

h u - ~ . The r e c i p r o c a l of t h i s r a t i o and a c o n s t a n t d r a g c o e f f i c i e n t , C h-l

u3, i s t h e mean t i d a l energy d i s s i p a t i o n r a t e per u n i t mass ( P i n g r e e e t a l . , Because of t h e l a r g e r a n g e of v a l u e s i n both p a r a m e t e r s , a l o g s c a l e i s

1978).

used to e s t i m a t e areas of s t r a t i f i c a t i o n ( l o g h u - ~L 2 on l o g h-’ t r a n s i t i o n a l a r e a s o r f r o n t s (1.5 or -1.5). -1).

L a r g e r t i d a l v e l o c i t i e s and/or

u3

5

-2,

and t i d a l l y well-mixed a r e a s ( 1 o r

shallower depths favor increased t i d a l

mixing.

m i n t h e N e w York B i g h t , a t i d a l v e l o c i t y of 25 c m sec-l

A t d e p t h s of 40-60

f o r l o g h u - ~ , and t h u s a s t r a t i f i e d w a t e r column i n

s u g g e s t s v a l u e s o f 3.41-3.59

the absence of wind f o r c i n g and t h e r m a l c o n v e c t i o n .

Consequently,

t h e annual

t e m p e r a t u r e c y c l e a t t h e 60 m i s o b a t h o f f New York ( F i g . 1 5 ) i s t h a t of a t y p i c a l b o r e a l s h e l f i n c o n t r a s t t o t h e summer u p w e l l i n g regime o f f Oregon a t t h e same l a t i t u d e (Walsh, 1 9 8 0 b ) .

The v e r n a l h e a t i n g c y c l e , r i v e r r u n o f f , and a d e c l i n e

i n wind e v e n t s a l l l e a d to i n t e n s e s t r a t i f i c a t i o n and a s s o c i a t e d n u t r i e n t deplet i o n of s u r f a c e waters by l a t e summer i n t h e New York B i g h t ( F i g . 7 ) . A t i d a l v e l o c i t y of

110 c m sec-’

a t similar d e p t h s on Georges Bank, however,

f o r log h u - ~ , i.e.,

s u g g e s t s v a l u e s o f 1.48-1.65

a r e a s of t i d a l mixing.

The

s e a s o n a l t e m p e r a t u r e c y c l e a t 60 m on Georges Bank, i n f a c t , r e f l e c t s t i d a l mixing w i t h an i s o t h e r m a l v e r t i c a l s t r u c t u r e a t a l l t i m e s ( F i g .

15).

Because of

t i d a l and wind mixing on Georges Bank, t h e w i n t e r t e m p e r a t u r e minimum i s about t h e same as t h a t of t h e New York s h e l f b u t t h e summer t e m p e r a t u r e maximum i s

similar to t h a t o f f Oregon d u r i n g c o a s t a l u p w e l l i n g ( F i g . 1 5 ) .

The e f f e c t i v e

r a t e of v e r t i c a l mixing on Georges Bank h a s been e s t i m a t e d ( F a l k o w s k i , p e r s o n a l

cm sec-’ i n c o n t r a s t t o a s e a s o n a l u p w e l l i n g v e l o c i t y

communication) t o be

of $10-2 cm sec-1 o f f Oregon. Although t h e s o u r c e w a t e r s f o r Georges Bank c o n t a i n less n i t r a t e ( F i g . 1 6 ) than c o a s t a l u p w e l l i n g water o f f Oregon ( F i g . l l ) , t h e r e l a t i v e l y h i g h and cont i n u o u s f l u x of n u t r i e n t s o n t o Georges Bank l e a d s t o an annual primary p r o d u c t i o n of $ 5 0 0 g C m-2

yr-l

i n c o n t r a s t t o 2.200-250 g C m-2 y r - l on t h e Oregon and N e w

York s h e l v e s (Walsh, 1 9 8 0 b ) .

G r a z i n g on Georges Bank by copepods consumes o n l y

$30% o f t h e d a i l y p r i m a r y p r o d u c t i o n (Dagg and G r i l l , 1 9 8 0 ) , a l l o w i n g a p o s s i b l e i n p u t of 350 g C m-2

yr-l

t o t h e Bank s e d i m e n t s , i . e . ,

s i m i l a r to t h e combined

n e a r s h o r e d e p o s i t i o n f l u x e s o f carbon d e r i v e d from e f f l u e n t of the M i s s i s s i p p i River (Thomas and Simmons, 1960 )

.

With a 1.5% c a r b o n c o n t e n t and a s e d i m e n t a t i o n r a t e o f 363 c m 1000 y r - l (Hathaway e t a l . ,

1 9 7 9 ) , t h e a c c u m u l a t i o n r a t e can be c a l c u l a t e d (Muller and

34

J

F

M

A

M

J

J

A

S

O

N

D

J

(A) NEW YORK

3

15

-

E

30

9

a

I!

0 W

45

9

50

J

F

M ( B ) OREGON

J

F

M

A

M

J

J

A

S

O

N

D

J

( C ) GEORGES BANK

F i g . 15. S e a s o n a l t e m p e r a t u r e s t r u c t u r e of t h e w a t e r column a t t h e 6 0 m i s o b a t h on A ) t h e N e w York, B ) Oregon, and C ) Georges B a n k s h e l v e s ( a f t e r Walsh, 1980b).

S u e s s , 1979) t o be 27 g C m-2

yr-'.

Accordingly,

less t h a n 10% of t h e w a t e r

column p r o d u c t i o n a p p a r e n t l y r e m a i n s on Georges Bank.

The downstream e x p o r t of

p h y t o p l a n k t o n p r o d u c t i o n w i t h a low C/N v a l u e from Georges Bank and Nantucket S h o a l s l e a d s t o modern s e d i m e n t s i n t h e "mud hole" and on the upper slope with a C/N

<6 ( F i g . 8 ) and 613C of a-19 t o -21

(Hunt, 1 9 6 6 ) .

As much a s 90% of t h e f i s h

y i e l d from C a p e Hatteras t o Nova S c o t i a i s t a k e n n o r t h of N e w Y o r k , s u g g e s t i n g t h a t e x p o r t from t h e t i d a l l y d r i v e n p r o d u c t i o n of Georges Bank may be t h e major s u p p l y of p h o t o s y n t h e t i c carbon to t h i s ecosystem.

35

OCTOBER 1978 NITRATE rpg- a t {-I)

“1

540;

EAST GEORGES BANK

1

I

50

100

I

200

i50

DISTANCE (km)

Fig. 16. C r o s s - s h e l f d i s t r i b u t i o n of n i t r a t e on t h e Georges Bank s h e l f d u r i n g October 1978 ( l o c a t i o n shown i n F i g . 8 ) .

B.

Bering Sea T i d a l v e l o c i t i e s o f 20-50

an sec-’

in t h e s o u t h e a s t B e r i n g Sea g e n e r a t e a

t i d a l l y mixed w a t e r column i n s h o r e of t h e 5 0 m i s o b a t h , 100 km o f f t h e c o a s t (Coachman and Walsh,

1980).

Without s i g n i f i c a n t h o r i z o n t a l a d v e c t i o n or r i v e r

d i s c h a r g e on t h e s o u t h e a s t Bering s h e l f , t h e s u p p l y of n i t r a t e depends upon a t i d a l l y d r i v e n “ d i f f u s i o n ” (Csanady, 1976) shoreward over t h e 4 0 0 Ian d i s t a n c e In contrast,

t h e d i s t a n c e to t h e 5 0 m i s o b a t h

from t h e s h e l f - b r e a k

(Fig. 17).

from t h e s h e l f - b r e a k

o f f Georges Bank ( F i g . 16) i s 40-50

km.

The d a i l y onshore

f l u x of n i t r a t e below t h e e u p h o t i c w n e of t h e Bering sea s h e l f i s s i m i l a r to

36

-E 120-

v

300 APRIL 1979 NITRATE (pg -at !-I) BERING SEA SHELF

420-

DISTANCE OFFSHORE ( km) Fig. 17. C r o s s - s h e l f d i s t r i b u t i o n of n i t r a t e on t h e S o u t h e a s t B e r i n g Sea s h e l f d u r i n g A p r i l 1979 ( l o c a t i o n shown i n Fig. 1 8 ) .

t h a t i n t r o d u c e d by u p w e l l i n g o f f P e r u (Walsh, 1975).

The t i d a l regime of t h e

wide B e r i n g Sea (500 km) l e a d s t o an e f f e c t i v e v e r t i c a l v e l o c i t y o f from d i f f u s i o n (Coachman and Walsh, s i d e r a t i o n s , however,

i n c o n t r a s t to a v e r t i c a l flow o f

w i t h i n 20-30 km of t h e P e r u coast.

an sec-'

1980) or a d v e c t i o n ( S t i g e b r a n d t , 1 9 8 0 ) cona n sec-'

compressed

As a r e s u l t of t h i s t e n f o l d greater v e r t i c a l

f l u x o f n u t r i e n t s , b o t h Peru s h e l f waters and Georges Bank remain e u t r o p h i c year-round,

w h i l e t h e s u r f a c e waters of t h e Bering Sea become d e p l e t e d of n i t r o -

gen by summer. The p h y t o p l a n k t o n p p u l a t i o n s of t h e Bering Sea have a mean C/N r a t i o of 5.7 (Loder, 1971) and a 613C v a l u e of -24.4

(McConnaughey and McRoy, 19791, s i m i l a r

t o t h a t of A n t a r c t i c p h y t o p l a n k t o n ( S a c k e t t e t a l . ,

1965).

The annual primary

(McRoy and Goering, 1976) as a r e s u l t of

p r o d u c t i o n i s o n l y s 2 0 0 g C m-2

yr-'

l i g h t and n u t r i e n t r e g u l a t i o n .

Because of d i f f e r e n t r e p r o d u c t i v e s t r a t e g i e s , the

o v e r w i n t e r i n g zooplankton of t h e o u t e r B e r i n g S h e l f (100-170 m) consume most of t h e s p r i n g bloom i n t h i s r e g i o n , whereas t h e annual zooplankton p p u l a t i o n s of t h e middle s h e l f (50-100 m) do n o t c r o p more t h a n 50% of t h e b l o a n i n t h i s a r e a ,

s i m i l a r to s e a s o n a l c y c l e s of carbon f l u x on Georges Bank and in t h e N e w York B i g h t (Walsh, 1 9 8 0 b ) .

D i f f e r e n t carbon i n p u t s t o t h e b o t t a n of t h e o u t e r and

middle s h e l f are i n d i c a t e d by t h e c r o s s - s h e l f

d i s t r i b u t i o n of C/N r a t i o s i n t h e

37

\..,, ...... ..

i

A

571

c

55

c

1 180

58

Fig. 18. The r a t i o of c a r b o n / n i t r o g e n w i t h i n s u r f a c e s e d i m e n t s of t h e S o u t h e a s t Bering Sea ( a f t e r L i s i t z i n , 1966; R. I v e r s e n , p e r s o n a l communication).

sediments ( L i s i t z i n , 1966; R.

I v e r s e n , p e r s o n a l communication), where r a t i o s < 6

are found on t h e middle s h e l f , w i t h v a l u e s i n c r e a s i n g towards t h e s h e l f - b r e a k (Fig. 1 8 ) . The 6 1 3 C v a l u e s of t h e s o u t h e r n B e r i n g S h e l f s e d i m e n t s a l s o i n d i c a t e marine o r i g i n , -22.0

t o -22.9

( P e t e r s e t al.,

1978).

The n-alkane

hydrocarbon f a c t i o n s ,

however, s u g g e s t a mixed t e r r e s t r i a l s o u r c e (Venkatesan e t a l . , t h e s e d i m e n t s off n o r t h w e s t Africa. 250-SO0

19801, s i m i l a r t o

The o r i g i n of t h e s e t e r r i g e n o u s s e d i m e n t s ,

km from t h e mouth of t h e Kuskokwin R i v e r , may be r e l a t e d to s e a s o n a l ice

f o r m a t i o n , r a f t i n g , and break-up

i n t h e Bering Sea r a t h e r t h a n t h e r e s u l t of

e o l i a n i n p u t o f t e r r e s t r i a l carbon as o f f Spanish S a h a r a .

The P l e i s t o c e n e s e d i -

ments are g e n e r a l l y less t h a n 100 m t h i c k on t h e Bering Sea s h e l f and the nearshore h o l o c e n e a c c u m u l a t i o n r a t e i s % 2 0 c m 1000 yr-' t e n f o l d less t h a n Georges Bank.

(Nelson e t a l . ,

1974), i . e . ,

Continuous t i d a l r e s u s p e n s i o n and g r a v i t a t i o n a l

s e t t l i n g a l o n g a s l o p i n g bottom may l e a d t o a n e t e x p o r t of p a r t i c u l a t e matter from t h e B e r i n g Sea.

S i m i l a r to o t h e r s h e l v e s , t h e g r a d i e n t of sediment o r g a n i c

m a t t e r i s from <0.5% c a r b o n over t h e mid-shelf

( L i s i t z i n , 1966; Sharma, 1974) t o

the >1.0% on t h e o u t e r s h e l f and upper slope ( G e r s h a n o v i t c h , 1962; I v e r s e n , p e r s o n a l communication).

38 North Sea

C.

The w i d t h and b o t t a n topography of t h e c o n t i n e n t a l s h e l f is remarkably similar i n t h e s o u t h e a s t B e r i n g Sea and t h e n o r t h e r n N o r t h Sea.

A 5 0 0 km s e c t i o n across

t h e North Sea from t h e Norwegian Deep between t h e S h e t l a n d I s l a n d s and Bergen, Norway t o t h e F i r t h of F o u r t h , S c o t l a n d , t r a v e r s e s t h e r i c h Fladen Ground a t d e p t h s o f 100-150 in.

A s e c t i o n of t h e same l e n g t h f r a n o f f Unalaska I s l a n d i n

t h e A l e u t i a n c h a i n to Cape Newenham on the Alaska mainland also i n t e r s e c t s the r i c h p o l l o c k f i s h i n g grounds, known as t h e Golden T r i a n g l e , on t h e broad o u t e r s h e l f (100-150 m d e p t h s ) of B r i s t o l Bay.

A s s o c i a t e d w i t h changes i n bottom

topography of t h e North Sea, a t l e a s t two f r o n t s are found a t b o t h t h e 30-50 m and 150-200 m i s o b a t h s i n r e l a t i o n to t r a n s i t i o n s i n r e s p e c t i v e l y , t h e physical dynamics o f t h e t i d a l l y mixed s h a l l o w areas ( P i n g r e e e t a l . ,

1978) and of t h e

i n t e r l e a v i n g w a t e r masses a t t h e s h e l f b r e a k ( S t e e l e , 1 9 6 1 ) .

S i m i l a r to the

B e r i n g Sea, c h a n g e s i n h o r i z o n t a l s a l i n i t y and p r o d u c t i v i t y p a t t e r n s s u g g e s t a d i f f e r e n t p h y s i c a l regime landward of t h e 100 m i s o b a t h i n t h e n o r t h e r n North Sea

as w e l l ( S t e e l e , 19561, r e f l e c t i n g i n c r e a s e d t i d a l mixing in t h i s a r e a compared t o t h e d e e p e r Fladen Ground. al.,

Recent o b s e r v a t i o n s i n t h e Bering Sea ( I v e r s e n e t

1979) s i m i l a r l y i n d i c a t e t h e p r e s e n c e of f r o n t s a t b o t h t h e 50 m and 170 m

i s o b a t h s , as w e l l a s a t h i r d t r a n s i t i o n area ( m i d d l e f r o n t ) a t t h e 100 m isobath. I f t h e hydrodynamic s t r u c t u r e i s s i m i l a r , t h e r a t e of c r o s s - s h e l f exchange from t h e s h e l f - b r e a k of t h e t w o seas may a l s o be s i m i l a r .

nutrient Furthermore,

s i n c e t h e s o u t h e a s t B e r i n g Sea and t h e n o r t h e r n North Sea a r e found a t t h e same t h e a n n u a l i n c i d e n t r a d i a t i o n i s about t h e s a m e i n both epi-

l a t i t u d e s , -55-60%, c o n t i n e n t a l seas.

The s p r i n g bloom commences a t t h e same t i m e (March-April) i n

t h e s o u t h e a s t B e r i n g Sea as i n t h e n o r t h e r n N o r t h Sea, and t h e annual primary p r o d u c t i o n i s a l s o similar, %100-200 g C m-2 Goering, 1976).

yr-’

( S t e e l e , 1956; McRoy and

N u t r i e n t d e p l e t i o n of t h e e u p h o t i c zone o c c u r s by J u n e i n

r e s p o n s e t o t h e a l g a l growth w i t h i n each s h e l f , and t h e f i s h y i e l d from t h e Fladen Ground and t h e Golden T r i a n g l e i s t h e s a m e , -5-10 1980b). C/N

A s might b e e x p e c t e d ,

t o n s km-2

yr-l

(Walsh,

t h e l o s s p r o c e s s a p p e a r s t o be s i m i l a r , such t h a t

r a t i o s < 6 a r e also found ( J a n s e n e t a l . ,

1979) i n the mud d e p o s i t s of t h e

Fladen Ground s e d i m e n t s . I n c o n t r a s t t o t h e B e r i n g S e a , however,

t h e s o u t h e r n N o r t h Sea r e c e i v e s large

a n t h r o p o g e n i c l o a d i n g s of n u t r i e n t s f r a n sewage w a s t e s and a g r i c u l t u r a l f e r t i l i z e r s i n t h e form of r i v e r r u n o f f .

The phosphate c o n t e n t of t h e Phine River has

i n c r e a s e d t e n f o l d over t h e l a s t 50 y e a r s and t h e t o t a l n i t r o g e n c o n t e n t is now 380 ug-at N I-’

(Postma, 1 9 7 8 ) .

much a s 350 ug-at

(Mommaerts e t a l . ,

NO3

Within t h e t i d a l l y mixed a r e a < 3 0 m depth, a s

I-1 h a s been s i m i l a r l y observed o f f t h e B e l g i a n c o a s t

1 9 7 9 ) ; t h e urban i n p u t of n i t r a t e can also be t r a c e d southward

a l o n g t h e e a s t c o a s t of England ( J o h n s t o n , 1 9 7 3 ) .

The r i v e r d i s c h a r g e of n i t r o -

gen to t h e s o u t h e r n N o r t h Sea now c o n s t i t u t e s 6 0 % o f t h e annual s u p p l y with the

39 remainder a d v e c t e d and/or t i d a l l y " d i f f u s e d " from t h e E n g l i s h Channel and t h e northern North Sea (Postma, 1 9 7 3 ) . increased from % 8 0 g C m-2

yr-'

The primary p r o d u c t i o n of t h e Waddensea h a s

i n 1950 t o %240 g C m-2

yr-'

i n 1970 (Postma,

1978) w i t h a c o n c o m i t t a n t i n c r e a s e in t h e o r g a n i c c o n t e n t of t h e s e d i m e n t s of this area ( D e G r o o t ,

1 9 7 3 ) , a s a r e s u l t of such n u t r i e n t s t i m u l a t i o n of t h e

c o a s t a l zone. S i m i l a r to t h e Amazon R i v e r , t h e suspended load of t h e S c h e l d t River drops o u t o f t h e w a t e r column a t t h e 1 t o 2 % s a l i n i t y r e g i o n ( N i h o u l e t a l . , estuary.

D e s p i t e a s e d i m e n t a t i o n rate of 400-600

cm 1000 y r - l

1979) of t h e

off the Sheldt

e s t u a r y (McCave, 1973) a l a c k of diatom accumulation i n t h e s e d i m e n t s i s a l s o observed a t t h e mouth of t h e r i v e r (Wollast and DeBroeu,

1971).

The C/N c o n t e n t

of t h e Rhine River s e d i m e n t s s i m i l a r l y r e l f e c t s t h e d e c l i n i n g t e r r e s t r i a l s o u r c e of carbon, w i t h a C/N

r a t i o of 21 f o u n d i n t h e r i v e r , 14 i n t h e lower e s t u a r i e s ,

and 11 i n t h e n e a r s h o r e Waddensea

(DeGroot, 1 9 7 3 ) .

Presumably, t h e n e a r s h o r e

t i d a l l y mixed a r e a p r e v e n t s b o t h h i g h p r o d u c t i o n a s a r e s u l t of t u r b i d i t y maxima and d e p o s i t i o n of marine o r g a n i c m a t t e r in t h e s e d i m e n t s by r e s u s p e n s i o n .

Where

sewage o u t f a l l s d i s c h a r g e b o t h d i s s o l v e d and p a r t i c u l a t e m a t e r i a l d i r e c t l y to aphotic zone o f t h e c o n t i n e n t a l s h e l f , e.g., C/N

r a t i o s of 13-20

carbon s e d i m e n t s (Sweeney e t a l . , pg-at NH3 9.-l)

White's Point off C a l i f o r n i a , high

(Word and Mearns, 1 9 7 9 ) a r e also found i n t h e a d j a c e n t 8 % 1978) d e s p i t e t h e h i g h n u t r i e n t c o n t e n t (a2500

of t h e sewage e f f l u e n t .

E s t i m a t e s of t h e n e t t r a n s p o r t ( E i s m a ,

1973) of f i n e s e d i m e n t s , o r i g i n a t i n g

mainly from r i v e r s (DeGroot, 1973) i n t h e s o u t h e r n N o r t h S e a , s u g g e s t a r e s i d u a l d r i f t o f o r g a n i c m a t t e r to t h e n o r t h e a s t .

From t h e area of h i g h n u t r i e n t d i s -

charge, t h e bottom carbon i n c r e a s e s t o w a r d s t h e > 3 %muds of t h e Norwegian Deep and t h e Skaggerak (Van Weering, 1 9 8 0 ) , where d e p o s i t i o n r a t e s a r e %loo-450 cm 1000 y r - l

1973).

(Eisma,

I f a l l of t h e s h e l f mud d e p o s i t s are also modern, how-

ever, p r e s e n t mud b u d g e t s c a n n o t account f o r enough s o u r c e m a t e r i a l , even a t a s e d i m e n t a t i o n r a t e of o n l y %10 c m 1000 y r - l

o v e r most of t h e N o r t h Sea s h e l f

s i m i l a r to t h a t i n t h e B e r i n g Sea.

(McCave, 1 9 7 3 ) , i . e . ,

Beneath a h o l o c e n e s u r f a c e l a y e r of

%

40 cm t h i c k n e s s w i t h a s i m i l a r C/N r a t i o

of 7-8 w i t h d e p t h in t h e muds o f t h e n o r t h e r n North Sea, an " a l l o c h t h o n o u s " terr e s t r i a l s e d i m e n t of 15-17 C/N r a t i o i s t h o u g h t t o have been d e p o s i t e d ' l 8 7 0 0 BP

on t h e F l a d e n Ground ( J a n s e n e t a l . , y r (Jansen, 1976). 0-2

1979) a f t e r a sea l e v e l s t a n d s t i l l of %1500

S i m i l a r to P e r u , t h e C/N r a t i o a t a nearby s t a t i o n is 7.5 a t

cm a n d 7.9 a t 81-83 cm, i n c o n t r a s t t o 0.77% carbon a t t h e t o p a n d 0.48% a t

t h e bottom of t h e c o r e ( J a n s e n , p e r s o n a l communication), s u g g e s t i n g l i t t l e d i a g e n e t i c change.

The h i g h e r c a r b o n c o n t e n t may r e f l e c t i n c r e a s e d primary prodUC-

t i v i t y (Jansen et al.,

1979) o r a " r e c e n t "

i n c r e a s e in t h e c a r b o n l o a d i n g as a

r e s u l t o f t h e 90% d e c l i n e in h e r r i n g s t o c k s over t h e l a s t 40 y e a r s (Burd, 1 9 7 8 ) , ~ n s i n 1955. with a maximum y i e l d of 1 . 4 ~ 1 0t o

I f t h i s h i g h C/N m a t e r i a l a t t h e

40 Holocene-Pleistocene

boundary i s n o t t h e r e s u l t of e a r l y d i a g e n e s i s , b u t r e f l e c t s

a terrestrial p l a n t o r i g i n s i m i l a r to t h e Gulf of Mexico, an accumulation rate of 40-80

cm 8700 y r - '

o r 5-10 cm 1000 y r - l

might have indeed o c c u r r e d d u r i n g the

Holocene i n p a r t s o f t h e North Sea. I n t h e a n o x i c s e d i m e n t s of t h e S a n t a Barbara Basin b e n e a t h C a l i f o r n i a c o a s t a l

waters, w i t h a p r o d u c t i o n of o n l y % 2 0 0 - 3 0 0

g C m-2

yr-'

(Eppley e t a l . ,

1979),

t h e r e s i d u a l t e r r e s t r i a l carbon is t h o u g h t to be more r e f r a c t o r y t h a n t h e marine carbon.

A h a l f - l i f e of 53,000 y r i s e s t i m a t e d f o r l a n d - d e r i v e d

15,000 y r f o r diatomaceous v a r v e s ( H e a t h e t a l . , of 400 c m 1000 yr-'

(Koide e t a l . ,

1972).

carbon i n s t e a d of

1977), being deposited a t a r a t e

The d e c l i n e in t o t a l n i t r o g e n c o n t e n t

o f t h i s sediment column is t h o u g h t t o be t h e r e s u l t of deamination of o r g a n i c

matter d u r i n g d i a g e n e t i c b a c t e r i a l a c t i v i t y ( R i t t e n b u r g e t a l . ,

1955).

Similar

t o Northwest A f r i c a , d e p o s i t i o n of marine d e t r i t u s on the C a l i f o r n i a s h e l f a c c o u n t s f o r o n l y 50 t o 673 o f t h e sediment n i t r o g e n , and t h e C/N r a t i o s are 11.2 i n t h e upper 8 c m of s e d i m e n t , 12-14 i n t h e 100-600 c m d e p t h i n t e r v a l , and 1 5 i n a n c i e n t r o c k s (Ebery and Uchupi,

1972; Heath e t a l . ,

1977, Sweeney e t a l . ,

1978).

Recent 615N a n a l y s e s s u g g e s t t h a t i n d e e d t h e t e r r e s t r i a l o r g a n i c n i t r o g e n i s s u f f i c i e n t l y bound w i t h c l a y m i n e r a l s t o be nondegradable by sediment m i c r o f l o r a i n t h e S a n t a Barbara b a s i n (Sweeney e t a l . ,

1978).

The marine o r g a n i c n i t r o g e n

c o n t e n t r e m a i n s c o n s t a n t w i t h i n t h e upper 3 - 4 m of t h e s e d i m e n t s , i.e., l a s t 1000 y r , and t h e n d e c l i n e s w i t h d e p t h . d e p t h (Heath e t a l . , and Hogqan, 1 9 5 8 ) .

over t h e

The t o t a l carbon also d e c r e a s e s with

1 9 7 7 ) , w h i l e t h e c o n c e n t r a t i o n of methane i n c r e a s e s (Ehery In contrast,

t h e amount of t e r r e s t r i a l n i t r o g e n does n o t

change w i t h d e p t h , s u g g e s t i n g t h a t t h e i n c r e a s e of t h e C/N r a t i o may r e f l e c t an i n c r e a s i n g t e r r e s t r i a l c o n t r i b u t i o n to t h e o r g a n i c matter w i t h d e p t h . S i m i l a r to t h e s e d i m e n t s o f f Southwest and Northwest A f r i c a ,

t h e percent car-

bon in t h e s e h i g h C/N s e d i m e n t s o f f C a l i f o r n i a d i d n o t i n c r e a s e a t t h e s u r f a c e , d e s p i t e a 903 r e d u c t i o n i n P a c i f i c s a r d i n e biomass over t h e l a s t 75 y r ( S o u t a r and I s a a c s , 1 9 7 4 ) .

The maximum t o t a l c l u p e i d l a n d i n g s from t h e s e upwelling eco-

s y s t e m s h a s been 3-8x105 t o n s y r - l

i n c o n t r a s t t o 1.4-12x106

t o n s yr-'

for the

h e r r i n g and anchovy f i s h e r i e s of t h e N o r t h Sea and P e r u , where t h e impact of o v e r f i s h i n g may have been " r e c o r d e d " i n t h e s e d i m e n t s . h i g h k i n e t i c energy environments (Didyk e t a l . ,

I n oxic s e d i m e n t s , with

1978) s u c h as t h e n o r t h e r n North

S e a , i n c r e a s e d d i a g e n e s i s of t h e marine carbon might o c c u r , however.

The

i n c r e a s e of t h e C/N r a t i o b e n e a t h 40 c m of North Sea sediment r a t h e r t h a n beneath 4 m of C a l i f o r n i a sediment may s t i l l r e f l e c t nondegraded t e r r e s t r i a l i n p u t to t h e former,

I f t h e accumulation r a t e of 10 cm 1000 y r - '

c o r r e c t , r a t h e r t h a n 100 cm 1 0 0 0 yr-'

f o r t h e North Sea s h e l f i s

o f f P e r u , most of t h e muds a r e n o t modern,

and p a r t of t h e p h y t o p l a n k t o n carbon is e x p o r t e d off t h i s European s h e l f as well.

41 CONCLUSIONS

The amount o f o r g a n i c m a t t e r i s g r e a t e r in t h e s e d i m e n t s o f t h e upper slope than t h o s e o n t h e s h e l f o f f P e r u , Southwest A f r i c a , Northwest A f r i c a , C a l i f o r n i a , Oregon, B r a z i l , Texas-Louisiana, i n t e r v a l s a l o n g t h e U.S.

Alaska, Europe, and i n c o m p o s i t e o v e r 50 m d e p t h

c o a s t from F l o r i d a to Maine ( F i g . 1 9 ) .

sediments p a s t t h e "mud l i n e " a t t h e s h e l f - b r e a k

All

(Murray and Renard,

of t h e s e 18911 con-

t a i n > 1 % c a r b o n such t h a t t h e lower C/N r a t i o s of t h e s e slope r e g i o n s ( F i g . 2 0 ) a r e n o t a r e s u l t of s o r p t i o n of n i t r o g e n on c l a y m i n e r a l s { M u l l e r , 1977: SUeSS and M u l l e r , 1 9 8 0 ) , b u t r e f l e c t m a r i n e o r i g i n of t h e d e t r i t u s (Walsh, 1 9 8 0 b ) .

In

184C sediment samples t a k e n between 24O a n d 44ON (Hathaway, 1 9 7 1 1 , mean C/N r a t i o s < 6 are o n l y found on t h e slope a t 400-1800

m ( F i g . 20), w i t h > 1 % c a r b o n

sediments e x t e n d i n g from 8 0 0 - 2 2 0 0 m ( F i g . 1 9 ) . Although 613C v a l u e s of p l a n k t o n r a n g e from - 1 9 . 6

t o -30.6

(Sackett e t ale,

1965) between t h e t r o p i c a l and p o l a r o c e a n s , a t any g i v e n l a t i t u d e of t h e above s h e l v e s 613C v a l u e s 5 2 5 a p p e a r to i n d i c a t e c a r b o n of t e r r e s t r i a l o r i g i n and 5 2 1 of marine o r i g i n .

The w e a l t h o f i n f o r m a t i o n summarized i n t h i s a n a l y s i s s u g g e s t s

t h a t most t e r r e s t r i a l m a t e r i a l of a C/N > l o , w i t h a 613C L 2 5 , i s now e i t h e r trapped i n e s t u a r i e s o r h a s been d e p o s i t e d on t h e s h e l f - s l o p e d u r i n g g l a c i a l

2.0

I .6

z

g

1.2

[r

a 0 0.8

a (3 a: 0.4

8 0.c

-0.4 50

t--i + 350 650 950 1250 1550 1850 2150 24502750 3050 DEPTH INTERVAL ( m )

Fig. 1 9 . The c o m p o s i t e s h e l f - s l o p e d i s t r i b u t i o n of p e r c e n t o r g a n i c carbon w i t h i n s u r f a c e s e d i m e n t s from F l o r i d a to Maine ( a f t e r Hathaway, 1 9 7 1 ) .

42

. ...

c a

z W

c3 0

K

.

0 .

K

T--

---I

k z 5

0

300

600 900 1200 1500 1800 2100 2400 2700 3000 DEPTH INTERVAL (rn)

Fig. 20. The composite s h e l f - s l o p e d i s t r i b u t i o n of c a r b o n / n i t r o g e n s u r f a c e s e d i m e n t s from F l o r i d a t o Maine ( a f t e r Hathaway, 1 9 7 1 ) .

periods of t h e Pleistocene.

a C/N

within

The marine c a r b o n , mainly ungrazed p h y t o p l a n k t o n of

<6 and a 613C 521, a p p e a r s t o t r a n s i t t h e p r e s e n t s h e l f and be d e p o s i t e d on

t h e upper s l o p e , whether t h e s o u r c e o f n u t r i e n t s i s a t t h e coast f r m c o a s t a l upw e l l i n g and r i v e r r u n o f f or a t t h e s h e l f - b r e a k from eddy-induced

upwelling and

t i d a l mixing. The magnitude of s h e l f c a r b o n e x p o r t , i t s mode of t r a n s p o r t , and t h e t i m e

scale of e a r l y d i a g e n e s i s are unknown.

Based on carbon and n i t r o g e n b u d g e t s of

t h e a n n u a l f l u x e s of t h e s e e l e m e n t s t h r o u g h food webs of t h e Mid-Altantic

Bight,

Gulf of Mexico, B e r i n g Sea, and t h e Peru Upwelling, however, about 50% (Walsh, 1980a) t o as much as 75% (Schopf, 1980) of t h e primary p r o d u c t i o n of t h e s h e l v e s may be e x p o r t e d to t h e c o n t i n e n t a l s l o p e .

A combination of

s i n k i n g phytoplankton

(Walsh e t a l , 1978; Malone and C h e r v i n , 1 9 7 9 ) , n o t consumed by coastal h e r b i v o r e s (Walsh, 1 9 7 6 ) , t h e i r r e s u s p e n s i o n i n a b o t t m boundary l a y e r by t h e t i d e s , and t h e o f f s h o r e f o r c e of g r a v i t y a l o n g a s l o p i n g bottom might l e a d to t r a n s p o r t of b o t h p h y t o d e t r i t u s and f e c a l p e l l e t s to a slope d e p o c e n t e r of weaker t i d a l curr e n t s , where l t o 2 5 % o f t h e s h e l f p r o d u c t i o n might e v e n t u a l l y be b u r i e d (Schopf, 1980; Walsh,

1980a).

Organic phosphorous i s p r e s e n t l y a m a j o r c o n s t i t u e n t of t h e

s e d i m e n t p o l of t h i s e l e m e n t on the N o r t h C a r o l i n a upper s l o p e , b u t n o t on the

r i s e (Morse and Cook, 1 9 7 8 ) , s u g g e s t i n g t h a t e a r l y d i a q e n e s i s of t h i s r e c e n t

43 marine c a r b o n ( F i g s . 19,ZO) h a s a p p a r e n t l y n o t y e t been completed. F u t u r e e x p e r i m e n t s and models w i l l p r o v i d e a d d i t i o n a l d e t a i l s on t h e i n t e r n a l coupling of t h e food webs and of t h e l i n k a g e s t o p h y s i c a l f o r c i n g of any p a r t i c u lar continental shelf.

Resolution of l a r g e - s c a l e

s o c i e t a l c o n f l i c t s i n terms o f

c o a s t a l zone e u t r o p h i c a t i o n , o v e r f i s h i n g , w a s t e d i s p o s a l , and c o n t r o l of atmcspheric C02 l e v e l s , change p r o c e s s e s .

however, must a w a i t f u r t h e r d e f i n i t i o n o f s l o p e - s h e l f

ex-

To a v o i d a m a r i n e " t r a g e d y o f t h e commons" ( H a r d i n , 19681,

a p p r o p r i a t e boundary flux c o n d i t i o n s must be e s t a b l i s h e d f o r t h e loss mechanisms of t h e s h e l f e c o s y s t e m .

ACKNOWLEDGMENTS T h i s r e s e a r c h w a s m a i n l y s p o n s o r e d by t h e Department of Energy ( D O E ) under c o n t r a c t No. program.

DE-AC02-76CH00016

a s p a r t of o u r A t l a n t i c C o a s t a l Ecosystem ( A C E )

A d d i t i o n a l s u p p o r t w a s p r o v i d e d by t h e N a t i o n a l S c i e n c e F o u n d a t i o n

(NSF) a s p a r t o f t h e P r o c e s s e s and Resources o f t h e B e r i n g Sea (PROBES) and Coastal Upwelling Ecosystem A n a l y s i s (CUEA) programs. Suess, R.

I v e r s o n , T.

Loder, F.

J a n s e n , J.

R y t h e r , P.

W e t h a n k G.

F o w e , E.

F a l k o w s k i , and L.

Atkinson

f o r use of t h e i r u n p u b l i s h e d data.

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49 Sweeney, R.E., L i u , K.K., and Kaplan, I . R . , 1978. Oceanic N i t r o g e n i s c t o p e s and t h e i r u s e s i n d e t e r m i n i n g t h e source of s e d i m e n t a r y n i t r o g e n . In: S t a b l e I s o t o p e G e o c h e m i s t r y , P r o c . I n t . Symp. N.F. Dep. S c i . Ind. R e s . 220: 9-26. Thomas, J.P., 1966. The i n f l u e n c e of t h e Altamaha R i v e r on primary p r o d u c t i o n beyond t h e mouth of t h e R i v e r . MSc T h e s i s , Univ. o f G a . , pp. 1-169. and Simmons, E.G., 1960. Phytoplankton production i n t h e Thomas, W . J . , I n : F.P. Shepard, F.B. P h l e g e r , and T.H. van Andel Mississippi D e l t a . ( E d i t o r s ) , Recent S e d i m e n t s , Northwest Gulf of Mexico. Publ. Amer. Assoc. P e t r o l . G e l . , T u l s a , pp. 103-116. 11. Trask, P.D., 1953. The s e d i m e n t s of t h e w e s t e r n Gulf of Mexico. Chemical s t u d i e s of s e d i m e n t s o f t h e w e s t e r n Gulf of Mexico. Paps. Phys. Oceanogr. Meteor. 12: 47-120. Turner, R.W., Woo, S.W., and J i t t s , H.R., 1979. E s t u a r i n e i n f l u e n c e s on a c o n t i n e n t a l s h e l f p l a n k t o n community. S c i e n c e 206: 218-220. V a n Weering, 1980. R e c e n t s e d i m e n t s and s e d i m e n t t r a n s p o r t i n t h e Skaggerak. I. S u r f a c e s e d i m e n t s . P r o c . K.N.A.W. ( i n press). Venkatesan, M . I . , Sandstrom, M., Brenner, S., Ruth, E., B o n i l l a , J., Kaplan, I.R., and Reed, W.E., 1980. O r g a n i c g e o c h e m i s t r y of s u r f i c i a l s e d i m e n t s from e a s t e r n B e r i n g Sea. ( U n p u b l i s h e d m a n u s c r i p t ) . Vukovitch, F.M., C r i s s m a n , B.W., B u s h n e l l , M., and King, W . J . , 1979. Some a s p e c t s o f t h e oceanography o f t h e Gulf of Mexico u s i n g s a t e l l i t e and & s i t u d a t a . J. Geophys. Res. 84: 7749-7768. Walsh, J.J., 1975. A s p a t i a l s i m u l a t i o n model o f t h e Peru u p w e l l i n g ecosystem. Deep-sea Res. 2 2 : 201-236. Walsh, J.J., 1976. H e r b i v o r y a s a f a c t o r in p a t t e r n s o f n u t r i e n t u t i l i z a t i o n i n t h e sea. Limnol. Oceanogr. 21: 1-13. A b i o l o g i c a l s k e t c h b o o k f o r an e a s t e r n boundary Walsh, J.J., 1977. current. In: J.H. Steele, J.J. O ' B r i e n , E.O. G o l d b e r g , and I.N. McCave ( E d i t o r s ) , The S e a , V o l . 6. W i l e y - I n t e r s c i e n c e , New York, pp. 923-968. Walsh, J. J., 1980a. Concluding remarks: m a r i n e p h o t o s y n t h e s i s and t h e global carbon c y c l e . I n : P.G Falkowski ( E d i t o r ) , Primary P r o d u c t i v i t y i n t h e Sea. Plenum P r e s s , New York ( i n p r e s s ) . Walsh, J.J., 1980b. S h e l f - s e a ecosystem. I n : A.R. L o n g h u r s t ( E d i t o r ) , A n a l y s i s o f Marine Ecosystems. Academic P r e s s , N e w York ( i n p r e s s ) . Walsh, J.J., 198Oc. A c a r b o n budget f o r o v e r f i s h i n g o f f Peru. Suhitted to Nature. 1976. P r o t e i n from t h e sea: a comparison of Walsh, J.J., and Iiowe, S.O., t h e s i m u l a t e d n i t r o g e n and c a r b o n p r o d u c t i v i t y of t h e P e r u Upwelling Ecosystem. I n : B.C P a t t e n ( E d i t o r ) , Systems A n a l y s i s and S i m u l a t i o n i n Academic P r e s s , N e w York, pp. 47-61. Ecology, Vol. IV. Walsh, J.J., W h i t l e d g e , T.E., B a r v e n i c , F.W., Wirick, C.D., Howe, S.O., Esaias, W.E., and S c o t t , J . T . , 1978. Wind e v e n t s and food c h a i n dynamics w i t h i n t h e New York B i g h t . Limnol. Oceanoqr. 23: 659-683. Williams, P.M., 1968. O r g a n i c and i n o r g a n i c c o n s t i t u e n t s of t h e Amazon River. N a t u r e 218: 937-938. Williams, P.M., C e s c h g e r , H., and Kinney, P., 1969. Natural radiocarbon a c t i v i t y of d i s s o l v e d o r g a n i c c a r b o n in t h e n o r t h e a s t P a c i f i c O c e a n , N a t u r e 224: 256-258. Study o f t h e b e h a v i o r o f d i s s o l v e d Wollast, R., and de Broeu, F . , 1971. s i l i c a i n t h e e s t u a r y of t h e S c h e l d t . Geochim. Cosmochim. A c t a 35: 613-620. Word, J . Q . , and Mearns, A . J . , 1979. 60-meter c o n t r o l s u r v e y o f f s o u t h e r n California. S.C.C.W.R.P. 'IM 229: 1-58. Yentsch, C.S., and S t u r b e , L.R., 1977. V a r i a t i o n i n ammonium Yentsch, C.M., enhancement and i n d i c a t i o n o f n i t r o g e n d e f i c i e n c y i n N e w England c o a s t a l marine p h y t o p l a n k t o n p o p u l a t i o n s . J. Mar. R e s . 537-555.

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51

CROSS THERMOCLINE F L O W O N CONT INE NT AL SHELVES A N D THE LO C A TI O N S OF SHELF F R O N T S .

Ander s S t i g e b r a n d t Department o f

O c e a n o g r a p h y , U n i v e r s i t y of

Gothenburg

ABSTRACT A

two-layer

i n g a n d -:ind bulence

thermocline model d r i v e n mixing

irom a

turbulenLe

i n

the

lower

Lower

is

l a y e r may

caused

production as nutrients

plant

plied

to t h e upper

It

flux

is found

from both

is equal

to the

speed,

the

local water of

that

the

between

lower

water

sides of

the

importance for

layer.

through thermo-

the biolo-

from below are p e r p e t u a l l y sup-

l a y e r d e s p i t e t h e e x i s t e n c e of

is i n a c c o r d a n c e w i t h t h e r e s u l t

in the

an exchange of

a great

tur-

thermocline towards the

thermocline. front

is created

current

speed

and t h e

depth.

Simpson,

the

shelf

s t r a t i f i c a t i o n b r e a k s down a n d a

a l e n g t h formed by t h e wind

buoyancy

be

by e n t r a i n m e n t

When o c c u r r i n g t h i s m a y h a v e

gical

where

the

by h e a t -

causeti by

thereby decrease the temperature difference

thermocline,

The t w o - l a y e r

layer

by m i x i n g ,

investigated. force

such circumstances there w i l l

cline.

i n the upper

layer

a s compared t o t h e case without mixing

the layers

the

in

bottom current, the

sea s u r f a c e and

Under

and

This later

result

A l l e n a n d Morris

(1978).

INTRODUCTION The g e n e r a t i o n a n d m a i n t e n a n c e of the B r i t i s h

has been treated

Isles,

Fearnhead

(1975) and Simpson,

The b a s i c

idea

velop such that

is t h a t

strong

t h e water

Allen

in particular

by Simpson and Hunter and Morris

the

tidal

(1974),

when

flowing over

strong heating

the

bottom,

from s u r f a c e

(buoyancy f l u x ) .

c u r r e n t s g e n e r a l l y are weaker and t h e t u r -

bott.om l a y e r w i l l n o t

a

around

( 1 9 7 E ) among o t h e r s .

column becomes p r a c t i c a l l y homogeneous

In d e e p e r water

surface layer,

fronts,

strong t i d a l currents on shallow shelves de-

turbulence fields,

t o b o t t o m e v e n i n t h e p r e s e n c e of

bulent

shelf

have any significant

"normal" thermal

influence on t h e

structure determined

ing and wind mixing w i l l d e v e l o p t h e r e .

by

the heat-

I n s p r i n g ar?d e a r l y summcr

52 the

border

between

t h e t h o r o u g h l y mixed

see S i m p s o n ,

may b e q u i t e s h a r p , often

be described

as a

of

the front

the

over

t h e bottom.

E

Cdb

can be

by

looked

upon

t h e wind

velocities

t h e wind

buoyancy

speed,

t h e tnodel

for

the effect of

t h e North Sea and

heat

flux,

of

for

a

shelf

summer

location of

The

a

fronts

lot of

i n the sea,

and,

that

heating

layer

origin.

Besides

the turbulence

t h e bottor..

f r o n t t h e model a l s o g i v e s t h e the front.

This

as i t c a n c r e a t e a n e t

there

A

therefore

w i l l

is a b u o y a n c y f l u x and a l s o t h e r e

thermocline

lower

thermocline

i n t h e lower

separates

layer

which

theories, layer e.g.

the water depth a t

( v e r t i c a l ) cross thermocline

f l o w may flow of

We

T h i s c u r r e n t may b e o f

giving an expression for

The

more

thermocline model.

interface

i n most

hopefully,

generally exists in the

period.

caused by t h e wind.

source for

flowing over

front.

by v i g o r o u s t i d a l s t i r r i n g ,

frox t h e v e r t i c a l l y homogeneous

current

the

is c o n s i d e r e d t o be a

front

the air-sea

in contrast to the situation

outsidr

the

stratification and

flow through

primarily

layer

Using

f r o n t s w i l l be considered.

and e x p l o r e a simple one-dimensional

turbulence

Simpsan shelf

stratification

caused

I n t o t h e v e r t i c a l l y homogeneous upper

turbulent.

wind mixing.

in a different

two-layer

ocean during the spring

the upper

Recently

t h e location of

thermal

shelf

approached

The e x i s t e n c e

caused by a heat

frontal loca-

and water d e p t h s t h e y were a b l e to conclude t h a t

of

also,

and

Isles

i n f r a r e d s a t e l l i t e images.

extendpd

t h e l n c a l breakdown,

construct

f l u x a r e known.

( 1 9 7 8 ) made a d e t a i l e d n u m e r i c a l c a l c u l a t i o n

c o n s e q u e n c e of the thermal

Having

the

is, however,

g e n e r a l way.

tidal

t h e t i d a l c u r r e n t s and

t h e l o c a t i o n of

paper

the

i n executing t h e buoyancy f l u x .

a considerable role

plays

this

problem

is

a s t h e r a t i o between

f r o n t c a n be p r e d i c t e d

from

(1978) have

tidal

through the air-

r e s u l t s c o m p a r e q u i t e s a t i s f a c t o r i l y w i t h known

d a t a of

In

flux

(cdbUb3)/(BH)

t h e mean

the

E

a l so t a k i n g a c c o u n t o f

tidal

t h e mean buoyancy

surrounding the British

tions determined

e t a1

=

is H ,

depth

location

the location of

Pingree and G r i f f i t h s

for t h e s h e l f

i t may

is a d r a g c o e f f i c i e n t f o r t h e t i d a l c u r r e n t

the value of

i n new a r e a s w h e r e

regions and

Thus t h e a u t h o r s de-

parameter E

the water

t h e work done

d i s s i p a t i o n and determined

their

Here

a m p l i t u d e is Ub and

i n t e r f a c e is B.

(19781,

is assumed t h a t t h e

local conditions.

non-dimensional

frontal location.

current sea

a

it

to above

is determined by

termined the value of a t

the str?tified

front.

referred

In a l l the works

and

Allen and Morris

i.n\~e l a r g e b i o l o q i c a l

n u t r i e n t s i n t o t h e upper

is

is a tidal the flow

implications layer.

53 THEORY

The g o v e r n i n g e q u a t i o n s We c o n s i d e r a n a r e a o f

t h e s e a w h e r e the d e p t h , H ,

is c o n s t a n t and

uniform. T h e r e is a b o t t o m c u r r e n t o f m e a n s p e e d Ub. T h e me3.n wind speed i s W and t h e n e t m e a n h e a t f l o w i n t o t h e s e a t h r o u g h t h e a i r sea i n t e r f a c e is Q i n . T h e b u o y a n c y f l u x , in t h i s c a s e c a u s e d by t h e heating, t o g e t h e r w i t h t n e t w o s o u r c e s of t u r b u l e n c e g e n e r a l l y c r e a t e s

a two-layer s y s t e m w h e n s t a r t i n g f r o m a v e r t i c a l l y h o m o g e n e o u s water mass. T h e t e m p e r a t u r e and t h e d e p t h o f t h e t w o l a y e r s a r e T 1 , h l and T 2 , h 2 r e s p e c t i v e l y . T h e t u r b u l e n c e in t h e t w o l a y e r s c r e a t e s e n t r a i n ment f l o w s t h r o u g h t h e t h i n p y c n o c l i n e . E x p e r i e n c e f r o m l a b o r a t o r y e x periments s h o w s t h a t t h e r a t e of e n t r a i n m e n t i n t o a layer is d e t e r mined by t h e t u r b u l e n t i n t e n s i t y in t h a t l a y e r . T h e c o u p l i n g b e t w e e n the t u r b u l e n c e f i e l d s o n e a c h s i d e o f

t h e p y c n o c l i n e s e e m s t o be

negligible, a t l e a s t i n l a b o r a t o r y e x p e r i m e n t s , s e e T u r n e r

(1973

p. 292). T h e e n t r a i n m e n t v e l o c i t y i n t o the s u r f a c e l a y e r , w e l , s h o u l d then be p a r a m e t e r i z e d by t h e w i n d s p e e d , W. S i m i l a r l y t h e e n t r a i n m e n t velocity i n t o t h e l o w e r l a y e r , w e 2 , s h o u l d be p a r a m e t e r i z e d b y t h e speed of t h e b o t t o m c u r r e n t , Ub. T h e m o d e l is s k e t c h e d i n F i g . 1 .

T2

- I

. .. .. ...-. .... ... .... .. .*.: . . . ....... ... .... .. ... .. .. .. .. .. ....... .. ...:.. ..... .... ... .. . . . .. . . . . . . . . . . . . . * . . . Fig. 1 .

T h e m o d e l and i t s p a r a m e t e r s .

T h e t h e r m o c l i n e m o d e l t h a t w i l l be d e v e l o p e d h e r e is o n e - d i m e n s i o n a l and t h u s t h e e f f e c t s o f h o r i z o n t a l a d v e c t i o n a r e s u p p o s e d negligible. If the t w o e n t r a i n m e n t v e l o c i t i e s a r e u n e q u a l t h e d e p t h o f t h e l a y e r s

54

w i l l c h a n g e . C o n s e r v a t i o n o f v o l u m e for t h e t w o l a y e r s t h e n y i v e s

d h l / d t = we1

dh2/dt

=

e2

(1)

we2 - w e l

( 2 )

-

W

T h e h e a t c o n t e n t in t h e t w o l a y e r s , Q , and

Q2

respectively, may

c h a n g e b e c a u s e of t h e h e a t f l o w t h r o u g h t h e a i r - s e a i n t e r f a c e and b e c a u s e o f e n t r a i n m e n t . T h e h e a t b a l a n c e s for t h e t w o l a y e r s are

5 cpT2 -

dQl/dt

=

bin +

dQ2/dt

=

W e 2 * cpTl -

In E q s .

( 3 ) and

We?

Wel

Wel

(3)

CpTl

P CpT2

(4)

( 4 ) we h a v e used t h e a p p r o x i m a t i o n

p

1c

w h e r e c p is a r e f e r e n c e v a l u e for t h e s p e c i f i c heat and

ZZ

P

p2cp2

= *Ci)'

is a r e -

f e r e n c e d e n s i t y for t h e s y s t e m . U s i n g t h e f i r s t d e r i v a t i v e s o f the relations Cll and

(4) and

=

P c p h l T l and Q 2 = P c p h 2 T 2 and c o m b i n i n g Eqs.

( 3 ) and

d T l / d t = 6in/(Fccphl) + ( T 2 - T 1 ) w e l / h l

dT2/dt

=

(1;

(2) respectively yives

(TI

-

51

61

T2)we2/h2

Entrainment velocities

in t h e s y s t e m .

W e c a n d e t e r m i n e t h e t e m p e r a t u r e s and d e p t h s o f the l a y e r s if we m a n a g e t o o b t a i n u s e f u l e x p r e s s i o n s for t h e e n t r a i n m e n t velocities. A s d e c l a r e d a b o v e t h e e n t r a i n m e n t v e l o c i t y i n t o t h e lower l a y e r ,

w e 2 , w i l l be p a r a m e t e r i z e d by Ub. T h e K a t o - P h i l l i p s f o r m u l a for e n trainment

( s e e T u r n e r 1 9 7 3 ) is

h2 where

np

1

(7')

i s t h e d e n s i y d i f f e r e n c e b e t w e e n t h e u p p e r and l o w e r layers.

. lower . _ layer m d y o e c- d , i~ u i d c e uL L U J I I T h e f r i c t i o n v e l o c i t y u h b in tlne I

the relation u

*

=

.

_

L

.

j

L - - -

~c d b~u b 2 , w h e r e c d b is t h e a p p r o p r i a t e d r a g coeffi-

c i e n t . T h e c o e f f i c i e n t m o w a s d e t e r m i n e d t o be 1 , 2 5 e x p e r i m e n t s by Ksto

l

&

Phillips, see Turner

( 1 9 7 7 ) D e n m a n and M i y a k e f o u n d m o = 1 , 0

in t h e laboratory

(1973). A c c o r d i n g t o Niiler

in a f i e l d s t u d y of s l o w

e r o s i o n a t o c e a n s t a t i o n Papa. F O ~s i m p l i c i t y

we use a linear equation of state,

p

=

P(l

-

aT),

55 = a ( T , - T ) a s a = - ap/aT is p o s i t i v e a n d T1 L T2 by 2 s t a b i l i t y r e q u i r e m e n t s . T h u s w e c o n s i d e r p r o c e s s e s c h a n g i ~ gt h e s a l i -

giving B p / F

nity to be unimportant mocline model.

for

the

The entrainment

b u o y a n c y flux i n t h i s s i m p l e t h e r velocity

into the

lower

layer

should

then be given by

a buoyancy f l u x through t h e air-sea

In the presence

of

the entrainment

velocity into the

we,.

i.ntprface

may b e

influenced

to

( 7 ' ) .

There are g e n e r a l l y t w o c o n t r i b u t i o n s buoyancy'flux

i n t o the upper

the atmosphere and If

layer,

be described by a n expression q u i t e similar

by t h i s a n d c a n n o t Eq.

upper

the other

layer,

of

different

by e n t r a i n m e n t

of

for a w h i l e , g o b a c k a n d l o o k a t E q .

we,

s l i g h t l y rewrite

where,

on the

l e f t hand

side,

is

buoyancy f o r c e s

energy used

now a s s u m e

heat

flux

water

we find

from

from b e l o w .

that

we can

t h i s equation to obtain

time a g a i n s t t h e turbulent

denser

(7')

to the

origin

one causer1 by t h e

per

unit

the efficiency of

found t h e e x e c u t e d work p e r and,

t i m e

the

on the

right

the

buoyancy f o r c e s t o be

source.

The

following energy balance

side,

to perform t h i s work.

turbulence with

against

hand

independent of for

respect the

the upper

lie

the w i l l

t o working

k i n d of

layer

unit

buoyancy

may t h e n

be f o r m u l a t e d

The e n t r a i n m e n t

velocity

into the

upper

layer,

w

e l '

should

from t h i s

be y i v e n b y

Here we above of

have,

for

is a b s o r b e d

near

t h e sea

assumed t h a t surface.

the heat supplied

the wind

speed

i n the upper

layer,

insignificant.

u k W , may b e c a l c u l a t e d

b y t h e w e l l k n o w n r e l a t i o n s h i p u * ~ ' = va/pcdwW2

is t h e d e n s i t y o f

air

from

Thus radiative penetration

h e a t d e e p i n t o t h e w a t e r mass i s c o n s i d e r e d

friction velocity

Pa

simplicity,

The from where

and cdw is t h e a p p r o p i i a t e d r a g c c e f f i c i e n t .

56 If

heating

tile

is s u f f i c i e n t l y s t r o n y ,

c i e n t l y weak a n d t h e d e p t h of

f o r m a l l y less t h a n z e r o .

becomes the

of

thermocline".

Of

sume n e g a t i v e v a l u e s . can be determined bulence cause of

i n the the

(cailsecl b y

haviour

e 1;

lower

i n the

t h e wind

usper This

is

the

velocity

r e g i m e of

the entrainment

(8) w i t h t h e the

"the retreat

then

retreat :

not

0.

and t h e depth there

If

l i m i t

(81

is t u r -

a r i s e so o f t e n he-

t o w a r d s more s h a l l o w t h e r m o c l i n e s f r o m b e l o l n i ) . Eq.

wel

v e l o c i t y c a n n o t as-

1.h.s.

problem w i l l

is s u f f i -

is too I.arge,

layer

thermocline w i l l

layer

tendency

has the

in that

case

r e a s o n a b l e be-

Gin+ 0 t h e e x p r e s s i o n f o r t h e e n t r a i n m e n t

t h a t g i v e n by

Kato a n d P h i l l i p s .

f i na l equations order

t o o b t a i n a more c o m p a c t n o t a t i o n

meters defined

the

same i n f o r m a t i o n .

(7)

- (12)

( 5 ) and

+

h2

=

H

F r o m Eq.

introduce

the para-

=

( 1 )

and

(2)

contain

obtain with

the

h e l p of

constant ( 2 ) we

Eqs.

Eqs

( 6 ) may b e r e w r i t t e n

Given the parameters A ( t ) , numerically

we

below.

As w e a s s u m e t h a t h l

Eqs.

The

the erosion

t ha t

course

f r o m Eq.

velocity approaches

Th -

the

for

B ( t ) and C ( t ) t h i s

a g i v e n s e t of

T2(0)].

Before we proceed

t i e s of

t h e model.

i n i t i a l

s y s t e m m a y be s o l v e d

conditions

to d o t h a t we w i l l

look

[n(O),

T1(0),

a t some p r o p e r -

57 Some p r o p e r t i e s

of

t h e model.

vious o n e o c c u r s when t h e t i d a l

is a b s e n t .

We t h e n p u t A

i n f l u e n c e upon

and o b t a i n

0

=

The f i r s t ob-

t h e moTe1

f e w s p e c i a l c a s e s of

We w i l l d i s c u s s a

the

t h e upper

mixed l a y e r

f o l l o w ng e q u a t i o n s f o r

the tipper mixed l a y e r

A w e l l k n o w n case

o c c u r s when d q / d t

C = B/[H(l-n)]

0.

=

or

H e r e L = U , ~ ~ / ( N B i) s t h e M o n i n - O b u k h o v

is B

=

we t h e n h a v e

gaQin/(6cp)

happens t h a t

N

(1973 p.301)

the

the wind mixed

=

and

K

i s

1/2m03 0,4

f o r "0

proportionality

layer

length.

The buoyancy f l u x

von Karmans c o n s t a n t .

=

(Incidentally it

1,25). A c c o r d i n g t o T u r ~ e r

between

the equlibrium depth of

f i r s t p o i n t e d o u t b y K i t a i g o r o d s k i i who a l s o p r e s e v t e d evidence from the ocean. giving

strong

entrainment forced

support for

velocity

the

into the

interesting

is q u i t e s t r o n g .

for

observational

( 1 6 ) m a y b e o b t a i n e d d i r e c t l y f r o m Eq.(8)

Eq.

validity of

that

upper

i n t h e p r e s e n c e of

layer

expression for

the a

buoyancy f l u x .

Another

speed

l e n g t h was

i n t h e o c e a n a n d t h e Monin-Obukhov

l i m i t

Given c o n s t a n t wind

and constant heating A,

the maintenance

c l i n e is

that

t h e model

of

of

B

than

the

t h e lower

laver,

speed, constant

and C are constant.

an existing quasisteady

t h e e n t r a i n m e n t of

be l a r g e r

o c c u r s when t h e

heat

into the

t o t a l h e a t s u p p l y times t h e

thus

or

s t i r r i n g

bottom current The c o n d i t i o n

(wel=

we2)

lower

layer must

thermonot

f r a c t i o n a l d e p t h of

58 Marginal

s t a b i l i t y o c c u r s when r- - 1

w e a k wincl m i x i n g

FI

H

and

the

two

t.here w i l l

sides

be

i n

(17) are equal.

With

for

no thermocline

5 A/C Fifr(,nt

=

used

=

is j u s t t h e c o n d i t i o n f o r

A/C

by Simpson and Hunter

Griffitlis

location

(1975) and

of

the

front

Pingree

and

(1978).

We c a n e a s i l y depth a t

the

(1974), Fearnhead

the

include the

front

for

effpct of

a quasi-steady

wind

mixing

state.

upon

the

With d'l/dt

=

water 0 Eq.(13)

gives

or

o b t a i n e d d i r e c t l y f r o m Eqs.

T h i s e y u a t i o n m a y a l s o be

For m a r g i n a l s t a b i l i t y is used

i n Eq.

If

i n different

(mGw,

respectively

observational

) = ~ ( A~H f~r o n~t / C~)

'I2

(7)

[from

and

(li')]

( 8 ) :

which

Allen

wind

and

t i d e mixing

n u m e r i c a l v a 1 . u e s of

mo

are unequal

i n Eqs.

t h i s w i l l

(10) and

(11)

m o b ) . S i m p s o n , A l l e n a n d Morris h e l d t h i s p o s s i -

later

support

S i m p s o n a n d Bowers for

this.

( 1 9 8 0 ) h a v e p r e s e n t e d some

The water

depth at

the

front

should

be

the

that

8

(1978).

b i l i t y open and

In

1

is e q u i v a l e n t t o t h e one g i v e n by Simpson,

the efficiencies for

r e f l e c t

:hen

r

(18) giving

This expression dntl Morris

(

numerical examples t h a t

mow

Eq. system

a

gives

Lluid

layer

because

flux.

I t

either

w i l l ,

however,

assume

m o b = mo.

=

(19) thus i n

f o l l o w below we

of

of

the

where

a one-dimensional

total depth H collapses into a

either

s h o u l ~ ib e

l i m i t

two-layer

single

homogeneous

t o o s t r o n g s t i r r i n g or t o o w e a k b u o y a n c y

possible

t o make u5e of

t h i s

l i m i t

mo or u* f r o m e x p e r i m e n t s w i t h g r i d - g e n e r a t e d

in determining turbulence.

59 NUME R I C A I, EX PERI ME NT S

t o l o o k a t t h e d e v e l o p m e n t of

In order

f o r c o n s t a n t a m o u n t s of system of

(13) -

Eqs.

a second order

valid

the

for

progressive

(W

4,3 m/s)

=

have used

W e

=

and

mo

1,25

the is

[q(O),

(nb3)ll3

=

=

(Ub3)

1/3

2 3 cm/s

(0.9,

=

__

Ub

2,

8.2,

i m s l i e d by

TABLE

=

8

(W

B

6.8

=

m/s).

p a r a m e t e r s were

The o t h e r

a t

8.0).

50 m

a depth of

about

2

=

I n i t i a l con-

T h e c u b i c m e a n of

( c C l b= 2

t h i s value

in Table

T

.

For

is e q u l v a l e n t

55 c m / s .

I

V a l u e s of

"3/"wcc]w

the parameters used

=

ag

=

Qin

-

1,43

shown

i f

::ater

depth.

perature

.

10-6

structure

Fig.2.

for

case

i n t h e upper

layer

the surface just

hope

to the

:04H-3/4

c

=

2

the

front,

w i l l

be

start

1 . o c a t i o n s of

a

increase

unequal in

the

tem-

depth outside

t h e model

indicated structure

set u p and a

w i l l presumably be

is

feature also found

(1978). As

to find exactly the

the

the

is a l s o a t e m p e r a t u r e

There

front,

(cm20K/s)

(cm"K/s)

i n c r e a s i n g water

starts!. a t

.

is a r a p i d

there

with

Horizontal pressure gradients parallel

=

100 d a y s a f t e r

1 ,

n a t u r e by S i m p s o n , A l l e n and Morris o n e may n o t

P

Isotherms are drawn between

One c a n see t h a t

(where t h e pycnocline

minimum a t

in the numerical experiment

17 . [cm2/(s2"K)] 1 7 0 [ c a l / ( c m 2d a y ) ]

The thermal

front

of

13

(1961).

we used

1 ,

t h e v a l u e of A

a s i n g l e component harmonic bottom c u r r e n t

to an amplitude

c o n s t a n t width and

values arc yiven i n Table I below.

T1 ( 0 ) , T 2 ( 0 ) ]

velocity

tidal

case

T h i s l a w is

see D e f a n t

case

run,

i n a11 c a l c u l a t i o n s .

held constant and t h e i r ditions:

f i r s t

i n the second run,

=

t h e v e l o c i t y ampll-

i n a channel of

is n e g l i g i b l e ,

In the

aIl-3'4.

1.1,

t o f o l l o w t h e €1-lI4-law.

long waves

the

h e l p of

t o i n a simple way i n -

In order

t h e water d e p t h ,

assumed

v a r y i n g d e p t h when d i s s i p a t i o n Thus we w r i t e A

s t r a t i f i c a t i o n

wind mixing and t i d a l mixing

method.

in A with

t i de was

thermal

( 1 5 ) was s o l v e d n u m e r i c a l l y w i t h t h e

Runge-Kutta

clude variations t u d e of

heating,

the

is

local,

i n nature.

frontaL

generated.

i n

jet,

Cross-frontal

60 advection the

b y m i x i n g ~ r o c e s s e sw i l l

caused

probably further

disturb

s i m i l a r i t y between t h e suggested structure

and t h e real one.

(1978) discussed the

frontal structure

Simpson,

A l l e n a n d Morris

t o some e x t e n t .

I

I

I

25

24

22

I

1

-

I '

18 11-41

1020 12

9

30-

1.4

11

40-

F i g . 2. The t h e r m a l s t r a t i f i c a t i o n f o r d i f f e r e n t water C a s e 1 (B=2) 1 0 0 d a y s a f t e r t h e o n s e t o f h e a t i n g .

According

front

72 m

=

Hfront

to E q .

i n case

(10 m according

This matter

cline.

next

The rise o f

the

3 we

case 2 which (W

to case

A t

( 1 6 ) ) . For

velocities and

depth

thermocline towards 200

m water d e p t h t h e

tides

its equilibrium depth

s h a l l o w e r water

there

are siyni-

and thereby exchanye through

its biological

the

significance

t h e pycnoi

is d i s c u s s e d

in

section.

In Fig.

1

have drawn t h e

is b e l i e v e d

6,8

=

m/s).

The

thermal

t o b e more

importance for

f a c t o r s may be o f

structure after

realistic with

f r o n t h a s moved

(93 m compared t o 72 m ) .

f i n i t e l y of other

s h o u l d be a t a water

t h e r m o c l i n e d e p t h is near to Eq.

ficant entrainment

speed

1.

front

is caused by t h e t i d a l mixing.

a r e weak a n d t h e

the

(19) the

depths H.

the

to deeper

Thus t h e wind

location of

still greater

the

c i t i e s i n a p r o g r e s s i v e l o n g wave v a r i e s l i k e be a very

important e ffe c t

i n

funnel-ljke

respect

t o wind

water compared

s t i r r i n g

front

importance.

100 d a y s for

but

is dei n nature

As o r b i t a l v e l o -

( w i d t h ) - ' I 2 t h i s may

areas.

61

50 --L

I

10

1

11.5

10.51

1

12.25

12.0

I I

20

J

30

T

13.C

8.1

9.0

8.5

10.0

1 I

I

1

40 (mI I

-!$A'

Fig. 3. The th'ermal s t r a t l f i c a t i o n f o r d i f f e r e n t w a t e r Case 2 (B=8) 1 0 0 d a y s a f t e r t h e o n s e t o f h e a t i n g .

The

thick

upper

to that

pared

layer

in case

1

r i a t i o n i s much s n a l l e r

i n case 2 has a and

gradient associated

with

compared t o t h e o n e

~n c a s e

tect

and

identify

shelf

l a r g e t h e r m a l c a p a c i t y com-

therefore the

the

r a n g e of

former case.

in the

front w i l l Thus

1.

fronts,

e.g.

the

depths H.

temperature va-

Also t h e t e m p e r a t u r e

i n case 2 g e n e r a l l y be possibility

on satsllite

small

to r e a d i l y de-

IR

imagery,

should

depend o n t h e c u r r e n t wind c o n d i t i o n s .

EXCHANGE THROUGH THE P Y C N O C L I N E During t h e heating

period

i n s p r i n g a n d e a r i y summer

cline r e t r e a t s from g r e a t e r depths. Turner

(1973). During

this period

normally no exchange with no t r a n s p o r t o f The

nutrients

hausted. In

This

e.g.

keeps

t h e upper

t h e underlying water.

i n t h e upper

t h e thermo-

is described

well-mixed

n u t r i e n t s from t h e lower,

i n the water

the preceding

This process

There

is p r a c t i c a l l y

nutrient-rich

well-mixed

by e . g .

layer has

layer

layer.

becomes ex-

t h e p r i m a r y p r o d u c t i o n down. section we

saw that for

ween s h a l l o w w a t e r s w h e r e t h e w a t e r

a

transition

range,

bet-

is thoroughly mixed from t h e

sea s u r f a c e t o t h e bottom and g r e a t water d e p t h s whpre t i d a l mixing

62 is

insignificant,

of

is a p e r p e t u a l

the

temperature difference

layers we cdn

the

( 8 ) and

velocity

between

In Table

into the

upper

s e c t i o n 3.

The c a l c u l a t i o n s

f o r d a y 30

the onset of

heating).

I1 w e

In Table is

tbe

lower

rate

AS

ing,

As

after

that

upper

the stability of

layer the

100 days

(100)

found

bc

are

2,

the en-

described

shown

rate,

from Eqs.

(30

(100)

V = wel/hl,

which

from Table

is renewed

pycnocline

in

I1 t h a t

l i t t l e more

increases during

t h e mixing the

the

in his ecological t h e mixing

h e a t i n g a t a water d e p t h of

4 where

in

is exchanged d a i l y with

that

find

l a y e r s a n d t h e depth4

rase

t h i s parameter

v e l o c i t y and

see a l s o F i g .

for

the mixing

layer

one month of

the

the entrainment

30 and

upper

(1974) uses

an extreme example we

cline decreases, a t

the

also listed

the

(Steele

is 0,12

T h i s means

week.

have

f r a c t i o n of layer

model).

the pycnocline,

and we2

11 below c a n

layer

days

after

the

immediately c a l c u l a t e wel

(7) respectively.

trainment

Pxchange through

are both non-zero.

and we2 Knowing

is f o r c e d t o w a r d s t h e sea s u r f a c e .

the thermocline

In such a case there

rate

100 m.

t h a n one the

across the

heatthermo-

entrainment velocities

are drawn.

I I

F i g . 4 . The e n t r a i n m e n t v e l o c i t y f o r d i f f e r e n t water d e p t h s H f o r c a s e 2 (B=8) 30 and ..' 100 days a f t e r t h e o n s e t of heating. ~

63 After

100 d a y s t h e m i x i n g r a t e h a s d e c r e a s e d t o a p p r o x i m a t e l y o n e

t h i r d of

the value a t

t i m e

the

charged a l l

Thus water

30 d a y s . into the

upper

layer

rich

tremendous e f f e c t upon t h e p l a n t productlon. zero entrainment during

the

a water

even a t

reached

heating period,

d e p t h of

in nutrients

and t h i s

should

Normal

are

is d i s -

have a

conditions,

i.e

i n t h i s example n o t

200 m.

Table I1 The e n t r a i n m e n t

B = 8, C = 2

ve o c i t y i n t o the upper a t d a y 30 (100)

.

layer

for

A

=

~ o ~ H - ~ ’ ~ ,

0,121 (0,041 1 0,056 (0,022) 0,035 (0,012) 0,015 (0,005) 0 ,007 (0,002)

T h u s t h e e f f e c t of be

important not

water

t i d a l mixing

only on the

shallow sides of

on t h e deep s i d e of

the

f r o n t s where t h e

the biological

nally high.

is p r o b a b l y n o t

It

f r o n t where a

production

bined a c t i o n o f

transport wind

i s known

l i k e

to be e x c e p t i o -

too s p e c u l a t i v e t o g u e s s t h a t

hiqh p r o d u c t i o n t o a l a r g e e x t e n t two-way

thermocline exists.

areas where s t r o n g t i d a l c u r r e n t s e x i s t s ,

I n many s h a l l o w s h e l f

the North Sea,

the

the

i s v e r t i c a l l y h o m o g e n e o u s a l l t h e way t o t h e bottom b u t a l s o

far out

of

upon t h e primary production should

t h i s

is dependent upon t h e e x i s t e n c e

through the pycnocline caused

b y t h e com-

and t i d a l mixing.

DISCUSSION The p e r h a p s m o s t

interesting

thermocline model developed turbulence far outside

i n the the

although there

lower

front.

r e s u l t obtained from t h e

i n t h i s paper

layer There

affects

upon t h e p r i m a r y p r o d u c t i o n o f i n the

the upper

wind-mixed

layer

i s a n e x c h a n g e b e t w e e n t h e two l a y e r s

is a thcrmocline.

nutrients available

two-layer

is t h a t t h e t i d a l l y d r i v e n

T h i s may h a v e a v e r y l a r g e i n f l u e n c e

b i o l o g i c a l matter

upper

as t h e amount o f

layer during the growth season

m a y i n c r e a s e by u p t o o n e o r d e r o f m a g n i t u d e . I n p r o d u c t i v i t y and e c o s y s t e m g o d e l s t h e r e is a need for a n e q u a t i o n for nut-rient concent r a t i o n . T h e m o r e r e a l i s t i c t h e p i c t u r e of t h e p h y s i c a l p r o c e s s e s

Is t h e b e t t e r w i l l be t h e e q u a t i o n for thn n u t r i e n t c o n c e n t r a t i o n and t h e r e b y a l s o t h e b i o l o g i c a l model. W i t h t h e h e l p o f t h e t h e r m o c l i n e m o d e l d e v e l o p e d in t h i s paper and k n o w i n g t h e l o c a l v a l u e s of bottom

( t i d a l ) c u r r e n t s , w i n d s and

heat e x c h a n g e t h r o u g h t h e s e a s u r f a c e it s h o u l d be p o s s i b l e t o make d e t a i l e d c a l c u l a t i o n s o f t h e e x p e c t e d e x c h a n g e t h r o u g h t h e thermoc l i n e , V , for s p e c i f i c s h e l f areas. T h e a i m w i t h t h i s p a p e r , however, is j u s t t o d e m o n s t r a t e t h e s i g n i f i c a n c e o f t h e e f f e c t and not t o m a k e a d e t a i l e d !napping of t h e e x p e c t e d v e r t i c a l e x c h a n g e t h r o u g h t h e t h e r m o c l i n e for e.g.

t h e N o r t h Sea.

A'nother r e s u l t f r o m t h e t h e o r e t i c a l m o d e l is t h e l i m i t w h e r e the two-layer

stratification breaks down into a single, homogeneous

l a y e r . I t t u r n s o u t t h a t t h e e x p r e s s i o n for the water d e p t h a t w h i c h t h i s o c c u r s , and the s h e l f f r o n t c a n be e x p e c t e d t o be found, w i t h tlie w i n d e f f e c t i n c l u d e d , is e q u i v a l e n t t o t h a t g i v e n by S i m p s o n , A l l e n and M o r r i s

(1978).

T h e l o g i c a l e x t e n s i o n o f t h e p r e s e n t w o r k , in a fluid d y n a m i c a l s e n s e , is to c o n s t r u c t a m o d e l in w h i c h t h e p r e s s u r e g r a d i e n t s , c a u s e d by t h e n o n - u n i f o r m m i x i n g , g e n e r a t e h o r i z o n t a l c u r r e n t s . T h e s e c u r r e n t s s h o u l d a t l e a s t p a r t l y be g e o s t r o p h i c a l l y balanced. Fr,?ntal d y n a m i c s in rotatinij s y s t e m s i s , h o w e v e r , a d i f f i c u l t topic and o n e m a y not hope f o r a q u i c k p r o g r e s s . T h e d i s c u s s i o n o f shelf f r o n t d y n a m i c s g i v e n by S i m p s o n , A l l e n and M o r r i s

( 1 9 7 8 ) underlines

this last conclusion.

AC K N O W L E D G E M E N T T h e n u m e r i c a l e x p e r i m e n t w a s c a r e f u l l y c o n d n c t e d by Mr O l a Akerlund

REFERENCES

I

D e f a n t , A., 1961. P h y s i c a l O c e a n o g r a p h y , vo1.2. P e r g a m o n P r e s s , 5 9 8 p Fearnheacl, P.G., 1975. O n t h e f o r m 3 t i o n o f f r o n t s b y t i d a l mixing around tlie B r i t i s h T s l e s , D e e p - S e a R e s . , 22: 3 1 1 - 3 2 1 . N i i l e r , P . P . , 1977. O n e - d i m e n s i o n a l m o d e l s o f t h o s e a s o n a l thermoclin In G o l d b e r g , E.D., M c C a v e , I.N.,O'Brien, J.J. and S t e e l e , J.H. ( e d i t o r s ) , T h e S e a , J o h n W i l e y & Sons, p p . 9 7 - 1 1 5 . P i n g r e e , R . D . and G r i f f i t h s , D.K., 1978. T i d a l f r o n t s o n the shelf a r e a s a r o u n d t h e B r i t i s h I s l e s , J.Geophys.Res., 8 3 : 4 6 1 5 - 4 6 2 2 . S i m p s o n , J . H . and H u n t e r , J . R . , 1 9 7 4 . F r o n t s in the Irish S e a , Nature, 250: 404-406. 1978. F r o n t s o n the S i m p s o n , J.H., A l l e n , C.M. ~ n c l M o r r i s , N . C . G . , c o n t i n e n t a l s h e l f , LJ.Geoptivs.Res., 3 3 : 4 6 0 7 - 4 6 1 4 . S i m p s o n , J.H. a n d R o w e r s , D.: 1980. M o d e l s o f s t r a t i f i c a t i o n and (Unpublished manuscript) frontal m o v e m e n t i n si:c?~f8 e a s .

65 Steele, J.H., 1974. The s t r u c t u r e o f m a r i n e e c o s y s t e m s , Harvard U n i v e r s i t y Press, 1 2 8 p p . Turner, J.S., 1973. Buoyancy e f f e c t s i n f l u i d s , Cambridge U n i v e r s i t y Press, 3 6 7 pp.

This Page Intentionally Left Blank

67

VERTICAL MIXING, A CONSTRAINT TO PRIlilARY PRODUCTION : HI^

EXT,5tVSION OF TFE CONCEPT OF AN OPTI>@L MIXING ZCNL

CHARLES S. YENTSCH Bigelow Laboratory for Ocean Science, West Boothbay Harbor, ME USA

04575

ABSTMC?'

The tieating by the sun's energy provides buoyancy to surface layers of tile oceans which limits vertical mixing of the entire water column. A water column stratified by tlie buoyancy of tne surface layers is low in important nutrients; thus, primary production and tne stocks of phytoplankton are small.

The buoyancy

of surface layers and resulting stratification of tlie water column is a constraint to primary production and in turn to the ecosystem as a whole.

Kenewewed vertical mixing of the water

column emphasizes the importance of an optimal depth of mixing: tnis is the zone of the mixed layer where stresses due to lignt limitation are balanced by the addition of nutrients to surface layers.

INTRODUCTION With the seasonal cnange in solar input which regulates the light intensity directly and the winds as stirring forces indirectly, tne mixeu layer depth can be viewed deepening and snoalinq in response to these forces.

At some zone an optimum is reached

wiien the detrimental effects of vertical mixing (i.e. lignt

limitation) are compromised by the benefits of vertical mixing (advection of nutrient-ricn water).

This depth, or more properly

"zone", is tne level of optimal mixing,

--

optimal conditicns for

phytoplankton production in a mixed water column. To introduce the reader, a famous model was proposed by Sverurup in 1953 which aemonstrated the role played by vertical mixing in light limiting primary production.

Later an important

contribution by Cu-shing (1962) emphasized the interaction of

68

photosynthesis, respiration and vertical mixing.

In the Sargasso

Sea Steele and Menzel (1962) applied light-limited concepts in concert with flux to describe the seasonal sequence of primary production. Thus the Steele and Menzel model 'introduced the concept of an optimal mixing depth. In my opinion, the general importance of this concept is still not fully appreciated. Although the dual-antagonistic role of vertical mixing has long been recognized, the concept of an optimal mixing depth zone and the factors regulating this zone are seldom addressed. The point of this paper is to extend the importance of this concept. Ily approach will be mechanically different from Steele and Menzel's, however, the concept is similar. One of the beauties of these models has been their simplicity. Thky tend to indicate specific topics where further research is needed either in the biological or physical processes of the system. Recent refinements have largely concerned the addition of physiological complexities. In my opinion, these recent formulations have tended to obscure the important interactions. But the point of this paper is not to discuss the inadequacies of these models, but to identify and reemphasize the degree to which mixing controls primary production. In the course of developing the optimal mixing depth concept, I believe the inadequacy of the modeling will become apparent. are ripe for future research.

It is these inadequacies which

Concepts concerning vertical mixing As the depth of thE mixed layer changes, the phytoplankton are subjected to changes in I) the average light quality and quantity and 2) the average nutrient concentration. As the mixed layer deepens, the average light intensity to the cells decreases, whereas the availability of nutrients depends on the scaler gradient of that substance distributed over the depth of the water column. It is the product of these two processes which establishes the potential for primary production in the water column. Thus, the mechanical effects of mixing on primary production concern two processes related to phytoplankton growth, namely light limitation of photosynthesis, and the availibility and uptake of nutrients. Light Limitation: In traditional mi.xing-production models, the depth where photosynthesis and respiration are equal is termed the critical mixing depth.

At the crux in the development

69

of these models is the relationship between the rate of phctosynthesis and the rate of respiration integrated over the depth in the mixeu water cclumn. For the persons unfamiliar with these models, I will very briefly describe the components. For more (1977). detail the reader is referred to Platt c t u Z . , The components of a so-called "integral model" are the relationship of photosynthesis and light, the so-called P vs I (photosynthesis vs. irradiance) curve and the distribution of downwelling irradiance, (Figure 1) .

k - - Pt

-~

Pt-P,= R

Pmax

z

/I/

+I I / 3

z,

-7

Fig. 1. (A) (B) (C) Components of the integral model. Curve A. The relationship between light and photosynthesis where P is total daily photosynthesis Pn is total daily net photosynthet sis. C is the compensation point and Ci is the compensention intensiEy. (Redrawn from Yentsch 1975). Curve B is the downwelling irradiance (I) in the water column of depth 2. Curve C is the product of A and B and represents the integral model in a water column of depth 2. Zc is the compensation depth and Ze the euphotic depth in meters. The prouuct of those two components yields the water column integral model shown in Figure lc. As the mixed layer deepens below the euphotic depth, the effect is to enlarge the influence of respiration. Therefore, as the mixed layer deepens, the relationship of (Pt:R) changes because of the increasing amount of R to the system. As previously mentioned, when (Pt:R) equals 1.0, there is no net production for the population. The depth of mixing responsible for this relationship is the critical mixing depth. Ir. the development of these models, one in forced to generalize

as to the interaction of light and photosynthesis and the assignment of the level of respiration.

The relationship between

70

photosynthesis and irradiance that I will use was obtained empirically from field data where the uptake of ca.rbon-14 was measured at light intensities ranging from 100% to 18 of sunlight (Yentsch, 1975 ) The model uses values for R expressed as a percentage of Pmax. Most commonly used is 10% which was an average obtained from field measurements by St.eemen-Nielsen and Hansen (1959). Using sensitive ETS measurements, Devol and Packard (1978) have found values for to'tal respiration to range between 2-45% with a mean around 5% of Pmax. There is no satisfactory method for measuring R specific for phytoplankton populations, and R undoubtedly varies a.s a function of species and population physiol.ogy. The values (Pt:R) were obtained by manually integrating the areas under the photosynthesis and respiration curves. The solar input and transmission features are generalized by selecting three euphotic depths which attempt to characterize the extremes founa in ocean environments (Figure 2).

01.O

2 .o i

3.0

4.0

5.0

t

I

I

A - COASTAL - Ze

30M

8-SLOPE - Z e

60M

C-

OFFSHORE Ze OCEANIC

6.0

1

I 2o

800 J

Fig. 2. Changes in Pt:R as a function of vertical mixing for three euphotic depths. (From Yentsch 1 9 7 5 ) .

( 2m )

The value (Pt:R) refers to the photosynthesis respiration ratio for populations where the mixed. layer depth in meters (Zm) is The results shown in equal to the euphotic depth in meters (2,). figure 2 demonstrates that the relationship between (Pt:R) and Zm is hyperbolic when Zm exceeds the d.epth of the euphotic zone

(Ze). Thus phctosynthetic to respiration ratios can be calculated for any mixed layer depth below the euphotic zone as follows: (Pt:R) = b/ZT,

(1)

Where b is a constant.

The two primary points on the curves

needed for the calculation are the euphotic depth (Ze) for a 0 given (Pt:R) and the critical depth (Zcr). Substitution in equation 1 , 0

(Pt:R) = b/Ze 1

=

and

(2)

b/Zcr.

(3)

From equation 2 one can write, 0

b = (Pt:R)

0

x Z and (Pt:R) = (Pt:R) e

x Ze/Z,.

The critical depth calculation is, Zcr =

(Pt:R)0 x Ze or,

(Pt:R)

=

Zcr/Z

m

(5)

(6)

The hyperbolic relationship between (Pt:R) and Zm demonstrates that the former decreases rapidly as the depth of mixing initially exceeds the euphotic depth. (Pt:R) declines more gradually as the critical depth is approached. For very transparent waters the critical depth (Zcr) resides at about 700 meters which is more than twice the observed isothermal layer depth in the Saryasso Sea. This suggests that if the assumption concerning respiration is correct then light limitation due to vertical mixing is never a severe problem to these populations.

The effect of decreasing the euphotic depth is to reduce the depth of critical mixing: In areas where the euphotic depth is shallow, small changes in vertical mixing markedly effect the ratio of photosynthesis to respiration. Therefore, the first point I wish to emphasize is that the role of vertical mixing - considering light effects alone - is to be a detriment to phytoplankton growth. And the severity of this detriment is strongly dependent upon the depth of the euphotic zone.

To emphasize this point, if we are to

72

dutrient Supply:

As tile mixed layer erodes the water column,

in autumn nutrient-rich water is advected into the euphotic zone. Consider the situation where a mixed layer gradually appears in a stratified water column. As the mixed layer deepens, it penetrates layers containing high concentrations of nutrients.

These are

entrained by the mixed layer. If the vertical distribution of nutrient concentration prior to mixing is known - the amount of nutrient (eg. nitrate) entrained (N m) is calculated by, 2'

m Nz,m =

0

NO -N 3

x

(7)

dz

To demonstrate the importance of the nutrient concentration compare the depth profiles for nitrate-nitrogen in the Sargasso Sea to that f o r the Gulf of Maine. Note that for mixing to entrain waters having 1.0 microgram atom per liter will entail a penetration to 30 meters in the Gulf of Maine while 100 meters in the Sarqasso Sea would be required. This difference illustrates the considerable difference in the amount of nitrate swept into the mixed layer (Figure 4). p g otoms liter

0

200

400

600

NO3-N ( p 4 O I O r 5 )

800

loci0

through deplh

I200

14

Zm

Fig. 4. The influence of concentration of nitrate as a function of depth and the level of entrainment of nitrate in the mixed layer. Data for Sargasso Sea ( S S ) taken on September 15, 1958, Lat. 32'10'N, Long. 64O3O'W. (Tech Rept. Bermuda Biol. Station 1960). Data for t the Gulf of Maine (GM) taken on September 2 1 , 1966 Atlantis 1001, Lat. 42°45'N, Long. 69O54'W. (T'ech. Report W.H.O.I. 67-27).

73

assume that respiration is approximately 10% of Pmax, then for a rough rule of thumb t,he depth of critical mixing can be estimated to be six times the euphotic depth. This estimate is very close to the measured values published by Gran and Brauud (1935). The effect of increasing the rate for respiration is to accentuate the influence of vertical mixing on the ratio of photosynthesis to respiration. Figure 3 illustrates the degree of accentuation.

1.0

2.0

3.0

5.0

4.0 I

1

I

6.0 10%

-cn -800I L

W

+ W

E

0

1.0 Ze

2.0

3.0

4.0

I

I

I

30%

20%

5.0

6.0

I 1 1 I

10O/O

v

E N

Fig. 3. Changes in Pt:R as a function of respiration for two euphotic depths (Ze). Here three values of respiration are shown in conjunction with two euphotic depths and demonstrates that if respiration is higher than 10% of Pmax then maximum isothermal mixed layers commonly observed (100-200m) are potentially capable of housing populations which are light limited.

74

For those unfamiliar, the emphasis on nitrate as a limiting substance may seem simplistic. Perhaps it is. However, conventional wisdon is that the amount of nitrate regulates and limits primary production in the sea. There are other forms of nitrogen. present however, it is the amount of nitrate which dictates net population growth. Tnus the low level of primary productivity in the Sargasso Sea as compared to the Gulf of Maine become apparent from the data shown in Figure 4. With the source of the limiting substance housed in layers below the euphotic zone and vertical mixing the principal means of transporting these to the surface - then for the same amount of work needed to mix the water columns the Sargasso Sea populations get much less than populations in the Gulf of Maine. Combination of light limitation with nutrient flux Assume that other than light, nitrate-nitrogen is limiting. The manner in which (Pt:R) change in the mixed layer can be estimated as follows. For comparison, the two areas, Sargasso Sea and the Gulf of Maine will be used. First, the critical depth (Zcr) is determined using equation 5. The value for Ze in the Gulf of Maine is 30 meters and 120 meters in the Sargasso Sea. The value (Pt:R)O is assumed to be 6.0 for populations in either area. For each, 10 meters of mixed depth (Pt:R) was calculated using equation 6. Phctosynthesis to respiration ratios are then placed in the context of net production (P,) , (Pt:R) values are normalized over the range 0 - 10 by,

The product of equation (7) and equation (8) yield the relative value of net production as a function of mixed layer depth,

where both the effects of light and nutrients are involved. At the optimal depth for vertical mixing ( Z opt) '

For the Gulf of Maine, Z centers around 90 met.ers. The opt critical depth (Zcr) for this region is 160 meters. For the

75

Sargasso Sea, Z centers around 250 meters with the critical opt depth Zcr at 700 meters.

I oc

20c 30C A

E 400 N v

500 600 700

Fig. 5. The influence of relative net production by the combined effects of light limitation and nutrient advection. For the Gulf of Maine (GM) Ze is 30 meters, for the Sargasso Sea ( S S ) 120 meters. These curves are interpreted to mean that as the penetrative mixing progresses to the optimum, the maximum amount of nutrient is entrained and the population is not overly stressed by light limitation. Further deepening of the mixing layer forces the population into a situation where nutrients are excessive, and light-limitation becomes the important factor. Obviously, mixing shallower than the optimum permits ample light yet the population is not supplied with enough nutrient to overcome a limitation.

76

Unlike the rather direct relationship between Z cr and Ze, no simple general relationship can be established between Z and opt Z or Zcr. This is largely because the Z is strongly influenced e opt by the depth distribution of the limiting nutrient. In general, the effect of either increasing respiration or decreasing the euphotic depth is to make the optimal depth shallower. DISCUSSION One dimension to two - the influence of baroclinicity For sake of this discussion it is convenient to divide the optimal mixing depth model into two compartments - light and

nutrients. In the "light" compartment it is possible to describe the relationship between mixed layer depth and (Pt:R) from fundamental principles of photosynthetic kinetics combined with assumptions concerning the magnitude of respiration. By contrast, the "nutrient" compartment requires knowing the depth profiles of the specific nutrient and an empirical calculation of entrainment. I n t h e one dimensional-depth t h e d e n s i t y d i s t r i b u t i o n of

model t h i s i s m a r k e d l y i n f l u e n c e d b y t h a t water mass; Furthermore

if

t h e nu-

t r i e n t - d e n s i t y r e l a t i o n s h i p i s p r o j e c t e d a s a c r o s s s e c t i o n of t h e w a t e r mass,

thereby adding t h e dimension of

distance,

the depth of

c r i t i c a l and o p t i m a l mixing w i l l be markedly a f f e c t e d by t h e d e n s i t y s t r u c t u r e i n w a t e r mass.

The degree of baroclinicity is proportional to geostrophic flow or mass transport in the horizontal direction. Thus the extremes in mass transport will reflect extremes in optimal and critical depths. To be specific, the large gyre as we have observed in Sargasso Sea will have deep critical and optimal depths. Whereas regions of active transport, e.g. where isopycnals are uplifted, will have shallow critical and optimal depths. The examples set down here as two extremes argues that in areas where high density nutrient rich water is near the surface (e.g. Gulf of Maine) the amount of nitrate supplied by mixing is greater than in the Sargasso Sea. Hence the standing crops of phytoplankton in the Gulf of Maine is proportionally greater than in the Sargasso Sea. This is clearly borne out by sea surface measurements (See Yentsch, 1974). This suggests that spatial patterns in primary production might be accurately assessed from estimates which combine baroclinicity and the depth of the mixed layer. The idea is not new, but

requires knowing the d.ensity distribution on a reasonably fine scale. It is possible to obtain the necessary data in areas where baroclinic change occurs over very short distances - for example in frontal regions. I have combined this approach with modeling to describe features such as the optimal and critical mixing depth. The model however fails in these frontal regions because there is no theory to combine isopycnal with vertical mixing. In other words, there is no way of estimating the mixing depth when isopycnals are anything less than vertical. SUMMARY The principal factors regulating phytoplankton growth in a mixed layer have been summarized. A two compartment model demonstrates
78

REFERENCES D.H. Cushing, An alternative method for estimating the critical depth. Jour. Cons. Perm. Int. Explor. Mer., ~ ( 1 9 6 2 ) 1 3 1 - 1 4 0 . H.H. Gran and T. Braruud, A quantitative study of the phytoplankton in the Bay of Fundy and the Gulf of Maine, J . B i o l . B d . C a n a d a , L(1935) 279-467. T. Platt, K. Denman and Alan Jassby, Modeling the productivity of phytoplankton, in THE SEA, 5(1977)807-856.

J.H. Steele and D.W. Menzel, Conditions for maximum primary production in the mixed layer, D e e p - s e a R e s e a r c h , 2(1962)3949. Steemann Nielsen and V . K . Hansen, Measurements with the carbon-14 technique of the respiration rates in natural populations of phytoplankton, D e e p - s e a R e s e a r c h , g(1959) 222-233. C.S. Yentsch, The influence of geostrophy on primary production, Z ' e t h y s , 5(1-2) (1974), p. 111. Yentsch, Critical mixing depth, in J.J. Cech Jr. e t a l . , (eds.) RESPIRATION OF MARINE ORGANISMS, Maine vs. Marine Biomed Sym. 1975, pp. 1-10.

C.S.

79

AN INVESTIGATION O F SEASONAL UPWELLING ALONG THE ATLANTIC COAST OF

FLORIDA NED P .

SMITH

Harbor Branch F o u n d a t i o n , I n c . R.R.

I , B o x 1 9 6 , F o r t Pierce, F l o r i d a 3 3 4 5 0 , U.S.A.

ABSTRACT S u b s u r f a c e w a t e r t e m p e r a t u r e d a t a a r e combined w i t h t i m e s e r i e s o f c o a s t a l winds and mid s h e l f c u r r e n t s t o i n v e s t i g a t e s e a s o n a l u p w e l l i n g i n s h e l f w a t e r s o f f South F l o r i d a ' s A t l a n t i c c o a s t .

Data from t h e

summer of 1 9 7 8 i n d i c a t e t h a t c o o l w a t e r moved o n t o t h e s h e l f by mid June and remained t h e r e u n t i l e a r l y September.

A t i m e series o f n e a r -

bottom t e m p e r a t u r e s from i n n e r s h e l f waters i n d i c a t e s t h r e e m a j o r p e r i o d s o f c o o l i n g , l a s t i n g o v e r t i m e i n t e r v a l s o f from one t o t h r e e weeks.

Water t e m p e r a t u r e s d e c r e a s e from

3 O

t o 7OC.

c o o l i n g e v e n t s are r e c o r d e d t h r o u g h o u t t h e r e c o r d .

More t r a n s i e n t The e f f e c t o f up-

w e l l i n g i s t o d e c r e a s e c o a s t a l water t e m p e r a t u r e s t o l e v e l s c h a r a c t e r -

istic of e a r l y winter o r late spring.

The c o h e r e n c e of n e a r - b o t t o m

t e m p e r a t u r e s r e c o r d e d o v e r t h e i n n e r s h e l f and j u s t beyond t h e s h e l f b r e a k i s l o w , and i n n e r s h e l f n e a r - b o t t o m t e m p e r a t u r e s a r e n o t s i g n i f i c a n t l y coherent with e i t h e r t h e longshore o r cross-shelf of t h e w i n d s t r e s s .

component

I t i s t h e r e f o r e u n l i k e l y t h a t Ekman dynamics p l a y

a m a j o r r o l e i n d r i v i n g u p w e l l i n g a l o n g t h i s p a r t of t h e coast.

Mid

s h e l f , near-bottom t e m p e r a t u r e s a r e c o h e r e n t w i t h t h e longshore c u r r e n t o v e r t i m e s c a l e s i n e x c e s s o f a b o u t two d a y s .

This suggests

t h a t u p w e l l i n g o c c u r s a s a dynamic a d j u s t m e n t t o v a r i a t i o n s i n t h e Florida Current.

----____________________________________-----------------INTRODUCTION

The p r o x i m i t y o f t h e F l o r i d a C u r r e n t t o t h e A t l a n t i c c o a s t o f S o u t h F l o r i d a h a s a dominant e f f e c t upon b o t h t h e h y d r o g r a p h y and t h e e c o l o g y of s h e l f w a t e r s .

The m a j o r i t y of p h y s i c a l a n d b i o l o g i c a l i n v e s t i g a -

t i o n s conducted i n t h e r e g i o n t h e r e f o r e have e i t h e r f o c u s e d d i r e c t l y upon some a s p e c t o f t h e F l o r i d a C u r r e n t , o r have had t o b e i n t e r p r e t e d

80 i n t e r m s o f one o r more o f i t s p h y s i c a l c h a r a c t e r i s t i c s . S t u d i e s o f t h e F l o r i d a Current covering t h e p a s t t h r e e decades have e v o l v e d from more g e n e r a l , d e s c r i p t i v e i n v e s t i g a t i o n s t o t h o s e dealing with p a r t i c u l a r processes o r events.

I n t e r e s t has focused

s p e c i f i c a l l y upon c h a r a c t e r i s t i c s o f t h e q u a s i - s t e a d y

f l o w , and upon

c y c l o n i c e d d i e s t h a t form a l o n g t h e s t r o n g s h e a r zone on t h e w e s t e r n edge of t h e c u r r e n t .

E d d i e s i n p a r t i c u l a r have t h e e f f e c t of c l e a n s -

i n g t h e s h e l f by mixing s h e l f w a t e r s w i t h w a t e r from w i t h i n t h e Florida Current.

L e e (1975) and L e e and Mayer ( 1 9 7 7 ) have d e s c r i b e d

t h e t y p i c a l l i f e c y c l e of s p i n - o f f 26O-27ON.

e d d i e s n o r t h of a p p r o x i m a t e l y

E d d i e s a r e a d v e c t e d northward w i t h t h e F l o r i d a C u r r e n t ,

b u t a t a somewhat s l o w e r s p e e d . An eddy embedded a l o n g t h e edge o f t h e F l o r i d a C u r r e n t h a s t h e e f f e c t bf p e r t u r b i n g t h e s t r e a m l i n e s of t h e q u a s i - s t e a d y

flow.

Mean-

d e r i n g i n t h e s t r e a m l i n e s h a s been d e t e c t e d b o t h by s a t e l l i t e imagery (Vukovich and Crissman 1 9 7 9 ) and by drogue measurements (Chew and B e r b e r i a n 1 9 7 0 , Richardson et a 1 1 9 6 9 ) .

Wavelengths may v a r y c o n s i d -

e r a b l y b u t a r e g e p e r a l l y on t h e o r d e r o f 1 0 0 - 2 0 0 km.

Chew and B e r -

b e r i a n found a n a m p l i t u d e o f 5 km f o r a meander i n t h e s t r e a m l i n e s i n t h e F l o r i d a S t r a i t s ; Webster ( 1 9 6 1 ) h a s s u g g e s t e d t h a t t h e a m p l i t u d e

of meanders o f f Onslow Bay (34'N)

i s on t h e o r d e r o f 1 0 km.

The gen-

e r a t i o n mechanism o f b o t h t h e e d d i e s and t h e meanders i s n o t w e l l u n d e r s t o o d , b u t Diiing e t a1 ( 1 9 7 7 ) have c o r r e l a t e d low-frequency v a r i a t i o n s i n t h e f l o w o v e r t i m e s c a l e s on t h e o r d e r of one t o two weeks w i t h m e t e o r o l o g i c a l f o r c i n g i n t h e form o f w i n d s t r e s s .

A l l of

t h e s e low-frequency v a r i a t i o n s a r e superimposed o n t o a n a n n u a l p a t t e r n which i n c l u d e s a mid summer maximum i n volume t r a n s p o r t ( N i i l e r and Richardson 1973)

.

Complementing t h e s e p h y s i c a l i n v e s t i g a t i o n s are b i o l o g i c a l s t u d i e s involving t h e e f f e c t of t h e F l o r i d a Current on F l o r i d a s h e l f w a t e r s . These i n c l u d e a n i n v e s t i g a t i o n which focused upon t h e c a l i c o s c a l l o p i n waters o f f Cape C a n a v e r a l (Lemming 1 9 8 0 ) , and a n o t h e r which des c r i b e d d i f f e r e n c e s i n phytoplankton a c r o s s t h e s h e l f a t t i m e s before and a f t e r t h e o n s e t of summer u p w e l l i n g (Green 1 9 7 9 ) .

Atkinson e t ai!

(1978) have shown t h a t i n t r u s i o n s o f Gulf Stream w a t e r o n t o t h e Florida c o n t i n e n t a l s h e l f a t l a t i t u d e 3 0 ° N correspond with high chlorophyll and d e n s e zooplankton p o p u l a t i o n s , a s a r e s u l t o f t h e shoreward t r a n s p o r t of n u t r i e n t s a t near-bottom

levels.

A l l of t h e s e i n v e s t i g a t i o n s

i n c l u d e d s h e l f hydrography d i r e c t l y o r i n d i r e c t l y i n t h e form o f t h e a n n u a l l y r e c u r r i n g upwelling--a

phenomenon found t o b e b e s t d e f i n e d

between a p p r o x i m a t e l y 27" and 28ON d u r i n g J u n e , J u l y and August.

81 S t u d i e s o f u p w e l l i n g i n A t l a n t i c s h e l f waters o f t h e s o u t h e a s t e r n U n i t e d S t a t e s c a n b e t r a c e d b a c k n e a r l y f o u r d e c a d e s t o a n o t e by Green ( 1 9 4 4 1 , which i n c l u d e d some p r e l i m i n a r y f i n d i n g s and documented a n o m a l o u s l y low s u r f t e m p e r a t u r e s a l o n g t h e c o a s t o f F l o r i d a a t a b o u t 29ON.

T h i s summertime f e a t u r e was a t t r i b u t e d t o an a n n u a l l y r e c u r r i n g

u p w e l l i n g which w a s most a p p a r e n t when s h e l f waters were a t t h e i r ann u a l maximum t e m p e r a t u r e , a n d t h u s i n g r e a t e s t t h e r m a l c o n t r a s t w i t h t h e c o o l e r , u p w e l l e d w a t e r from f u r t h e r o f f s h o r e . s i v e follow-up

A m o r e comprehen-

s t u d y ( T a y l o r and S t e w a r t 1 9 5 7 ) i n c o r p o r a t e d a l a r g e r

d a t a b a s e , which i n c l u d e d m o n t h l y mean w i n d s from c o a s t a l s t a t i o n s . W i n d s t r e s s w a s p o s t u l a t e d t o b e t h e dominant d r i v i n g f o r c e f o r t h e observed upwelling.

F i g u r e 1 I s b a s e d upon d a t a p r e s e n t e d by T a y l o r

and S t e w a r t , a n d shows t h e t h e r m a l e f f e c t s o f c o a s t a l u p w e l l i n g conf i n e d i n f i m e t o t h e m i d summer months and r e s t r i c t e d i n a s p a t i a l s e n s e t o t h e c o a s t l i n e between a p p r o x i m a t e l y 2 7 " a n d 30"N.

Intrusions

F i g . 1. M u l t i - a n n u a l mean m o n t h l y s u r f t e m p e r a t u r e s ( i n " C ) f o r summer months b e t w e e n 2 4 O a n d 33'N. A f t e r T a y l o r and S t e w a r t ( 1 9 5 7 ) .

of o p e n o c e a n w a t e r a t n e a r - b o t t o m l e v e l s o v e r t h e s h e l f h a v e b e e n n o t e d somewhat f u r t h e r n o r t h , i n t h e Onslow Bay a r e a ( B l a n t o n 19711, t h o u g h t h i s Gulf S t r e a m w a t e r may n o t move o n t o t h e i n n e r s h e l f . Several possible causes of t h i s cross-shelf

e x c h a n g e mechanism i n -

c l u d e w i n d s t r e s s , Gulf S t r e a m meanders a n d a c c e l e r a t i o n s of t h e Gulf Stream. The l i n k b e t w e e n s h e l f u p w e l l i n g , o r i n t r u s i o n s o f open o c e a n w a t e r , and a m a j o r c o a s t a l boundary c u r r e n t w a s f i r s t s u g g e s t e d by Bumpus ( 1 9 5 5 ) , who d e s c r i b e d t h e p r o c e s s i n s h e l f w a t e r s s o u t h of Cape Hatteras.

More r e c e n t l y , Hsueh a n d O ' B r i e n

a t h e o r e t i c a l account of t h e p r o c e s s .

(1971) have g i v e n

The u p w e l l i n g mechanism i n -

v o l v e s t h e d e t e r i o r a t i o n o f g e o s t r o p h y when a l o n g s h o r e c u r r e n t comes i n contact with a continental slope o r shelf.

A frictional retarda-

82

tion of the flow at near-bottom levels results in a decrease in the Coriolis force at that depth and at least a temporary dominance of the pressure gradient. In a case where the longshore motion is to the north and the coast lies to the left--as with the Florida Current moving along the Atlantic coast of South Florida--a dominance of the pressure gradient force in the benthic boundary layer will accelerate near-bottom water shoreward. Continuity then requires a compensating offshore transport in the surface layer. The result will be an upwelling pattern that may be indistinguishable in appearance from another driven by surface windstress. The difference will be that the former will be coherent with the longshore current, while the latter will be coherent with the longshore windstress. In view of the meandering nature of the streamlines in the Florida Current, one may expect coastal upwelling to occur in the form of events, with a temporal variability similar to that of the meanders themselves. This paper presents results of a recent study conducted to document and characterize upwelling in Atlantic shelf waters off Fort Pierce, Florida, near latitudPs 27O30'N (Fig. 2). The eastern extreme of the

W

a\-

Fig. 2. Study area on the Atlantic shelf of South Florida. Hatched line shows multi-annual mean position of Florida Current and Gulf Stream. study area is directly affected by the Florida Current continuously. Effects which may be traced back at least indirectly to the Florida Current move shoreward across the study area with lesser frequency. The study combined sub-surface temperature measurements with time series of coastal winds and mid shelf currents to investigate upwelling

83

as a response to both windstress and the Florida Current. The purpose here is to focus upon the cause of the seasonal upwelling in these shelf waters and thereby complement previous and ongoing studies of the effects on local plant and animal populations.

THE OBSERVATIONS Temperature data needed to document upwelling were obtained in two ways- Top-to-bottom temperature profiles were recorded with a Plessey Model 9 0 6 0 Salinity-Temperature-Depth Profiling System, or with a Beckman Model RS5-3 Field Salinometer in the shallow waters of the inner shelf. Temperatures were digitized at intervals of 1 m or 2 . 5 m, depending upon the vertical temperature gradients at the time and the place of measurement. Temperature profiles were calibrated at top and bottom levels with reversing thermometers. Corrected temperatures are accurate to within 0.2OC. Seven stations were visited weekly between 1 8 July and 2 9 August, and again on 26 September, 1 9 7 8 . Figure 3 shows the sampling sites for the 1 9 7 8 study. Stations were equally spaced between the first, in approximately 8 . 5 m of water 1.5 km from the coast, and the seventh, in 103 m of water 33 km from the coast and at a point just beyond the shelf break. Station relocation was by LORAN-C on the R/V SEA DIVER. Environmental Devices Corporation Type 1 0 9 temperature recorders were positioned just above the bottom on a taut-line mooring at Station 1 and Station 7. Temperatures were recorded bihourly between 31 May and 2 4 September at the inner station, and between 2 2 June and 16 August at the outer station. Temperature recorders were accurate to 0.2OC, according to the manufacturer's specifications. Environmental Devices Corporation Type 105 recording current meters were used at Station 1 from 13 June to 2 9 August, 1 9 7 8 , to record the net longshore drift during periods of upwelling; and again in mid shelf waters near Station 5 from 1 7 July to 2 9 September, 1 9 7 9 , to correlate variations in the longshore flow with fluctuations in bottom temperatures. The current speed and direction measurements are accurate to within 2 . 5 cm/sec and 7O, respectively, according to the manufacturer's specifications. Wind measurements were recorded with an anemometer located 7.9 km northwest of Station 1. Hourly values were digitized from an analog record that covered the time interval from 31 May through 24 September, 1978. Wind speeds were recorded to the nearest 1.6 km/hour; wind diWind vectors were converted rections were estimated to the nearest 2'.

84

t

Fig. 3 . Study area, showing t h e 1978 h y d r o g r a p h i c s t a t i o n s . Insert shows t h e s t u d y area a l o n g t h e s o u t h e a s t c o a s t o f t h e United S t a t e s . t o w i n d s t r e s s v e c t o r s , u s i n g a d r a g c o e f f i c i e n t s u g g e s t e d by Wu ( 1 9 6 9 ) f o r moderate wind s p e e d s .

The w i n d s t r e s s v e c t o r was t h e n decomposed

i n t o l o n g s h o r e and c r o s s - s h e l f

components f o r comparison w i t h t h e tem-

p e r a t u r e t i m e series from S t a t i o n 1.

RESULTS Temperature r e c o r d e r d a t a The t i m e s e r i e s o f near-bottom t e m p e r a t u r e s from S t a t i o n 1 provides a good i n t r o d u c t i o n t o t h e 1978 u p w e l l i n g s t u d y . F i g u r e 4 shows temp e r a t u r e s r e c o r d e d one m e t e r above t h e bottom between 31 May and 2 4 September. pattern.

Two p e r i o d s of r e l a t i v e l y low t e m p e r a t u r e s dominate t h e The f i r s t b e g i n s s h o r t l y a f t e r t h e s t a r t of t h e r e c o r d and

c o n t i n u e s f o r a b o u t a week.

The second o c c u r s o v e r a 24-day p e r i o d

from 2 9 J u l y t o 2 2 August.

Throughout t h e f i r s t 1 2 weeks t h e r e a r e

t r a n s i e n t p e r i o d s of c o o l i n g d u r i n g which t h e t e m p e r a t u r e may d e c r e a s e by a s much a s 3-4°C.

Lowest t e m p e r a t u r e s of about 20.5OC o c c u r i n

e a r l y August, a t t h e s t a r t o f t h e second p e r i o d of g e n e r a l l y lower temperatures.

A f t e r a r e t u r n t o t e m p e r a t u r e s of n e a r l y 2 9 O C i n l a t e

August, t h e r e i s a f i n a l b r i e f p e r i o d of c o o l i n g b e f o r e w a t e r s warm a g a i n t o 2 9 O C and remain t h e r e t h r o u g h t h e end o f t h e r e c o r d . The near-bottom

t e m p e r a t u r e s from t h e o u t e r s h e l f a r e shown i n

85

Fig. 4. Time-plot of bihourly, near-bottom temperatures (in corded at Station 1, 31 May to 2 4 September, 1 9 7 8 .

"C)

re-

Figure 5. The pattern is characterized by a series of poorly defined periods of cooling, superimposed onto a very slow cooling trend during this 58-day period of time. There is a substantial amount of highfrequency temperature variability in the bihourly values. This may reflect a vertical movement of isothermal surfaces at the top of the permanent thermociine. Lowest temperatures of approximately 8°C occur in the middle of August.

JUNE

JULY

AUGUST

Fig. 5. Time-plot of bihourly, near-bottom temperatures (in corded at Station 7, 22 June to 17 August, 1 9 7 8 .

"C)

re-

The Similarity of near-bottom temperature variations at these two locations is quantified by the coherence-squared spectrum (Fee 1 9 6 9 ) shown in Figure 6. Two peaks appear at the diurnal and semi-diurnal tidal periods, but these are most likely related to either internal wave activity or advection by tidal currents. A third peak occurs at a period of 5 0 hours, however this rises only to the 9 5 % confidence limit. Also, the phase spectrum (not shown) indicates temperature

86 v a r i a t i o n s o v e r t h e i n n e r s h e l f l e a d i n g t h o s e o v e r t h e o u t e r s h e l f by a p p r o x i m a t e l y 140O.

A t t h e very longest p e r i o d i c i t i e s ,

coherences

i n c r e a s e t o t h e i r h i g h e s t l e v e l s , b u t t e m p e r a t u r e v a r i a t i o n s o v e r the i n n e r s h e l f l e a d t h o s e o v e r t h e o u t e r s h e l f by 2 0 ' .

I n general, the

c o h e r e n c e s p e c t r u m c o n f i r m s t h e i m p r e s s i o n o n e g e t s from a q u a l i t a t i v e

PERIOD (HOURS)

Fig. 6. C o h e r e n c e - s q u a r e d s p e c t r u m computed from b i h o u r l y near-bottom t e m p e r a t u r e s a t S t a t i o n s 1 and 7 , 2 2 J u n e t o 1 7 A u g u s t , 1978. S p e c t r a l r e s o l u t i o n i s 0.0025 c y c l e / h o u r . c o m p a r i s o n of F i g u r e s 4 a n d 5:

There i s r e l a t i v e l y l i t t l e s i m i l a r i t y

i n near-bottom temperature v a r i a t i o n s recorded a t t h e s e t w o l o c a t i o n s , and c o o l i n g a t t h e s h e l f b r e a k d o e s n o t a p p e a r t o p r e c e d e l o w e r t e m peratures over t h e inner s h e l f .

Thus, i t seems t h a t c o o l e r w a t e r mov-

i n g t o w a r d t h e i n n e r s h e l f c r o s s e s t h e s h e l f b r e a k a t some l e v e l w e l l above t h e bottom. Hydrographic c r o s s - s e c t i o n s A series o f s e v e n weekly c r u i s e s , c o n d u c t e d between 1 8 J u l y and 2 9

A u g u s t , p r o v i d e d t e m p e r a t u r e c r o s s - s e c t i o n s e x t e n d i n g from t h e c o a s t t o a p o i n t a p p r o x i m a t e l y 5 km beyond t h e s h e l f b r e a k .

Data from t h e

seven s t a t i o n s along t h i s t r a n s e c t (Fig. 3 ) g i v e t h e r e q u i r e d s p a t i a l r e s o l u t i o n , and t h e weekly s a m p l i n g i n t e r v a l a p p e a r s t o b e a d e q u a t e

t o t r a c e t h e d e v e l o p m e n t and d i s a p p e a r a n c e o f t h e u p w e l l i n g p a t t e r n s t h a t appeared d u r i n g t h i s t i m e . F i g u r e 7 shows t h e t e m p e r a t u r e c r o s s - s e c t i o n o b t a i n e d from d a t a coll e c t e d on 1 8 J u l y .

A l t h o u g h d i s t i n c t l y c o o l e r w a t e r had n o t moved a l l

t h e way i n t o t h e c o a s t a t t h i s t i m e ( F i g . 4 ) , i t i s a p p a r e n t t h a t t h i s

i s n o t a pre-upwelling

pattern.

There i s a s h o r e w a r d - d i r e c t e d s u r f a c e

t e m p e r a t u r e g r a d i e n t , and 19OC w a t e r i s r e c o r d e d w i t h i n 1 2 km o f t h e

coast.

I s o t h e r m s s l o p e upward t o w a r d t h e coast a t i n t e r m e d i a t e depths.

The f o l l o w i n g week, t e m p e r a t u r e d a t a s u g g e s t a d i s t i n c t l y d i f f e r e n t and n o n - u p w e l l i n g s i t u a t i o n ( F i g . 8 ) .

Surface w a t e r s a r e very nearly

i s o t h e r m a l , t h e 1 9 O C i s o t h e r m h a s r e t r e a t e d t o t h e s h e l f b r e a k , and i s o t h e r m s g e n e r a l l y i n t e r s e c t , r a t h e r t h a n p a r a l l e l t h e bottom.

87 26 27

20

-E

28

-40-

24

26

0

5

DKm

IG

F i g . 7. Temperature c r o s s - s e c t i o n ( i n " C ) f o r S t a t i o n s 1-7, 1978. See F i g u r e 3 for s t a t i o n l o c a t i o n s .

18 July,

0 20 40

z

801

25 July

IWt

Fig.

8.

Same a s F i g u r e 7 , b u t f o r 2 5 J u l y , 1 9 7 8 .

28

22 20 18

IG 14 12

F i g . 9.

Same a s F i g u r e 7 , b u t f o r 1 A u g u s t , 1 9 7 8 .

T e m p e r a t u r e d a t a o b t a i n e d on 1 A u g u s t ( F i g . 9 ) i n d i c a t e a f u l l y d e v e l o p e d u p w e l l i n g p a t t e r n , w i t h c o o l e r w a t e r p r e s e n t a t S t a t i o n 1, 1 . 5

88

km from the coast. The time-plot of inner shelf bottom temperatures (Fig. 4 ) shows that upwelled water had arrived about three days earlier on 29 July. The 28OC isotherm is nearly 24 km offshore at the surface, and there i s a definite onshore-directed surface temperature gradient. A well developed thermocline exists seaward of a point approximately 7 km from the coast and continues to the shelf break, where it rapidly descends in the Florida Current.

Fig. 10. Temperature differences (in " C ) for the period 25 July to 1 August, 1978. Negative values indicate net cooling. TO look more closely at the 7-day interval over which the full upwelling pattern developed, a cross-section of temperature differences was constructed by subtracting values recorded on 25 July from those recorded on 1 August. The result shows the net warming and cooling that occurred across the shelf (Fig. 10). The pattern is characterized

2 5 Z 3

27

28

28 24

P E l 18 14

P Fig. 11.

Same as Figure 7, but for 8 August, 1978.

89

by n e g a t i v e v a l u e s ( n e t c o o l i n g ) a t a l l l o c a t i o n s e x c e p t i n t h e u p p e r layers over t h e shelf break.

The most pronounced c o o l i n g a p p e a r s i n

a near-bottom l a y e r , approximately 1 0 m t h i c k , w i t h l a r g e s t n e g a t i v e v a l u e s o v e r t h e i n n e r s h e l f and a t t h e s h e l f b r e a k . The t e m p e r a t u r e c r o s s - s e c t i o n

from t h e 8 August c r u i s e ( F i g . 11)

shows a c o n t i n u a t i o n o f t h e u p w e l l i n g p a t t e r n , w i t h a s t r o n g thermoc l i n e c e n t e r e d a t about t h e 10-15 m l e v e l . o v e r t h e i n n e r s h e l f a r e j u s t above 2OOC.

Near-bottom t e m p e r a t u r e s The 28OC i s o t h e r m r e m a i n s

o v e r 25 km from t h e c o a s t a t t h e s u r f a c e .

* E

-40 I

~

I-

Fig. 12.

Same as F i g u r e 7 , b u t f o r 1 5 A u g u s t , 1978.

The p a t t e r n r e c o r d e d on 1 5 August ( F i g . 1 2 ) i s b a s i c a l l y s i m i l a r t o t h a t o b t a i n e d t h e p r e v i o u s week.

The t h e r m o c l i n e i s a t a somewhat

s h a l l o w e r d e p t h i n i n n e r a n d mid s h e l f w a t e r s , s u g g e s t i n g t h a t t h e s h e l f i s c o n t i n u i n g t o f i l l w i t h c o o l e r , upwelled w a t e r .

I t i s of

i n t e r e s t t o n o t e t h a t i s o t h e r m s a t d e e p e r l e v e l s beyond t h e s h e l f b r e a k

'O0

Fig. 13.

t

Same a s F i g u r e 7 , b u t f o r 2 2 A u g u s t , 1 9 7 8 .

90

slope downward toward the coast. The temperature cross-section from 22 August (Fig. 1 3 ) shows an upwelling pattern at a time when the inner shelf bottom temperatures were rapidly increasing (Fig. 4). A very sharp thermocline at about the 10 m level over the mid shelf becomes quite diffuse over the inner shelf and beyond the shelf break. The 29OC isotherm appears for the first time at the offshore end of the cross-section. Near-bottom water beyond the shelf break has warmed substantially also.

4

2

E

v

4 .4

40.4

+6

loot

Fig. 14. Temperature differences (in " C ) for the period 15-22 August, 1978. Positive values indicate net warming. Data from 15 and 22 August have been compared to form the crosssection of temperature differences shown in Figure 14. The pattern is dominated by warming (positive differences) at all but two small areas over the outer shelf. The core of strong warming, centered at approximately 15 m over the middle shelf, is a result of a lowering of the thermocline during this period. Inner shelf waters are over 4OC warmer in near-bottom layers. The time-plot of inner shelf bottom temperatures (Fig. 4 ) indicates that rapid warming was in progress at the time the temperature profiles were obtained. The last of the weekly cruises provided a temperature cross-section that indicated a continued warming (Fig. 15). The 28OC isotherm occurs intermittently across the entire shelf, and the 22OC isotherm intersects the shelf over 10 km further from the coast than on the preceding week. A well defined thermocline persists over the outer shelf, but the water column within 10 km of the coast is very nearly isothermal. The near-bottom encroachment of cooler water is summarized by isotherms on a time-distance plot (Fig. 16), constructed from the bottom calibration temperatures for each profile. At the start of the plot,

91

ia

-

.

24

E -40 I ,

n

F

x)

0

1 "0 O0t

F i g . 15.

lOKm

5

18

\

29August

Same a s F i g u r e 7 , b u t f o r 2 9 A u g u s t , 1978.

b o t t o m t e m p e r a t u r e g r a d i e n t s a r e s t r o n g e s t o v e r t h e i n n e r s h e l f and a t t h e s h e i f b r e a k , beyond a p p r o x i m a t e l y 25 km from t h e c o a s t .

Rapid

warming d u r i n g t h e f i r s t week i n c r e a s e d n e a r - b o t t o m t e m p e r a t u r e s o v e r t h e i n n e r and m i d d l e s h e l f by a s much a s 5OC. 2 3 O C i s o t h e r m r e t r e a t e d n e a r l y 2 0 km.

During t h a t t i m e , t h e

The m a j o r u p w e l l i n g e v e n t re-

c o r d e d d u r i n g t h e s t u d y i s shown h e r e a s a s h o r e w a r d a d v a n c e o f a l l i s o t h e r m s across t h e s h e l f .

I n p a r t i c u l a r , t h e 21°, 2 2 O a n d 23°C i s o -

t h e r m s move a p p r o x i m a t e l y 23 km i n s i x d a y s , a v e r a g i n g 0 . 1 6

km/hour.

By e a r l y A u g u s t , n e a r - b o t t o m t e m p e r a t u r e s o v e r t h e i n n e r s h e l f a r e below 22"C, a n d t h e c r o s s - s h e l f

g r a d i e n t i s much m o r e u n i f o r m .

For

t h e f i n a l t h r e e weeks o f t h e p l o t , a s l o w a n d s t e a d y warming o c c u r s

F i g . 1 6 . Bottom t e m p e r a t u r e s , a s a f u n c t i o n o f t i m e and d i s t a n c e offs h o r e , 1 8 J u l y t o 2 9 A u g u s t , 1 9 7 8 . C o n s t r u c t e d from d a t a c o l l e c t e d weekly a t S t a t i o n s 1 - 7 ( S e e F i g . 3 ) .

92

across t h e s h e l f , a l t h o u g h t h i s p a t t e r n i s i n t e r r u p t e d f o r a week i n mid August j u s t beyond t h e s h e l f b r e a k .

A t t h e end o f t h e p l o t , there

i s a pronounced n e a r - b o t t o m warming w i t h i n a p p r o x i m a t e l y 2 0 km of the c o a s t , b u t o n l y s l i g h t warming o v e r and beyond t h e o u t e r s h e l f .

20 ,-. E -40 I I-

b60

ao

Fig. 17.

Same a s F i g u r e 7 , b u t f o r 2 6 S e p t e m b e r , 1 9 7 8 .

A f o l l o w - u p c r u i s e a b o u t o n e month

t e m p e r a t u r e cross-se+on

l a t e r w a s intended t o provide a

a t a t i m e w e l l a f t e r t h e upwelling period

s u g g e s t e d by T a y l o r and S t e w a r t ( 1 9 5 7 ) . non-upwelling,

The d a t a show a d i s t i n c t l y

and p r e s u m a b l y p o s t - u p w e l l i n g

condition.

The u p p e r

30 m a r e v e r y n e a r l y i s o t h e r m a l , w i t h t e m p e r a t u r e s o v e r 28OC a c r o s s the entire shelf.

I s o t h e r m s beyond t h e s h e l f b r e a k have d e s c e n d e d

20-30 m and i n t e r s e c t w i t h t h e u p p e r p a r t of t h e c o n t i n e n t a l s l o p e . Causes o f u p w e l l i n g Having e s t a b l i s h e d t h e e x i s t e n c e and s o m e t h i n g o f t h e t e m p o r a l n a t u r e o f u p w e l l i n g d u r i n g t h e mid summer months o f 1 9 7 8 , i t i s l o g i c a l t o a t t e m p t t o d e t e r m i n e t h e f o r c i n g r e s p o n s i b l e f o r t h e observed upwelling of water onto t h e s h e l f .

Because p r e v i o u s s t u d i e s ( T a y l o r

and S t e w a r t 1 9 5 7 , Lemming 1 9 8 0 ) have n o t e d a r e l a t i o n s h i p between s h e l f h y d r o g r a p h i c p a t t e r n s and c o a s t a l w i n d s t r e s s , w e c o n s i d e r f i r s t t h e r e l a t i o n s h i p between t h e n e a r - b o t t o m

temperatures recorded a t

S t a t i o n 1 a n d b i h o u r l y wind d a t a r e c o r d e d 8 km t o t h e n o r t h w e s t . F i g u r e 1 8 shows t h e c o h e r e n c e - s q u a r e d s p e c t r a o b t a i n e d by p a i r i n g t h e t i m e s e r i e s o f t e m p e r a t u r e w i t h t h e l o n g s h o r e and c r o s s - s h e l f components o f t h e w i n d s t r e s s .

C o h e r e n c e s a r e g e n e r a l l y w e l l below

t h e 95% c o n f i d e n c e l e v e l , e v e n a t t h e l o n g e r t i m e s c a l e s n o r m a l l y a s s o c i a t e d w i t h m e t e o r o l o g i c a l f o r c i n g , f o r b o t h components of t h e windstress.

Although one c a n n o t d i s m i s s t h e l i k l i h o o d o f w i n d s t r e s s

f o r c i n g p l a y i n g a s u p p l e m e n t a r y r o l e , t h e a v a i l a b l e d a t a do n o t

93

s u g g e s t t h a t i t p l a y s a major r o l e .

I t i s noteworthy t h a t t h e r e s u l -

t a n t w i n d s t r e s s v e c t o r f o r t h e e n t i r e s t u d y p e r i o d was a l o n g a heading

of 280°, o r 60° t o t h e l e f t of t h e l o c a l l o n g s h o r e d i r e c t i o n .

If

t h e r e w e r e an Ekman t r a n s p o r t i n s h e l f w a t e r s 90° t o t h e r i g h t o f t h e w i n d s t r e s s v e c t o r , it would have an o f f s h o r e - d i r e c t e d c r o s s - s h e l f

com-

I t i s l i k e l y t h a t windstress

ponent, b u t it would be r e l a t i v e l y s m a l l .

d u r i n g t h e s t u d y c o n t r i b u t e d more t o t h e l o n g s h o r e component o f t h e current than t o t h e cross-shelf

component and t h e a s s o c i a t e d u p w e l l i n g .

1.0

Longshore Component

-

U

04 OGt

PERIOD (I-IOwiS)

Y

Cross-shelf Component

95'b Confidffct . . . . . . -

"

:& 0

24

15

10

8

6

PERIOD (HOURS)

Fig. 1 8 . Coherence-squared s p e c t r a f o r near-bottom t e m p e r a t u r e s a t S t a t i o n 1 and b o t h l o n g s h o r e and c r o s s - s h e l f w i n d s t r e s s components, 3 J u n e t o 2 1 September, 1978. S p e c t r a l r e s o l u t i o n i s 0.00125 cph. An a l t e r n a t e and e q u a l l y a t t r a c t i v e p o s s i b i l i t y f o r e x p l a i n i n g t h e observed u p w e l l i n g i n v o l v e s t h e F l o r i d a C u r r e n t , which on o c c a s i o n moves a c r o s s t h e s h e l f b r e a k a l o n g t h i s p a r t of t h e c o a s t .

A t such

t i m e s , t h e temporary d e t e r i o r a t i o n of g e o s t r o p h y l e a v e s t h e shorewardd i r e c t e d p r e s s u r e g r a d i e n t l o c a l l y dominant a t near-bottom l e v e l s . The o n s h o r e a c c e l e r a t i o n i n t h e b e n t h i c boundary l a y e r a d v e c t s c o o l e r w a t e r o n t o t h e mid and i n n e r s h e l f .

To t e s t t h e r e l a t i o n s h i p between

v a r i a t i o n s i n l o n g s h o r e f l o w and bottom t e m p e r a t u r e s , a s t u d y was c a r r i e d o u t i n mid t o l a t e summer months o f 1 9 7 9 i n 26 m of w a t e r n e a r Station 5 (Fig. 3 ) .

Longshore c u r r e n t components r e c o r d e d 2 m above

t h e bottom w e r e compared w i t h t e m p e r a t u r e s r e c o r d e d 1 m above t h e bottom on a t a u t - l i n e mooring.

F i g u r e 1 9 shows t h e coherence-squared

and phase s p e c t r a computed w i t h d a t a c o l l e c t e d o v e r a 75-day p e r i o d from mid J u l y t h r o u g h l a t e September.

The r e s u l t s a r e encouraging.

S t a t i s t i c a l l y s i g n i f i c a n t c o h e r e n c e s a r e computed o v e r t i m e scales

94

50 25

125

8

5

PERIOD (HOURS)

'

pd,&, , I8O

K)

;5 25

I

I65 1 25

I

1

8

1 5 5

b

PERIOD (HOURS)

Fig. 19.. Coherence-squared and phase spectra for near-bottom temperatures and local longshore currents near Station 5 (See Fig. 3), 1 7 J u l y to 29 September, 1 9 7 9 . Spectral resolution is 0. 002 cycle/hour. in excess of approximately two days, and the phase spectrum indicates that increases in northerly-directed current speeds lead lower temperatures by 6 0 " to 1 2 0 " at these periodicities. Thus, the data suggest that from one to three days after an increase in longshore motion to the north cooler water arrives at this location--presumably on its way shoreward. It is likely, however, that not all upwelling events affecting mid shelf waters would continue moving in all the way to the coast and be recorded over the inner shelf. Annual temperature cycle The effects of mid summer upwelling can be put in a better perspective by plotting bottom temperatures from Station 1 over one complete annual cycle. Figure 20 shows the daily average bottom temperatures recorded between 5 September, 1 9 7 8 , and 4 October, 1 9 7 9 . The plot

1978

1979

Fig. 2 0 . Time-plot of daily average, near-bottom temperatures (in " C ) from Station 1, 5 September, 1 9 7 8 , through 4 October, 1 9 7 9 .

95 b e g i n s a t a b o u t t h e p o i n t where t h e t i m e series shown i n F i g u r e 4 e n d s . The s e a s o n a l p a t t e r n i s c l e a r l y a p p a r e n t , w i t h h i g h e s t t e m p e r a t u r e s i n

l a t e S e p t e m b e r , 1 9 7 8 , and a g a i n from l a t e J u n e t h r o u g h mid J u l y , 1 9 7 9 . bottom t e m p e r a t u r e s r i s e t o n e a r l y 3 O o C . The e f f e c t o f summer u p w e l l i n g i s t o i n t e r r u p t t h e s e a s o n a l i n c r e a s e i n t e m p e r a t u r e a t a t i m e when t h e a n n u a l maximum would o t h e r w i s e o c c u r . The d e c r e a s e i n t e m p e r a t u r e due t o u p w e l l i n g i s v a r i a b l e , d e p e n d i n g upon t h e i n t e n s i t y and d u r a t i o n of t h e event. However, i t a p p e a r s t h a t w a t e r t e m -

A t both t i m e s ,

p e r a t u r e s c a n decrease a t l e a s t t e m p o r a r i l y t o v a l u e s more c h a r a c t e r -

i s t i c of l a t e s p r i n g o r e a r l y w i n t e r .

I t s h o u l d be n o t e d t h a t t h e

e x t r e m e d e c r e a s e i n t e m p e r a t u r e r e c o r d e d i n e a r l y September, 1 9 7 9 , was i n r e s p o n s e t o t h e p a s s a g e o f H u r r i c a n e David, a n d t h u s r e p r e s e n t s a n exceptional upwelling event.

DISCUSSI O N The r e l a t i v e l y b r o a d d a t a b a s e a s s e m b l e d i n t h i s s t u d y p o i n t s t o t h e p r o b a b i l i t y t h a t f o r c i n g i n s e v e r a l forms i s important i n producing t h e observed upwelling.

P e r h a p s t h e m a s t n o t e w o r t h y r e s u l t of t h e

s t u d y i s t h e l a c k o f c o h e r e n c e computed between t h e w i n d s t r e s s a n d bottom t e m p e r a t u r e t i m e series.

I n c o n t r a s t t o p r e v i o u s s t u d i e s con-

d u c t e d i n t h e same g e n e r a l area (Green 1 9 4 4 , T a y l o r a n d S t e w a r t 1 9 5 7 , Lemming 1 9 8 0 ) , it a p p e a r s t h a t w i n d s t r e s s f o r c i n g p l a y s o n l y a s u p p l e mentary role a t b e s t .

The r e s u l t a n t w i n d s t r e s s v e c t o r had a r e l a t i v e l y

s m a l l l o n g s h o r e component d u r i n g t h e s t u d y p e r i o d , t h o u g h t h i s may n o t be t h e case a n o t h e r y e a r or o v e r s e l e c t e d , s h o r t e r t i m e i n t e r v a l s . For t h i s s t u d y s i t e , a n d f o r t h i s s t u d y a t l e a s t , it a p p e a r s t h a t t h e p r o x i m i t y o f t h e F l o r i d a C u r r e n t a n d t h e dynamic a d j u s t m e n t o f s h e l f w a t e r s t o t h e p r e s s u r e f i e l d i s a more l i k e l y e x p l a n a t i o n .

The

w i d t h o f t h e s h e l f a t l a t i t u d e 27O30'N i s o n l y a b o u t 30 k m - - s i g n i f i c a n t l y n a r r o w e r t h a n it i s f u r t h e r n o r t h where Lemming c o n d u c t e d h i s studies.

Thus, t h e r e l a t i v e i m p o r t a n c e o f t h e w i n d s t r e s s r e l a t e d pro-

cesses may be r e d u c e d by a l o c a l l y dominant f o r c i n g by t h e l o n g s h o r e current.

F u r t h e r n o r t h , where t h e s h e l f i n c r e a s e s i n b r e a d t h , o r

f u r t h e r s o u t h , where t h e s h e l f e s s e n t i a l l y d i s a p p e a r s a l t o g e t h e r , t h e

r e l a t i v e i m p o r t a n c e o f f o r c e s may b e q u i t e d i f f e r e n t . While t h e e m p h a s i s i n t h i s p a p e r h a s been upon t h e u p w e l l i n g associated with t h e cross-shelf

component of t h e s h e l f c i r c u l a t i o n , it i s

a p p r o p r i a t e t o n o t e a t l e a s t i n p a s s i n g t h e r e l a t i v e dominance of t h e l o n g s h o r e component i n t h e s e s h e l f waters.

A t l o c a t i o n s o v e r and be-

yond t h e s h e l f b r e a k , t h e F l o r i d a C u r r e n t , w i t h s p e e d s a s h i g h a s 2 0 0 cm/sec,

provides a quasi-steady t r a n s p o r t t o t h e north.

The shoreward

t r a n s p o r t a t s u b s u r f a c e l e v e l s t h e r e f o r e must i n v o l v e a n o n s h o r e def l e c t i o n o f a predominantly longshore flow a t t h a t l o c a t i o n . Over t h e i n n e r s h e l f , on t h e o t h e r h a n d , a n e t s o u t h e r l y t r a n s p o r t a t n e a r b o t t o m l e v e l s i s i n d i c a t e d by u n p u b l i s h e d d a t a r e c o r d e d d u r i n g t h e 1 9 7 8 study.

S p e c i f i c a l l y , t h e n e t d i s p l a c e m e n t p a s t S t a t i o n 1 between 2 8

J u l y a n d 2 2 A u g u s t , when u p w e l l i n g was b e s t d e f i n e d , w a s 1 . 1 8 km/day. Thus, if t h e u p w e l l i n g p r o c e s s c a n s e r v e a s a s h o r e w a r d t r a n s p o r t p r o c e s s , c o n n e c t i n g t h e quasi-steady northward flow o v e r t h e o u t e r s h e l f w i t h t h e q u a s i - s t e a d y southward f l o w o v e r t h e i n n e r s h e l f , then o n e may p o s t u l a t e a r e c y c l i n g mechanism of s o r t s a l o n g t h i s p a r t o f the coast.

Suspended m a t e r i a l moving n o r t h w a r d a t s u b s u r f a c e l e v e l s

i n t h e F l o r i d a C u r r e n t c a n b e b r o u g h t t o w a r d t h e o u t e r s h e l f by a m e a n d e r i n g i n t h e s t r e a m l i n e s , t h e n be d e f l e c t e d f u r t h e r shoreward i n A t s o m e point across t h e s h e l f , longshore

t h e upwelling pattern.

m o t i o n may cease e n t i r e l y , t h e n r e v e r s e .

Suspended m a t e r i a l r e a c h i n g

t h e i n n e r s h e l f c a n t h e n be a d v e c t e d back t o t h e s o u t h - - a t

l e a s t as

f a r a s a p p r o x i m a t e l y 27ON, where t h e s h e l f b r e a k i s so c l o s e t o t h e c o a s t t h a t a s h e l f c i r c u l a t i o n d i s t i n c t from t h a t of t h e F l o r i d a Current. i s u n l i k e l y . I n s p i t e o f t h e s u g g e s t i o n from t h e m u l t i - a n n u a l mean m o n t h l y s u r f temperatures t h a t upwelling along t h e A t l a n t i c c o a s t of South Florida i s r e s t r i c t e d t o t h e summer months ( T a y l o r a n d S t e w a r t 19571, it i s c o n c e i v a b l e t h a t a s i m i l a r u p w e l l i n g o n t o t h e s h e l f c o u l d be o c c u r r i n g throughout t h e year.

Atkinson e t a t have n o t e d t h i s p o s s i b i l i t y i n

t h e i r s t u d y o f s h e l f waters o f f S t . A u g u s t i n e .

D u r i n g w i n t e r months,

t h e water column i s n e a r l y i s o t h e r m a l t h r o u g h t h e u p p e r 60-80 m (Lemming 1 9 8 0 , C l a r k e t a 2 1 9 7 0 ) .

A t t h a t t i m e of y e a r ,

some o t h e r t y p e

o f b i o l o g i c a l o r c h e m i c a l t r a c e r would be r e q u i r e d t o document t h e process. The r e l a t i v e l y r a p i d warming a n d c o o l i n g r e c o r d e d o v e r t h e i n n e r s h e l f d u r i n g t h e summer months u n d e r l i n e t h e n e e d f o r measurements c l o s e l y spaced i n t i m e .

S i m i l a r l y , t h e p e r i o d s of t r a n s i e n t c o o l i n g

c a n n o t b e d e s c r i b e d c o m p l e t e l y e v e n w i t h weekly s y n o p t i c c r u i s e s .

The

s u b s t a n t i a l t e m p o r a l v a r i a b i l i t y i n n e a r - b o t t o m t e m p e r a t u r e s over t h e i n n e r a n d o u t e r s h e l f ( F i g s . 4 a n d 5 ) , and p r e s u m a b l y a c r o s s t h e e n t i r e s h e l f , s h o u l d b e k e p t i n mind when c o n s i d e r i n g t h e i s o t h e r m a l p a t t e r n s shown i n F i g u r e 1 6 .

I n r e a l i t y , t h e p a t t e r n i s u n d o u b t e d l y more com-

p l e x , b u t it i s f e l t t h a t weekly b o t t o m t e m p e r a t u r e s a t Seven s t a t i o n s a c r o s s t h e s h e l f a r e a d e q u a t e t o d e s c r i b e i n a g e n e r a l way t h e advance and retreat o f i s o t h e r m s a l o n g t h e t r a n s e c t .

97

CONCLUSIONS One may c o n c l u d e from t h e a v a i l a b l e d a t a b a s e t h a t t h e u p w e l l i n g r e c o r d e d d u r i n g t h e 1 9 7 8 s t u d y was most l i k e l y i n r e s p o n s e t o t h e Florida Current.

W i n d s t r e s s may h a v e p l a y e d a s u p p l e m e n t a r y r o l e ,

b u t t h i s c a n n o t be d e m o n s t r a t e d a t a s t a t i s t i c a l l y s i g n i f i c a n t l e v e l . The t e m p e r a t u r e d a t a from 1978 a n d 1 9 7 9 s u g g e s t t h a t t h e e f f e c t o f u p w e l l i n g i s t o c o o l n e a r - b o t t o m l a y e r s by a s much a s 8OC o v e r t h e i n n e r s h e l f , a n d t o r e p l a c e t h e a n n u a l maximum t e m p e r a t u r e w i t h v a l u e s more r e p r e s e n t a t i v e of l a t e s p r i n g o r e a r l y w i n t e r . One c a n n o t c o n c l u d e s a f e l y t h a t t h e e n c r o a c h m e n t of w a t e r o n t o t h e s h e l f is i n fact seasonal.

I t s d e t e c t i o n t h r o u g h t e m p e r a t u r e cross-

s e c t i o n s , however, may b e r e s t r i c t e d t o t h e summer months.

To t h e

e x t e n t t h a t t h e p r o c e s s i s i n f l u e n c e d by t h e s t r e n g t h o f t h e F l o r i d a Current',

i t may b e b e s t d e v e l o p e d d u r i n g t h e summer m o n t h s , when t h e

volume t r a n s p o r t i s a t i t s a n n u a l maximum. The u p w e l l i n g p r o c e s s a p p e a r s t o be a s i g n i f i c a n t c r o s s - s h e l f

ex-

c h a n g e mechanism, which c a n t r a n s p o r t any s u s p e n d e d m a t e r i a l t h e en-

t i r e w i d t h of t h e c o n t i n e n t a l s h e l f .

It is l i k e l y t h a t not every

way t o t h e coast t o a f f e c t t h e s u r f t e m -

u p w e l l i n g e v e n t moves , l a t h e

p e r a t u r e , however, e s p e c i a l l y f u r t h e r n o r t h , where t h e s h e l f b r o a d e n s . I n a n y area, t h o u g h , t h e p r o c e s s c l e a r l y h a s a p r o f o u n d e f f e c t upon t h e h y d r o g r a p h y o f s h e l f w a t e r s a n d , i n a l l p r o b a b i l i t y , upon t h e ecology as w e l l .

ACKNOWLEDGMENTS The a s s i s t a n c e o f George H . W.

Kierspe, L e w i s E.

G i l l i l a n d a n d Dove

Green I11 on t h e h y d r o g r a p h i c c r u i s e s and i n t h e i n s t a l l a t i o n and

r e c o v e r y o f t h e r e c o r d i n g i n s t r u m e n t a t i o n i s acknowledged g r a t e f u l l y . George K i e r s p e d i g i t i z e d t h e wind d a t a and p e r f o r m e d most o f t h e comp u t e r a n a l y s i s of t h e d a t a .

Lew G i l l i l a n d d i g i t i z e d t h e t e m p e r a t u r e

p r o f i l e s and c o n t o u r e d t h e t e m p e r a t u r e and t e m p e r a t u r e d i f f e r e n c e cross-sections.

J o h n Reed, H a r b o r Branch F o u n d a t i o n , k i n d l y p r o v i d e d

t h e t e m p e r a t u r e d a t a from which t h e d a i l y a v e r a g e s shown i n F i g u r e 2 0

w e r e computed. Harbor Branch F o u n d a t i o n ,

Inc.,

C o n t r i b u t i o n No. 1 9 6 .

98 REFERENCES P a f f e n h o f f e r a n d W.M. A t k i n s o n , L . P . , G.-A. Dunstan. 1978. The c h e m i c a l a n d b i o l o g i c a l effect o f a Gulf S t r e a m i n t r u s i o n o f f S t . Augustine, F l o r i d a . B u l l . Mar. S c i . 28:667-679. 1971. Exchange o f G u l f S t r e a m w a t e r w i t h N o r t h Blanton, J . O . C a r o l i n a s h e l f w a t e r i n Onslow Bay d u r i n g s t r a t i f i e d c o n d i t i o n s . Deep-sea R e s . 18:167-178. Bumpus, D.F. 1 9 5 5 . The c i r c u l a t i o n over t h e c o n t i n e n t a l s h e l f s o u t h o f Cape H a t t e r a s . T r a n s . Am. Geophys. Un. 36:601-611. Chew, F. a n d G . A . B e r b e r i a n . 1970. Some m e a s u r e m e n t s o f c u r r e n t by shallow drogues i n t h e F l o r i d a Current. Limnol. O c e a n o g r . 1 5 :88-99. 1970. S t u d i e s o f C l a r k , J . , W . S m i t h , A. K e n d a l l a n d M. Fahay. e s t u a r i n e dependence o f A t l a n t i c coastal f i s h e s . Data R e p t . 11: Southern Section. Tech. P a p e r s , Bur. S p o r t F i s h . W i l d l . , N o . 59, U.S. D e p t . I n t . , Wash. D.C. DEing, W:O., C . N . Mooers a n d T.N. L e e . 1 9 7 7 . Low-frequency v a r i a b i l i t y i n t h e F l o r i d a C u r r e n t and r e l a t i o n s t o atmospheric forcing from 1972 t o 1974. J . Mar. R e s . 35:129-161. Fee, E.J. 1969. D i g i t a l computer programs f o r spectral a n a l y s i s o f t i m e series. Univ. W i s . M i l w . , C e n t . G r . L a k e s S t u d . , S p e c . R e p t . No. 6, 1 7 pages. G r e e n , C. 1944. Summer u p w e l l i n g - - n o r t h e a s t S c i e n c e 100:546-547.

coast of F l o r i d a .

1 9 7 9 . The d i s t r i b u t i o n o f p h y t o p l a n k t o n i n t h e s h e l f G r e e n , D.W. waters b e t w e e n F t . P i e r c e a n d Cape C a n a v e r a l ( F l o r i d a ) . Unpubl. M.S. T h e s i s , F l a . I n s t . T e c h n o l . , M e l b o u r n e . 64 p a g e s . 1971. S t e a d y coastal u p w e l l i n g induced Hsueh, Y . a n d J. O ’ B r i e n . b y a n a l o n g - s h o r e c u r r e n t . J . P h y s . O c e a n o g r . 1:180-186. 1975. L e e , T.N. 22:753-763.

Florida Current spin-off

eddies.

Deep-sea

Res.

1 9 7 7 . Low f r e q u e n c y c u r r e n t v a r i a b i l i t y L e e , T.N. a n d D . A . Mayer. a n d s p i n - o f f eddies a l o n g t h e s h e l f o f f S o u t h e a s t F l o r i d a . J. Mar. R e s . 35:193-220. Lemming, T . D . 1 9 8 0 . Observations of t e m p e r a t u r e , c u r r e n t a n d wind v a r i a t i o n s o f f t h e c e n t r a l e a s t e r n coast o f F l o r i d a d u r i n g 1 9 7 0 a n d 1 9 7 1 . NOAA S o u t h e a s t F i s h . C e n t . , T e c h . Mem. NMFS-SEFC-6, 186 pages. P . P . a n d W.S. R i c h a r d s o n . 1973. Seasonal v a r i a b i l i t y of t h e Florida Current. J . Mar. R e s . 31:144-167.

Niiler,

1 9 6 9 . The R i c h a r d s o n , W.S., W . J . S c h m i t z J r . a n d P.P. N i i l e r . v e l o c i t y s t r u c t u r e o f the F l o r i d a C u r r e n t from the S t r a i t s o f F l o r i d a t o Cape F e a r . Deep-sea R e s . 1 6 ( S u p p l . ) : 2 2 5 - 2 3 1 . 1957. Summer u p w e l l i n g a l o n g t h e e a s t T a y l o r , C. a n d H.B. S t e w a r t . coast o f F l o r i d a . J . Geophys. R e s . 64:33-39. V u k o v i c h , F.M. a n d B.W. C r i s s m a n . 1 9 7 9 . A s p e c t s of G u l f S t r e a m w e s t e r n b o u n d a r y eddies f r o m s a t e l l i t e a n d i n s i t u d a t a . Research T r i a n g l e I n s t . , NOAA, Wash., D . C . , 92 p a g e s .

Webster, F. 1 9 6 1 . A d e s c r i p t i o n o f G u l f S t r e a m m e a n d e r s o f f Onslow Bay. Deep-sea R e s . 8:130-143 Wu, J .

1969.

J . Geophys.

Wind stress a n d s u r f a c e r o u g h n e s s a t a i r - s e a i n t e r f a c e . R e s . 74:444-455.

99

UPWELLING IN THE GULF OF GUINEA Results of a mathematical model

A. BAH MBcanique des Fluides gBophysiques, UniversitB de Liege, Liege (Belgium)

ABSTRACT A numerical simulation of the oceanic response of an the

x-y-t

two-layer model on

@-plane to an increase of the wind stress is discussed in the case of the tro-

pical Atlantic Ocean. It is shown first that the method of mass transport is more suitable for the present study than the method of mean velocity, especially in the case of non-linearity. The results indicate that upwelling in the oceanic equatorial region is due to the eastward propagating equatorially trapped Kelvin wave, and that in the coastal region upwelling is due to the westward propagating reflected Rossby waves and to the poleward propagating Kelvin wave. The amplification due to nonlinearity can be about

25 %

in a month. The role of the non-rectilinear coast is

clearly shown by the coastal upwelling which is m r e intense east than west of the three main capes of the Gulf of Guinea; furthermore, by day

90 after the wind's

onset, the maximum of upwelling is located east of Cape Three Points, in good agreement with observations.

INTRODUCTION When they cross over the Gulf of Guinea, monsoonal winds take up humidity and subsequently discharge it over the African Continent in the form of precipitation (Fig. 1). The upwelling observed during the northern hemisphere summer along the coast of the Gulf of Guinea can reduce oceanic evaporation, and thereby affect the rainfall pattern in the SAHEL region. Years of intense upwelling could be very dry and years of reduced upwelling should result in periods of relatively high rainfall. Clearly, a better understanding of the upwelling regime might contribute significantly to improved land-use. Many investigators have attempted to explain the generation and evolution of up+

welling in the Gulf of Guinea. It was soon apparent that local,%inds

.

could not provide

an adequate forcing mechanism (Houghton, 1976) Philander ( 1 9 7 9 concluded that the

100

Fig. 1. Sketch of t h e monsoon wind p a t t e r n over t h e Gulf of Guinea ( a f t e r Dhonneur, 1974).

upwelling i s n o t due t o l o c a l oceanic c i r c u l a t i o n , b u t r a t h e r i s p a r t of t h e large s c a l e oceanic c i r c u l a t i o n system. This explanation seems reasonable s i n c e Adamec and O'Brien (1978) have already shown t h a t v a r i a t i o n of t h e t r a d e winds regime i n t h e western t r o p i c a l A t l a n t i c Ocean could e x c i t e an e q u a t o r i a l l y trapped Kelvin wave which would induce upwelling on i t s way eastwards ( s e e a l s o Moore, 1968; Moore and Philander, 1977; Moore e t a l . ,

1978).

But t h e i r study does not e x p l a i n t h e i r r e g u l a r i n t e n s i f i c a t i o n of upwelling locally along t h e northern c o a s t of t h e Gulf of Guinea. Some previous workers have t r i e d t o demonstrate t h e e f f e c t s of zonal and meridional c o a s t s on e q u a t o r i a l waves (Philander. 1979; Weisberg e t a l . , 1979). Recently, t h e study of Clarke (1979) d e a l t with l o c a l longshore v a r i a t i o n s i n t h e wind s t r e s s and t h e r e s u l t i n g long trapped waves t r a v e l l i n g along t h e northern c o a s t of t h e Gulf of Guinea. Yoshida (1967) and Arthur (1965) have described enhanced upwelling near

a cape. Their r e s u l t s suggest t h a t t h e r o l e played by t h e i r r e g u l a r geometry of the n o r t h e r n coast of t h e Gulf of Guinea should be examined. T h i s i s t h e o b j e c t of the p r e s e n t paper.

101 1. THE NUMERICAL MODEL 1.1.

Model geometry

In contrast with the model developed by Adamec and O’Brien (1978), our model deals with a non-rectilinear coastline. The numerical simulation concerns the oceanic response of an x-y-t two-layer model on the

x and y

@-plane

to an increase in the wind stress

increase eastwards and northwards, respectively. The bottom of the Ocean is

assumed flat, and the depth of the upper layer is constant. Fig. 2 shows the geometry of the basin, where horizontal dimensions L, and L

Y

are respectively

3000 and

5000 km.

-

0

Fig. 2 .

1.2.

1000 km

The model geometry with the irregular coastline.

Model formulation

The quasi-hydrostatic and Boussinesq approximations are made. The layer densities p1

and p 2 are constant. The effects of atmospheric pressure, tides and thermohaline

mixing are neglected. If there is no pressure gradient in the second layer (i.e. Vp2 = 01, the linearized equations for a two-layer viscous flow reduce to :

av at

=

- B y U - c f G ah

+

TY

+ Ah V2v

102

The equations governing t h e mass t r a n s p o r t a r e , on t h e o t h e r hand,

where

A

and

Ah

a r e t h e h o r i z o n t a l eddy v i s c o s i t i e s (assumed c o n s t a n t ) , h

undisturbed depth of t h e upper l a y e r , ness,

H

Ho

the

t h e p e r t u r b a t i o n of t h e upper l a y e r thick-

t h e t o t a l ( d i s t u r b e d ) depth and

t h e reduced g r a v i t y . D e f i n i t i o n s of t h e o t h e r t e r m s are obvious. This model repres e n t s t h e s i m p l e s t formul&on

Bah e t a l . ,

-av=

aaht

1979) :

ah +

- y u -

at

a:!

aY

+ a , &

ax

of t h e f i r s t b a r o c l i n i c response.

form, t h e system o f equations (1-3) can be r e w r i t t e n (Bah,1979;

In non-dimensional

av + -

ay

1. + a3 P

-

a 2v ax2

+

a4

a 2~

aY2

0

where

Lx

and

L y a r e t h e z o n a l and t h e meridional l e n g t h scales r e s p e c t i v e l y .

Working with t h e system of equations (4-6) one g e t s from t h e equation of continuity

ah + at

au + a1 -

ax

av ay

+ alh

au ax

+

alu

ah ax

+ h

av aY

+ v

ah aY

=

0

103 Thus, working with e q u a t i o n s (1-3) r e l a t i v e t o t h e mean v e l o c i t y r e s u l t s i n neg l e c t i n g t h e l a s t f o u r terms of equation

(lo),

which i s equivalent t o n e g l e c t i n g

c o n t r i b u t i o n s a t l e a s t o f t h e same o r d e r of magnitude a s t h e r e s p e c t i v e second terms

of t h e r i g h t s i d e o f eqs ( 7 ) and ( 8 ) . ap

,

4.47 x l o 3

,

The values f o r tively

2.24

,

,

a1

and

a 3

a+

50 m

f o r t h e case of a

2.24 x

and

4.47

depth a r e respec-

(Bah, 1979).

X

1.3. Numerical scheme The numerical model u s e s t h e numerical scheme developed by Ronday (1976) : v

u

and

a r e computed according t o t h e following s p a t i a l g r i d .

for for for

4

0

I

o

l o I

1

- - - -0 - 1

[

Fig.

3.

u v h

I

AY

S p a t i a l g r i d used f o r t h e computations.

We have f o r t h e temporal g r i d , i n t h e unidimensional case f o r example u h

u

n+l

n+l

,

= a u n + b h " n+l

= c u v

and

+ d h n a r e computed a t t h e same moment, but i n t h e computation of

h

mated values of

u

and

v

h ,

esti-

a r e used. All t h e boundaries a r e w a l l s , and t h e normal

v e l o c i t y i s assumed equal t o zero a t t h e c o a s t . All c a l c u l a t i o n s a r e done with a c o n s t a n t g r i d r e s o l u t i o n of

5 0 km

i n both

x

and

y

d i r e c t i o n s . The s t a b i l i t y

condition

At Ax

+ v

At s Ay

requires

At

t o be

a u

=

1

5

18248 s

(about

5 h ) . The chosen temporal s t e p w a s

At = 3 h

104 (1/8 d a y ) . O t h e r c o n s t a n t s a r e

6

lo-''

= 2 x

:

Hg = 50 m ; A = 10'

rn2s-'

i

g' = 2 x

lo-'

m s-'

i

.

m-'s-'

S i n c e w e are i n t e r e s t e d i n s t u d y i n g t h e p r o b a b l e e f f e c t o f t h e i r r e g u l a r c o a s t l i n e geometry on t h e u p w e l l i n g g e n e r a t i o n , e v o l u t i o n and i n t e n s i f i c a t i o n , w e have chosen t o s t u d y t w o major aspects :

-

t h e f i r s t one w i t h p r o m i n e n t c o a s t l i n e f e a t u r e s s u c h a s Cape Palmas, Cape Three

P o i n t s , C a p e Formoso and Cape Lopez;

- t h e s e c o n d , f o r comparison, w i t h a l i n e a r c o a s t l i n e f o r t h e w e s t a f r i c a n coast. F o r b o t h cases, t w o s i t u a t i o n s a r e i n v e s t i g a t e d : 1.3.1. and

a standard l i n e a r s i t u a t i o n with an i ncr ease of r espect i vel y i n t h e westward wind stress o v e r t h e w e s t e r n

0.0125 N m - '

1 5 0 0 km

G.025 Nm-' of the

b a s i n ( f i g . 41 and w i t h o u t any m e r i d i o n a l wind;

0

F i g . 4.

1.3.2.

1

2

3

4

5

S p a t i a l v a r i a t i o n o f t h e z o n a l wind stress.

a second s i t u a t i o n , non l i n e a r , s i m i l a r t o t h e f i r s t b u t i n c l u d i n g advec-

t i v e e f f e c t s , l o c a l d e p t h i n t h e stress t e r m , n o n - l i n e a r i t i e s t i o n and an i n c r e a s e o f

0.0125 N m - '

i n t h e c o n t i n u i t y equa-

o f t h e westward wind stress.

I n e a c h s i t u a t i o n , i n t e g r a t i o n s a r e performed a t l e a s t o v e r from r e s t

(u = v = 0

at

90

days, s t a r t i n g

t = O ) , w i t h a sudden i n c r e a s e of wind stress ( f i g . 5)

remaining c o n s t a n t throughout t h e following p e r i o d o f i n t e g r a t i o n . To a l l o w a n easy comparison o f t h e r e s u l t s , w e have u s e d t h e s a m e denomination for b o u n d a r i e s a s d i d Adamec and O ' B r i e n (1978) : t h e e a s t e r n boundary e x t e n d i n g 500 km n o r t h o f t h e E q u a t o r and 1500 km s o u t h i s t h e s o u t h - e a s t e r n

( S - e a s t e r n ) boundary;

t h e e a s t e r n boundary e x t e n d i n g 500 km n o r t h o f t h e E q u a t o r t o 1500 km i s t h e north-

e a s t e r n ( N - e a s t e r n ) boundary; t h e n o r t h e r n boundary i s t h e n t h e n o r t h e r n boundary of t h e Gulf o f Guinea, e x t e n d i n g a p p r o x i m a t e l y from Cape Palmas t o C a p e Formoso, i.e.

105

Fig. 5.

Temporal v a r i a t i o n of t h e wind s t r e s s .

from 3 0 0 0

to

5000 km

e a s t of t h e western boundary; t h e north-northern

boundary i s t h e northern boundary of t h e basin extending

3 0 0 0 km

(N-northern)

from t h e western

boundary ( f i g . 2 ) .

2 . THE ANALYTICAL MODEL

For a b e t t e r understanding and i n o r d e r t o i n t e r p r e t t h e numerical r e s u l t s , anal y t i c a l expressions a r e considered. They a r e derived from l i n e a r theory and w i l l be used a s a guide. Because of t h e p e c u l i a r i t y of t h e wind stress (which i s f i r s t l y uniform over t h e e n t i r e p e r i o d of i n t e g r a t i o n , and secondly z o n a l l y v a r i a b l e ) , t h e s o l u t i o n s w i l l i n clude t h e l o n g i t u d i n a l l y unbounded i n t e r i o r response, t h e e x c i t a t i o n of e q u a t o r i a l l y trapped waves and t h e r e f l e c t i o n s of t h e s e waves a t t h e boundaries. Moreover, with t h e i r r e g u l a r c o a s t l i n e , t h e e x i s t e n c e of capes and b i g h t s should cause l o c a l i n t e n s i f i c a t i o n of upwelling along t h e northern boundary.

2.1.

E q u a t o r i a l waves Kindle (1979) h a s reviewed some a s p e c t s of e q u a t o r i a l wave dynamics. I t i s u s e f u l

t o examine h e r e t h e procedure he used t o d e s c r i b e t h e n a t u r e of waves generated i n a model such a s o u r s . Consider t h e l i n e a r , i n v i s c i d , h y d r o s t a t i c , non-divergent system of equations on the equatorial

B-plane

:

106

air

i s t h e mean d e n s i t y g r a d i e n t i n t h e v e r t i c a l d i r e c t i o n . az According t o t h e formulation of G i l l and Clarke ( 1 9 7 4 ) by expanding i n s e r i e s of

where

t h e v e r t i c a l modes of t h e system, a r e s u l t i n g equation can be w r i t t e n i n terms of t h e meridional v e l o c i t y , i . e .

where f o r c i n g t e r m s have been added. Note t h a t

A,

i s t h e g r a v i t y wave speed, and

i s expressed a s 1, = (g'H)

1

Now, i f we assume a waveform dependance i n t h e zonal d i r e c t i o n i . e .

e

i ( k x -ut)

t h e n , equation (12) reduces t o :

Bk

-

- k2 -

w

)

V

=

y +-

2 co

G(y)

A', whose s o l u t i o n i f bounded a s V = e

i(kx -wt)

where

$J,(Y)

I

can be w r i t t e n

m t O

(14)

i s a Hermite f u n c t i o n .

$,(y)

So long a s

C(2m+l)A,l4

IYI

5

B

t h e s o l u t i o n i s o s c i l l a t o r y , but as soon as

'

IYI

C (2m +

1) A,]

4

a

i t becomes "monotonic" i . e .

i t decays exponentially a f t e r it has changed i t s nature

a t the point C(2m+ 1 ) A J Y =

f

B

(Kindle, 1979). The corresponding d i s p e r s i o n r e l a t i o n of

(13) i s

107 where

k = k(m,w)

.

This relation includes four types of waves

:

inertia-gravity

waves with high frequencies, mixed Rossby-gravity waves with low frequencies, Rossby waves, Kelvin waves [set

0 and solve equations (1-3);

v

for details, see Moore

and Philander (1977) or Adamec and O'Brien (1978) 1. Solving equation (15)

,

we get

Special cases When

m

=

,

0

However, the solution with growth of

U

and

P

with

k2

y

is not acceptable because of the exponential

(Moore and Philander, 1977); with

k = kl

, the

so-

lution is

i[(F-

&)x

v = e

-

3

wtl $0

(Y)

and corresponds to a Yanai wave or mixed Rossby-gravity wave. For this wave, the group velocity is eastwards, but the phase velocity is either eastwards or westwards. When

m 2 1 , and so long as

waves are gravity waves; as soon as

they are planetary waves. w 2 2 (2m+ 1) BA,

For

, Kindle

(1979) has shown that inertia-gravity waves may

exist, so that at the Equator, and for a given mode, the inertial oscillations period is

where

m

2 1 .

In our case, Ti is slightly more than

9

days.

108

1

1

Fig. 6a. Variation of the interface in the linear case 20 days after the wind's onset: dashed lines denote upwelling and full ones downwelling with values in meters (from O'Brien et al., 1978).

0

10

20

3'0

YO

Fig. 6b. Variation of the interface 40 days after the wind's onset (from O'Brien et al., 1978).

109

0

10

20

YO

30

Fig. 6c. Upwelling in the Gulf of Guinea 60 days after the wind's onset (from O'Brien et al, 1978).

2

H

D A Y 80

In N

0 c.

%

r:

x

la

VI . I

0

10

20

KM

30

YO

Y102

'Fig. 6d, Upwelling and downwelling pattern 80 days after the wind's onset (from O'Brien et al, 1978).

110 3. RESULTS 3.1.

The s t a n d a r d l i n e a r case with r e c t i l i n e a r c o a s t l i n e

F i r s t , t o t e s t t h e method, we consider t h e case with r e c t i l i n e a r c o a s t s using an i n c r e a s e of

0.025 N m-'

i n t h e westward wind s t r e s s over t h e western

1 5 0 0 km

of

t h e basin and no meridional wind. The r e s u l t s ( f i g . 7) a r e i n good agreement with t h o s e of O'Brien e t a l .

(1978) [ f i g . 61; f o r i n s t a n c e on day 10, one can recognize

t h e w e l l d e f i n e d e l l i p t i c a l shape of t h e upwelling c e l l , t h e symmetry about t h e equat o r and e q u a t o r i a l t r a p p i n g , t h e maximum value o f 30 cm s - '

f o r t h e a s s o c i a t e d corresponding maximum

13 m

u

f o r t h e perturbation

h

and

component.

The eastward propagation of t h e p e r t u r b a t i o n along t h e Equator i s also c l e a r l y ohservable. Note t h a t by day 50, t h e p e r t u r b a t i o n has reached t h e e a s t e r n boundary, and then begins t o propagate polewards from t h e Equator along t h e e a s t e r n and t h e northern boundaries of t h e Gulf of Guinea. Upwelling i s more and more important and i t s maxi-

mum i n t e n s i t y occurs along n e a r l y a l l t h e northern c o a s t (days 80 and 9 0 ) .

0

0

Fig. 7a.

V a r i a t i o n of t h e i n t e r f a c e

10

days a f t e r t h e wind's o n s e t .

111

0

Fig. 7b.

Upwelling and downwelling pattern on day 20.

Fig. 7 c . 30 days after the wind's onset, upwelling occurs in the western part of the Gulf of Guinea.

112

Fig. Id. Is land.

On day 40, the leading edge of the upwelling cell reaches the S o Thome

Fig. 7e. 50 days after the wind's onset, the upwelling cell has already reached the South-eastern boundary.

113

Fig. 7f. Guinea.

Occurrence of upwelling o n day 60 along the northern coast o f the Gulf of

Fig. 7g.

By day 7 0 , upwelling is present in the entire Gulf of Guinea.

114

Fig. 7h. Poleward propagation of t h e upwellinq alonq t h e north-eastern c o a s t on day 80. The maximum o f u p w e l l i n g occurs-along t h e m o s t p a r t of t h e northern boundary.

Fig.

7i.

Upwelling and downwelling p a t t e r n

90

days a f t e r t h e wind's o n s e t .

115 3 . 2 . Standard l i n e a r c a s e with i r r e g u l a r c o a s t l i n e

Fig. 8a. Foreward propagation of t h e p e r t u r b a t i o n i n t h e case of a non r e c t i l i n e a r c o a s t l i n e 40 days a f t e r t h e o n s e t of t h e wind s t r e s s .

Fig. 8b.

Upwelling i n t h e Gulf of Guinea

50

days a f t e r t h e wind's o n s e t .

116

Fig. 8c. North-westward propagation of the perturbation along the African coast, 60 days after the wind's onset.

Fig. 8d.

Upwelling is present in the entire Gulf of Guinea (day 70).

117

Fig. 8e.

On day 80, the maximum of upwelling occurs in the Bight of Benin.

Fig. 8f. The maximum of upwelling is located east of Cape Three Points by day 90, after the wind's onset.

118 Q u a l i t a t i v e l y , t h e r e s u l t s (Fig. 8 ) confirm those a l r e a d y obtained, and t h e gener a t i o n and t h e e v o l u t i o n of t h e upwelling i n t h e Gulf of Guinea can be explained a s follows. A s does t h e western boundary of t h e b a s i n ,

so t h e e a s t e r n edge of t h e f e t c h zone

of t h e wind stress (1500 km from t h e western boundary) e x c i t e s eastward propagating Kelvin waves, eastward o r westward propagating Yanai waves and westward propagating Rossby waves (e.g. Kindle, 1979). Let

K1

be t h e Kelvin wave e x c i t e d with t h e o n s e t of t h e wind s t r e s s a t t h e

e a s t e r n edge of t h e wind f e t c h zone, and

t h e r e s p e c t i v e Kelvin wave a t t h e

K~

western boundary o f t h e b a s i n . I n t h e e q u a t o r i a l zone, upwelling should r e s u l t from t h e eastward propagating Kelvin waves

K1

and

Kp

(Yanai waves eventually) excited

a t t h e edges of t h e t r a d e wind f e t c h zone; i n t h e c o a s t a l zone (northern c o a s t ) , it should be due t o t h e poleward propagating Kelvin wave and t h e westward propagating RossbG waves e x c i t e d by t h e former ( e . g . Hulburt and Thompson, 1976; Hulburt e t a l . , 1976; Adamec and O’Brien, 1978). Indeed, i n l i n e a r theory, t h e combination o f

Ap

and

H

g i v e s t h e phase velocity

of t h e i n t e r n a l Kelvin wave

4025 km

Fig. 9. Upwelling a t an E q u a t o r i a l p o i n t , (standard case).

from t h e western boundary

Fig. 9 shows t h e development of upwelling a t an e q u a t o r i a l p o i n t s i t u a t e d from t h e western boundary. W e can s e e t h a t with such a phase speed wave

K1

c

4025 km

(c = 1 rn s - ’ ) ,

a r r i v e s a f t e r 29 days. The r a t e of i n c r e a s e i n v e r t i c a l displacement re-

mains r e l a t i v e l y unchanged from day 40 u n t i l day 60, except f o r a s l i g h t modification due t o t h e eastward c r o s s i n g of t h e wave

K,

on day 47. There i s a dramatic change

about day 66, however, with t h e a r r i v a l of wave boundary. As f o r wave

R2

r e f l e c t e d from wave

s i d e r a t i o n about t h e day 8 4 .

R,

K2

r e f l e c t e d a t t h e south-eastern

,

it reaches t h e p o i n t under con-

119

N o wind s t r e s s

10

0 loo

days

b

N o wind s t r e s s

0 0

"

40

.

50

60

70

80

90

100

days

Fig. 10. Upwelling i n t h e v i c i n i t y o f Cape Three P o i n t s ; a) e a s t of t h e cape, b) w e s t of t h e cape.

r

n

a

.

40

0

50

60

70

80

90

100

days

b

rn

;20 h

N o wind s t r e s s

E

10

0 40

0

50

60

70

80

90

100

days

Fig. 11. Upwelling i n t h e v i c i n i t y of Cape Palmas; a ) e a s t of t h e cape, b) west of t h e cape.

Upwelling begins about day 60 with t h e a r r i v a l of t h e leading edge of t h e Rossby wave Fig.

R1

, followed by i n t e n s i f i c a t i o n before reaching a maximum value a f t e r day 70.

10 and 1 1 show t h a t t h e o n s e t , i n t e n s i f i c a t i o n and maximum of upwelling west of

Cape Three P o i n t s a r e delayed about 10 days r e l a t i v e t o t h e region e a s t of t h e cape. This d e l a y i s t h e same a s t h a t observed i n t h e r e v e r s a l of t h e c u r r e n t between t h e s e two c o a s t a l a r e a s , separated by about 300 km (Fig. 1 2 ) , and it i s due t o wave

R,

120

Fig. 12a. Velocity f i e l d 60 days after t h e o n s e t of the wind s t r e s s . The reversal of t h e c u r r e n t occurs e a s t of Cape Three Points.

121

.

........

\\.,.,..... .......... ...... 1 l l l l . A * ‘ .

\ \ \ \ L , & . . * .

Fig. 12b. (day 70).

Intensification of the eastward current east of Cape Three Points

............ ............. ftfii;;;::;::. ..... \\\\\\\\\\,,..., \ \ \ \ \ \ \ $ I t

F i g . 12c. 80 days a f t e r t h e wind‘s o n s e t , t h e eastward c u r r e n t is p r e s e n t along t h e e n t i r e Northern c o a s t .

123 whose phase speed should be, from l i n e a r t h e o r y , c R ,=

C

ms-’.

= 0.33

3

The speed of t h e westward propagation of t h i s r e v e r s a l is i.e.

nearly

28

Indeed, 36

and

64

cR,

days

300 kmday-I

10.35 m s - ’ )

,

.

days a r e required f o r wave f o r wave

K1

t o reach t h e south-eastern boundary

t o a r r i v e e a s t o f Cape Three P o i n t s , t h a t i s roughly

R1

days a f t e r t h e wind s t r e s s f o r c i n g began. The divergence zone accompanying c u r r e n t r e v e r s a l i s due t o t h e f a c t t h a t eastward

propagating Kelvin waves produce a flow t o t h e west, while westward propagating waves produce a flow t o t h e e a s t . T h i s phenomenon could e x p l a i n t h e i n t e n s i f i c a t i o n of t h e Guinea Current f r e q u e n t l y observed near Cape Three P o i n t s . C a l c u l a t i o n s from l i n e a r theory i n d i c a t e t h e presence o f wave about day

R1

near Cape Palmas

i n agreement with t h e numerical r e s u l t s shown i n f i g . 11 and t a b l e 1.

?la,

TABLE 1

Values f o r

h

i n meters

20

30

40

East

0

West

0

0 2

1 2

Cape Three P o i n t s

East West

0

0

0

0

Cape Formoso

East West

0 0

Davs Cape Palmas

I n t h e same way, wave

Rp

60

70

80

90

100

1

2

3

2

5 3

12 7

17 12

18 15

0 1

0

1

6 2

19 7

21 15

20 19

17 18

0

1

0

0

8 3

19 10

21 19

19 21

14 18

12 13

50

i s p r e s e n t i n t h e Bight of Benin about day 76 where t h e

r e v e r s a l of t h e westward c u r r e n t , t h e i n t e n s i f i c a t i o n and t h e maximum of t h e upw e l l i n g a r e c l e a r l y shown (Fig. 12c and 8 e ) . I f w e compare now r e s u l t s from t h e r e c t i l i n e a r c o a s t l i n e c a s e (Fig. 7 ) with those from t h e non r e c t i l i n e a r case (Fig. 81,

some important f e a t u r e s are evident. About

day 50, southwards from Cape Formoso along t h e south-eastern c o a s t , t h e poleward propagation i s more important when t h e c o a s t i s i r r e g u l a r . This corresponds t o a n extens i o n of t h e upwelling zone and an i n t e n s i f i c a t i o n of t h e upward movement. The northern edge of t h e upwelling c e l l i s moved southwards near Cape Palmas. L a t e r , t h e i n t e n s i f i c a t i o n goes forwards a s f a r a s t h e Gulf of Benin. On t h e o t h e r hand, i n t h e v i c i n i t y of Cape Three P o i n t s , t h e upwelling i s weaker from day 60 u n t i l day 8 0 than i n t h e r e c t i l i n e a r c a s e when i n t e n s i f i c a t i o n of t h e upwelling begins with t h e maximum centered e a s t o f t h i s cape. Since upwelling i s due t o t h e north-westward propagation of t h e c o a s t a l l y trapped wave following t h e a r r i v a l of waves

5

K1 and K p

a t t h e south-eastern boundary (see

3 . 2 ) , t h e extension i s observed f i r s t towards t h e p o l e , and then westwards if a

zonal boundary i s p r e s e n t . In t h e c a s e of a r e c t i l i n e a r c o a s t , t h e zonal boundary i s

124 reached earlier, so that the westward prspagation of the perturbation is initiated earlier than when the coast is irregular (in this case, the tendancy of the propagation is northwards into the bights). This could explain the delay of upwelling intensification east of Cape Three Points. In any case, upwelling is always stronger east than west of the CAPES, as can be seen from table 1. To understand this feature, we now estimate the upward displacement rate of the pycnocline in the vicinity of Cape Three Points.

3.3. Estimation of

ws

Consider the system of equations (1) and ( 2 ) where advective terms have been added; viscous terms are temporarily neglected.

In addition, we have the continuity equation

a

Doing

a

(18) -

b

aY

(17) , and using equation ( 1 9 ) , we get

d

c

5

where

a -

=

av ax

-

e

au ay

Introducing characteristic length-scales, we find that

5

-

s-l ;

BY

-

Obviously, the term

Therefore, if

By

aw

By

-

5v

is preponderant in ( e ). Also

,

then

terms into account, we get

where

A

b

-2.

~ O - ” S - ~;

(at 5 0 ~ ) .

s-‘

is assumed constant.

w

-

ms-’

. Note

(c)

- (d)

-

s-’

and

that if we take viscous

125 So the use of equation (20) requires only the terms

dt

and

Bv

in the left

member of the equation, and

3.3.1.

East of Cape Three Points

On day 80, the current is eastwards near Cape Three Points (fig. 12c). To estimate - , we use the following equation (e.g. Arthur, 1965)

i:

where

V

is the velocity of the current, R

line near the coast, and For the values of

ms-'

-

the radius of curvature of the stream-

the velocity gradient normal to the streamline.

,

V = 0.03 ms-'

and (22), w50 = 0.28 give

;:

-

or

R = 15.5 lo3 m , we obtain from equations (21) 2.4 m/10 days. Numerical results (see table 1)

weaSt 2 m/10 days.

3.3.2. West of dape Three Points Similar calculations give

-

wWest 1.5 m/lO days

.

Thus

wWest< weaSt as expected

from theory, indicating that in the presence of a cape, upwelling is more intense off that cape, downwards in the direction of the flow. Moreover, the value obtained by the analytical calculation is smaller than the corresponding numerical value. This result is understandable since 1')

estimation of

wWest is done with the assumption that only the presence of the

cape could influence the creation and the development of the observed upwelling; 2") upwelling near the cape is related essentially to the westwards propagating

Rossby waves

R1

and

Rp

.

3 . 4 . Non-linear case

Including non-linear terms for advection and instantaneous depth in the standard case, numerical results are in good agreement with those expected from theory. Since h

is negative during upwelling periods, the phase speed

c [c = g '

(Hg

+ h)' 1

is reduced so that the propagation of the Kelvin wave is slower (Figs. 13, 14, 15 and 16). The leading edge of the perturbation cell elongates, while its trailing edge flattens because of faster phase propagation away from maximum upwelling values region. For the same reason, even if the poleward

propagating Rossby waves and the resul-

ting energy transfer prevents a growth of the wave amplitude as proposed by many authors (Hurburt and Thompson, 1976; Hurburt, Kindle and O'Brien, 1976; Adamec and O'Brien, 1978), the wave's effects are still amplified. Indeed,

126

F i g . 13a. Upwelling w i t h a reduced wind stress l i n e a r case w i t h r e c t i l i n e a r coasts on d a y 3 0 .

T '

=

- 0.0125

NIII-~

i n t h e standard

I I I

............. .-

I

I

I I 1

-.......... 0:

.5

i.

0

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

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

\, \ \,\ \,\.

'\.\\ \,

\ \

F i g . 13b. The u p w e l l i n g c e l l r e a c h e s t h e s o u t h - e a s t e r n boundary, o n s e t of t h e wind stress.

50 days a f t e r the

127

Fig. 13c.

Upwelling is present in the entire Gulf of Guinea on day 70.

5

Fig. 13d.

Q

-

-.,, ,

.

,

.. .,. .

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

Upwelling and downwelling pattern on day 90.

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

............ ... .. .......'

128

Fig. 14a. (day 30).

Upwelling pattern in the non-linear case with rectilinear coastline

Fig. 14b.

On day 50, the upwelling cell reaches the Sdo Thome Island.

129

Fig. 14c.

Upwelling in the G u l f of Guinea, 70 days after the onset of the wind stress

i

I

Fig. 14d. The maximum o f upwelling is extending almost along all the northern boundary (day 9 0 ) .

130

Fig. 15a. Upwelling with a reduced wind stress T' = - 0.0125 Nm-' in the standard linear case with non-rectilinear coasts, 50 days after the onset of the wind.

Fig. 15b. (day 70).

Poleward propagation of the perturbation along the African coasts

131

-

-- -

-. 3m--

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

5

:I

Fig. 15c. 80 days after the onset of the wind stress, the maximum of upwelling occurs in the Bight of Benin.

;...5') . .

C._

-

lo

Fig. 15d.

_. /.- -.'

-. I

5

,'

..........

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

1

........

By day 90, the maximum of upwelling is confined east of Cape Three Points.

132

Fig. 16a. Upwelling p a a e r n in the non-linear case. 50 days after the onset of the wind stress, the upwelling cell is reaching the Sdo Thome Island.

Fig. 16b. 70 days after the wind's onset, upwelling is still absent in the vicinity of Cape Three Points.

133

Fig. 16c. Westward propagation of t h e p e r t u r b a t i o n along t h e northern c o a s t t h e Gulf of Guinea (day 8 0 ) .

Of

Fig. 16d. By day 90, t h e maximum of upwelling i s l o c a t e d east of Cape Three Points i n t h e Gulf of Benin.

134 This amplification can be about

25

%

during one month (from day 2 0 to day 50),

as demonstrated in table 2. TABLE 2 Maximum upwelling values at the Equator with a westward wind stress ~

Days hma~

(m)

linear case non-linear case

10

20

30

40

50

60

70

6

10 13

9 13

9

10

12

11

10 10

10 11

7

CONCLUSIONS Our investigations suggest that

:

1. The sudden onset of the wind stress in the western Atlantic Ocean can excite wind induced eqdatorially trapped Kelvin waves which generate upwelling in the Equatorial region on their way eastwards.

2. The poleward propagating trapped Kelvin wave and the westward propagating reflected Rossby waves induce upwelling along the northern coast of the Gulf of Guinea. Previously, some investigators concluded from measurements of temperature and velocity at the Equator, that there was no evidence of the propagation of a seasonal upwelling along the Equator from the western Atlantic (e.9. Clarke, 1979; Weisberg et al, 1979).

*

The monthly maps of Sea Surface Temperature (SST) anomalies

(Fig. 17) clearly

show the appearance and the intensification of the negative equatorial anomalies from West to East (look at line - 1'C)

with a speed of 980 km per month, i.e.

.

cK = 0.38 ms-'

Moreover the meandering of the equatorial negative anomalies front suggest an 1 half-sinusoid so that the eastward wave number component kcomputed - -385 km-'. 1 -1 This should be compared with the observed value at the coast kabserved = 400 km (Clarke, 1979). Looking at line

- 1 'C,

in the coastal region for August and Septembe?, one

can see the westward displacement with a speed of 332.5 km month-' ( 0 . 1 3 ms-'), 1 that is 7 cK This result is in very good agreement with the linear theory.

.

3. The coastal upwelling is more intense east than west of Cape Three Points and Cape Palmas, and thus the presence of a non-rectilinear coastline influences the location and the intensification of coastal upwelling. About 90 days after the wind's onset in the western Atlantic Ocean, equatorial and coastal upwellings are present in the Gulf of Guinea. The maximum is located east of Cape Three Points, in good agreement with observations (e.9. Bakun, 1978).

*

Computed for the period, 1946-1972.

135

Fig. 17a. SST-anomalies in the G u l f of Guinea in May. Only warm waters are present (continuous lines).

Fig. 17b. The appearance in June of equatorial oceanic cold waters, i.e. equatorial upwelling (dashed lines).

136

Fig. 17c.

In July, the equatorial cold waters have moved northwards

Fig. 17d. Occurrence of coastal cold waters in the vicinity of Cape Three Points and Cape Palmas in August.

Fig. 17f.

SST anomalies pattern in the G u l f of Guinea in October.

138

Fig. 17g.

Fig. 17h.

Southward displacement of oceanic cold waters and disparition of Coastal

Reduction of oceanic upwelling in December.

139 4. The upwelling persists for approximately two months. 5. The coastal upwelling is not due to local advection, nor to the monsoonal winds (e.g. Adamec and O'Brien, 1978; Bah, 1979). 6. The amplification due to non-linearities can be about

25 8 during one month.

ACKNOWLEDGEMENTS The author gratefully acknowledges the help of Prof. J.J. O'Brien of the Florida State University, who suggested the problem, and of Prof. J.C.J. Nihoul who encouraged its realization and presentation at the "lZth International Liege Colloquium on Ocean Hydrodynamics". Discussions with Dr. Ronday have been of immense value. Computer assistance given by P. Closset, J. Ozer and Y. Runfola is highly appreciated. The supports of the "Centre Belge d'Oc6anoqraphie" and the "Ministere de la Politique Scientifique de Belgique" to acquire the SST data are gratefully acknowledged. I am indebted to Prof. J.C.J. Nihoul, Prof. O'Brien, Prof. Parker and Dr. Ronday

for their advises in the redaction of the manuscript.

REFERENCES Adamec, D. and O'Brien, J.J., 1978. The seasonal upwelling in the Gulf of Guinea due to remote forcing. J. Phys. Oceanogr., 8:1050-1060. Arthur, R.S., 1965. On the calculation of vertical motion in eastern boundary currents from determinations of horizontal motion. J. Geophys. Res., 70:2799-2803. Bah, A., 1979. Interactions air-mer et problemes de la secheresse en zone sahelienne. Rapport, Fondation Roi Baudoin, 90 pp. Bah, A . , Loffet, A. and Schayes, G., 1979. Air-Sea Interactions. ICES Hydrography Committee CM 1979/c:48. Bakun, A., 1978. Guinea Current upwelling. Nature, 271:147-150. Clarke, A.J., 1979. On the generation of the Seasonal Coastal upwelling in the Gulf of Guinea. J. Geophys. Res., 84:3743-3751. Gill, A.E. and Clarke, A.E., 1974. Wind-induced upwelling, coastal currents and sealevel changes. Deep-sea Res., 21:325-345. Houghton, R.W., 1976. Circulation and hydrographic structure over the Ghana Continental shelf during the 1974 upwelling. J. Phys. Oceanogr., 6:910-924. Hulburt, H.E., Kindle, J.C. and O'Brien, J.J., 1976. A numerical simulation of the onset of El Nino. J. Phys. Oceanogr., 6:621-631. Hulburt, H.E. and Thompson, J.D., 1976. A numerical model of the Somali Current. J. Phys. Oceanogr., 6:646-664. 1979. Equatorial Pacific Ocean Variability-Seasonal and El Nino time Kindle, J . C . , scales. Mesoscale Air-Sea Interaction Group. Technical Report, 134 pp. Moore, D.W., 1968. Planetary-gravity waves in an equatorial Ocean. Ph. D. Thesis, Harvard University. Moore, D.W. and Philander, S.G.H., 1977. Modelling of the tropical oceanic circulation. In: E.D. Goldberg, I.N. Mc Cave, J.J. O'Brien and J.B. Steele (Editors), The Sea, VI. John Wiley and Sons, New York, 319-362. Moore, D.W., Hisard, P., Mc Creary, J., Merle, J . , O'Brien, J.J., Picaut, J., Verstraete, J.M. and Wunsch, C., 1978. Equatorial adjustment in the Eastern Atlantic. Geophys. Res. Lct., 5:637-640. O'Brien, J.J., Adamec, D. and Moore, D.W., 1978. A simple model of upwelling in the Gulf of Guinea. Geophys. R e s . Lct., 5:641-644. Philander, S.G.H., 1979. Upwelling in the Gulf of Guinea. J. Mar. Res., 37:23-33.

140 Ronday, F.C., 1976. Moddles hydrodynamiques. In: J.C.J. Nihoul and F.C. Ronday ( E d i t o r s ) , P r o j e t Mer, 3:270 pp. Weisberg, R . H . , Horigan, A. and C o l i n , C . , 1979. E q u a t o r i a l l y t r a p p e d Rossby-gravity wave p r o p a g a t i o n i n t h e Gulf of Guinea. J . Mar. R e s . , 3 7 ~ 6 7 - 8 6 . Yoshida, K . , 1967. C i r c u l a t i o n i n t h e E a s t e r n T r o p i c a l Oceans w i t h s p e c i a l references t o upwelling and u n d e r c u r r e n t s . Japan J . Geophys., 4:l-75.

141

ON TWO MARINE ECOSYSTEMS OF SENEGAL SEPARATED BY A PENINSULA Y.

GALLARDO

Centre de Recherches Oceanographiques de Dakar-Thiaroye,

Dakar (SBndgal)

ABSTRACT

Gallardo Y . ,

1981. On two marine ecosystems of Senegal separated by a peninsula.

Hydrological and h a l i e u t i c c o n d i t i o n s on both s i d e s of t h e Cap-Vert Peninsula a r e v e r y ' d i f f e r e n t : t h e southern c o a s t washed with waters c o l d e r than those of t h e northern edge h a s c l e a r l y a d i r e c t i o n more s u i t a b l e t o c o a s t a l upwelling. However, s t r o n g d i f f e r e n c e s observed n o t only during t h e hydrometeorological w i n t e r b u t a l s o , i n t h e summer p e r i o d , i n d a i l y measurements of chlorophyll d o n o t depend only on t h e l o c a l wind. The wide and g e n t l y i n c l i n e d southern s h e l f undergoes i n a d d i t i o n a deep turbulence a r i s i n g from t h e "Cape e f f e c t " ; i n f a c t , a d i f f e r e n t and l a r g e r s c a l e southern upwelling system may e x i s t during t h e major p a r t of t h e year. Connections between t h e e x i s t i n g g r e a t oceanic f e a t u r e s , e q u a t o r i a l upwelling events and f e r t i l i z a t i o n of t h e southern c o a s t o f Senegal a r e r e l a t e d . INTRODUCTION

The northern and southern c o a s t s of Cap-Vert peninsula where t h e c i t y of Dakar i s l o c a t e d o f f e r , t o the mind of f i s h e r y b i o l o g i s t s , d i f f e r e n c e s and d i s c o n t i n u i t i e s adequate Lo d i s t i n g u i s h two marine ecosystems, t h e southern system being more s u i t a b l e f o r the l i f e and development of l a r v a l forms and immature f i s h (Champagnat and Domain, 1978).

-

Hydrological o b s e r v a t i o n s support t h i s d i s t i n c t i o n

t h e e x i s t e n c e of an oceanic f r o n t which seems "fixed" a t t h e extremity of t h e

p e n i n s u l a (Fig. 1) , named "Pointe des Almadies"

-

:

t h e g r e a t d i f f e r e n c e s of temperature

Dakar-Thiaroye,

i

and s a l i n i t y a t t h e c o a s t a l s t a t i o n s o f

l o c a t e d r e s p e c t i v e l y on t h e northern and southern s i d e s o f t h e

peninsula. The e s s e n t i a l o b j e c t i v e o f t h i s r e p o r t i s t o show t h a t t h e chlorophyll biomass h a s n o t t h e same l e v e l , s t r u c t u r e and e v o l u t i o n along t h e northern and southern s i d e s and, consequently, may d e f i n e two d i f f e r e n t marine ecosystems.

I t i s w e l l known

(Margalef, 1978) t h a t , f o r example, diatoms and d i n o f l a g e l l a t e s , both important and very d i s t i n c t s p e c i e s of phytoplankton have an e v i d e n t l y d i f f e r e n t geometry i n o r d e r t o s u r v i v e r e s p e c t i v e l y more e a s i l y i n w e l l mixed o r s t r o n g l y s t r a t i f i e d waters. Thus, a well comprehensive study of two marine ecosystems l i v i n g o r surviving on b o t h s i d e s of a p e n i n s u l a , one ( t h e southern) being f r e q u e n t l y washed by g e n t l y

ATLANTIC

\

\, '/

-35'

'\

\\

L,

\

Shelf s t a t i o n

c--,

;

\

8"

Q

-14'30' 35' I

S

BATHURS

O7,

17 '30'

25'

1

20 I

Fig. l a The Cap-Vert Penisnula; i s o b a t h s and loca'ion c o a s t a l and s h e l f s t a t i o n s .

15

of t h e

Fig. l b D i r e c t i o n s of southern, northern c o a s t s and t y p i c a l d i s t r i b u t i o n of s u r f a c e isotherms, i n w i n t e r , with r e s p e c t t o wind.

143 s t r a t i f i e d waters, i n v e r s e l y the o t h e r s i d e s t r o n g l y s t r a t i f i e d , should include a comparative a n a l y s i s of t h e northern and southern d i s t r i b u t i o n s of d i f f e r e n t s u r v i v a l forms of phytoplankton. tunately not realized.

A t the present t i m e ,

t h i s necessary c l a s s i f i c a t i o n i s unfor-

However we remark f a i r l y f r e q u e n t occurences of brown matter

which may o r i g i n a t e from North and i s a p p a r e n t l y blocked o f f "Cap Manuel" (Fig. l a )

:

t h o s e -presumably t o x i c - waters of t h e northern s i d e are s u r e l y c l o s e l y r e l a t e d t o dinoflagellates.

BIOGEOPHYSICAL SURVEY AND MESOSCALE CIRCULATION

R e e f s r u n along t h e northern and e a s t e r n s i d e s o f the Peninsula.

I n t h e bay of Thus,

Goree, f i n e o r c o a r s e sand with a high c o n t e n t of carbonate covers t h e bottom. o r g a n i c m a t t e r i s more abundant a t t h e southern bordure and t h e same i s t r u e of t h e phytobenthic populations.

The n o r t h c o a s t s t r e t c h e s south-westwards whereas t h e

s o u t h c o a s t h a s t h e same d i r e c t i o n a s the dominant "maritime trade-wind",

that is t o

s a y NNW (Fig. l b ) . The width of t h e c o n t i n e n t a l s h e l f changes considerably between t h e northern and southern f r o n t i e r s of Senegal, r e s p e c t i v e l y 2 7 and 54 n.m., o f f t h e Cap-Vert.

w i t h a minimum of 5 n.m.

This geometrical f e a t u r e i s important f o r i t s consequences on t h e

o r g a n i z a t i o n of h y d r o l o g i c a l s t r u c t u r e s and of b i o l o g i c a l populations : f o r example, supposing that t h e plant-biomass o r enrichment of t h e " b a i e de Gorge" depends p r i n c i p a l l y upon a shoreward s h e l f c i r c u l a t i o n , we may i n f e r a l a r g e r ( t w i c e ) accumulation during southward c u r r e n t , because of t h e g r e a t e r a r e a of t h e southern s h e l f .

In fact,

t h e annual e v o l u t i o n of t o t a l c h l o r o p h y l l (Fig. 2) i n d i c a t e s a w e l l s u s t a i n e d enrichment a t t h e Thiaroye c o a s t a l s t a t i o n during t h e summer months of dominant northward c u r r e n t , though t h e l o c a l wind and r e s u l t i n g c o a s t a l upwelling a r e weaker i n Summer than i n winter. A real processus of accumulation s e e m s to e x i s t , which i s r e p r e s e n t a b l e , t o our

mind, by an oceanic upwelling d r i v e n bv t h e curl of t h e wind-stress and averaged with three-months running means

;

c o r r e l a t i o n s "chlorophyll-oceanic upwellings" are thus

s a t i s f y i n g and show, i n s h o r t , a q u i t e l i k e l y e f f e c t of t h e mesoscale c i r c u l a t i o n "chlorophyll-index o f c o a s t a l upwellinq" i s u n e x i s t a n t d u r i n g t h e summer and autumn periods. Northward c y c l o n i c b i f u r c a t i o n s of t h e A t l a n t i c C.C.E.

and, s u r e l y , eastward

[onshore) c i r c u l a t i o n d r i v e n by t h e changes of t h e atmospheric c i r c u l a t i o n , t h a t is t o say, the o s c i l l a t o r y motions of t h e I n t e r t r o p i c a l Convergence Zone, a r e sources Of

a g r e a t summer primary production and v e c t o r s of i t s accumulation along t h e southern c o a s t of Senegal.

The annual chlorophyll biomass e q u a l s 9 mg/m

3

.

144

monthly t o t a l chlorophyll

.

index of coastal : ' upwelling $ ,'

0

I

1

,

I

,

'.

,-*"

, '

?

,

I

,

J

F M A M a J u X A u S 0

Fig. 2

I

,

,

, c

N D J

T o t a l chlorophyll "a" c o n t e n t and upwellings : c o a s t a l and oceanic.

PLANT-BIOMASS AND UPWELLING AROUND THE PENINSULA : LOCAL AND LARGE SCALE EFFECTS

The t o t a l c h l o r o p h y l l "a" c o n c e n t r a t i o n s of t h e northern c o a s t a l s t a t i o n a r e l e s s abundant, about 3 mg/m

3

p e r year

(Fig. 3 ) ; however t h e s e values a r e r e l a t i v e l y high

and r e s u l t s u r e l y o f e i t h e r local v e r t i c a l motions o r advected cold c o a s t a l waters from t h e North because of t h e southern b a r r i e r and of t h e dominant southward surface current.

An i d e n t i c a l wind d r i v e s t h e waters washing both s i d e s of t h e Peninsula

b u t i t s d i r e c t i o n i s o f t e n favourable t o a higher Ekman o f f s h o r e t r a n s p o r t from the southern c o a s t (see t h e upper g r a p h i c s of Fig. 3 ) . f o r t h e p e r i o d of A p r i l t o September, i . e .

T h i s remark i s v a l i d p r i n c i p a l l y

s p r i n g and summer.

Also chlorophyll con-

c e n t r a t i o n s a r e w e l l s u s t a i n e d a t the "Dakar-South'' s t a t i o n b u t n o t a t t h e "DakarNorth" s t a t i o n where t h i s p e r i o d corresponds t o a minimum.

Consequently, t h i s period

must be, with r e s p e c t t o the wind d i r e c t i o n , t h e most p r o p i t i o u s t o t h e hydrodynamic s e p a r a t i o n between t h e two ecosystems. Moreover t h e comparison of t h e w i n t e r s and s p r i n g s of 1979 and 1980 (Fig. 3) i n d i c a t e s a p o s i t i v e c o r r e l a t i o n between t h e wind v e l o c i t y and t h e southern chlorophyll biomass : while v e l o c i t i e s changed, from about 4.7 m / s

(1979) t o 6.0 m / s

(1980),

w i n t e r and s p r i n g chlorophyll c o n c e n t r a t i o n s approximately doubled from 10.5 t o 19 mg/

m3 a s t h e wind s t r e s s e s

:

t h e squares o f wind speeds 4 . 7 and 6.0 a r e r e s p e c t i v e l y 21

and 36. F i n a l l y , when a l o c a l upwelling i s n o t p o s s i b l e , t h a t i s t o say, during December 1979 a t t h e Thiaroye-station and during t h e "15 May-15 September" period a t t h e Yoffs t a t i o n , we remark a good c o r r e l a t i o n t o o with an annual minimum of chlorophyll. O n t h e whole, t h e s e r e s u l t s confirm t h e r e a l e f f e c t s of t h e l o c a l upwelling on thc

145 g l o b a l v a r i a t i o n s of chlorophyll : concordance between t h e maximums of wind v e l o c i t i e s and of c h l o r o p h y l l on t h e one hand, minimums of plant-biomass i n t h e case of non f a vourable wind d i r e c t i o n s on t h e o t h e r hand.

However, as mentioned above, t h e r e i s no

upwelling" during t h e summer, when t h e wind v e l o c i t i e s

c o r r e l a t i o n "chlorophyll-coastal

e q u a l o n l y 3-4 m / s and give, consequently, v e r t i c a l v e l o c i t i e s two o r t h r e e t i m e smaller while chlorophyll c o n c e n t r a t i o n s s t i l l remain r e l a t i v e l y high and f r e q u e n t l y 3 As a m a t t e r of f a c t , t h e standard d e v i a t i o n s com-

comprised between 8 and 9 mg/m

.

puted on s e r i e s of d i f f e r e n t averaged months f o r t h e y e a r s 1973-1979 i n d i c a t e a doubled v a r i a b i l i t y during t h e s p r i n g months with r e s p e c t t o t h e summer months, r e s 3 p e c t i v e l y about 4 and 2 mg/m , t h a t i s t o say 30 % and 20 % of t h e s p r i n g and summer means ( s e e t a b l e I ) .

Fig. 3 Chlorophyllian comparison o f northern and southern s i d e s of t h e peninsula with r e s p e c t t o the wind v e l o c i t y and d i r e c t i o n f i v e days averages.

146 The s e r i e s 73-79 i n d i c a t e t o o a low v a r i a b i l i t y f o r January and November whereas October and December a r e more v a r i a b l e ; l o g i c a l l y , g r e a t v a r i a b i l i t y a r i s e s from upw e l l i n g b u t a glance a t t h e monthly l o c a l winds of t h e s e r i e s 73-79 shows t h e imposs i b i l i t y of an Ekman c o a s t a l upwelling i n c r e a s i n g t h e chlorophyll i n October 1976 and December 1977 (see t a b l e I).

As a m a t t e r of f a c t , the v a r i a b l e r e l a t i o n s h i p between

t h e chlorophyll c o n c e n t r a t i o n s and l o c a l c o a s t a l upwelling i s corroborated by the s m a l l c o r r e l a t i o n between t a b l e s I and I1 : only January 1977, February 1977 and May 1974 a r e i n coincidence.

TABLE I

3 Mean monthly c o n c e n t r a t i o n s of t o t a l chlorophyll "a" (mg/m ) a t t h e Thiaroye T-Station 1973-79 ; p o s i t i v e anomalies a r e underlined.

Month IV

v

VI

VII

4.1 11.6 12.0 17.5 9.4 14.0 8.3

6.7 8.9 10.3 18.8 10.5 10.7 14.2

7.7

7.5 7.3 18.0 8.1

-

10.8

11.0

8.5

4.3

I

I1

5.9 3.3 6.2 5.0 9.9 7.5 10.8

7-4 4.7 8.0 7.2 29.6 11.5 7.3

mean

6.9

~~~~~~~~n

2.7

I11

VIII

IX

x

XI

XI1

2.5 4.1 7.6

3.4 3.4 5.1

7.3 1.7 4.2 4.5 7.1

Year 1972 1973 74 75 76 77 78 79

--

20.4

-

11.6 9.1 10.2 6.9 13.2

15.3 9.2 12.6

12.3 13.1 12.4 10.1 8.0 8.4

11.4

11.3

11.1

4.0

4.6

4.2

-

7.8 10.6

14.3

9.0 8.0 11.1

15.0 8.7

9.4 8.5 9.0

12.3

11.7 3.5 8.0

7.4 3.2 7.0

17.5

7.8 8.8

10.7

9.9

9.5

7.5

5.5

6.1

2.2

2.3

1.8

4.6

2.3

5.0

3.0 3.6

TABLE 11

Mean monthly s u r f a c e thermal anomalies a t t h e Thiaroye T-Station 1973-79 ; negative anomalies a r e underlined ( t e n t h of degrees and a f t e r s e r i e s 60-62, 65-79). Month I

I1

I11

IV

v

VI

VII

VIII

IX

x

XI

XI1

- 2 -18

+ 5 -3

year 1973 74 75 76 77 78 79

Standard deviation

-14 - 6 +15 + 1 -18 + 4 + 5 12

- 4

- 2 + 1

- 4 -11 -12 -12 7 - 6 - 6

10

13

- 2

- 2 -16 -14 - +

+

1

+16

-=

+23

-9 -2 -22 -16 -12 - 5 - 7 -11 + 2 - 3 + 3 11

-

2 6 - 1 + 1 + 3

- 7

- 7

+

+ 2 -15 - 6 += + 4 - 4 3 - 1

0 - 8 +3 0

+ 6 +20 + 9

- 1 +12 +20

7

10

16

15

+ 1 1 4 + 2 - 9

-12 + 5 + 6

- 5 +17 +21

+ 5

+

+ 2

- 3

16

19

8

s 7

+

-5 -16 - 7 -16

147 On t h e c o n t r a r y , an examination of long temperature s e r i e s ( s e e t a b l e s 111, IV) f u r t h e r North a s a t t h e Saint-Louis c o a s t a l s t a t i o n , o r f u r t h e r South as a t t h e Abidjan c o a s t a l s t a t i o n , which i s r e p r e s e n t a t i v e o f t h e e q u a t o r i a l upwelling, g i v e s rat h e r s u r p r i s i n g r e s u l t s : a g r e a t p a r t o f p o s i t i v e chlorophyll anomalies c o i n c i d e s e i t h e r with, to our mind, l a r g e p u l s a t i o n s o f t h e Mauritanian upwelling o r with r e i n forcements of t h e e q u a t o r i a l upwelling. Such events occur namely i n 1976-77 n o t o n l y i n t h e A t l a n t i c b u t a l s o i n t h e e q u a t o r i a l P a c i f i c (Wyrtki, 1979) and a r i s e from an a c c e l e r a t i o n of t h e t r a d e s along t h e e q u a t o r i a l band. Phytoplanktonic blooms may r e s u l t from t h e mauritanian upwelling p r i n c i p a l l y dur i n g June 1975, February and October 1977 ; from e q u a t o r i a l upwelling during October and November 1976, June and December 1977. F i n a l l y , it i s l i k e l y t h a t during more than two y e a r s , s i n c e June 1975 u n t i l December 1977,

l a r g e - s c a l e e f f e c t s a r e dominant on t h e chlorophyll concentrations of

t h e southern c o a s t .

TABLE I11

Monthly sea-surface temperatures a t t h e Saint-Louis

(North-Senegal)

station.

Month I

I1

I11

IV

153 -

162 166 162

164 161 160 162 169 165 170

177 176 175 176 182 179 178

v

VI

VII

-

260

269 267 269 274 268 270 273

VIII

IX

278

272

285 281 280 285 283

281 284 181 278 284 182

x

XI

XI1

209

185 186 177

Year 1973 74 75 76 77 78 79

-

169 160 156 172 176

156

158 - 169 165

232 191 233 203

196 193 201 208

240 241 254 264

274

245

236

189

272 251 243 258

297 209 207 222

-

-

167 185 200

-

TABLE IV

Monthly sea-surface temperatures at t h e Abidjan (Ivory coast) s t a t i o n . Month I

I1

I11

IV

v

VI

VII

VIII

289 278 279 275 280 293

266 286 277

242 264 250 229 238

228 239 229 222

IX

x

XI

XI1

266 242 234

290 279 275

280 273 282

245 250

284

Year 1973 74 75 76 77 78

275 264 273 259 256 274

273 273 271 257 269 269

- -

285

279

268

267

273 282 270 269

-

273 288 273 280

251

253 210 253 214

236

214 220

210 237 264 267 222

264

148 I n o r d e r t o o b t a i n a schematic r e p r e s e n t a t i o n of t h e very d i f f e r e n t upwelling e f f e c t s around t h e p e n i n s u l a , it i s u s e f u l t o reproduce (Fig. 4 and 5) f i r s t a conc e p t u a l model of t h e hydrological s t r u c t u r e (isotherms and c u r r e n t s ) on both coasts according t o Rebert (unpublished manuscript, 1 9 7 9 ) .

To our mind, two e s s e n t i a l fea-

t u r e s r e s u l t from t h e d i f f e r e n c e o f t h e s h e l f s .

SOUTH

COAST

1

SECTION

200

14 k m

Fig. 4

50 km

t

2ooL L

Weak upwelling of t h e n o r t h c o a s t s t a r t i n g from 50 m depth only.

Fig. 5 Upwelling of t h e s o u t h c o a s t ; d e s t a b i l i z a t i o n of t h e thermocline and large v e r t i c a l flow s t a r t i n g from 100 m depth.

The f i r s t one i s t h e o p p o s i t e cross-shelf

flow, o f f s h o r e a t t h e northern c o a s t

and onshore a t the southern coast. The second one i s t h e d e s t a b i l i z a t i o n o f t h e thermocline i n t h e c a s e of t h e gently i n c l i n e d southern slope. above t h e shelf-edge,

As a r e s u l t , s t r o n g t r i d i m e n s i o n a l turbulence may develop

i n t h e same t i m e as a divergence of s u r f a c e c u r r e n t s (Fig. 6 ) .

The r e s u l t i n g doming o f isotherms i s o f t e n observed along t h e a x i s of t h e southern s h e l f i n w i n t e r i n t h e v i c i n i t y o f t h e 30-50 m i s o b a t h s .

(Recall t o o t h e f i g u r e l b

g i v i n g t h e same isothermal c o n f i g u r a t i o n than f i g u r e 6). The doming s t r u c t u r e of t h e southern upwelling enables it t o t r a p a t t h e c o a s t , on t h e l e f t s i d e o f t h e divergence, high n u t r i e n t s which upwelled along i t s r i g h t side.

On t h e c o n t r a r y , t h e pure Ekman o f f s h o r e t r a n s p o r t o f f t h e southern c o a s t re-

moves q u i c k l y t h e upwelled n u t r i e n t s away from t h e Yoff c o a s t a l s t a t i o n .

Chlorophyll

c o n c e n t r a t i o n s are consequently h i g h e r a t t h e Thiaroye c o a s t a l s t a t i o n ( o r Dakar-South station).

I n the n e x t c h a p t e r w e s h a l l t r y t o "model" v a r i a t i o n s of chlorophyll on

both s i d e s of t h e p e n i n s u l a with the a i d o f c u r r e n t and temperature g r a d i e n t s measurements above t h e s h e l f (50 m bottom) and a t t h e c o a s t .

149 ATTEMPT TO MODEL CHLOROPHYLL VARIATIONS ON BOTH SIDES OF CAP-VERT

I n a d d i t i o n t o t h e d a i l y c o a s t a l measurement, hydrological and c u r r e n t observat i o n s w e r e made on t h e s h e l f as mentioned above (Fig. l a ) .

The p e r i o d s of measure-

ments w e r e always s e l e c t e d to coincide with Neap t i d e s . Thus, f o u r t e e n sequences i n c l u d i n g g e n e r a l l y t h r e e northern and t h r e e southern hydrological s t a t i o n s were made i n A p r i l , July, August, September, November and December of t h e year 1979 and t h e f i r s t t h r e e months of t h e year 1980.

These sequences w e r e s h o r t and c u r r e n t , depth,

temperature and c o n d u c t i v i t y r e c o r d i n g s with Aanderaa instruments permit only elementary s t a t i s t i c s on t h e r e s u l t s . I n a d d i t i o n t o t h a t , high c o n c e n t r a t i o n s of n i t r a t e s and o f t e n too of chlorophyll were observed e i t h e r on t h e northern o r t h e southern s h e l f from t h e s u r f a c e t o

l+O'

b0'

14'0'

0'

13'0'

Fig. 6 The doming s t r u c t u r e of isotherms above t h e southern s h e l f of Senegal and t h e remarkable divergence of s u r f a c e c u r r e n t s ; March 1974. (After J . P . R e b e r t ) .

150 t h e bottom.

The same remark however cannot be made f o r t h e summer when n i t r a t e data

are absent.

However, because of the e x i s t e n c e o f domings and r i d g i n g s of the thermo-

c l i n e o n l y o f f t h e southern s h e l f , w e may presume t h a t t h e n i t r a t e maximum disappears from t h e northern c o a s t i n summer. F i r s t , it i s u s e f u l t o r e c a l l (Fig. 2 and 7) t h e i n t e r e s t i n g concordance between t h e annual e v o l u t i o n of t h e southern c o a s t chlorophyll and an oceanic mesoscale upw e l l i n g d r i v e n by t h e c u r l of t h e s t a t i s t i c a l wind s t r e s s i n t h e v i c i n i t y of the s h e l f edge.

The monthly averages computed by t h e author a f t e r meteorological data

s u p p l i e d by t h e U.S.

National Oceanic and Atmospheric Administration a r e grouped i n

two degrees-side subsquare Marsden and, consequently, g i v e o n l y a poor image of the i n t e n s i t y of mesoscale e d d i e s which may develop t o g e t h e r i n both Atmosphere and Ocean. The improvement in f i g u r e 7 i s obtained by averaging t h e summer upwelling o f f river Casamance, a t t h e southern e x t r e m i t y of Senegal, w i t h t h a t of t h e south-Dakar shelf, t h a t i s t o say, subsquares c e n t r e d r e s p e c t i v e l y a t t h e l a t i t u d e s 11.5 N and 13.5 N along 17.7 W.

This averaging i s n o t a r b i t r a r y s i n c e t h e summer r e v e r s a l of the shelf

c i r c u l a t i o n from south t o n o r t h may advect t h e n u t r i e n t s upwelled o f f Casamance as f a r as t h e southern s i d e o f t h e Peninsula.

I

OFF CASAMAWCE (11.5W)

12-

8-

4-

Fig. 7 Modelling o f t h e annual chlorophyll w i t h mesoscale upwellings d r i v e n by the c u r l s of s t a t i s t i c a l wind stress.

W e emphasize a l s o t h a t excess of chlorophyll with r e s p e c t t o mesoscale upwelling du-

r i n g t h e summer months (June, J u l y , August and September) may a r i s e from continental f e r t i l i z a t i o n a s summer i s t h e r a i n y season.

A t l a s t , i n o r d e r t o p o i n t o u t the

slow

151 onshore advection of n u t r i e n t s along t h e s l o p e , t h r e e months running means o f upw e l l i n g were used and centred on t h e t h i r d month. Thus we have obtained a simple s t a t i s t i c a l model which g i v e s t h e broad f e a t u r e s of t h e seasonal e v o l u t i o n of c h l o r o p h y l l .

However, t h e v e r t i c a l v e l o c i t i e s computed with

t h i s model are smaller than 1 2 m/month o r than 5.1Ob4 cm/s, whereas t h e observed ris i n g o f coastal isotherms and r a p i d growing of chlorophyll r e q u i r e v e r t i c a l velocit i e s equal o f t e n t o 10-2 cm/s o r 10 m/day.

These values a r e frequent i n t h e upwel-

l i n g s of west A f r i c a (Hagen, 1974) and it i s obvious t h a t upwelling e f f e c t s should be modelled a t t h e s c a l e s (day-10 k m ) , because of l i k e l y resonance phenomena between t h e wind and t h e c u r v a t u r e s of i s o b a t h s around t h e peninsula

:

mesoscale hydrographic

c o n d i t i o n s may be caused by t h e modal s t r u c t u r e o f b a r o t r o p i c c o n t i n e n t a l s h e l f waves generated by wave f l u c t u a t i o n s i n t h e meridional component of NE-trade winds (Hagen, 1979). I f we 'follow Arthur (1965), w e a r e a b l e t o e s t i m a t e v e r t i c a l motions a t t h e south o f a cape, s t a r t i n g from t h e v o r t i c i t y equation and n e g l e c t i n g a l l t h e t e r m s ( f r i c t i o n included) which do n o t comprise t h e r e l a t i v e v o r t i c i t y .

With t h e s e approximations,

we o b t a i n

where D / D t r e p r e s e n t s t h e i n d i v i d u a l time r a t e of change, f t h e C o r i o l i s parameter, the relative vorticity,

av/ax - au/ay,

5

z t h e z e n i t h a l a x i s and w the v e r t i c a l velo-

c i t y , p o s i t i v e i n c a s e of upwelling. W e can e s t i m a t e t h e lagrangian change o f t h e r e l a t i v e v o r t i c i t y and t h u s o f t h e

v e r t i c a l g r a d i e n t of t h e v e r t i c a l v e l o c i t y by t h r e e d i f f e r e n t , m e t h o d s :

(i) use the d a t a of f i g u r e 6, r a d i i of curvature of isotherms and v e l o c i t i e s of c u r r e n t s (with Arthur, we n e g l e c t t h e v e l o c i t y g r a d i e n t normal t o t h e streamline) : (ii) c a l c u l a t e , using t h e c u r r e n t measurements a t t h e s h e l f - s t a t i o n s ,

av/ax

-

t h e term

a d a y on t h e same f i g u r e :

(iii) e s t i m a t e

-

au/ay f o r t h e s t a t i o n s i n 1979-1980 l o c a t e d o f f Yoff and o f f

Thiaroye. I n o u r a r e a of i n t e r e s t , near t h e peninsula, we g e t t h e following values

:

1)

2.4

s-l

2)

5

s-',

3)

23 values, all p o s i t i v e , of which 2 2 a r e comprised between t h e values 4.2 lob5 and 0.3

(from Fig. 6 ) with a r a d i u s of curvature equal t o 24 km; o f which 3.10-5

f o r t h e term av/ax (from Fig. 6 ) ;

9-l.

The most f r e q u e n t value i s equal t o 4.10-5

and t h e mean i s 1.6

: t h a t gives

a vorticity

by e x t r a p o l a t i o n from 2.

With t h i s v a l u e of t h e v o r t i c i t y , t h e c h a r a c t e r i s t i c time o f change around t h e pen i n s u l a i s 3.10-l'

and by i n t e g r a t i o n between t h e depths 0 and 100 m, we o b t a i n an

152 upwelling of 4.10-*

cm/s-l

o r 33 m p e r day.

T h i s v e r t i c a l v e l o c i t y appears too high,

d o u b t l e s s because of t h e numerous approximations : b u t "10 m p e r day" i s a very plaus i b l e value.

An i n t e r e s t i n g r e s u l t a r i s e s from t h e t h i r d method and concerns the va-

r i a b i l i t y of t h e upwel1ing:the h i g h e s t v e l o c i t i e s may be two t o f o u r times t h e average o r t h e most f r e q u e n t value. Thus, f o r a y e a r l y averaged chlorophyll concentration of 3 about 10 mg/m , it w i l l be n o t s u r p r i s i n g t o observe some maxima a t 30 o r even 3 50 mg/m Moreover t h e r a t i o of t h e extremes values of chlorophyll, equal to about

.

1/30 i s of t h e same o r d e r as t h e r a t i o of extreme v o r t i c i t i e s ,

1/14.

Comparison o f t h e l o c a l winds and t h e i n d i v i d u a l v o r t i c i t i e s estimated by the t h i r d method shows an absence o f c o r r e l a t i o n which may be r e l a t e d t o t h e mesoscale and large s c a l e e f f e c t s suggested above : t h e l o c a l v o r t i c i t y depends on t h e mauritanian and maybe t o o on t h e e q u a t o r i a l winds : it must vary moreover (Rebert, personal communic a t i o n ) w i t h t h e c o a s t a l thermohaline c i r c u l a t i o n . T h e ' l a s t attempt i n modelling (Fig. 8) i s to use t h e north-south g r a d i e n t of surf a c e bimonthly averaged temperatures between t h e two c o a s t a l s t a t i o n s , namely an i n dex o f c i r c u l a t i o n , i n o r d e r t o e s t i m a t e t h e annual v a r i a t i o n of t h e r e l a t i v e abundance of c h l o r o p h y l l between both s i d e s of t h e peninsula.

The c y c l e o f t h e r a t i o

southern/northern c h l o r o p h y l l , which may d i f f e r l a r g e l y from one year t o another seems t o be p a r t i a l l y c o n t r o l l e d by t h e south-north g r a d i e n t of s u r f a c e temperature \

and p e c u l i a r l y by t h e r e v e r s a l of s u r f a c e c u r r e n t s . On t h e whole, t h e r a t i o follows an e v o l u t i o n along a schematic c y c l e c o n s i s t i n g of f o u r branchs which coincide well with t h e f o u r seasons ; i n w i n t e r t h e r a t i o increases slowly whereas t h e s u r f a c e southern waters a r e r a p i d l y c o l d e r ; i n s p r i n g t h e temperature g r a d i e n t reaches i t s maximum and, i n the same time, t h e r a t i o increases much, e s p e c i a l l y i f t h e winds a r e s t r o n g and enduring, l i k e i n 1980 u n t i l t h e end of June.

T h i s process o f n u t r i e n t and c h l o r o p h y l l accumulation on t h e southern shelf

must be l o g i c a l l y dependent on t h e i n t e n s i t y of t h e mesoscale wind v o r t i c i t y which advects waters both warmer and r i c h e r .

I n summer a high r a t i o i s s u s t a i n e d but the

a b s o l u t e values of chlorophyll c o n c e n t r a t i o n decrease on both s i d e s because of the growing grazing by numerous young f i s h .

Since October, with t h e r o t a t i o n of winds

and t h e north-south r e v e r s a l of c u r r e n t s , t h e r e i s a n e t decrease of t h e south-north chlorophyll r a t i o , from t e n o r more, t o one.

SUMMARY

Since a long time f i s h e r y b i o l o g i s t s suspect d i f f e r e n c e s i n t h e abundance and dist r i b u t i o n ( l o c a t i o n , s i z e ) of f i s h on both s i d e s of t h e peninsula.

This difference

i s f i r s t m a t e r i a l i z e d by an oceanic f r o n t l o c a t e d a t t h e "Pointe des Almadies", with

s t r o n g l y s t r a t i f i e d waters on i t s n o r t h e r n f l a n k . Northern waters a r e o f t e n two or t h r e e degrees warmer than southern waters.

Chlorophyll observations p o i n t o u t a

g r e a t e r d i f f e r e n c e between both s i d e s than s u r f a c e p h y s i c a l c o n d i t i o n s : i n f a c t ,

153

40{RATlo

SOUTHERN CHLOROPHYLL NORTHERN

Ju

t (80) i

30-

I SPRING j

'\

20-

\

. A 1 (80)

*

10

-

\\

\

Maximums OF WIND

\

\

*

\

\

\

87-

\\

\ \ \

\

* \ M a , (80)

6-

I*

5-

l M 2 (80) I

I

4-

REVERSALOF

32J1

* *

* 0_ 2 ___c------

0

* F t (80)

I

Evolution of t h e c h l o r o p h y l l i a n south-north r a t i o with r e s p e c t t o t h e south-north g r a d i e n t of temperature.

Fig. 8

154 v e r t i c a l v e l o c i t i e s , threedimensional turbulence and mesoscale eddies p l a y an import a n t r o l e i n t h e space-time v a r i a b i l i t y of t h e n u t r i e n t s and t h u s of chlorophyll. A d e s c r i p t i v e review, axed on t h e d i f f e r e n t s c a l e s of motions d r i v i n g t h e upwellings

o f f Senegal, shows

1)

:

t h e real e f f e c t s of t h e l o c a l upwelling by Ekman o f f s h o r e t r a n s p o r t e s p e c i a l l y during w i n t e r with a well s u s t a i n e d divergence on t h e southern s h e l f (Fig. 6 ) ;

2)

t h e g r e a t negative anomalies of temperature i n s p r i n g which suggest a double act i o n of both mesoscale and l o c a l upwelling;

3)

t h e p o s s i b l e e f f e c t s during s p e c i a l y e a r s of t h e l a r g e - s c a l e c i r c u l a t i o n with an i n s i g h t i n t o t h e e q u a t o r i a l upwelling. T e n t a t i v e models show t h e i n f l u e n c e of t h e slope and width of t h e s h e l f (Fig. 4

and 51, a p l a u s i b l e c o r r e l a t i o n (Fig. 8 ) between t h e north-south g r a d i e n t o f surface temperature and t h e r e l a t i v e chlorophyll on both s i d e s , suggesting a four seasons cycle.

Cyclonic v o r t i c i t y i s t h e most f r e q u e n t and i t s v a r i a b i l i t y may explain t h a t

of t h e c h l o r o p h y l l by upwelling. The most a p p l i c a b l e r e s u l t seems t o be, on t h e whole, t h e c l o s e d c o r r e l a t i o n exist i n g between t h e s t a t i s t i c a l annual e v o l u t i o n s of t h e chlorophyll and of t h e c u r l s of t h e mesoscale wind s t r e s s (Fig. 7 ) .

A convincing demonstration should experiment the

r e a l synoptic winds from moored s h i p s or buoys

:

a p o s i t i v e conclusion could suggest

t h a t t h e p r i n c i p a l r o l e of mesoscale eddies i s t o damp t h e g r e a t f l u c t u a t i o n s and to balance t h e g e n e r a l oceanic c i r c u l a t i o n .

REFERENCES

1965. On t h e c a l c u l a t i o n of v e r t i c a l motion i n e a s t e r n boundary curArthur, R.S., r e n t s from determinations of h o r i z o n t a l motion. J . Geophys. Res., 70, 12:323-327. Champagnat, C. and Domain, F., 1978. cBtes o u e s t a f r i c a i n e s de 10 2 24' Ocganogr., 16, 3-4:239-261.

Migrations des poissons d e m e r s a u l e long des de l a t i t u d e nord. Cah. O.R.S.T.O.M., S6r.

Hagen, E., 1974. A simple scheme of t h e development of c o l d water upwelling circul a t i o n c e l l s along t h e northwest a f r i c a n coast. B i t r . Meereskunde, 33:115-125. Hagen, E. and Weiss, R., 1979. Mesoscale c o a s t a l upwelling dynamics o f f t h e N-W a f r i c a n c o a s t and hypothetic r e l a t i o n s t o t h e chub mackerel concentrations. I.C.E.S. C.M. 1979/C:21:1-8. Margalef, R,, 1978. Life-forms of phytoplankton as s u r v i v a l a l t e r n a t i v e s i n an unstable environment. Ocean. A c t a , 1, 4:493-509. Wyrtki, K.,

1979.

E l Nino.

L a Recherche, 10, 106:1212-1220.

155

DIFFERENTIAL DISPERSION AND NUTRIENT-PLANKTON

R.

A.

DISTRIBUTIONS

PARKER

Departments o f Zoology and Computer Science, Washington S t a t e University, Pullman (USA)

ABSTRACT

D i f f e r e n t i a l d i s p e r s i o n r a t e s were p o s t u l a t e d f o r d i s s o l v e d n u t r i e n t s , plankton, and f i s h i n an upwelling plume w i t h c o n s t a n t i n p u t s . Observations o f f t h e c o a s t of Peru prompted a n e c o l o g i c a l model involving phytoplankton, zooplankton, n i t r a t e , ammonium, s i l i c a t e , and anchoveta. The biological-chemical i n t e r a c t i o n s were l i n e a r i z e d and coupled t o t u r b u l e n t t r a n s p o r t . Steady s t a t e s o l u t i o n s assuming a f i x e d anchoveta d i s t r i b u t i o n showed t h a t t h e h o r i z o n t a l d i s t r i b u t i o n of phytoplankton w a s q u i t e s e n s i t i v e t o d i f f e r e n t phytoplankton d i s p e r s i o n r a t e s , whereas n u t r i e n t s and zooplankton were not.

INTRODUCTION

Much i s known about t h e hydrodynamics of oceanic c i r c u l a t i o n , based p a r t l y on t h e e i g h t e e n t h century t h e o r e t i c a l work of Euler.

B i o l o g i c a l and chemical i n t e r -

a c t i o n s have been s t u d i e d n e a r l y a s long i n an e c o l o g i c a l c o n t e x t , y e t attempts t o couple a l l of t h e s e processes a s t o t a l ecosystem models d i d not become comonp l a c e u n t i l t h e l a s t two decades.

The advent of r e l a t i v e l y inexpensive, powerful

computers l e d many i n v e s t i g a t o r s of t h e e a r l y s e v e n t i e s t o c o n s t r u c t extremely l a r g e and complex models, hopefully t o mimic t h e r e a l world more completely. Successful r e a l i z a t i o n s of t h e s e hopes were r a r e , prompting more r e c e n t attempts devoted t o a few s i g n i f i c a n t v a r i a b l e s .

S t i l l , t h e computing e f f o r t required t o

s o l v e dynamic systems of d e s c r i b i n g p a r t i a l d i f f e r e n t i a l equations i s o f t e n prohibitive.

Hydrodynamic elements tend t o be neglected i n an e f f o r t t o reduce

c o s t , b u t a d i s p r o p o r t i o n a t e amount of a t t e n t i o n s t i l l i s focused on b i o l o g i c a l chemical phenomena.

Typically, then, hydrodynamics a r e o v e r s i m p l i f i e d by using

only l i n e a r t e r m s , whereas o t h e r processes a r e included a s highly nonlinear contributions. Turbulent d i s p e r s i o n rates f o r d i s s o l v e d substances have been f r e q u e n t l y measured, both i n t h e l a b o r a t o r y ( e . g . S u l l i v a n , 1971) and i n t h e f i e l d (Wilson and Okubo, 1978; Chatwin and S u l l i v a n , 1979).

Hinze (1972) has suggested t h a t

t h e d i s p e r s i o n of d i s c r e t e p a r t i c l e s may be more r a p i d than t h a t of t h e t r a n s p o r t i n g f l u i d ; however, much evidence supports t h e view t h a t , f o r p a r t i c l e s s l i g h t l y more dense than t h e f l u i d , d i s p e r s i o n i s less r a p i d (Peskin, 1962;

Snyder and Lumley, 1 9 7 1 ) .

Under a s t r i c t a s s u m p t i o n o f l i n e a r r e s i s t a n c e , Hinze

(1975) c o n c l u d e d t h a t t h e d i f f e r e n c e between f l u i d and p a r t i c u l a t e s p h e r e v e l o c i t i e s tends to zero over t i m e .

Of c o u r s e , Landau and L i f s h i t z (1959) p o i n t e d o u t l o n g

ago t h a t s t e a d y s t a t e d i s p e r s i o n i s i n v e r s e l y p r o p o r t i o n a l t o p a r t i c l e d i a m e t e r , a g a i n based on a l i n e a r e x p r e s s i o n f o r d r a g f o r c e .

Unfortunately, d a t a are lacking

on r e l a t i v e d i s p e r s i o n r a t e s f o r p l a n k t o n i c o r g a n i s m s , where i r r e g u l a r s h a p e s may g e n e r a t e h i g h Reynolds numbers and t h u s change t h e t u r b u l e n c e .

The i s s u e i s

f u r t h e r c o m p l i c a t e d by t h e e f f e c t s o f m o l e c u l a r d i f f u s i o n on o v e r a l l d i s p e r s i o n

of s o l u b l e m a t e r i a l s .

I t is not surprizing,

t h e r e f o r e , t h a t a r i g o r o u s mathe-

m a t i c a l t r e a t m e n t o f n u t r i e n t - p l a n k t o n d i s t r i b u t i o n s i n t h e ocean i s lacking. Major o c e a n i c c u r r e n t s move i n r a t h e r p r e d i c t a b l e ways, a d v e c t i n g p l a n k t o n i c o r g a n i s m s and d i . s s o l v e d n u t r i e n t s ( e . g . n i t r a t e , ammonium, s i l i c a t e ) i n a t u r b u l e n t flow.

P h y t o p l a n k t o n , e s p e c i a l l y , t h r i v e i n r e g i o n s where u p w e l l i n g i s p r e v a l e n t ,

s i n c e a V i r t u a l l y c o n t i n u o u s s u p p l y o f n u t r i e n t s i s b r o u g h t t o t h e s u r f a c e and increases photosynthetic a c t i v i t y .

The e a s t e r n boundary r e g i o n s o f t h e P a c i f i c

Ocean a r e c h a r a c t e r i z e d by p e r s i s t e n t u p w e l l i n g and h i g h p r i m a r y p r o d u c t i v i t y . t h e c o a s t of P e r u , f o r example, t h i s p r o d u c t i o n s u p p o r t s a d e n s e p o p u l a t i o n

Off

o f a n c h o v e t a , a f i s h t h a t i s phytophagous d u r i n g much o f i t s l i f e .

Anchoveta

a r e l o c a l l y a b u n d a n t ( C u s h i n g , 1971), o f t e n c o n c e n t r a t i n g where a v a i l a b l e food is the g r e a t e s t .

These a n i m a l s , i n t u r n , e x c r e t e l a r g e q u a n t i t i e s o f ammonium

which f u r t h e r s t i m u l a t e s a l g a l growth.

A s e x p e c t e d , t h e r e s u l t i n g long-term

d i s t r i b u t i o n p a t t e r n s f o r n u t r i e n t s and p l a n k t o n i n t h e Peru u p w e l l i n g s y s t e m

are r a t h e r complicated (Kelley e t a l . ,

1975).

The f o l l o w i n g report e x p l o r e s

some p o s s i b l e e x p l a n a t o r y mechanisms c o v e r i n g a p e r i o d o f s e v e r a l weeks d u r i n g which p h y s i c a l f e a t u r e s , g r a z i n g p r e s s u r e by f i s h , and s y s t e m i n p u t s a r e assumed constant.

Because t h e o c e a n r e p r e s e n t s a r a t h e r s t a b l e e n v i r o n m e n t , i t seems

r e a s o n a b l e t o look a t t h e consequences of l i n e a r i z e d e c o l o g i c a l p r o c e s s e s i n t h e neighborhood o f long-term p o p u l a t i o n means.

Of c o u r s e , t h e s e d e v i a t i o n s e x c l u d e

t h e d r a m a t i c changes a s s o c i a t e d w i t h v i o l e n t ( a l t h o u g h u s u a l l y b r i e f ) d e p a r t u r e s , but

t h e r e s u l t s s h o u l d p o i n t toward l a r g e - s c a l e e f f e c t s .

THE MODEL

M o s t o f t h e models t h a t i n c o r p o r a t e f i s h ( e . g . Walsh, 1975) d o so by assuming

t h a t t h e a n i m a l s a r e u n i f o r m l y d i s t r i b u t e d o v e r t h e modelled r e g i o n .

But as

a l r e a d y o b s e r v e d , a n c h o v e t a t e n d t o c o n c e n t r a t e i n p r o d u c t i v e areas.

O f course

t h e s e f i s h a r e n o t d i s p e r s e d by t h e u p w e l l i n g plume, s c r i b e a s t e a d y spatial arrangement.

so one i s prompted t o p r e -

s u p p o s e t h a t a 20-m v e r t i c a l l y mixed l a y e r

i s g r a z e d by a v e r y d e n s e p o p u l a t i o n of a n c h o v e t a o v e r a n area 4 0 x 100 km. Although t h e f i s h a r e a t t r a c t e d t o t h e t h e r m o c l i n e , d i e 1 v e r t i c a l m i g r a t i o n

157 creates a n a v e r a g e d a i l y g r a z i n g p r e s s u r e o v e r t h e mixed l a y e r .

The f o l l o w i n g

g e n e r a l h o r i z o n t a l d e n s i t y d i s t r i b u t i o n h a s been p o s t u l a t e d h e r e f ( x , y ) = al + a [ l 2

2

+ a 3x ] e x p [ - a 4 x - a 5y ]

L e t - 2 0 km 5 y I 20 km and 0 5 x 5 100 km r e p r e s e n t l a t e r a l and l o n g i t u d i n a l

S p e c i f i c v a l u e s o f a used i n t h i s s t u d y i p r o d u c i n g a maximum d e n s i t y o f 300 i n t h e middle

d i m e n s i o n s of t h e plume, r e s p e c t i v e l y .

w e r e 1 5 , 235, 0 . 2 , 0 . 1 , and 0 . 0 1 ,

o f t h e plume ( y = 0 ) and 5 km downstream.

Also n o t e t h a t d e n s i t y r a p i d l y approaches

1 5 as one moves toward t h e e d g e s of t h e plume ( F i g . 1 ) .

1

F i g . 1. Assumed a n c h o v e t a d i s t r i b u t i o n o v e r 40 x 1 0 0 km.

Now assume a c o n s t a n t l o n g i t u d i n a l v e l o c i t y V from l e f t t o r i g h t i n F i g . 1, w i t h no l a t e r a l f l o w .

S i n c e dV/dy = 0, l a t e r a l d i s p e r s i o n i s t y p i c a l l y less t h a n

l o n g i t u d i n a l d i s p e r s i o n ( s e e Hinze, 1975 o r N i r and Pismen, 1979) and i s n e g l e c t e d i n model f o r m u l a t i o n . St

=

DS

- VS

xx

+

Consider t h e system o f e q u a t i o n s

c h e m i c a l and b i o l o g i c a l dynamics

where S i s a v e c t o r o f n u t r i e n t c o n c e n t r a t i o n s and o r g a n i s m d e n s i t i e s . and S cients. S2

St, Sm,

a r e p a r t i a l d e r i v a t i v e s , and D i s a d i a g o n a l m a t r i x o f d i s p e r s i o n c o e f f i T a b l e I summarizes p r o p o s e d r e l a t i o n s h i p s among S1 ( p h y t o p l a n k t o n ) , (fish). 6 The p a r a m e t e r s

( z o o p l a n k t o n ) , S3 ( n i t r a t e ) , S4 (ammonium), S5 ( s i l i c a t e ) , and S

A l l r e s u l t s a r e e x p r e s s e d a s mg-atoms

o f n i t r o g e n m-3

e x c e p t S5.

c o n s i s t o f p h y t o p l a n k t o n growth and s i n k i n g r a t e s k l and k 2 , z o o p l a n k t o n and anchoveta g r a z i n g rates k

and k4, p h y t o p l a n k t o n t o z o o p l a n k t o n c o n v e r s i o n 3 e f f i c i e n c y k5, n a t u r a l m o r t a l i t y and p r e d a t i o n losses f o r z o o p l a n k t o n k and k I’ 6 p l a n k t o n t o f i s h c o n v e r s i o n e f f i c i e n c y k8, f i s h m o r t a l i t y k g , f l u x r a t e k for 10 n u t r i e n t s e n t e r i n g t h e mixed l a y e r f r o m below, c o n c e n t r a t i o n kll o f s i l i c a t e i n p h y t o p l a n k t o n r e l a t i v e t o n i t r o g e n , f r a c t i o n k12 o f p l a n k t o n e a t e n by f i s h t h a t i s e x c r e t e d a s ammonium, f r a c t i o n k13 o f p h y t o p l a n k t o n consumed.by z o o p l a n k t o n t h a t

158 TABLE I

Chemical and b i o l o g i c a l r e l a t i o n s h i p s

- k2 - k3P2S2 - k p S I S

S i = [klP1

4 3 6

Si

= [k5k3P2S1

S;

=

-k1p1S1S3

s;

=

-k p S S /is3 exp(-K S ) 1 1 1 4 2 4

- k6 - k p

S IS

7 3 6

1

2

exp(-K S ) / { S exp(-K S ) 2 4 3 2 4

+ s4}

f

+

S4}

+

k12{k p S 4 3 1

klO(HN - S ) 3

+

k7p3S2]S6

+

k13k3p2S1S2

+

klO(HS

+ k (HA-S) 10 4 S & = -kllklplS1 S'

6

= [k { k p S

8

4 3 1

+ kI4kl2{k4p3S1 + k 7p 3S 2 IS 6 + k 1 4k 1 3k 3p 2 S 1S 2 + k p

S

7 3 2

-

k IS

9

-

'5)

6

where

i s e x c r e t e d as ammonium, and k14 i s t h e s i l i c a t e f r a c t i o n of t o t a l consumption excreted by zooplankton and f i s h .

I n a d d i t i o n , HN, H A , and H S a r e f i x e d concentra-

t i o n s of n i t r a t e , ammonium, and s i l i c a t e beneath t h e mixed l a y e r . K1,

K2,

K3,

S 3 exp(-K S

and K4 appear i n pl,

2 4

Parameters

which includes an e f f e c t i v e n i t r o g e n pool

1 + S4 where t h e exponential term mimics ammonium i n h i b i t i o n of

m2 ml m2 expression of t h e form N1ml N2 / ( K 1 + N N ) 1 2 was adopted t o r e f l e c t n i t r o g e n - s i l i c a t e growth r a t e i n t e r a c t i o n s i n phytoplankton n i t r a t e uptake.

A Michaelis-Menten

w i t h a N:Si r a t i o of m :m . Since marine forms o f t e n have a r a t i o near 1:1, 1 2 ml and m2 were s e t accordingly. The second t e r m i n p1 r e p r e s e n t s t h e average l i g h t i n t e n s i t y over t h e mixed l a y e r , modified t o include a self-shading e f f e c t by phytoplankton (K3 and K4 a r e e x t i n c t i o n c o e f f i c i e n t s m u l t i p l i e d by 2 0 ) . F i n a l l y , p 2 and p3 a r e grazing f u n c t i o n s c o n s i s t e n t with d a t a of Parsons e t a l . (1969) and F r o s t (1972), as w e l l a s arguments given by S t e e l e (1974)

.

C l e a r l y t h i s model i n c l u d e s f a r more complexity than i s j u s t i f i e d by t h e t r e a t ment o f t u r b u l e n t t r a n s p o r t .

L i n e a r i z a t i o n of t h e chemical and b i o l o g i c a l

r e l a t i o n s h i p s i n Table I around e q u i l i b r i a S ? l e a d s t o a new system f o r

159 deviations s = S

st = D s

- Vs

xx

-

S*, t h a t i s ,

+ 6s

A

where B i s a m a t r i x o f c o e f f i c i e n t s g e n e r a t e d from f i r s t - o r d e r T a y l o r e x p a n s i o n s . However, t h e a n c h o v e t a a r e n o t a l l o w e d t o move or grow d u r i n g t h e s i m u l a t i o n I n s t e a d , a s t e a d y - s t a t e s o l u t i o n was found f o r t h e r e d u c e d s y s t e m of

period.

f i v e equations

st = 0

=

Ds

-

xx

+

VS

+

Bs

[f(X,y) - 1 5 ]S -6

B i s t h e m a t r i x formed by d e l e t i n g t h e s i x t h row and column from

r e p r e s e n t s t h e f i r s t f i v e e l e m e n t s i n column s i x . S(X,y) = - [ I

+

0.2XI

and

6 .6

The s o l u t i o n i s

+ 0.2(B + 0.1VI + 0.0l.D) -1( V I + 0.2D)I a

+

6,

exp[0.5x{VD

-1

-

[B

+

0.1VI

+

0.01D]

- 4D-1B)'}]

((VD-l)

*

*

235 exp[-O.lX

-

2 ^ 0.01y ]B

.6

C

where C = s(0,O)

+

[I

+

0.2(B

+

0.1VI

+

' [B

+

+

O.OlD)-'(VI

0.1VI

+

0.2D)I

O.OlD]

-

235 exp[-0.01y2]g

-6

A

P a r a m e t e r v a l u e s c o n t r i b u t i n g t o B were b a s e d p r i m a r i l y on t h e P e r u u p w e l l i n g l i t e r a t u r e , b u t k S , ki, k9, klO, t h e n o n l i n e a r system S '

=

kll, and k12 w e r e t a k e n as t h o s e v a l u e s s a t i s f y m g

0 ( T a b l e I).

P o s t u l a t e d e q u i l i b r i u m l e v e l s cannot be

d e t e r m i n e d s o f i r s t a p p r o x i m a t i o n s w e r e d e r i v e d from o f f s h o r e d a t a ,

F i n a l parameter

and e q u i l i b r i u m v a l u e s a r e shown i n T a b l e 11.

RESULTS AND DISCUSSION

The s o l u t i o n s ( x , y ) w a s c a l c u l a t e d a t each p o i n t o f a 2-km s q u a r e g r i d , assuminq 2 z o o p l a n k t o n and a l l n u t r i e n t i n p u t p r o p o r t i o n a l t o e x p ( - 0 . 0 4 y 1 . Then i s o p l e t h s

w e r e p l o t t e d u s i n g a l i n e a r i n t e r p o l a t i o n scheme.

Realize t h a t the r e s u l t s

d e p i c t e d i n e a c h o f t h e f o l l o w i n g f i g u r e s are b a s e d on 1 0 7 1 p o i n t s , s u f f i c i e n t

t o i d e n t i f y p a t t e r n s b u t n o t enough t o p r o d u c e e x t r e m e l y smooth c o n t o u r s .

Since

t h e d i s p e r s i o n r a t e s f o r p h y t o p l a n k t o n are open t o q u e s t i o n , t h e model was r u n -1 2 1 . 0 , and 2 . 0 km d a y , i n c l u d i n g h a l f and d o u b l e t h e n u t r i e n t d i s p e r 2 Only t h e p h y t o p l a n k t o n d i s t r i b u t i o n depended h e a v i l y s i o n r a t e o f 1 k m day-'.

using 0.5,

on t h e s e r a t e s , so t h e f i g u r e s r e f e r r i n g t o o t h e r components a r e l i m i t e d t o t h e In a l l simulation c a s e o f e q u a l d i s p e r s i o n r a t e s f o r p h y t o p l a n k t o n and n u t r i e n t s . 2 -1 -1 r u n s , z o o p l a n k t o n d i s p e r s i o n w a s 0 . 1 km day and v w a s 1 7 km d a y

.

160 TABLE I1

h

Parameter and e q u i l i b r i u m v a l u e s used t o f i n d t h e e l e m e n t s o f B l i s t e d below

kl = 2.80

k8

= 0.13

K1 =

3.2

s*1 =

8.0

s (0,O) =

1

k2

=

0.17

kg

= 0.008

K

=

0.5

s*2

=

0.3

s (0,O)

=

1

k3

=

0.50

k10

= 0.11

K

=

2.8

s*3

=

3.3

s (0,O)

=

25

k4 = 0.13

kll

=

S4(0,O) =

2

=

20

2

3

k12 = 0.56

K5 =

0.04

s*5

k6 = 0 . 0 5

k13 = 0 . 3 6

K

=

0.01

55 = 15.0

k7 = 0.13

k14 = 0.045

HN = 18.0

5

2

3

0.58

= 0.36

k

1

6

HA =

=

1.0

S,(O,O)

S 6 ( 0 , 0 ) = 250

b

3.0

HS = 1 3 . 6

-0.5053 0.0010 -0.1112

1.2558 0.0

-0.0017

0.2538

0.0

0.0

0.0117

-0.8362

-0.1468 -0.4431

0.0

-0.8374

0.0267

0.2566

-0.4 184

0.0211

0.0211

0.0

-0.0003

0.0793

i m p a c t on t h e p h y t o p l a n k t o n .

greater.

0.0016

0.8113

0.0

0.0

Zooplankton i s n o t a b u n d a n t i n t h e Peru u p w e l l i n g system. d e n s i t y i s t y p i c a l l y 25-fold

-0.0023

0.0002

-0.9209

0.0

-0.0624

0.0361 0.0

I n f a c t , phytoplankton

Consequently, t h e zooplankton has l i t t l e

Anchoveta, a l t h o u g h p r i m a r i l y phytophagous, do feed

on z o o p l a n k t o n and t h e i m p a c t o f t h e i r h i g h numbers i s d e m o n s t r a t e d c l e a r l y i n Fig.

2.

F i s h c o n c e n t r a t e d i n t h e i n s h o r e waters remove s i g n i f i c a n t q u a n t i t i e s of

z o o p l a n k t o n , s u g g e s t i n g t h a t g r a z i n g may b e r e s p o n s i b l e f o r t h e low p o p u l a t i o n s f r e q u e n t l y o b s e r v e d i n u p w e l l i n g areas. Another o b v i o u s e f f e c t o f t h e f i s h i s a p p a r e n t i n t h e d i s t r i b u t i o n o f ammonium (Fig. 3 ) .

L a r g e amounts a r e e x c r e t e d i n s h o r e , t h e n a d v e c t e d by t h e plume.

r e s u l t i n g p a t t e r n resembles a r a t h e r drawn o u t v e r s i o n o f F i g . 1. s t i m u l a t e s p h y t o p l a n k t o n p r o d u c t i o n and i n h i b i t s n i t r a t e u p t a k e . r e f l e c t e d i n F i g . 3 by d i s t o r t e d downstream i s o p l e t h s .

The

Ammonium b o t h The l a t t e r i s

S i l i c a t e , on t h e o t h e r

hand, e x h i b i t s a smooth p a t t e r n l i n k e d c l o s e l y w i t h i t s i n p u t d i s t r i b u t i o n . B u t what o f t h e p h y t o p l a n k t o n ?

An e a r l i e r s t u d y e x c l u d i n g f i s h ( P a r k e r 1979)

l e d t o t h e c o n c l u s i o n t h a t l a r g e amounts o f p h y t o p l a n k t o n must s i n k from t h e

161

I

F i g . 2 . Simulated zooplankton d i s t r i b u t i o n .

mixed l a y e r to m a i n t a i n a b a l a n c e d system.

But t h i s is cont r ar y t o t h e s t u d i e s

o f Menzel ( 1 9 6 7 ) which showed r e l a t i v e l y c o n s t a n t p a r t i c u l a t e c a r b o n l e v e l s i n d e e p w a t e r b e n e a t h s p a t i a l l y v a r y i n g l e v e l s i n t h e mixed l a y e r .

Thus o n e n e e d s

a s i n k f o r p h y t o p l a n k t o n , s u p p o r t i n g a n e s s e n t i a l r o l e f o r a n c h o v e t a or o t h e r fish. R e s u l t s u t i l i z i n g t h e t h r e e d i s p e r s i o n rates f o r phytoplankton a r e i l l u s t r a t e d i n F i g . 4.

C e r t a i n l y t h e assumed d i s p e r s i o n r a t e s l e a d t o markedly d i f f e r e n t

p h y t o p l a n k t o n d i s t r i b u t i o n s ; a low r a t e a l l o w s t h e r a p i d b u i l d u p n e a r s h o r e ( u p p e r p a n e l i n F i g . 4 ) whereas a h i g h r a t e d o e s n o t ( l o w e r p a n e l ) .

I n every

case, t h e a n c h o v e t a , where a b u n d a n t , remove l a r g e q u a n t i t i e s of p l a n t material. I n t h e r e a l w o r l d , d i f f e r e n t p h y t o p l a n k t o n d i s t r i b u t i o n s l i k e l y would a f f e c t t h e a n c h o v e t a d i s t r i b u t i o n , p e r h a p s compensating f o r v a r i a b i l i t y and s t a b i l i z i n g t h e phytoplankton d i s t r i b u t i o n p a t t e r n . i n o v e r a l l s y s t e m dynamics.

Thus t h e f i s h a p p e a r t o p l a y a dominant r o l e

Why d i f f e r e n t p h y t o p l a n k t o n d i s t r i b u t i o n s do n o t

change n u t r i e n t d i s t r i b u t i o n p a t t e r n s i s a l s o open t o s p e c u l a t i o n .

When n u t r i e n t

d i s p e r s i o n i s g r e a t e r , t h e d i s s o l v e d components w i l l move toward r e g i o n s of g r e a t e r demand by t h e p l a n t s , t h a t i s , n u t r i e n t s a r e drawn i n t o t h e r e g i o n from o u t s i d e o f t h e s i m u l a t e d area. o u t s i d e s o u r c e s is reduced.

When n u t r i e n t d i s p e r s i o n i s less, demand from

I f t h e area w e r e c l o s e d , o f c o u r s e , p h y t o p l a n k t o n

would d e p l e t e n u t r i e n t s u p p l i e d i n d i r e c t p r o p o r t i o n t o growth r a t e .

M o s t models

r a i s e m o r e q u e s t i o n s t h a n t h e y answer, and t h i s one i s no e x c e p t i o n !

Neverthe-

l e s s , r e s u l t s s u g g e s t t h a t t h e d i s p e r s i o n p r o p e r t i e s o f a l l components must b e s t u d i e d more i n t e n s i v e l y i f w e are t o f u l l y u n d e r s t a n d u p w e l l i n g induced productivity.

162

Ammonium

5

Nitrate

Silicate

F i g . 3. S i m u l a t e d n u t r i e n t d i s t r i b u t i o n s .

163

0.5 krn2 day-’

1 8

2 -1 2.0 km day

Fig. 4. Simulated phytoplankton distributions.

164 REFERENCES

Chatwin, P.C. a n d S u l l i v a n , P.J., 1979. Measurements o f c o n c e n t r a t i o n f l u c t u a t i o n s i n r e l a t i v e t u r b u l e n t d i f f u s i o n . J . F l u i d Mech., 94:83-101. 1971. Upwelling and t h e p r o d u c t i o n o f f i s h . Adv. M a r . B i o l . , C u s h i n g , D.H., 9:255-334. F r o s t , B.W., 1972. E f f e c t s o f s i z e and c o n c e n t r a t i o n o f food p a r t i c l e s o n t h e f e e d i n g b e h a v i o r o f t h e m a r i n e p l a n k t o n i c copepod C a l a n u s p a c i f i c u s . Limnol. Oceanogr., 17:805-815. I n : G. H e t s r o n i , H i n z e , J.O., 1972. T u r b u l e n t f l u i d and p a r t i c l e i n t e r a c t i o n . S . Sideman and J.P. H a r t n e t t ( E d i t o r s ) , P r o g r e s s i n H e a t and Mass T r a n s f e r , Volume 6 . Pergamon, New York, pp. 433-452. H i n z e , J . O . , 1975. T u r b u l e n c e . M c G r a w - H i l l , N e w York, 790 p p . K e l l e y , J . C . , W h i t l e g e , T.E. and Dugdale, R . C . , 1975. R e s u l t s o f sea S u r f a c e mapping i n t h e P e r u u p w e l l i n g s y s t e m . Limnol. Oceanogr., 20:784-794. Landau, L . D . a n d L i f s h i t z , E.M., 1959. F l u i d Mechanics. T r a n s l a t e d from t h e R u s s i a n by J . B . Sykes and W . H . R e i d . Pergamon, London; Addison-Wesley, Reading, 536 p p . 1967. P a r t i c u l a t e o r g a n i c c a r b o n i n t h e d e e p sea. Deep-sea R e s - , Menzel, D.W., 1 4 : 229-238. N i r , A . and Pismen, L.M., 1979. The e f f e c t o f a s t e a d y d r i f t on t h e d i s p e r s i o n o f a p a r t i c l e i n t u r b u l e n t f l u i d . J. F l u i d Mech., 94:369-381. 1979. Some e f f e c t s o f t u r b u l e n t t r a n s p o r t on n u t r i e n t - p l a n k t o n P a r k e r , R.A., d i s t r i b u t i o n s . P r o c e e d i n g of I n t e r n a t i o n a l Symposium on M a t h e m a t i c a l Modeling o f Man-Environment I n t e r a c t i o n . Computation C e n t e r o f Academy o f S c i e n c e s o f USSR, MOSCOW, pp. 149-163. P a r s o n s , T.R., L e B r e s s e u r , R . J . , F u l t o n , J . D . a n d Kennedy, O . D . , 1969. P r o d u c t i o n s t u d i e s o n t h e S t r a i t o f G e o r g i a . 11. Secondary p r o d u c t i o n u n d e r t h e F r a s e r R i v e r plume, F e b r u a r y t o May, 1967. J . Exp. M a r . B i o l . E c o l . , 3:39-50. P e s k i n , R.L., 1962. The d i f f u s i v i t y o f s m a l l suspended p a r t i c l e s i n t u r b u l e n t f l u i d s , N a t i o n a l Meeting A.I.Ch.E., Baltimore. 1971. Some measurements o f p a r t i c l e v e l o c i t y S n y d e r , W.H. and Lumley, J . L . , a u t o c o r r e l a t i o n f u n c t i o n s i n t u r b u l e n t f l o w . J . F l u i d Mech., 48:41-71. S t e e l e , J . H . , 1974. The S t r u c t u r e o f Marine Ecosystems. H a r v a r d Univ. P r e s s , Cambridge, 128 pp. S u l l i v a n , P . J . , 1971. L o n g i t u d i n a l d i s p e r s i o n w i t h i n a two-dimensional t u r b u l e n t s h e a r f l o w . J. F l u i d Mech., 49:551-526. Walsh, J . J . , 1975. A s p a t i a l s i m u l a t i o n model o f t h e P e r u u p w e l l i n g ecosystem. Deep-sea Res., 22:201-236. W i l s o n , R.E. and Okubo, A . , 1978. L o n g i t u d i n a l d i s p e r s i o n i n a p a r t i a l l y mixed e s t u a r y . J. Mar. R e s . , 36:427-447.

165

HYDRODYNAMICS AS A LIMITING FACTOR IN THE DEVELOPMENT OF THE BALTIC SEA ECOSYSTEM A.M. AITSAM Department of the Baltic Sea, Institute of Thermophysics and Electrophysics, Academy of Sciences

of the Estonian S.S.R., U.S.S.R.

ABSTRACT Different examples Of the influence of dynamics on the development of an ecosystem, on the basis of the Baltic Sea, are considered. Characteristic features and scales of the variability of the Baltic Sea waters are given. Relying on the expeditional data obtained by the Department of the Baltic Sea of the Institute of Thermophysics and Electrophysics on the R/V "Ayu-Dag" the synoptic and smallscale variabilities pf the Baltic are discussed.

INTRODUCTION Hydrodynamics has an effect on the development of sea ecosystems mainly through plankton, either directly or indirectly, changing the conditions for the development of plankton. The direct influence is expressed by the transport of plankton

by

flowing water, i.e. by processes of advection and diffusion. The patchiness of phytoplankton in seas is caused by the simultaneous influence of diffusion dying off (Platt,Denmann,l975). From the variance spectra for chlorophyll

and and

current speed in Lake Tahoe, California (Powell et a1.,1975), Fig.1, it can be seen that up to spatial scales of the order of lo0 m the development of

phyto-

plankton is controlled by turbulence, but at larger scales the influence of other factors arises.

.

The main effect of Marine Hydrodynamics i s the variations of the plankton living

conditions, of salinity, temperature and water stratification, of the nutrients in water, that of light etc. Synoptic eddies, appearing in oceans and seas, depending on rotation direction, may either enrich surface layers with nutrients (cyclonic ,sddies), lifting bottom cold waters to the surface (Figs. 2 and 3 ) or lowering surface warm waters, poor in nutrients deep into the oceans (Fig.4).

At that, this kind of large scale eddies or a r e s carry along vast

water masses for long periods of the order of

several years. After the

kinetic

energy of eddies is transformed into wave motion, the water masses transported by eddies mix with the

neighbouring water.

166 POWER SPECTRA v5 INVERSE WAVELENGTH

7 x-CHLOROPHYLL SPECTRUM \

SEPT. 27 1973

1

I

10-6

1

10-4

1

1 1Q-2

-1 INVERSE WAVELENGTH, cm

Fig.1. Variance spectra for chlorophyll and

current speed in Lake Tahoe,

California. Vertical lines are the limits of 80 per cent reliability (Powel et.a1.,1975). Processes of upwelling (Fig.5) are the second source for lifting deep waters, saturated with nutrients ,to surface layers. Fronts in the open sea as well as in its coastal areas exercise a considerable influence on the plankton development. The example of fronts, presented in Fig.5 and 6 is a good illustration for the latter phenomenon. Changes in water stratification under the influence of various hydrological processes are of an essential Relying on

the above-given facts we may conclude that the characteristic time

scales of the planktons scales of

importance in the development of the ecosystem.

growth may be

commensurable with the

limitative physical processes. Platt

corresponding

et al. (1975) showed that the

characteristic time frequency of the phytoplankton turnover was of the order Of

(0.5-3.0). 10-5sec-1 corresponding to periods of several days comparable with the average time scales of upwelling processes and of vertical and horizontal diffusion processes.

To determine the limitative role of Hydrodynamics, the whole variability range of physical processes in the sea must be well studied.

167

N 37O29' W 66O06'

35044'

66O04'

I

0

50 100 150 km

b

Fig.2.Temperature distribution in°C (a) and that of salinity in 8% (b) on meridional sections through one 3 Of the Gulfstream rings on January 10-12, 1966 (Puglister, 1972).

71°

70°

69'

68'

28O 27O 26O N Fig.3. The distribution of phosphates mg-at/l at boo m depth in a cyclonic eddy in the POLYMODE areain June 1978 (Chernyakova,l98O).

168

72'

71'

70'

69'

68OW

3oo 29' 28'

27'N

30' 29'

28' 27'N Fig.4. The distribution of a) phosphates mg-at/l and b ) nitrates mg-at/l at the 800 m depth in the anti-cyclonic eddy in the POLYMODE area in May 1978 (Chernyakova,l980).

I

--

-c--C CROSS-STREAM

CIRCULATION AXIS OF FRONTAL LAYER (INTERNAL BOUNDARY LAYER

C CONVERGENCE D DIVERGENCE

Fig.5. The circulation scheme across the coast during upwelling (Mooers, et al.,19781,

169

Fig.6.

COLOR

DETRITUS

LINE

LINE

FOAM LINE

I

I

I

S c h e m a t i c s e c t i o n of t h e c o a s t a l f r o n t ( K l e m a s and P o l i s , 1 9 7 7 ) .

The Main C h a r a c t e r i s t i c s o f t h e B a l t i c Sea

The B a l t i c Sea i s t h e l a r g e s t b r a c k i s h w a t e r body i n t h e w o r l d . The a r e a of t h e B a l t i c Sea w i t h o u t t h e

volume

Danish S t r a i t s i s 374 t h o u s a n d s q u a r e

k i l o m e t e r s and i t s

21.6 t h o u s a n d c u b i c k i l o m e t e r s . The maximum d e p t h i s 459 m and t h e

average

d e p t h a b o u t 60 m. The B a l t i c Sea i s c o n n e c t e d w i t h t h e North Sea t h r o u g h t h e s h a l l o w Danish S t r a i t s ( t h e d e p t h o f s i l l s b e i n g 7-17 m ) a n d t h r o u g h S k a g e r r a k and K a t t e g a t t ( F i g . 7 ) . The

B a l t i c Sea c o n s i s t s o f s e p a r a t e d b a s i n s c o n n e c t e d w i t h s h a l l o w s i l l s

( F i g . 8 ) . The B a l t i c P r o p e r between t h e Arcona B a s i n and t h e G u l f s of F i n l a n d and B o t h n i a c o m p r i s e s t h e most p a r t of t h e s e a . The main f e a t u r e s of t h e B a l t i c Sea hydrology are t h e f o l l o w i n g ; 1.The water b a l a n c e i s p o s i t i v e , i . e . t h e sum of r i v e r i n f l u x and p r e c i p i t a t i o n exceeds e v a p o r a t i o n . 2.The

s a l i n i t y o f s u r f a c e waters d e c r e a s e s from w e s t t o e a s t - from 18%

Danish S t r a i t s up t o 2%. 3.The

a t the

a t Leningrad.

waterexchange between t h e B a l t i c and North S e a s t a k e s p l a c e a c c o r d i n g t o t h e

b a r o t r o p i c regime and i s mainly i r r e g u l a r . The p a t h of t h e North Sea s a l t y w a t e r s i n t h e bottom l a y e r s o f t h e B a l t i c Sea i s s c h e m a t i c a l l y shown i n F i g . 9 . The s a l i n i t y

of t h e s e waters r e m a i n s above 10%. and t h e y r e a c h up t o T a l l i n n in t h e Gulf

of

Finland. 4.Waters of t h e B a l t i c a r e h e a v i l y s t r a t i f i e d ( F i g . 1 0 ) . V e r t i c a l l y w a t e r

may b e d i v i d e d i n t o two l a y e r s c l e a r l y

s e p a r a t e d by a h a l o c l i n e .

t h e r e a r e s a l t y waters of t h e North S e a , and

l e s s s a l t y above t h e

The d e p t h o f t h e h a l o c l i n e d e c r e a s e s from w e s t t o e a s t ( F i g . 1 1 ) .

masses

Under t h e h a l o c l i n e halocline.

I n summer t h e t h e r m c l i n e d i v i d e s the a b o v e - h a l o c l i n e water masses i n t o t w o s u b l a y e r s . Above the h a l o c l i n e

170

a comparatively t h i n c o l d l a y e r of w i n t e r waters can be found.

5. Continuous exchange of momentum and

substances between lower and upper

water l a y e r s i n t h e open s e a i s p r a c t i c a l l y missing. The exchange of momentum and substances t a k e s p l a c e by discontinuous processes, mainly i n c o a s t a l regions.

6. The c h a r a c t e r i s t i c p e r i o d of Qaterexchange of t h e B a l t i c Sea i s about y e a r s , b u t t h a t of bottom l a y e r s

20

60-100 y e a r s .

7 . The s a l i n i t y and temperature i n t h e bottom l a y e r s of t h e B a l t i c Sea during

171

0

BY2A BY5A I I

50

I

BYYA I

I

I

I I

I

I I

BYrjA

,

I I

I

I I

1

BYYA , 0Yn3i3A

I

I I

400

450

200

25C M

Fig.8. The longitudinal section of the Baltic Sea (Matthaus,l979).

Fig.9. The main

path of the North Sea waters in the bottom layers of the Baltic

Sea [Matthaus,l979).

172

100; Fig.10.

TEMP. S f f i M A T

MAX 20, 20

The stratification of the Baltic Sea water in the Gotland D e e p .

Bornholm Sea

Gotland DeeD Gulf of Finland

120.

Fig.11. The mean annual density of the Baltic Sea waters in May [Bock,1971).

173 the l a s t hundred y e a r s h a s

increased by 1

%,

0 and 0.8 - 1.5 C ,

respectively

!Matteus, 1 9 7 9 ) . 8.The main d r i v i n g f o r c e s of t h e B a l t i c a r e freshwater

i n f l u x , causing k l i m a t i c

c i r c u l a t i o n with c h a r a c t e r i s t i c v e l o c i t i e s of t h e o r d e r of 1 c m / s and wind f r i c t i o n . A t t h a t , t h e B a l t i c Sea responds t o t h e

b a r o t r o p i c a l l y (Kielmann e t . a l . ,

f o r c i n g with a p e r i o d of more than 5 0 hours

1973).

In t h e B a l t i c Sea t h e i n f l u e n c e of Hydrodynamics on the ecosystem appears f i r s t i n t h e above-mentioned i n c r e a s e d s a l i n i t y of t h e s e a . I n connection with t h i s phenomenon, mre and more oceanic s p e c i e s of organisms a r e discovered

i n the B a l t i c .

A c o n s i d e r a b l e i n f l u e n c e on t h e development of ecosystems has t h e water exchange

with t h e North Sea. In p e r i o d s

between

v a s t North Sea water inflows, t h e concentra-

t i o n of hydrogen d e c r e a s e s i n bottom l a y e r s and hydrogen sulphide may exchange between by a stron'g

appear-The

bottom and s u r f a c e water l a y e r s i s p r a c t i c a l l y reduced

vertical stratification.

t o zero

Consequently, a l s o t h e t r a n s p o r t of n u t r i e n t s

from bottom l a y e r s t o upper l a y e r s i s considerably l i m i t e d . In Fig.12,

the mean

annual v a r i a t i o n s of temperature and d i s s o l v e d hydrogen i n t h e Bornholm

Basin

a r e p r e s e n t e d (Matteus,l978).

b

020

40 -

60z t ml80 Fig.12. The mean annual v a r i a t i o n s of temperature i n t h e Bornholm Basin (Matteus,l979).

a ) and oxygen concentration

174 Well-developed coastal fronts are characteristic of the Baltic Sea. These fronts may form as a result of eddy instability phenomena. On the development of the ecosystem in the Baltic Sea, other physical processes may also have a considerable influence. In a greater detail they will be discussed further on.

Variability Scales of Processes in the Baltic Sea.

Hydrodynamics in seas and oceans is determined by the set of the following dimensional parameters; Kinematic

v ~L/T~I

viscosity

Turbulent energy dissipation rate

E

Brunt-Vaisala

N [1/T 1

frequency

rL2/T31

The Coriolis parameter

f fl/T 1

Gravitational acceleration

9 [L/T

2

1

Latitudinal variation of the Coriolis parameter

5 [1/~~1

Besides, sea hydrodynamics is determined by the scale

,

L

vertical scale

H

characteristic horizontal

and by the scale of bottom roughnesses Vh (inclina-

tion). Four characteristic length scales may be constructed from these parameters

:

-1/4

the internal Kolmogorov Scale

n

the Ozmidov buoyancy scale

1 =(E/N

=(E/V)

3 1/2 )

the internal Rossby radius of deformation Ri=NH/f

the external Rossby radius of deformation Re=JgH/f Considering the following values of the parameters of the Baltic Sea. -1 0.01 sec

N H

2

50-200 m

f = 1.2

.

-4

10

-1 sec

the following characteristic variability scales for- the Baltic Sea are obtained

n

= 0.1

cm

Rim 0 ( 5 - 2 0 )

1= 0.1-3.0 m

km

R

=

O(150-300) km

Consequently,the characteristic scales of the Baltic Sea may be expected in these orders. It should be pointed out that the

radii of the Rossby

Baltic are considerably smaller than the

Finestructure of

deformation in the

corresponding values in the ocean.

the Open Baltic Sea Water

The finestructure of the Baltic Sea thermohaline fields has not been

well

175 studied yet. That is why intensive investigations of the finestructure Of the open part of the Baltic, using a CTD probe of the USA Neil Brown firm, are being carried out by the Department of the Baltic Sea since 1977. The main results of these investigations are presented in the following papers; Laanemets, Lilover, 1980 Aitsam et al., 1978

; Aitsam

i

et al., 1980. Relying on the latter studies, some

results of the Baltic Sea finestructure investigations will be considered below. In September 1977, under the leadership of the SCOR Working Group 42 an international experiment BOSEX was carried out in the central part of the Baltic. During the experiment, a series of 17 profiles with the interval of 10 minutes was completed in the northern station of the area. In June 1979, in the same area, a series consisting of 150 profiles in a layer of 70-95 m with the time interval of 3 minutes was carried out. of 30

As each parameter is measured with the frequency

and the rate of the probe lowering is

lution is about 1 cm.

25 cm/sec

,

the depth reso-

Considering the transmission function of the calculation

operation by the constant time, temperature and conductivity registers, functions of spectral densities are calculated only up to the wave number of 25 m-'. The spectral analysis of the vertical profiles done during the international BOSEX experiment, showed that in the upper mixed layer there is no subinterval with the " - 5 / 3 " law in the spectra. The slope of spectral curves in a logarithmic system of coordinates varies from -2 to - 3.2. It must be noted that the series Of profiles was carried out in calm weather after the cyclon has passed. The activity of turbulence decreased and as Batchelor (1959) showed, a pure deformation of temperature fields with velocity field requires no

existence of an inertial

interval in temperature spectra. Gregg (1976) has given spectral densities

of

temperature inhomogeneities in the oceans upper layer after storm, the inertialconvective subinterval being absent in them. In Fig.13 spectral densities of temperature inhomogeneities in the thermocline are given. The slope of the spectra changes with the wavelength of 0.1-0.4 m depending on local conditions. This scale is a kind of transition scale from finestructure to microstructure in the Baltic Sea. In the thermocline of the microstructure area there is a subinterval of the local isotropic turbulence with the law "-5/3" in some spectra. This subinterval may possibly be due to wave-eddy turbulence.In the area of the finestructure the slope of spectral curves varies in most cases from

- 2.7 to - 3.5. This can be

interpreted as the influence

of internal gravity waves on the vertical structure of temperature. Spectral densities of temperature, salinity and density inhomogeneities in a layer of 70-95 m are presented in Fig.14. A s it can be seen from the figure interval with the law "-5/3" is absent. Up to the boundary scale of 4 cm slope of spectral densities is about -3 or more.

the

the

Hereafter it may be concluded

that the vertical structure of temperature, salinity and density in this layer

176

10-8

10° Fig.13.

10'

kIl /mI

S p e c t r a l d e n s i t i e s of temperature inhomogeneities i n t h e thermocline.

i s a r e s u l t of t h e kinematic e f f e c t

3f

i n t e r n a l waves up t o t h e v e r t i c a l s c a l e

of 4 cm. Processes of t h e v e r t i c a l exchange a r e not well-developed. noted t h a t t h e

I t must

be

experiment was c a r r i e d out during calm weather.

By t h e a n a l y s i s of t h e s p e c t r a l d e n s i t i e s of temperature has been a s c e r t a i n e d

inhomogeneities i t

t h a t t h e r e i s no i n e r t i a l - c o n v e c t i v e s u b i n t e r v a l

during

calm weather. A s u b i n t e r v a l w i t h t h e "-5/3"

small-scale

law h a s been discovered i n the thermocline, b u t a l s o

temperature, s a l i n i t y and d e n s i t y i n v e r s i o n s which a r e

i n l a y e r s of t h e v e r t i c a l s c a l e of about 1 m. The t r a n s i t i o n from

concentrated finestructure

t o m i c r o s t r u c t u r e t a k e s p l a c e a t s c a l e s of 10-40 cm. The a n a l y s i s of s p e c t r a l d e n s i t i e s i n a deep l a y e r shows t h a t t h e r e i s a s t r o n g i n f l u e n c e of i n t e r n a l waves on t h e v e r t i c a l s t r u c t u r e of temperature, s a l i n i t y and d e n s i t y . The a n a l y s i s of t h e r e l a t i o n of h e a t and s a l t c u r r e n t s

177

'.m~ 3 12.m

10-91

I

I

1 I Illll

I

I

I I 1 1 1 1 1

103

I

10' k [ l / m 1

Fig.14. Ensemble-averaged spectral densities of temperature - salinity x, density

0 in the deep layer of the Baltic Sea.

shows that the process of convection in layers

is quite

improbable.

Synoptic Variability of the Open Part of the Baltic Sea.

In the Baltic Sea, as well as in the World Ocean, a considerable part of the kinetic energy comes to low-frequency motions with periods longer than the

178 i n e r t i a l one ( F i g . 1 5 ) .

w

Io

-~

16’

10-

0

Fig.15. The s p e c t r a l d e n s i t y of t h e k i n e t i c energy c u r r e n t s i n t h e open B a l t i c (Krauss, 1 9 7 3 ) .

I n view of t h e s m a l l dimensions of t h e B a l t i c Sea and t h e considerable v a r i a b i l i t y of t h e bottom topography of t h e s e a it can be assumed t h a t , d i f f e r e n t l y from t h e ocean, t h e i n f l u e n c e of t h e

f3

-effect,

i n t h e Baltic, on t h e formation

o f t h e s y n o p t i c v a r i a b i l i t y i s n o t e s s e n t i a l and i s r e p l a c e d by t h e i n f l u e n c e of bottom topography. I n t h e b a r o c l i n i c case, Rossby’s p o t e n t i a l v o r t i c i t y theorem gives d --

-(

dt

c:+f

)= 0

H

t h e c o n d i t i o n f o r t h e e q u a l i t y of t h e e f f e c t o f bottom topography on t h e r e l a t i v e v o r t i c i t y and t h e

where

(3

- e f f e c t may be obtained i n t h e following form

5 -

relative vorticity,

H

-

t h e depth o f t h e sea,

R

-

r a d i u s of t h e e a r t h .

Under oceanic c o n d i t i o n s

c1

> 0(10-2), b u t i n t h e B a l t i c Sea .C > O(lO-’).

179 In the baroclinic case the potential vorticity is conserved according to the Ertel’s relation

f3

The condition for prevalence of topography over from the equality of and

frequency

disturbing the density

caused by

field

-effect may be obtained

the motion forced up the

to the frequency provided by

slope

6 -effect

alone in the following form (mines 1977)

fL a>------

(4)

R N .

Under conditions of the Baltic Sea, we obtain

a > In view of the fact that there is a great number

a >

in the Baltic, the

of

regions with the slope

appearance of topographic baroclinic waves is

most probable. Synoptic eddies in the Baltic Sea were observed first by Keunecke and Magaard in 1975. In 1976, topographic waves in the Bornholm Basin in the south-west part

were obtained by Simmons as a result of calculations on a

of the Baltic

multilayered model ( Simmons, 1976). In 1977,the BOSEX out in the Baltic Baltic Sea;

experiment of the ICES/SCOR

Joint Working Group was carried

Two mooring stations were installed, by the Department of the

one of them in the

the eastern corner of it. The

northern corner of the polygon and the other in

site of the BOSEX area in the Baltic is given in

Fig. 16, and the bottom topography as well as the locations of mooring stations in Fig. 17. Let us consider currents in deep

horizons of station

N

of 1977 polygon. In

Fig. l8,time series of the velocity components and of temperature at station N are presented, for period 400 hours. We see that inertial fluctuations are dominant there. After filtering out short periods, observed in the time series of the

fluctuations of low frequency can be

considered characteristics (Fig.19). The dominant

periods were found equal to 68 and 44 hours. In Fig. 18 and 19, we can see that the current velocity and temperature have the same dominant periods but with a phase shift. The effect can be

explained by topographic waves. In the

Baltic

Sea temperature increases with in the depth in bottom layers. Thus the upward

180

Fig.16. Location of the BOSEX area in the Baltic Sea.

Fig.17. Bottom-topography in the BOSEX-77 area.

181

15

ws 0

-15

11.70 OC

5.10

400 hrs

Fig.18. Variation of the velocity component and temperature at the 105 m level at

0

station

10

N

during

20

30

the

BOSEX experiment.

40

L,ig.19. Variation of the velocity component and temperature after high-frequency filtrations at the 105 m level during the BOSEX-77 experiment.

182 fluxes

along t h e slope t r a n s p o r t warm water up. When t h e d i r e c t i o n of v e l o c i t y

changes and water

begins t o move downwards, temperature must

have i t s maximum

value. d i s p e r s i v e r a t i o of bottom-trapped topographic waves i s w r i t t e n a s

The

[Rhines,l980)

w =

N a L

-

N K H

cth

where

k2

= k

f

2

+ L

2 k, R

-wave numbers along and

a For

c1 =

(5)

~

E

0.015 and

across the slope,

-bottom slope.

N = 0.015 sec

-1

from r e l a t i o n ( 5 ) , p e r i o d s equal t o o r

l a r g e r than 40 hours a r e obtained. This corresponds t o t h e observed p e r i o d s . By bottom-trapped topographic waves t h e k i n e t i c energy i n c r e a s e s with depth. I n F i g . 20 t h e v e r t i c a l d i s t r i b u t i o n of t h e ’ k i n e t i c energy

N

and

E i s presented.

about bottom-trapped

measured a t s t a t i o n s

I t can be seen t h a t i n accordance with t h e assumption

topographic waves a t s t a t i o n

N

k i n e t i c energy i n c r e a s e s

with depth. I n 1979, experiments t o study synoptic v a r i a b i l i t y on t h e BOSEX a r e a were repeated.

However, t h e dimensions and l o c a t i o n of t h e a r e a were a s l i g h t l y

changed ( F i g . 2 1 ) . I n 1979 cross-like,

autonomous mooring s t a t i o n s

(AMS) were i n s t a l l e d

so t h a t simultaneously t h r e e AMS were l o c a t e d along t h e bottom

slope and t h r e e i n t h e

t r a n s v e r s a l d i r e c t i o n . The d i s t a n c e between AMS was 10

miles. All t h e AMS were provided with Aanderaa RSM-4 c u r r e n t meters, whereas one of t h e instruments was always i n a bottom l a y e r . During t h e s t a g e o f c u r r e n t measurements and a f t e r it up t o the l a t e autumn,

8 d e n s i t y mappings with a N e i l Brown Mark I11 CTD probe were completed i n t h e a r e a . Each mapping

c o n s i s t e d of 2 1 s t a t i o n s

with a 5 m i l e s t e p . The

d u r a t i o n of a

mapping, one day, ensured q u a s i s t a t i s t i c a l approach. The d a t a obtained by CTD mappings w e r e l a t e r used t o i n v e s t i g a t e t h e s p a t i a l s t r u c t u r e of thermohaline f i e l d s and t o c a l c u l a t e dynamic topography with t h e aim of t h e i n d i r e c t determination

of a geostrophic c u r r e n t f i e l d i n t h e a r e a .

For a more d e t a i l e d study of t h e s p a t i a l d i s t r i b u t i o n of thermohaline

fields

i n t h e upper layer,experiments with a towed measuring complex were c a r r i e d o u t i n t h e a r e a . The complex,which was constructed i n t h e

Department of t h e B a l t i c Sea

of t h e I n s t i t u t e of Thermophysics and E l e c t r o p h y s i c s

of t h e Estonian S.S.R.

of t h e Academy of Sciences

i n 1978,enables us t o o b t a i n i n t h e 4 0 meters upper l a y e r

with a h o r i z o n t a l r e s o l u t i o n of 200 meters, temperature, s a l i n i t y and d e n s i t y s e c t i o n s . This i s achieved by t h e s t a b l e

wave-like motion of t h e

c a r r y i n g body

183

50

,

250 [cp */sec2

I50

I

I 20

40 60

80

100 120

Fig.20. V a r i a t i o n of k i n e t i c energy along t h e v e r t i c a l a t s t a t i o n s i n t h e BOSEX-71

of CTD

N

and

E

area.

r e g i s t e r s , being towed a f t e r t h e v e s s e l with t h e v e l o c i t y of 5-7 knots.

The r e s u l t s of t h e i n v e s t i g a t i o n s c a r r i e d o u t i n the a r e a a r e r e p o r t e d i n t h e paper by A i t s a m , Elken, Pavelson, Talpsepp ( 1 9 8 0 ) . I n t h e following, t h e main r e s u l t s are b r i e f l y discussed. For t h e i n d i r e c t determination of t h e v e l o c i t y f i e l d , t h e r e l a t i v e dynamic topography (RDT) ( d i f f e r e n c e between dynamical h e i g h t s ) was c a l c u l a t e d according

P

t o formula

where

pl;

g

- gravitational acceleration,

p

- water d e n s i t y , p2 - p r e s s u r e v a l u e s .

A s f a r a s t h e r e i s no

c l e a r l y expressed zero s u r f a c e i n t h e B a l t i c S e a , t h e

determination of t h e a b s o l u t e v e l o c i t y using t h e dynamic method remains undecided. RDT i s t h e stream f u n c t i o n of t h e r e l a t i v e v e l o c i t y and i n our c a s e , t o t h e change

of RDT

by 1 cm per 5 miles corresponds t h e r e l a t i v e v e l o c i t y change 8 . 6 5 cm/sec.

While compiling RDT maps, t h e q u e s t i o n about t h e

e x a c t n e s s of i t s

calculation

on t h e b a s i s of s i n g l e mappings without any time averaging a r i s e s . I n p r o f i l e s of

184

N

Po I

Fig.21. Location ( r i g h t ) and t h e map of t h e bottom-topography

( l e f t ) of t h e

BOSEX a r e a .

a s i n g l e mapping, high-frequency n o i s e i s p r e s e n t . Other causes of e r r o r s are t h e

asynchronism of measurements and t h e presence o f t h e time t r e n d of synoptic processes i n t h e obtained data. To e v a l u a t e e r r o r s , d a i l y s e r i e s of p r o f i l e s w e r e twice carried o u t a t t h e c e n t r a l s t a t i o n and t h e mean square e r r o r s o u t t h a t i n t h e presence of a pycnocline between l e v e l s square e r r o r

u

E

were determined. I t turned p1

and

p2

,

o f RDT along h o r i z o n t a l plane more than twice exceeds

is no pycnocline i n t h e l a y e r (pl

;

p 2 ) , then values o f

ff

and

E

are

t h e mean E

.

I f there

of the

same o r d e r of magnitude.

I n f i g u r e s 2 2 and 23, RDT maps c a l c u l a t e d by making use of o b j e c t i v e a n a l y s i s are presented.

185

Fig.22. Maps of t h e r e l a t i v e dynamic topography f o r surveys

On maps 1-4

1-4.

(Fig.22) a p o s i t i v e eddy-like p e r t u r b a t i o n of RDT w i t h a weak inten-

s i t y i s observed i n t h e upper c e n t r a l p a r t of t h e area. On the b a s i s of t h e s i n g l e mapping, it may be assumed t h a t t h e p e r t u r b a t i o n i s a random r e s u l t o f t h e i n t e r n a l wave noise.

However, t h e presence of t h e p e r t u r b a t i o n on maps o f r e p e a t e d mappings

allows u s t o show q u i t e convincingly t h a t t h e p e r t u r b a t i o n (lowering of i s o p y c n a l ) , R 20 km, Rx 2 15 km, i s o f synoptic o r i g i n . The v e l o c i t y of Y I t h e p e r t u r b a t i o n displacement i s o f t h e o r d e r of C ?. 1.5 cm/sec, whereas t h e ve-

with axes

l o c i t y i s d i r e c t e d along averaged i s o b a t h with shallower water l e f t t o t h e r i g h t . A t t h e c e n t r a l s t a t i o n t h e d i r e c t l y measured r e l a t i v e v e l o c i t y corresponds w e l l

enough t o t h e geostrophic v e l o c i t y determined from RDT. On maps 6 and 7 iFig.23) a n e g a t i v e eddy-like p e r t u r b a t i o n o f RDT (lift of isopycnal) of t h e whole water column w a s p r e s e n t i n August. meter of t h e almost c i r c u l a r p e r t u r b a t i o n i s placement

C

R

2 2 cm/sec, whereas t h e v e l o c i t y

The h o r i z o n t a l d i a -

2 20 km and t h e v e l o c i t y o f d i s i s d i r e c t e d along t h e i s o b a t h s

186

3 (90,101

I \

35,-16.08.79

Fig.23. Maps of the relative dynamics topography for surveys 6 - 7 .

187 a 3 f o r maps 1-4.

I n 10 days

t h e r e l a t i v e v e l o c i t y i n c r e a s e d b y a f a c t o r two.

Eddy-like p e r t u r b a t i o n s of RDT and t h e i r displacement may be described a s t h e

sums of two f l a t

1,

topographic waves with wave numbers ( -k,X

( k,R

).

The

averaged topography of t h e deep p a r t of t h e a r e a was approximatedby a plane with

a

values

= 5-10-~

Ax

.

S i t u a t i o n s , presented i n Fig.23 were modelled by Elken and

X

=40 km,

-f

Y

=-40 km were used. Numerically estimated phase v e l o c i t y

Cf = (0; -3) cm/sec and p e r i o d Tp = 1 5 . 6 days correspond t o t h i s case. The

fact

t h a t t h e phase v e l o c i t y of waves exceeds t h e v e l o c i t y of p e r t u r b a t i o n displacement -3

C = (0 ; -2)

cm/sec.

No i n s t r u m e n t a l

may be caused by t h e average c u r r e n t

measurements were r e a l i z e d during

"u

= (0 ; 1) cm/sec.

t h e period. R e l a t i o n s of t h e

geostrophic s h i f t s of v e l o c i t y i n thermocline and h a l o c l i n e correspond t o topographic waves. Doubling of t h e amplitude may be

explained by t h e v e r t i c a l s h i f t of t h e

100 m l e v e l , b u t i n t h a t case

average v e l o c i t y 1.3 cm/sec on t h e

t h e value of

t h e phase v e l o c i t y becomes worse. I n t e r p r e t i n g maps 1-4 f o r which values c u r r e n t measurements was estimated.

(Fig.22) wave l e n g t h s were estimated

i

as

t h e average

I n t h e presence of t h e average c u r r e n t

i s determined a s follows ;

+

Cf

=

+

Cf

km,A = 4 0 km, Y instrumental

, T = 23.8 days. From P c u r r e n t value i!i = (-0.4 ; 1.0) cm/sec

Cf = ( 0 ; 1 . 9 ) cm/sec

,

X =25

o=;I

with t h e displacement v e l o c i t y of t h e RDT

+

+ u

i

u = ( 0 ; V), t h e phase v e l o c i t y

and i t s value i s comparable

perturbation

-f

C

2

(0;

1.5) cm/sec.

From t h e experiments described above, it may be concluded t h a t low-frequency processes with s p a t i a l s c a l e s of t h e order of t h e Rossby i n t e r n a l r a d i u s and with time s c a l e s from s e v e r a l days t o s e v e r a l

decades become apparent i n t h e

BOSEX

a r e a . The r e s u l t s of t h e measurements c a r r i e d o u t i n 1977 may be i n t e r p r e t e d i n

t e r m s o f bottom-trapped waves. A considerably complicated s p a t i a l s t r u c t u r e of thermohaline f i e l d s w a s observed

i n t h e upper l a y e r . But p e r t u r b a t i o n s with s c a l e

R

2

30 km were v i s i b l e even

i n t h e s e d a t a . I n t h e d a t a of v e l o c i t y measurements a t mooring s t a t i o n s i n 1979, p e r t u r b a t i o n s of t h e synoptic scale become apparent, b u t t h e i r i n t e r p r e t a t i o n on t h e b a s i s of l i n e a r t h e o r i e s w a s found impossible.

Acknowledgements

The a u t h o r is o b l i g e d t o the whole s t a f f of t h e Section of t h e Marine Physics of t h e B a l t i c Sea Department f o r c a r r y i n g o u t experiments i n t h e BOSEX a r e a . H e i s p a r t i c u l a r l y thankful t o h i s follow s c i e n t i s t s J. Elken, J. Laanemets, J . Pavelson and L. Talpsepp by whom the experimental d a t a used i n t h e paper were processed and analized.

188

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processes in the Baltic,Tallinn (in press).

Ratchelor G.K.,1959. Small-scale variation of convected quantities like temperature in turbulent fluid. ,J.Fluid Mech., 5,l; pp.113-133. Bock K.H.,1971.Monastkarten der Dichte des Wassers in der Ostsee verschiedene

dargestellt fur

Tiefhorizonte.Deutsche Hydrographische Institut Hamburg.

Falkenmark M., Mikulski Z.,1974. Hydrology of the Baltic Sea International Hydrological Decade Project Document Nr.1. Stockholm-Warszawa. Fuglister F., 1972. Cyclonic rings formed by the Gulf Stream 1965-1966. Studies in physical oceanography

. v.1.A.

Gordon (Ed.) Gordon and Breach

Science Publishers.

Gregg M.C., 1976. Finestructure and Microstructure Observations During the Passage of a Mild Storm. J. Phys. Oceanogr. 6, pp.528-555. Kielman J., Krauss W., Keunecke K.H.,1973. Currents and

stratification in the Belt

Sea and the Arcona Basin during 1962-1968. Kieler Meeresforshungen. 29,2,pp.90-111. Keunecke K.M., Magaard L. 1975. Measurements by means of towed thermistor cables and

problems of their interpretation to mesoscale processes. Memoires Societe

des Sciences de Liege

6e serie, 7; 147-160.

Klemas V., Polis D.F.,1977. Remote sensing of estuarine fronts and their effects on pollutants. Programmetric engineering and remote sensing, 43; 594-612 Krauss W.,1973. Wind driven

oscillations of an encloused basin with bottom friction.

Deutsche Hydrographische Zeitschrift.,26, 1 ; 1-9. Laanemets J.,Lilover M.,1980. The Data Processing Scheme of the Measurements with Neil Brown Mark I11 CTD. The Study and Modelling of Processes in the Baltic

I

[in press). Matthaus W.,l979. Langzeitvariationen von Temperatur Salzgehalt und Sauerstaftgehalt der zentralen Ostsee

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Beitr.zur Meereskunde,Nr.42;41-93.

Mooers C.N.K.,Flagg C.N., Boicourt W.C.,1978.

Prograde and Retrograde fronts. Oceanic

Fronts in Coastal Processes. Ed.by M.J. Browmann and Wayne E. Esiaias.Springer Werlag. Nygvist B., 1974. Osterjon blomnar. Forsking och

Framsteg. 6;l-2.

Platt T., Denman K., 1975. A general equation for the

mesoscale distribution of

phytoplankton in the Sea. Memoires Societe Royale des Sciences de Liege. 6e serie tome

7; 31-42.

Powell T.M., Richardson P.I., Dillon T.M., Dozier B.A., Godden D.A.,Myrup L.O.,1975.

189 Spatial scales of current speed and phytoplankton fluctuations in Lake Tahoe. Science 189; 1088-1090. m i n e s P., 197+. Edge-, bottom- and Rossby waves in a rotating stratified fluid. Geophys. Fluid Dyn.,l, 273-302. m i n e s P.,1977. The Tsernjakova A.M.,

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Romanov A.S.,1980. Nonuniformities of the chemical fields in the

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This Page Intentionally Left Blank

191

+

HYDRODYNAMIC CONTROL OF MARINE PHYTOPLANKTON PRODUCTION: THE PARADOX OF STABILITY

L. LEGENDRE GIROQ, D6partement de biologie, Universitk Laval, Qukbec, QUEBEC

G1K 7P4

ABSTRACT Phytoplankton studies in a given environment

are generally conducted on a small

range of scales, so that no clear picture emerges as to the factors fundamentally critical to the dynamics of phytoplankton.

In the Estuary of the St Lawrence, where

a wide range of observation scales are covered, stability of the water column is the only hydrodynamic factor significant to phytoplankton that is observed on all spatiotemporal scales.

In various environments (estuarine,coastal, oceanic, frontal

regions) vertical stability is reported to influence phytoplankton on scales from 6.2 h to one year, the forcing mechanisms being climatic, river runoff, tides or

winds.

An apparent paradox is that neither stabilization nor destabilization of the

water column favours phytoplankton production: indeed, at any

spatio-temporal scale,

only the alternation of stabilization and destabilization is an hydrodynamic mechanism conducive to enhance primary production. A simple conceptual model of phytoplankton dynamics accounts for instances of the temporal succession of stratification and destratification of the water column, observed on a wide range of scales, and it may be applied to such structures as fronts and intermittent upwellings.

It is therefore proposed to characterize the phytoplankton production

potential of marine ecosystems by their frequency of stabilization-destabilization, since the resulting input of mechanical energy does enhance the primary production. Other factors such as temperature, turbidity, nutrient background, and so on, may limit the production potential built up by the alternation of stabilization and destabilization.

Contrary to marine ecosystems driven by nutrient regeneration,

which are vertically closed systems, those dominated by stabilization-destabilization vertically exchange nutrients regenerated at depth and energy stored by the phytoplankton at surface, which is one of the basic mechanisms of marine phytoplankton production.

'Contribution to the programme of GIROQ (Groupe interuniversitaire de recherches ockanographiques du Qukbec).

192 FACTORS CONTROLLING THE DYNAMICS OF PHYTOPLANKTON Understanding marine hydrodynamics, as a constraint on the dynamics of ecosystems, requires an assessment of its impact on the production of phytoplankton.

Indeed,

phytoplankton production is primarily responsible for the transfer of materials from the abiotic environment to the ecosystem, and also for the input of energy into the marine biosphere. Since the works of Denman (1976) and Denman and Platt (1975, 1976), oceanographers describe the spectral dynamics of phytoplankton in terms of an interplay between hydrodynamics and ecophysiology.

Using data series from the Estuary and the Gulf of

St Lawrence, these authors interpreted the variance spectrum of chlorophyll as a dependence of phytoplankton abundance on the rate of turbulent energy transfer at high wavenumbers, and a dominance of the lower wavenumbers by the rate of cell

-

.

reproduction.

On the contrary in the Middle Estuary of the St Lawrence, inhibition

of phytoplankton production, rather than growth, was invoked by Demers et al. (1979) as controlling the low frequencies of the chlorophyll spectrum. Furthermore, Lekan and Wilson (1978) observed, in Long Island Sound, characteristic scales on which phytoplankton distribution was respectively related to nutrients, hydrodynamics, and biological growth rate.

This new approach to marine phytoplankton (other papers are

cited below) stresses the fundamental importance of the spatio-temporal scales, and also the diversity of factors involved in the dynamics of phytoplankton according to the scales. However, despite this diversity, unifying concepts must be sought. For instance, a recent work by Fortier and Legendre (19791, in the St Lawrence Estuary, showed that fine-scale fluctuations of phytoplankton photosynthetic activity are related to the vertical by the Richardson number.

stability of the water column, as measured

The analysis of a stability spectrum gave some insight

into the low frequency control of phytoplankton dynamics by the hydrodynamics, thus potentially extending over a broad range of scales a unifying hydrodynamic concept. The main problem in defining such concepts is that, in a given environment, only a few studies are generally devoted to the phytoplankton, so that only a limited range of scales is covered.

On the contrary, many studies must be

conducted on various observation scales and on various phytoplankton parameters, for a clear picture to emerge as to the factors fundamentally critical to the dynamics of phytoplankton over a significant range of spatio-temporal scales. The phytoplankton of no marine ecosystem has yet been studied under such a broad perspective.

However a wide range of observation scales

tens of kilometres, and from a few minutes to months

- from a few metres to

- are covered by

19 of the

papers, recently published on the phytoplankton of the St Lawrence Estuary, in which phytoplankton biomasses (number of cells, chlorophyll, ATP) and production dynamics (primary production, photosynthetic capacity, photosynthetic efficiency)

are considered. According to the observation scale (Table 1: columns) and to the phytoplankton parameter investigated (within Table l), various environmental and/or endogenous factors are reported to influence the phytoplankton, on different spatio-temporal scales (Table 1: rows); M and M are the lunar fortnightly f 2 (327.9 h) and the principal lunar semi-diurnal (12.4 h) harmonic tidal components. It is obvious from Table 1 that, in the St Lawrence Estuary, many different environmental and biological factors interplay to shape the dynamics of phytoplankton The wind, which is a dominant factor in other coastal environments (see below), is not reported here since, in a stratified estuary, vertical mixing is caused mainly by the shear between layers with different relative velocities and densities rather than by the wind. and the observation scales

The relationship between the factors in Table 1

is striking, and it stresses dramatically the critical

importance of the observation window.

Biological oceanographic studies are

classically conducted on a monthly or a weekly basis, and on a grid of stations many nautical miles apart, which is clearly inadequate for estuarine or coastal phytoplankton. Another problem apparent from Table 1 is that only biomasses (especially in situ fluorescence, as an index of in vivo chlorophyll a: Lorenzen, 1966) may technically be sampled with high frequency; experiments on new methods to measure automatically primary production (Massol and Ballester, 1976; Roy and Legendre, 1979, 1980) will eventually overcome this constraint. In Table 1, hydrodynamic factors are evidenced at each observation scale; these factors also occur on various spatio-temporal scales. However, stability of the water column emerges as the only hydrodynamic factor, significant to phytoplankton, observed on all spatio-temporal scales. On a large geographic scale, Sinclair (1978) found that l o w phytoplankton biomasses in the St Lawrence Estuary are associated with areas of intense horizontal and vertical mixing, conditions that are not conducive to phytoplankton growth and may therefore explain the low biomasses.

On the contrary, regions

with greater stratification are potentially more productive environments, thus supporting higher biomasses.

Temporal variability of phytoplankton biomasses

and production in the Lower Estuary of the St Lawrence is interpreted by Sinclair (1978) in terms of the neap-spring (M ) tidal cycle. The increased tidal mixing f of the spring tide, with consequent reduction in stratification, is paralleled by reduced phytoplankton production; this is caused by an increased rate of loss of cells from the photic layer, due to higher vertical diffusivity and decreased upward advection.

The same is observed by Demers et al. (1979) in the Middle

Estuary, where phytoplankton cells, healthier during the neap tide, show higher chlorophyll concentrations per unit cell than during the spring tide. A l s o , pure endogenous rhythms of the photosynthetic capacity may be evidenced (Demers and Legendre, 1979) in the relatively homogenous environment resulting from the spring-tidal destratification.

194 TABLE 1 Schematic c o n c l u s i o n s of 1 9 s t u d i e s on t h e phytoplankton of t h e S t Lawrence Estuary.

I OBSERVATION SCALE FACTORS LARGE SCALE FACTORS

Month

Week

10-50 km

Seasonal v a r i a t i o n s Salinity gradients

CELLS ( C a r d i n a l and B6rardT h e r r i a u l t , 1976; C a r d i n a l and L a f l e u r , 1977)

Circulation

CHLOROPHYLL ( P l a t t , 1972; S i n c l a i r , 1978)

Nutrients

PRODUCTION (Sevigny e t a l . , 1979; Steven, 1974)

Vertical s t a b i l i t y

CHLOROPHYLL and ATP ( S i n c l a i r , 1978)

Turbulence Mf VARIATIONS

Vertical s t a b i l i t y

CHLOROPHYLL and PRODUCTION ( S i n c l a i r , 1978)

C r i t i c a l depth

CHLOROPHYLL and PRODUCTION ( S i n c l a i r , 1978)

Tidal incursion M2 VARIATIONS

Vertical s t a b i l i t y T and S g r a d i e n t s

I n t e r n a l waves

SLACK WATER VARIATIONS Vertical s t a b i l i t y LIGHT

Vertical d i s t r i b u t i o n High frequency v a r i a t i o n s [=1Hz) PHYTOPLANKTON Endogenous rhythms

C a r b o x y l a t i o n pathways Growth Senescence

195 TABLE 1 (continued)

OBSERVATION SCALE Hour 10-50 m

FACTORS

Minute -5 m

LARGE SCALE FACTORS

Seasonal v a r i a t i o n s S a l i n i t y gradients Circulation

Nutrients Vertical stability CHLOROPHYLL (Denman, 1976; Denman and P l a t t , 1975, 1976) PHOTOSYNTHETIC CAPACITY (Demers and Legendre, 1979)

CHLOROPHYLL (Demers e t a l . ,

Turbulence M

VARIATIONS f Vertical s t a b i l i t y

1979)

CHLORO. and PHOTOS. CAPACITY ( F o r t i e r and Legendre, 1979)

C r i t i c a l depth

CELLS (Demers and Legendre, 1979; L a f l e u r e t a l . , 1979)

Tidal incursion M

2

VARIATIONS

Vertical s t a b i l i t y

PHOTOSYNTHETIC CAPACITY ( F o r t i e r and Legendre, 1979) CELLS ( F o r t i e r e t a l . ,

1978)

T and S g r a d i e n t s

I n t e r n a l waves

CELLS ( L a f l e u r e t a l . , 1979) CHLOROPHYLL ( D e m n , 1976; CHLOROPHYLL ( T h e r r i a u l t and Denman and P l a t t , 1975, 1976) Lacroix, 1976) PHOTOSYNTHETIC CAPACITY ( F r e c h e t t e and Legendre, m s )

SLACK WATER VARIATIONS

CHLOROPHYLL (Auclair e t a l . , m s )

Vertical s t a b i l i t y LIGHT

PHOTOSYNTHETIC EFFICIENCY (Roy and Legendre, 1980)

Vertical distribution

PHOTOSYNTHETIC CAPACITY

High frequency v a r i a t i o n s (=I Hz)

( F r e c h e t t e and Legendre, 1978)

PHYTOPIANKTON

~

PHOTOSYNTHETIC CAPACITY (Demers and Legendre, 1979) CHLOROPHYLL ( A u c l a i r e t a l . , m s )

Endogenous rhythms

PHOTOSYNTHETIC CA PAC I TY ( F r g c h e t t e and Legendre, 1978)

C arboxy l a t i o n pathways

CHLOROPHYLL ( F o r t i e r and Legendre, 1979)

CHLOROPHYLL (Denman, 1976; Denman and P l a t t , 1975, 1976)

Growth

CHLOROPHYLL (Demers e t a l . , 1979)

Senescence

A l t e r n a t i n g stratification-destratification a l s o occurs, i n an e s t u a r y , on a semi-diurnal

(M

2

)

scale.

I n t h e S t Lawrence Estuary, F o r t i e r and Legendre (1979)

r e p o r t p e r i o d i c maxima of t h e p h o t o s y n t h e t i c c a p a c i t y coincident with maximum s t r a t i f i c a t i o n on a 12.5-h c y c l e , a s estimated by t h e Richardson number; high c a p a c i t y p e r s i s t s f o r about 1 t o 3 hours a f t e r t h e beginning of t h e v e r t i c a l mixing (low Richardson numbers).

( m s ) have observed

Furthermore, Auclair e t a l .

5 t o 6-h endogenous p e r i o d i c i t y of c h l o r o p h y l l , i n phase with s l a c k waters.

Turbulent mixing of phytoplankton c e l l s causes t h e i r l i g h t regime t o be l e s s

- according ( i n press) - i n

p r e d i c t a b l e , which r e s u l t s

t o t h e light-shade a d a p t a t i o n mechanism

described by Falkowski

t h e development of l a r g e i n t e r n a l

chlorophyll pools; conversely, a t t i m e s of s l a c k water, smaller concentrations of a c t i v e chlorophyll are observed. I n a d d i t i o n t o t h e S t Lawrence Estuary, o t h e r papers s t r e s s t h e i n f l u e n c e of v e r t i c a l s t a b i l i t y on phytoplankton.

The b e s t known a r e those of Gran and

Braarud (1935), Riley ( 1 9 4 2 ) and Sverdrup (19531, explaining t h e seasonal phytoplankton dynamics of temperate regions i n terms of v e r t i c a l mixing: t h e autumn bloom i s followed by a progressive i n t e n s i f i c a t i o n of t h e mixing, which l e a d s t o t h e l i g h t l i m i t a t i o n of w i n t e r phytoplankton and a l s o t o the replenishment of t h e s u r f a c e l a y e r i n n u t r i e n t s ; a t t h e end of t h e w i n t e r , i n c r e a s i n g s t r a t i f i c a t i o n ( c r i t i c a l depth: Sverdrup, 1953) r e s u l t s i n t h e s p r i n g o u t b u r s t , which r a p i d l y exhausts t h e a v a i l a b l e n u t r i e n t s , s o t h a t t h e following summer production depends e s s e n t i a l l y on t h e i n s i t u regeneration of n u t r i e n t s .

The

l e a d i n g f o r c e s of t h i s mechanism a r e c l i m a t i c , but r i v e r runoff may a l s o d r i v e t h e seasonal dynamics of c o a s t a l phytoplankton, a s i n Indian A r m , a f j o r d of WesteA Canada (Gilmartin, 1964) : t h e increased r i v e r runoff i n winter d e s t a b i l i z e s t h e water column and t h u s favours a replenishment of t h e p h o t i c l a y e r i n n u t r i e n t s , which a r e used by t h e phytoplankton a t springtime, when t h e water column s t a b i l i z e s v e r t i c a l l y with decreasing r u n o f f . Neap-spring t i d a l v a r i a t i o n s a r e known t o i n f l u e n c e t h e dynamics of phytoplankton i n c o a s t a l a r e a s .

I n t h e York River, a t r i b u t a r y of Chesapeake

Bay, s p r i n g - t i d a l d e s t r a t i f i c a t i o n r e d i s t r i b u t e s n u t r i e n t s and oxygen i n t h e water column (Webb and D ' E l i a , 1980). r e i n t e r p r e t e d d a t a from Winter e t a l . Northwestern United S t a t e s

-,

According t o S i n c l a i r (1978), who (1975) on t h e Puget Sound

s t r a t i f i c a t i o n , which p a r t i a l l y follows t h e neap-spring c y c l e . Pingree e t a l .

-a

fjord i n

primary production t h e r e i s w e l l c o r r e l a t e d t o Surveys by

(1975, 1976, 1977, 1978) on phytoplankton d i s t r i b u t i o n s on t h e

northwest European Shelf showed f r o n t a l movements, caused by t h e c y c l e of v e r t i c a l mixing induced by t h e a l t e r n a t i o n of neap and s p r i n g t i d e s .

Summer f r o n t s a r e

between regions of well-mixed and of w e l l - s t r a t i f i e d water: i n c r e a s e d t i d a l

mixing a t s p r i n g t i d e s modifies t h e p o s i t i o n of t h e f r o n t , by changing t h e s t r a t i f i c a t i o n of t h e w a t e r column.

The p e r i o d i c enrichment of s u r f a c e waters

i n n u t r i e n t s , followed by s t a b i l i z a t i o n a t neap t i d e s , d e l i n e a t e s a r e a s of t h e A s i m i l a r mechanism i s described by

ocean with high phytoplankton production.

Fournier e t a l . (1979) f o r the S c o t i a n Shelf (Eastern Canada), where changes i n w i n t e r c h l o r o p h y l l c o n c e n t r a t i o n s are c o r r e l a t e d t o t h e s t e e p n e s s of a subs u r f a c e shelf-break f r o n t ; according t o t h e f o r c i n g mechanism p o s t u l a t e d , t h e o s c i l l a t i o n p e r i o d of t h e f r o n t i s estimated between 15 and 60 days.

Decreased

f r o n t a l steepness reduces t h e depth of t h e mixed l a y e r , which enhances t h e phytoplankton production. The wind i s another d e s t a b i l i z i n g a g e n t , t o which t h e dynamics of phytoplankton responds.

Takahashi e t a l .

(1977) r e p o r t abrupt i n c r e a s e s i n n u t r i e n t s , ascribed

t o s t r o n g winds, i n t h e t o p 1 0 m of Saanich I n l e t (Western Canada), l e a d i n g t o occasional*summer phytoplankton blooms. noted by Webb and D'Elia

However, examination of t h e i r d a t a , a s

(1980), a l s o suggests a r e l a t i o n s h i p t o t h e neap-

Iverson e t a l . (1974) observed, i n Auke Bay (Alaska), -1 ) mixed n i t r a t e i n t o t h e p h o t i c l a y e r from deeper i n

spring t i d a l cycle.

t h a t high winds ( > 4 m ' s

t h e water column, r e s u l t i n g i n major summer phytoplankton blooms. Legendre e t a l .

Similarly

( m s ) p a r t i a l l y e x p l a i n t h e d i f f e r e n c e i n phytoplankton production

between s o u t h e a s t e r n Hudson Bay and i t s c o a s t a l Manitounuk Sound, i n t h e summer months, a s a response of phytoplankton t o l o c a l l y reduced wind stress, t h e more productive upper Sound being s h e l t e r e d behind t h e Manitounuk I s l a n d s . e t al.

Therriault

(1978) have demonstrated t h a t phytoplankton production is indeed

c o n t r o l l e d by wind s t r e s s induced turbulence, f o r wind v e l o c i t i e s g r e a t e r than

-1

4-5 m-s

S t a b i l i t y a l s o i n f l u e n c e s t h e phytoplankton t a x a found i n t h e w a t e r column. The seasonal succession of diatoms and d i n o f l a g e l l a t e s i n temperate regions p a r a l l e l s t h e seasonal v a r i a t i o n s i n primary production, and t h e v e r t i c a l s t r u c t u r e of phytoplankton communities responds ( I g n a t i a d e s , 1979) t o seasonal changes i n s t a b i l i t y . .

I n a r e a s s u b j e c t e d t o t i d e induced v a r i a t i o n s i n s t a b i l i t y ,

a s t h e C e l t i c Sea, p a t t e r n s of phytoplankton succession vary with t h e c h a r a c t e r i s t i c s of t h e mixing (Holligan and Harbour, 1977).

According t o Wangersky (1977),

s p e c i e s composition i n upwelling ecosystems r e f l e c t v a r i a t i o n s i n * n u t r i e n t s , which depend on t h e s u r f a c e s t a b i l i z a t i o n of upwelled water.

THE PARADOX OF STABILITY I t follows t h a t (Takahashi e t a l . ,

polar w a t e r s ,

[.- -3

1977)

' I . . .

p a r t i c u l a r l y i n temperate o r

t h e upper l a y e r s of t h e water column, where most p l a n t

a c t i v i t y occurs, a r e mixed or replaced with deep or i n t e r m e d i a t e depth w a t e r by v a r i o u s p h y s i c a l a c t i o n s : t i d e s , winds, r i v e r run-off

, and

currents

[..-3

FREQUENCY OF STAB1 LIZATION- DESTABILIZATION ( N o . sequences of rtabilizotion-destabilization per yeor)

Fig. 1. Frequencies of stabilization-destabilization significant to the dynamics of phytoplankton. Nonperiodic instances of stabilization-destabilization are also encountered. Unvarying environments are those seldom stabilized or destabilized.

Such water movements abruptly supply various nutrients to the surface

on

...‘I

a wide range of scales, as shown above, so t h a t the alternating stabilizationdestabilization of the water column emerges as a fundamental hydrodynamic control of phytoplankton production.

The available literature reports

periodicities significant to production from 5-6 h (Auclair et al. ms) to one year (traditional seasonal pattern), thus exceeding a range of three orders of magnitude (Fig. 1).

It must be noted that stabilization-destabilization is

not only of periodic character (astronomicalrhythms: seasons, tides) but may also be nonperiodic (meteorological factors such as the wind, or others).

The

stzatification-destratification mechanism thus appears as a unique environmental factor by its range of action and by its direct control of the phytoplankton dynamics. There is some degree of discussion in the literature as to the relationship between stability and production, some authors finding that reduced stability parallels reduced phytoplankton production, while others report an inverse correlation between stability and production.

This apparent paradox is

obviously the result of inappropriate observation scales, since neither stabilization nor destabilization of the water column favours phytoplankton production.

At any spatio-temporal scale, only the alternating stabilization

199 and d e s t a b i l i z a t i o n of t h e w a t e r column, i n time and/or i n space, i s an hydrodynamic mechanism conducive t o enhance primary production.

The g e n e r a l i t y

of t h i s mechanism i s e a s i l y understood using a simple conceptual model.

MODEL AND DISCUSSION

The conceptual model of phytoplankton production, schematized on F i g . 2 , s y n t h e s i z e s most of t h e conclusions reported above on t h e c o n t r o l of phytoplankton dynamics by a l t e r n a t i n g stratification-destratification of t h e w a t e r column. A s f a r as phytoplankton i s concerned, t h e water column s t a b i l i z e s when t h e

mixed l a y e r becomes shallower than t h e c r i t i c a l depth.

The b a s i c equations

modelling phytoplankton production a r e known s i n c e Riley ( 1 9 4 6 ) .

The curves f o r

t h e s t r a t i f i e d environment ( F i g . 2 ) a r e from S t e e l e ( 1 9 5 8 ) , as i n Riley ( 1 9 6 3 ) . The phase, of d e s t a b i l i z a t i o n i s dominated by increased mechanical energy, which r e s u l t s i n s t r o n g e r mixing and t h u s favours a replenishment of t h e p h o t i c l a y e r i n n u t r i e n t s , up t o maximum c o n c e n t r a t i o n s equal t o t h o s e i n t h e underlying waters ( i f they are n u t r i e n t - r i c h )

.

Phytoplankton production i s then l i m i t e d

by a shortage of l i g h t , r e s u l t i n g from t h e increased mixing t o g r e a t e r depth. On t h e o t h e r hand, t h e phase of s t a b i l i z a t i o n i s c h a r a c t e r i z e d by t h e a c t i v e use of s o l a r energy and m a t e r i a l s by t h e phytoplankton.

The i n i t i a l phytoplankton

bloom r a p i d l y exhausts t h e n u t r i e n t s a v a i l a b l e i n t h e p h o t i c l a y e r , s o t h a t subsequent production i s a f u n c t i o n of i n s i t u n u t r i e n t regeneration and of d i f f u s i o n of n u t r i e n t s from deeper w a t e r s , t h e l a t t e r being very l i m i t e d under s t r a t i f i e d conditions.

The phase of d e s t a b i l i z a t i o n i s t h e r e f o r e d r i v e n by

mechanical mixing, while t h a t of s t a b i l i z a t i o n i s dominated by b i o l o g i c a l processes, both being e q u a l l y e s s e n t i a l t o prevent t h e b i o l o g i c a l c y c l e from c l o s i n g up.

The i n p u t of e x t e r n a l mechanical energy a c t i v a t e s t h e turnover of

materials, incorporated i n t h e ecosystem by t h e phytoplankton under s t a b l e conditions.

N u t r i e n t s a r e t h u s r e d i s t r i b u t e d over t h e e n t i r e water column,

becoming a v a i l a b l e f o r t h e production of phytoplankton upon s t a b i l i z a t i o n .

The

i n p u t of mechanical energy t h e r e f o r e does enhance primary production. These c h a r a c t e r i s t i c s do shape t h e f o u r curves of F i g . 2 .

(1) Changes i n

s t a b i l i t y i n the marine environment a r e s h a r p , b u t obviously not a s much a s schematically drawn on Fig. 2 .

However, t h e d r a s t i c changes caused by winds

o r t i d e s , o r the f r o n t a l d i s c o n t i n u i t i e s , a r e examples of very s t e e p s t a b i l i t y t r a n s i t i o n s i n the oceans.

( 2 ) N u t r i e n t s a r e a p a s s i v e s c a l a r , c o n t r o l l e d by

t h e dominant r e a c t i n g parameter: v e r t i c a l mixing, i n t h e d e s t r a t i f i e d phase, uptake by phytoplankton and i n s i t u r e g e n e r a t i o n , under s t a b l e c o n d i t i o n s . Within t h e s t r a t i f i e d phase, n u t r i e n t s regenerated i n t h e mixed l a y e r a r e d i r e c t l y recycled i n t o t h e production of phytoplankton, t h e well-known d i n o f l a g e l l a t e blooms ( r e d t i d e s ) being supported by increased b a c t e r i a l

200

Unstable

St rat if ied

I

Unstable

Fig. 2 . Simple conceptual model of phytoplankton dynamics.

r e g e n e r a t i o n (Wangersky, 1 9 7 7 ) .

( 3 ) A s f a r a s t h e model i s concerned, production

is a t h r e s h o l d f u n c t i o n of both s t a b i l i t y ( l i g h t ) and n u t r i e n t s .

The concepts

of c r i t i c a l depth and of n u t r i e n t l i m i t a t i o n b o t h emphasize t h e independence of primary production above t h e s e t h r e s h o l d s , and i t s i n c r e a s i n g dependence below them.

( 4 ) Phytoplankton biomass depends on t h e balance between n e t

201 production and l o s s e s .

Under c o n d i t i o n s of high mixing, low production and

continuous d i s p e r s i o n i n t h e water column keep t h e biomass a t a very low l e v e l . I n t h e s t a b i l i z e d phase, g r a z i n g by t h e zooplankton, s i n k i n g of c e l l s , l y s i s of senescent c e l l s , e t c . t r a n s f e r t h e biomass produced i n t h e p h o t i c zone t o t h e remainder of t h e ecosystem.

Ecosystems with high production a r e o f t e n

c h a r a c t e r i z e d by s t r o n g h o r i z o n t a l advection, phytoplankton being exported a t t h e s u r f a c e and n u t r i e n t s imported a t depth. The model may be applied t o a l l temporal successions of s t r a t i f i c a t i o n and d e s t r a t i f i c a t i o n , on any t i m e s c a l e .

The seasonal production dynamics i s

obviously w e l l accounted f o r , a s a r e a l l o t h e r i n s t a n c e s of time changing production r e p o r t e d above, whatever t h e f o r c i n g agent may be

- tides

(M

f'

M2'

According t o the t i m e

s l a c k w a t e r s ) , winds, r i v e r r u n o f f , o r h e a t i n g .

c h a r a c t e r i s t i c s of t h e system ( h o u r s , weeks o r months), t h e time a b s c i s s a of F i g . 2 must only be d i f f e r e n t i a l l y expanded or c o n t r a c t e d , t h e phases of s t a b i l i t y and mixing being s u c c e s s i v e l y repeated a s many times as needed, from four times a day t o once a y e a r .

A peak i n phytoplankton production i s t h u s modelled a t

t h e beginning of each p e r i o d of s t r a t i f i c a t i o n , leading t o a phytoplankton bloom when o t h e r c o n d i t i o n s a r e p r o p i t i o u s (depth of t h e p h o t i c l a y e r , d u r a t i o n of t h e s t a b i l i z a t i o n , e t c . ) ; indeed, a s observed f o r i n s t a n c e i n t h e S t Lawrence Estuary by F o r t i e r and Legendre (1979), high photosynthetic p o t e n t i a l does not develop i n t o a biomass o u t b u r s t when t h e p h o t i c l a y e r i s t o o shallow.

If the

p e r i o d of s t a b i l i t y i s s h o r t enough, c o n d i t i o n s of n u t r i e n t l i m i t a t i o n a r e never encountered by t h e phytoplankton.

Periods of mixing, preceding and following

t h e p e r i o d of s t r a t i f i c a t i o n , a r e c h a r a c t e r i z e d by low phytoplankton production,

l o w phytoplankton biomass, and replenishment of n u t r i e n t s i n t h e p h o t i c l a y e r . B u r s t s of phytoplankton biomass t h e r e f o r e occur i n t e r m i t t e n t l y , t h e concept

Of

i n t e r m i t t e n c y r e f e r r i n g , as i n hydrodynamics (Mollo-Christensen, 1973), t o t h e

t i m e f r a c t i o n occupied by t h e "events"

- here

t h e phytoplankton blooms.

The model i s a l s o a p p l i c a b l e t o t h e h o r i z o n t a l s t r u c t u r e of f r o n t a l a r e a s . This s t r u c t u r e i s modelled by a s i n g l e sequence of u n s t a b l e and s t r a t i f i e d phases (two l e f t t h i r d s of Fig. 2 ) , t h e a b s c i s s a being then t h e c r o s s - f r o n t a l axis.

The i n c r e a s e i n s t a b i l i t y (Fig. 2 ) corresponds t o t h e f r o n t a l zone,

between w e l l mixed and w e l l s t r a t i f i e d regimes. t h e English Channel f o r i n s t a n c e (Pingree e t a l . ,

I n t h e Western Approaches t o

1975, 1976), t h e f r o n t i s

l o c a t e d between c o a s t a l regions of s t r o n g t i d a l stream, where t h e water column remains mixed throughout t h e summer, and s h e l f a r e a s , which a r e c h a r a c t e r i z e d by weak t i d e s , a s t a b l e thermocline and low s u r f a c e n u t r i e n t s .

According t o

t h e model ( F i g . 21, maximum phytoplankton biomass should be found on t h e s t r a t i f i e d s i d e of t h e f r o n t .

Pingree e t a l .

(1976) observed t h a t high s u r f a c e

c h l o r o p h y l l c o n c e n t r a t i o n s a r e d i s p l a c e d towards t h e s t r a t i f i e d s i d e of f r o n t a l

202 boundaries; furthermore Pingree e t a l .

(1977) reported a phytoplankton bloom f o r

both t h e s u r f a c e waters and t h e thermocline on t h e s t r a t i f i e d s i d e of t h e f r o n t . S i m i l a r l y on t h e Scotian S h e l f , Fournier e t a l .

(1979) found a sudden drop i n

c h l o r o p h y l l upon e n t e r i n g t h e well mixed slope water, t h e chlorophyll concentration being i n g e n e r a l d i r e c t l y r e l a t e d t o t h e s t a b i l i t y of t h e water column. I n a "permanent" upwelling, t h e r e i s l i m i t e d v e r t i c a l mixing over t h e e n t i r e water column (except a t t h e s c a l e of t h e World Ocean!), s i n c e most of t h e nutrient-rich advection).

upwelled water i s l a t e r a l l y advected ( l i m i t e d o r no downward

I n such a case both c o n d i t i o n s of n u t r i e n t enrichment and v e r t i c a l

s t a b i l i t y occur w i t h i n a r e l a t i v e l y small i n t e r v a l , l e a d i n g t o high phytoplankton production i n t h e r e c e n t l y upwelled water and export of biomass. upwelling ecosystems may show spatio-temporal

However,

changes i n t h e production and

biomass o f phytoplankton, r e l a t e d t o t h e v e r t i c a l s t a b i l i t y of t h e water column. The numerical model, developed by Wroblewski (1977) f o r t h e wind driven upwelling ecosystem o f f t h e Oregon c o a s t , p r e d i c t s t h e h i g h e s t phytoplankton biomass t o occur upon r e l a x a t i o n of s t r o n g winds, when t h e phytoplankton c e l l s remain longer i n t h e n u t r i e n t - r i c h p h o t i c zone. observed during f i e l d s t u d i e s .

Such phytoplankton blooms w e r e c l e a r l y

Whenthe model i s run with t h e observed

t i m e f l u c t u a t i n g wind r e c o r d s , t h e response of phytoplankton t o t h e r e s u l t i n g i n t e r m i t t e n t upwelling i s an i n c r e a s e i n primary production following each major i n t e n s i f i c a t i o n of t h e wind s t r e s s , t h e production maxima being always observed upon r e l a x a t i o n of winds ( F i g . 19 i n Wroblewski, 1977).

A

s e r i e s of phytoplankton blooms a r e t h u s forced during t h e season favourable f o r c o a s t a l upwelling, i n r e l a t i o n t o f l u c t u a t i o n s i n t h e wind s t r e s s . According t o Wangersky (1977) diatom growth responds t o s t a b i l i z a t i o n of nutrier& r i c h water, while d i n o f l a g e l l a t e s become dominant when t h e major source of n u t r i e n t s i s i n s i t u r e g e n e r a t i o n , from t h e degradation of dissolved organic m a t t e r by b a c t e r i a .

This r e l a t e s s p e c i e s composition t o t h e n u t r i e n t s t a t u s Of

t h e ecosystem, and provides a g e n e r a l scheme t o analyze succession and d i s t r i b u t i o n of s p e c i e s .

I n temperate r e g i o n s , t h e seasonal succession of diatoms and

d i n o f l a g e l l a t e s t h u s r e f l e c t s t h e n u t r i e n t changes caused by t h e mixing and t h e production of phytoplankton. northwest European Shelf

D i s t r i b u t i o n and succession of s p e c i e s on t h e

(Holligan and Harbour, 1977; Pingree e t a l . , 1978) show

diatoms t o be t h e most abundant taxa i n t h e n u t r i e n t - r i c h mixed water, while small f l a g e l l a t e s dominate t h e s u r f a c e water i n s t r a t i f i e d regions; populations of mixed diatoms and d i n o f l a g e l l a t e s , of d i n o f l a g e l l a t e s , and of small f l a g e l l a t e s , s u c c e s s i v e l y occupy t h e thermocline of s t r a t i f i e d w a t e r s , following t h e c h a r a c t e r i s t i c s of t h e mixing.

High phytoplankton c o n c e n t r a t i o n s i n f r o n t a l

regions a r e formed of a mixture of d i n o f l a g e l l a t e s and diatoms, which agrees with successive s t r a t i f i c a t i o n ( i n s i t u n u t r i e n t r e g e n e r a t i o n ) and d e s t r a t i f i c a t i o n

203 (upwelling of nutrient-rich water) on a fortnightly Mf cycle.

Wangersky (1977)

explains in the same way the differences in species composition observed from upwelling systems. The spatio-temporal sequence of stratification and destratification,despite the variety of hydrodynamic mechanisms encountered in the various oceanic conditions, therefore appears as a basic control of the phytoplankton dynamics. It follows that the frequency of stabilization-destabilization is a fundamental characteristic of any water column (except in shallow waters), as significant to phytoplankton production as temperature, turbidity, trace elements, or any other factor traditionally considered. For instance, summer chlorophyll concentrations in Auke Bay (Iverson et al., 1974) are about 40 mg.m-2, while they exceed 160 mg-m-2 in the wind driven summer blooms.

Maximum chlorophyll

concentrations in the spring and autumn blooms, reported by Takahashi et al. (1977)'for Saanich Inlet, are respectively 22 and 9 m9-m-3, while twelve summer blooms, between the two main blooms, range from 3 to 15 m9-m-3 at their peaks. -2 at a station of Puget

Annual production (Winter et al., 1975) is 275 9C.m

Sound with fairly uniform assimilation from March through September; it is 465 -2 gC-m at a station with a number of intense blooms between early May and September. On the northwest European Shelf (Pingree et al., 1975, 1976, 19781, -3

summer chlorophyll recorded in the tide driven frontal zones are 7 mgsm -3 -3 (Orkney - Shetland Isles), 19 mg-m (Ushant), and as high as 100 m9.m

(western English Channel), while the average surface concentrations on both -3 sides of the fronts are about 1 mg-m - On the Scotian Shelf (Fournier et al., 1979), intermittent growth for as few as 30% of the winter days increases the annual phytoplankton production in the frontal area by 25%. Takahashi et al. (1977) have already suggested that

"

...

a common feature in

temperate to sub-polar regions seems to be several Occasional phytoplankton blooms during summer caused by short term temporal nutrient increases and a possible supply of phytoplankton seed stock from deep or intermediate depth water by partial mixing, regional upwelling, or replacement of water masses. The seasonally changing pattern of phytoplankton bimodal or unimodal, based on seasonal climatic variations seems oversimplified. Summer blooms may contribute significantly to the total annual primary production

[. . .]

Summer blooms

probably occur frequently both in higher latitudes and coastal waters, and less frequently in open oceanic waters and in lower latitudes

. . _ ' I

In fact, this

mechanism is even more general (Fig. l), since winter blooms may contribute significantly to the annual production, as may do alternation of stabilization and destabilization on very short time scales.

It follows that seasonal patterns

with only two, one, or even no phytoplankton blooms, are extreme cases on a wide scale of frequencies (Fig. 1).

Even if they cover large geographic areas, these

ecosystems with a low periodicity of stratification-destratification must be studied within the framework of broad conceptual models, covering the full spectrum of frequencies significant to the dynamics of phytoplankton. According to Margalef (1978), "careful models of the dependence of primary production on light, nutrients, temperature, and so on, may be useful in many situations, but in upwelling areas they may be replaced, probably with advantage, by the simple dependence of primary production on the auxiliary energy made available.

It is like in agriculture, where yield can be simply related to the

input of subsidiary energy (in machines, oil power, fertilizers, irrigation)

."

Following the same approach, it is proposed here to characterize the phytoplankton production potential of marine ecosystems by their frequency of stabilizationdestabilization, defined as the number of sequences of stabilization and destabilization per unit time.

On this scale (Fig. l), a near zero frequency

identifies systems seldom stabilized or destabilized, while upwellings tend toward the upper limit of stabilization-destabilization;in the laboratory, the turbidostat is the best example of a system with maximum production, simultaneously taking advantage of both stabilization and destabilization of the water, and therefore characterized by a maximum frequency of stabilization-destabilization. As discussed above, the input of mechanical energy enhances primary production, so

that the frequency of stabilization-destabilizationis an index of potential

phytoplankton production.

However, factors such as temperature, turbidity, low

nutrient background, and so on, may limit the production potential built up by the alternating stratification-destratification,these limiting factors being passive, while the alternation of stabilization and destabilization is an active input of energy.

This concept does not apply to shallow environments, where

high mixing does not lead to light limitation of phytoplankton.

To become

operational, the concept of stabilization-destabilization must be translated into physical terms (spatio-temporal domain significant to phytoplankton, measurements at sea, etc.), and it must take into account the spatio-temporal characteristics of the phytoplankton (response times, growth rates, patchiness, etc.). Considering that vertical mixing plays a significant role in only a limited number of oceanic systems, Wangersky (1977) proposed that phytoplankton dynamics is mainly controlled by nutrient regeneration, which increases with the number of bacteria present, this number being in turn a function of the particle content of the water.

In contrast, the present work hypothesizes that stabilization-

destabilization of the water column is of general occurrence in most of the productive oceanic areas. This does not exclude, however, that production of phytoplankton may be significantly enhanced by increased nutrient regeneration, especially in areas with low frequency of stabilization-destabilization.

205 Ecosystems d r i v e n by n u t r i e n t r e g e n e r a t i o n , s u c h as the Sargassum f o r i n s t a n c e ,

are l i m i t e d t o t h e mixed l a y e r , by d e f i n i t i o n , and t h e y are t h e r e f o r e v e r t i c a l l y c l o s e d systems.

These e c o s y s t e m s , which a l s o i n c l u d e t h e r e d t i d e s , c o n c e n t r a t e

t h e o r g a n i c matter n e a r t h e s u r f a c e , i n a way somewhat a n a l o g o u s t o t h e bog lakes.

On t h e c o n t r a r y , e c o s y s t e m s dominated by s t a b i l i z a t i o n - d e s t a b i l i z a t i o n

are v e r t i c a l l y o p e n , s i n c e n u t r i e n t s r e g e n e r a t e d a t d e p t h and e n e r g y s t o r e d by p h y t o p l a n k t o n a t s u r f a c e are v e r t i c a l l y exchanged.

T h i s v e r t i c a l t r a n s f e r of

e n e r g y and m a t e r i a l s , d r i v e n by t h e s t a b i l i z a t i o n and d e s t a b i l i z a t i o n o f t h e

w a t e r column, i s one o f t h e b a s i c mechanisms of p r o d u c t i v e m a r i n e ecosystems.

ACKNOWLEDGMENTS The a u t h o r w i s h e s t o t h a n k P r o f . J. P. O'Kane

(University College, Dublin),

P r o f . P. Bougis, P r o f . P . N i v a l and D r . L . P r i e u r ( S t a t i o n marine de V i l l e f r a n c h e s u r - M e r ) , D r . M. E s t r a d a ( I n s t i t u t o de I n v e s t i g a c i o n e s P e s q u e r a s , B a r c e l o n a ) and D r . J. Flos

manuscript.

( U n i v e r s i d a d d e B a r c e l o n a ) , f o r t h e i r u s e f u l c r i t i c i s m s of t h e I n d i v i d u a l o p e r a t i n g g r a n t no. A9689 from t h e N a t u r a l S c i e n c e s and

E n g i n e e r i n g R e s e a r c h C o u n c i l o f Canada w a s i n s t r u m e n t a l i n t h e c o m p l e t i o n of t h i s work.

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207 Roy, S . and Legendre, L . , 1979. DCMU-enhanced f l u o r e s c e n c e a s an i n d e x of p h o t o s y n t h e t i c a c t i v i t y i n phytoplankton. Mar. B i o l . , 55: 93-101. Roy, S. and Legendre, L . , 1980. F i e l d s t u d i e s of DCMU-enhanced f l u o r e s c e n c e a s an i n d e x of i n s i t u phytoplankton p h o t o s y n t h e t i c a c t i v i t y . Can. J . F i s h . a q u a t . S c i . , 37: 1028-1031. S i n c l a i r , M . , El-Sabh, M . I . , P o u l e t , S . and Coote, A . , 1979. Sevigny, J . M . , Summer p l a n k t o n d i s t r i b u t i o n s a s s o c i a t e d w i t h t h e p h y s i c a l and n u t r i e n t p r o p e r t i e s of t h e n o r t h w e s t e r n Gulf of S t . Lawrence. J . F i s h . R e s . Board Can., 36: 187-203. S i n c l a i r , M . , 1978. Summer phytoplankton v a r i a b i l i t y i n t h e lower S t . Lawrence e s t u a r y . J . F i s h . Res. Board Can., 35: 1171-1185. S t e e l e , J . H . , 1958. P l a n t p r o d u c t i o n i n t h e n o r t h e r n North Sea. S c o t . Home Dep., Mar. Res. 1958, ( 7 ) : 1-36. Steven, D.M., 1974. Primary and secondary p r o d u c t i o n i n t h e Gulf of S t . Lawrence. M a r . S c i . C e n t . , M c G i l l Univ., Montreal, Quebec. MS Rep., ( 2 6 ) , viii 116 p .

+

Sverdrup, H.U., 1953. On c o n d i t i o n s for t h e v e r n a l blooming of phytoplankton. J . Cons. perm. i n t . Explor. M e r , 18: 287-295. Takahashi, M:, S i e b e r t , D.L. and Thomas, W.H., 1977. Occasional blooms of p h y t c p l a n k t o n d u r i n g summer i n Saanich I n l e t , B.C., Canada. Deep-sea R e s . , 24: 775-780. T h e r r i a u l t , J . C . and L a c r o i x , G . , 1976. N u t r i e n t s , c h l o r o p h y l l , and i n t e r n a l t i d e s i n t h e S t . Lawrence E s t u a r y . J. F i s h . Res. Board Can., 33: 2747-2757. T h e r r i a u l t , J . C . , Lawrence, D . J . and P l a t t , T . , 1978. S p a t i a l v a r i a b i l i t y of phytoplankton t u r n o v e r i n r e l a t i o n t o p h y s i c a l p r o c e s s e s i n a c o a s t a l environment. Limnol. Oceanogr., 23: 900-911. Wangersky, P . J . , 1977. The r o l e of p a r t i c u l a t e m a t t e r i n t h e p r o d u c t i v i t y of s u r f a c e w a t e r s . Helgolander w i s s . Meeresunters., 30: 546-564. Webb, K.L. and D ' E l i a , C.F., 1980. N u t r i e n t and oxygen r e d i s t r i b u t i o n d u r i n g a s p r i n g neap t i d a l c y c l e i n a temperature e s t u a r y . S c i e n c e , 207: 983-985. Winter, D . F . , Banse, K. and Anderson, G . C . , 1975. The dynamics of phytoplankton blooms i n Puget Sound, a f j o r d i n t h e n o r t h w e s t e r n United S t a t e s . Mar. B i o l . , 29: 139-176. Wroblewski, J . S . , 1977. A model of phytoplankton plume formation d u r i n g v a r i a b l e Oregon upwelling. J. mar. Res., 35: 357-394.

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209

DIFFUSION AS A CONSTRAINT ON THE BIOLOGICAL IMPORTANCE OF MICROZONES IN THE SEA P.J.L. WILLIAMS and L.R. MUIRl Department of Oceanography, The University, Southampton, (England)

ABSTRACT Excretion patches produced by marine zooplankton have length scales on the order of to metres, and their dissipation is controlled by molecular diffusion. These microzones have been considered by many biologists and are thought to explain certain features of plankton production. It is shown that there cannot be enough of these patches, nor can they persist for long enough to be of importance in maintaining primary productivity in the ocean. The question of how phytoplankton maintain their observed growth rates is still open. INTRODUCTION Planktonic processes and events have space scales ranging from lo3 metres to metres if molecular processes are ignored. Parsons, Takahashi and Hargrave (1977) show that the major biological activity in the oceans is associated with small organisms whose size is between loW3and metres and their awareness will be primarily on a scale not too far removed from their own size. Our comprehension of planktonic processes on the molecular level is quite good as is our knowledge of processes on scales of more than one metre. However, in the critical region between I and metres our notions are hazy. We have, for example, no indication of the variability of important chemical parameters for algal growth (e.g., inorganic nitrogen and phosphorous sources, or chelating ability) on scales less than 10-1 metre.

Classical experimental methods for the determination of plant nutrients offer no sign of providing resolution on scales finer than metres while de-

tailed profiling of chlorophyll (Derenbach, et al, 1979) demonstrates variability on a

lo-’ metre length scale with indications that there is variability on even

finer scales. One could argue that if we have no understanding of processes on the microscale, then the usefulness of information on larger scales cannot be known. There is, therefore, no direct experimental evidence for assuming either homogeneity or variability on length scales between

and

metres.

Inevitably,

Permanent address: Ocean and Aquatic Sciences, Canada Centre for Inland Waters, P.O. Box 5050, Burlington, Ontario, Canada.

210 this lack of firm experimental evidence has meant that the subject of microzones in the marine environment is open to speculation. The notion of microzones is not new and a variety of biological observations have been explained by the assumption that there exist small patches of high chemical concentration which dominate the bulk chemical properties of the natural oceanic waters.

Since biological activity

is associated with small organisms which are discrete sources and sinks, then some chemical variability, on the approximate length scales of the organisms must inevitably occur. The approximate Reynolds number of the flows being considered is less than 1, and this would indicate that molecular diffusion rather than turbulent diffusion is the most important dissipation mechanism for these microzones. In this paper, we shall be concerned with the excretion patches of zooplankton as a source of nutrients for photosynthetic algae. We shall consider molecular diffusion to be the most important dissipation process and we shall mainly be to metres. We shall attempt conce'rned with length scales on the order of to answer the question : may the number, size and duration and chemical concentration in these patches be such that they are of importance in maintaining the primary productivity?. We show that, given the current knowledge of planktonic processes, microzones cannot play any important role. 2.0

PREVIOUS WORK

It has been argued for some time (Goering, Dugdale

&

Menzel, 1964; Beers and

Kelly, 1965 and Dugdale, 1967) that there is a close link between the excretion products of marine zooplankton and the phytoplankton, since these excretion products provide nitrogen which is essential for photosynthesis. Recent developments on this theme are given in the papers by Goldman, McCarthy and their co-workers (McCarthy and Goldman, 1979; and Goldman, McCarthy and Peavey, 1979). The argument runs as follows: The effect of nitrogen limitation on the rate of algal growth in cultures is reflected in the amount of inorganic nitrogen in the cell which is determined experimentally as the C/N ratio. When nitrogen limits the rate of growth, the nitrogen content of the cell is reduced, thus raising the C/N ratio. By measuring the C/N ratio of natural populations it is found that these ratios are indicative of growth rates which are too great to be sustained by the ambient inorganic nitrogen concentrations. However, these ambient nitrogen concentrations are measured as averages over relatively large volumes. Goldman and McCarthy draw attention to the fact that planktonic algae can assimilate their nitrogen in relatively short periods of time when exposed to high inorganic concentrations. They then speculate that:

211

"Such situations could conceivably exist when cells randomly and perhaps frequently pass into microenvironments in which nitrogenous nutrient concentrations are elevated as a result of either metabolic waste excretion by animals or the degradation of organic matter by bacteria." They produce, as an example, a calculation for the diatom Thalassiosira which indicates that the organism would need to spend 3% (40 minutes per day) of its time in an excretion patch produced by an adult calanoid zooplankter. The notion has been made more sophisticated by introducing the effect of nutrient status on buoyancy.

Steele and Yentsch (1960) haveobserved that under

nutrient deficient conditions, the phytoplankter Skeletonema costatum became negatively buoyant. Thus one could extend the McCarthy and Goldman hypothesis to suggest that algae could actively seek out and exploit nutrient rich zones by becoming negatively buoyant and sinking when they are deficient in nitrogen and then adjusting their buoyancy, when entering a patch, to maintain themselves in that patch. So long as the phytoplankter can find enough patches of high enough concentration to spend at least 3% of its time in these patches, then it is of no consequence to the phytoplankter that the ambient average nitrogen concentrations are too low to maintain its growth rate. 3.0

PATCH DYNAMICS

In the above argument, the critical assumption is that the patches produced by the zooplankton persist long enough that the mean length of time that a phytoplankter can spend in one or more patches exceeds 3%. Before we can have a quantitative discussion of the patch dynamics, it is necessary to define what is meant by a patch. We assume that the boundary of a patch will be defined as a concentration which significantly exceeds the background environment and which allows the algal growth rate to approach a maximum. Ammonia concentrations in the offshore environment are typically less than 0.5 pg-atoms N / 1 and a value between 0.05 and 0.2 may be regarded as a background concentration. The relationship between algal growth and the ambient nutrient concentration may be described by a hyperbolic curve which contains a constant (the uptake constant), and this uptake constant is numerically equal to the nutrient concentration which gives rise to one half of the maximum growth rate. McCarthy and Goldman consider algal growth rates, in nutrient rich patches, within 17% of the maximum growth rates. Such growth rates will be realized at nutrient concentrations which are approximately five times greater than the uptake constant. Typical values for the uptake constant for ammonia are in the region of 0.5 pg-atoms N / 1 (MacIsaac and Dugdale, 1969).

These two lines of argument

imply that a value between 2.5 and 15 pg-atoms N / 1 would be an appropriate value

212

to adopt for the boundary of an ammonia rich patch.

We shall consider a patch to

consist of a concentration higher than 2.5 pg-atoms N / t to allow the most favourable condition for the patch. Throughout the remainder of this paper, when alternatives or uncertainties exist, we shall assume the case which would be most favourable for the persistance of a patch and which would therefore strengthen the argument for the importance of the microzones. Zooplankton exhibit two types of motion.

The first is continuous motion which

produces an excretion plume behind the zooplankter. Jackson (1980) has considered this type of motion and has found that the plumes cannot contribute significantly to the growth of phytoplankton. intermittant motion.

We have assumed the other alternative, that of

We assume that the zooplankter is stationary while excreting

and then moves away from the spherical patch without disturbing it with its swimming appendages. We also assume that the zooplankter excretes through its body surface and that 'the growth and subsequent decay of the patch is controlled by molecular diffusion.

By assuming that the zooplankter is stationary while excreting, we

obtain the maximum patch size, and by assuming that it does not disturb the patch with its swimming appendages while moving away, we allow the patch to exist for the maximum period of time. There are two possible models for the method of excretion by the zooplankter. The first model assumes that the zooplankter excretes material at a constant rate through its body surface, and this leads to an expression for the concentration at any time during the excretion process and at any distance from the body surface which is (Carslaw and Jaeger, 1 9 4 7 , p. 261) c(x,t) =

2ERFC [ 2 4

4nDx

where;

c = concentration

D = diffusion coefficient x = distance from the body surface

Q

=

flux of material from the source

t = time

and ERFC is the complement of the Error Function. The difficulty with this model is that the concentration at the body surface is infinite and this is clearly impossible. If we assume, alternatively, that the body surface concentration is a constant and that we have spherical symmetry, then initially the zooplankter may be considered to be a semi-infinite source with a constant internal concentration of 2c for t > 0 the concentration is given by

.

Then

213

=

coERFC

I2G)

and while the zooplankter is excreting, the body surface concentration is constant at c

.

The average rates of amonia excretion from a variety of zooplankton have been determined (Ikeda, 1970), but the concentration of material in the body fluids and the precise excretion mechanism is not well known. However, if after a time, T a total mass M has been excreted, then m

M

4nc(x,T)xzdx

= 0

and

so,

during the excretion phase, 0

< t <

T

,

M

c =

(3)

2 O . 6 6 6 D 3 t 2 T3t2

In this model, during the growth phase of the patch, the body surface concentration is a constant, and this body surface concentration drives the excretion by molecular diffusion. This seems to be biologically realistic and produces a larger patch than does equation (1). After the zooplankter stops excreting (t> T ) we assume that the concentration distribution in the patch is still described by (2) but that the concentration at the centre of the patch decays and is given by cob> =

M

(4)

2 0 . 6 6 G ~ ~t3I2 /~

In what follows, we shall assume that the dynamics of the patches are given by and that the body surface concentration is given by (3) while the animal is excreting and the patch is growing. The zooplankter then moves away without disturbing the patch, and during the decay phase, the concentration at the centre of (2)

the patch is given by ( 4 ) 4.0

MODEL RESULTS

McCarthy and Goldman (1979) used a mean excretion rate for Oithona and Clausocalanus of 2.6 x g-atoms N-NH3 in about 5 seconds and this is consistent with values determined by Ikeda (1970). We used this rate of excretion for the zooplankton to calculate a mean surface concentration during the growth

214

.

phase of the patch, using equation ( 3 ) , of 0.1 g-atoms m3 We assume the boundary concentration of the patch to be defined by a concentration of 2.5x103~g-atoms/m3 and a mean molecular diffusion coefficient of 1.5 x lo-’ m2/s which is consistent with Pasciak and Gavis (1974) and with Jackson (1980). The maximum radius of the patch, may be calculated by solving (2) numerically A plot of maximum patch radius using various values of the growth time, T g versus growth time is given in Figure 1. It shows that if the zooplankter remains

.

stationary and excretes continuously for 200 seconds (which is an unreasonably long time) the maximum patch radius is approximately 0.9 mu.

, - l s 0

0 .oo

40.00

GRUHTH

Fig. 1.

80.00

120.00

TIME OF

160.00

.

200 00

PflTCH

Maximum patch radius vs. zooplankter excretion time.

By rearranging (41, making use of ( 3 ) , and defining cb as the boundary concentration, the time taken for the patch to decay is given by

215

(5) =

1.52 T

g

and after this time, the concentration at the centre of the patch is below the boundary concentration. We have assumed that the zooplankton remains stationary while it excretes for T

g

seconds and then moves instantly to a new location while the original patch

decays in Td seconds. Hence the number of discrete patches present at any given time due to a single zooplankter is given by

By varying either cb or c or both, it is possible to get a variation in the decay time as a function of the growth time and so to get a variation in the number of patches present. of

cb and

c

However, the limits that are possible in choosing the values

will not make very much difference to N

.

Now that we know the patch dynamics and the mean number of patches that one zooplankter produces it is possible to calculate the expected exposure time for a randomly distributed algal cell once we know the number of zooplankton per unit volume of seawater and the mean excretion time for these zooplankton.

It is not an easy matter to obtain a value for the mean number of zooplankton per F i t volume of seawater. However, it is possible to put an upper limit on the number that would be expected in an oceanic environment. Using data from the CEPEX study (Grice et al, 19801, which was conducted near Vancouver Island where zooplankton numbers are higher than would be expected in oceanic locations, and assuming that all species and both the adult and the copepodite stages may be treated alike, gives a rough estimate of about 10 individuals per litre.

Inde-

pendant calculations of oxygen consumption for the wjor species and their individual larval stages, when converted to ammonia excretion rates, using molar O:N of 2 0 : 1 , gives very similar answers.

If it is further assumed that the copepods account for

approximately 50% of the overall animal excretion of nitrogen then a reasonable upper limit on the zooplankton population is about 20 individuals per litre. Hence there would be, on average, about 5.0

x

lo4 patches per cubic metre at any given

instant in time, The probability of a randomly distributed algal cell being in a patch at any particular instant is given by the ratio of total patch volume per unit volume of seawater. Hence the exposure time for a particular algal cell is given, in seconds

216

per day as

E

=

4 7 r3N

86400

(7)

where r = mean patch radius N = number of patches per cubic metre and there are 86400 seconds in a day. It is very difficult to calculate the mean patch radius, however, if we assume that the mean patch radius is given by the maximum radius, then we shall be conservative.

XO u s b*

a a-

zg -,’.

w

N

r -

C? &

aW I--

u

Wg

k =W 0

?

0

0 .oo

Fig. 2.

I

1

40.00

1

1

80.00

I

1

120.00

I

I

160.00

I

1

200.00

GROWTH TIME OF P A T C H

Expected time in patch (secondsfday) for a randomly distributed algal cell versus mean zooplankter excretion time.

If the zooplankton remain stationary for an average of 200 seconds then the exposure time for an algal cell would be approximately 32.3 seconds per day. The exposure time is plotted versus the average time of excretion in Figure 2. The argument by McCarthy and Goldman required exposure times of about 2600 seconds which is about two orders of magnitude longer than the maximum time available. Assuming that the phytoplankton do have 2600 seconds of exposure time, then the zooplankton would have to remain stationary but metabolically active for more

217 than 3 . 5 hours. Alternatively, if they do not excrete for longer than 200 seconds in one place then the zooplankton population must be in excess of 4000 individuals per litre. Both of these possibilities seem unrealistic biologically, even though they are very conservative estimates, since we have always erred on the side of allowing the patch to persist longer than it would in nature. So far, we have not made any allowance for the larval stages of the zooplankton. Data is not readily available for the nitrogen excretion rate of the small larval stages but as a first approximation, since the excretion rate is a function of the surface area and the biomass of the larvae is approximately 0.01 of the biomass of the adults, then the excretion rate should be about 0.05 of the excretion rate of the adult. Hence, although there will be more larvae, the patches produced by them would diffuse away even faster than those produced by the adults, since the patches would be much smaller. In the same way, it is possible to ignore the effects of the bacterial decay of organic matter. There are many bacteria, but their patches decay away too rapidly to be of any use. The remaining factor to be considered is the possible effect of the algae settling into patches by adjusting their bouyancy. This argument assumes that the algae are settling at a rate which is greater than the rate of contraction of the patch.

Bienfang (1979) has recently published data on careful measurements of the

settling rates of marine algae, both in cultures and in the natural environment, and the mean value is close to 1 metre per day. A rough shrinking rate for the patch may be calculated by dividing the maximum radius by the decay time.

If the

mean excretion time is less than 15 seconds, the patches decay too quickly for the phytoplankton to fall into them., but if the mean excretion time is 200 seconds, the shrinking rate is about 0.1 metres per day.

In any case, the expected ex-

posure time may still be calculated by equation (7) but with the number of patches, N

, increased by the factor

(1. + net settling velocity).

This would mean that

the maximum exposure time could be increased by perhaps a factor of two over the exposure time that would be expected if the algae did not settle. 5.0

CONCLUSIONS

The present study has shown that molecular diffusion is sufficient to disperse microzones far too rapidly for them to be of any particular importance in providing for the nitrogen requirements of the marine phytoplankton. The qualitative arguments that were given at the beginning of this paper are very attractive, but assuming values that would tend to make the patches persist for the maximum length of time shows that molecular diffusion disperses the patches at least 50 times too fast. If other forms of dispersion are important, or if smaller numbers of zooplankton are present, or if they do not excrete for long periods of time, the discrepancies will become even greater. Hence the question of how marine phytoplankton manage

218

to obtain their nitrogen requirements from water that is deficient (on large length scales) in nitrogen remains an open question. ACKNOWLEDGEMENTS This research was done while the second author was on educational leave at the University of Southampton, and he wishes to thank the Government of Canada for their financial support during this period. REFERENCES Beers, J.R., and Kelly, A.C., 1965. Short-term Variation of Amnonia in the Sargasso Sea off Bermuda. Deep-sea Res., 12:21-25. Bienfang, P.K., 1979. A New Phytoplankton Sinking Rate Method Suitable for Field Use. Deep-sea Res., 26:719:729. Carslaw, H.S. and Jaeger, J.C., 1947. Conduction of Heat in Solids. Oxford University Press. Derenbach, J.B., Astheimer, H., Hansen, H.P. and Leach, H., 1979. Vertical Microscale Distribution of phytoplankton in Relation to the Thermocline. Marine Ecology, 1:187-193. Dugdale, R.C., 1967. Nutrient Limitation in the Sea: Dynamics, Identification and Significance. Limnology and Oceanography, 12:685-695. Goering, J.J., Dugdale, R.C., and Menzel, D.W., 1964. Cyclic Diurnal Variations in the Uptake of Ammonia and Nitrate by Photosynthetic Organisms in the Sargasso Sea. Linmology and Oceanography, 9:448-451. Goldman, J.C., McCarthy, J.J. and Peavey, D., 1979. Growth Rate Influence on the Chemical Composition of Phytoplankton in Oceanic Water. Nature, 279:ZlO-215. Grice, G.D., Harris, R.P., Reeve, M.R., Heinbokel, J.F. and Davis, C.O., 1980. Large Scale Enclosed Water Column Ecosystems: An Overview of Food Web 1, The Final CEPEX Experiment. J. Marine Biological Association, U.K., 60:391-399. Ikeda, T., 1970. Relationship Between Respiration Rate and Body Size in Marine Plankton Animals as a Function of the Temperature of Habitat. Bull.Fac.Fish. Hokkaido Univ., 21:91-112. Jackson, G.A., 1980. Phytoplankton Growth and Zooplankton Grazing in Oligotrophic Oceans. Nature, 284:439-441. McCarthy, J.J., and Goldman, J.C., 1979. Nitrogenous Nutrition o f Marine Phytoplankton in Nutrient Depleted Water. Science, 203:670-672. MacIsaac, J . G . , and Dugdale, R.C., 1969. The Kinetics of Nitrate and Ammonia Uptake by Natural Populations of Marine Phytoplankton. Deep-sea, 16:45-57. Parsons, T.R., Takahashi, M., and Hargrave, B., 1977. Biological Oceanographic ' Processes. 2nd Edition, Permagon Press, London. Pasiac, W.J., and Gavis, J., 1974. Transport Limitation of Nutrient Uptake in Phytoplankton. Limnology and Oceanography, 19:881-888. Steele, J.H. and Yentsch, C., 1960. The Vertical Distribution of Chlorophyll. J. Marine Biological Association, U.K., 39:217-266.

219

THE RESIDUAL CIRCULATION IN THE NORTH SEA

Jacques C.J. NIHOUL

1

and Yves RUNFOLA

Geophysical Fluid Dynamics, LiPge University, Belgium 'Also at the Institut d'Astronomie et de Ggophysique, Louvain University (Belgium)

INTRODUCTION

Hydrodynamic models of the North Sea are primarily concerned with tides and storm surges and the associated currents which can have velocities as high as several meters per second. However the period of the dominant tide is only about a half day and the characteristic life time of a synoptic weather pattern is of the order of a few days. The very strong currents which are produced by the tides and the atmospheric forcing are thus relatively transitory and a Marine Biologist will argue that over time scales of biological interest, they change and reverse so many times that they more or less cancel out, leaving only a small residual contribution to the net water circulation. The importance of tidal and wind induced currents for the generation of turbulence and the mixing

0.f

water properties is of course not denied but many biologists would

be content with some rough parameterization of the efficiency of turbulent mixing and, for the rest, some general description of the long term transport of "water masses". Although the concept of "moving water masses", and its train of pseudo-lagrangian misdoings, appeal to chemists and biologists who would like to find, in the field, near-laboratory conditions, it is impossible to define it in any scientific way and charts of the North Sea's waters like the one shown in figure 1 and reproduced from Laevastu (1963) are easily misinterpreted and often confuse the situation by superposing a flow pattern on an apparently permanent "geography" of water masses. The notion of "residual" circulation - which, at least, has an Eulerian foundation

- has long remained almost as vague.

Some people have defined it as the observed flow

minus the computed tidal flow. Such a definition is understandable from a physical point of view but one must realize that the residual flow so-defined contains all wind-induced currents, including small scale fluctuations. It is definitely not a steady or quasi-steady flow and some attempts to visualize it by means of streadlines are questionable. What it represents, in terms of marine chemistry or marine ecology is not at all clear.

Actually, if one wants to take the point of view of the marine ecologist, one should really look at the mean flow over some appropriate period of time of biological interest. It is customary for experimentalists to compute, from long series of observations, daily, weekly and monthly averages. What such averages actually represent is debatable. No doubt that tidal currents are essentially removed in this process. However with tidal velocities, one or two orders of magnitude higher than residual velocities and the latter of the order of traditional current-meters'errors, one may fear that, as a result of the non-linearities of the equipment, the error remains the same order of magnitude after averaging and leads to a 100

%

inaccuracy in the calculated mean re-

sidual. (e.g. Nihoul, 1980). Moreover the choice of the periods of time over which the averages are made is not obviois as it seems to rely more on the calendar than on physical processes. One must be quite clear of what one gets from such averages. With tides reversing four times daily and changes in the synoptic weather pattern taking several days, one may expect daily averages to remove tidal motions while still catching most of the residual currents responding to the evolving meteorological conditions. Monthly averages, on the other hand, will have a more "climatic" sense and will presumably represent the residual circulation which is induced by macroscale oceanic currents (such as the North-Atlantic current in the case of the North Sea) and the mean effect of non-linear interactions of mesoscale motions (tides, storm surges

...) .

Here, the terms "macroscale", "mesoscale" (and later on "microscale") are used in reference with the time scales of motion. In general time scales and length scales are related but it doesn't have to be so and no such assumption is made here at this stage. The role of residual currents and residual structures (fronts

...)

in the dynamics

of marine populations, the long term transport of sediments or the ultimate disposal of pollutants, for example, is universally recognized but different schools of theoreticians and experimentalists still favour different definitions which, in the case

of the North Sea, may have little in common,apartfrom the fact that the strong tidal oscillations have been removed. Obviously each definition addresses a particular kind of problem and if, as it is now universally agreed, the residual circulation is defined as the mean motion over a period of time sufficiently large to cancel tidal oscillations and transient windinduced currents, there is still the problem of choosing the time interval of averaging, taking into account the objectives of the study. In any case, it is not demonstrated that such a time average may be obtained with sufficient accuracy from experimental records. As pointed out before, the averaging takes away more than 90 the instrumental error.

%

of the signal and the final result is of the same order as

221

F i g . 1. Water types i n t h e North Sea according t o Laevastu ( 1 9 6 3 ) . [Adapted from F o l i o 4 of S e r i a l A t l a s of t h e Marine Environment with t h e permission of t h e American Geographical S o c i e t y . ]

222

In the following, one examines how the problem can be approached through mathematical modelling.

THE GOVERNING EQUATIONS

The three-dimensional hydrodynamic equations applicable to a well-mixed continental sea, like the North Sea, can be written (e.g. Nihoul, 1975)

0.v

0

=

av +

0 . (VV)

at

where

n

+

2

n

A

V

=

- Vq

+ Q.R

is the Earth's rotation vector, q =

P

+ gx, , p is the pressure,

p

the speci-

fic mass of sea water, x3 the vertical coordinate and R the turbulent Reynolds stress tensor (the stress is here per unit mass of sea water) resulting from the non-linear interactions of three-dimensional microscale turbulent fluctuations. The turbulent Reynolds stress tensor can be parameterized in terms of eddy viscosity coefficients. In microscale three-dimensional turbulence, these coefficients are of the same order of magnitude in the horizontal and vertical directions. Then, horizontal length scales being much larger than the depth, the last term in the righthand side of eq.(2) can be written simply, with a very good approximation

where C is the vertical eddy viscosity and K the turbulent Reynolds stress (vector). The residual flow is defined as the mean flow over a time T sufficiently large to cover at least one or two tidal periods. If the subscript

"o"

denotes such an average,

one may write

v

=

vo + v,

(4)

with (V), =

vo

(5)

What Vo and V, respectively include depends on the time of integration T. If T is of the order of one day (exactly two or three periods of the dominant Mp tide), T

- lo5

,

the averaging eliminates the tidal currents and smoothes out all

current fluctuations, - generated by variations of the wind field, for instance which have a characteristic time smaller than T.

,

223 However, as mentioned before, changes in the synoptic weather pattern often have time scales comparable with T

-

gible meteorological forcing, T

10'.

Then, unless one considers periods of negli-

- lo5

does not correspond to a valley in the energy

spectrum of the currents. In that case, one cannot derive an equation for V, by averaging eq.(2) and assuming that, as for an ensemble average, the averaging commutes with the time derivative. Furthermore, V, defined in this way, depends very much on time and doesn't correspond to the quasi-steady drift flow the biologists have in mind when they talk about residuals. One might argue that such a time dependent daily mean is still worth calculating to follow the response of the sea to the evolving w e a t h e r p a t t e r n , e s p e c i a l l y in storm conditions. 5

This however would be equivalent to modelling a storm surge with a time step of 10 and the results cannot be very accurate. It is much wiser, in that case, to solve equations (I) and ( 2 ) , without averaging for tides and storm surges simultaneously. Actually, "daily" residuals (i.e. mean currents over exactly two or three tidal periods) are meaningful only when the atmospheric forcing is negligible or exceptionally persistent. In the first case, they represent the so-called "tidal residuals" which result from in - and out-flowing macroscale oceanic currents and from the residual effect of non-linear tidal interactions. Tidal residuals represent a major contribution to the total residual circulation and, with very much less computer work needed, they already give a good idea of the long term residual circulation, such as the climatic circulation described below, where asubstantial part of the atmospheric contribution is actually removed by averaging over a variety of different weather conditions. If one takes, for instance, the averaging time T between l o 6 (- two weeks) and lo7 (-four months), one may expect, over such a long time, a diversity of meteorological conditions resulting in an almost random atmospheric forcing on the sea. The current patterns will reflect the atmospheric variability and, on the average, there will be only a small residue. The mean flow over a time T

- l o 6 , lo7

may be regarded as the "climatic residual"

flow which affects the dynamics of biological populations, the long term transport of sediments and the slow removal of pollutants. As

pointed out before, one may conceive a third kind of residuals obtained by ave-

raging over two or three tidal periods

(T 2 lo5

s)

in conditions of exceptionnally

persistent atmospheric forcing. The persistence of the meteorological conditions drives off the atmospheric energy input to small frequencies and a time of the order of

lo5 is acceptable for averaging

as it corresponds again to a valley in the energy spectrum. This kind of residuals may be called in brief "wind residuals". One must be aware, however, that they give a rather limited view of wind-induced currents in the sea.

224 If a typical weather pattern has a characteristic time of a few days, one must either determine the time dependent wind-induced and tidal flow described by equations ( l ) and ( 2 ) or the climatic residual flow which contains only the macroscale residue of changing weather patterns. Still, with moderate computer work needed, wind residuals may perhaps provide a first idea of various wind effects on the residual flow pattern which would not be apparent in the climatic or tidal residual pattern but which might occasionally be spotted by instruments in the field. In the following "residual circulation" will refer to the climatic residual circulation

(T

2 lo6

s)

or the tidal and wind residual circulations

(T 2 lo5 s ) with

the restrictions made above. The equations for the residual flow may be obtained by taking the average of equations (1) and ( 2 ) over the chosen time T. The time derivative in the left-hand side of equation ( 2 ) gives a contribution

One may argue that, since the time T is always a multiple of the main tidal period, the numerator of ( 7 ) is of the same order as the residual velocity V,. Then, for T 2 105

,

The average of the Coriolis acceleration is

One may thus neglect the contribution of the time derivative in the equation for v,. The residual circulation is then given by the steady state equations

v.v,

where

= 0

Since V,

is one or two orders of magnitude smaller than V, which contains in

particular the tidal currents, the first term in the left-hand side of eq.(12) is completely negligible. The tensor N

in the right-hand side plays, for mesoscale

motions, a role similar to that of the turbulent Reynolds stress tensor R

in eq.(2)

and may be called the "mesoscale Reynolds stress tensor". The last term in the righthand side of eq.(11) represents an additional force acting on the residual flow and resulting from the non-linear interactions of mesoscale motions (tides, storm surges

... ) .

The importance of this force was discovered, first, by depth-integrated numerical models of the residual circulation in the North Sea (Nihoul 1974, Nihoul and Ronday 1975) and the associated stress was initially referred to as the "tidal stress" to emphasize the omnipresent contribution of tidal motions.

THE MESOSCALE REYNOLDS STRESS TENSOR

The tensor N

can be computed explicitly by solving eqs.(I) and (2) for mesoscale

motions and taking the average of the dyadic V,V,

.

In fact the solution of eqs.(l) and (2) with appropriate wind forcing and open sea boundary conditions yields

v

=

v, + v,

and one may reasonably ask the question why one must go through the process puting N

and solving eqs. (10) and ( 1 1 ) to obtain the residual velocity V,

why one cannot solve (1) and ( 2 ) for the total velocity V from V

d i r e c t l y , by averaging the solution of eqs.(1) and 6V

on V

of, say, 10

%,

1.e.

and simply derive V, (2).

The problem here, again, is that, in the North Sea, V, represents 90 If one allows for an error

of com-

%

of V

.

resulting from the imprecision

of open-sea boundary conditions and from the approximations of the numerical method,

.

the error is of the same order of magnitude as the residual flow V, Because of non-linearities, one may fear that, in the averaging process, this error does not, for the essential, cancel out as V, does. Thus averaging the solution V

of eqs. (1) and (2), one gets V,

an error which may be as large as

100

%

+

(6V),

i.e. the residual velocity with

(Nihoul and Ronday, 1976a).

The procedure is conceivable when modelling a very limited area (near a coast, for instance) where the mesh size of the numerical grid can be reduced and where the open-sea boundary conditions can be determined with greater accuracy by direct measurements. Then

6V can be made small enough for the average V,

a satisfactory evaluation of the residual flow V,

.

+

(6V),

to provide

226 In the case of the North Sea or, even, the Southern Bight or the English Channel,

models of such a high accuracy are prohibitively expensive and cannot be considered for routine forecasting.

v, to compute the mesoscale stress tensor N However, the classical models give

with a fair accuracy and they can be used

.

The latter can be substitutdd in eq.(11) and the system of eqs.(10) and (11) can be solved very quickly to obtain V,

.

One can show that, in this way, one can determine V,

with good accuracy.

Typical values for the North Sea show that, in general, the two terms and

8 . (- V,V,),

If

2

n

A V,

are of the same order of magnitude.

6V, is the error on V,

This error induces an error

, one

has

6Vo on V,

given by

i.e.

Hence the r e l a t i v e error is the same on error as before. Thus if

v,

and on

v, and not the absoZute

v, can be computed with, say, a

90 % precision, the solu-

tion of the averaged eqs.(10) and (11) will give the residual circulation with the same 90

8

precision.

THE EQUATION FOR THE HORIZONTAL TRANSPORT

If one writes

u

v = u + w e 3

=

u, +

emphasizing the horizontal velocity vector u transport as

uo -

u, dx, -h

=

-

H, u,

(131 i (13')

U(

,

one defines the residual horizontal

227

co

where

is the depth-averaged velocity, H, = h

the residual surface elevation. (H,

h

because

+ 5,

,

L o << h)

h

is the depth and

5,

.

The derivation of equations for the residual transport by integration of eqs.(10) and (11) over depth is quite straightforward (e.g. Nihoul, 1975a). One finds, after some reordering, V.U,

=

0

f e3

A

U,

(15)

=

- n o Vq, - K U, +

e

(16)

where

u,

denoting the depth-mean of U , and Q

standing in brief for

Tz

f

TI - Ti

where (i) Tg

is the residual wind stress

(ii) T:

is the mesoscale Reynolds stress

(iii)

$A

is the mesoscale “friction stress”

The friction stress is the part of the residual bottom stress (the first part is

-

K U,)

which results from the non-linear interactions of mesoscale motions. It is

analogous to the Reynolds stress t,” and represents an additional forcing on the residual flow. Since

u,

is a two-dimensional horizontal vector, eq.(15) suggests the introduc-

tion of a stream function $(x,,x2)

such that

228 Eliminating

q

between t h e two h o r i z o n t a l components of e q . ( 1 6 ) , one obtains

then a s i n g l e e l l i p t i c equation f o r

K ; v 2 J ,+

~a

$ [ a xa ,

(K) + ax,

( -hf) I

, viz.

J,

+

[using (20)1

= ax, [ a a x , - ( hK )

This equation must be solved with a p p r o p r i a t e boundary conditions. J, = const.

p l y take

I f one can s i m -

along t h e c o a s t s , t h e c o n d i t i o n s on t h e open-sea boundaries are

much more d i f f i c u l t t o a s s e s s . One has e s t i m a t e s of t h e t o t a l inflows through t h e 3 -1 7400 km . y (Van Veen, 1938; C a r r u t h e r s , 1935)1, t h e Northern S t r a i t s of Dover 3 boundary [- 23000 krn .y-' (Kalle, 1949; Laevastu, 196311, through t h e Skagerrak 3 .-1 [- 479 km .y (Svansson, 1968; Tomczak, 196811 a s well a s of t h e c o n t r i b u t i o n of the 3 main r i v e r s [- 245 km .y-l ( M c Cave, 1974)l but t h e d i s t r i b u t i o n of t h e s e flows

c-

along t h e boundaries are p o o r l y known and one must r e s o r t t o i n t e r p o l a t i o n formulas which may o r may n o t r e p r e s e n t adequately t h e c o n t r i b u t i o n , t o t h e r e s i d u a l c i r c u l a t i o n of t h e North Sea, of inflowing o r outflowing macroscale c u r r e n t s . The open-sea boundary c o n d i t i o n s used i n t h e p r e s e n t model a r e derived from t h e above e s t i m a t e s following Ronday (1965). Ronday (1965) has shown t h a t they r e p r e s e n t t h e a v a i l a b l e observations reasonably well and t h a t eventual d e v i a t i o n s from t h e i n t e r p o l a t e d v a l u e s a t t h e open-sea bound a r i e s d o n o t g e n e r a t e errors which could propagate f a r i n t o t h e North Sea. S t i l l , a b e t t e r determination of t h e c o n d i t i o n s along open-sea boundaries i s needed and should be considered with t h e h i g h e s t p r i o r i t y i n t h e near f u t u r e . Eq.(22) shows t h e i n f l u e n c e on t h e r e s i d u a l flow of t h e r e s i d u a l f r i c t i o n c o e f f i c i e n t K and i t s g r a d i e n t , of t h e d i s t r i b u t i o n of depths, of t h e c u r l of t h e r e s i d u a l wind s t r e s s and of t h e mesoscale s t r e s s e s

T," and

T:

.

I n r e l a t i v e l y c o a r s e g r i d models of t h e whole North Sea (where t h e v a r i a t i o n s of K

and

h

a r e p a r t l y smoothed o u t ) , t h e e f f e c t of t h e mesoscale stresses appears t o

be t h e most s p e c t a c u l a r . T h i s i s i l l u s t r a t e d by f i g s . ( 2 ) , (3) and ( 4 ) , f i g u r i n g t h e r e s i d u a l c i r c u l a t i o n i n n e g l i g i b l e wind conditions.

F i g . ( 2 ) shows t h e r e s i d u a l flow

p a t t e r n assuming a c o n s t a n t depth of 80 m and n e g l e c t i n g

T," and

Ti

.

F i g . ( 3 ) shows t h e flow p a t t e r n t a k i n g t h e depth d i s t r i b u t i o n i n t o account and neglecting

T:

and

T:

.

F i g . ( 4 ) shows t h e flow p a t t e r n t a k i n g t h e depth d i s t r i b u t i o n i n t o account and including

T:

and

T ! ,

computed from t h e r e s u l t s of a preliminary time dependent model

of mesoscale flows. The d i f f e r e n c e s between f i g s . ( 2 ) and ( 3 ) a r e s m a l l . They both reproduce t h e broad t r e n d of t h e r e s i d u a l c i r c u l a t i o n induced by t h e in-and out-flow of two branches of t h e North A t l a n t i c c u r r e n t b u t they f a i l t o uncover r e s i d u a l g y r e s which c o n s t i t u e

229

----%---'

b'

3'

2'

I'

0'

I'

2'

3'

4'

5'

6'

7'

8'

9'

Ib

1'1

Ih

I$

Fig. 2. Residual c i r c u l a t i o n i n t h e North Sea c a l c u l a t e d i n n e g l i g i b l e wind c o n d i t i o n s assuming a c o n s t a n t depth and n e g l e c t i n g t h e mesoscale s t r e s s e s . (Streamlines i n l o 3 m 3 . s - ' )

230 61'

6d

5 9'

5 6'

57'

56'

5 5'

5i'

53'

5 2'

5 1'

5 0'

't9'

Fig. 3. Residual circulation in the North Sea calculated in negligible wind conditions with the real depth distribution, neglecting the mesoscale stresses. (Streamlines in l o 3 rn3.s-')

231 6 1'

60'

5s'

5s'

57.

56 '

55'

5c'

53'

52.

51'

50'

b9'

I

I b'

3'

2'

I'

d

I'

2'

3'

4'

5'

6'

7'

R'

9'

tb

1'1

I5

15

Fig. 4. Residual circulation in the North Sea calculated in negligible wind conditions with the real depth distribution, taking the mesoscale stresses T : and T: into account. (Streamlines in l o 3 m3.s-')

232

essential features of the residual flow pattern and which have been traced in the field by observations ( e . g . Zimmerman, 1976; Riepma, 1977; Beckers et al, 1976).

Fig. 5. Residual circulation in the Southern Bight calculated in negligible wind conditions, with the real depth distribution, taking into account the mesoscale (Streamlines in lo3 m3.s-’) stresses T,” and

‘ri .

A comparison between fig.(4) and fig.(I) shows a good agreement between the predictions of the model and the expected circulation of water masses in the North Sea. However, as mentioned before, a model covering the whole North Sea does not have a sufficiently fine resolution (of bottom topography, for instance) and cannot detect all the existing gyres. For that reason, three models were run simultaneously, one covering the North Sea, another one, the Southern Bight and the third one, the Belgian coastal waters; the lar.ge scale models providing open-sea boundary conditions for the smaller scale models. Fig.(5) shows the residual circulation in the Southern Bight. One notices in particular a gyre off the Belgian coast which was not apparent on fig.(4). This gyre is produced by the mesoscale stresses in relation with the spatial variations of the depth and of the residual friction coefficient K (Nihoul and Ronday, 1976).

233 The presence of the gyre has been shown to play

an important role in the distri-

bution of sediments (Nihoul, 1975b) and in creating o f f the Northern Belgian coast the conditions of an outer-lagoon with specific chemical and ecological characteristics (Nihoul, 1974; Beckers et al., 1976).

THE ENERGY EQUATIONS

Using eq.(3), one can write the equations for V

+

0. (V,V,)

av, a t

+

2

V.cV,V,

V,

A

+

V,V,

=

+

- Vq, V,V, -

+

+ ax3

,

and

V,

v, in the form

V.N

( V I V l ) , 1+ 2 CJ

A

V,

with

v.v

=

v.v,

= V.VI = 0

One can see that the equation for V

v 1 is essentially the same as the equation for

. They only differ by terms which are orders of magnitude smaller. It is the reason

why, dne can, with the appropriate boundary conditions, determine the mesoscale velocity

v, ,

in a first step, and the residual velocity

,

V,

in a second step, ta-

king the coupling between the two types of motion into account in the calculation of

v, only. Taking the scalar products of eqs. (231, and

V,

, using

( 2 4 ) and (25) respectively by

( 2 6 ) , (27) and ( 2 8 ) , and averaging 3ver

T

,

V

one finds, neglecting

again the contributions from the time derivatives under the assumption that sufficiently large

;

, Vb T

is

234 The terms i n t h e left-hand s i d e s of eqs. (291,

( 3 0 ) and (31) a r e of t h e divergence

form. They r e p r e s e n t f l u x e s of energy i n p h y s i c a l space. The terms i n t h e right-hand s i d e s r e p r e s e n t r a t e s of energy production o r d e s t r u c t i o n o r energy exchanges between s c a l e s of motion. I n t e g r a t i n g over depth, one can see f o r i n s t a n c e t h a t t h e f i r s t terms r e p r e s e n t t h e average r a t e of work of t h e wind s t r e s s

where

Vs

T’

,

i.e.

denotes t h e s u r f a c e v e l o c i t y .

The second term i n t h e right-hand s i d e of e q . ( 2 9 ) i s r e l a t e d t o t h e average d i s s i p a t i o n of energy. using e q . ( 3 ) , one has, indeed

- T . -

av ax3

where

3

-

- 3

av IIax,II

(33)

i s t h e eddy v i s c o s i t y .

The depth-averaged d i s s i p a t i o n r a t e

can be s p l i t i n t w o p a r t s , a s seen from eqs. (30) and ( 3 1 ) , i.e.

THE CONTRIBUTION OF THE RESIDUAL STRESS

T o TO THE ENERGY BUDGET

The second term i n t h e right-hand s i d e of e q . ( 3 5 ) i s obviously r e l a t e d t o t h e energy d i s s i p a t e d by t h e mesoscale motions. I t i s , by f a r , t h e e s s e n t i a l c o n t r i b u t i o n t o E

and may serve a s a f i r s t approximation of it. I t i s however t h e f i r s t term one i s

i n t e r e s t e d i n , h e r e , t o e x p l a i n t h e p h y s i c a l mechanisms which c o n t r i b u t e t o shape the residual circulation. I n e v a l u a t i n g t h i s t e r m , one can obviously r e s t r i c t a t t e n t i o n t o t h e h o r i z o n t a l components of t h e v e c t o r s d u c t of t h e form

av

T.2x3

To and

v o , and t h i s i s a l s o t r u e f o r any s c a l a r pro-

235 One has indeed, from the continuity equation, aw

5

v.u

x3

where

L

-

o);(

is the characteristic scale of horizontal varia ions. On the other hand

Since h << L

,

the contributions from the vertical velocity are completely negli-

gible in the integrals of eq.(35). The application of the three-dimensional equation (1) and (2) to the North Sea (Nihoul, 1977; Nihoul et al., 1979) shows that (i) the turbulent stress can be written

where

T'

and

T~

are respectively the surface stress and the bottom stress (per

unit mass of sea water),

5

= H-'

(x,

+

h)

,

H = h

the surface elevation, the A n ' s are functions of Tb

and their time derivaties, K

and the functions fn(5)

a,

+

5

,

h

t , x, and

5

is the depth and

x2 involving T s

,

is the Von Karman constant,

are the eigenfunctions of the problem

being the corresponding eigenvalue. The last term in the right-hand side of eq.(36) plays an important role in the de-

termination of the velocity field v periods of weak currents

but its effect is limited to relatively short

(at tide reversal, for instance) (Nihoul, 1977; Nihoul

et al., 1979) and it contributes very little to the residual turbulent Reynolds stress

obtained by averaging over a time

T

covering several tidal periods.

236 Hence, setting

+

z = x3

h

, one

may write, with a good approximation

(ii) the bottom stress T~

is a function of T S

and the time derivaties of

u .

,

the depth-averaged velocity 3

If one excepts, again, short periods of weak currents,

Tb

can be approximated by

the classical "quadratic bottom friction law"

where

D

is the drag coefficient.

Averaging over a time

T

as before and neglecting small order terms, one obtains

then

i.e., using eqs. (17) and (19)

Changing variable to

z

and using (39), one can write

The horizontal velocity u

,

however it may for the rest vary with depth, always

has a logarithmic profile near the bottom. This implies that near

z = 0

.A

au az

behaves like

z-'

first consequence of this asymptotic behaviour of the velocity pro-

file is that integrals over depth are, strictly speaking, not taken from the surface but from some very small height

zo

z = 0

to

(the "rugosity length") to the

surface. This has been taken into account in eq.(43).

A

second consequence is that t h e

first integral in the right-hand side of eq.(43) is largely dominant, the singularity at

z = 0

being cancelled in the second integral by the factor

z

.

Since the second integral is only a small correction, one may make the approximation

237

Eq. (43) can thus be rewritten

Integrating by parts, one gets

i.e., using eq. ( 4 2 )

The first two terms in the right-hand side of eq. (30) integrated over depth give then

i.e., the same result one would have obtained from the depth integrated transport equation for the contribution of the wind stress and the bottom stress, by taking the scalar product of eq.(16) by

Go

.

One notes that, in the right-hand side of eq.(46), only the first term can be associated without ambiguity with the dissipation of energy. The second term represents the rate of work of the mesoscale friction stress. Although its "bottom friction" origin is clear, its sign cannot be set a p r i o r i and there is no reason why it could not actually provide energy to the residual flow. The same can be said for the last term in the right-hand side of eq.(30). This term appears with the opposite sign in eq.(31). It thus represents an exchange of energy

between residual and mesoscale flows: this term can be either positive or

negative. There is no way of knowing a p r i o r i wether the energy is extracted from the mean flow and goes from macroscales to mesoscales or if it is supplied to the mean flow by mesoscale motions.

238 THE EXCHANGE OF ENERGY BETWEEN SCALES OF MOTION

The exchange of energy between macroscales and mesoscales can be characterized, at each point of the North Sea, by the depth-averaged rates of energy transfer

These quantities, which may be positive or negative should be compared with the rate of energy dissipation by the residual motion

:

i.e.

- 2

ED

(50)

uo

= K

The mesoscale Reynolds stress tensor N

also contributes to the term

V.(- N.V,)

in the left-hand side of eq. ( 3 0 ) . This is a completely different effect because it implies a flux of energy in physical space while

N

: VV,

,

appearing in boths eq.(30) and (31), represents a trans-

fer of energy between scales, i.e., a flux of energy in Fourier space. This effect cannot however be ignored if one wants to understand the mechanisms by which the mesoscale stresses act on the residual flow. One shall write

It is convenient to normalize the rates of energy transfer using the rate of energy dissipation

E~

as the normalizing factor, Let

S = - 6

(52)

ED

EN

=

EN -

(53)

EF -

(54)

ED

EF

=

ED

2,

..= 6

+ i, + i, +

1

(55)

In non-dimensional forms, (i) S

is the rate of change of kinetic energy due to energy divergence or convergence

in physical space.

239 (ii) E N is the rate of energy exchange between macroscale and mesoscale motions resulting from the action of the mesoscale Reynolds stresses. (iii) t F is the rate of energy exchange between macroscales and mesoscales resulting from the action of the mesoscale friction stress. (iv)

+ 2,

is the rate of work of the mesoscale Reynolds stresses on the residual

flow.

E T is the net rate at which energy is extracted from the residual flow

(v)

by the combination of energy fluxes in physical space, energy transfers between scales of motion and energy dissipation by bottom friction. positivevalue of

A

eN

or

CF

implies a transfer of energy from the mean flow to

the mesoscale motions. At the opposite, negative values indicate a transfer of energy from the mesoscales to the mean flow. Using turbulence terminology, these situations will be referred to as cases of positive eddy viscosity and negative eddy viscosity respectively. [The word "eddy" is here used in an extended sense referring to mesoscal e non-linear waves and turbulence. A similar definition was proposed by Rhines and

Holland (1979). 1

TIDAL R E S I D U A L S

A detailed study of the tidal residuals in the North Sea was made by means of two coupled three-dimensional models, one for tides and storm surges (Nihoul, 1977; Nihoul et al., 1979) and one for the residual circulation described by eqs.(10) and (11).

The data of the three-dimensional models were used to compute the depth-averaged cir&lation EN

,

EF

and the spatial distributions of the depth-averaged transfer functions and

.

*

The results are presented in figs. ( 6 ) to (12)

.

Fig.(6) shows the residual streamlines. One can see that there is, in general, a good agreement between the result of the three-dimensional models and those of the depth-integrated model represented in fig.(4). The main differences are observed in regions of very weak residual circulation where the three-dimensional models have a better resolution. The existence of extended regions of very small residual currents (less than 1 cm

s-')

is one important characteristic of the tidal residual flow pattern. It has been found

*

In interpreting these figures, and those which follow in the next section, one must remember that, having to calculate horizontal gradients, the model can only provide results one grid point away from the coast. One cannot say anything from the figures about the coastal fringe.

240

2'

I

0

I

2'

9'

4

5'

6'

7

a'

9'

Fig. 6. Tidal residuals in the North Sea. Residual flow pattern. Streamlines IL = const. in l o 3 m3.s-'.

241

58

57

56

55

54

53

52

51

Fig. ?a. Tidal residuals in the North Sea. Map of positive values of the non-dimensional function 8 representing the rate at which the residual kinetic energy is redistributed in physical space. (Positive values indicate regions of residual energy divergence.) 8 = 50 Heavy line Slender line - 6 = 1 0 Broken line Z = O

----

58

52

56

55

54

5s

12

5!

Fig. 7b. Tidal residuals in the North Sea. Map of negative values of the non-dimensional function 8 representing the rate at which the residual kinetic energy is redistributed in physical space. (Negative values indicate regions of residual energy convergence.) Heavy line $ = - 50 Slender line $ = - 10 Broken line 6 = 0

-----

243

I - sa

- 57

- 56

- 55

54

5s

52

51

Map of positive values of the non-dimensional function EN representing the rate of energy transfer between residual and mesoscale flows by the mesoscale Reynolds stresses. (Positive values indicate regions of positive eddy viscosity.) EN = 5 0 Heavy line EN = l o Slender line Broken line EN = 0

----

244

58

57

56

55

sb

59

52

5!

Fig. 8b. T i d a l r e s i d u a l s in t h e North Sea. representing t h e r a t e Map of n e g a t i v e values of t h e non-dimensional f u n c t i o n S, o f energy t r a n s f e r between r e s i d u a l and mesoscale flows by t h e mesoscale Reynolds s t r e s s e s . (Negative values i n d i c a t e regions of negative eddy v i s c o s i t y . ) SN = - 50 Heavy l i n e Slender l i n e - i, = - 10 Brpken l i n e ---- ZN = 0

-

245 almost impossible to give any comprehensible representation of the flow field using the traditional methods which consist in drawing the velocity vector at each grid point. To display the residual flow in some regions, it has been necessary to draw streamlines 5 lo3 m3 s-'

apart while, in other regions, the difference between two

consecutive streamlines is

20

lo3

m3 s-' or more.

Although the small scale gyres are essential to understand the hydrodynamics of the North Sea, especially in coastal zones, they contain little of the total residual energy of the North Sea and the tidal residual circulation appears to be constituted essentially of two main energetic streams corresponding to the penetration in the North Sea of two branches of the North-Atlantic current. These are the analogue of the macroscale gyres of oceanic circulation and, in this sense, the residual circulation which has been qualified as "macroscale" with reference to its time scale (i.e. its quasi steady character) may be classified also among macroscale motions with respect to length scales (with a peak of energy in the small wave numbers range in a spectral analysis of the North Sea energy). The maps of the functions 6

, EN

and

EF

(figs. 7, 8 and 9) show a marked

patchiness with alternating positive and negative values. Absolute values are one or two orders of magnitude larger for for

2,

and

ED

(ED

=

8

and

EN

than

1, in non-dimensional form). Thus the mesoscale Reynolds

stresses play the main role in the energetics of the tidal residual flow. They are responsible for a transfer

EN

"in Fourier space", i.e. an exchange of energy between

macroscale residual flow and mesoscale motions, and for a flux "in physical space", i.e. a transport of energy from one region of the North Sea to another. These two effects tend to compensate each other and the sum

a^

iE N

is about one order of

magnitude smaller than each of its terms (fig. 10). Thus, when energy is supplied to the mean flow in some region (negative viscosity effect), it is, to a large extent, exported to other regions where energy is extracted from the mean flow by the mesosca-

le motions. The pattern of streamlines (fig. 6) shows that the regions of negative eddy viscosity contain little residual energy (the residual currents are in general very small as indicated by the wide spacing of the streamlines) and most of the residual vorticity (the streamlines are curved and often closed, forming secondary gyres). This is confirmed by the vorticity pattern (fig. 12) showing vorticity scales as small as 10 km associated with the gyres. In the regions of negative eddy viscosity where the mesoscale stresses transfer energy from the mesoscale motions to the residual flow, they also generate vorticity in the residual flow. What is actually happening is that the energy supplied to the residual flow in these regions is immediately exported away to the regions of positive eddy viscosity related to the main streams. This energy supply thus contributes to enhance the large scale currents and, in this sense, the energy is truly going from mesoscales to macroscales, referring now indifferently to time scales or length scales.

246

-

58

. 57

' 5 6

55

54

58

52

51

Fig. 9. Tidal residuals in the North Sea. Map of positive and negative values of the non-dimensional function EF representing the rate of energy transfer between residual and mesoscale flows by the friction stress,

247

58

57

56

55

59

52

51 2'

1

0

1

2

9

i

5

6

7

6

9

Fig. 10. Tidal residuals in the North Sea. Map of positive and negative values of the non-dimensional function d + C N representing the rate o f work of the mesoscale Reynolds stresses on the residual f l o w .

248

58

57

56

58

54

53

52

51

Fig. 11. Tidal residuals in the North Sea. Map of positive and negative values of the non-dimensional function Z T = 6 + EN + S, + 1 representing the rate at which energy is extracted from the residual f l o w (positive values) or supplied to the residual flow (negative values).

249

58

57

56

55

54

53

52

51

Fig. 12. T i d a l r e s i d u a l s i n t h e North Sea. Map of t h e function 110 A U o l l w =

-

11TnIl ,.

..

I

-

indicating the scale Heavy l i n e 3 Slender l i n e - 3 Broken l i n e --- 3

of t h e r e s i d u a l vorticity. =

m-'

= 5 10-5 =

,,-I

m-l

250 The secondary flows which are generated in the regions of negative eddy viscosity contain little energy but most of the vorticlty. This vorticity is characterized by length scales smaller in many places than the typical length scale of tidal motions (referred to as the mesoscale motions before) i.e. the energy cascade to larger scales is paralleled by an enstrophy cascade to smaller scales. It is tempting to see here a case of two-dimensional turbulence and identify the patches of intense energy exchanges between scales of motions as the "synoptic eddies" of the North Sea. The fact that,in these eddies, the bottom dissipation is comparatively completely negligible is perhaps an argument in favor of such interpretation. As

a final remark, it is interesting to note that

gT

,

the net rate at which

energy is extracted from the residual flow (or supplied to it) is not positive everywhere. A rather extensive patch of negative values (in the range -1, -10) spreads out from the Western North Sea, off the coasts of Scotland and Northern England, into the central part of the North Sea. Going back to eq. ( 3 0 ) where the term

VZ

8. (v, 2) is always completely negligible, 2

one sees that, in the absence of wind forcing, negative values of V.(V, 9,)

= v,.vq,

iT imply

'0

i.e. the mesoscale stresses are actually driving the residual flow "up the residual slope and pressure gradient".

WIND RESIDUALS

As pointed out in the introduction, the tidal residuals considered in the preceding sections can only constitute a first approximation of what a real climatic residual circulation is. The atmospheric forcing has been neglected both in determining the mesoscale motion and in computing the resulting residuals. The advantage was that the time of averaging could be limited to two or three tidal periods. This is not possible if one includes the effect of a wind field which itself evolves with a characteristic time of the same order. In some cases, one may have to go to averaging over several weeks to ensure that the average is meaningful. This implies that the mesoscale velocity field must be calculated over the same period of time and the cost of operating the model becomes rapidly prohibitively large. Although an effort of this size is now being considered to model the residual circulation during the period of the JONSDAP 76 experiment, it has not been possible so far to apply the three-dimensional model with real atmospheric conditions. However, to have some idea of the effect of wind forcing, two cases of constant uniform wind fields have been considered.

251 The concept of a uniform wind f i e l d over t h e whole North Sea i s c e r t a i n l y i d e a l i s -

tic. Moreover, t h e d i r e c t e f f e c t of t h e wind o n t h e r e s i d u a l c i r c u l a t i o n , which i s a s s o c i a t e d with t h e c u r l of t h e wind s t r e s s , i s not taken i n t o account. Going back t o e q . ( 2 4 ) , one can see t h a t if one t a k e s t h e c u r l of t h i s equation t o eliminate

vqo

,

t h e second term i n t h e right-hand s i d e w i l l g i v e a c o n t r i b u t i o n

(56)

Eq.(36) shows t h a t t h e Reynolds s t r e s s

T

c o n t a i n s a term

Ts5

where

Ts is

t h e wind stress. Hence, a c o n s t a n t wind stress c o n t r i b u t e s t o ( 5 6 ) a t e r m

(57)

I f t h e wind f i e l d i s uniform, t h e f i r s t term of t h e right-hand s i d e of e q . ( 5 7 ) drops o u t . The e f f e c t of t h e wind s t r e s s on t h e r e s i d u a l c i r c u l a t i o n i s then due, i n p a r t , t o t h e l a s t t e r m i n t h e right-hand side of e q . ( 5 7 ) and, i n p a r t , t o t h e modif i c a t i o n of t h e mesoscale s t r e s s e s r e s u l t i n g from t h e a c t i o n of t h e wind f i e l d on t h e time dependent mesoscale motions. There i s t h u s n o " d i r e c t " t r a n s f e r of v o r t i c i t y from t h e wind f i e l d t o t h e r e s i d u a l circulation. In t h e p r e s e n t c a s e , it i s perhaps p r e f e r a b l e s i n c e t h e o b j e c t i v e

of

t h e study

i s t o e l u c i d a t e t h e r o l e played by t h e mesoscale s t r e s s e s i n determining t h e r e s i d u a l flow p a t t e r n and i n p a r t i c u l a r i n generating secondary g y r e s . The hypothesis t h a t t h e wind i s c o n s t a n t i n time ( i . e . , t h a t it has a very l a r g e c h a r a c t e r i s t i c time of e v o l u t i o n ) i s of course l i m i t a t i v e . I t j u s t i f i e s however t h e averaging over a few t i d a l p e r i o d s a s t h i s corresponds again t o a v a l l e y i n t h e

P

energy spectrum of t h e c u r r e n t s . In t h i s p r o c e s s , t h e t i d a l c u r r e n t s a r e a l s o removed but they a r e e v i d e n t l y taken i n t o account i n t h e time dependent mesoscale flow which determines t h e mesoscale

stresses. One should n o t be mislead by t h e name "wind r e s i d u a l s " . The e f f e c t of t h e wind cannot be d i s s o c i a t e d from t h e e f f e c t of t h e t i d e s . A l l "wind r e s i d u a l s " a r e wind and t i d a l r e s i d u a l s . Two c a s e s of reasonably s t r o n g wind have been considered

a c o n s t a n t wind of

15 m s-'

from t h e North-West,

(ii)a c o n s t a n t wind of

15 m s-'

from t h e South-West.

(i)

:

The r e s u l t s a r e presented i n f i g s . (13) t o ( 1 9 ) f o r t h e f i r s t case and i n f i g s . ( 2 0 ) t o (26) f o r t h e second case. I n both c a s e s , t h e s t r e a m l i n e s p a t t e r n ( f i g . 13 and 20) show a d e f l e c t i o n , under t h e i n f l u e n c e of t h e wind f i e l d , of t h e main streams o r i g i n a t i n g from t h e North

252

58

57

56

55

54

5s

52

51 2

I

I

I

1

0

I

I

1

2

I

3

c'

I

I

I

5

6

I

7

Fig. 13. Wind residuals in the North Sea. (Uniform constant wind of 15 m s-' from the North-West.) Residual flow pattern. Streamlines $J = const. in l o 3 1 n ~ 5 - I

I

I

8

S'

253

58

57

56

55

54

5s

52

S! I

I

2'

I

0'

I

2'

3'

b

5

6'

7

a'

9'

Fig. 14a. Wind residuals in the North Sea. (Uniform constant wind of 15 m s-' from the North-West:) Map of positive values of the non-dimensional function 6 representing the rate at which the residual kinetic energy is redistributed in physical space. (Positive values indicate regions of residual energy divergence.) Heavy line = 50 Slender line - f; = 10 Broken line 6 = 0

-

----

254

5a

57

56

55

54

53

52

51 2

1

0

1

2'

3'

\

5'

6'

a'

S

Fig. 14b. Wind r e s i d u a l s i n t h e North Sea. (Uniform c o n s t a n t wind of 15 m s - ' from t h e North-West:) Map of p o s i t i v e values of t h e non-dimensional f u n c t i o n 6 r e p r e s e n t i n g t h e r a t e a t which t h e r e s i d u a l k i n e t i c energy i s r e d i s t r i b u t e d i n p h y s i c a l space. (Negative values i n d i c a t e regions of r e s i d u a l energy convergence.) Heavy l i n e $ = - 50 Slender l i n e ___ 6 = - 1 0 Broken l i n e 8 = 0

-----

255

58

57

56

55

5L

5.3

52

51

Fig. 15a. Wind residuals in the North Sea. (Uniform constant wind of 15 m s - ’ from the North-West.) Map of negative values of the non-dimensional function ?, representing the rate of energy transfer between residual and mesoscale flows by the mesoscale Reynolds stresses. (Positive values indicate regions of positive eddy viscosity.) Heavy line ?, = 5 0 Slender line - C N = 10 Broken line EN = 0

-----

256

58

57

56

55

5\

5s

52

61

Fig. 15b. Wind residuals in the North Sea. from the North-West.) (Uniform constant wind of 15 m s - ' Map of negative values of the non-dimensional function Z N representing the rate of energy transfer between residual and mesoscale flows by the mesoscale Reynolds stresses. (Negative values indicate regions of negative eddy viscosity.) E N = - 50 Heavy line Slender line - EN = - 10 Broken line EN = 0

-----

251

sa

57

56

55

54

59

52

51 2'

1

0'

1

2

3

4'

5

6'

7'

9

Fig. 16. Wind residuals in the North Sea. (Uniform constant wind of 15 m s-' from the North-West.) Map of positive and negative values of the non-dimensional function E F representing the rate of energy transfer between residual and mesoscale flows by the friction stress.

58

57

56

55

5b

5s

52

51

Fig. 17. Wind r e s i d u a l s i n t h e North Sea. 15 m s - ’ from t h e North-West.) (Uniform c o n s t a n t wind of Map of p o s i t i v e and n e g a t i v e v a l u e s of t h e non-dimensional f u n c t i o n 8 + ?, repres e n t i n g t h e r a t e of work of t h e mesoscale Reynolds s t r e s s e s on t h e r e s i d u a l flow.

259

58

57

56

55

54

59

52

51

Fig. 18. Wind residuals in the North Sea. (Uniform constant wind of 15 m s - ’ from the North-West.) Map of positive and negative values of the non-dimensional function ? T = 6 + 2, + ?, + 1 representing the rate at which energy is extracted from the residual flow (positive values) or supplied to the residual flow (negative values).

260

58

57

56

55

54

5s

52

51

I

2'

0

1

2

3

t'

5

6'

Fig. 19. Wind r e s i d u a l s i n t h e North Sea. (Uniform c o n s t a n t wind of 15 m s-' from t h e North-West.) Map of t h e f u n c t i o n

-

w =

IIV

A

Go11

..Ilii, II " 1 1

-w

i n d i c a t i n g t h e s c a l e of t h e r e s i d u a l v o r t i c i t y . = m-' Heavy l i n e Slender l i n e - 2 = 5 m-l Broken l i n e ---- 6j = m-t

7

8

9

261

5.9

57

56

55

54

59

52

51 2

1

0

1

2

3

4

5

6’

7

Fig. 20. Wind r e s i d u a l s i n t h e North Sea. 15 m s - ’ from t h e South-West.) (Uniform c o n s t a n t wind of Residual flow p a t t e r n . Streamlines J, = const. i n l o 3 m 3 s - ’ .

8

9

262

58

57

56

55

5c

59

52

51

Fig. 21a. Wind residuals in the North Sea. (Uniform constant wind of 15 m s - ' from the South-West:) Map of positive values of the non-dimensional function 6 representing the rate at which the residual kinetic energy is redistributed in physical space. (Positive values indicate regions of residual energy divergence.) Heavy line S = 50 Slender line - 6 = 10 Broken line ---- 8 = 0

-

263

58

57

56

55

5b

53

52

51

Fig. 21b. Wind residuals in the North Sea. from the South-West.) (Uniform constant wind of 15 m s - ’ Map of negative values of the non-dimensional function 6 representing the rate at which the residual kinetic energy is redistributed in physical space. (Negative values indicate regions of residual energy convergence.) fi = - 50 Heavy line Slender line - 6 = - 1 0 Broken line ----- X = O

-

264

58

57

56

55

54

5s

52

5!

Fig. 22a. Wind residuals in the North Sea. (Uniform constant wind of 15 m s-' from the South-West.) Map of positive values of the non-dimensional function E N representing the rate of energy transfer between residual and mesoscale flows by the mesoscale Reynolds stresses. (Positive values indicate regions of positive eddy viscosity.) Heavy line E N = 50 Slender line - E N = 10 Broken line ---- E N = 0

-

265

sa

57

56

55

54

59

52

51

Fig. 22b. Wind r e s i d u a l s i n t h e North Sea. 15 m s-’ from t h e South-West.) (Uniform c o n s t a n t wind of Map of n e g a t i v e v a l u e s of t h e non-dimensional f u n c t i o n E N r e p r e s e n t i n g t h e r a t e of energy t r a n s f e r between r e s i d u a l and mesoscale flows by t h e mesoscale Reynolds s t r e s s e s . (Negative v a l u e s i n d i c a t e r e g i o n s of n e g a t i v e eddy v i s c o s i t y . ) E N = - 50 Heavy l i n e Slender l i n e - E N = - 10 Broken l i n e EN = 0

----

266

Fig. 23. Wind residuals in the North Sea. (Uniform constant wind of 15 m s-’ from the South-West.) Map of positive and negative values of the non-dimensional function C F representing the rate of energy transfer between resldual and mesoscale flows by the friction stress.

267

58

57

56

55

54

5s

52

51

Fig. 24. Wind residuals in the North Sea. (Uniform constant wind of 15 m s - ' f r o m the South-West.) Map o f positive and negative values of the non-dimensional function 8 + C N representirig the rate of work of the mesoscale Reynolds stresses on the residual flow.

268

58

57

56

55

5k

5s

52

51

Fig. 25. Wind residuals in the North Sea. from the South-West.) (Uniform constant wind of 15 m s-' Map of positive and negative values of the non-dimensional function representing the rate at which energy is extracted from the E , = 8 + i, + E , + 1 residual flow (positive values) or supplied to the residual flow (negative values).

269

58

57

56

55

54

5s

52

51

Fig. 26. Wind residuals in the North Sea. (Uniform constant wind of 15 m s - ’ from the South-West.) Map of the-function i j = IIV A u,II I I i i O

II

-

indicating the scale Heavy line Slender line Broken line ----~

of the residual vorticity. 5 = m-l 6 = 5 l o + m-l ;= m-l

270

Atlantic current's inflows. The tracery of the streamlines is more contorted and encloses large (length) scale gyres associated with relatively strong residual currents. These gyres appear to determine the vorticity distribution and only few small scale secondary gyres are apparent in regions of weak residual currents. The maps of energy transfer functions reflect the streamlines patterns. The energy dissipation

E,,

is more important (stronger currents) than in the absence of wind

and the rates of energy transfer the normalized functions

8 ,

significantly larger than

1

EN

,

E~

and

E,

E~

... are

found generally comparable to

E

~

having only a few located peaks of values

.

One can still find "eddies" where the exchange of energy between scales of motion sharply dominates the energy dissipation by bottom friction and, induced to look for it by one's understanding of tidal residuals, one can still see a relationship between negative viscosity eddies and small (length) scale vorticity in secondary gyres but basically, bottom friction has gained control of energy and enstrophy cascades and an interpretation of the residual flow's energetics in terms of two-dimensional turbulence is no longer profitable.

REFERENCES Beckers, O., Nihoul, J.C.J. and Wollast, R., 1976. La circulation residuelle et la caracterisation des masses d'eau dans la zone c6tiere belge. In :J.C.J. Nihoul (Editor), Modelisation des systemes marins. Projet Mer. Rapport final. Services du Premier Ministre. Programmation de la Politique Scientifique, Bruxelles, 1976, 1:95-&30. Carruthers, J.N., 1935. The flow of water through the Straits of Dover. Fishery Invest., London, 2, 14:l-67. Kalle, K., 1949. Die naturlischen Eigenschaften der Gewasser. In: Schweizerbart (Editor), Handbuch der Seefischerei Nordeuropas, Stuttgart, 1:part 2. Laevastu, T., 1963. Water types in the North Sea and their characteristics. In: Amer. Geogr. SOC. (Editor), Serial Atlas of Marine Environment, Folio 4. MC Cave, I.N., 1974. Mud in the North Sea. In : E . D . Goldberg (Editor), North Sea Science, M.I.T. University Press, Cambridge, Mass., pp. 74-100. Nihoul, J.C.J., 1974. Mesoscale secondary flows and the dynamics of ecosystems in the Southern Bight of the North Sea. Memoires SociBt6 Sc. Lg., 7:83-91. Nihoul, J.C.J., 1975a. Modelling of marine systems. Elsevier, Amsterdam, 272 pp. Nihoul, J.C.J., 1975b. Effect of the tidal stress on residual circulation and mud deposition in the Southern Bight of the North Sea. Pure and Appl. Geophys., 113: 577-581. Nihoul, J.C.J., 1977. Three-dimensional model of tides and storm surges in a shallow well-mixed continental sea. Dynamics of Atmospheres and Oceans, 2:29-47. Nihoul, J.C.J., 1980. Residual circulation, long waves and mesoscale eddies in the North Sea. Oceanologica Acta, 3:309-316. Nihoul, J.C.J. and Ronday, F.C., 1975. The influence of the tidal stress on the residual circulation. Tellus, 29:484-490. Nihoul, J.C.J. and Ronday, F.C., 1976. Hydrodynamic models of the North Sea. Memoires Soci6t6 Sc. Lg., 10:61-96.

,

271 Nihoul, J.C.J., Runfola, Y. and Roisin, B., 1979. Non-linear three-dimensional modelling of mesoscale circulation in seas and lakes. In: J.C.J. Nihoul (Editor), Marine Forecasting. Elsevier, Amsterdam, pp. 235-259. Rhines, P.B. and Holland, W.R., 1979. A theoretical discussion of eddy-driven mean flows. Dynamics of Atmospheres and Oceans, 3:289-325. Riepma, H., 1977. Spatial variability of residual currents in an area of the Southern North Sea. ICES Hydrography Committee, CM 1977/C:43, 7 pp. Ronday, F.C., 1975. Modeles de circulation hydrodynamique en mer du Nord. Ph. D. dissertation, Liege University. Svansson, A., 1968. Hydrography of the Katteqat and the Skaqerrak area. Swedish observations, Meddn. Havsfiskelaboratoriet, Lysckil, 48, 2. Tomczak, G., 1968. Die Wassermassenverteilunq und Stromunqsverhaltnisse am Westausgang des Skaqerraks, wahrend der Internationalen Skaqerrak-Expedition in Sommer 1966. Deut. Hydr. Zeit., 21:97-105. Van Veen, J., 1938. Water movements in the Straits of Dover. J. du Conseil, Copenhagen, 13:7-38. Zimmerman, J.T.F., 1976. Mixing and flushing of tidal embayments in the Western Dutch Wadden Sea - 11. Neth. J. Sea Res., 10:397-439.

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273

MODELLING THE PHYSICAL MECHANISMS IN THE MARINE UPPER LAYERS WITH A SECOND-ORDER TURBULENCE CLOSURE

P. KLEIN*~** and M. COWTIC* W

Institut de Mecanique Statistique de la Turbulence. 12, Avenue du General Leclerc - 13003 MARSEILLE - FRANCE

XW

Departement EAA, DER-EDF. 6, Quai Watier

-

78400 CHATOU - FRANCE

ABSTRACT A one-dimensional unsteady model with second-order turbulence closure has been established and implemented. The assumption made is that the methods recently developed for the local modelling of turbulence possess a sufficient degree of universality to be used in marine applications. 'This model is used to study the marine physical mechanisms induced by the local atmospheric forcinqs which govern the mixed layer and thermocline evolution. The model is also applied to the simulation of the thermal structure observed in the Gulf of Lion during the COFRASOV I1 expedition.

INTRODUCTION A rather accurate prediction of the physical mechanisms which govern the behaviour of the oceanic mixed layer and thermocline is a prerequisite to the modelling of the marine ecosystems. Indeed, the spatial and temporal distributions of the biological processes within the marine upper layers seem to be strongly influenced by the vertical turbulent transport mechanisms (Stefan et al., 1975

;

Jamart

et al., 1977). The evolution of these mechanisms can be adequately simulated by using one-dimensional time-dependent models. Most models developed to date assume a well mixed layer with an uniform distribution of mean quantities (temperature, current and salinity)

:

these are the so-called "integral models". Their advantage

is the rather simple computational scheme required. They suffer, however, of a major inconvenience

:

they require a priori assumptions about the integral effects

of turbulent marine mechanisms, the experimental knowledge of which is still quite unsatisfactory. A better modelling of the marine upper layexsobviously necessitates a detailed description of their turbulent structure, which can be obtained by means of the so called second-order turbulence closure methods. This approach is based on the

274 assumption that the second-order closure schemes, mainly calibrated after laboratory data, have a sufficient degree of universality to be used for modelling geophysical turbulence (Lumley and Khajeh-Nouri, 1974). This has already successfully been done for the atmospheric boundary layer (Wyngaard and Cote, 1974 Mellor, 1975

;

;

Yamada and

Andre et al., 1976). Mellor and Durbin (1975) applied it to the

marine upper layers with a quite simple model, equivalent in fact to the classical eddy diffusivity approach. The present study makesuseof an effective second order closure scheme, allowing the prediction of the terms governing the turbulent kinetic energy and temperature variance budgets.

THE MODEL The general hypotheses done are the Boussinesq approximation, the existence of an average horizontally homogeneous situation and (for the sake of simplicity) the neglect of salinity effects. They lead to the classical equations for the first order moments

:

where t represents time

;

u, v and w the three components of the velocity vector -

along East, North and the upwards vertical rage current field

-

(z u + =

;

Z is a complex notation for the ave-

i.7 with i2 = - 1) relative to the geostrophic current ____ ; u'w', v'w' and B'w' respectively designate the com~

@ is the average temperature

ponents of the turbulent shear stress (divided by density) and heat flux (divided -

by the product of density and specific heat) penetrates to a depth z

;

LI and

thermal molecular diffusivity

;

X

;

R is the radiative heat flux which

are respectively the kinematic viscosity and the

f is the Coriolis parameter.

_____ The calculation of the vertical turbulent fluxes ofvelocity (u'w',v'w')andtem~

perature B'w' requires the knowledge of other second order moments. In secondarder turbulent moment modelling, the following equations have to be considered (see e.g. Coantic, 1978)

:

;

275

+ 9.B.8'2Ai3

with i,j = 1 , 3 . g is the gravity constant, B the coefficient of thermal expansion of sea water, and P the pressure. These equations bring into the picture third order turbulence terms, terms involving pressure fluctuations, and dissipation terms, which need to be parameterized for the system to be closed. An Hanjalic and Launder (1972) type parameterization is selected for the third order turbulence terms. Launder's (1975) sugqestion is chosen for those concerning pressure fluctuations. Dissipation rates are parameterized using the integral length suggested by Blackadar (1962). After the closure of the system of turbulence equations, Mellor and Yamada's (1974) "level 3" assumptions which neglect tendency and diffusion terms for the cross correlations are used. Equations ( 3 ) , (4), (5), for second order moments can then be simplified and reduced to

-

u'w'

=

with

:

-

&. au

-

K M

=

K*

=

and

:

A1.wl2

R

-

+

. w'2 C5.e

,

A2

v'w' =

-

-

$. av ,

:

276

+

~

where e2 is the turbulent kinetic energy (e2 E u'2

I

v'2

+

_

_

w'z), and

C . , (i = 1,7)

are numerical constants given by the literature. - Initial values for u , V and 0 are given or observed values, while those for ez

-_

and 8 ' '

can be generated by the model. Surface boundary conditions for the tempe-

rature and momentum equations are respectively the surface heat flux and the surface wind stress. The turbulent kinetic energy flux from the atmosuhere to the sea, produced by surface waves breaking, is stipulated as a boundary conditions for e2. The surface flux of (z = -D),

-

is set to zero. Boundary conditions at some depth

chcsen in order that the atmospheric effects have no influence, are nil

values for

and

7

and a given value for

0.A l l

turbulent moments are by defini-

.tion equal to zero at this depth. To solve the four non-linear parabolic type partial differential equations ( l Y , (2 ) ,

( 6 ) , (7),we use an implicit scheme for differentiation over time because

of the duration requested for the simulations (of the order of several days). This type of scheme does not

a priori

impose a stability constraint on the time step.

The so-called "implicit trapezoidal" method is selected for the term responsible for inertial oscillations (Kurihara, 1965). The spatial differentiations were carried out with a finite element method. The non-linear nature of the equations, due to the diffusion operators, has, after an analysis of the non-linear problem, led to choose iterative methods developed in other scientific areas (Sermange, 1978). In most simulations realised, the depth D is set at 60 meters, grid spacing at 1 m and the time step at one hour. A computation time of some 57 seconds is required for a 100 hours simulation using an I.B.M. 370-3033 computer with virtual storage.

RESULTS Oceanic response to an impulsive wind stress Several typical situation were simulated with the model described above. The first results presented here illustrate the response of the marine upper layers to an impulsive wind stress. The ocean is initially at rest and its initial temperature profile is stable (see. Fig. 1).

A surface stress corresponding to

217

6

8

10

Fig.1. Variation of temperature profile due to an impulsive wind and a zero surface heat flux. Temperature profiles are plotted every 6 hours, each one displaced by 1 . 2 5 " C .

iYnl i -60

0

0.2

-

0

02

ms-'

I

0

02

Y

--- 0

02

m 5-1

m s-1

rn s-1

0

02

0

02

ms-1 02

Fiq.2. Variation of the current modulus, I Z

1,

profile due to an impulsive wind.

278

a 11 rn.s-l. West wind is applied after t

=

0

;

the surface heat flux is assumed

to be zero at all times. The evolution of temperature (Fig.1) shows that themixed layer thickens very rapidly during the first few hours and more slowly later. The distribution of current appears as non-uniform within the mixed layer (Fig. 2)

;

it i s constantly varying both in direction and modulus and presents periodically a strong shear close to the thermocline. The dimensionless turbulent kinetic energy budget (i.e. Eq. ( 6 ) ) divided by ui/a, where R is the integral length scale used to parameterizedissipation,at 24 h and 42 h is presented in Figure 3 and Figure 4. Referring to the initial form of equation (6) :

-

. -au az- c

j g at

-

v'w'

~

av,)- 2 . g . a . m , .a

f

c

04,

-5

-*

- r_

-10

-

-10

-15

-

-15

-20

-

-25

-

-25

-30

-

-30

-35 -

-35

\

-LO P -45'

s x 10

- 2C

-

-LO

'

-t5 -1.0

' -0.5

' 0

.

0.5

'

1.0

'

1.5

Fig.3. Dimensionless turbulent kinetic energy budget at t = 24 h.

-45 -1,s-1.0-0.5

I

0

0.5

1.0

Fig.4. Dimensionless turbulent kinetic energy budqet at t = 42 h.

-aG - + *aZ

it can easily be seen that the shear production term, G = -2.(u'w' -

and the dissipation term, D

1.5

-

__ a V v'w'.-),

av

are very important and practically equal within __ the mixed layer. The buoyancy term, P = 2.g.$.e'w', presents a maximum close to = E,

the bottom of the mixed layer. The distribution of the shear production term, G , presentsa bump just above that level. The temporal term

a 2

) which is the at rate of storage of turbulent kinetic energy is very small. The diffusion term, __ a(T = -- e2w'), negative in the first meters (e2w' is set to zero in this aZ z=o simulation), becomes positive within the mixed layer, then again negative and

(S =

1

finally positive within the thermocline. In thus appears that a part of the turbulent kinetic energy is produced locally by the current shear at the bottom of the

219 mixed layer, carried within the thermocline and then used here for the thermocline erosion (see Fig. 5). These results show the important role of the diffusion of turbulence in the deepening mechanism.

Fig. 5. Profile of vertical turbulent flux of turbulent kinetic energy at t=42h.

Another simulation of the same typical situation is set with a non-zero surface

-

turbulent kinetic energy flux (e2w’

I z=o

=

- m.u;,

with m

=

10) to explore the

effect of wave breaking upon mixed-layer deepening. The evolution of the temperature distribution is not significantly affected by this surface flux. Analysis

of the dimensionless budget of turbulent kinetic energy (Fig. 6) reveals that most of the turbulent kinetic energy diffusing from the surface is dissipated within the first meters. The most important effect is that the shear production term is less important near the surface, because of the greater homogeneity of the current in this region. These results have been compared with those from a simpler model, in which, like in Mellor and Durbin (1975), the tendency and diffusion effects are ignored for all second order moments. The mixed layer deepening resulting from an impulsive wind appears to be less important with the simpler model than with the present one (see Klein, 1980 a,b).

Simulation of an observed oceanic situation The model has also been applied to the simulation, on the basis of meteorological observations, of the evolution of the thermal structure observed in the Gulf of Lion (42ON, 4’45‘E) during COFXASOV I1 expedition in July 1976. During the simulated period, preceded by a situation of low winds, the weather was very sunny and windy

;

the observed thermal structure (Fig. 7), obviously strongly

affected by internal waves, shows that the average depth of the thermocline increases from 26 meters on July 18th to about 37 meters on July 28th. Surface radiative and turbulent fluxes are determined from observed meteorological

280

~

l.5‘ -1.5

-1.0

-0.5

0

0.5

1.0

1.5

Fig. 6. Dimensionless turbulent kinetic energy budget at t = 24 h with the effect of waves (e’w’ = mU3 with m = 10).

I z=o

0

-10

-20

-30

-40

-50

1

I

t

t

t

t

t

19 20 Jvly 1¶7S

21

22

23

2L

L

1

I

I

t

t

t

2s

26

21

Fig. 7. Observed time-depth isothermal contours during “COFRASOV 11”.

28

281 parameters, calculated sea surface temperature and the use of bulk parameterization formulas, with the classical value 1.5

for the exchange coefficient.

The calculated thermal structure (Fig. 8) is not modulated by internal waves, these being ignored by the modeL and the time-depth isothermal contours under the thermocline have on the average an almost constant depth, since advection phenomena are not taken into account. Furthermore, the temperature gradient within the thermocline is significantly smaller after July 23rd

than the one shown by mea-

surements. Nevertheless, the calculated thermal structure shows a rather satisfactory overall agreement with the observations, both with respect to surface temperature (even though there is a difference of some 0 . 3 O C on the last day) and the deepening of the thermocline (in spite of a slight lead of the model with respect to reality). It is to be noted that the thermal structure observed during the COFRASOV I1 expedition can be well predicted by a simpler model (close to the Mellor and Durbin's 1975 one), but only when the ocean-atmosphere exchange coef-3

ficient is given the high value 1.7 x 10

(see Klein, 1980 b). The confrontation

of these results shows that diffusion effects for the variances of turbulent

fluctuations are non-negligible and have thus to be taken into account.

22.5oc 22oc

21 *C

21.5 OC

-1 0

- 20 - 30 -LO

17.C

I

16.C

n

-50

-

\

L--

1Loc

n -60

. I

15.C

I

t

19 20 July 1976

t

n

t

t

22

23

t

u

t

25

t 26

t

n

Fig. 8. Computed time-depth isothermal contours during "COFRASOV 11".

t' 28

282

CONCLUSION The few results presented in this paper demonstrate the ability of oceanic models including second-order turbulence closure schemes

to describe the physi-

cal mechanisms which govern the evolution of the mixed layer and thermocline. Thus, simulations with constant atmospheric forcings have revealed in particular the current modulus variations within the mixed layer, and shown the importance of the diffusion of turbulent kinetic energy near to and within the thermocline and the very weak influence of surface wave breaking on the deepening of an established mixed layer. Furthermore,the success of the COFRASOV I1 data simulation emphasizes the capacity of the model to reproduce a real marine situation without any coefficient adjustment. Using such models should allow to predict and to parameterize more precisely the physical mechanisms which are responsible

of the mean and turbulent transports of the nutrients and plankton within the marine upper layers.

ACKNOWLEDGEMENTS This work was partly carried out under E.D.F./I.M.S.T.

contracts 16336/16175/

16079. Experimental data from COFRASOV I1 expedition were kindly provided by the

team of the Laboratoire d'oceanographie Physique du MusGum, Paris.

REFERENCES J.C. Andre, G. De Moor, P. LacarrPre and R. DU Vachat, Turbulence approximation for inhomogeneous flows. J. Atmos. Sci., 1976, 3 3 , 476-491. A.K. Blackadar, The vertical distribution of wind and turbulent exchange in neutral atmosphere. J. Geopliys. Res., 1 9 6 2 , 6 7 , 3095-3102. M. Coantic, An introduction to turbulence in geophysics and air-sea interactions. AgaGdograph n 0 2 3 2 , 1978. K. Hanjalic, B.E. Launder, A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech., 1972, 52, 609-638. B.M. Jamart, D.F. Winter, K. Banse, G.C. Anderson and R.K. Lam, A theoretical study of phytoplankton growth and nutrient distribution in the Pacific Ocean off the northwestern U.S. coast. Deep Sea Res., 1 9 7 7 , 2 4 , 753-773. P. Klein, a, Modelisation des mecanismes turbulents dans les couches marines superficielles (couche melang6e et thermocline). Th. Doct. Etat, 1980, Universit6 Aix-Marseille 11, I.M.S.T. Bull. Direction des Etudes et Recherches Electricit6 de France, serie A , 3 . P. Klein, b, A simulation of the effects of air-sea transfer variability on the structure of marine upper layers. To appear in J . Phys. Oceanogr., 1980. Y . Kurihara, On the use of implicit and iterative methods for the time integration of the wave equation. Monthly Weather Rev., 1965, 9 3 , 33-46. B.E. Launder, G.J. Reece and W. Rodi, Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech., 1975, 6 8 , 537-566. J.L. Lumley and B. Khajeh-Nouri, Computational modeling of turbulent transport i in'Turbul. Diffus. Environ. Pollut.",AdV. Geophys., 1974, vol. 18a, Academic Press, New-York, 169-192. G.L. Mellor and P.A. Durbin, The structure and dynamics of the ocean surface mixed layer. J. Phys. Oceanogr., 1975, 5 , 718-728. G.L. Mellor and T. Yamada, A hierarchy of turbulence closure models for planetary boundary layers. J . Atmos. Sci., 1974, 3 1 , 1791-1806.

283 Sermange, Une methode numerique en b i f u r c a t i o n . Application B un probl6me de f r o n t i s r e l i b r e de l a physique d e s plasmas. Rapp. de Rech. n012, 1 9 7 8 , I R I A LABORIA, Le Chesnay, France. H . S t e f a n , T . Skoglund and R.O. Megard, Wind c o n t r o l of a l g a e growth i n eutrophic l a k e s . J. Environm. Eng. Div., ASCE, 1 9 7 6 , 1 0 2 , 1201-1213. J . C . Wyngaard and O.R. Cote, The e v o l u t i o n of t h e convective p l a n e t a r y boundary l a y e r . A higher-order c l o s u r e model study, Boundary Layer Meteorol., 1 9 7 4 , 7 , 3 , 289-308. T. Yamada and G . Mellor, A s i m u l a t i o n of t h e Wangara atmospheric boundary l a y e r d a t a . J. Atmos. S c i . , 1 9 7 5 , 3 2 , 1 2 , 2309-2329. M.

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285

MODELLING TURBIDITY MAXIMUM I N THE SEINE ESTUARY

J.C.

SALOMON

U n i v e r s i t e d e B r e t a g n e O c c i d e n t a l e , 2 9 2 8 3 BEST

CBdex (FRANCE)

ABSTRACT A two d i m e n s i o n a l ,

laterally-averaged,

n u m e r i c a l model h a s b e e n s e t up and ap-

p l i e d t o t h e S e i n e e s t u a r y , t o compute t h e t i d e p r o p a g a t i o n , t h e c o n c e n t r a t i o n of s o l u t e s , and t h e d i s p e r s i o n of s e d i m e n t . The n u m e r i c a l p r o c e d u r e i s e s s e n t i a l l y t h a t due t o Hamilton

(1975) w i t h modi-

f i c a t i o n s which g i v e a b e t t e r t r e a t m e n t o f boundary c o n d i t i o n s , a n d g e n e r a l i z a t i o n t o t h e s i m u l a t i o n of t u r b i d i t y . The model s i m u l a t e s s a t i s f a c t o r s l y t h e phenomena o b s e r v e d i n t h e S e i n e e s t u a r y and p r o v i d e s a new e x p l a n a t i o n of t h e s e t u r b i d a c c u m u l a t i o n s . The r e a s o n why a s e d i m e n t p l u g r e m a i n s i n t h e lower e s t u a r y even though t h e r e s i d u a l v e l o c i t i e s a r e s e a - g o i n g i s t o b e found i n t h e p e c u l i a r s h a p e o f t h e i n s t a n t a n e o u s v e l o c i t y c u r v e . Owing t o a v e r y s h o r t d u r a t i o n of r i s e , and d i f f e r i n g d u r a t i o n s o f s l a c k

water a t h i g h and low t i d e , t h e r e s i d u a l s e d i m e n t t r a n s p o r t i s u p - r i v e r

(opposite

t o the residual velocity).

INTRODUCTION

E s t u a r i n e t u r b i d a c c u m u l a t i o n s have b e e n s t u d i e d i n t h e p a s t , above a l l f o r t h e c o n s t r a i n t s which t h e y impose on s h i p p i n g . Nowadays, one i s a l s o i n t e r e s t e d i n e v a l u a t i n g t h e i r e f f e c t s o n t h e dynamics o f e s t u a r i n e e c o s y s t e m s , as i t i s w e l l known t h a t mud i n s u s p e n s i o n

:

- r e d u c e s l i g h t p e n e t r a t i o n and t h u s a f f e c t s t h e growth o f p h y t o p l a n c t o n and plants ;

- a d s o r b s and c o n c e n t r a t e s some p o l l u t a n t s s u c h as heavy m e t a l s , t h e r e b y c r e a t i n g v e r y t o x i c zones ;

- consumes g r e a t q u a n t i t i e s of d i s s o l v e d oxygen by o x i d i z i n g o r g a n i c m a t t e r -

;

h i n d e r s t h e development o f a n i m a l l i f e a s it d o e s n o t p r o v i d e a s o l i d b a s e ,

and c a n even b u r y l a r v a e and s m a l l b e n t h i c a n i m a l s . T h e s e t u r b i d a c c u m u l a t i o n s which a r e found i n t h e v i c i n i t y o f t h e s a l i n e l i m i t may have a c o n s i d e r a b l e m a s s , s u c h i s t h e case i n t h e Gironde e s t u a r y , where i t i s t h o u g h t t o b e o f t h e o r d e r of 3 M . t .

w i t h corresponding t u r b i d i t i e s near t h e

286 bed of some 100 g / l . I n t h e S e i n e e s t u a r y , t h e phenomenon i s n o t s o m a s s i v e . The t o t a l m a s s i n v o l v e d i s c o n s i d e r e d t o a t t a i n o n l y 40 000 t d u r i n g h i g h r i v e r f l o w ; t h e a v e r a g e residence t i m e v a r i e s from 4-5 months d u r i n g low r i v e r f l o w , t o s e v e r a l weeks o r l e s s d u r i n g h i g h r i v e r flow. N e v e r t h e l e s s as s e d i m e n t a r y p r o c e s s e s a r e among t h e dominant e s t u a r i n e mechan i s m s , and a s i n r e c e n t y e a r s w a t e r q u a l i t y i n t h e S e i n e e s t u a r y h a s g r e a t l y d e t e r i o r a t e d , a l a r g e s c a l e m u l t i d i s c i p l i n a r y s t u d y o f t h e e s t u a r y i n c l u d i n g b o t h samp l i n g and n u m e r i c a l m o d e l l i n g w a s i n i t i a t e d by u n i v e r s i t y l a b o r a t o r i e s and r e g i o n a l authorities. F o r t h i s p u r p o s e , t h e whole e s t u a r i n e a r e a c o v e r e d by t h e s t u d y h a s been d i v i d e d i n t o t h r e e d i s t i n c t z o n e s , e a c h of them s i m u l a t e d by a n u m e r i c a l model

1 - a two-dimensional 2

(Fig. 3 )

:

model ( h o r i z o n t a l p l a n e ) , f o r t h e o u t e r e s t u a r y

- a two-dimensional model ( v e r t i c a l p l a n e ) , f o r t h e m i d d l e p a r t

of t h e e s t u a r y

3 - a o n e - d i m e n s i o n a l model ( s e c t i o n a l l y a v e r a g e d ) , f o r t h e u p p e r e s t u a r y Only t h e second model d e a l s w i t h t u r b i d i t y and i s t h e s u b j e c t o f t h e p r e s e n t paper.

REGIONAL SETTING

E s t u a r i n e morpholoqy

(Fig. 1)

The S e i n e r i v e r and e s t u a r y d r a i n a l a r g e , h e a v i l y u r b a n i z e d and i n d u s t r i a l ba2 , which c o n t a i n s 30 % of t h e c o u n t r y ' s p o p u l a t i o n , and 40 % o f

s i n o f 7 4 250 km

i t s economic a c t i v i t y .

The e s t u a r y i s f u n n e l shaped

;

a t i t s mouth it i s 9 km wide a t h i g h t i d e , w h i l e

25 km u p s t r e a m t h e w i d t h i s o n l y 500 m . The main c h a n n e l i s t o d a y c o m p l e t e l y enbanked by d y k e s which a r e above h i g h t i d e l e v e l a s f a r a s H o n f l e u r ( 1 2 km upstream from t h e mouth) and c o m p l e t e l y t r a i n t h e r i v e r d i s c h a r g e , s e p a r a t i n g it from t h e i n t e r t i d a l s h o a l s a d j a c e n t t o t h e c h a n n e l . Between H o n f l e u r and t h e mouth, t h e t o p o f t h e d y k e s becomes l o w e r and a t t a i n s a d e p t h o f t h r e e m e t r e s above c h a r t datum ( L . A . T . )

a t t h e i r e x t r e m i t y . The t r a i n e d c h a n n e l d e p t h i n t h e e s t u a r y i s

g e n e r a l l y c o n s t a n t , and m a i n t a i n e d by d r e d g i n g , a t 5 t o 6 m e t r e s d e p t h . The w i d t h of t h e t r a i n e d c h a n n e l v a r i e s from 1 000 m a t t h e mouth, t o 400 m

15 km u p s t r e a m .

287

I

Fig.

1. Location map f o r t h e Seine e s t u a r y .

River i n p u t s

3

The mean average discharge of t h e Seine i s 485 m / s . River flow v a r i e s s e a s o n a l l y 3 3 from a maximum i n January (700 m / s ) t o a minimum i n September ( 2 0 0 m / s ) . During extreme f l o o d s , which occur between December and A p r i l , and l a s t s e v e r a l days, t h e 3 flow can a t t a i n 2 000 m / s . Tide The t i d e i n t h e "Baie de l a Seine" i s t h e r e s u l t of t h r e e processes : a ) t h e response of t h e N . E .

A t l a n t i c Ocean t o t h e t i d e - r a i s i n g f o r c e s of t h e sun

and moon, which g i v e s it i t s semi-diurnal c h a r a c t e r ; b) t h e c o - o s c i l l a t i o n s of t h e C e l t i c Sea and English. Channel which amplify it ;

c ) t h e d i s t o r t i n g e f f e c t s of shallow water which cause i t t o vary from an almost sinusoidal oscillation. Figure 2 shows t h e t i d e curve observed i n t h e e s t u a r y i n l e t . The r i s i n g t i d e

288 is of s h o r t d u r a t i o n

( 3 h o u r s ) , f o l l o w e d by a 2 t o 2 . 5 hour p e r i o d d u r i n g which

t h e w a t e r l e v e l r e m a i n s a t t h e h i g h t i d e l e v e l . The f a l l i n g t i d e l a s t s g e n e r a l l y

6 t o 6.5 hours.

h

E VeI oci t y

FLOOD

---

Height

I

-

rn -5 I

-+-I-

N

< t

0

m

-

3

F i g . 2 . Stream v e l o c i t y , w a t e r h e i g h t , and c o r r e s p o n d i n g bottom s t r e s s i n t h e middle e s t u a r y .

S i n c e t i d e r a n g e s v a r y from 3 m i n neap t i d e s t o 8 m i n s p r i n g t i d e s , t h e e s t u a r y

i s m a c r o t i d a l . T h i s l a r g e t i d a l r a n g e i n comparison w i t h t h e r e l a t i v e l y s h a l l o w d e p t h s of t h e e s t u a r y c h a n n e l ( 5 t o 6 m below maximum low t i d e ) , m a i n t a i n s and a m p l i f i e s t h e asymmetry of t h e t i d e wave a s it p r o p a g a t e s u p s t r e a m . The t i d e e x t e n d s

289 to Pose, 160 km from the mouth, where it is stopped by a weir.

TWO-DIMENSIONAL MODEL OF THE MIDDLE ESTUARY At the start of this study, it seemed that the middle estuary (i.e. the compartment included between the end of the dykes which fringe the channel and the outskirts of la Mailleraye) would be likely to exhibit different modes of transport at different distances above the bottom

:

thus the transports could not be correc-

tly simulated by their depth mean values. This comment is valid a fortiori for the mechanisms of sedimentation which apply to mud

;

it is known that the dynamics of

the turbidity maximum are closely dependent on the density structure (nodal point).

C . D'ANTIFER

C . DE LA HEVE

Fig. 3 . The Seine estuary and its schematization by a set of three numerical models.

This compartment of the estuary was therefore represented by a two-dimensional model in the (x,z) plane (i.e. distance along the estuarine axis against height) Each quantity was represented by its value averaged over the width of the flow channel. This model computes the elevation

:

:

5 (x,t)

the component rates of the stream the concentration of a solute the concentration of the mud

:

:

:

U(x,z,t) and W(x,z,t)

C(x,z,t) (including salt)

Cs(x,z,t)

290 The equations of hydrodynamics a r e derived from t h e well known Navier Stokes equations by i n t e g r a t i n g them t w i c e , over a small time s t e p (order of magnitude one minute) and over t h e width ( s e e f o r example E l l i o t t , 1976). The r e s u l t i n g e q u a t i o n s a r e t h e following :

ax

at

The p a r t of t h e e s t u a r y covered by t h i s model has been s u b j e c t t o c o n s i d e r a b l e reclamation, and i s today c o n s t r a i n e d by dykes. T h i s f a c t allows u s t o s i m p l i f y t h e system of e q u a t i o n s , by schematizing t h e e s t u a r y i n t o a s e r i e s of r e c t a n g u l a r s e c t i o n s , whose width v a r i e s slowly with x. Thus we may w r i t e :

aB<< 0 ax A l s o , we can n e g l e c t momentum d i s p e r s i o n i n t h e h o r i z o n t a l p l a n e , compared with

t h e corresponding term i n t h e v e r t i c a l . The equations reduce t o :

291

t o which may b e a d d e d t h e e q u a t i o n o f c o n s e r v a t i o n o f mass f o r t h e s e d i m e n t :

at

az

ax

az

B

ax

az (9)

where W s i s t h e t e r m i n a l v e l o c i t y of t h e s e d i m e n t .

Boundary c o n d i t i o n s Seaward a n d landward b o u n d a r i e s The seaward boundary o f t h i s model ( t h e end of t h e d y k e s ) i s w i t h i n t h e model o f t h e o u t e r e s t u a r y , t h e landward boundary i s w i t h i n t h e one-dimensional

model.

Thus a t t h e s e two b o u n d a r i e s t h e a d j a c e n t models make a v a i l a b l e t h e water l e v e l , t h e d e p t h mean stream v e l o c i t y and t h e d e p t h mean s a l i n i t y . I t m e r e l y r e m a i n s t o r e s o l v e t h e s e i n t e g r a t e d v a l u e s i n t o t h e i r components a t a l l d e p t h s . A t t h e landward e n d , a b o v e t h e s a l i n e z o n e , w e s e t t h e s a l i n i t y t o z e r o a t a l l

d e p t h s , and assume t h a t t h e r a t e v a r i e s l o g a r i t h m i c a l l y w i t h h e i g h t

U(Z) =

Log

P

:

2i.20

___ BH

n

ezo or, expressing

where. <

>

u

a s a power o f z

:

u

a

za

denotes averaging over t h e depth

The t u r b i d i t y h a s t o b e s p e c i f i e d d u r i n g t h e e b b , b e c a u s e it i s n o t c a l c u l a t e d by t h e r i v e r model, even i n t h e form o f a n i n t e g r a t e d v a l u e . W e t h e r e f o r e i n t r o d u c e a v a l u e which i s b a s e d e i t h e r on o b s e r v a t i o n s or on a s i m u l a t i o n u s i n g t h e model. A t t h e seaward e n d , t h e model i s bounded by a l i n e o f e l e v a t i o n p o i n t s

(see

below f o r d e t a i l s o f t h e n u m e r i c a l s c h e m e ) , so t h a t no a s s u m p t i o n s a r e r e q u i r e d f o r t h e v e r t i c a l s t r u c t u r e o f t h e s t r e a m . Only t h e n u m e r i c a l scheme i s m o d i f i e d ,

292 by s h i f t i n g t h e h o r i z o n t a l d e r i v a t i v e s of t h e v e l o c i t y away from t h e c e n t r e o f each c e l l , and by n e g l e c t i n g t h e v i s c o s i t y i n t h e h o r i z o n t a l . A l s o , by n e g l e c t i n g t h e h o r i z o n t a l d i s p e r s i o n compared w i t h a d v e c t i o n , w e a r e n o t s p e c i f y i n g any p a r t i c u l a r v e r t i c a l d i s t r i b u t i o n of s a l i n i t y d u r i n g t h e ebb. On t h e f l o o d , however,

w e have t o d e f i n e a f u n c t i o n S ( z ) , b a s e d on t h e mean s a l i n i t y . F o r t h i s , w e may e i t h e r i n t r o d u c e a t o t a l l y e m p i r i c a l r e l a t i o n b a s e d on o b s e r v a t i o n s o f t h e p r o t o t y p e , o r a d o p t a n a n a l y t i c a l e x p r e s s i o n which s a t i s f i e s t h e boundary c o n d i t i o n s of z e r o g r a d i e n t a t t h e s u r f a c e and t h e bottom

A third-order

where

As

:

polynomial s a t i s f i e s t h e s e c r i t e r i a , e.g.

:

=

s-h

-

s

5

The o n l y a p p r o x i m a t i o n of n o t e c o n c e r n s t h e t e r m S / < S > , which w a s t h o u g h t t o b e s m a l l d u r i n g t h e p l a n n i n g s t a g e s of t h e p r o j e c t , when one c o n s i d e r e d t h e s t r a t i f i c a t i o n i n d i c e s s u c h a s t h e r a t i o o f r i v e r d i s c h a r g e t o t h e volume of t h e t i d a l p r i s m , o r t h e r a t e o f e n e r g y d i s s i p a t e d by f r i c t i o n , compared w i t h t h e g a i n o f p o t e n t i a l e n e r g y o f f r e s h w a t e r d u r i n g t h e m i x i n g p r o c e s s . From measurements made i n t h e f i e l d (Avoine, 1 9 8 0 ) , i t a p p e a r s now t h a t f o r low t o medium d i s c h a r g e s , t h i s o r i g i n a l i d e a i s c o n f i r m e d , b u t d u r i n g a f r e s h e t , t h i s t e r m c a n b e of t h e o r d e r of u n i t y , p a r t i c u l a r l y a t t h e commencement of t h e f l o o d . I t i s t h e r e f o r e e n v i s a g e d t h a t t h e model w i l l f u n c t i o n by i t s e l f f o r low f r e s h - w a t e r mial t e r m

;

f l o w , u s i n g t h e polyno-

d u r i n g f r e s h e t s , o n e w i l l have t o have r e c o u r s e t o t h e r e s u l t s o f re-

c e n t l y o b t a i n e d o b s e r v a t i o n s , i n o r d e r t o c o r r e c t t h e v a l u e of t h e t e r m

S/<S>,

n e a r t h e end o f t h e dyke o f " l e R a t i e r " . The seaward boundary c o n d i t i o n s f o r t u r b i d i t y a r e a l s o d e t e r m i n e d f r o m measurements i n s i t u o r from s i m u l a t i o n r u n s . S u r f a c e and bottom b o u n d a r i e s A t t h e s u r f a c e , t h e boundary c o n d i t i o n a p p l i c a b l e t.o t h e s t r e a m i s d i c t a t e d by

t h e s h e a r i n g s t r e s s o f t h e wind (more o f t e n t h a n n o t s e t t o z e r o ) . T h i s t e r m i s e a s i l y introduced

:

293 V a r i o u s e x p r e s s i o n s f o r t h e f u n c t i o n f a r e a v a i l a b l e from l i t e r a t u r e ( f o r examp l e Wilson,

1966).

W e assume t h a t t h e r e i s no f l u x o f s a l t from w a t e r t o a i r o r v i c e v e r s a

:

F o r t h e suspended s e d i m e n t , t h e v e r t i c a l f l u x due t o s e t t l e m e n t i s b a l a n c e d by the v e r t i c a l dispersion a t the surface

:

A t t h e b o t t o m , t h e f r i c t i o n a l stress on t h e b e d ,

T~

i s g i v e n by :

I n f o r t u n a t e l y , owing t o t h e d i f f e r e n c e i n magnitude between t h e v e r t i c a l g r i d s t e p and t h e t h i c k n e s s of t h e l a m i n a r s u b - l a y e r ,

it i s very d i f f i c u l t t o obtain

a n u m e r i c a l v a l u e f o r t h e v e l o c i t y g r a d i e n t n e a r t h e bottom. V a r i o u s a t t e m p t s t o u s e t h i s f u n c t i o n w e r e made, w h i c h , a l t h o u g h n o t c a u s i n g d i v e r g e n c e i n t h e c a l c u l a t i o n s , n e v e r t h e l e s s d i d n o t prove s a t i s f a c t o r y . W e t h e r e f o r e p r e f e r r e d t o use a f u n c t i o n o f t h e s p e e d i t s e l f , r a t h e r t h a n of i t s d e r i v a t i v e , of t h e u s u a l form :

The c o e f f i c i e n t k ( o r d e r of magnitude 2 t o 3 ) i s a c o e f f i c i e n t of f r i c t i o n anal o g o u s t o t h o s e of Chezy and of S t r i c k l e r f o r a v e r t i c a l l y - i n t e g r a t e d model

The v e r t i c a l component of v e l o c i t y a t t h e bottom i s z e r o :

w-h

= 0

T h e r e i s no f l u x of s a l t t h r o u g h t h e bed

:

:

294 The v e r t i c a l f l u x of s e d i m e n t i s e q u a l t o t h e d i f f e r e n c e " e r o s i o n - d e p o s i t i o n "

K'z

acs az

_ I _

- ws cs =

(5) erosion

deposition

The e r o s i o n f u n c t i o n i s g i v e n i n t h e form o f P a r t h e n i a d e s r e l a t i o n

:

=M(+-I)

erosion

ce

and t h e d e p o s i t i o n f u n c t i o n i s t h a t g i v e n by E i n s t e i n - K r o n e

=

w s cs

(1961) :

(1 - %)

deposition The c o n s t a n t of e r o s i o n M , d e t e r m i n e d i n t h e l a b o r a t o r y f o r v a r i o u s t y p e s o f sediments (Harrison e t a l . ,

1971

;

C o r m a u l t , 1971) i s o f t h e o r d e r o f 0.001 S . I .

and f o r d e p o s i t i o n T~~ may b e ce o b t a i n e d e i t h e r by measurement i n t h e f i e l d ( o r by d e f a u l t i n t h e l a b o r a t o r y ) , o r u n i t s . The c r i t i c a l bottom stress f o r e r o s i o n

T

from P o s t m a ' s d i a g r a m .

If If

T

T~~

I f T

ce

<

< T <

T~~

dep o s it io n w i l l occur

T

no change w i l l t a k e p l a c e

ce

(-ve s e d i m e n t f l u x )

e r o s i o n w i l l occur (+ve sediment f l u x )

< T

C o e f f i c i e n t s of d i s u e r s i o n E q u a t i o n s ( 7 ) t o ( 9 ) i n t r o d u c e d i s p e r s i o n terms i n t h e x- a n d z - d i r e c t i o n s ,

for

mass ( i n s o l u t i o n and s u s p e n s i o n ) a n d f o r momentum. L i t t l e information e x i s t s a t p res en t concerning t h e h o r i z o n t a l c o e f f i c i e n t s

which r e p r e s e n t t h e e f f e c t of h i g h - f r e q u e n c y f l u c t u a t i o n s , and o f t h e i n t e g r a t i o n a c r o s s t h e w i d t h o f t h e e s t u a r y . Very f o r t u n a t e l y , t h i s l a c k o f knowledge i s n o t c r i t i c a l f o r models which u s e i n s t a n t a n e o u s v a l u e s , b e c a u s e t h e h o r i z o n t a l exchan-

g e s a r e e s s e n t i a l l y t h e p r o d u c t of t h e a d v e c t i o n terms. W e c a n t h e r e f o r e b e c o n t e n t t o u s e n u m e r i c a l v a l u e s which are t h e same t h r o u g h o u t t h e w a t e r column ( t h e p r e c i s i o n o b t a i n e d by u s i n g a f u n c t i o n of z b e i n g i l l u s o r y ) and p r o p o r t i o n a l t o t h e v e r t i c a l exchange c o e f f i c i e n t s . The c o e f f i c i e n t o f p r o p o r t i o n a l i t y s u g g e s t e d by t h e l i t e r a t u r e s u r v e y (Dyer, 1973) i s o f t h e o r d e r o f l o 5 , a v a l u e s i n c e a d o p t e d by KUO

e t al.

(1978)

:

295 On the other hand, the vertical exchange coefficients have to be determined with great care, because they have a strong influence on the results of the computations. In the case of a steady-state flow, without stratification or turbidity, the following relation, stemming from the theory of Prandtl is

Kz

=

Nz

=

Ka (z

+

in general use

:

h) V

Bowden et al. (1975) have published a list of the various relationships obtained in density-stratified flow Munk et al. (1948)

Nz = A0

:

:

-1/2

(1 + 10 Ri)

Kz = A 0 (1

+ 3.33 Ri)- 3 / 2

Pritchard (1960)

:

while they themselves use the relationships

Nz = 5.10-*

K~

=

5.10-~

P

i

:

1

+

H < U >

(1

+

7 Ri)-l/*

1

+

H < U > (1

+

Ri)-7/4)

Kuo et al. (1978) used Pritchard's formua, but took account of wind effects

:

where H is the height of the waves, L is the wavelength of the swell,

and T is the period of the swell.

Blumberg (19751, however, used a formula slightly different from the above, based on the theory of Montgomery and the numerical results of Kent and Pritchard

Nz =

Kz (1

+

Ri)

:

296 Nz

=

Kz = 0 i f R i > R i c

He t h u s i n t r o d u c e d a c r i t i c a l R i c h a r d s o n number, n u m e r i c a l v a l u e 10, above which a l l v e r t i c a l exchanges c e a s e d t o e x i s t . I n t h e a p p l i c a t i o n o f t h i s model t o t h e S e i n e e s t u a r y , we have s u c c e s s i v e l y u s e d r e l a t i o n s h i p s c l o s e t o t h o s e q u o t e d by Hamilton, and a l r e a d y e s t a b l i s h e d f o r t h e Gironde (De Grandpri., Nz = No

Kz =

+

KO +

1978).

U

(N1~

f(z)

+ N2)

(1 + 7 R i ) - 0 . 2 5

H U F

(K1

f(z)

+ Kz)

(1

H

+

Ri)-1-75

with : f ( z ) =

t h e n s i m p l a r e m p i r i c a l f u n c t i o n s , s u c h t h a t t h e v e r t i c a l exchange c o e f f i c i e n t s i n c r e a s e d t o w a r d s t h e s u r f a c e , o f t h e form

:

I n f a c t t h e n u m e r i c a l r e s u l t s o b t a i n e d d i d n o t d i f f e r much, and t h e a v a i l a b l e o b s e r v a t i o n s a r e t o o few t o a l l o w one t o d e t e r m i n e which r e l a t i o n s h i p i s b e t t e r . I n o u r p r e s e n t s t a t e of knowledge o f n a t u r a l phenomena, it seems t h a t one c a n a r r i v e a t s u f f i c i e n t l y a p p r o x i m a t e r e s u l t s whichever o f t h e d i f f e r e n t f o r m u l a e i s u s e d f o r t h e exchange c o e f f i c i e n t s : p r o v i d e d t h a t t h e c o e f f i c i e n t s i n c r e a s e i n v a l u e w i t h d i s t a n c e o f f t h e bottom i n t h e l o w e r p a r t o f t h e f l o w . Even l e s s i s known a b o u t t h e c o e f f i c i e n t of d i s p e r s i o n f o r t h e s e d i m e n t

e t al.

;

Kuo

(1978) a d o p t e d t h e same e x p r e s s i o n a s f o r t h e d i s p e r s i o n of s a l t .

During s u c c e s s i v e r u n s it a p p e a r e d t h a t t o o s m a l l v a l u e s o f t h i s c o e f f i c i e n t

K ' z n e a r t h e bottom c o u l d l e a d t o n u m e r i c a l i n s t a b i l i t y erosion -h

+

deposition

+

:

WsCs

K'z

In t h i s case, t h e c o n c e n t r a t i o n g r a d i e n t computed a t c e r t a i n t i m e s l e d t o spur i o u s v a l u e s a t t h e b o t t o m , b e c a u s e o f t h e e x t r a p o l a t i o n u s e d i n a p p l y i n g t h e bound a r y c o n d i t i o n s . The e x p r e s s i o n f o r K ' z w a s t h e r e f o r e s i m p l i f i e d t o t h e form

:

297 NUMERICAL SCHEME To date, the number of numerical models of this kind is small, because one has

not only all the difficulties associated with two-dimensional models (such as the outer estuary model), but a l s o that of integrating within a domain with continuously variable geometry (at the free surface), and the problem of representing the river-bed. Among the models of this type, several schematize the bed geometry to coincide with the mesh boundaries, and consider the case of a tide of small amplitude, which does not require any modification of the computation procedure as simulation proceeds (Blumberg, 1975

;

Elliott, 1976

;

Wilson, 1977

;

Kuo et al., 1978).

The resulting staircase-like appearance of the bed (fig. 4) is certainly inadequate to represent the phenomena of sedimentation

;

and the simplified schematiza-

tion employed is totally inapplicable to the Seine, where the tidal range is of the same order of magnitude as the depth.

(I,-V Variables _M_-

;th

Variables

_vu__

( i+ l P Variables

-

(i?2)"d Variables __h_-

Fig. 4. An example of a grid pattern for a multilayered model.

The inconveniences can be greatly reduced by introducing a transformation of co-ordinates whereby the computational grid becomes rectangular. Of course, this

298 c a u s e s new t e r m s t o a p p e a r i n t h e e q u a t i o n s o f hydrodynamics, which c o n s i d e r a b l y lengthen t h e calculations. T h i s t y p e of " l a y e r e d " hydrodynamic model w a s t h e r e f o r e shunned i n f a v o u r of a model u s i n g l o c a l v a l u e s , e s s e n t i a l l y si m i l a r t o t h a t p u b l i s h e d by Hamilton ( 1 9 7 5 ) . i n F i g . 5. The c o m p u t a t i o n p o i n t s f o r t h e

The c o m p u t a t i o n a l g r i d i s shown

s t r e a m components and t h e c o n c e n t r a t i o n a r e h e r e s e p a r a t e d t o a l l o w f o r a b e t t e r a p p r o x i m a t i o n of d e r i v a t i v e s by f i n i t e d i f f e r e n c e s .

Computatlon points

1:

:

F i g . 5. The f i n i t e d i f f e r e n c e g r i d .

s cs

ws

299 The method of integration is explicit, and uses centred approximations of the spatial derivatives, except for the advection term for the concentration, which is offset upstream. Unfortunately, this first-order "upstream" discretization introduces a spurious numerical dispersion, but nevertheless it is the most suitable, and the most economical in terms of computation time, for stabilizing the scheme. However, to try to reduce this effect, the dispersion term has been expressed in terms of a centred second-order scheme. The finite-difference form of the equations finally used was as follows

AS

t

= S . i+1, j

=

s t.

.

1,i

-

t

+

U2) < 0

- 'i, j

si ( U 1

t s.

s1 (U1 + U2) > 0

1-1,j

:

300

The equation of conservation of mass for the sediment has been rendered in a finite-difference form in exactly the same way as the equation of advectiondispersion for a solute, having taken into account the terminal velocity Ws, calculated at t.he same point as the concentration.

Modifications of the scheme near the boundaries The particularly interesting aspect of this numerical scheme is that it allows the relevant equations to be solved right up to the upper and lower limits of the domain, whatever their position. To do this, the computation requires values at nine grid-points surrounding the current calculation point. Near the boundaries, some of these points will lie outside the domain of integration. Accordingly, at each time-step, values of U,

S

and Cs are extrapolated to points above the surface,

and under the river-bed, using polynomial functions. For example, in fig. 6, the value So is obtained by parabolic extrapolation from the adjacent values

S1

and S 2 , and the condition of zero derivative at the

surface

~

Similary, SN+l is computed from SN-l and S using the condition of zero deriN vative at the bottom. Nevertheless, this second-order extrapolation proved insufficient to evaluate the dispersion terms near the boundaries, which correspond in fact to a second derivative

a

:

3

(

Kz az

We therefore use an extrapolation based on a polynomial of the third degree, passing through the points S

S 2 and S 3 and satisfying the condition of zero first

301 derivative at the surface.

Z

5-

\

\

\

-h-

Fig. 6. Salinity profile near the boundaries.

The calculation is identical for the salinity at the bottom, also for the stream velocity and the sediment concentration, but only at the surface. To compute the stream velocity near the bottom, Hamilton used a similar parabolic extrapolation based on the points

U

N-2'

U

N-1

and U N , whence he obtained U N + l

and

UIIllThis procedure, which is perfectly satisfactory numerically, is in practice in-

convenient, because it leads to a non-zero stream on the bottom. T h i s in turn leads to doubtful values for the stream rate one metre off the bottom, and for the total discharge in the water column (by integration of the function U ( z ) defined by interpolation).

A different technique has been introduced here, by assuming between the bed and the point suffixed N (fig. 7) a power law of the form

:

The coefficient A and a in this function are determined by keeping at point N the value of the function U ( z ) and its first derivative (obtained by the parabola UN-2,

u

~ and - ~ u,)

.

302

Fig. 7. Velocity p r o f i l e near t h e bottom.

C a l c u l a t i o n o f t h e t u r b i d i t y and i t s d e r i v a t i v e s near t h e bottom p r e s e n t s d i f f i c u l t i e s analogous t o t h o s e j u s t explained f o r t h e stream. I t i s even more important t o reproduce a c c u r a t e l y ( a s f a r a s p o s s i b l e ) t h e c o n c e n t r a t i o n c l o s e t o t h e bottom, because t h e d e p o s i t i o n f u n c t i o n uses t h i s value

:

In an o r i g i n a l v e r s i o n of t h e model a p p l i e d t o t h e Gironde (Du Penhoat and Salomon, 1 9 7 9 ) , a p a r a b o l i c e x t r a p o l a t i o n was used, and was open t o c r i t i c i s m a s f a r a s t h e accuracy of t h e r e s u l t s w a s concerned. I n o r d e r t o s i m u l a t e more c l o s e l y phenomena on a smaller s c a l e than t h e mesh s i z e , w e have here come c l o s e r ( a s f o r t h e v e r t i c a l stream p r o f i l e s ) t o t h e anal y t i c a l s o l u t i o n . We know t h a t i n a s t e a d y s t a t e , when t h e f a l l speed i s balanced by t h e v e r t i c a l d i s p e r s i o n , t h e c o n c e n t r a t i o n v a r i e s w i t h h e i g h t according t o :

We have t h e r e f o r e r e t a i n e d t h e q e n e r a l form of t h i s f u n c t i o n t o d e s c r i b e t h e

303 c o n c e n t r a t i o n n e a r t h e bottom : - B (z+h) C s ( z ) = Cs(-h) e

A f t e r f i n d i n g t h e c o n c e n t r a t i o n C s a t t h e p o i n t s s u f f i x e d N-2, N-1 and N , a par a b o l i c interpolation allows u s t o f i n d t h e derivative

& at az

the point N (fig. 8 ) .

z

-h

m

F i g . 8. T u r b i d i t y p r o f i l e n e a r t h e b o t t o m .

W e t h e n s e e k a n e x p o n e n t i a l e x p r e s s i o n which s a t i s f i e s e q u a t i o n ( l o ) and u s e s

t h e known v a l u e s CsN and __ az

.

T h i s e x p r e s s i o n t h e n g i v e s t h e v a l u e o f C s on t h e

b o t t o m , and a l s o t h e e x t r a p o l a t e d v a l u e C s

N+1T h i s p r o c e d u r e , a l t h o u g h numerically v e r y dangerous ( a t i n y e r r o r i n t h e t u r -

b i d i t y g r a d i e n t l e a d i n g t o c o n s i d e r a b l e d i f f e r e n c e s i n Cs on t h e b o t t o m , or i n i t s second d e r i v a t i v e ) , o n l y r a r e l y c a u s e d n u m e r i c a l i n s t a b i l i t y ; and w e were always a b l e t o e l i m i n a t e i t by a n a d e q u a t e p a r a m e t e r i z a t i o n o f t h e t u r b u l e n t exchange

t e r m s (principally K ' z ) .

S t a b i l i t y o f t h e scheme A s t a b i l i t y a n a l y s i s r e f e r i n g t o Von Neumann r e q u i r e m e n t s h a s been c a r r i e d o u t

by Hamilton (1975) f o r t h e cases o f a l i n e a r i z e d s y s t e m , and w i t h o u t t a k i n g i n t o a c c o u n t t h e p e c u l i a r t r e a t m e n t o f p o i n t s a t t h e b o u n d a r i e s . The c h a n g e s made h e r e t o t h e o r i g i n a l scheme a r e i n s u f f i c i e n t t o modify t h e c o n c l u s i o n s o f t h e s t a b i l i t y s t u d y , which g a v e

:

304

(+,

At < minimum

Ax

u

2gH

For the sub-critical flow dealt with in this study, the second criterion turns out to be less stringent than the third. The first and the third criteria therefore allow us to fix limits to two of the three integration steps (At, Ax, A z ) , the third being fixed by the density of results required. But of course, that the scheme is stable does not automatically imply that the solution is good, notably owing to the numerical dispersion introduced by the offsetting of certain derivatives. So, in the absence of a complete study of numerical perturbations, a very careful1 analysis of the results will have to be done.

Choice of steps for the integration A maximum depth of water of some 14 m suggests for the third criterion

:

At < 0.06 Ax It is awkward to calculate the limitation imposed by the vertical integration step, since the vertical speed is not well known a priori. We can deduce an order of magnitude for W by using the maximum rise rate (4 metres per hour) 35 W(<) 2 - 10-3

:

I

at whence

:

At < 1000 Az

All evidence suggests that the first criterion is the more stringent ponds to At

=

;

it corres-

:

1 minute for

Ax

=

1000 m (Az > 6 cm)

To unify the mesh-size and time-step of all three models, so that they might run simultaneously, the value of Ax

=

1000 m was used in this model. Accordingly,

the time-step is one minute, which has the advantage of being a simple fraction of the time-step in the vertically-integrated models, and facilitates their running in tandem. For the mesh-size Az, a value of 1.5 rn was chosen as a compromise between the desire for precision and the need to economise on computation time. It could have been very much reduced had the need been manifest.

RESULTS

Figures 9 to 12 give a picture of the circulation throughout a tidal cycle for a mean range of tide and low fresh-water flow. Particularly notable is the large area occupied by slack water at the end of the flood (fig. 9a), compared with the more abrupt reversal of the ebb (fig. llb or llc), and accompanied by a slight difference in phase between the bottom and the surface. This phenomenon is well-known in estuaries, but it appears here even

t

-5

-7

-9

1

-11

rnrn/s

i 360 350

f

* 1 m/s

340

I

330

320

310

ABSC155

KM

*

-9 -11

”

1

a

1 rn/s

360

350

330

340

320

310 KM

ABSCISS

9t

r)

1 rn/s 41

360

350

340

330

320

1

310 ABSCISS

Fig. 9. Instantaneous velocity field in the middle estuary (hour by hour)

KM

306

-7.

b

1

mm15

t +

-9 -

-7 -9

1 m/s

c

*

1m / s

11

Fig.

1

rnm/sf

10. I n s t a n t a n e o u s v e l o c i t y f i e l d in t h e m i d d l e e s t u a r y ( h o u r by h o u r , continued).

307

I l1 9

5u 7 iil5 = 3 1 -1 -3

-5

a

-7

*

-9

1m / s

-11

, _ _ J

360

350

340

330

-5

320

310 ABSCISS KM

-

-9

1 m/s

-11

Fig.

360

350

340

330

360

350

340

330

320

310 ABSCISS KM

320

310 ABSCISS KM

11. I n s t a n t a n e o u s v e l o c i t y f i e l d i n t h e m i d d l e e s t u a r y (hour by h o u r , continued).

308

11

= 9

*

-9 -11

1m / s

360

350

340

330

320

310 AB5CIS5

KM

310 ABSCISS

KM

11

' 9 1 I-

I

P Ly

I

-11 L-

Fig.

360

350

340

330

320

12. I n s t a n t a n e o u s v e l o c i t y f i e l d i n t h e m i d d l e e s t u a r y ( h o u r by h o u r , continued).

though the estuary is well mixed, under the conditions stated above. Furthermore, it is remarkable that this phase-lag at Commencement of Flood (surface lagging bottom) exists only in the lower reaches of the model, where there is a horizontal salinity gradient. It disappears further up-river, where the water is completely slack. Note also the intensity of the early flood compared with that of the ebb. The following diagram (fig. 13) represents the vectors obtained by integrating the stream over the same tidal cycle. We are well aware of the caution required in interpreting these integrated values as the residual current ; nevertheless, in this particular case the rate of the averaged stream (about 1 knot for low freshwater flow) is exceptional, and so clear that its essential character is undeniable. We may add that these results have been confirmed by measurements in the field (Avoine, 1980). This (Eulerian) residual sea-going current can be at once explained by the peculiar form of the tide in the Seine, and by the artificial works (dykes and training-banks) which have been carried out in this portion of the estuary. The very rapid rise in water level, followed by a near stand at high tide, accentuate the difference in mean water level between the flood and the ebb which one generally observes in estuaries. This difference in level, of the order of 2 metres in the region of the dykes, implies a difference in the flow cross-sections which has its repercussions on the streams, since the volume which comes in on the flood differs only slightly from that expelled on the ebb. The more the flow cross sections increase rapidly with height, the more important this effect becomes reinforcing the flood rates, and thus opposing the penetration of marine sediments into the estuary.

The submarine training-banks are very efficient in doing this, as far as sand is concerned (Salomon, 1976). As far as the fine sediment isconcerned, the dynamics are more obscure, but the

model herein described can throw some light on the problem. Simulation of the turbidity maximum It appears that, on examining measurements in the field (Avoine, 1980) that turbid accumulations exist in a quasi-permanent state in the reach between kilometres 320 and 360 from Paris, a sediment plug which is only occasionally and partially expelled from the channel. Since the Eulerian residual current is seaward, as we have just described, it does not seem that the classical explanation linked to the nodal point of density, is valid. We therefore decided to investigate, with the aid of the model, another interpretation. For this, we considered that the bed of the estuary was initially inerodable, and we imposed a turbidity of 1 g/1 everywhere. After running the model for a few tidal cycles, supposing that there had been no input of sediment at the landward and seaward boundaries, we obtained the results presented in figures 15 to 17. The fine sediments collect in a sort of nucleus, and oscillate with the tide, practi-

311

. 02

03

04

_ 0.5 a6

~

0.7

0.8

~

0.919/1)

360

350

0.2

0.3

0.4

0.5

a6

0.7

0.8

340

330

320

310 UPSTREAM

DOWNSTREAM

-1OKmd

0.9 (9, I I

360 DOWNSTREAM

350

340 k l O K m

330

4

320

310 UPSTREAM

Fig. 15. Computed instantaneous distribution of sediment concentrations (two hours between e a c h ) .

312

360

350

DOWNSTREAM

340 (--lo

330 Km

~

320

310 UPSTREAM

-!

H,

a 7 6

0.2

0.3

04

0.5

0.6

0.7

0.8

0.9(9/1)

2

1 0 -1

-2

-3 -4

-5 360 DOWNSTREAM

Fig.

350

340

330

320

310 UPSTREAM

klOKm-(

16. Computed i n s t a n t a n e o u s d i s t r i b u r i o n o f s e d i m e n t c o n c e n t r a t i o n s ( t w o hours between e a c h , c o n t i n u e d ) .

31 3

-1

5c

41

360

350

DOWNSTREAM

340

330

i1OKm

320

-4

310 UPSTREAM

?

0.2

03

04

05

a6

0.7

360 DDWNSTRFAM

350

340

330

-10 K m -

320

310 UPSiREAM

Fig. 17. Computed i n s t a n t a n e o u s d i s t r h u t i o n ot sediment concentrations (two h o u r s between each, continued).

314 c a l l y without being e x p e l l e d from t h e e s t u a r y . Figure 18 summarises t h e process ; seaward t r a n s p o r t during t h e ebb, a weak s e t t l i n g i n t h e lower reaches before being completely re-suspended,

then t r a n s p o r t up-river,

with a more g e n e r a l s e t t l i n g

owing t o t h e downward v e r t i c a l v e l o c i t i e s , t o t h e more p r o t r a c t e d s l a c k water and t h e g r e a t e r volume of water (and t h e r e f o r e of s e d i m e n t ) , and t h e p r o g r e s s i v e r e suspension by t h e ebb. I t t h e r e f o r e follows t h a t t h e Lagrangian r e s u l t a n t f o r f i n e sediment i s more o r l e s s n i l i n t h i s p a r t of t h e e s t u a r y : t h e p a r t i c l e s a r e recycled. I t can a l s o be seen t h a t t h e i r r e g u l a r i t i e s of t h e bottom a c t a s sediment traps.

CONCLUSION

The numerical model described above appears t o reproduce favourably v e l o c i t y f i e l d s and t u r b i d i t y p r o c e s s e s . Because it o p e r a t e s on instantaneous v a l u e s , it

i s p a r t i c u l a r l y s u i t e d t o reproduce u l t r a - t i d a l dynamic p r o c e s s e s , b u t not long term t r e n d s . In t h e p r e s e n t a p p l i c a t i o n t o t h e Seine e s t u a r y , examination of t h e r e s u l t s y i e l d s a p o s s i b l e i n t e r p r e t a t i o n of e s t u a r i n e sediment behaviour. According t o t h e c h a r a c t e r of t h e t i d e , and i t s importance r e l a t i v e t o t h e f l u v i a l d i s c h a r g e , a t l e a s t two mechanisms can e x p l a i n t h e formation of an e s t u a r i n e t u r b i d i t y maximum :

- d e n s i t y phenomena, which have been c l a r i f i e d many t i m e s , and which a r e cert a i n l y dominant i n s t r a t i f i e d e s t u a r i e s (small t i d e , important f l u v i a l discharge, deep) ; -

dynamic t i d a l phenomena, which we have evidenced i n t h e s p e c i f i c case of t h e

Seine, and d o u b t l e s s r e l a t i v e l y more important f o r t h e t i d e t h e r e i s b i g (and even favourably d i s t o r t e d ) , t h e f l u v i a l discharge i s small and t h e water i s shallow. Probably t h e s e two t y p e s of causes e x i s t simultaneously, with v a r i a b l e i n t e n s i t y , i n t h e Seine it seems t h a t t h e dynamic phenomenon i s v e r y important i n t h e dyked r e a c h e s , b u t it would not be impossible f o r a nodal p o i n t t o e x i s t seaward o t t h e dykes, mainly during high r i v e r flow, and t h a t t h e dynamics of accumulation t h e r e be q u i t e d i f f e r e n t , t h e more so s i n c e t h e l a t e r a l dimension would have t o be taken i n t o account.

Svmbols used B : width of t h e e s t u a r y

g

:

a c c e l e r a t i o n of g r a v i t y

h : depth

(below maximum low t i d e )

H : t o t a l depth

k

:

(from s u r f a c e t o bottom)

friction coefficient

K x , Kz : d i s p e r s i o n c o e f f i c i e n t s f o r mass ( s o l u t e ) , b e f o r e width averaging

Ka : Karman's c o n s t a n t K'x, K'z : d i s p e r s i o n c o e f f i c i e n t s f o r sediment, b e f o r e width averaging

31 5

..

h

LOW TIDE

! m '

Concentration

5

- 5O

I

h ~FlDOD(L,T.+Zh30)

(1 0

. .

-5

Fig.

18. Computed sediment behaviour d u r i n g a t i d a l c y c l e .

I-.-.I

0.5 04

,

-

03 0.2

316 I<x, Kz

:

dispersion coefficients for mass (solute), after width averaging

K'x, K ' z

:

Nx, Nz

dispersion coefficients for momentum, before width averaging

Nx,

:

dispersion coefficients for sediment, after width averaging

Nz : dispersion coefficients for momentum, after width averaging

1'

Q =

Udz

-h Ri

:

Richardson number

S

:

salinity

t

:

time

U , W : horizontal and vertical components of velocity

V*

:

friction velocity

Ws

:

settling velocity

x, z

:

z,

bed roughness

5

:

:

horizontal and vertical axis

surface elevation

P : density

p

: p

T

:

averaged over H

shear stress

REFERENCES Avoine, J . , 1980. S.A.U.M. de l'estuaire de la Seine. Etudes hydroskdimentaires. Internal report, university of Caen (France). Bowden, K.F. and Hamilton, P., 1975. Some experiments with a numerical model of circulation and mixing in a tidal estuary. Estuarine and coastal marine science, 3

:

281-301.

Blumberg, A.F., 1975. A numerical investigation into the dynamics of estuarine circulation. Chesopeake bay institute, technical report 91. Blumberg, A.F., 1978. The influence of density variations on estuarine tides and circulations. Estuarine and coastal marine science, 6

:

209-215.

Cormault, P., 1971. Determination experimentale du debit solide d'krosion de s6diments fins cohesifs. Fourteenth congress of I.A.H.R., 4

:

D2.

De Grandpr6, C., 1979. ModBle bidimensionnel en temps reel de la circulation verticale estuarienne. Application Du Penhoat, Y . and Salomon, J . C . ,

a

la Gironde. Oceanologica acta, 2

:

61-68.

1979. Simulation numerique du bouchon vaseux en

estuaire. Application 2 la Gironde. Oceanologica acta, 2 Dyer, K., 1973. Estuaries

:

:

253-260.

a physical introduction. John Wiley, New York.

Elliott, A.J., 1976. A numerical model of the internal circulation in a branching tidal estuary. Chesapeake bay institute, special report 54. Festa, J.F. and Hansen, D.V., 1976. A two-dimensional numerical model of estuarine circulation

:

the effects of alternating depth and river discharge. Estuarine

and coastal marine science, 4

:

309-323.

317 Hamilton, P., 1975. A numerical model of the vertical circulation of tidal estuaries and its application to the Rotterdam waterway. Geophysical journal of the royal astronomical society, 40

:

1-21.

Harrison, A.J.M. and Owen, M.W., 1971. Siltation of fine sediments in estuaries. Fourteenth congress of I.A.H.R., 4

:

D1.

K u o , A., Nichols, M. and Lewis, J., 1978. Modeling sediment movement in the turbi-

dity maximum of an estuary. Virginia institute of marine science, bulletin 111. Munk, W.H. and Anderson, E.R., 1948. Note on the theory of the thermocline. Journal of marine research, 7

:

276-295.

Pritchard, D.W., 1960. The mixing and movement of contaminants in tidal estuaries. In proceedings of the first international conference on waste disposal in the marine environment, university of California at Berkeley, Perganion press. Salomon, J.C., 1976. Modele mathematique de la propagation de la maree en estuaire et des transports sableux associes. Application aux estuaires de la Loire et de la Seine. Thesis, university of Brest (France). Wilson, B.W., 1966. Note on surface wind stress over water at low and high wind speed. Journal of geophysical research, 65

:

3377-3382.

Wilson, R.E., 1977. A model of dynamics in the lower potomac river estuary. Chesapeake science, 18

:

177-187.

This Page Intentionally Left Blank

319

NUMERICAL SIMULATIONS OF SALINITY, TURBIDITY AND SEDIMENT ACCUMULATION IN THE SCHELDT ESTUARY

W. BAEYENS’, Y. ADAM2, J.P. MOMMAERTS2 and G. PICHOT’

’Dienst Analytische Scheikunde, Vrije Universiteit Brussel, Brussels (Belgium) 2Beheerseenheid Model Noordzee en Schelde, Ministerie van Volksgezondheid en Leefmilieu, Brussels (Belqium)

ABSTRACT In order to simulate the physical behaviour of the Scheldt estuary, a hydrodynamic and a dispersion model have been devised. Both models are two dimensional, vertically integrated, and are solved numerically with a multioperational finite difference scheme, using a grid of 300 x 300 meters. The hydrodynamic model, which allows the simulation of instantaneous water levels and mean velocities over depth is controlled at the downstream boundary by time-varying water levels and at the upstream boundary by the river flow. The dispersion model, which predicts the evolution of salinity and turbidity in the water column and the sedimentary budget at the bottom, is controlled at the upstream and the downstream boundary by timevarying salinity values dependent on the river flow and by time-varying turbidity values averaged over the river flow. An increase of the river flow causes a downstream shift of the brackish water zone. Due to the influence of the salinity on flocculation and therefore on sedimentation of suspended material, the sedimentation zone is also shifted downstream. This results in higher turbidities and a lower sedimentary budget at the bottom in the upstream part of the estuary. Under average hydrodynamic conditions the computed sedimentary budget integrated over a tidal cycle at the different grid points agrees well with observations of mud accumulation in the same area.

INTRODUCTION The physical behaviour of the Scheldt estuary i.e. the flow of water, salts and particulate matter, has a great influence on the dynamics of the ecosystem (growth of living organisms, transport of heavy metals, etc.). For instance, the heterotrophic bacterial activity is very high in the upstream part of the Scheldt estuary but drops dramatically at about 60 km from the river mouth

(G.

Billen et

320 al., 1977). This drop has been explained by the effect of increased salinity which causes (1) flocculation of suspended matter and organic matter and subsequent sedimentation, (2) inhibition of the activity of the fresh water bacteria. Considering the dynamics of phytoplankton, primary production is controlled by the incident light and the transparency of the water which can be inferred from the turbidity. As soon as the intensity of the incident light is sufficient to ensure photosynthesis, the development of diatoms starts at the mouth of the estuary where the turbidity is minimum

(0.

Beckers and R. Wollast, 1977). During summer

the area of development progressively moves upstream as a result of an increasing light intensity and an exhaustion of silica in the downstream part of the estuary. It is obvious from the few examples mentioned above, that a sound understanding of estuarine physics is a prerequisite for all concerned with the dynamics of estuarine ecosystems. Unfortunately, the complex geometry of the estuary (ebb and flood channels, tidal flats, meanders) as well as non-tidal fluctuations of the hydrodynamic boundaries (river flow and tidal amplitude range from 10 m3/s to

400 m3/s and from 2.96 m to 4.42 m respectively) make the description and prediction of the velocity field and hence of the dispersion of salinity and turbidity very difficult. Moreover, the behaviour of the turbidity is strongly depending on direct and indirect interactions with the other physical variables. Flocculation of the fine grained material supplied by the river starts as soon as the salinity exceeds

1

This flocculation zone has no fixed position but moves to and fro during

a tidal cycle. In periods of high (low) river flow and decreasing (increasing) tidal amplitude at the mouth, the tidal flocculation zone is shifted downstream (upstream). Local hydrodynamic conditions govern the settlinq down of the flocculated material. Considering the annual amount of material accumulating at tlfe bottom in various areas of the Scheldt estuary (Wollast, 1977), two distinct sedimentation zones can be defined. In the area Rupelmonde (km 90) - Doel (km 60) the accumulation amounts to 2000

lo3 tons/year

Hansweert (km 35) it amounts to 220

lo3

and in the area Doel (km 60) -

tons/year (these values only reflect the

balance of sedimentation and erosion). In order to gain better insight in processes such as flocculation, sedimentation and erosion and consequently in the interactions between the physical variables, we decided to construct a mathematical model which should enable us to simulate these phenomena and to predict the evolution in space and time of the selected variables. It should also allow to calculate local sedimentary budgets.

MATHEMATICAL EQUATIONS

:

HYDRODYNAMICS

In shallow seas as well as in well-mixed estuaries it is generally sufficient to consider depth-averaged variables. The momentum and continuity equations governing the dynamics of the fluid after integration over the depth become

:

321

3H

*

R . VH

- - t

at

. v

-

=

H

with :

''

-h

=

0

v dz

-

v e l o c i t y vector V -

mean v e l o c i t y v e c t o r over depth

Vh

gradient i n horizontal directions

f

Coriolis factor

e

u n i t vector i n t h e v e r t i c a l d i r e c t i o n

Ll

gravitational acceleration

5

s u r f a c e water l e v e l r e l a t i v e t o t h e r e f e r e n c e plane

h

d i s t a n c e from t h e r e f e r e n c e p l a n e t o t h e bottom

H

t o t a l depth

V

viscosity coefficient

Ts, Tb s u r f a c e and bottom stresses P

f l u i d density

D E F I N I T I O N OF THE CONTROL PARAMETERS

The t h r e e c o n t r o l parameters V,

T

'rb i n equation

and

A s t h e v i s c o s i t y term i n c l u d e s i n f a c t two e f f e c t s

:

( 1 ) need t o be s p e c i f i e d .

on t h e one hand eddy

v i s c o s i t y caused by e r r a t i c s m a l l s c a l e motions and on t h e o t h e r hand shear t u r b u l e n c e due t o t h e inhomogeneous v e r t i c a l v e l o c i t y f i e l d , t h e o v e r a l l v i s c o s i t y c o e f f i c i e n t ( V ) i s t h e sum of t h e eddy (V

V V

1 . According t o Kolmogorov's t h e o r y ,

(V )

e

V

and t h e s h e a r v i s c o s i t y c o e f f i c i e n t equals 5 m 2 / s ,

while an e s t i m a t i o n of

on t h e b a s i s of Nihoul's work (Nihoul, 1975) gave a value of 20 m 2 / s .

Hence

e q u a l s about 2 5 rn2/s. The s h e a r s t r e s s a t t h e s u r f a c e ( T

can become s i g n i f i c a n t i n p e r i o d s of very

s t r o n g winds, b u t i s g e n e r a l l y very small i n e s t u a r i e s compared with t h e shear s t r e s s a t t h e bed ( 7 ) . Therefore T i s n o t included i n t h e model. b By d e f i n i t i o n , bottom stress and s h e a r v e l o c i t y (V a r e r e l a t e d a s follows k

:

However, i n two dimensional, v e r t i c a l l y i n t e g r a t e d models, t h e s h e a r stress must be i n f e r r e d from t h e mean v e l o c i t y over depth. Often t h e following expression

i s used Tb

=

:

P D V ' I

1 1 1

(5)

where D i s a drag c o e f f i c i e n t , dependent on t h e roughness of t h e channel bed. I n

322 h y d r a u l i c engineering e x t e n s i v e use i s made of Chezy's formulation :

.D

=

(6)

g/C2

with C t h e Chezy c o e f f i c i e n t . From v e r t i c a l v e l o c i t y p r o f i l e s and corresponding s h e a r v e l o c i t i e s ( s e e SOURCES AND S I N K S ) , w e deduced f o r t h e bottom of t h e Scheldt e s t u a r y a t y p i c a l f r i c t i o n c o e f f i c i e n t (Manning's n) of 3.3

lo-*.

NUMERICAL METHOD AND BOUNDARY C O N D I T I O N S

The p a r t i a l d i f f e r e n t i a l e q u a t i o n s (1) and ( 2 ) a r e approximated by t w o f i n i t e d i f f e r e n c e e q u a t i o n s , one e x p l i c i t t h e o t h e r i m p l i c i t , used a l t e r n a t i v e l y f o r a s t e p by s t e p s o l u t i o n i n time. The advantage of such a procedure i s t h a t over a whole time s t e p t h e d i f f e r e n t t e r m s i n e q u a t i o n s (1) and ( 2 ) are e i t h e r c e n t r a l i n time o r averaged over t h a t time i n t e r v a l , allowing less s e v e r e s t a b i l i t y c o n d i t i o n s concerning t h e time s t e p . This scheme i s v e r y c l o s e t o L e e n d e r t s e ' s (Leendertse e t a l . ,

1971a) multi-

o p e r a t i o n method. Only t h e advection t e r m s are c a l c u l a t e d on a h i g h e r time l e v e l by an i t e r a t i v e procedure, and t h e v i s c o s i t y term, which i s added t o t h e momentum equation i s c a l c u l a t e d e x p l i c i t l y . The c a l c u l a t i o n s a r e c a r r i e d o u t with a 300 x 300 m mesh-size

g r i d (Figure 1 ) .

The downstream boundary i s s i t u a t e d a t 45 km f r o m t h e mouth, t h e upstream boundary

a t 1 2 0 km from t h e mouth. From km 65 on, t h e S c h e l d t becomes s o narrow (about

500 t o 600 m e t e r s ) , t h a t we have " s t r a i g h t e n e d " t h e r i v e r , l e a v i n g i t s crosss e c t i o n a l geometry (width, depth, t i d a l f l a t ) unchanged. The g l o b a l t i m e s t e p e q u a l s 2 minutes. AS one of our o b j e c t i v e s r e q u i r e s a mean hydrodynamic s i t u a t i o n , t h e following

boundary c o n d i t i o n s a r e used :

- Downstream

:

- Upstream

a mean (Q

:

a mean i n p u t t i d e =

80 m 3 / s ) ,

a high ( Q = 350 m 3 / s )

and a low (Q = 1 m 3 / s )

r i v e r flow The i n i t i a l c o n d i t i o n s ( v e l o c i t i e s a r e z e r o and t h e water l e v e l e q u a l s t h e low water l e v e l a t t h e downstream boundary) do n o t have any i n f l u e n c e on t h e f i n a l r e s u l t s , because s i m u l a t i o n s a r e c a r r i e d o u t u n t i l a c y c l i c p a t t e r n ( g e n e r a l l y a f t e r t h r e e t i d e s ) i s obtained.

RESULTS

In o r d e r t o s i m u l a t e f l o o d i n g of t i d a l f l a t s d u r i n g r i s i n g t i d e and subsequent r e t r e a t i n g of t h e land-water boundary d u r i n g ebb, an adapted numerical procedure was used. To i l l u s t r a t e t h i s procedure, t h e v a r i o u s d r y ( c i r c l e s ) and wet g r i d p o i n t s ( i n t e r s e c t i o n s ) a t low w a t e r a r e r e p r e s e n t e d on F i g u r e 1.

323

Fig. 1 : The numerical g r i d a t high water (on t h e l e f t ) and a t low water (on t h e r i g h t ) . The d r y g r i d p o i n t s a t low water a r e i n d i c a t e d by c i r c l e s . The agreement between measured and computed t i d e l e v e l s i s very qood. But achieving a good agreement between measured and computed v e l o c i t i e s , and p o s s i b l y a d j u s t i n g t h e model a c c o r d i n g l y , i s of course more important f o r c o n s t i t u e n t t r a n s p o r t s i m u l a t i o n s . This i s , however, a very d i f f i c u l t t a s k , because one needs r e l i a b l e d a t a on i n s t a n t a n e o u s mean v e l o c i t i e s over depth, f o r t h e hydrodynamic boundary c o n d i t i o n s used i n t h i s model (mean i n p u t t i d e , mean r i v e r f l o w ) . Although

w e were n o t able t o compare t h e c a l c u l a t e d v e l o c i t i e s with f i e l d d a t a , two f a c t s suggested t h e c a l c u l a t e d v e l o c i t y f i e l d was r e a l i s t i c : ( 1 ) with a comparable hydrodynamic model of Jamaica Bay, Leendertse e t a l .

(1971b) observed a f a i r l y

good agreement between t h e i r c a l c u l a t e d and measured d a t a ; (2) w e c a l c u l a t e d t h e water m a s s t r a n s p o r t through f o u r c r o s s s e c t i o n s and found t h a t agreement with observed d a t a was good (Ministere des Travaux P u b l i c s , personal communication) and t h a t t h e law of conservation of t o t a l f l u i d mass was s a t i s f i e d . From t h e computed v e l o c i t y p a t t e r n s a t d i f f e r e n t moments of t h e t i d e , it i s c l e a r t h a t most of t h e time very high v e l o c i t i e s occur i n t h e channels, whereas i n t h e shallow p a r t s , t h e v e l o c i t i e s a r e much lower, causing l a r g e v e l o c i t y g r a d i e n t s on a l o c a l s c a l e . Small v e l o c i t i e s a r e only observed h a l f an hour before and a f t e r t h e t u r n of t h e c u r r e n t . The c a l c u l a t e d v e l o c i t y p a t t e r n one hour before

324 high water and a t t h e moment of c u r r e n t i n v e r s i o n i s shown on Figure 2 .

.Fig. 2 : The c a l c u l a t e d v e l o c i t y p a t t e r n one hour b e f o r e high water (on t h e l e f t ) and a t t h e t u r n of t h e c u r r e n t (on the r i g h t ) . F i n a l l y , v e l o c i t y p a t t e r n s were c a l c u l a t e d f o r t h e t h r e e d i f f e r e n t r i v e r flows Very small d i f f e r e n c e s i n l o c a l v e l o c i t i e s were observed, confirming t h a t t h e instantaneous v e l o c i t i e s a r e almost e n t i r e l y due t o t h e t i d a l a c t i o n .

MATHEMATICAL EQUATIONS : DISPERSION

The e v o l u t i o n of suspended s o l i d m a t t e r and s a l i n i t y can be described by t h e i r mass conservation equation. This equation i s i n t e g r a t e d over depth.

. __ am at with

t

: P

R

vh .

HIP

=

D c1

+

HR

t

(7)

HS

c o n c e n t r a t i o n of c o n s t i t u e n t P i n t e r a c t i o n term (production-destruction

r a t e o f P by i n t e r a c t i o n s

with o t h e r c o n s t i t u e n t s ) S

source - s i n k term ( i n p u t - o u t p u t r a t e of P)

D c1

diffusion t e r m

325 As the velocity field is known, only the terms in the right hand side of equation ( 7 ) must be specified

:

DIFFUSION (Da) The global diffusion takes into account eddy diffusion and shear diffusion. The eddy diffusion coefficient ( A ) can be calculated in a way analogous to the eddy viscosity coefficient and equals 5 m2/s. It appears from the studies of Elder (1959) and Nihoul et al. (1975) that the magnitude of shear diffusion is proportional to the velocity and depth and that it acts in the same direction as the velocity vector. Hence, we expressed the shear diffusion coefficient (1 ) as

.

As

Q

:

VH G / C

The global diffusion coefficient ( A ) is then the sum of A and As,

(8)

which is isotropic,

which is anisotropic.

INTERACTIONS (HR) While the salinity is a passive constituent (other constituents have no influence on its evolution), biological and chemical reactions could produce or eliminate certain specific compounds of the suspended matter. This would result in a substantial modification of the solid matter composition in time and space. Such a modification, however, was not observed by Wollast (1973). His results, on the contrary, indicate a remarkably constant composition in the major elements. As the concentration of suspended matter is not affected by such interactions, these terms were not considered in the model.

SOURCES AND SINKS (HS)

This term includes sewage and industrial outfalls as well as interactions with the bottom sediments. The outfalls are actually spread over a large part of the upstream estuary. As the simulation model cannot represent channels with a dimension smaller than

the mesh-size, the lateral inputs are grouped at four locations. At each discharge point the flux of suspended matter, based on regular surveys, equals 250 kg particulate matter/minute. The interaction between the water column and the bottom involves erosion and sedimentation. The sedimentation flux depends on the sedimentation velocity of the particles and the turbulence or shear stress at the bottom. When a viscous bottom layer is maintained on the estuarine floor, the flux of material is simply due to the slow sedimentation of particles. To allow for the periodic disruption of the viscous layer and ejection of sediments, a correcting factor, which is

326 related to the degree of sublayer instability, is introduced

with

:

S

sedimentation flux

U

sedimentation velocity

P

suspended matter concentration or turbidity

:

H

total depth

Tb

bottom shear stress

T

limiting shear stress above which no deposition takes place

Studies on flocculation processes, particle size distribution and sedimentation velocities (Wartel, 1971b

;

Migniot, 1968) allowed us to derive the following

relation between 0 (meters/minute) and salinity (m S )

. .

U

=

1.6 10

-*

U

=

1.6 10

-2

-

1.1 10

-' (10 -

Sa1.)/8

:

Sal. >

10 m S

(10)

Sal. <

10 m S

(11)

T o express the bottom shear stress or the shear velocity

- both of which are

related according to equation (4) - in terms of the mean velocity over the depth, the vertical velocity profiles must be known. In the Scheldt river Wartel (1971a) found generally a very good agreement between the vertical velocity distribution and the Von Karman-Prandtl equation. Ratio's of shear velocity

:

mean velocity

over depth, lay for a broad range of mean velocities (0.14 m/s to 1.60 m/s) between 0.06 and 0.07. This mean that in first approximation the ratio shear velocity

critical shear velocity can be replaced by mean velocity

.

Tb/TC

=

with V

a

:

:

critical mean velocity

;

(12)

II~ll2/V~

about 0.7 m/s, based on simultaneous measurements of velocity and turbidity

at 1 m above the bottom (Wartel, 1972). Similar to the sedimentation flux, the erosion flux may be expressed as

. s

=

with

:

--M

( 1 --Tb/ Te)

T

b

>

7

S

erosion flux

M

mass of sediments removed per unit bed area and per unit time

7

critical erosion velocity

After replacing T

:

(13)

by Te relation (12) is also valid here. A critical erosion ve-

locity of 0.7 m/s has been used. Data for M were found in the literature (Cormault, 1971). For a similar sediment concentration (200 g/l) a value of 12 g/m2/minute looked realistic. The adjustment of the model concerning the mean sedimentary budget (see RESULTS - SEDIMENTARY BUDGET) necessitated, however, different

sections.

M values for downstream and upstream

327 NUMERICAL METHOD AND BOUNDARY CONDITIONS

The numerical scheme used t o s o l v e equation ( 7 ) i s a l s o an e x p l i c i t - i m p l i c i t m u l t i o p e r a t i o n method. The numerical g r i d i s t h e same as f o r t h e hydrodynamical c a l c u l a t i o n s , b u t t h e model i s now bounded upstream a t Rupelmonde (km 9 0 ) . The g l o b a l t i m e s t e p i s i n c r e a s e d t o 8 minutes. C a l c u l a t i o n s a r e c a r r i e d out u n t i l a c y c l i c p a t t e r n i s obtained ( i n g e n e r a l a f t e r t h r e e t i d a l p e r i o d s ) . The computation s t a r t s w i t h an i n i t i a l s a l i n i t y and t u r b i d i t y g r a d i e n t , i n o r d e r t o reduce t h e number of t i d e s . According t o f i e l d measurements c a r r i e d o u t a t t h e downstream and upstream boundary o f t h e model, w e imposed a t each boundary t h e following conditions :

- time-varying s a l i n i t y values dependent on t h e r i v e r flow (both v a r i a b l e s Nere inversely correlated)

-

;

time-varying t u r b i d i t y values averaged over t h e r i v e r f l o w (both v a r i a b l e s showed no c o r r e l a t i o n ) .

RESULTS

- WATER COLUMN

The agreement between c a l c u l a t e d and measured s a l i n i t y p r o f i l e s f o r a r i v e r flow of 80 m3/s a t km 45, 55 and 65 from t h e mouth i s f a i r l y qood (Figure 3 ) .

I

I

Fig. 3 : C a l c u l a t e d and measured s a l i n i t y p r o f i l e s , a t t h r e e l o c a t i o n s , f o r a mean and a high r i v e r f l o w . The s a l i n i t y p r o f i l e s f o r a r i v e r flow of 350 m 3 / s lower than f o r a mean r i v e r flow (80 m 3 / s ) , b r a c k i s h water: zone.

a t t h e same l o c a t i o n s a r e much

due t o a downstream s h i f t of t h e

328

0

2

4

6

Fiq. 4 : Calculated t u r b i d i t y p r o f i l e s ,

a

10

12

a t two l o c a t i o n s , f o r a mean and a high

r i v e r flow.

F i g . 5 : The c a l c u l a t e d iso-concentration curves of s a l i n i t y (on t h e l e f t ) and of t u r b i d i t y (on t h e right) a t l o w water f o r a mean r i v e r flow.

329

Fig. 6 : The calculated iso-concentration curves of salinity (on the left) and of turbidity (on the right) at high water for a mean river flow. The calculated turbidity profiles for a river flow of 80 m3/s at 55 and 65 km from the mouth, are on the other hand much lower than those obtained f o r a high river flow (Figure 4). A s ( 1 ) the boundary conditions for the turbidity are identical for both river flows, and ( 2 ) the instantaneous velocities show only minor differences, the much higher turbidity profiles observed in the case of high river flow at 55 and 65 km from the mouth are due to a downstream shift of the brackish water zone, and the influence of the salinity on flocculation and therefore on sedimentation of suspended material. The sedimentation zone is thus also shifted downstream resulting in 'higher turbidities in the upstream area. The spatial patterns of salinity and turbidity respectively obtained at low (Figure 5) and at high water (Figure 6 ) illustrate the quite different behaviour of both variables. As the salinity is a passive variable, small gradients are

locally observed. On the contrary, large variations in erosion-sedimentation fluxes between neighbouring points, cause very large turbidity gradients on a local scale, which are not at all compensated by turbulent diffusions. Furthermore, whilst the salinity is strongly correlated with the tide, the turbidity shows no clear relationship with the tide because different inputs are involved as well as local interactions with the bottom.

330 RESULTS - SEDIMENTARY BUDGET A few tests on the sensitivity of the control parameters - 0, Tc, Te and M -

revealed that the yield coefficient M must be modified to give better agreement with the mean annual sedimentary budget estimated by Wollast (1977). By assigning lower M values to the upstream sediments than to the downstream sediments, we obtained the following results

:

TABLE 1 Mean annual sedimentary budget Upstream area

Downstream area

(Wollast, 1977)

120 kg/m2year

2 kg/m2year

Model

90.6 kg/m2year

- 1.7 kg/m2year

The variability in the nature of the bottom sediments (in the upstream area, for example, the Scheldt is incised in the Boom clay which is very cohesive) probably explains the differences for the erosion yield coefficient (Hjuistrom,

1935).

ii

I 1

k

I

-

0'

745'

Fig. 7 : The sedimentary budget distribution, integrated over a tidal cycle, for a mean river flow (on the left) and for a high river flow (on the right).

331 The i n t e g r a t e d sedimentary budget over a t i d a l p e r i o d i n t h e various g r i d p o i n t s f o r a mean r i v e r flow and a r i v e r flow of 350 m 3 / s

(Fiqure 7 ) c l e a r l y suggest

n e t e r o s i o n i n t h e channels and sedimentation i n t h e shallow a r e a s . The lower sedimentary budqet obtained f o r high r i v e r flow, i s caused by a downstream s h i f t of t h e f l o c c u l a t i o n zone a s explained i n t h e previous s e c t i o n for the turbidity profiles. A t an a r b i t r a r i l y choosen g r i d p o i n t we compared t h e e v o l u t i o n of t h e sedimentary

budget d u r i n g a t i d a l p e r i o d f o r a mean r i v e r flow, with t h a t obtained f o r a high r i v e r flow (Figure 8 ) . A s soon a s t h e v e l o c i t y f a l l s beneath t h e c r i t i c a l sediment a t i o n v e l o c i t y , t h e budget i n c r e a s e s , b u t a t a much f a s t e r rate i n t h e case of a mean r i v e r flow. When t h e v e l o c i t y exceeds t h e c r i t i c a l e r o s i o n v e l o c i t y t h e budget d e c r e a s e s i n a s i m i l a r way f o r b o t h r i v e r flows. F i n a l l y , a t t h e choosen g r i d p o i n t , t h e i n t e g r a t e d budget shows a n e t e r o s i o n even f o r t h e lower r i v e r flow.

sedimentary budget 5 0

-

(glrn')

- 0,.80 -- 0, , '

/

400

/

-.-

m3n

"Sl0Cit)r

(mi%)

350 m h

- - --.

V 1.0-

\

\

-1.4-

\ \

--a00

\

'----

.-loo0

Fig. 8 : The e v o l u t i o n of t h e sedimentary budget during a t i d a l c y c l e , a t an a r b i t r a r i l y choosen g r i d p o i n t , f o r a mean and a high r i v e r flow.

CONCLUSIONS The mathematical model p r e s e n t e d h e r e i s capable of simulatinq t h e e v o l u t i o n of s a l i n i t y , t u r b i d i t y and t h e sedimentary budget a t t h e bottom i n a r e a l i s t i c

, T c , M) i n t h e e t u r b i d i t y model, agreed f a i r l y w e l l with those determined by f i e l d measurements.

way. The v a l u e s a t t r i b u t e d t o t h e c o n t r o l parameters ( G ,

T

Q u i t e d i f f e r e n t t u r b i d i t y p r o f i l e s and sedimentary budgets a t t h e bottom were obtained f o r l o w and high r i v e r flow due t o t h e i n f l u e n c e of t h e s a l i n i t y on

332 flocculation and sedimentation. Although this model is open to improvement (for example, the vertical dimension and the nature and characteristics of the bottom are not included), it can yet provide valuable information for similar studies as well as for models involving biological processes.

REFERENCES Beckers, 0. and Wollast, R., 1977. Comportement de la silice dissoute dans l'estuaire de 1'Escaut. In : J.C.J. Nihoul and R. Wollast (Editors), 1'Estuaire de l'bscaut, Vol. 10, Projet Mer. La Politique Scientifique, Bruxelles, pp. 153-170. Billen, G., Smitz, J., Somville, M. and Wollast, R., 1977. Degradation de la matiere organique et processus d'oxydo-reduction dans l'estuaire de 1'Escaut. In : J.C.J. Nihoul and R . Wollast (Editors), 1'Estuaire de l'Escaut, Vol. 10, Projet Mer. La Politique Scientifique, Bruxelles, pp. 102-152. Cormault, P., 1971. Determination experimentale du debit solide d'erosion de sediments fins cohesifs. Proc. 14th Congress IAHR, Paris, 4 : 9-16. Elder, J.W., 1959. The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech., 5 : 544. Hjulstrom, F., 1935. Studies of the morphological activity of rivers as illustrated by the river Fyris. Bull. Geol. Inst. Uppsala, 25 : 221-527. Leendertse, J.J. and Gritton, E.C., 1971a. A water-quality simulation model for well mixed estuaries and coastal seas, V o l . 11, Computational procedures. The Rand Corporation, 53 pp. Leendertse, J.J. and Gritton, E.C., 1971b. A water-quality simulation model for well mixed estuaries and coastal seas, Vol. 111, Jamaica Bay simulation. The Rand Corporation, 73 pp. Migniot, Cl., 1968. Etude des proprietes physiques de differents sediments trPs fins et de leur comportement sous des actions hydrodynamiques. La Houille Blanche, 7 : 591-620. Nihoul, J.C.J., 1975. Hydrodynamic Models. In : J.C.J. Nihoul (Editor), Modelling of Marine Systems, Oceanography Series No 10. Elsevier, Amsterdam, pp 41-67. Nihoul, J.C.J. and Adam,Y., 1975. Dispersion et sedimentation autour d'un point de deversement en mers peu profondes, J. Hydr. Res., 13 : 171. Wartel? S., 1971a. Bepalen van wrijvingssnelheden tegen de bodem op basis van stroomsnelheidsverticalen. Koninklijk Belgisch Instituut voor Natuurwetenschappen, Brussels, 21 pp. Wartel, S., 1971b. Studie van het flokulatieproces op Schelde sedimenten, Koninklijk Belgisch Instituut voor Natuurwetenschappen, Brussels, 15 pp. Wartel, S., 1972. Sedimentologisch onderzoek van de opbouw van hetischelde-estuarium. Doctorate's thesis, Leuven, V o l . 111, 188 pp. Wollast, R., 1973. Origine et mecanisme de l'envasement de l'estuaire de 1'Escaut. Rapport de Synthese, Ministere des Travaux P u b l i c s , Borgerhout, 140 pp. Wollast, R., 1977. Transport et accumulation de polluants dans l'estuaire de 1'Escaut. In : J.C.J. Nihoul and R. Wollast (Editors), 1'Estuaire de l'Escaut, V o l . 10, Projet Mer. La Politique Scientifique, Bruxelles, pp. 191-218.

333

MATHEMATICAL MODELLING OF RECENT SEDIMENTOLOGY IN THE SHALLOW WATERS ALONG THE BELGIAN COAST

Y. ADAM, W. BAYENS, J.P. MOMMAERTS, G. PICHOT

Unite de Gestion du Mod&le Mathgmatique de la Mer du Nord et de 1'Estuaire de 1'Escaut

INTRODUCTION

The winning of sand and gravel from the seabed has increased, for the last few years, in a very spectacular manner.

The origin of this fast growth rate is to be

found, on the one hand, in the increasing demand of the building industry (public works, highways, harbours) and, on the other hand, in several factors inhibiting further developments of material winning in land quarries (conflict with other land uses like urbanization, environmental protection policies,

...)

In 1974, the European production of sand from the continental shelf amounted to

50 millions tons per year.

It is expected to increase continuously within the

next twenty years by a factor of 5 to 20. The winning of sand (and gravel to a lesser extend) may bear some influence on the marine environment, which must be carefully studied in order to define a working strategy that causes minimal damage to the coastal ecosystem. The complexity of the ecosystem dictates an integrated study from geophysical and from ecological point of views. The present study aims at evaluating, by a simulation with mathematical models of physical phenomena, the impact of the foreseen maximum winning on the coastal ecosystem.

The present official authorizations for winning operations are valid for

3 years, and for a maximum amount of 10.10.6 Tons/year.

The final purpose of the

whole study is to assess whether the authorizations may be renewed and under what conditions.

PRESENT STATE OF KNOWLEDGE

Two zones of the Belgian shelf are presently subject to winning of sand (Fig. 1)

- A first zone in the region of the Flemish Banks (divided into 2 parts), where the depth is shallow and the topography very complex.

This zone was originally

defined on the basis of biological considerations (no known occurence of fish

nurseries).

Authorizations have been delivered for winning only in the western

part.

- A second zone offshore of the harbour of Zeebrugge, at the boundary between a sandy and a rather muddy region, on a deeper sand bank, with a lot of ripples. The present state of knowledge on the marine environment in the region of the Belgian continental shelf is based upon the results of the National

R-D Programme on

Environment, Project Sea. The sediments are particularly well known, thanks to a very dense sampling net. Data on granulometry, composition (sands, gravel, carbonates, shell debris, organic matter, etc...)as well as mineralogical analyses of fine fractions metal content have been put on map.

and the heavy

The map in Fig. 2 shows that excepted for the

Wandelaar, fractions inferior in size to 74 microm represent only a small part (0 to 1

%)

of the sands involved in the exploitation.

The coarser sands are found more towards the open sea. The Northern extremity of the sand banks in zone 1 and, more specifically the Oost Dijk Bank, show a content in coarse sand which can amount to 80

%

of the total.

Also the distribution of nutrients in the interstitial waters of these sediments and the microbiological mechanisms which account for the observed profiles are relatively well known. As far as the fauna of the sites is concerned, only few direct informationareavailable.

POSSIBLE IMPACT ON THE MARINE ENVIRONMENT

Winning of sand from the seabed can have a series of consequences out of which the major ones are

:

- Geological and geophysical modifications The bottom topography and the structure of the sediments will be changed by an intensive winning.

In some places, taking into account the huge amount of mate-

rial to be extrated, one can compute that the depth will be increased by half a meter, which is not negligible in a shallow sea where the average depth is

12 meters and the tidal amplitude around 4 meters. As a consequence of the changes in the topography, changes will occur in the distribution of currents (instantaneous and residual) and in the erosion properties of the flow.

An increase of erosion due to winning may cause the vanishing

of the bank, whilst a decrease could indicate that the bank is steadily restoring and is thus stable. measurement

These changes cannot be evidenced but by a long term field

programme.

- Biological consequences The primary production depends on the water transparency.

The sand winning tech-

...)

niques release a lot of fine suspensions (mud, fine sands,

that increase

1

the

B e l g i a n C o o s1

u3

O l s l r l b u t l o n 01 d ep t h s a l o n g

m

./

m

Figure1

336 the turbidity and modify the effect of light on the system. Nutrients are recycled in the upper layer of the sediments

:

the amount of this

flux is so important that is has been computed that the nutrient content of the seawater would be completely exhausted in one week (in the region of interest) if this flux would vanish.

The benthic communities could also be destroyed if the

winning takes place over a too large area, preventing recolonization. This survey of the possible effects of sand winning shows that the evolution of the system where exploitation takes place must be carefully studied, using mathematical models and field measurements, before a definitive decision could be taken on their continuation and possible extension.

The effects of sand winning on the

behaviour of the planctonic ecosystemn are delt with in another paper (Adam 8 al, 1980).

WORKING ASSUMPTIONS

In order to eliminate, in a first approach, all the effects of sand winning that would bear a negligible influence on the coastal ecosystem, one has deliberately chosen, in most questions not accurately answered in the present state of knowledge, the most unfavourable assumption.

Many of these assumptions are necessary to fill

gaps in scientific,technical or economic knowledge concerning this kind of (rather new) industrial activity.

Some of the assumptions may appear to be false, after a

thorough analysis of the results of the simulations.

Annual amount of sand extracted 6

A maximum winning rate of 5.10 ton/year, evenly distributed on the 20 km2 of the 6

first zone, and of 5.10 ton/year on the 7 km2 of the second zone has been assumed. Though the present market in Belgium for this kind of material is estimated to Z.l&ton/year,

one may think that the market could increase under various circums-

tances (for instance, as a result of an exportation policy).

Winning technique

Very few quantitative information areavailable on the winning technique which is in principle the following one

:

A ship travels along the sand bank and pumps the thin upper sediment layer through

a nozzle and a pipe; the mixture of water, fine sand (
The efficiency of winning (i.e. the ratio of the

amount of sand effectively gathered to the amount of sand stirred up from the bottom

337

layer) is not known, but is certainly less than unity.

However, the sand which is

not carried along by the ship is assumed to settle down very

rapidly in the close

neighbourhood of the ship'strack and does not appear in the budget of winning; thus, with respect to volume changes, the efficiency

of winning is unity.

During the operations, the upper sediment layer is destroyed, with all its living structure, which is a very important factor of nutrient recycling.

The destruction

is limited to the surface where the sand has been sucked.

Modifications of topography

One assumes that the winning effort is evenly distributed on the defined zones; the density of sand is 1.5 ton/m3 (taking into account the interstitial water). One also assumes that there is no immediate restoring of the bank (this latter assumption might be inconsistent with simulation results). Under these assumptions, one computes that the annual deepening is 0.2 rn in zone I, and 0.5 m in zone

11.

The simulations dealing with the effects of the bottom topography have been performed assuming a 3-year period of intensive winning activity.

EROSION PROPERTIES OF THE FLOW IN SHALLOW WATER

Sand winning has the effect of modifying the bottom topography because the volume of the sand layer diminishes and the depth therefore increases at the place where winning takes place, at least temporarily.

This modification of the topography

induces,as a first perturbation, slight changes in the magnitude and direction of current?.

Modifications of the mean surface elevation are by experience known to

be much less important, because the elevation of the free surface has a much larger caracteristic length scale (several tens of hundreds kilometers, while the length scale of bottom topography gradients is of order of ten or one kilometer, or less). Other caracteristics modified.

of the flow andmainlyits properties of erosion, are also

In turn, these changes may affect the bottom topography on a long term.

The changes in the spatial distribution of the physical parameters associated with the erosion properties may be interpreted to forecast the influence of sand winning on the long term evolution of bottom topography. Sedimentation and erosion of the upper sediment layers are phenomena which are presently poorly understood and even

less modelled.

However, we shall show that,

with only the help of global erosion parameters like erosion

energy and erosion

stress, one can describe some general features of the recent sedimentology in the coastal shallow waters under study;

we thus will be allowed to use these global

parameters as tools for forecasting the evolution of the bottom.

339 MATHEMATICAL MODEL OF THE ENERGY AND STRESS OF EROSION

I n a non-stationary

flow l i k e a t i d a l s e a , t h e l o c a l instantaneous energy i s

E = 112 p > 1

:

(1)

y-

where p i s t h e s p e c i f i c mass of water and

y-(x,t) t h e

=

l o c a l instantaneous

velocity. The energy a v a i l a b l e f o r t h e e r o s i o n of t h e bottom sediment i s u s u a l l y i n some t e r m s of t h e v e l o c i t y a t some h e i g t h above t h e bottom x

expressed

3 = z+ (2)

F. + = 112 p ,+.l-k

In shallow water, t h e v e r t i c a l v e l o c i t y i s always n e g l i g i b l e from t h e energy p o i n t

= Eh =

E

of view, s o t h a t :

1/2pv h'xh

(3) and

I+= zh[xh,z + , t

I

However, f i e l d d a t a a r e l a c k i n g f o r a good knowledge of t h e v e l o c i t y p r o f i l e i n t h e bottom l a y e r ; on t h e o t h e r hand, most c u r r e n t measurements only provide t h e v e l o c i t y a t one depth, and most mathematical models only compute t h e 2-dimensional and time e v o l u t i o n of t h e depth-averaged h o r i z e n t a l v e l o c i t y .

u

--n

= 1 h + [ 1.

t

1- < vh'xh, x 3 ,

3

t I dx3

.h

where h i s t h e mean depth

(4)

i s t h e s u r f a c e e l e v a t i o n (due t o long waves)

x i s t h e horizontal p o s i t i o n vector. -h A s we s h a l l use t h e r e s u l t s of such a mathematical model, we now t r y t o parameterize

t h e energy E

a s a f u n c t i o n of t h e average speed.

Using t h e dimensionless v a r i a b l e

=

T)

x+h 3

+h

1

U = \ v I xh,q, t I d q -h '0-h

equation ( 1 ) may be w r i t t e n :

(5) Moreover, i f one assumes t h a t t h e c u r r e n t has t h e same d i r e c t i o n a t every depth, a good hypothesis i n a shallow s e a , except during s h o r t Lntervals around t h e t u r n of t h e t i d e , one can w r i t e :

Vh

=

w

iXh,?,

Now, i n a shallow n o n s t r a t i f i e d s e a , y l q

)

t I

Uh iZh,t

(6)

i s a f u n c t i o n , which v a r i e s slowly with

-

x and t , and i t s v a r i a t i o n with 1) i s very s t r o n g i n a shallow l a y e r c l o s e t o t h e bottom, whereas it i s almost f l a t above t h a t l a y e r .

Therefore, i f z

is greater

than t h e h e i g t h of t h i s l a y e r , y depends s l i g h t l y on Z +' Returning t o ( 2 ) we g e t

E,

= 112 p y 2 l -h)rl+)t x

With t h e assumption about t h e s l i g h t dependence of

( 7 ) becomes

E+

2

2

)

'-

x t (7) h) a g a i n s t xh,z+ and t ,

2

= 1/2PCUh

(8)

340 2 is roughly that of u h' In the course of the year, the dominant phenomena in the Southern Bight are the

The distribution of E

periodic tide and the aperiodic atmospheric forcing. Though at times, the storms may have a significant influence on sand banks, the main energy source is, by far, the tide.

The main tidal component is the semi-

diurnal lunar tide M2, and, following Ronday,11976), the mean annual energy which we assume to govern the long term erosion trend may be written as proportional to the mean energy over a tidal M

<E+>

=

2

period.

I/2prp2X1.LX<E+ZM

(9)

2

where I

(10)

The mean annual energy of the flow available for erosion may thus be computed from the results of a hydrodynamical numerical model of the tidal circulation. Such a model is available to us (Ronday and Belhomme, 1978). Developing the same arguments, one can also parameterize the bottomstressas a function of the average horizontal velocity, which is commonly done in the literature, and again express the mean annual stress as a function of the stress averaged over a tidal M,-period

:

I

L

<:+>

rr 1.LpCdrp2"lV12

where Cd is the friction coefficient.

UhUh

dt

(11)

0

Some authors (e.g. Bagnold, 1956) prefer to use the power instead of the energy, relying on mechanical considerations. The choice between power and energy is not crucial in this matter, as far as we only want to study the distribution of global parameters describing the erosion phenomena, and to not attempt to explain the mechanisms.

In fact, we are interested in the localization of extrema of the dis-

tribution of energy, wh,ich are the same as the extrema of the power. Indeed, both distributions depend on the modulus of the velocity of the current, averaged over a tidal period.

RESPECTIVE ROLE OF ENERGY AND STRESS IN THE SEDIMENTATION-EROSION PROCESS

The physical influence of the two parameters previously described on the sedimentation-erosion process may be summarized as follows : In a region where the energy has a local minimum, the suspended particles have a greater probability to settle down and the sediment layer has a low probability of being eroded.

On the contrary, where the energy is maximum, the probability of

D ~ e t r ~ b u l ~ 0o1 n energy

e r o s i o n i s higher and, following Hjiilstrom

(19391, one should observe i n t h e s e

r e g i o n s , i f t h e mathematical model i s c o r r e c t , e i t h e r r a w sands o r muds, t h e f i n e sands being more e a s i l y eroded.

Regions of minimum energy should, on t h e o t h e r

hand, correspond t o p l a c e s where t h e f i n e s a n d s a r e abundand. However, energy d i s t r i b u t i o n does n o t r e p r e s e n t , a l o n e , t h e whole process :

if

sediments e v e n t u a l l y eroded and resuspended a r e n o t taken away by t h e flow from t h e r e g i o n s , nothing b u t a t u r b i d i t y i n c r e a s e could be observed. The d i s t r i b u t i o n o f < z > m a y t h u s h e l p i n e x p l a i n i n g t h e p a t t e r n of mud accumulation o r sand bank s t a b i l i z a t i o n . I f t h e d i s t r i b u t i o n o f < z > i s such t h a t

a l l v e c t o r s a r e d i r e c t e d outwards a region

of maximum energy, t h i s could mean t h a t a c o n s t a n t e r o s i o n o c c u r s t h e r e ; i f t h e v e c t o r s a r e d i r e c t e d inwards, t h i s might induce a high t u r b i d i t y l e v e l i n t h e water column, and a s t a b l e bed.

T h e < r > v e c t o r f i e l d may a l s o e x p l a i n t h e o r i g i n of t h e

deposited sediments and t h e f a t e of eroded m a t e r i a l .

W e s h a l l thus t r y t o correlate

t h e d i s t r i b u t i o n of energy and s t r e s s with t h e map of s u p e r f i c i a l sediments of t h e c o a s t a l a r e a under study.

DISCUSSION OF THE RESULTS

The d i s t r i b u t i o n of energy i s p l o t t e d on Figure 3 and t h e v e c t o r d i s t r i b u t i o n of s t r e s s on Figure 4 . From t h e f i r s t 'of

Units a r e a r b i t r a r y . t h e s e f i g u r e s , one can see t h a t sand banks a r e c h a r a c t e r i z e d

by l o c a l maxima of t h e energy i n Region I (Flemish Banks), b u t t h a t

o t h e r maxima

appear, e i t h e r c l o s e t o t h e banks o r even n o t t i g h t e n with t h e g e n e r a l bank s t r u c ture.

For i n s t a n c e , j u s t SW of t h e Oost Dijk Bank, t h e r e i s alocalmaximum t h a t

does n o t coincide with any bank.

The same phenomenon appears i n t h e region of t h e

Akkaert Bank and Goote Bank. On t h e c o n t r a r y , t h e Wandelaar Bank, which i s a f l a t bank of d i f f e r e n t n a t u r e than t h e o t h e r s (more mud i n t h e s e d i m e n t s ) , i s c h a r a c t e r i z e d by a f l a t minimum of t h e energy. On t h e o t h e r , deeper channels l i k e t h e Westdiep, t h e Scheur and t h e Oostgat a r e p l a c e s where t h e energy i s higher. From t h e viewpoint of e r o s i o n s t r e s s , w e s t e r n b a n k s show a d i s t r i b u t i o n of small s t r e s s v e c t o r s t h a t g e n e r a l l y t u r n around t h e heads of t h e banks inducing t h a t m a t e r i a l eroded from t h e banks tend t o r o t a t e around them.

Whereas t h e stress i s

markedly s t r o n g and d i r e c t e d along t h e d i r e c t i o n of t h e main t i d a l c u r r e n t s near t h e Akkaert and Goote Bank, t h e r e g i o n of t h e Wandelaar shows a t y p i c a l s t r e s s pattern. In t h e r e g i o n westwards of t h i s bank, t h e stress i s d i r e c t e d eastwards, i n t h e d i r e c t i o n of t h e r e s i d u a l t i d a l c i r c u l a t i o n i n t h e Southern Bight.

figure 4

Oistribution

of e r o s i o n

stress

343

344 I n t h e region eastwards, t h e stress i s d i r e c t e d northeastwards, a probable e f f e c t of t h e d i s c h a r g e of t h e S c h e l d t e s t u a r y . The c e n t e r of t h e Wandelaar i s t h e v e r y p l a c e where t h e s t r e s s e s converge. This means t h a t suspended m a t t e r o r i g i n a t i n g from t h e surroundings of t h e bank w i l l converge towards t h e bank.

A s a l o c a l energy minimum e x i s t s t h e r e , i t follows t h a t

t h e bank i s a p l a c e where accumulation of sediments t a k e s p l a c e . Since t h e major source of suspended sediment i n t h i s region i s t h e Scheur channel. (higher energy, h i g h e r s t r e s s , e s t u a r i n e d i s c h a r g e ) , where f i n e sands and mud domin a t e t h e sedimental c o n t e n t , t h i s i n d i c a t e s t h a t t h e f a t e of t h e upper l a y e r of t h e Wandelaar Bank i s t o become even more muddy. A l a s t i n t e r e s t i n g f e a t u r e of t h e s t r e s s f i e l d i s t h e g e n t l e t u r n i n g of t h e

s t r e s s v e c t o r s around t h e

W a l v i s c h s t a a r t Bank.

A t f i r s t s i g h t , it seems t h a t t h e r e a r e more than random f e a t u r e s i n t h e energy and s t r e s s f i e l d s computed from t h e hydrodynamical numerical model.

However, up

t o now, one could argue t h a t one has no experimental evidence of t h e v a l i d i t y of t h i s approach. D i r e c t experimental evkdence i s of course impossible, b u t t h e r e i s an i n d i r e c t proof showing t h a t t h e model r e s u l t s r e p r e s e n t a t l e a s t some a s p e c t s of t h e geophysical r e a l i t y . Figure 2 i s a map of t h e d i s t r i b u t i o n of f i n e sands i n t h e region of i n t e r e s t . BY f i n e sands, we mean p a r t i c l e s with a mean diameter of l e s s t h a n 74 microm.

The map shows t h e d i s t r i b u t i o n of t h e r a t i o of f i n e sand t o t h e t o t a l mass of sandy sediments.

One s e e s a t f i r s t s i g h t a s t r o n g n e g a t i v e c o r r e l a t i o n between t h i s r a t i o

and t h e energy l e v e l :

t h e h i g h e s t t h e energy, t h e lowest t h e r a t i o .

In g e n e r a l , r e g i o n s c l o s e t o t h e c o a s t , where t h e energy i s low, a r e p l a c e s of high f i n e sand c o n t e n t , t h e only exceptions being t h e Scheur channel, which t r a n s p o r t s t h e f i n e sands and muds from t h e e s t u a r y . Typical c o r r e l a t i o n s a r e :

- t h e presence of high f i n e sand r a t i o i n a region responding t o a l o c a l minimum of energy

NW of t h e Oost Dijk Bank, cor-

;

- a b l o t of f i n e sands between t h e Buiten Rate1 Bank and t h e Oost Dijk Bank : - two tongues of f i n e sands extending, on one and another s i d e of an energy maximum l o c a t e d on t h e Oostende Bank, up t o both ends of t h e Kwinte Bank ;

- t h e f i n e sand region of t h e Steendiep, a l s o a s s o c i a t e d w i t h an energy minimum l o c a t e d i n a deep channel. A l l t h e s e c o r r e l a t i o n s show t h a t t h e r e

i s a good

correspondance between energy

and stress d i s t r i b u t i o n s o n t h e one h a n d , a n d t h e sedimentological f e a t u r e s of t h e seabed i n t h e c o a s t a l zone on t h e o t h e r hand. The d e f i n e d energy and stress, which a r e parameters computed from a hydrodynamica1 numerical mode1,are much more e a s i l y a v a i l a b l e than sediment samplings and

345 can be used, with some confidence, t o study and f o r e c a s t t h e e v o l u t i o n of t h e upper sediment l a y e r of t h e c o a s t a l s h e l f . However, t h i s s u r p r i z i n g l y good agreement between experimental survey and model f e a t u r e s , has been o b t a i n e d without t a k i n g i n t o account such important p h y s i c a l phenomena as t h e e f f e c t of s u r f a c e waves and t h e s p a t i a l v a r i a t i o n of bottom f r i c t i o n . The r e l a t i v e s m a l l impact of t h e s e f e a t u r e s may however been explained.

E f f e c t of s u r f a c e waves

T h e c o n s i d e r e d a r e a i s a g i t a t e d by very s t r o n g t i d a l c u r r e n t s . t h e mean depth i s g r e a t e r than 10 m , they are

I n regions where

more e n e r g e t i c than s u r f a c e waves.

I n more shallow r e g i o n s , t h e t o t a l i n f l u e n c e by waves i s s i g n i f i c a n t , from an energ e t i c p o i n t of view.

However, it is w e l l known ( e . g . Gullentops & a l , 1976) t h a t

s u r f a c e waves i n t h e Flemish Banks are n o t as high n e i t h e r a s s t r o n g a s elsewhere, because t h i s region l i e s i n t h e shadow o f o f f s h o r e banks, which

break t h e most

e n e r g e t i c long p e r i o d waves (mainly t h o s e coming from NW, which have t h e l o n g e s t fetch).

From t h e mean annual p o i n t of view, one can assume t h a t t h e s t r e s s induced

by waves i s p e r i o d i c , with a s h o r t time s c a l e , and with random d i r e c t i o n :

the

resulting s t r e s s is therefore negligible.

E f f e c t of t h e n a t u r e of t h e bottom on f r i c t i o n

Most experiences with hydrodynamicalnumericalmodels ( e . g . Ronday, 1976) show t h a t parameterized bottom f r i c t i o n i s almost c o n s t a n t , and t h a t t h e v a r i a t i o n s of t h e f r i c t i o n c o e f f i c i e n t s l i g h t l y change t h e r e s u l t s .

One can assume t h a t t h e bottom

f r i c t i o n i s o n l y s t r o n g l y i n c r e a s e d i n p l a c e s where sand r i p p l e s a r e observed, but such l o c a t i o n s have a very l i m i t e d s u r f a c e a s compared t o t h e t o t a l a r e a under study

.

FORECASTING THE EVOLUTION OF THE SEABED UNDER SAND W I N N I N G

I t i s n o t claimed t h a t t h i s simple model e x p l a i n s a l l t h e mechanisms and f e a t u r e s

of e r o s i o n and sedimentation i n t h e c o a s t a l zone.

However, t h e c o r r e l a t i o n s s t r e s s e d

formerly allow u s t o have some confidence i n a p o s s i b l e use of t h i s model t o f o r e c a s t t h e e v o l u t i o n of t h e r e c e n t sediments i n t h e c o a s t a l zone under t h e e f f e c t of sand winning. The technique i s t h e following :

- compute t h e energy and s t r e s s from t h e v e l o c i t i e s provided by t h e hydrodynamical numerical model, run using t h e a c t u a l depth d i s t r i b u t i o n ;

- compute a new d e p t h d i s t r i b u t i o n i n t h e winning a r e a s , using t h e aforementioned

346 assumptions, and assuming moreover t h a t during t h e l i m i t e d time span of 3 y e a r s , the p e r t u r b a t i o n s caused by t h e winning have no feedback e f f e c t . (In o t h e r words, t h i s means t h a t t h e time s c a l e necessary f o r an e f f e c t i v e i n f l u e n c e of t h e p e r t u r b a t i o n s on t h e system is much longer t h a t t h e time s c a l e of t h e o p e r a t i o n s t h a t cause the perturbation.

This assumption may not be t r u e f o r l a r g e l o c a l p e r t u r b a t i o n s and i s

only a f i r s t approximation f o r small d i s t u r b a n c e s .

However, t h i s approach i s the

only one p o s s i b l e i f one t r i e s t o deduce long term changes from t h e r e s u l t s of s h o r t term models and experiments.

A more a c c u r a t e study would indeed r e q u i r e t h e design

of a long term e v o l u t i o n model o r measurement s t r a t e g y , t h e l a t t e r i s s u e allowing p r a c t i c a l l y no f o r e c a s t ) .

- With new topography run t h e hydrodynamical numerical model t o compute new space and time d i s t r i b u t i o n of v e l o c i t i e s ;

- perform f i r s t s t e p again with p e r t u r b a t e d v e l o c i t i e s

;

- compute d i f f e r e n c e s i n energy and stress f i e l d s and p l o t t h e maps

;

- deduce from t h e d i f f e r e n c e f i e l d t h e p o s s i b l e e v o l u t i o n of t h e system. This i s what we u s u a l l y c a l l a d i f f e r e n t i a l study.

Provided t h a t t h e mathematical

model reasonably reproduces t h e p h y s i c a l r e a l i t y , such an approach i s r a t h e r r e l i able. I t i s t o be noted t h a t a l l feedback e f f e c t s a r e h e r e n e g l e c t e d , which may cause

over- o r underestimation of t h e e f f e c t s .

This f a c t must be taken i n t o account

during t h e i n t e r p r e t a t i o n phase.

RESULTS OF THE DIFFERENTIAL STUDY

Figures 5 and 6 show r e s p e c t i v e l y t h e d i f f e r e n c e s i n energy and stress a s s o c i a t e d with sand winning a c t i v i t y .

Energy d i s t r i b u t i o n

(full lines :

increase; dotted

lines

:

The i n f l u e n c e v a r i e s from bank t o bank.

decrease) On t h e Kwinte Bank, t h e energy i n c r e a s e s

s l i g h t l y ( 1 % ) around t h e n o r t h e a s t e r n and s o u t h w e s t e r n ends.

A s l i g h t increase

of t h e same magnitude o r a b i t l a r g e r appears on both s i d e s of t h e Buiten Rate1 Bank and on t h e e a s t e r n s i d e of t h e Oost Dijk Bank, whereas a s l i g h t d e c r e a s e may be observed on t h e western s i d e of t h e Oost Dijk Bank. decrease i s much more pronounced (up t o 4 % ) .

o f t h i s l a t t e r bank, one observes i n c r e a s e s of about

Scheur

.

On t h e Wandelaar Bank, t h e

On t h e Southern and Western s i d e s

3

%,

and of about 1

%

i n the

I Figure 5

Energy

dilferences

347

w

rp -3

348 Stress distribution

V a r i a t i o n s i n t h e s t r e s s f i e l d a l s o c h a n g e from p l a c e t o p l a c e ; t h e d i f f e r e n c e vectors a r e generally opposite t o t h e o r i g i n a l vectors. d i f f e r e n c e i s about 10 %.

The maximum m a g n i t u d e o f t h e

L e t u s n o t i c e t h a t t h e s c a l e of d i f f e r e n c e v e c t o r s on

Figure 6 i s 2 0 times t h e s c a l e of s t r e s s v e c t o r s on Figure 4.

Combining t h e r e s -

p e c t i v e r o l e of energy and stress, one can deduce w i t h a l o t of c a u t i o n , a p o s s i b l e e v o l u t i o n of t h e banks and t h e i r neighbourhood.

The i n c r e a s e of energy does n o t

seem t o be s u f f i c i e n t t o a c c e l e r a t e s i g n i f i c a n t l y t h e e r o s i o n of t h e sands t h a t form t h e banks, b u t may i n f l u e n c e t h e d e p o s i t i o n of f i n e r sands. A l l western banks show a s i m i l a r e v o l u t i o n p a t t e r n :

i n c r e a s e of energy on

both s i d e s , and a s l i g h t decrease of e r o s i o n s t r e s s ; t h e s e v a r i a t i o n s should not i n f l u e n c e t h e p o s i t i o n of t h e bank. The s i t u a t i o n seems t o b e c l e a r e r on t h e WandeLaar.

On t h e bank i t s e l f , t h e

energy d e c r e a s e s , and t h e d i f f e r e n c e s s t r e s s v e c t o r s p o i n t towards t h e c o a s t . The decrease of energy should induce t h e r e an i n c r e a s e of f i n e p a r t i c l e s c o n t e n t s i n t h e new sediment l a y e r .

Since, i n t h e r e g i o n s surrounding t h e bank, energy

i n c r e a s e s (except between t h e bank and t h e c o a s t ) , t h e p r o b a b i l i t y of p a r t i c l e s coming and s e t t l i n g on t h e bank i n c r e a s e s .

finer

The sand q u a l i t y on t h e

Wandelaar should s t i l l decrease. A s most of t h e suspended p a r t i c u l a t e m a t t e r i s t h i s r e g i o n comes from t h e Scheur,

t h i s can be i n t e r p r e t e d a s a displacement southwestwards of t h e S c h e l d t e s t u a r y . Let u s r e c a l l t h a t t h e hydrodynamical p e r t u r b a t i o n s have been computed under t h e assumption t h a t t h e r e i s no immediate r e s t o r i n g of t h e bank.

As this

assumption i s p a r t l y wrong ( a s i t can be deduced from t h e l a t t e r a n a l y s i s ) , t h e p e r t u r b a t i o n s should i n f a c t be l e s s important t h a t computed.

They a r e , however,

f a r from being n e g l i g i b l e on a long term b a s i s , mainly on t h e Wandelaar. BIBLIOGRAPHY

Adam Y . , W. Bayens, J . P . Mommaerts, G. P i c h o t , 1980. Ecological modelling a s a t o o l f o r t h e s c i e n t i f i c management of sand winning i n c o a s t a l w a t e r s , i n D. Dubois ( E d i t o r ) , Second I n t e r n a t i o n a l Conference on t h e S t a t e - o f - t h e - a r t i n Ecological Modelling Elsevier-Amsterdam. 1956. An approach t o t h e sediment t r a n s p o r t problem from g e n e r a l Bagnold R.A., physics. U . S . Geol. Surv. Prof. Papers 4221. Gullentops F . , M. Moens, A . Ringele, R. Sengier, 1976. Geologische kenmerken van de suspensies en sedimenten i n J. Nihoul & F . Gullentops ( E d i t o r s ) , Rapport F i n a l du P r o j e t Mer-S6dimentologie - E d i t i o n s d e s S e r v i c e s de l a Programmation de l a P o l i t i q u e S c i e n t i f i q u e . B r u x e l l e s . Hjiilstrom F . , 1939. Transport of sediment by moving w a t e r i n P.D. Track ( E d i t o r ) , Recent Marine Sediments 5-31, Am. ASSOC. P e t r o l . G e o l o g i s t s , T u l s a , Oklahoma. Ronday F . , 1976. ModSles Hydrodynamiques de l a c i r c u l a t i o n e n mer peu profonde, i n J . Nihoul & F. Ronday ( E d i t o r s ) , Rapport F i n a l du P r o j e t Mer-ModSles Hydrodynamiques, E d i t i o n d e s S e r v i c e s de l a Programmation d e l a P o l i t i q u e S c i e n t i f i q u e . Bruxelles.

Ronday F . , G. Belhomme, 1978. Modele Mathematique de l a Zone CBtiere Belge Rapport f i n a l - Unpublished manuscript.

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351

SUBJECT I N D E X

Abidjan,

147.

A b i o t i c environment, 192. Advection, 6,

60,

77,

104,

150,

165,

193, 201,

Africa - Southern A f r i c a , 18, 19, 40, 41. - Northern A f r i c a , 18. - Northwest A f r i c a , 19, 37, 40, 41. - West A f r i c a , 15, 151. Alaska, 13. A l e u t i a n chain, 38. Amazonia,

15,

Anchoveta,

19,

155,

22,

156,

23, 157,

30,

31,

158,

33,

39.

161.

A n t a r t i c , 36. Arcona Basin, 169. Antlantic - A t l a n t i c Ocean, 99, 287. - North A t l a n t i c , 220, 228, 270. Mid A t l a n t i c Bight, 2 0 , 24, 25, - South A t l a n t i c Bight, 28, 32. - A t l a n t i c c i t y , 26. - A t l a n t i c s h e l f , 81.

28.

Auke Bay, 197. B a l t i c Sea, 165,

169,

173,

174,

B a r o c l i n i t y , 76,

102,

178,

179.

175, 177.

Bay of GorBe, 143. Belgian Coast, 232, Bering Sea, 4,

7,

233.

15,

35,

36,

37,

39,

Boom, 330. Bothnia, 169. Boussinesq approximation, 101. B r a z i l , 41. B r i t i s h Isle, 33,

51,

52.

Bristol - B r i s t o l Bay, 38. - B r i s t o l Coast, 10. Brunt-Vaisala frequency, 174. Buoyancy, 51, 67, 174, 211, 217, 278. - Buoyancy f l u x , 52, 531 54, 56, 58. California,

13,

39,

Cape Canaveral, 80.

40,

41,

165.

40,

42.

281, 295,

322.

352 Cape Formoso, 104,

123.

Cape H a t t e r a s , 34, 81. Cape Lopez, 104. Cape Newenham, 38. Cape Palmas, 104,

119, 104,

Cape Three P o i n t s , Cap-Vert,

141,

123,

134.

123,

124,

125,

134.

143.

Casamance, 150. C e l t i c Sea, 197, 287. Chesapeake Bay, 25, Chile,

196.

16.

C i r c u l a t i o n , see a l s o c u r r e n t , 7, 143, 154, 239. - Residual c i r c u l a t i o n , 224, 225, 226, 228, 232, - F r o n t a l c i r c u l a t i o n , 11. - Oceanic c i r c u l a t i o n , 154, 155, 156.

234,

239,

245,

251.

Clausocalanus, 2 13. c h l o r o p h y l l , 15, 23, 28, 80, 197, 201, 202, 203, 209. C o r i o l i s parameter, 82,

141,

144,

145,

174, 224, 274,

321.

147,

149,

150,

151,

152,

153,

165,

193,

Crabs, 6. Current, see a l s o c i r c u l a t i o n , 3, 30, 31, 119, 197, - C u r r e n t d i s t r i b u t i o n , 1, 278. - C u r r e n t v e l o c i t y , speed, 3, 83, 94, 165, 179. - Current d i r e c t i o n , 83. - Residual c u r r e n t , 4, 220, 270, 310. - Boundary c u r r e n t , 29, 31, - Loop c u r r e n t , 31, 62. - Bottom c u r r e n t , 51. - T i d a l c u r r e n t , 52, 64, 86, 149, 222, 225, 251. - Surface c u r r e n t , 144, 148, 152. - C u r r e n t reversal, 123. - Macroscale c u r r e n t , 228. Dakar, south-Dakar,

219,

223,

236,

245,

251,

150.

Danish S t r a i t s , 169. Delaware, 25. Density, 7, 54, 76, 175, 176, 179, - S p e c t r a l d e n s i t y , 175, 176. Diagenesis,

39,

183,

193,

290.

40,

Diffusion, s e e a l s o d i s p e r s i o n , 3, 6, 35, 165, 166, 193, 199, 209, - Molecular d i f f u s i o n , 156, 209, 210, 212, 214, 217, 274. D i n o f l a g e l l a t e , 141,

143,

197,

Dispersion, see a l s o d i f f u s i o n , D i s s i p a t i o n , 209,

281, 325.

199, 202. 155,

156, 157, 159,

161, 201,

324.

210.

Eddy, s e e a l s o turbulence, 4, 26, - Cyclonic eddy, 10, 80. - Spin-off eddy, 28, 31. - Eddy v i s c o s i t y , 102, 239, 250. - Eddy d i f f u s i o n , 325. - Synoptic eddy, 165, 179.

150,

152,

154,

174,

185,

186, 270.

278,

282.

353 Ekman - Ekman s u c t i o n , 26. - Ekman t r a n s p o r t , 144, - Ekman upwelling, 146.

148,

153.

Energy - Energy d i s s i p a t i o n , 8, 9, 11, 174, 234, - Energy exchange, 238, 239. - Turbulent energy t r a n s f e r , 192. English Channel, 226, Erosion,

295,

297,

237,

270.

287.

325,

326,

330,

331.

E r t e l ' s r e l a t i o n , 179. Euphotic - Euphotic zone, 13, 14, 22, - Euphotic depth, 71, 72.

26,

35,

38,

70,

71,

73,

74.

Europe, 41. Eutrophic,

15, 36,

43.

Fauna, 4. Feeding ground, 2. F i n i t e element method, 276. Finland,

169.

F i s h , 3,

7,

158.'

Fladen Ground, 38. Flamborough Head, 10. F l o c u l a t i o n , 319,

320,

326,

329,

331.

F l o r i d a , 26, 28, 30, 31, 32, 41, 79, 80, 82, - West F l o r i d a , 21, 31, 32. - South F l o r i d a ' s A t l a n t i c Coast, 79, 96. F o r t P i e r c e , 82. F r i c t i o n , 7, 270, 293. - F r i c t i o n v e l o c i t y , 54, 55. - F r i c t i o n c o e f f i c i e n t , 322. - F r i c t i o n stress, 227, 239, 294. - Residual f r i c t i o n , 232. - F r i c t i o n a l drag, 31. - F r i c t i o n a l r e t a r d a t i o n , 82. Front, 10, - Frontal - Frontal - Frontal

134, 141, 152, 166, c i r c u l a t i o n , 11. movement, 196. d i s c o n t i n u i t y , 199.

George Bank, 25, Georgia, 29,

26,

33,

34,

30.

Geostrophic - Geostrophic f l o w , 76. - Geostrophic c u r r e n t , 182. - Geostrophic s h i f t , 187. German Bight, 10. Gironde, 285, Gulf of Benin,

297. 123.

191.

36.

83,

88,

93,

95,

96,

97.

3 54 Gulf of Guiana, 20, 30, 31, 99, 100, 104, 123, 134. Gulf o f Lion, 279. Gulf of Maine, 73, 74, 76. Gulf of Mexico, 15, 21, 22, 23, 29, 31, 42. Gulf Stream, 80. Gyre, 165, 232, 233, 245, 251, 270. - R e s i d u a l g y r e , 228. H a l o c l i n e , 169, 187. H e a t , 10, 176, 201. - H e a t flux, 53, 55, 274, 276, 278. H e a t exchange, 64.

-

H e r b i v o r e , 6. Honfleur,

286.

Hudson, 23, 25, 26. - Hudson Canyon, 24. H u r r i c a n e David, 95. Indian Arm,

196.

I s o b a t h , 23, 38, 148, 151, 185. I s o p l e t h , 31, 159, 160. I s o t h e r m , 59, 71, 86, 88, 151, 281. Jamaica Bay, 323. J e l l y f i s h , 7. K a t t e g a t t , 169. Kolmogorov s c a l e , 174. Lake Tahoe, 165. L e n i n g r a d , 169. Le R a t i e r ,

293.

L i g h t , 72, 74, 165, 320. - L i q h t q u a l i t y , 98. - L i g h t i n t e n s i t y , 98, 158. - L i g h t e f f e c t , 71. - L i g h t l i m i t a t i o n , 74, 75, 76, 204. - ' S h o r t a g e o f l i g h t , 199. Long I s l a n d Sound, 192, 193. L o u i s i a n a , 22, 23, 28, 41. Manitounuk I s l a n d s , 197. M a u r i t a n i a , 147. Mesoscale, 143, 150, 152, 154. - Mesoscale wind v o r t i c i t y , 152, 233. - Mesoscale Reynolds stress t e n s o r , 225, 227, 238, 239, 245. - Mesoscale flow, 237. Microzone, 209, 210,

212, 217.

M i g r a t i o n , 2. - M i g r a t i o n v e l o c i t y , 3 , 4.

Mississipi River, 19, 20, 22, 23.

355 Mixing, 5, 7, 33, 201, 203, 293. - Mixing r a t e , 63. - V e r t i c a l mixing, 67, 68, 71, 72, 74, 77, 193, 196, 202. - Mixing d e p t h , 68, 76. - Mixed layer, 75, 156, 158, 161, 175, 199. Montauk P o i n t , 26. N a n t u c k e t S h o a l s , 26. N e w J e r s e y , 25. New York, 13, 25, 32. - N e w York B i g h t , 23, 33.

N o r t h e r n England, 250. North-Hinder,

3.

N o r t h Sea, 2, 3, 4, 10, 11, 15, 38, 39, 52, 63, 64, 169, 219, 220, 2 2 2 , 225, 226, 228, 232, 239, 245, 250, 251. N o r w a y , 38. - Norwegian Deep, 38.

Nova S c o t i a , 34. N u t r i e n t , 1, 5, 7, 10, 13, 15, 16, 18, 19, 20, 23, 2 8 , 38, 42, 51, 52, 61, 63, 64, 67, 73, 74, 75, 76, 77, 8 0 , 143, 148, 150, 152, 153, 155, 156, 166, 173, 191, 192, 196, 198, 199, 200, 201, 204, 205, 209, 210, 2 1 1 , 282. - N u t r i e n t i s o p l e t h , 31. - N u t r i e n t c o n c e n t r a t i % n , 68. - N u t r i e n t d e n s i t y , 76. O i t h o n a , 213. O l i g o t r o p h i c , 15, 19, 26. Onslow Bay, 81. Oregon, 33, 41. Ozmidov buoyancy s c a l e , 174. P a c i f i c Ocean, 147, 156. papa ( o c e a n s t a t i o n ) , 54. P e r u , 13, 15, 16, 17, 18, 19, 20, 21, 2 2 , 36, 40, 41, 42, 155, 156, 159, 160. Photic layer,

193, 196, 197, 199, 201, 202.

Photosynthesis,

18, 34, 68, 69, 70, 71, 72, 74, 76, 156, 192, 201, 210, 320.

Phytophagous, 156. P h y t o p l a n k t o n , 6 , 10, 11, 13, 14, 1 5 , 16, 19, 20, 2 1 , 2 2 , 34, 36, 40, 42, 67, 68, 70, 71, 77, 80, 141, 143, 155, 157, 158, 160, 161, 165, 191, 192, 193, 196, 197, 198, 199, 200, 201, 202, 203, 204, 209, 210, 216, 217, 285, 320. P l a i c e , 2. P l a n k t o n , 23, 41, 155, 156, 165, 209, 210, 282. P o i n t e des Alrnadies,

141, 152.

Pose, 290. P u g e t Sound, 196. p y c n o c l i n e , 23, 53, 60, 61, 63, 124, 184. R e s i d u a l f l o w , 225, 239, 245, 250. R e s p i r a t i o n , 68, 69, 70, 71, 72, 74.

3 56 Rhine River, 38.

192,

Richardson number,

196.

R i j k s s t a t i o n voor Z e e v i s s e r i j Oostend, 3. River River - River - River - River

-

r u n o f f , 19, 23, i n f l u x , 169. flow, 324, 331. discharge, 19.

28,

33,

191,

196,

197,

Rossby - Rossby's p o t e n t i a l v o r t i c i t y theorem, 178, - Rossby wave, 105, 182, 187. - Rossby r a d i u s of deformation, 174, 187.

198,

201.

179.

Rupelmonde, 327. Saanich I n l e t , 197. Sahel, 99. S t . Lawrence, 191,

192,

196,

201.

S t . Louis, 147. S a l i n i t y , 170, 173, 175, 325, 327, 329, 331.

176,

274,

292,

293, 294,

297,

302,

310,

319,

320,

324,

Santa Barbara Basin, 40. Sargasso Sea, 68,

71,

73,

74,

Scale - T i m e scale, 1, 7, 11, 14, - Length s c a l e , 1, 3, 4, 7, S c h e l d t , 319,

322,

75,

76.

166, 192, 193, 203, 219, 220, 245. 8, 14, 124, 187, 192, 193, 209, 220,

222,

245.

330.

Sediment ( s e d i m e n t a t i o n ) , see a l s o t u r b i d i t y , 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 219, 220, 223, 233, 285, 294, 295, 297, 301, 302, 310, 315, 319, 320, 325, 329, 330. - Sedimentation v e l o c i t y , 292, 325, 326, 331. Seine, 285,

286,

Senegal, 143,

287,

298,

315.

150.

S h e l f , 52, 64, 147, 148. - Shelf break f r o n t , 4. - Shelf f r o n t , 5. - Middle s h e l f zone, 6. - Outer s h e l f zone, 7, 84. - European C o n t i n e n t a l s h e l f , 7, 9, 11. - Shelf bottom sediments, 15. - Shelf-slope, 41. - Inner s h e l f 79. - Shelf break, 83, 88, 89, 90, 91, 92, 93, - Shelf c i r c u l a t i o n , 150. Southern s h e l f , 141. - C o n t i n e n t a l s h e l f , 97, 143.

-

Shetland I s l a n d s , 38. Skagerrak, 169. Skeletomena costatum, 211. Solar - S o l a r r a d i a t i o n , 1. - S o l a r energy, 199.

95.

357 Southern Bight, 3, 226, 232. Spanish Sahara, 37. Spawning - Spawning ground, 2, 3. - Spawning p e r i o d , 3. s t a b i l i t y , 197, 200, 201. - V e r t i c a l s t a b i l i t y , 191, 192, 196, 202. - S t a b i l i t y spectrum, 192. - S t a b i l i z a t i o n , 197, 198, 199, 203. - l D e s t a b i l i z a t i o n , 198, 203. S t r a i t s o f Dover, 228. S t r a t i f i c a t i o n , 23, 33, 51, 64, 141, 143, 152, 165, 166, 169, 173, 191, 193, 196,

197, 199, 201, 202, 203, 204, 295.

-

-

D e s t r a t i f i c a t i o n , 192, 193, 196, 199, 201, 203, 204. Thermal s t r a t i f i c a t i o n , 52, 59, 67.

Stream, 299, 303, 310. - Stream f u n c t i o n , 227. - Streamline, 80, 96, 236, 245, 251, 270. - Stream v e l o c i t y , 292, 302. S t r e s s , s e e a l s o turbulence, f r i c t i o n . - Reynolds stress Turbulent Reynolds stress, 222, 225, 251. - Mesoscale Reynolds stress t e n s o r , 225, 227, 238, 239, 245. - Residual s t r e s s , 234. - Surface s t r e s s , 235. - Bottom stress, 235, 236, 237. - Turbulent stress, 235. - Mesoscale stress, 250. - Shear stress, 274, 321. Structure - F i n e s t r u c t u r e , 5, 174, 175, 176. - Microstructure, 174, 175. Synoptic - Synoptic - Synoptic - Synoptic - Synoptic

v a r i a b i l i t y , 177, p r o c e s s e s , 183. o r i g i n , 185.

78, 82.

scale,187.

Temperature, 1, 2, 11, 13, 51, 53, 54, 59, 61, 62, 79, 81, 83, 84, 86, 87, 88, 9 0 ,

91, 96, 97, 141, 147, 149, 152, 165, 170, 175, 176, 179, 191, 203, 204, 274, 276, 278, 279, 281. Texas, 21, 23, 29, 41. - W e s t Texas, 30. T h a l a s s i o s i r a , 211. Thermocline, 5, 13, 51, 52, 55, 56, 5 7 , 58, 60, 62, 63, 64, 77, 85, 88, 89, 90, 143,

148, 150, 156, 169, 175, 176, 187, 201, 202, 273, 278, 279, 281, 282. Vhermohaline, 174, 182. - Thermohaline mixing, 101. - Thermohaline c i r c u l a t i o n , 152. - Thermohaline f i e l d , 187. Thiaroye, 143, 148, 151. Tide, 7, 42, 101, 191, 193, 197, 219, 223, 250, 285, 287, 288, 298, 310, 322, 323,

329.

-

Red t i d e , 205.

358

- Tidal - Tidal - Tidal - Tidal - Tidal - Tidal -

Tidal

- Tidal - Tidal - Tidal - Tidal - Tidal - Tidal

-

Tidal

front, 7 v e l o c i t y , 3, 32, 33, 34, 52, 59, 220. motion, 32, 220, 225, 250. mixing, 8, 11, 15, 16, 26, 32, 33, 38, excursion, 11. energy, 33. resuspension, 37. d i s s i p a t i o n , 52. i n f l u e n c e , 57, 324. c y c l e 193, 305. stream, 201. p e r i o d , 250, 251, 331. prism, 293. o s c i l l a t i o n , 220.

T u r b i d i t y , see also sediment, 18, 21, 310, 315, 319, 326, 327, 329, 331.

39,

39,

191, 203,

42,

204,

Turbulence, see a l s o eddy, 4, 51, 52, 53, 55, 56, 58, 165, 175, 197, 219, 270, 273, 274, 275, 279, 281.

58,

60,

285,

141,

61,

290,

148,

63.

292, 296,

152,

155,

304,

156, 158,

Unalaska I s l a n d , 38. upwelling, 8, 13, 15, 16, 18, 19, 21, 23, 84, 86, 87, 89, 91, 92, 93, 94, 95, 96, 145, 146, 147, 148, 150, 152, 153, 154, 203, 204. - Eddy-induced ufiwelling, 26, 29, 30, 31,

26, 28, 30, 31, 33, 36, 79, 80, 81, 82, 83, 99, 104, 110, 118, 119, 123, 124, 141, 144, 156, 158, 160, 161, 166, 191, 197, 202, 42.

Vancouver I s l a n d , 215. Velocity, 33, 53, 54, 99, 106, 227, 236, 274, 293, - Velocity s c a l e , 3, 11. - Velocity p a t t e r n , 7. - Current v e l o c i t y , 3. - Entrainment v e l o c i t y , 55, 57, 60, 62, 63, 76. - Mean v e l o c i t y , 103. - V e r t i c a l v e l o c i t y , 145, 151, 152, 235. - Longitudinal v e l o c i t y , 157. - Velocity f i e l d , 175, 183, 250, 320, 321, 325. - Phase v e l o c i t y , 187. - Residual v e l o c i t y , 224, 225, 233, 285. - Shear v e l o c i t y , 326. V i s c o s i t y , 245, 293, 321. - Eddy v i s c o s i t y , 102, 222, 239, 250, - Kinematic v i s c o s i t y , 174, 274. Vorticity,

26,

Water column, 202, 203.

31,

151,

152,

19, 23, 29,

32,

154, 33,

301,

319,

323,

324.

193,

196,

197,

270.

178, 245, 34,

294,

39,

Wave - B a r o c l i n i c wave, 179. - Barotropic s h e l f wave, 151. - E q u a t o r i a l wave, 105. - Gravity wave, 107, 175. - Kelvin wave, 99, 100, 107, 118, 123. - I n t e r n a l wave, 176, 185. - Wave l e n g t h , 175, 187. - Wave number, 187, 192. - Rossby wave, 107, 118, 119, 134. - Wave speed, 106, 165. - Topographic wave, 179, 187.

250,

69,

251,

185,

270.

191,

192,

199, 201,

359

-

Trapped wave, 105, 182, Yanai wave, 107, 118.

187.

Wind, 7, 99, 151, 191, 193, 197, 201, 202, 219. Wind c u r l , 29, 30. Wind c u r r e n t , 11, 61. Wind energy, 32. Wind f i e l d , 251. Wind f o r c i n g , 33. Heating wind, 77. Local wind, 152. Wind r e s i d u a l , 223, 224, 251. Wind s t r e s s , 26, 81, 82, 83, 84, 92, 93, 97, 154, 197, 227, 228, 234, 237, 276. Trade wind, 19, 100, 143. Wind v e l o c i t y , 55, 144, 145, 197. Mesoscale wind v o r t i c i t y , 152, 233. Yoff,

148,

100,

101,

110,

118,

123,

144,

151.

York River, Yucatan,

99,

196.

31.

Zooplankton, 7, 28, 215, 216, 217.

36,

80,

155,

158,

159,

160, 201,

209,

210, 211, 212,

213, 214,

Acknowledgments The e d i t o r i s indebted t o h i s research s t u d e n t s P . J o r i s and M .

t h e index.

J o s s a f o r t h e i r h e l p i n preparing

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