HYDRODYNAMICS OF SEMI-ENCLOSED SEAS
FURTHER TITLES IN THIS SERIES 1 J.L. MERO THE MINERAL RESOURCES OF THE SEA 2 L.M.FOMlN THE DYNAMIC METHOD I N OCEANOGRAPHY 3 E.J.F.WOOD MICROBIOLOGY OF OCEANS AND ESTUARIES 4 G.NEUMANN OCEAN CURRENTS 5 N.G. JERLOV OPTICAL OCEANOGRAPHY 6 V.VACQUIER GEOMAGNETISM IN MARINE GEOLOGY 7 W.J. WALLACE THE DEVELOPMENTS OF THE CHLORINITY/SALINITY CONCEPT I N OCEANOGRAPHY 8 E. L l S l T Z l N SE A-LEV E L CHANGES 9 R.H. PARKER THE-STUDY OF BENTHIC COMMUNITIES 10 J.C.J. NIHOUL (Editor) MODELLING OF MARINE SYSTEMS 11 0.1. MAMAY EV TEMPERATURE-SALINITY ANALYSIS OF WORLD OCEAN WATERS 12 E.J. FERGUSON WOOD and R.E. JOHANNES TROPICAL MARINE POLLUTION 13 E. STEEMANN NIELSEN MAR1N E PHOTOSY NTH ESlS 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. NIHOUL (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 DRILLING RESULTS I N THE I N D I A N OCEAN 22 P. DEHLINGER MARINE GRAVITY 23 J.C.J. NIHOUL (Editor) HYDRODYNAMICS OF ESTUARIES AND FJORDS 24 F.T. BANNER, M.B. COLLINS and K.S. MASSIE (Editors) THE NORTH-WEST EUROPEAN SHELF SEAS: THE SEA BED AND THE SEA I N MOTION 25 J.C.J. NIHOUL (Editor) MARINE FORECASTING 26 H.G. RAMMING and 2.KOWALIK NUMERICAL MODELLING MAR I N E H Y DRODY N A M lCS 27 R.A. GE,YER (Editor) MAR I NE ENVl RONMENTAL POLLUTION 28 J.C.J. NIHOUL (Editor) MARINE TURBULENCE 29 M. WALDICHUK, G.B. KULLENBERG and M.J. ORREN (Editors) MARINE POLLUTANT TRANSFER PROCESSES 30 A. VOlPlO (Editor) THE BALTIC SEA 31 E.K. DUURSMA and R. DAWSON (Editors) MARINE ORGANIC CHEMISTRY 3 2 J.C.J. NIHOUL (Editor) ECOHYDRODYNAMICS
Elsevier Oceanography Series, 34
HYDRODYNAMlCS OF SEMI-ENCLOSED SEAS PROCEEDINGS OF THE 13th INTERNATIONAL LIEGE COLLOQUIUM ON OCEAN HYDRODYNAMICS
Edited by JACQUES C.J. NIHOUL Professor of Ocean Hydrodynamics, University of Li&e Lisp, Belgium
ELSEVIER SCIENTIFIC PUBLISHING COMPANY Amsterdam - Oxford - New York
1982
ELSEVIER SCIENTIFIC PUBLlSHlNG COMPANY 1, Molenwerf, P.O. Box 21 1. 1000 AE Amsterdam, The Netherlands
Distribution for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 52, Vanderbilt Avenue New York. N.Y. 10017
Library of Congrrbs Cataloging i n P u b l i r a l i o n D a l a
International Liege Colloquium on Ocean Hydrodynamics (13th : 1981) Hydrodynamics of semi-enclosed seas. (Elsevier oceanography series ; 34) Includes index. 1. Oceanography--Congresses. 2. Hydrodynamics-Congresses. I. Nihoul, Jacques C. J. 11. Title. 111. Series. ~~200.1571981 551.47 82-2455 ISBN 0-444-42077-0(U.S.) AACR2
ISBN 0 4 4 4 4 2 0 7 7 4 (Vol. 34) ISBN 0 4 4 4 4 1 6 2 3 4 (Series) 0 Elsevier Scientific Publishing Company, 1982
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Scientific Publishing Company, P.O. Box 330,1000 A H Amsterdam, The Netherlands Printed in The Netherlands
V
FOREWORD
The International LiSge Colloquia on Ocean Hydrodynamics are organized annually.
Their topics differ from one year to another and try to address, as much as
possible, recentproblems and incentive new subjects in physical oceanogranhy. 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 recommendations for future research. Following a suggestion from the steering committee of the Medalpex Project (IOC), the thirteenth colloquium was devoted to the Hydrodynamics of Semi-enclosed Seas, with emphasis on the Mediterranean and the Baltic. Essentially bounded by lands, semi-enclosed seas are threatened by increasing pollution resulting from man's activities.
They constitute, on the other hand,
quasi closed moderate scale systems for which general interdisciplinary models, integrating all aspects from hydrodynamics to chemistry and ecology, can be developed, calibrated and applied to the definition of control and management POlicies. But, there is perhaps a more cogent reason for devoting a special research effort to the hydrodynamics of semi-enclosed seas
:
in many aspects
they are redu-
ced-scale models of the world oceans. Gyres, synoptic eddies, meanders and fronts are often found in semi-enclosed seas at relatively much smaller scales, easier to observe and to represent in mathematical models. The papers presented at the Thirteenth International Liege Colloquium on Ocean Hydrodynamics, not only constitute a necessary state of the art review preparing the Medalpex experiment, they also contribute to a better understanding of Ocean Hydrodynamics.
Jacques C.J. NIHOUL.
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VII
The S c i e n t i f i c O r g a n i z i n g Committee of t h e T h i r t e e n t h I n t e r n a t i o n a l Liege
Colloquium on
Ocean Hydrodynamics
and a l l t h e p a r t i c i p a n t s their gratitude to the o f Education,
wish t o e x p r e s s Belgian
Minister
t h e N a t i o n a l S c i e n c e Foun-
d a t i o n of Belgium, t h e U n i v e r s i t y o f Liege, t h e Intergovernmental
Oceanographic Com-
mission a n d t h e D i v i s i o n o f M a r i n e Sciences (UNESCO)
and t h e O f f i c e o f Naval
f o r t h e i r most v a l u a b l e s u p p o r t .
Research
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IX
LIST OF PARTICIPANTS
AITSAM, A., Prof., Dr., Department of the Baltic Sea, Academy of Sciences Estonian SSR, Tallinn, USSR. ALENIUS, P., Mr., Tnstitute of Marine Research, Helsinki, Finland. AMBROSIUS, V., Dr., Department of the Baltic Sea, Academy of Sciences Estonian SSR, Tallinn, USSR. BADAN-DANGON, A., Dr., CICESE, Ensenada, B.C. Mexico. BAH, A., Dr., Ecole Polytechnique de Cdnakry, Guinea. BERGAMASCO, A., Dr., C.N.R., Venice, Italy. BETHOUX, J.P., Dr., Laboratoire de Physique et Chimie Marines, Villefranche s/mer, France. BOUKARI, S., Mr., University of Niamey, Niger. BOWMAN, M.J., Prof., Dr., State University of New York at Stony Brook, U.S.A. CANDELA, J., Mr., CICESE, Ensenada, B.C., Mexico. CLEMENT, F., Mr., Universite de Liege, Belgium. CREPON, M., Dr., Museum d'Histoire Naturelle, Laboratoire d'oceanogranhie Phvsique, Paris, France. DISTECHE, A., Prof., Dr., Universite de Liege, Belgium. DJENIDI, S., Ir., 2, Rue BP, Cite Plaisance, Annaba, Algerie. ELKEN, J., Mr., Dewartment of the Baltic Sea, Academy of Sciences Estonian SSR, Tallinn, USSR. FRACHON, B., Mr., Museum d'Histoire Naturelle, Laboratoire d'oceanogranhie Physique, Paris, France. FRASSETTO, R., Dr., C.N.R., Venice, Italy. GASCARD, J.C., Dr., Museum d'Histoire Naturelle, Laboratoire d'oceanographie Physique, Paris, France. HAPPEL, J.J., Ir., Universite de Liege, Belgium. HECQ, J.H., Dr., Universite de Liege, Belgium. HEBURN, G.W., Dr., Science Applications Inc., Slidell, La., U.S.A. HOWARTH, M.J., Mr., I.O.S., Bidston Observatory, Birkenhead, U.K. HUA, B.L., Dr., Museum d'Histoire Naturelle, Laboratoire d'Oc6anographie Physique, Paris, France. HURLBURT, H.E., Dr., NORDA, NSTL Station, Ms., U.S.A. JACOBSEN, T., Dr., Marine Pollution Laboratory, Charlottenlund, Denmark. JAMART, B.M., Dr., University of California, Santa Barbara, U.S.A. KAHRU, M., Mr., Department of the Baltic Sea, Academy of Sciences Estonian SSR, Tallinn, USSR. KAUP, El, Dr., Department of the Baltic Sea, Academy of Sciences Estonian SSR, Tallinn, USSR.
X KRAAV, V . , D r . , Deuartment o f t h e B a l t i c S e a , Academy o f S c i e n c e s E s t o n i a n SSR, T a l l i n n , USSR.
KULLAS, T . , D r . , DeDartment o f t h e B a l t i c S e a , Academv of S c i e n c e s E s t o n i a n S S R , T a l l i n n , USSR. KULLENBERG. G . ,
Prof.,
KVASNOVSKY, G . ,
Mr.,
U n i v e r s i t y o f Co>enhayen, Denmark.
SACLANT ASW R e s e a r c h C e n t r e , La S n e z i a , I t a l y .
LACOME, H . , P r o f . , Museum d ' H i s t o i r e N a t u r e l l e , L a b o r a t o i r e d ' O c 6 a n o g r a n h i e Phys i q u e , P a r i s , France.
LEBON, G . , LEKIEN,
Prof.,
B.,
U n i v e r s i t e d e L i e g e , Belgium.
I r . , U n i v e r s i t e d e L i e g e , Belgium.
LILOVER, M . J . , DeDartment of t h e B a l t i c S e a , Academy of S c i e n c e s E s t o n i a n SSR, T a l l i n n , USSR.
LOFFET, A . ,
I T . , U n i v e r s i t e d e L i s g e , Belgium.
LOKK, J., M r . , Department o f t h e B a l t i c S e a , Academy o f S c i e n c e s E s t o n i a n SSR, T a l l i n n , USSR.
Dr.,
MANZELLA, G . ,
C.N.R.,
L e r i c i , La SDezia, I t a l y .
MILLOT, C . , D r . , Museum d ' H i s t o i r e N a t u r e l l e , L a b o r a t o i r e d ' O c 6 a n o g r a n h i e P h y s i que, P a r i s , France. MOEN, J., D r . ,
SACLANT ASW R e s e a r c h C e n t r e , La SDezia, I t a l y .
J.M., M r . ,
MOLINES,
I n s t i t u t d e MBcanique de G r e n o b l e , F r a n c e .
YYUURISEPP, S . , M r s . , De?artment SSR. T a l l i n n , USSR.
of t h e B a l t i c S e a , Academy of S c i e n c e s E s t o n i a n
NADAILLAC D e , G . , M r . , Museum d ' H i s t o i r e N a t u r e l l e , L a b o r a t o i r e d ' o c e a n o g r a n h i e Physique, P a r i s , France. NGENDAKUMANA, NIEHAUS, NIHOUL,
P.,
Y.c.w., J.c.J.,
I r . , B.P.
Dr., prof.,
936, Bujumbura, B u r u n d i .
U n i v e r s i t y o f L i v e r n o o l , DeDartment o f Oceanogranhy, U . K . Dr.,
U n i v e r s i t e de L i e g e , Belgium.
PEDERSEN, F . B . , P r o f . , D r . , T e c h n i c a l U n i v e r s i t y o f Denmark, I n s t i t u t e o f Hydrodynamics, Lyngby, Denmark. PHILIPPE,
M.,
Dr.,
C e n t r e de M6teorologie S D a t i a l e , Lannion, France.
PODER, T . , D r . , Denartment of t h e B a l t i c S e a , Academy of S c i e n c e s E s t o n i a n SSR, T a l l i n n , USSR. P . , M r . , Department o f t h e B a l t i c S e a , Academy o f S c i e n c e s E s t o n i a n SSR. T a l l i n n , USSR.
PORTSMUTH,
PRELLER, R . , RENOUARD, D . ,
Miss, JAYCOR, NORDA, NSTL S t a t i o n , M s . , Dr.,
U.S.A.
I n s t i t u t d e Mecanique de G r e n o b l e , F r a n c e .
RICHEZ, C . , M r s , Museum d ' H i s t o i r e N a t u r e l l e , L a b o r a t o i r e d ' O c 6 a n o g r a n h i e P h y s i que, P a r i s , France. RONDAY,
F.c.,
RUNFOLA, Y . ,
Dr.,
Mr.,
U n i v e r s i t e d e L i e g e , Belgium. U n i v e r s i t e d e L i e g e , Belgium.
SAINT G U I L Y B . , P r o f . , Museum d ' H i s t o i r e N a t u r e l l e , L a b o r a t o i r e d ' 0 c G a n o g r a n h i e Physique, P a r i s , France. SCHAUER, U . ,
Miss,
I n s t i t u t f u r Meereskunde, U n i v e r s i t a t K i e l ,
SMITZ, J . , I r . , U n i v e r s i t B d e LiGge, Belgium.
W.
Germanv.
XI TANG, C . ,
Dr.,
THOMASSET, F . ,
Bedford I n s t i t u t e of Oceanogravhy, Dartmouth, N.S.,
Canada.
IT., I N R I A , Le Chesnay, F r a n c e .
TOOMPUU, A . , M r . , Department of t h e B a l t i c S e a , Academy of S c i e n c e s E s t o n i a n SSR, T a l l i n n , USSR. VAULOT,
D.,
Mr.,
U n i v e r s i t 6 d e M o n t v e l l i e r , France.
Miss, Museum d ' H i s t o i r e N a t u r e l l e , Laboratoire d'Oc6anogravhie Physique, P a r i s , F r a n c e .
WACONGNE,
S.,
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XI11
CONTENTS
.................................................................. ACKNOWLEDGMENTS ........................................................... FOREWORD
NIHOUL
OceanograDhy of semi-enclosed s e a s
:
LACOMBE and C.
H.
RICHEZ
R. PRELLER and H . E . HURLBURT
...........................................
L.
13
75
Surface temperature f r o n t s i n t h e Mediterra-
:
..................................
nean from i n f r a r e d s a t e l l i t e imagery J.P.BETHOUX,
. . . .. . ..
1
A reduced g r a v i t y numerical model of c i r -
:
c u l a t i o n i n t h e Alboran s e a
M. PHILIPPE and L. HARANG
......................
The regime' of t h e S t r a i t s of G i b r a l t a r
:
VI I IX
LIST OF PARTICIPANTS....................................................... J.C.J.
V
PRIEUR and F. NYFFELER
:
91
The water c i r c u l a t i o n i n t h e
North Western Mediterranean s e a , i t s r e l a t i o n with wind and atmomhe-
.........................................................
r i c Dressure C. MILLOT
:
Analysis o f uDwelling i n t h e Gulf of Lions
SAINT-GUILY
B.
:
RENOUARD
:
143
Discontinuous upwelling along a r e c t i l i n e a r c o a s t with
a series of small c a w s D.P.
.................
129
..............................................
155
Deviation with r e s p e c t t o C o r i o l i s period f o r g r a v i t y -
i n e r t i a l - i n t e r n a l waves generated i n an ocean b a s i n by an imnulsional
................................................................. R I Z Z O L I and A. BERGAMASCO : Hydrodynamics of t h e A d r i a t i c sea .....
wind P.M. A.
ESPOSITO and G. MANZELLA HOWARTH
M.J.
Non-tidal flow i n t h e North Channel of t h e I r i s h sea
:
HURLBURT and J . D .
H.E.
THOMPSON
:
HEBURN, T . H .
KINDER, J . H .
ALLENDER and H . E .
HURLBURT
................ :
A model f o r f r o n t a l upwelling
TANG
M.J.
BOWMAN and S.M.
:
CHISWELL
Hauraki Gulf, New Zealand PEDERSEN : made impact
F.B.
:
187
205
243
A numerical
............ ..............................
model of eddy g e n e r a t i o n i n the Southeastern Caribbean s e a C.L.
177
The dynamics of t h e loop c u r r e n t and
shed e d d i e s i n a numerical model of t h e Gulf of Mexico G.W.
.. ....
Current c i r c u l a t i o n i n t h e Ligurian s e a
:
165
299 329
Numerical t i d a l s i m u l a t i o n s within t h e
.............................................
349
The s e n s i t i v i t y of t h e B a l t i c Sea t o n a t u r a l and man-
...........................................................
385
G. KULLENBERG
:
Mixing in the Baltic sea and imnlications for the
...............................................
environmental conditions A.
AITSAM, J. LAANEMETS, and M.J. LILOVER open parts of the Baltic sea
A. AITSAM and J. ELKEN
:
Fine structure of the
..........................................
A. AITSAM and L. TALPSEPP
..,........
................................
J. HEINLOO and A. TOOMPUU
J. LOKK and A. PURGA
:
............................... cascade model of turbulent diffusion .....
A
:
511 517
Water quality study of the Baltic Sea by optical
remote sensing methods :
503
Modelling of some hydrodynamical Drocesses by a model of
rotationally anisotropic turbulent flow
M. KAHRU
489
Modelling of the climatic scale variabilitv
of the hydrodynamics of the Baltic sea :
469
The variability of the temwrature, sali-
:
nity and density fields in the u p m r layers of the Baltic sea :
433
Synoptic variability of currents in the
:
A. AITSAM and J. PAVELSON
J. HEINLOO
..........
.........................................................
T. KULLAS and V. KRAAV
419
Synontic scale variability of hydronhysical
:
fields in the Baltic ProDer on the basis of CTD measurements
Baltic Proper
399
................................................
523
The influence of hydrodynamics on the chlorophyll field in
the o w n Baltic
.......................................................
V.I. ZATS and R.V. OZMIDOV
:
Subject index
Characteristic properties of turbulent
............................................ ............................................................
transport in the Black sea
531
543 547
1
OCEANOGRAPHY OF SEMI-ENCLOSED SEAS Medalpex
:
an i n t e r n a t i o n a l f i e l d experiment i n t h e Western Mediterranean
Jacques C . J . NIHOUL
*
MBcanique des F l u i d e s GBophysiques
-
Universite? de Liege
INTRODUCTION There i s no c l e a r - c u t d e f i n i t i o n o f a semi-enclosed s e a .
A c o n t i n e n t a l sea
which, l i k e t h e B a l t i c and t h e Mediterranean, i s e s s e n t i a l l y bounded by land i s c a l l e d an "enclosed sea" or a "semi-enclosed sea".
The c h a r a c t e r i s t i c of semi-
enclosed seas i s the l i m i t e d communication with a d j a c e n t s e a s or oceans, c o n t r a r y t o "semi-open s e a s " l i k e t h e North Sea o r t h e China Sea o r "open seas" with a long i n d e f i n i t e boundary with t h e ocean l i k e t h e Sea of Andaman. A t t h e Nato Conference on Modelling of Marine Systems (OFIR, Portugal, June 1973
a s p e c i a l working group was s e t up on enclosed s e a s . I t i s i l l u m i n a t i n g t o r e c a l l t h e main conclusions of t h i s working group (Nihoul, 1975) "Enclosed s e a s lend themselves p a r t i c u l a r l y w e l l t o t h e study of t h e whole u n i t a s an ecosystem, f o r t h e following reasons
:
(1)
Boundary c o n d i t i o n s a r e u s u a l l y r e l a t i v e l y w e l l defined.
(2)
N u t r i e n t , s a l t and water budgets can o f t e n be framed with more p r e c i s i o n
than elsewhere. (3)
Small b a s i n s lend themselves t o whole-system f i e l d experiments.
Moreover, from t h e p r a c t i c a l viewpoint, enclosed s e a s o f t e n serve a s waste s i n k s and g i v e r i s e t o s e r i o u s management problems, such a s c o n f l i c t of i n t e r e s t between waste d i s p o s a l and r e c r e a t i o n o r aquaculture. A fundamental component of a good model of an a q u a t i c ecosystem i s t h e hydrody-
namic s t r u c t u r e . We recommend t h a t support be given t o continued development and refinement of fundamental hydrodynamics. Outputs of t h e hydrodynamic models w i l l be s p e c i f i c a t i o n of flow p a t t e r n s under varying c o n d i t i o n s of f o r c i n g p a r t i c u l a r l y by f o r c e s of meteorological o r i g i n . These flow f i e l d s w i l l include c i r c u l a t i o n p a t t e r n s , upwelling phenomena, long s u r f a c e and i n t e r n a l waves, and t h e formation, movement and d i s s i p a t i o n of i c e . These o u t p u t s provide t h e b a s i s f o r enhanced understanding of t h e physics of t h e K
Also a t t h e
" I n s t i t u t d'Astronomie e t de GQophysique" Universite de Louvain.
system, and serve as the essential framework for an integrated model of an ecosystem. Progress in modelling must proceed hand-in-hand with experiments and field verification, through collection of relevant physical, chemical and biological data observed as nearly simultaneously as possible. For many such field operations, large coordinated programmes will be required. The design of such programmes should depend on the results of preliminary modelling and the results of the programmes should be used to modify and improve the models. Planning and implementation of a collaborative programme should include the following stages
:
(1)
A review of existing data and an initial attempt at modelling,leading to
(2)
Optimization of field programmeswith respect to improved data coverage,
coordinated collections, standardized and automated methods. (3) Experiments in laboratory and field to elucidate mechanisms not sufficiently understood.
(4)
As
a consequence and parallel development, successive improvements in mo-
delling. Equipment needed for such a programme should include ships and aircrafts, instruments for automated data collection (e.g. moored buoys) and access to the largest available computers." Two of the main reasons to devote a special research effort to the study of semi-enclosed seas are stressed in the recommendations. Essentially bounded by lands, semi-enclosed seas are threatened by increasing pollution resulting from man's activities. They constitute, on the other hand, quasi-closed moderate scale systems for which general interdisciplinary models, integrating all aspects from hydrodynamics to chemistry and ecology, can be developed, calibrated and applied to the definition of control and management policies. One point that the working group did not raise the question was much less evident
-
,
though,
-
because, in 1973,
is that semi-enclosed seas are, in many aspects,
reduced-scale models of the world oceans. Gyres, synoptic eddies, meanders and fronts are often found in semi-enclosed seas at relatively much smaller scales, easier to observe and to represent in mathematical models.
The title of this paper "Oceanography of semi-enclosed seas"
has been chosen to emphasize this important feature. The Working Group's recommendations on the planning and implementation of large scale international programs include
,
in priority
(i) a review of existing data and models (ii) an optimization of field programmes with respect to important data coverage, coordinated collections, standardized and automatic methods. The first point is the objective of the 13th International Liege Colloquium (with emphasis on the Baltic and the Mediterranean).
The second recommendation is adressed - with an exceptional deployment of technical and human means 1981-1982
-
by the Medalpex experiment in the Mediterranean, in
u-
.
THE ALPEX-MEDALPEX EXPERIMENT
I
Recognizing the global importance of the influence of mountain complexes on the atmospheric circulation and weather developments, the Joint Organizing Committee (WMO, ICSU) for the Global Atmospheric Research Programme (GAW) recommended the
establishment of a sub-programme on "Air Flow over and around Mountains". As a first step, a field experiment, "ALPEX" was planned in the region of the Alps
(fig. 1) for a period of 13 months from,,.September1, 1981, to September 30, 1982, with an intensive special period of observations from February 15 to April 30, 1982. The Executive Council of the International Oceanographic Commission (IOC) decided to support the development, during the same period, of an oceanographic programme in the Mediterranean Sea, and in particular the Liguro-ProvenGal Basin and the Adriatic Sea
: "MEDALPEX".
The mobilization of several vessels to provide the required sea-air interaction data for Alpex, the intense coverage of meteorological observations in the area, (fig. 2 , table 1) offers a unique opportunity to study oceanographic processes which strongly depend on atmospheric forcing (heat and momentum fluxes). In the Liguro-ProvenGal Basin, in the summer, a marked seasonal thermocline is formed and, when the wind is blowing, a well-defined mixed layer develops. In the winter, under the action of cold, dry coatinental winds (Tramontane, Mistral), the stratification wears off, but the center is affected earlier than the periphery
:
fairly deep convection takes place first in the central area, while outside the usual three-layer system of "bottom", "intermediate" and "surface" waters remains. A front is thus created (analonnlrs to the polar front, with a scaling factor of the order of 1/100). As a result of baroclinic instability, the front meanders and generates couples of eddies in the vicinity of the convective region. Vertical motions associated with the instability may produce patches of nutrient enriched waters with intense primary production and may result, in the center region, in the intermediate warm water coming to the surface. Thus, the water temperature of the surface layer increases in the central area with subsequent heat loss through evaporation and increase of density. The position of this excess heat in the central area presumably plays a role in the atmosphere's behaviour.
*
The material presented in the following is partly borrowed from successive reports written, under the auspices of IOC, by a working group of expert of which the author was a member.
4
Fig.
1. Proposed Inner and Outer Experimental Area.
2
0
0
0
0
0
N
5
6 TABLE 1
ALPEX data requirements
I RESOLUTION
SCIENTIFIC OBJECTIVE!
PARAMETERS
REMARKS
VsrtiCsl
1.0 km
50 km
5h
1.0 km
50 km
5h
0.2 km
50 km
6h
0.2 km 0.2 km
50 km 50 km
6h
5h
1.0 km 1.0 km
0.2 km
150 km
I
148
Ill
3h 20 % 0.5 K
-
p "'W'
UU'W'
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x+
W'P'
2 - 3 km
km
stadarc
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6h
0.5 km 2 - 3 km
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cp'- W ' T
L .w'q'
5.. 8 " r f . a
tomuaretun
9;
9:
150 km
6h
150 km
24 h
1.5 km
dbdo
9:
9:
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1K
1.6 km
10%
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Rolmvsnt S 111
C ~ M :
-- 1 OOO km -
121 200 km 131 20.30 km
0 : fluxet f r m oircran 5.10wm-
1.5 km
i
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Processes i n t h e Western Mediterranean a r e reminiscent of what happens i n t h e Labrador Sea o r t h e A n t a r t i c , l e a d i n g t o t h e formation of deep oceanic waters. However o b s e r v a t i o n s needed t o v a l i d a t e models a r e more e a s i l y c o l l e c t e d i n t h e Mediterranean. Strong upwellings a r e generated i n t h e Gulf of,Lion when t h e M i s t r a l o r t h e Tramontane i s blowing. I n t e r n a l waves, generated a t t h e shore, propagate t o t h e deep s e a . A l l t h e s e phenomena a r e d i r e c t l y r e l a t e d t o t h e c o n d i t i o n s of t h e atmosphere
and, e s p e c i a l l y , t o t h e i r s p a t i a l p a t t e r n . The absence of s i g n i f i c a n t t i d e s i n t h e Mediterranean makes it p o s s i b l e t o observe t h e e f f e c t s of meteorological forcing,,without b i a s . Remote sensing techniques a r e e a s i l y a p p l i c a b l e t o t h e Mediterranean sea a s t h e sky, when t h e M i s t r a l o r t h e Tramontane blows, i s r e l a t i v e l y f r e e of clouds. I n t h e r e l a t i v e l y shallow A d r i a t i c Sea, i n a d d i t i o n t o t h e seasonal c y c l e of s t r a t i f i e d water i n t h e summer and mixed water i n t h e w i n t e r , t i d e s and seiches a r e s i g n i f i c a n t . During some w i n t e r s , under t h e i n f l u e n c e of Bora, a strong dry n o r t h e a s t e r l y wind, very dense water i s formed i n t h e Northern p a r t .
This water
flows down t o t h e South and c o n t r i b u t e s t o t h e formation of deep mediterranean water. Under t h e a c t i o n of s t r o n g winds coming from t h e South with some 500 km f e t c h , i n t e n s e storm surges can occur i n t h e North and deeply a f f e c t Venice. From an economic p o i n t of view, f o r e c a s t i n g t h i s phenomenon i s e s s e n t i a l and Medalpex i s a unique opportunity t o g a t h e r t h e necessary information f o r b e t t e r understanding and more a c c u r a t e modelling.
SPECIFIC CASE STUDIES I N THE SCOPE OF MEDALPEX (i)
Offshore dynamic response under s e v e r e weather c o n d i t i o n s
Although Mediterranean hydrodynamics has
been i n v e s t i g a t e d by s c i e n t i s t s of
s e v e r a l c o u n t r i e s f o r many y e a r s , one must admit t h a t very l i m i t e d information i s a v a i l a b l e on t h e behaviour of t h e Mediterranean sea i n severe weather conditions when oceanographic v e s s e l s cannot o p e r a t e . During t h e S p e c i a l Period of i n t e n s i v e o b s e r v a t i o n s of t h e GARP Alpine Experiment, time s e r i e s of c l a s s i c a l oceanographic o b s e r v a t i o n s may o c c a s i o n a l l y be i n t e r r u p t e d by bad weather b u t they w i l l be complemented by information from remote sensing surveys, moored l a b o r a t o r y buoys and f i x e d platforms, d r i f t i n g buoys, sea-level gauges and near-shore i n v e s t i g a t i o n s .
I t i s t h u s reasonable
t o expect t h a t t h e
importance of t h e unique experimental network ( p a r t of which w i l l be serviced, i f only f o r t h e meteorological experiment) w i l l provide enough d a t a t o gain, with t h e h e i p of s p e c i a l l y devised mathematical models, a f a i r l y good and new understanding of t h e response of t h e s e a t o atmospheric f o r c i n g . T h i s understanding w i l l i n c l u d e t h e e f f e c t s of t h e passing storms
f
N f 0
W
9
10
( i l on t h e g e n e r a l c i r c u l a t i o n
-
t h e g e n e r a l f e a t u r e s of which a r e reasonably well-
xnown i n moderate weather c o n d i t i o n s ,
( i i )on v e r t i c a l motions,
( i i i )on t h e con-
d i t i o n s of b a r o t r o p i c and b a r o c l i n i c i n s t a b i l i t i e s w i t h increased c u r r e n t s h e a r s , ( i v ) on t h e response of oceanic f r o n t s t o modified hydrological c o n d i t i o n s during storms,
( v ) on t h e g e n e r a t i o n of mesoscale eddies (which, i n Mediterranean f e a t u r e
a t smaller - e a s i e r t o observe
-
s c a l e s t h e synoptic e d d i e s of t h e o c e a n ) , and
4
( v i ) on t h e i d e n t i f i c a t i o n of p e r i o d s of i n t e n s e t u r b u l e n t mixing and d i s s i p a t i o n l e a d i n g t o a reassessment of t h e t u r b u l e n t d i s s i p a t i o n r a t e i n t h e ocean, t a k i n g time i n t e r m i t t e n c y i n t o account. Such an i n t e n s i v e i n v e s t i g a t i o n o f t h e response of t h e sea t o s e v e r e weather c o n d i t i o n s w i l l be new i n t h e s e n s e t h a t f o r t h e f i r s t time a l i m i t e d b u t represent a t i v e a r e a w i l l be adequately covered both from t h e meteorolgical a d t h e oceanographic p o i n t of view
(fig. 3 ) .
( i i ) Storm s u r g e s and c o a s t a l p i l i n g - u p For t h e A d r i a t i c Sea, t h e v e r i f i c a t i o n of storm surge p r e d i c t i o n models which a r e now based on s e a l e v e l o b s e r v a t i o n s along t h e Venetian c o a s t l i n e and on wind s t r e s s over t h e A d r i a t i c derived from t h e atmospheric p r e s s u r e g r a d i e n t using d a t a of t h e s y n o p t i c network, can be improved with a more d e t a i l e d information on t h e wind f i e l d (speed and d i r e c t i o n ) over the s e a . The Ligurian Sea has p r a c t i c a l l y no t i d e s b u t t h e sea l e v e l and t h e c o a s t a l waves during c y c l o g e n e s i s , m i s t r a l g u s t s and l i b e c c i o (SW wind with 500 n.m. produce damage on t h e c o a s t l i n e .
fetch)
So f a r no model has been developed t o simulate
storm s u r g e s o r c o a s t a l water p i l i n g - u p i n semi-enclosed b a s i n s such a s t h e LiguroProvenqal and t h e Tyrrhenian Basins. With a good determination of t h e wind f i e l d , with i t s time and space v a r i a t i o n , and wave and s e a l e v e l d a t a , such a model can be developed and v e r i f i e d . The envisaged model can be improved f u r t h e r i f s e a l e v e l o b s e r v a t i o n s along t h e African c o a s t l i n e a s well a s t h e e n t i r e Algero-Provenqal
and Spanish Basin can be included,
t h u s forming a closed boundary model f o r t h e e n t i r e Western Mediterranean.
For such s t u d i e s , a network of t i d e and wave gauges s e p a r a t e d by 200 o r 300 km
w i l l be installed,implementing t h e e x i s t i n g s e a l e v e l and wave observing system along t h e c o a s t of t h e Western Mediterranean. The network w i l l work over t h e e n t i r e ALPEX p e r i o d and w i l l a l s o be of g r e a t i n t e r e s t t o t e s t , l a t e r on, c l i m a t e r e l a t e d
s t u d i e s on mean s e a l e v e l v a r i a t i o n s
(iii)Air-sea boundary-layer
(fig. 4 ) .
studies
The importance of s e a - a i r i n t e r a c t i o n s has been s t r e s s e d i n t h e Alpex Design Proposal. Fluxes of momentum, energy, s e n s i b l e and l a t e n t h e a t and r a d i a t i o n budgets a s l i s t e d i n t a b l e 1 m u s t be measured near t h e s e a s u r f a c e from f i x e d platforms i n shallow water, and from moored l a b o r a t o r y buoys a s well a s from s h i p s recording d a t a
from a u x i l i a r y buoys i n deep water. An e f f o r t must be made t o i n c r e a s e t h e accuracy by using simultaneously d i f f e r e n t methods f o r t h e c a l c u l a t i o n of t u r b u l e n t f l u x e s ( c o r r e l a t i o n a n a l y s i s from d i r e c t measurement of t u r b u l e n t f l u c t u a t i o n s , f i t t i n g of mean p r o f i l e s , e t c . ) and t o c o r r e l a t e o b s e r v a t i o n s i n t h e atmospheric boundyy
l a y e r with observations i n
t h e upper l a y e r of t h e sea. These measurements a r e i n d i s p e n s a b l e f o r t h e study of a i r - s e a i n t e r a c t i o n s and such problems a s mixed-layer deepening with i t s i m p l i c a t i o n s i n primary production.
(iv)
Upwelling
T r a n s i e n t upwellings have been obseryed i n t h e A d r i a t i c Sea and i n t h e Gulf of Lion. They a r e e a s i l y observed i n t h e summer when t h e thermal g r a d i e n t s a r e important. Their o f f s h o r e l e n g t h s c a l e i s roughly of t h e o r d e r of t h e i n t e r n a l r a d i u s o f deformation and t h e i r spin-up time of some hours. Their shape is l i n k e d t o t h e shore geometry and t h e space v a r i a b i l i t y of t h e wind a s it can be seen from i n f r a - r e d s a t e l l i t e thermography. Numerical models have been developed. They o f t e n succeed i n reproducing t h e complicated upwelling p a t t e r n s b u t they have been s o f a r l i m i t e d by an approximate knowledge of t h e wind f i e l d . The d a t a provided by Medalpex w i l l c o n t r i b u t e t o a b e t t e r c a l i b r a t i o n of t h e models.
(v)
Marine ecosystems and p o l l u t i o n
D i f f e r e n t c o n d i t i o n s of water q u a l i t y and o f water dynamics i n shallow w a t e r ( A d r i a t i c ) with i n t e n s e run-off
from seven r i v e r s , one of which
-
t h e Po
-
i s one
of t h e major r i v e r s of t h e Mediterranean and i n deep water (Liguro-Provensal a r e a ) with r i v e r s more spaced (Arno, Rhone) can be b e t t e r s t u d i e d when t h e meteorological and p a r t i c u l a r l y wind p a t t e r n s a r e known,during on-going measurements. Marine e c o l o g i c a l and p o l l u t i o n models cannot provide r e a l i s t i c r e s u l t s without t h e c o r r e c t values of wind, waves, evaporation, depth of mixed l a y e r and of t h e thermocline, and c u r r e n t p a t t e r n s i n space and t i m e . Medalpex w i l l provide a unique s e t of d a t a f o r t h e s e models.
(vi)
Climate modelling
Directmeasurements o f f l u x e s a t t h e a i r - s e a i n t e r f a c e and energy budget d e t e r mination w i l l provide u s e f u l observations f o r c l i m a t e s t u d i e s . The s i z e of t h e Mediterranean and t h e subsequent p o s s i b i l i t y of monitoring i t with r e l a t i v e l y modest f a c i l i t i e s (which were never implemented s y s t e m a t i c a l l y , except i n l i m i t e d a r e a s ) , tend t o prove t h a t t h i s s e a may be a good f i e l d f o r studying t h e ways i n which t h e s e a responds t o atmospheric and energy exchange f o r c i n g
12 The f a c t , a l s o recognized, t h a t t h e long-term
( c e n t u r y ) e v o l u t i o n of t h e sea-
s u r f a c e temperature i n t h e Mediterranean i s i d e n t i c a l with t h a t recorded f o r a l l s t u d i e d a r e a s of t h e Northern hemisphere demonstrates t h a t t h i s s e a may be a " p i l o t " b a s i n f o r t h a t time s c a l e . REFERENCES
Alpex Experiment Design Proposal, ( r e v i s e d February 1980). Report of t h e I n t e r n a t i o n a l Study Conference on Airflow Over and Around Mountains h e l d i n S v e t i S t e f a n , Yugoslavia and Venice, I t a l y , May 1976. C o a s t a l Ecosystems of t h e Southern Mediterranean : Lagoons, D e l t a s and S a l t Marshes - Report of a Meeting of Experts, Tunis, September 1978. UneSCO r e p o r t s i n marine s c i e n c e No. 7 (Unesco 1979). Lacombe, H . , Gascard, J . C . , Gonella, J., Bethoux, J . P . , 1979. Response O f t h e Mediterranean t o t h e water and energy f l u x e s a c r o s s i t s s u r f a c e , on seasonal i n t e r a n n u a l and c l i m a t i c s c a l e s (paper p r e s e n t e d a t t h e General Assembly of I n t e r n a t i o n a l Union of Geodesy and Geophysics, Camberra, A u s t r a l i a , December 1979Symposium "Ocean and atmospheric boundary l a y e r s " . Marine Ecosystem Modelling i n t h e Mediterranean - Report of t h e Second Unesco Workshop on Marine Ecosystem Modelling, Dubrovnik, Yugoslavia, October 1976, Unesco r e p o r t s i n marine s c i e n c e No. 2 (Unesco 1977). Nihoul, J . C . J . , 1975. Modelling of Marine Systems, E l s e v i e r Publ., Amsterdam, 272 pp. Oceanographic Aspects of t h e F i r s t GAW Global Experiment (Prepared j o i n t l y by IOC and GAO/WMO), IC€/INF-351 (Unesco, November 1978). Rapports e t Proces-Verbaux des Reunions - Commission I n t e r n a t i o n a l e pour 1'Explor a t i o n S c i e n t i f i q u e de l a Mer Mediterrange - V o l . 25/26, Fasc. 7 (Monaco 1979). Rapport concernant l ' a c t i v i t 6 du Cornit6 d'Oc6anographie physique durant l e XXVIe Congr+s-Assembl6e p l e n i e r e (Antalya, November 1978). Report of t h e IOC/GFCM/ICSEM I n t e r n a t i o n a l Workshop on Marine P o l l u t i o n i n t h e Mediterranean. I O C Workshop Report No. 3 (Unesco 1975).
13
THE REGIME OF THE STFAIT OF GIBRALTAR H. LACOllBEland C.
RICHEZJ
1. L a b o r a t o i r e d ' o c e a n o g r a p h i e Physique du t:us&un N a t i o n a l d ' H i s t o i r e N a t u r e l l e 43-45,
rue Cuvier
75231 P A R I S Cedex 05
FRANCE
LBSTKACT The s t r a i t o f G i b r a l t a r , and t h e a s s o c i a t e d s i l l ( a b o u t 300 m deep) i s a rer:ark a b l e model f o r t h e s t u d y o f t h e regime o f a s t r a i t c o n n e c t i n g t h e ocean w i t h a " c o n c e n t r a t i o n b a s i n " , i . e . a b a s i n which, t h r o u g h i t s s u r f a c e and f r o m i t s w a t e r shed, r e c e i v e s l e s s w a t e r t h a n i t l o s e s by e v a p o r a t i o n . I n t h e l o n r u n , t h e r e s u l t i n g w a t e r d e f i c i t i s compensated b y i n p o r t a n t exchanges t h h e s t r a i t . The c o n s e r v a t i o n o f t h e w a t e r volume i n t h e sea and o f i t s s a l t c o n t e n t makes i t p o s s i b l e t o e x p e c t t h e presence, i n t h e s t r a i t , o f two o p p o s i t e movements : t h e f i r s t e n t e r i n g n e a r t h e s u r f a c e , c a r r y i n g a f l u x o f r e l a t i v e l y s m a l l s a l i n i t y ( A t l a n t i c w a t e r ) ; t h e second, o u t f l o w i n g a t depth ( f o r i t i s d e n s e r ) , c a r r y i n g a somewhat s n a l l e r f l u x ( a b o u t 4 %) b u t s a l t i e r ( a b o u t + 4 % ) , so t h a t i t c a r r i e s t h e same amout o f s a l t t h a n t h e i n f l o w i n g f l u x .
-
I n t h e s t r a i t , t h e s e two mean f l u x e s ( w h i c h can be e v a l u a t e d f r o m c u r r e n t measurements o f s u f f i c i e n t d u r a t i o n ) a r e s e p a r a t e d b y an " i n t e r f a c e " , o r t r a n s i t i o n l a y e r o f h i g h v e r t i c a l s a l i n i t y g r a d i e n t . I t s mean depth decreases f r o m I k s t (180 m) t o E a s t (100 m) w i t h i n t h e s t r a i t i t s e l f . The shape o f t h e s t r a i t s e c t i o n s i n t h e West (where i t i s " t r i a n g u l a r " and widens o u t a t t h e s u r f a c e ) and i n t h e E a s t (where i t has a deep "U" shape) governs i n t h e \ l e s t a s u r f a c e c u r r e n t which i s much s m a l l e r t h a n i n t h e E a s t : w h i l e i n t h e E a s t t h e r e e x i s t s a s t r o n g (and r a t h e r s h a l l o w ) s u r f a c e e a s t e r l y s e t and a v e r y s l o w deep w e s t e r l y f l o w .
To t h i s mean regime, whose c h a r a c t e r i s t i c s a r e r e l a t i v e l y w e l l known, complex phenomena a r e superimposed w h i c h r e s u l t : e i t h e r f r o m t h e a c t i o n o f processes g e n e r a t e d i n t h e ocean ( t h e t i d e s which a r e p e r i o d i c ) and o f a p e r i o d i c a t m o s p h e r i c f a c t o r s ( l o c a l winds and f i e l d o f p r e s s u r e o v e r t h e H e d i t e r r a n e a n ) . The f o r m e r generates s t r o n g t i d a l streams i n t h e s t r a i t and t i d a l i n t e r n a l waves which a r e propagated on t h e i n t e r f a c e between t h e A t l a n t i c and f k d i t e r r a n e a n w a t e r s . These waves have a g r e a t e r a n p l i t u d e on t h e s o u t h e r n s i d e o f t h e s t r a i t . The l a t t e r i n d u c e v a r i a t i o n s o f t h e mean d a i l y f l u x e s o f w a t e r exchanged t h r o u g h t h e s t r a i t ; - o r f r o m t h e e f f e c t s , on t h e r e s u l t i n g c u r r e n t (mean v a l u e , t i d a l p a r t , a p e r i o d i c p a r t due t o a t m o s p h e r i c c o n d i t i o n s ) , o f complex n o n - l i n e a r phenonena, which a r e g e n e r a t e d i n t h e s t r a i t and which i n t r o d u c e d r a s t i , c m o d i f i c a t i o n s o f t h e i n s t a n t a neous f l o w regime, s p e c i a l l y i n t h e s u r f a c e A t l a n t i c l a y e r , E a s t o f t h e s i l l . I n p a r t i c u l a r , an " i n t e r n a l f r o n t " on t h e i n t e r f a c e and an a s s o c i a t e d c u r r e n t f r o n t a r e g e n e r a t e d n e a r t h e s i l l a t a b o u t t h e t i n e o f h i g h w a t e r and a r e propagated towards t h e E a s t a t a v e l o c i t y o f 3-4 k n o t s , i n t o t h e w e s t e r n A l b o r a n Sea. L a s t l y , t h e s t r a i t regime has a g r e a t i n f l u e n c e on t h e s u r f a c e c u r r e n t s i n t h e A l b o r a n Sea ( t o t h e E a s t ) and on t h e near-bottom c u r r e n t s on t h e A t l a n t i c slope.
-
14
INTRODUCTION
The information contained i n the present paper r e s u l t s mainly from f i e l d measurenents taken during the 6 0 ' (1960-1967), p a r t of which has not y e t been published systematically: however, the renewed i n t e r e s t in the Mediterranean, which the present Liege XIIIth Symposium on Hydrodynamics of t n e ocean i l l u s t r a t e s , i s an opportunity t o present a number of r e s u l t s on t h i s very i n t e r e s t i n g area. Throwing a glance on t h e Mediterranean s u f f i c e s t o demonstrate t h a t t h i s "semienclosed" sea i s a succession of basins and s i l l s , among which the s t r a i t o f Gib r a l t a r i s merely one : i t s i n t e r e s t l i e s i n t h e f a c t t h a t i t i s a typical model of " s t r a i t and s i l l " system i n which a number of phenomena occur with so g r e a t c l a r i t y t h a t they a r e "exemplary" o f the o t h e r s t r a i t-and-si 11-systems i n the Mediterranean, a concentration basin communicating f i n a l l y with t h e ocean. I n a d d i t i o n , the S t r a i t of G i b r a l t a r i s a r e l a t i v e l y well known a r e a , due, i n p a r t i c u l a r , t o the f a c t t h a t t h e NATO subcommittee on Oceanic Research, from 1960 t o 1965, under the Chairmanship of Prof. Hakon HOSBY, from Norway, organised a number of c r u i s e s in t h e area ( s e e c h a r t s A and B ) . As presented i n NATO Technical Report ( T . R . )
n o 2 ( s e e bibliography), the NATO subcommittee on Oceanographic Research, following t h e preceding work by t h e Spanish and the French during 1957-58 (IGY) and during September 1960,decided t o organize in may-june 1961 a multi-ship survey of the s t r a i t o f G i b r a l t a r . A working group, which one of us had the honour t o c h a i r , was s e t u p t o prepare t h e program. I t s aim was e s s e n t i a l l y : - t o continuously monitor during t h e period nay 15-june 15, 1961, the hydrological regime as well as the c u r r e n t regime in a central point considered as representative ( P o i n t A.4, - see c h a r t A - 5 miles North of Cape S p a r t e l ) ;
-
t o study t h e hydrology by simultaneous measurements made i n p r i n c i p l e every two hours f o r 24 hours, during s p r i n g and neap t i d e s , a t hydro-stations d i s t r i b u t e d on one longitudinal section of t h e s t r a i t and on f i v e transverse s e c t i o n s . The t h e East and t o the West of t h e s t r a i t , measurements of hydrology and c u r r e n t should be made t o r e l a t e the regimes of t h e s t r a i t t o those present t o the East and t o t h e blest. i i d a l records and meteorological observations were t o be made t o t r y t o c o r r e l a t e the sea regime in t n e s t r a i t and t h e meteorological regime. The ships involved i n t h e concerted work &ere :
- "Aragonese" from Saclantcen
-
( H . CHARNOCK)
"Calypso" France ( H . LACOMBE) "Eupen" Belgium ( A . CAPART)
15
3 16
BATHYMETRY OF THE WESTERN APPROACHES OF THE STRAIT (METRES).
17
-
"Helland-Hansen"
Norway
"Origny"
(G. PELUCHON)
-
"Amiral-Mouchez"
France
"Staffetta"
(H. NOSBY, t h e n G. BOYUM)
I t a l y ()I.CANO)
I n a d d i t i o n , two s h i p s has an a c t i o n c o o r d i n a t e d w i t h t h e main programme : "Xauen"
Spain
France ( G. BRIE) Echo-sounding-'and
GEK i n t h e A l b o r a n Sea
(N. MENENOEZ)
A g r e a t p a r t o f t h e i n f o r m a t i o n p r e s e n t e d i n t h i s paper r e s u l t s f r o m t h e m u l t i p l e s h i p s u r v e y . However some a d d i t i o n a l d a t a r e s u l t f r o m c r u i s e s made by t h e French, CALYPSO (H. LACOMBE) and ESPADON (P. TCHERNIA) i n 1960,fromthe NATO " K e d i t e r r a n e a n O u t f l o w p r o j e c t " o f 1 9 6 5 , ( c f T.R.
n o 34, 35, 36
-
f i n a l l y , f r o m t h e CHARCOT c r u i s e o f 1 9 6 i (H. LACOHBE and a1-1968
G. BOYUM) and,
-
F. FlkOELAIN
1970). Most o f t h e M e d i t e r r a n e a n S t r a i t s , such as t h e G i b r a l t a r one, a r e p l a c e s where v e r y v a r i e d hydrodynami c a l phenomena o c c u r , w h i c h r e s u l t f r o m exchanges o f w a t e r between b a s i n s and f r o m t h e e f f e c t s , on t h e i r regime, o f phenomena gene. r a t e d o u t s i d e t h e s t r a i t . a r e a such as t h e t i d e s o r t h e m e t e o r o l o g i c a l c o n d i t i o n s These, i n t u r n ,
may s t a r t
complex phenomena o f waves and i n s t a b i l i t i e s which
a r e g e n e r a t e d b y non l i n e a r f l o w s . I t seems a p p r o p r i a t e t o b e g i n w i t h t h e "mean regime" i n t h e S t r a i t o f G i b r a l t a r , t h e n , h a v i n g i n m i n d t h e f a c t o r s w h i c h m a i n t a i t , t o d e a l w i t h phenomena o f s m a l l e r t i m e s c a l e .
T h i s p a p e r w i l l b e m a i n l y d e s c r i p t i v e and r e l a t e t h e r e s u l t s o f o b s e r v a t i o n s and we s h a l l n o t g i v e any dynamical c o n s i d e r a t i o n s .
We must add, however, t h a t t h e v a r i o u s s m a l l s c a l e motions which a r e kwown t o e x i s t i n t h e S t r a i t , g e n e r a t e m i x i n g between a d j a c e n t l a y e r s w h i c h have an i n c i d e n c e on t h e "mean regime'' o r , a t l e a s t , on t h e way i n which t h i s regime i s e v a l u a t e d . I n a d d i t i o n , what
o c c u r s i n t h e S t r a i t have an i m p o r t a n t e f f e c t on
t h e hydrography o f a d j a c e n t areas, l i k e t h e A l b o r a n Sea, on one s i d e , on t h e G u l f o f Cadix on t h e o t h e r . We s h a l l g i v e few i n d i c a t i o n s on t h i s p o i n t .
1.
1HE WEAN REGIME T h i s regime i s governed b y t h e c l i m a t i c c o n d i t i o n s p r e v a i l i n g o v e r t h e Medi-
t e r r a n e a n b a s i n and i t s w a t e r s h e d : i n f a c t t h i s sea forms a system which t r a n s forms t h e A t l a n t i c w a t e r f l o w i n g i n t o t h e sea ( S g 36,15 %,)
i n t o an o u t f l o w i n g
w a t e r which becomes t y p i c a l l y m e d i t e r r a n e a n under t h e e f f e c t o f t h e c l i m a t e o v e r t h e sea area.
18
The c l i m a t e o f t h e sea i t s e l f and o f i t s w a t e r s h e d i s c h a r a c t e r i z e d b y a g r e a t d i v e r s i t y : d e s e r r i c i a n d s occupy a g r e a t p a r t on t h e E a s t o f i t s s o u t h e r n s h o r e . I n s t e a d , t h e w a t e r s n e d w h i c h feeds i t i n t h e NH i s woody and humid, p a r t i c u l a r l y i n w i n t e r : t h e f l o w o f r i v e r s i n t o t h e sea i s m a i n l y i m p o r t a n t on t h e N o r t h e r n s h o r e and i n t o t h e B l a c k Sea ; t h e o n l y i m p o r t a n t r i v e r o f t h e Southern s n o r e i s t h e N i l e . I f t h e f l o w s f r o m t h e RhBne, t h e P6, t h e Danube and t h e N i l e a r e r e l d t i v e l y r e g u l a r , t h o s e f r o m t h e Russian r i v e r s t o t h e B l a c k Sea e x h i b i t a maximum volume a t t h e end o f s p r i n g and a t t h e b e g i n n i n g o f summer. F o r t h e watershed, t h e summer i s d r y , t h e w i n t e r humid. I n summer t h e Azores a n t i c y c l o n e proceeds o v e r l l e s t e r n Europe ; t h e s o l a r h e a t i n g o v e r g r e a t c o n t i n e n t a l areas on t h e E a s t and South o f t h e sea g e n e r a t e s r a t h e r l o w p r e s s u r e t h e r e ,
so t h a t t h e r e i s a tendency o f an a n t i c y c l o n i c w i n d
, blowing
from North over
t h e E a s t e r n sea and f r o m E a s t o v e r t h e Fiorth A f r i c a n a r e a . i n \ , i n t e r ,
rieteorolo-
g i c a l lows coming f r o m t h e A t l a n t i c sweep o v e r t h e b a s i n frorn \!est t o E a s t ; however t h e y o f t e n t e n d t o remain and t o become deeper i n c e r t a i n areas l i k e t h e Gulf of Genova, t h e A d r i a t i c , Cyprus. As a consequence, t h e winds t e n d t o be c y c l o n i c and t o g e n e r a t e p r e c i p i t a t i o n s which a r e p a r t i c u l a r l y i m p o r t a n t on c o a s t s f a c i n g \ l e s t . Behind t h e l o w s , s t r o n g winds f r o m NI1 t o N blow o v e r t h e N o r t h e r n s h o r e s , kjhich a r e p a r t i c u l a r l y v i o l e n t i n t h e G u l f o f L i o n s (Tramontane, M i s t r a l ) , over the North A d r i a t i c (Bora). I n w i n t e r also, the Northern p a r t s o f t h e sea may be s u b n i t t e d t o b u r s t s o f p o l a r c o n t i n e n t a l
air
-
-
c o l d and d r y
when t h e Southern s l o p e s o f a n t i c y c l o n e s s i t u a t e d o v e r C e n t r a l and E a s t e r n Europe d i r e c t E a s t e r l y winds o v e r t h e N o r t h e r n areas o f t h e k d i t e r r a n e a n .
A p a r t i c u l a r m e t e o r o l o g i c a l c h a r a c t e r i s t h e presence o f t r a n s i e n t of s m a l l s c a l e , b u t v e r y v i o l e n t , f o r
phenomena,
t h e winds as w e l l as f o r t h e p r e c i p i t a t i o n s :
t h e s e may be t o r r e n t i a l and g e n e r a t e v e r y s t r o n g f l o o d s o f c o a s t a l r i v e r s , which may p l a y an i m p o r t a n t r o l e on t h e d i s p e r s i o n o f sediments. 1.A The mean regime o f t h e s t r a i t as i n f e r r e d f r o m t h e balances o f w a t e r and s a l t i n t h e sea The M e d i t e r r a n e a n ( i n c l u d i n g t h e B l a c k Sea), b e i n g c l o s e d i n t h e E a s t , t h e mass o f s a l t and t h e v o l u n e o f w a t e r i t c o n t a i n s a r e i n v a r i a b l e ( a t a t i m e s c a l e of human l i f e ) , s i n c e i t s l e v e l and i t s s a l i n i t y r e n a i n i n v a r i a b l e i n t i n e , ( t ' i e s a l i n i t y s i n c e t h e "THOR" c r u i s e i n 1907-1910). On t h e o t h e r hand, t h e e v a p o r a t i o n E exceeds t h e w a t e r g a i n s P r e s u l t i n g f r o m t h e p r e c i p i t a t i o n s and t h e r i v e r f l o w .
BETHOUX (1980) p r e s e n t s t h e w a t e r b u d g e t across t h e sea s u r f a c e i n v a r i o u s I l e d i t e r r a n e a n areas. Everywhere ( e x c e p t t h e B l a c k Sea and t h e N o r t h e r n A d r i a t i c )
,
t h e r e i s w a t e r d e f i c i t across t h e sea s u r f a c e . I n t h e Gulf o f L i o n s t h e budget
i s n i l . It r e s u l t s t h a t t h e rlediterranean i s a c o n c e n t r a t i o n b a s i n : t h e t y p i c a l
19 M e d i t e r r a n e a n o u t f l o w i n g w a t e r ( S P 3 8 X,)
i s denser t h a n t h e e n t e r i n g A t l a n t i c
w a t e r and f l o w s n e a r t h e b o t t o m o f t h e s t r a i t o f G i b r a l t a r .
Ift h e w a t e r d e f i c i t was conpensated o n l y b y e n t e r i n g A t l a n t i c water, t h e s a l t b r o u g h t i n b y t h e l a t t e r would c o n t i n u o u s l y i n c r e a s e t h e anount o f s a l t w i t h i n t h e sea, c o n t r a r y t o what occurs. Then, i n t h e s t r a i t t h e r e t a k e
place
an i n f l o w o f A t l a n t i c w a t e r ( n e a r t h e s u r f a c e ) and, below, o v e r t h e bottom, an o u t f l o w o f s a l t i e r (+ 4 %) and denser H e d i t e r r a n e a n w a t e r which, under a somewhat s m a l l e r volume ( - 4 % ) , c a r r i e s t h e same q u a n t i t y o f s a l t as t h e e n t e r i n g A t l a n t i c water. Expressing
-
t h e conservation o f
pi.Vi.Si =po.Vo.%(
p
i n t h e K e d i t e r r a n e a n , we have
L
d e n s i t y , V volume, S s a l i n i t y ; i n d e x refers t o the inflow, 2 Po s i n c e yo - pi = 2.10-3, we may w r i t e :
index
2 t o t h e o u t f l o w ) . As pi
\i.Si
= Vo.So
-
salt
water
the conservation o f
i n t h e sea :
V i t P = V o + E
+ r i v e r d i s c h a r g e t o t h e sea, E = e v a p o r a t i o n
( P p r e c i p i t a t i o n o v e r t h e sea fron; t h e sea). Combining t h e two r e l a t i o n s : Vi/So = Vo/Si = ( V i and V i = VoSo/Si All
-
Vo)/(So
-
Si) = I E
- P)ISo -
S i ) = gV/ A S
(1)
t h e f a c t o r s e n t e r i n g e q u a t i o n 1 can be measured i n t h e s t r a i t o r eva-
l i r a t e d f o r t h e sea, b u t n o t w i t h t h e same desree o f s i m p l i c i t v o r accuracv.
I.A.l
The exchanges o f w a t e r f r o m measurements i n t h e s t r a i t : Among them,
t h e most a c c e s s i b l e a r e t h e l o c a l values which have t o be measured o n l y
the
s t r a i t : V i , Vo, S i , So ; b u t we must have access t o t h e i r mean l o c a l value. However t h e e l i m i n a t i o n o f t h e e f f e c t s o f t i d e s , m e t e o r o l o g i c a l c o n d i t i o n s , o f f l u c t u a t i o n s due t o many f a c t o r s r e q u i r e s , i n d i f f i c u l t m a r i n e c o n d i t i o n s ( g r e a t depth, s t r o n g c u r r e n t s , h i g h v e r t i c a l shear, i n t e n s e n a v i g a t i o n , f r e q u e n t f o g , E o r W winds ...) measurements o f l o n g d u r a t i o n . The presence o f i m p o r t a n t m i x i n g
between t h e superimposed w a t e r nasses r e q u i r e s t h a t a l l f a c t o r s t o be measured i n t h e same r e p r e s e n t a t i v e p o i n t . The h y d r o l o g y i s g i v e n b y h y d r o c a s t s made a t t h e same p l a c e d u r i n g , a t l e a s t , one t i d a l c y c l e ( f i g . 1). Our measurementsof 1960 a t p o i n t A.4 (see c h a r t . A) l e a d us t o S i 2 36,15
%O
and S o 2 37,9 5 0 . T h i s e v a l u a t i o n i s d e l i c a t e because
o f t h e changing depth o f t h e t r a n s i t i o n a l l a y e r between t h e A t l a n t i c and k d i t e r r a n q a n w a t e r s , whose t h i c k n e s s depends on t h e i n t e n s i t y o f m i x i n g and on t h e v e l o c i t y shear and, o f course, on t h e p o s i t i o n .
A S i s t h e n about 1.75
%,.
20
0
1
100 -
100
1
20 Jl
2w
-
300
0 3
300
-
B
BOTTOM A 4
600
5w
500
I
-
500 -
-
t I
1960 ~~
C2.3
C2.L 700 WtWS
BOTTOM C 2 m
.~
_______
FIG.1
600
c2.2
V e r t i c a l p r o f i l e s o f s a l i n i t y : i n t h e West ( A 4 ) and i n t h e E a s t (C2) o f t h e s t r a i t .
The e v a l u a t i o n o f V i , Vo i s rnore d i f f i c u l t : t h e v a l u e s f o u n d a r e p r e s e n t e d ( T a b l e I , f i g . 2) f o r p o i n t A.4 a l s o , where S i and So have been determined.
It
i s seen t h a t t h e r e a r e v e r y l a r g e f l u c t u a t i o n s o f t h e mean f l u x f o r 12 h and
24 h (100 % ) . Besides t h e d i u r n a l t i d a l component i s n o t n e g l i g i b l e . The a c c u r a c y w i t h w h i c h t h e s e f l u x e s a r e o b t a i n e d i s d i f f i c u l t t o e v a l u a t e : however, t h e deep s e c t i o n b e i n g much s m a l l e r t h a n t h e upper s e c t i o n t h r o u g h which V i goes, t h e deep f l u x Vo i s , p r o b a b l y , more a c c u r a t e : i t s mean v a l u e as found by t h e d i r e c t measurements (1960, 1961) i s Vo = 1,15
lo6
d / s a t p o i n t A.4
or about 36.1012 m3/year. The i n c o m i n g f l u x V i measured i s 1,26106 m3/s and somewhat exceeds b y 5 % what w o u l d be determined
b y t h e r e l a t i v e excess o f So.
However, Vo b e i n g more a c c u r a t e we s h a l l t a k e ( f r o m e q u a t i o n 1) V i = So Vo/Si 1,20 106 m3/s = 37.7 1 0 1 2 d / y . The n e t g a i n o f w a t e r t h r o u g h t h e s t r a i t i s a b o u t 1,7.1012 n 3 / y ; as t h e n e t gain through the Dardanelles i s
0,2.101*
m3/y (TIXERONT, 1970). The t o t a l d e f i c i t
21
TABLE I STRAIT OF GIBRALTAR (Sept. 1960- May-June 1961)
b a n flux averaged over 12h and 2411, i n 106 n-'/s. Western Section through A4 Infl Vi wer. over 12h aver. over 24h
Sept. 960 n t A4)
0.60
1.37 0.53 1.15 0.95 1.68 1.33
0.92 0.95 ,Ll .34 '1.05 1.31 1.50
0.42
1.57
0.46
1.87 0.25
1.06
0.59 1.42
1.01
1.05 2.49 1.19 2.45
1.77 1.84 1.82
0.39
3.37 1.26 0.53
0.63 0.92
1.61 1.55 1.22 1.27 1.14
1.35 0.72 1.43 0.73 1.15 1.07
1.33 1.07 1.08 0.94 1.11
1.27 1.20
1.71 0.90 2.28
1.30 1.59
1.18 1.44 1.64 1.57 1.30 0.96 1.26 1.08 0.69 0.45
0.98 2.17 0.78 1.67 0.80 1.13 1.31 1.81 1.22 1.51 1.39
1.58 1.48 1.23 1.24 0.97 1.22 1.56 1.52 1.37 1.45
-
-
-
Recalculated values
0.88
3.98 1.11 1.15 0.95 3.82 3.77
1.05
-
(Point A4)
1.11 0.35 1.38 0.94 0.99 3.66
-
-
May June 1961
Outflow vo rver. over 1211 wer. over 24:
0.99
2.24 0.86
1.58 0.96 1.32
-
-
-
3.97 1.57 0.83
-
-
1.50 0.86 2.02 1.26 1.89 0.72 1.21 1.31 0.85 0.53 0.38
0.82
22
FLUXES
IN A 4
MAY
FLUX
F I G . 2 Mean inflow and outflow
- fluxes averaged over
in A4 (Western entrance). May-june 1961.
-o----o
---- - - -
}
INFLOW OVER 12h OUTFLOW MEAN FLOW OVER 24h
12h and 24h
23 f o r t h e K e d i t e r r a n e a n p r o p e r ( e x c l u d i y t h e B l a c k Sea) i s 1,9x1012 m3/y. As t h e s u r f a c e o f t h e M e d i t e r r a n e a n p r o p e r i s 2 , 5 3 ~ 1 0 ~ ~ m t3h,e mean w a t e r d e f i c i t across ! i i t h t h e v a l u e o f P a d m i t t e d b y TIXEt h e s u r f a c e i s 1 , 9 ~ 1 0m3/y ~ ~ L" o,75 2,53X1012m2 RONT (1970), i.e. 0,55 m/y, t h e mean e v a p o r a t i o n o v e r t h e t l e d i t e r r a n e a n p r o p e r i s 1,30 m/y. On t h e o t h e r end, t h e t o t a l f l u x e n t e r i n g t h e !4editerranean p r o p e r i s 37,7x1012
m3/y ( t h r o u g h G i b r a l t a r )
+
0,4x1012 m3/y ( t h r o u g h D a r d a n e l l e s ) =
3 8 . 1 ~ 1 0 1 2 m3/y ; t h i s g i v e s t h e renewal t i m e o f t h e M e d i t e r r a n e a n w a t e r - 3,71x1015 38,1x1012
m3
= 98 y e a r s ,
r a t i o o f t h e t o t a l volume o f t h e sea t o t h e
m3/y
incoming f l u x . I.A.2
The exchanges o f w a t e r f r o m e v a l u a t i o n s o v e r t h e whole sea combined
w i t h measurements i n t h e s t r a i t . BETHOUX (1978,79) had t h e i d e a o f e v a l u a t i n g E, t h e evaporation,using
t h e h e a t budget o f t h e sea : t h e h e a t l o s s by e v a p o r a t i o n
i s t h e d i f f e r e n c e between t h e h e a t i n g processes ( s o l a r r a d i a t i o n s r e c e i v e d t t h e weak a d v e c t i o n s t h r o u g h t h e s t r a i t ) and c o o l i n g processes ( i n f r a - r e d r a d i a t i o n s , l o s s o f s e n s i b l e h e a t ) . On t h e o t h e r hand, he e v a l u a t e s P. From t h e r e he deduces
E
-
P = V i -Vo. The m a n u n i t a r e a v a l u e o f E
-
P i s t h u s f o u n d t o be about
h / y e a r . T a k i n g t h e v a l u e s of S i and So, g i v e n above i n I . A . l ,
he o b t a i n s V i and
Vo b y eq. ( 1 ) . He f i n d s V i = 5 3 ~ 1 0 1m3/y ~ ; Vo = 5 0 , 5 ~ 1 0 m3/y. ~~
I n addition,
n e g l e c t i n g t h e i n f l o w by t h e B l a c k Sea he f i n d s a renewal t i m e o f :
3J71x105 = 70 y e a r s . These f l u x e s exceed b y a b o u t 30 % t h o s e o b t a i n e d f r o m 53x1012 d i r e c t measurements i n t h e s t r a i t . Given t h e i n c e r t a i n t y d i f f i c u l t t o evaluate
-
o f elements i n v o l v e d i n t h e two methods o f e s t i m a t i o n , t h i s d i s c r e p a n c y i s n o t surprising. 1.B C h a r a c t e r s of t h e mean regime i n v a r i o u s p l a c e s i n t h e s t r a i t I . B . 1 V e r t i c a l p r o f i l e o f mean v e l o c i t y and l o n g i t u d i n a l s l o p e o f t h e mean i n t e r f a c e . One o f t h e i m p o r t a n t c h a r a c t e r s o f t h e mean regime i s t h e v e r t i c a l mean v e l o c i t y p r o f i l e i n v a r i o u s p l a c e s . The w i d t h o f t h e channel f o r v a r i o u s depths on d i f f e r e n t c r o s s - s e c t i o n s ,
as w e l l as t h e d e p t h o f t h e " i n t e r f a c e "
between t h e two superimposed waters,play
a c o n s i d e r a b l e r o l e on t h e v e r t i c a l
mean c u r r e n t p r o f i l e ( f i g . 3, 4, 5 ) . I n t h e !Jestern p a r t of t h e s t r a i t , i n A.4 ( s e e c h a r t . A ) ,
t h e sea d e p t h does
n o t exceed 400-450 m and t h e s e c t i o n o f f e r e d t o t h e deep o u t f l o w i s much s m a l l e r t h a n t h a t o f f e r e d t o t h e i n f l o w : t h e s e c t i o n i s more o r l e s s t r i a n g u l a r ( f i g . 3 ) On t h e c o n t r a r y , on s e c t i o n s more t o t h e E a s t ( T a r i f a , G i b r a l t a r ) t h e s e c t i o n offered t o the outflow i s
much g r e a t e r t h a n t h a t o f f e r e d t o t h e i n f l o w , t h e
24
3m-
Section through A4
r, 53w
LOO 650
Om
Section through Sill
loo 200
A
T
1
d
iJ-.
uunr 8
4 0 4 8Km
I.++
Om
1w TARIFA Section
200
7
interface
3,LlKm’
I
mean interface
5,73Km‘
It 6 4 0
18
12.16 Km’
GIBRALTAR Rock Section
-i
IyKm
interface
FIG.3 Cross channel a r e a o f d i f f e r e n t s e c t i o n s o f t h e s t r a i t (see c h a r t A : The p o s i t i o n s o f t h e s e c t i o n s ) .
25
I
FIG.4 Mean velocity profiles for nine successive tidal cycles i n A4.
26
rSTATlON
C2
14-15- IX- 1960 0 ,
W.
,
,
I 1m /set.
ISTATION si 27- IX- 1960
I
300m
400m 500 m
600m
832m
-
PM. 10h.32 22h.38 (TU t l )
FIG.5 Mean v e l o c i t y profiles i n C2 ( a ) and 8 ' 2 ( b ) .
FIG.6
100 rn 200
300 500
i n t e r n a l wave f o r a s a l i n i t y 37 X,.
Longitudinal mean s a l i n i t y s e c t i o n along the a x i s of the s t r a i t W t o the meridian of G i b r a l t a r . Amplitude of the Mean current i n t h e two layers.
from 6'40'
700
STRAIT AXIS
600 n,1 .Om/s
1967 CHARCOT c,
400 2crn/s
c.89-84 NPEU C.92-(Y XAUEN CALYPSO
c.91-TI c.95-a4 ORIGUY STAFFETTA
c.95-7s C.rn.89
c-84-67 C = 63- 69 HELLANO HAUSEU
800
28
more as ( f i g 1, 6 ) t h e i n t e r n a l i n t e r f a c e i s ascending f r o m !lest t o East, t h u s reducing t h e water thickness f o r t h e i n f l o w .
I n t h e L e s t e r n approaches, t h e l i e d i t e r r a n e a n deep o u t f l o w i s g u i d e d b y a deep v a l l e y which p r o l o n g s t o t h e West t i l l about 6'25'
t h e v a l l e y South o f S p a r t e l bank ( " t h e Ridge")
G.! ; more t o t h e ! l e s t t h e deep v a l l e y widens ( s e e c h a r t 6 ) . . t h u s
t h e deep o u t f l o w i s c o n c e n t r a t e d i n t h e v a l l e y w h i l e t h e i n f l o w t a k e s p l a c e i n a very l a r g e section.
I.!
F i g . 6 r e p r e s e n t s a s e c t i o n o f t h e mean l o n g i t u d i n a l s a l i n i t y f r o m 6'40' ( i n the Nest) t o the meridian o f G i b r a l t a r
Rock (5'20'W ) f o r s p r i n g t i d e s . I t
i s seen t h a t t h e mean l o n g i t u d i n a l s l o p e o f t h e i s o h a l i n e 37,O %',,(which
may be
c o n s i d e r e d as t h e i n t e r f a c e ) i n c r e a s e s toward t h e !lest and i s c l o s e t o t h e b o t t o n s l o p e between m e r i d i a n s 6"14' t.1 and 6'40' r e l a t i v e l y s m a l l t i l l 6'25'!!, these
I!.
As t h e w i d e n i n g o f t h e channel i s
t h i s implies t h a t the v e l o c i t y o f the outflow i n
deeper l a y e r s i n c r e a s e s , d e s p i t e t h e n i x i n g w i t h o v e r l y i n g w a t e r s . I n f a c t ,
a c c o r d i n g t o o u r Norwegian c o l l e a g u e s ' measurements
on b o a r d o f t h e "HELLAND-
HANSEN" i n may 1965 (TR 34, 35, 36 G. BOYUtl 1967), i n l o n g i t u d e s about 6'14'
6'20'
and
Id, t h e mean c u r r e n t down t o about t h e i n t e r f a c e i s weak t o t h e E a s t ( a b o u t
20 cn/s o r . 4 k n ) The s i t u a t i o n i s q u i t e d i f f e r e n t i n t h e deeper l a y e r o f "ifediterranean water".
I n l o n g i t u d e 6'14'
b! n e a r t h e s o u t h e r n f l a n k o f t h e v a l l e y ,
where t h e i n t e r f a c e i s deeper, t h e mean v e l o c i t y between 250 and t h e b o t t o n a t 430 m i s about 140 cm/s ; w h i l e i n l o n g i t u d e 6"ZO' W, deeper t h a n 250 m , t h e mean v e l o c i t y may exceed 150 c n / s ( 3 k n ) . I t i s i n t h i s a r e a t h a t o u r c o l l e a g u e s have measured a r e c o r d v e l o c i t y of 245 cm/s ( a l m o s t 5 kn) i n 6"14', d i n g 200 cm/s n e a r 6'20'
1.1. On t h e c o n t r a r y , i n 6'47'
and o t h e r s excee-
tl, a f t e r t h e w i d e n i n g o f
t h e v a l l e y t h e mean deep v e l o c i t i e s decrease t o a b o u t 80 t o 100 cm/s (1,6 t o 2 kn) ("Campagne GIBRALTAR
-
UN", 1970),10 m above t h e b o t t o m (705 rn) i n 35"48' N
6'44'11. I n a d d i t i o n i t i s seen on f i g u r e 6 ( . m i d d l e ) t h a t t h e v e r t i c a l d i s p l a c e n e n t of
t h e i n t e r f a c e a t s p r i n g s i s a l s o maximum i n t h e v i c i n i t y o f t h e s i l l . I n t h e V e s t e r n e n t r a n c e o f t h e s t r a i t , p o i n t 4.4, f i g . 4, t h e nean c u r r e n t i n t h e s u r f a c e l a y e r i s weak, w h i l e i t i s s t r o n g i n t h e deeper ones. Near t h e m e r i d i a n s o f T a r i f a ( f i g 5b) and G i b r a l t a r ( f i g 5 a ) t h e mean c u r r e n t i s c o n v e r s e l y , h i g h i n t h e s u r f a c e l a y e r s and I.B.2
s m a l l i n t h e deeper one.
liean h y d r o l o g i c a l s t r u c t u r e and m i x i n g
between l a y e r s . Lle have t i l l
now used t h e t e r n s " i n f l o w i n g A t l a n t i c w a t e r " , " o u t f l o w i n g K e d i t e r r a n e a n w a t e r " t o designate
t h e w a t e r s a f f e c t e d by o p p o s i t e m a n novenents. I t i s u s e f u l t o
b e t t e r d e f i n e t h e i r c h a r a c t e r i s t i c s and t o e v a l u a t e t h e e f f e c t o f n i x i n g between them on t h e l o c a l T and S o f t h e w a t e r p r e s e n t .
FIG.7
b
%\
4
T.S. diagrams for stations A4, 18-20 sept. 1960.
29
30
The l i e d i t e r r a n e a n w a t e r which i s p r e s e n t i n t h e deeper l a y e r s a t t h e E a s t e r n end o f t h e s t r a i t ( s e c t i o n o f G i b r a l t a r r o c k ) i s n e a r l y a " w a t e r t y p e " , whose T and S a r e v e r y c l o s e t o t h o s e o f t h e Deep ! l a t e r o f t h e I l e s t e r n K e d i t e r r a n e a n : T ~ ) 1 2 " 9 , S s 38.40 %,(In
f a c t GASCARD r e c e n t l y showed t h a t t h e deep w a t e r was
a b l e t o c r e e p towards t h e s t r a i t c l o s e t o t h e ascending b o t t o m ) . On a l l the., f o l l o w i n g T.S.
diagrams t h i s w a t e r i s r e p r e s e n t e d b y p o i n t I.1.
On t h e A t l a n t i c s i d e , t h e s i t u a t i o n i s more complex and we have t o d e a l , n o t w i t h a water-type,
b u t w i t h allwater-mass",
t h e "North A t l a n t i c C e n t r a l ! l a t e r "
(NACW) d e f i n e d b y SVERDRUP (1942) ; n e a r t h e Llestern e n t r a n c e o f t h e s t r a i t ( P o i n t A4) t h e T a n d S f a l l o n a l i n e between T = 16"C, S = 36:2 %, S =35.9
%o.
and T = 13.5
OC,
T h i s i s segment PN on t h e T.S diagrams. Above ( i e fro'h 0 t o 50 m
i n summer) t h e
T
and S p r e s e n t do n o t f a l l on t h i s l i n e ( d u e t o t h e s o l a r h e a t i n g )
b u t on a segment n o t e d QP. Idhen, under t h e e f f e c t o f t i d e , t h e i n t e r f a c e between t h e A t l a n t i c and Medid i t e r r a n e a n w a t e r s i s deeper, t h e T and S o f t h e NAC!J a t i t s l o w e r l e v e l a r e s m a l l e r t h a n when t h e i n s t a n t a n e o u s i n t e r f a c e i s h i g h e r . I n p o i n t A4 (Cape o f Spartel meridian),the
l o w e r v a l u e s f o u n d were T = 13.3"C
; S = 35.84
%o.
The c h a r a c t e r i s t i c s p r e s e n t w i t h i n t h e t r a n s i t i o n l a y e r between t h e two w a t e r s r e s u l t f r o m t h e m i x i n g between them, which i s i n c r e a s e d b y t h e c u r r e n t shear present a t
t h a t l e v e l a t c e r t a i n moments of t h e t i d e ( f i g . 7 ) . The f a c t t h a t
t h e T. S p o i n t s i n t e r m e d i a t e between N and I1 a r e above l i n e NM shows t h a t t h e w a t e r p r e s e n t a t t h e c o r r e s p o n d i n g l e v e l s r e s u l t from m i x i n g o f w a t e r 11 ( l i e d i t e r ranean w a t e r - t y p e ) w i t h l e s s deep A t l a n t i c w a t e r : t h i s may be due t o t h e f a c t t h a t , when t h e m i x i n g r e s p o n s i b l e o f these p o i n t s t o o k p l a c e , t h e lovier l a y e r o f t h e NACW p r e s e n t was sonewhat s h a l l o w e r ( d i f f e r e n t s t a t e o f t h e t i d e and s h a l l o wer i n t e r f a c e w i t h h i g h e r T and S) o r may be due t o ascending n o t i o n s h a v i n g taken place a t
other p l a c e s
i n t h e s t r a i t and " b u i l d i n ? up" t h e n i x i n g elsewhere
i n t h e s t r a i t ( i n t h e s i l l a r e a ? ) : t h e c u r r e n t p r e s e n t may s u b s e q u e n t l y have advected t h i s w a t e r t o them. The d e n s i t i e s i n t h e l o w e r l a y e r s o f NACl! a r e s m a l l e r b y about 0.002 t h a n those
o f the Mediterranean water. This d e n s i t y s h i f t , apparently very small,
i s s u f f i c i e n t t o a c t as a s h i e l d f o r the exchange o f p r o p e r t i e s and novecients
o f t h e w a t e r above and below : t h e t r a n s i t i o n l a y e r i s , a t l e a s t i n P.4, r e l a t i v e l y t h i n ( 5 0 m) ; t h e k i n e t i c energy must f e e d t h e l a y e r s w i t h t h e p o t e n t i a l energy needed t o b u i l d t h e t r a n s i t i o n l a y e r
.
More t o t h e E a s t , n e a r t h e m e r i d i a n o f t h e Rock, ( P o i n t C 2 ) , t h e T.S diagrar: ( f i g . 8 ) shows t h a t t h e NAC!I i s o n l y p r e s e n t on a s m a l l range o f d e p t h n e a r t h e s u r f a c e (30-50
m)
; t h e v e r t i c a l p r o f i l e o f s a l i n i t y ( f i g . 1 r i g h t ) a l s o shows
t h a t t h e t r a n s i t i o n l a y e r reaches a b o u t 100 m i n t h i c k n e s s .
FIG.8 T.S.
diagrams f o r s t a t i o n C2, 14-15 sept. 1960.
31
w
h3
FIG.9 1.5. diagrams for s t a t i o n s S s , 25 sept. 1960.
21*
20"
25- 1x4 - 20'
~
-
- 19'
18' -
- 18'
-
- 17.
16' -
-1 6'
19.
17'
i nc
HW-
15' __ 1C. -
F
13. -
-
33
The T and S c o n d i t i o n s p r e s e n t on t h e s i l l ( P o i n t Sson c h a r t A, f i g . 9) a r e s u b j e c t t o d r a s t i c v a r i a t i o n s d u r i n g t h e t i d a l c y c l e and a c c o r d i n g t o t h e t i n e w i t h r e s p e c t t o High w a t e r , one f i n d s e i t h e r c o n d i t i o n s s i m i l a r t o t h o s e found i n t h e V e s t (A4) when t h e i n t e r f a c e i s deep i n t h e s i l l o r a mixed l a y e r c o n i n g up t o t h e s u r f a c e , i n p a r t i c u l a r n e a r t h e t i m e of,High
Water, when t h e s a l i n i t y
minimum ascends n e a r t h e s u r f a c e , d u r i n g t h e phase o f v i o l e n t a c c e l e r a t i n g t i d a l s u r f a c e c u r r e n t (see below 1 I . C ) .
mean f l o w s
Due t o C o r i o l i s ' f o r c e , t h e e x i s t e n c e of o p p o s i t e
on t h e v e r t i c a l
generates a w a n t r a n s v e r s e s l o p e o f t h e i n t e r f a c e , which i s deeper on t h e Southern s i d e ( w h i l e t h e sea surface i s h i g h e r ) t h a n on t h e N o r t h e r n s i d e ; t h i s s l o p e i s i m p o r t a n t , s i n c e f o r a r e l a t i v e d e n s i t 9 of 0.002 between l a y e r s , and f o r l a t i t u d e 36',
i t reaches 4.3 m / l km f o r a r e l a t i v e c u r r e n t o f ln/s : one must e x p e c t depths
o f t h e i n t e r f a c e t o be g r e a t e r on t h e Southern s i d e b y an o r d e r o f 50 n : as a consequence, t h e i n t e r f a c e n a y r e a c h t h e s u r f a c e i t s e l f n e a r t h e N o r t h e r n c o a s t o f the s t r a i t (see fig.36).
O f course i n a d d i t i o n we s h a l l see ( 1 I . E ) t h a t t h e
t i d a l streams i n such a " c h a n n e l " induces a d d i t i o n a l more o r l e s s g e o s t r o p h i c transverse slope o f the i n t e r f a c e .
I 1 FLUCTUATION OF THE PiEAN REGIME FORCED BY THE TIDE The d i f f e r e n c e o f t h e c h a r a c t e r s o f t h e t i d e i n t h e Gulf o f Cadix, t o t h e ! l e s t , and i n t h e A l b o r a n Sea, t o t h e East, generates i n t h e s t r a i t i m p o r t a n t p e r i o d i c m o d i f i c a t i o n s o f t h e l o c a l hydrologyand o f t h e c u r r e n t s . The t i d e i n t h e a r e a i s e s s e n t i a l l y s e m i - d i u r n a l
; i t s a m p l i t u d e i s much g r e a t e r
a t t h e Western e n t r a n c e t o t h e s t r a i t ( a b o u t 2 m) t h a t i n t h e c e n t e r (1.3
1;1
in
T a r i f a ) and a t t h e E a s t e r n end (0.8 t o 1 m). The t i d a l wave o f t h e A t l a n t i c reaches t h e !!estern approaches t o t h e s t r a i t about two h o u r s a f t e r t h e ( l o w e r o r u p p e r ) moor)
t r a n s i t o f Greenwich n e r i d i a n ;
i t reaches T a n g i e r somewhat e a r l i e r t h a n Cadix. But, i n t h e a r e a between t h e s i l l and G i b r a l t a r , t h e H i g h H a t e r t a k e s p l a c e a l m o s t a t t h e same t i m e , which i s about 2 hours b e f o r e t h e t i m e o f t h e c o r r e s p o n d i n g h i g h w a t e r i n B r e s t . The t i d e a f f e c t s t h e regime o f t h e s t r a i t as w e l l as t h a t o f i t s ! l e s t e r n and E a s t e r n approches, b y t h e t i d a l streams and b y t h e t i d a l e f f e c t s on t h e h y d r o l o g i c a l s t r u c t u r e . !ie s h a l l r a p i d l y survey these e f f e c t s i n t h e s u r f a c e and deep l a y e r s where s u f f i c i e n t processed d a t a a r e a v a i l a b l e . Lie s h a l l f o l l o w t h e e v o l u t i o n o f phenomena f r o m ! i e s t ( a b o u t 6'40' ( a b o u t 5'20'
H) t o East W ) . We s h a l l see t h a t t h e phenomena s u f f e r d r a s t i c changes on t h e
s i l l and Eastward, so as t o d e e p l y i n f l u e n c e t h e w h o l e regime t o t h e East. We a l s o g i v e (1I.E) s i m u l t a n e o u s i n t e r n a l t i d a l wave p r o f i l e s on a number o f
34
transverse s e c t i o n s (on t h e b a s i s o f the m u l t i - s h i p measurenents o f 1961, see the i n t r o d u c t i o n ) so as t o p u t i n evidence i n d i c a t i o n s o f the transverse slope o f the i n t e r f a c e and i t s v a r i a t i o n w i t h t i d e . F i n a l l y we a l s o p r e s e n t s i n u l t a -
neous T.S.
diagram f o r 5 s t a t i o n s along t h e c e n t r a l a x i s o f t h e s t r a i t , from A4
t o Gc, a t springs and neaps f o r a number o f t i d a l hoi-rrs.
1 I . A T i d a l f o r c i n g i n t h e !.Jestern approaches
I.Je s h a l l l i m i t ourselves here t o the v i c i n i t y o f meridian 6"40' 1'. F i g . 10,
11 show (TR 34 35 36 G. B O W 4 1967) t h e r e s u l t s o f ourNorwegian colleagues on the b a s i s o f data c o l l e c t e d i n may 1965 under the NATO p r o j e c t "llediterranean Ourflow". Near 6"38' W ( f i g . 10) i t i s seen,within
o f l a y e r o f about 40-50 m
above the b o t t o h , an i n d i v i d u a l i s e d deep Mediterranean d e n s i t y f l o w i s present w i t h l i t t l e depth v a r i a t i o n under t h e e f f e c t o f t i d e . A l s o ,
i t seems t h a t
l i t t l e c u r r e n t v a r i a t i o n w i t h t i d e takes place. I n 6"20'H and 6"14 ( f i g . l l ) , w i t h i n the deep v a l l e y , t h e deeper s a l i n i t i e s are much g r e a t e r and close t o those o f the Mediterranean. A c l e a r t i d a l i n t e r n a l wave i s apparent, the mean i n t e r face being about 100-150 m above t h e bottom. The "High N a t e r " o f t h e i n t e r n a l
,
i n 6'14 ' W , takes p l a c e near the time o f the surface"High Ilater"". As i n d i c a t e d above i n I.B.l t h e m a n c u r r e n t i s very s t r o n g o n l y i n t h e deep
wave
l a y e r . I t seems t o be s t r o n g e r
between HW -5h and HW-lh ( i . e . between 5 hours and
1 hour b e f o r e t h e s u r f a c e High \.later i n T a r i f a ) . 1I.B
T i d a l f o r c i n g i n t h e v a l l e y n o r t h o f Cape S p a r t e l ( p o i n t A4)
We have i n d i c a t e d e a r l i e r (I.B.1) t h a t the v a r i a t i o n w i t h depth o f the w i d t h mean c u r r e n t weak values near t h e
o f the channel ( c f f i g . 4) imposed t o the
surface, b u t h i g h values i n the deeper l a y e r s .
*On a number o f f i g u r e s t h e l e t t e r C ( f o r " c o e f f i c i e n t " o f the t i d e ) appears. L e t us r e c a l l t h a t t h e " c o e f f i c i e n t " i s d i r e c t l y p r o p o r t i o n a l t o t h e amplitude o f one d e f i n i t e t i d e , provided t h e phenomenon i s e s s e n t i a l l y semi-diurnal
:
i t i s then v a l i d f o r a l l places. The C o e f f i c i e n t i s expressed i n "centiemes" ("hundredths").
As a comparison : t h e mean s p r i n g t i d e range corresponds t o C = 95 t h e mean t i d e range corresponds t o C = 70 t h e mean neap t i d e range corresponds t o
C = 45
The h i g h e s t p o s s i b l e t i d e range i s c h a r a c t e r i z e d by C = 120 The lowest p o s s i b l e t i d e range i s c h a r a c t e r i z e d by
C = 20
The mean e q u i n o x i a l s p r i n g t i d e range corresponds t o C = 100
35
Salinity structure i n the Western approaches to the strait ("HELLAND-HANSEN" ; may 1965), near longitude 6'38'W. FIG.10
:
36
20 Moy 1965
[ 21 May 1965
4 6 8lDl2Ul61)1oZZoh2 4 6 8 I l , l , l , l , l , l , l , I , l , Dm
NWi154 l55 l56 l57 158 139 WIO
l61M
mOm
mrn
Xam
a
m
500m
HWwb9
c* m
HWlmU C=M
HWEJLU
c=m
Anchor rtotlon : 3So48'N 6 '20'W
Fl6.11
Salinity structure i n the Western approaches t o the strait. ("HELLAND-HANSEN"; May 1965). near longitudes 6'20'W (Sp) and 6'14'W (Below).
31
A t i d a l c u r r e n t , w i t h a d o n i n a t i n g s e n i - d i u r n a l component (12h,4
h o u r s ) and
a weak d i u r n a l one, i s superimposed t o t h e nean regime. The c o r r e s p o n d i n g per i o d i c c u r r e n t ConstitEntd-everse w i t h t i d e , b u t t h e amplitude o f t h e t i d a l c u r r e n t i s g r e a t e r t h a n t h e mean c u r r e n t i n t h e s u r f a c e l a y e r f a c e ) b u t weaker t h a n t h e mean results that the cycle i n
total c u r r e n t
(above t h e i n t e r -
c u r r e n t i n t h e deeper l a y e r (beyond 250 n). I t (nean
+
t i d a l ) r e v e r s e d u r i n g a semi d i u r n a l t i d a l
t h e s u r f a c e l a y e r while i t i s always o u t f l o w i n g i n t h e deeper ones, t h u s
k e e p i n g a c o n s t a n t d i r e c t i o n t h e r e ( f i g . 12). On t h i s f i g u r e , hours b e f o r e and a f t e r t h e l o c a l h i g h water ( T a r i f a ) are along t h e v e r t i c a l ( f r o n
+
-
7 hours t o
7 h o u r s ) , w h i l e i n a b s c i s s a t h e i n s t a n t a n e o u s t o t a l c u r r e n t i s a l o n g ox
( p o s i t i v e when i n f l o w i n g , n e g a t i v e when:outflowing).
The c u r r e n t s a t 5 depths
are p l o t t e d . The t o t a l c u r r e n t , as w e l l as i t s a l t e r n a t i v e components, have t h e i r maximum a l u e s ( i n and o u t ) a t a b o u t t h e same monent a t a l l depths : 3 t o 4 h o u r s b e f o r e High \ l a t e r (HW
-
3 t o HW
-
4) f o r t h e maximum o u t f l o w ; 3 h o u r s a f t e r HI.1 f o r
t h e i n f l o w c u r r e n t ( o r t h e minimum o f o u t f l o w i n t h e deeper l a y e r s ) . I n t h e upper l a y e r s , t h e i n f l o w c u r r e n t b e g i n s a b o u t 1 h o u r b e f o r e HI! (HI1 t h e o u t f l o w about HLI
+
-
l h ) and
6 h.
The mean maximum v a l u e s reached i n A4, a c c o r d i n g t o o u r measurenents o f 1960 are : depth
t o t h e East
t o t h e West
10 m
1.8 kn 2.1
1.4 kn
50
1.2
100
1.8
1.1
200
1.8
2.3
t o the \lest 350
0.5 (N.B.
But t h e r e are appreciable t o the followingone
2.25
100 cn/s = 1,94 k n )
f l u c t u a t i o n s o f c u r r e n t f r o n one s e n i - d i u r n a l t i l e
( T a b l e I,f i g . 2 ) . One w i l l n o t e t h e f a s t e v o l u t i o n o f t h e
g l o b a l c u r r e n t a t 200 m n e a r HW
+
l h , which c o i n c i d e s w i t h t h e maxinum descent
r a t e o f t h e i n t e r f a c e : b e f o r e t h i s hour, a t 200 m, k d i t e r r a n e a n w a t e r i s p r e s e n t ( S 2 37.5
%o)
; a f t e r A t l a n t i c w a t e r i s met ( S
The 10s Wormley ( D r THORPE, p e r s o n a l
36.5
%o)
(see f i g . 12)
communication) c a r r i e d o u t i n 1974
( j u l y - S e p t e m b e r ) a v e r y nice c u r r e n t r e c o r d n e a r p o i n t A4 about 60 m above t h e bottom. The r e c o r d shows t h e i n v a r i a n c e o f t h e
c u r r e n t and, i n s p r i n g
t i d e , d u r i n g a few t i d a l c y c l e , s h o r t i n v e r s i o n s ( i n f l o w s ) o f t h e g l o b a l c u r r e n t .
38
1 STATION 2n I
18 -Q-m
-
I m/s
OUTFLOW
A41
COEFz 67
1,n
1n
INFLOW
I
I
0.5m/s
.s -1
0.5m/s
2p I
Im/s
-6
t2 t3
+4
lorn Q
50m
0
v
lWm 200m
0
350m
t5
t6
.-
tl
FIG.12 T i d a l v a r i a t i o n of t h e l o n g i t u d i n a l c o m p o n e n t of t h e g l o b a l c u r r e n t
i n A4, for d i f f e r e n t d e p t h s .
m.13
8x -4
0
E 0
8"
(u
6
8 Internal wave o f salinity in A4. 18-20 sept. 1960.
B
39
FIG.14
'
: : , I
1
.; .. . ..: : .
. . .. .. . .. ~.. .. ,. ~ , .
._ . .. _ . ..
i + i n 92 001
00;
Internal wave o f s a l i n i t y i n A4. 8 may 1967. Bathysonde yoyo-ing ( N / O "Jean C h a r c o t " ) .
41 The h y d r o l o g i c a l
regime i s a l s o s u b j e c t t o i m p o r t a n t t i d a l e f f e c t s ; a
determined i s o t h e r m , o r isohaline,changes F i g . 14 i s r e s u l t i n g
i t s depth
with
t i n e ( f i g . 13 and 1 4 ) .
f r o m t h e use of a y o - y o i n g bathysonde e v e r y 15 mn. I n t e r n a l
waves a r e p r e s e n t ; t h e i r a m p l i t u d e i s 5 0 t o 60
m ; the "high water" o f the i n t e r n a l
t i d e i s about one h o u r i n advance w i t h r e s p e c t t o t h e s u r f a c e t i d e , and c o i n c i d e s i n time w i t h
t h e b e g i n n i n g o f t h e g l o b a l i n f l o w - c u r r e n t a t t h e s u r f a c e . The
"low w a t e r " o f t h e i n t e r n a l t i d e , on t h e c o n t r a r y , c o i n c i d e s w i t h t h e inonent when t h e o u t f l o w - c u r r e n t b e g i n s a t t h e s u r f a c e . The s a l i n i t y i s r e l a t i v e l y homogeneous beyond 300 m : i t i s a l m o s t " p u r e " t l e d i t e r r a n e a n w a t e r .
1 I . C T i d a l f o r c i n g i n t h e c e n t r a l sectio,ns o f t h e s t r a i t , between t h e s i l l and t h e s e c t i o n o f p o i n t C i r i s ( 5 " 9 0 ' b!) Clearly there i s a r a p i d evolution 1I.C.Al cycle,
The s i l l .
i n t h a t central sector.
As r e g a r d s c u r r e n t s and t h e i r e v o l u t i o n d u r i n g a t i d a l
f i g . 15 shows t h a t , i n t h e s u r f a c e l a y e r s , as w e l l as i n t h e deeper ones,
t h e phase of t h e a l t e r n a t i v e component o f t h e c u r r e n t w i t h r e s p e c t t o t h e s u r f a c e t i d e i s s i m i l a r t o t h e phase i n A4 : t h e c u r r e n t s e t s E a s t a t about
-
1h
( T a r i f a ) . One n o t e s , however, t h a t i n t h e upper 100 II t h e v e l o c i t i e s a r e much h i g h e r ( a b o u t 3.5 kn (180 c n / s ) t o t h e E a s t and 2 kn (100 cn/s) t o t h e I ' e s t ) a f t e r a sudden r e v e r s a l a b o u t i n h a l f an h o u r (between
-
-
Oh 30 ( T a r i f a ) : t h e v a r i a t i o n i s about 3 kn
l h a n d a h 3 0 T a r i f a ) . On t h e s i l l i t s e l f , t h e phase
o f o u t f l o w i n g c u r r e n t ( - 5h 30 t o -Oh30 T a r i f a ) i s accoryanied i n t h e s u r f a c e b y q u a s i permanent l i n e o f eddjes,a f e a t u r e w h i c h must be l i n k e d t o t h e h y d r o l o y i c a l s t r u c t u r e d u r i n g t h a t phase. The a v a i l a b l e deep c u r r e n t neasurenents a r e however scarce.
As f o r t h e h y d r o l o g y ( f i g . 16, 17 f o r t h e South s i l l S s ) and f i g . 18 ( f o r t h e N o r t h s i l l Sn) t h e h y d r o - s t a t i o n s nade d u r i n g t h e c u r r e n t measurements o f f i g . 15 e x h i b i t v e r y complex v a r i a t i o n s i n depth, f o r t h e i s o t h e r m s as f o r t h e i s o h a -
l i n e s ( f i g . 16). I n 1967, on t h e b a s i s o f measurenents b y a y o - y o i n g bathysonde ( f i g . 17 f o r Ss and 18 f o r Sn), t h e shape o f t h e i n t e r n a l wave i s d i f f e r e n t . I n a d d i t i o n , i n t h e same p l a c e , Ss, i t i s d i f f e r e n t f o r two s u c c e s s i v e s e m i - d i u r n a l t i d e s . It must be n o t e d however, t h a t t h e s e neasurenents were made f r o m a d r i f t i n g s h i p , manoeuvering t o keep t h e same p o s i t i o n
...
I n s t e a d o f e x h i b i t i n g , as i n t h e case i n 8 4 ( f i g .
14),a
regular sinusoidal
p r o f i l e , h e r e t h e i n t e r f a c e i s s u b j e c t t o i r r e g u l a r motions and, sometimes, occupy two l e v e l s o n l y , one around 150 m between t h e t i m e of low w a t e r and HW4h T a r i f a ; t h e n a n o t h e r one around 80 m, between tit1 followed
-
4 and till t Oh 30 ( T a r i f a ) ,
b y a f a s t deepening o f t h e i n t e r f a c e ( f i g . 1 6 ) . I t i s p r o b a b l e t h a t
such a b e h a v i o u r does n o t o c c u r f o r a l l t i d e s ( c f . BOCKEL NATO, TI? n"2 1962 p. 325).
oct. 2
42
LSTATION
SILL
I
25-IX-1960 c-82
OUTFLOW
I t-
INFLOW
FIG.15 Tidal v a r i a t i o n o f the longitudinal component o f the global current on t h e s i l l ( p o i n t Ss). 25 s e p t . 1960.
1 .
25 sept. 1960.
SALlN ITY
m TU
eh I
OOrn
OOm
FIG.16 Simultaneous water structure on the s i l l ( p o i n t Ss).
25- IX - 60
OOm
44
FIG.17a
... .. .. ..... .. ......
0
8
8 Internal wave o f salinity during a diurnal cycle in SS. 6-7 may 1967. Bathysonde yoyo-ing (N/O "Jean Charcot").
t0
Em
M . 1 7 b Internal wave of salinity during a diurnal cycle i n Ss.
6-7 may 1967. Bathysonde yoyo-ing (N/O "Jean Charcot")
POINT Ss 6-7 MAY 1967 7 MAY 1967 llh
2/’1
I
8
31h 4
4,h
5,h
I
I
6,h, I
7,h I
8,h
9,h
10,h
11,h
12,h.
13,h
14,h
1
I
I
I
I
I
1
0
100
200
300
ji
m
LC = TIDE -RIP P
u1
FIG.18
POINT SN 7 - 8 MAY 1967
‘Internal wave o f salinity on t h e s i l l ( P o i n t Sn) 7-8 nay 1967. Bathysonde yayo-ing (N/O Jean C h a r c o t ) .
47
B e f o r e t r y i n g t o e x p l a i n such a v a r i a b i l i t y , we s h a l l compare t h e e v o l u t i o n i n t i m e o f c u r r e n t s ( f i g . 15) and t h e i n t e r n a l wave ( f i g . 1 6 ) , observed t h e same day.
From
-
5 h to
-
Oh 30 ( T a r i f a ) , t h e c u r r e n t i s o u t f l o w i n g i n t h e 200
upper meters ; t h i s i s a l s o t h e p e r i o d when t h e i s o h a l i n e s and i s o t h e r m a r e s h a l l o w e r : t h e t y p i c a l l y M e d i t e r r a n e a n w a t e r s ( S = 38.3 "/.) come c l o s e t o t h e s u r f a c e and, somewhat b e f o r e HW (H11
-
Oh45), t h e s u r f a c e temperature drops by
more t h a n 3 degrees C i n 45 mn, w h i l e t h e s a l i n i t y minimum reaches t h e s u r f a c e . T h i s shows t h a t most o f t h e w a t e r t h e n p r e s e n t o v e r t h e s i l l i s d i r e c t l y i n f l u enced b y M e d i t e r r a n e a n w a t e r r a p i d l y moving West and which has had t o f l o w o v e r t h e M e d i t e r r a n e a n s i d e o f t h e s i l l and almost r e a c h i n g t h e s u r f a c e . The phenomenon i s v i s i b l e a l s o on BOCKEL's c u r v e (,JR ascending
NATO no 2 p. 3 2 6 ) . T h i s g e n e r a l
m o t i o n up t o n e a r t h e s u r f a c e generates n e a r t h e s i l l , d u r i n g t h e
p e r i o d o f o u t f l o w , v e r y v i s i b l e e d d i e s a l r e a d y quoted. I t i s a t t h e end o f t h a t p e r i o d t h a t , on t h e s i l l (South s i l l Ss),the
sudden
r e v e r s a l o f c u r r e n t t a k e s p l a c e i n t h e s u r f a c e l a y e r s a t about H!'-Oh30 ; i t a f f e c t s a t l e a s t t h e 100 upper meters and i t s phase i s l o c k e d on t h e s u r f a c e t i d e . A f r o n t i s g e n e r a t e d t h e n , c o r r e s p o n d i n g t o a sudden b e g i n s a t t h e same t i n e i n A4. T h i s sudden
i n f l o w o f A t l a n t i c w a t e r which f l o w deeply n o d i f i e s t h e l o c a l hydro-
g r a p h i c a l s t r u c t u r e and t h e i n t e r f a c e s i n k s r a p i d l y d u r i n o a l e n g t h o f t i m e o f about 15 mn. The phenomenon i s analogous t o t h e b o r e , e x c e p t t h a t h e r e , t h e bore i s i n t e r n a l t o t h e f l u i d . The f r o n t o f t h e i n t e r n a l w a v e becomes s t e e p e r and tends t o an " i n t e r n a l b r e a k e r " w h i c h i s made o f a f r o n t p r o p a g a t i n g E a s t a t a speed o f 3 t o 3.5 kn which can be f o l l o w e d t o t h e E a s t o f the s t r a i t and even beyond. T h i s k i n d o f d i s c o n t i n u i t y appears when t h e wave a m p l i t u d e i s g r e a t w i t h r e s p e c t t o t h e f l u i d depth. II.C.2
On T a r i f a s e c t i o n .
"Ihat i s p a r t i c u l a r l y s t r i k i n g on T a r i f a s e c t i o n
i s t h e f a c t t h a t , w i t h i n t h e 50 upper meters, t h e c u r r e n t has p r a c t i c a l l y no i m p o r t a n t component t o t h e \ l e s t , c o n t r a r y t o what happens on t h e s i l l between
- 5h 30 and - Oh 30 ( T a r i f a ) ; i n s t e a d , t h e i n f l o w i n 9 component i s s u b m i t t e d t o a genuine d i s c o n t i n u i t y between and + 2h 30
+
l h 30 ( T a r i f a ) i n t h e c e n t e r o f t h e s e c t i o n
( T a r i f a ) i n t h e South, s i n c e ( f i g . 19, 20, 21) t h e c u r r e n t i n c r e a s e s
by about 3 k n i n a l e n g t h o f t i r e o f about 30 nn. The f a c t t h a t t h e i n f l o w c u r r e n t i n t h e s u r f a c e l a y e r s i s weak between - 3 and
-
l h 30 ( T a r i f a ) , t h a t t h e o u t f l o w i n g deep c u r r e n t i s s t r o n g between these
hours, t h a t , l a s t l y , t h e maximum o f o u t f l o w c u r r e n t i s met when t h e i n t e r f a c e on t h e s i l l i s s h a l l o w e r l e a d t o t h i n k t h a t t h e deep I l e d i t e r r a n e a n o u t f l o w , c r e e p i n g o v e r t h e E a s t s i d e o f t h e s i l l , reaches t h e s u r f a c e t h e r e , as t h e hydrography suggested i t , and b r i n g s i n t h e necessary compensation o f f l u i d which i s necessary t o f i l l i n t h e d i v e r g e n t s u r f a c e f l o w between t h e s i l l and T a r i f a
8P P-PQ 3
-
.s*
.SIC
FIG.19
Tidal v a r i a t i o n of the longitudinal component o f the global current i n B'2 ( T a r i f a s e c t i o n ) . 27 s e p t . 1960.
49
23-IX-60 2,.
61.
-c
=97
FIG. 20 Tidal variation o f the longitudinal component o f the global
current i n B3 (Tarifa section). 23 sept. 1960.
50
24 -25- IX-60
.
2450 650
2"
1" 1
0
I
c.92 * 1" I
'2 I
3"
I
Ln !
2m/s
FIG.21 Tidal v a r i a t i o n of t h e longitudinal component of the global
current in B4 ( T a r i f a s e c t i o n ) . 24-25 s e p t . 1960.
0 UT+lh 12 II
11
HW
3 MAY 1967
LC = TIDE -RIP
22h 21h 20h 19h l 8 h
100
300 m
FIG.22 ,Internal wave o f s a l i n i t y i n the'North o f T a r i f a section ( p o i n t B5). 3 may 1967. Bathysonde yoyo-ing ( N / O "Jean Charcot").
UT+l h
1
I
17h 16h
I I
L. c
LC 401
ic
15h 14h 13h 12h
1 I
I I
11h 9h3010h
3 M A Y 1967 POINT Bs
N
FIG.23
UI
~
-~ ~~ ~~
-
LC =TIDE -RIP
I I
Internal wave o f salinity i n the South o f Tarifa section ( p o i n t 66) 4 may 1967 ( N / O "Jean Charcot").
Ul+lh
17h 15h
I
16h 14h 13h 12h 11h lOh 9 h 8 h
4 MAY1967 8 6 ~.
POINT
I 7;
4 MAVIS67 .
-
53
s e c t i o n : as a m a t t e r o f f a c t , t h e s u r f a c e c u r r e n t i s o u t f l o w i n g on t h e s i l l w h i l e i t i s i n f l o w i n g on T a r i f a s e c t i o n :
t may be t h a t , l a t e r a l l y , a s u r f a c e
f l o w a l o n g t h e N o r t h and South shores blest o f T a r i f a s e c t i o n t a k e s p l a c e a l s o . The c u r r e n t f r o n t i s g e n e r a t e d on t h e s i 1 ( S s ) s l i g h t l y b e f o r e HI1 and i t s passage c o i n c i d e s w i t h
t h e sudden
deepening o f t h e i n f e r f a c e ( f i g . 15, 16),
j u s t a f t e r HW. I t i s propagated E a s t and reaches T a r i f a s e c t i o n a t about + l h ?O i n m i d channel and t 2h 30 ( T a r i f a ) i n t h e South ( f i g . 19, 20, 2 1 ) . The passage o f t h e f r o n t and t h e deepening o f t h e i n t e r f a c e c o i n c i d e w i t h t h e appearing, on t h e sea s u r f a c e , o f " s l i c k s " w h i c h propagate l o c a l l y t o t h e ESE ( f r o m 290") a t about 3 kn. I n 1967, d u r i n g t h e bathysonde y o - y o i n g iw'B6, s l i g h t l y t o t h e NI! o f B4, we observed h a l f an dozen passages o f those s l i c k s ( o r f i g u r e s ) w i t h i n 10 t o 20 mn
tide-rips
-
L. C
.
on t h e
t i m e d i f f e r e n c e s between t h e s u c c e s s i v e ones ; t h e
h o r i z o n t a l d i s t a n c e between them was about 1500 m. T h i s a l s o g i v e s about 3 kn as t h e p r o p a g a t i o n speed. The passage o f t h e f r o n t i s v e r y conspicuous i n B6 ( f i g . 2 3 ) . I n t h e N o r t h e r n p a r t o f t h e s e c t i o n , i n B5, ( f i g . 2 2 ) , t h e i n t e r n a l wave i s much s m a l l e r and i t s p r o f i l e i s much m r e r e g u l a r . Nore t o t h e E a s t , n e a r m e r i d i a n 5" 3 0 ' , t h e h y d r o - s t a t i o n s made on s e c t i o n Cn, Cc, Cs ( c h a r t A) ( s e e f i g . 35, l a t e r ) d i p l a y t i d a l i n t e r n a l waves more o r l e s s i n phase w i t h t h e s u r f a c e t i d e , w i t h an i n t e r f a c e s l o p i n g down South. B u t no evidence o f passage o f t h e i n t e r n a l f r o n t v i s i b l e i n p o i n t 86 appears, perhaps due t o an i n s u f f i c i e n t frequence o f s t a t i o n s
However ( f i g . 24) t h e c u r r e n t
measurements a t 10 m (TR no 30 M. CANO, 1966
show f o r Cc n o t o n l y a r a p i d i n -
crease o f t h e e v e r - i n f l o w i n g c u r r e n t between HI.! t Oh 30 and H!! a v e r y a b r u p t i n c r e a s e somewhat b e f o r e H!!
+
+
2h, b u t m a i n l y
4.h 00. T h i s corresponds p r o b a b l y
w i t h t h e passage o f t h e f r o n t . 1I.D
T i d a l f o r c i n g near t h e Eastern entrance (near n e r i d i a n o f G i b r a l t a r ) .
The t i d a l e f f e c t s a r e f a i r l y d i f f e r e n t o f t h o s e o c c u r r i n g on Cape S p a r t e l m e r i d i a n (A4) and i n t h e c e n t r a l s e c t o r . As regards t h e c u r r e n t s and p a r t i c u l a r l y a t p o i n t C2 (see c h a r t A ) , s t r o n g
c u r r e n t s a r e met o n l y i n t h e s u r f a c e l a y e r down t o 80-100 m.Fig. 25, which presents t h e l o n g i t u d i n a l c u r r e n t s a t v a r i o u s depths as a f u n c t i o n o f t h e t i d a l hour shows t h a t , c o n t r a r y t o what happens i n t h e \ l e s t , t h e g l o b a l c u r r e n t does n o t r e v e r s e w i t h t i d e i n t h e s u r f a c e l a y e r b u t r e v e r s e s i n t h e deeper l a y e r s , i n which t h e c u r r e n t s a r e weak, b u t w i t h a s m a l l mean component
t o t h e !lest. The
mininum o f t h e i n f l o w c u r r e n t i n t h e upper l a y e r occurs a t about t 2h 30 ( T a r i f a : i.e.2h 30 a f t e r t h e High !!ater a t T a r i f a ) , t h e n a x i n u n a t about + 6 h ( T a r i f a ) ; a t de?th, t h e phases o f t h e a l t e r n a t i n g p a r t o f t h e c u r r e n t seen o f o p p o s i t e
54
STAFFETTA
7
-5
3i
-a-
STATION Cc 3 JUNE 1961 17h20 U.T.
NORTHERLY COMPONENT 1Om
I7 +1-
i 2
&L E STERLY COMPONENT 10m
17hM U.T.
FIG. 24 Northerly and Easterly c u r r e n t components i n Cc (meridian 5"30' W ) . June 3 1961.
FIG.25
D
D
0
n
0
5
5
8
9
8
N0113n03t4 31V3S
i n C2. 14-15 sept. 1960 ( l e f t ) and s a l i n i t y s t r u c t u r e ( r i g h t ) .
T i d a l v a r i a t i o n o f the l o n g i t u d i n a l component o f the g l o b a l c u r r e n t
55
56
--I4 h -
-
15h
16 h - -
7 HW - 6
-17hI-lEh-
.-
19 h -
7Om
I
I
7
-20h-
5-21h-
-HW =21 50
-22 h -23h-
-- 0 h -
-
2h-
?-
-
-
-
5om
Ih-
<+6
4h5h-
HW -6
6h7h-
- 8h- 9h- 10 h-
E - Ilh- 12 h:-13h9-14
h
'-15h1 -16h-
-
I7 h-
-H W = I O h 4 0
2
5
__
_Ir;l.;.".NT
HW-6
-18 h -
- I9 h -20 h-
- 21h-22 h~
t
_ ~ . .
- 2 3 h-
--
__ H W
= 22 h30
0 h-
FIG. 26 T i d a l v a r i a t i o n o f the l o n g i t u d i n a l component o f c u r r e n t (75-255") i n Gc, m e r i d i a n of G i b r a l t a r .
FIG.27 Internal wave o f s a l i n i t y in the South o f G i b r a l t a r meridian ( p o i n t C4). 4-5 may 1967. Bathysonde yoyo-ing ( N / O "Jean Charcot").
POINT C4 4-5 M A Y 1967
5 MAY 1967
4MAY 671 Oh
HW
(C
0
l h
2 h
3 h
4 h
5 h
6 h
7 h
I
I
I
I
I
I
I
531 q
8 h I
9 h
lOh
I
I
11h 1
12h 1
13h
1 i::
UT+lh
nw
581 149
-0
100
200
300
400 BOTTOM : 600 t o 7 0 0 m
m
58
FIG.28
0 OD
c
t-
P
I
.. ... .... .\' :
..
.........
Internal wave o f s a l i n i t y i n the North o f G i b r a l t a r meridian ( p o i n t C2) 5-6 may 1967. Bathysonde yoyo-ing (N/O "Jean Charcot").
FIG.29
. .
- N
E
cU
?
I
c
Surface current roses o f f the Eastern entrance t o t h e s t r a i t point E6 (13 june 1961) and E3 (14 june 1961).
59
60
phase : t h e maximum i n f l o u p a r t i s about about
-
+ 2
( T a r i f a ) , t h e naximun o u t f l o w a t
3 h. I n t h e Southern p a r t o f t h e s t r a i t (C4, c h a r t A ) , i n g r e a t deapths,
( l a t i t u d e 35"57:6), and naxirlum (2,5
t h e s u r f a c e g l o b a l i n f l o w i s minimum (1.2 k n ) around
k n ) around
+
+
5h
2h ( T a r i f a ) .
Coming back t o t h e c e n t e r o f t h e watevway ( p o i n t Gc) (TR no 30. M. CANO, 1966) t h e maximum Eastward
f l o w ( f i g . 26) i s , as i n C2, maximum around HIi'6h 00, t h e n
d e c r e a s i n g s l o w l y , a t 10 n as w e l l as 50 D. A remarkable f a c t ( s t u d i e d b y CAVANIE 1973) i s t h e
front
o f c u r r e n t , w h i c h i s s t r o n g e r i n 50 D (and 100 m a c c o r d i n g t o
CAVANIE's measurements) t h a n i n t h e s u r f a c e ; b u t a n o t h e r c u r i o u s f a c t i s t h a t , a t l e a s t a t neaps, t h e f r o n t t a k e s p l a c e a b o u t
HW
+
3h f o r a t i d e and t h e n e x t
one a t HIJ + 5h 30. T h i s i s an i n d i c a t i o n o f an i n p o r t a n t e f f e c t o f t h e d i u r n a l t i d a l component on t h e s e n o n - l i n e a r d i s c o n t i n u i t i e s . As f o r t h e h y d r o l o g i c a l regime, t h e i n t e r n a l waves have a s m a l l e r a m p l i t u d e than
i n t h e blest and, a l s o , a r e s h a l l o w e r : however t h e i r a n p l i t u d e i s niuch
g r e a t e r n e a r t h e Southern s h o r e ; i t i s weak n e a r t h e N o r t h e r n one ( f i g . 27, 2 8 ) . Moreover,in t h e South a t l e a s t ( p o i n t C4 - f i g . 2 7 ) t h e sudden i n c r e a s e o f t h e d e p t h o f t h e i s o h a l i n e s about Hk!
+
t h e passage o f t h e f r o n t g e n e r a t e d
4h 00 i s most p r o b a b l y t o be connected w i t h on t h e s i l l a t HII
-
Oh 30, p a s s i n g i n p o i n t
B3, B4, B6 between H!I t l h 30 and HI1 t 2h 30, p a s s i n g t h r o u g h t h e p o i n t C i r i s s e c t i o n s l i g h t l y b e f o r e HII
+
4h and about t h e same t i m e i n C4 ( o r Gs i n f i g . 36).
The f r o n t may be r e s p o n s i b l e o f t h e s m a l l k i n k a t H!i t 5h 30 i n C2 ( f i g . 28). P r o f . FRASSETTO (1960) as w e l l as ZIEGENBEIN (1969-70) have t r a c k e d i t i n t h e A l b o r a n Sea. I n a d d i t i o n CAVANIE (1972) observed t h e n d u r i n g a c r u i s e under NATO a e g i s and was a b l e t o f o l l o w t h e movenent of t h e f r o n t b y t h e r a d a r - s e a r e t u r n f m n t h e s i l l t o w r i d i a n 5"10'bl,in
t h e Southern h a l f o f t h e s t r a i t .
Somewhat more t o t h e E a s t , measurenents o f c u r r e n t i n CALYPSO Anchor s t a t i o n s E3 (36'02'
N
-
5" 0 4 ' !!) and E6 ( 3 6 " 0 8 ' N
-
5" 0 9 ' l!),
i n a d d i t i o n t o a probable
l a r g e d i u r n a l component ( f i g . 2 9 ) , show, i n t h e s u r f a c e l a y e r ( 1 0 m), an i n p o r t a n t component t o t h e N o r t h s p e c i a l l y n o t a b l e a b o u t tl!l
-
5h 00 c o r r e s p o n d i n g t o a
c l o c k w i s e r o t a t i o n o f t h e c u r r e n t . I n t h e c e n t r a l waterway (E3) t h e vaximun c u r r e n t exceeds 3 k n a t s p r i n g s . I n t h e deeper l a y e r s t h e c u r r e n l s a r e n u c h weaker w i t h a mean component t o t h e E a s t deeper t h a n 100
I".
The e x i s t e n c e o f an i m p o r t a n t n o r t h e r l y component f o r t h e nean c u r r e n t may be rel a t e d w i t h t h e a n t i c y c l o n i c g y r e i n t h e Western F l b o r a n sea.
1I.E
The s y n o p t i c h y d r o l o g y
The m u l t i - s h i p s u r v e y c a r r i e d o u t i n 1961 naltes i t p o s s i b l e t o be i n f o r m e d on t h e w a t e r s t r u c t u r e a t t h e same t i m e i n d i f f e r e n t
p l a c e s . a l t h o u g h we a r e
r
61 f a r t o have e v e r y two hours, as i n i t i a l l y scheduled, h y d r o s t a t i o n s made on a l o n g i t u d i n a l s e c t i o n and on f i v e t r a n s v e r s e s e c t i o n s , a t s p r i n g s and neaps, y e t we a r e a b l e t o p r e s e n t h e r e some i n d i c a t i o n s which a r e p r o b a b l y unique.
_L_o_n g_i t_u d_i _n a_l _s_t r _u c_t u_r_e _on_ _t h_e_l_i n_e_A4, - _ _Ss, _ - -Tc, - _ -Cc, --
Gc ( f i g . 30) t h e r e s u l t s
a r e p r e s e n t e d on a s e r i e s o f TS diagrams i n neap t i d e (above) and s p r i n g t i d e
,,
(below) f o r two s i m u l t a n e o u s h o u r s ( t o w i t h i n f Oh 30) f o r HI' t Oh 30 and HW f o r neaps ; and f o r HW
-
5h 00 and HII
-
+
6h 00
1 h 00 f o r s p r i n g s . The e v o l u t i o n o f t h e
TS curves show t h a t t h e e f f e c t o f m i x i n g i s much s t r o n g e r i n s p r i n g t i d e (below) t h a n i n neap t i d e .
Transverse_structure_of_saliaity I n t h e f o l l o w i n g f i g u r e s ( 3 1 t o 36) a r e sh'6wn t h e simultaneous e v o l u t i o n o f t h e w a t e r s t r u c t u r e i n 2 o r 3 p o i n t s across t h e s t r a i t . T h e i n s t a n t a n e o u s t r a n s v e r s e s l o p e may be deduced f r o m t h e graphs.
%ctjgnh_AZ,_A4 ( f i g . 3 1 ) i n neap t i d e ( C o e f f i c i e n t f r o m 42 t o 6 5 ) . I t i s seen t h a t depth o f t h e i n t e r f a c e i s g r e a t e r by a b o u t 30 t o 40 m i n A4 w i t h r e s p e c t t o A2. The a m p l i t u d e i s s m a l l e r i n A2.
sectjgn-sn-ss
( f i g 32) i n s p r i n g t i d e . As a l r e a d y seen on f i v u r e s 18 and 19
( n o t s i m u l t a n e o u s ) , h e r e we have simultaneous, a l t h o u g h much n o r e sparse,rieasurnents ( c l a s s i c a l h y d r o s t a t i o n s ) ; t h e p r o f i l e i s bunpy and t h e s h a l l o w i n t e r f a c e i s f o u n d somewhatbefore HLI. I n g e n e r a l t h e i n t e r f a c e i s deeper t o t h e South.
~ ~ t j g n - ~ n , _ T c , _( If ~i g
33) and Tn Ts ( f i g 34).The s t r o n q descent o f t h e i n t e r -
f a c e a f t e r HW i s c l e a r on f i g . 33 f o r Tn and Tc ; and on f i q . 34 i n Ts.
~ectjgn-~~~-cc,C ( f si g .
3 5 ) . The i n t e r f a c e i s v e r y c l o s e t o t h e s u r f a c e i n t h e
N o r t h and t h e c e n t e r o f t h e s e c t i o n . No c l e a r i n d i c a t i o n o f t h e f r o n t passage appears.
SeAjgn-Grii-Gc,_Gs ( f i g 3 6 ) . The most remarkable f a c t i s t h a t t h e i n t e r f a c e (37
%o)
p r a c t i c a l l y reaches t h e s u r f a c e i n t h e N o r t h (Gn), w h i l e i t i s a t l e a s t
i n 60 m i n Gs. T h i s phenomenon which i s r e o u l a r l y p r e s e n t may have a g r e a t i n f l u e n c e i n t h e g e n e r a t i o n o f t h e i n s t a b i l i t i e s o f t h e i n t e r n a l waves and o f t h e f r o n t which, a c c o r d i n g t o C A V A N I E (1972), i s o n l y v i s i b l e on t h i s Southern h a l f o f t h e s t r a i t . An i m p o r t a n t r o l e o f t h e e a r t h ' s r o t a t i o n i s t h u s t o be expected and s h o u l d be i n c l u d e d i n dynamical models. I n c o n c l u s i o n t o t h i s c h a p t e r , one nay say t h a t , i f , i n t h i s Glestern p a r t o f t h e s t r a i t ( A 4 ) , t h e i n t e r n a l wave i s " l o c k e d " on t h e s u r f a c e t i d e phase and keeps a r e g u l a r q u a s i - s i n u s o i d a l p r o f i l e , an a d d i t i o n a l complex phenomenon i s superimposed i n t h i s E a s t e r n s t r a i t : t h i s phenomenon yenerated on t h e s i l l
62
SPRINGS C
= 89
FIG.30 S y n o p t i c t i d a l v a r i a t i o n o f T/S d i a g r a m i n five p o i n t s o f a
l o n g i t u d i n a l s e c t i o n i n the s t r a i t a t two i n s t a n t s o f t h e t i d e a t n e a p s ( a b o v e ) and s p r i n g s ( b e l o w ) .
63
A
I
I
W n h W
HWlDhM
I
HILLAND-HANSEN I ]BOTTOM: 2 6 0 m I C=(b
c.w
mnhm
HW i i h 00
c=55
Cz60
FIG.31 Simultaneous internal wave o f salinity on section A2 A4. (Western entrance)
- neap tide.
64
I
I
I
I
EUPEN 4mm
1
I
SN HWtn% CzM
2 june1981
HW15hM
HWOJ h15
c=ei
C=B
HWOthl5 cz77
13jurwl981 O h 2
b
6
F16.32 Simultaneous internal wave o f s a l i n i t y on section SN SS (Si1l)Spring tide
65
.
HG.33
I
'
l
l
I
Simultaneous i n t e r n a l wave o f s a l i n i t y on s e c t f o n Tn Tc Ts ( T a r i f a )
-
s p r i n g tide:
66
27 may 1961 8
I
28 may 61
10 12 U M l 8 2 0 2 2 O h 2
I
I
4
\\
6
\ Y
8
Loan
STAFFElTA
Ts
FIG.34
Slwltaneous Internal wave o f s a l l n l t y on section Tn Ts (Tarlfa). Mean tlde.
61
I I
3 junr1961 u m 10
H) 12
14 june 61 c I
2 0 2 2 oh 2
ORICNY
cs
~~
~
FIG. 35 Simultaneous internal wave o f s a l i n i t y on section Cn, Cc, Cs
(5'30'W).
Spring tide.
68
GN EUPEN
. p(h
u
nw mu) C.W
I 2022Oh2
twC.6622h30 ] 26 may m
25 may 1961
4 8 8 lQ1214181820220h2 4 6
Gc
C.W
C.55
'FIG.36 Simultaneous internal wave o f salinity
(EaPtiern entrance). Neap tide.
on section Gn, Gc, Gs
69
i s very intense and made of an i n t e r n a l breaker which, more t o the E a s t , and p a r t i c u l a r l y near the Southern shore of the s t a i t , deeply modifies the i n t e r n a l wave p r o f i l e and c o n t r o l s , i n f a c t , t h e t i d a l p a r t of t h e c u r r e n t .
I11 METEOROLOGICAL EFFECTS
B u t t h e t i d e i s not t h e only phenomenon which induces, i n the s t r a i t , important modifications of the regime ; i f the t i d e was the only f a c t o r t h e values of the fluxes exchanged during a diurnal cycle should be the same. Clearly i t i s not the case. Table I l i s t i n g the r e s u l t s based on d i r e c ? measurements a t point A4 i n 1960 and 1971 shows t h a t v a r i a t i o n s of a t l e a s t 50 % are present f o r the diurnal f l u x e s . Following our measurements of 1958 (LACOMBE 1961), we examined meteorological e f f e c t s . These may a c t on two s c a l e s : 1 - the e f f e c t s of local winds over the s t r a i t : 2 - t h e e f f e c t s of "lows" on the tlediterranean and, more p r e c i s e l y , over the Western Mediterranean. 1II.A Effects of t h e local meteorology The wind regime, over t h e s t r a i t , i s only l'ongitudinal a t sea level ; in autumn and winter t h e prevailing winds a r e from the Kest ; in sumner from the East and and they may be strong 25-35 kn f o r over a week i n August. The f r i c t i o n a l force on t h e s u r f a c e tends t o increase the surface c u r r e n t i n t h e d i r e c t i o n of the wind ; t o slacken oreven reverse the c u r r e n t flowing upwind . The velocity modification of the c u r r e n t a r e mainly within the upper 20 m ; these may induce currents of . 5 k n along the wind. I n A4, i n t h e Western end of t h e s t a i t , i n may-june 1961, when t h e wind was strong from SSW, t h e incoming f l u x was p a r t i c u l a r l y strong ( 5 june 1961), f i g . 2 .
1II.B The e f f e c t s of the general d i s t r i b u t i o n of atmospheric pressure over the Western Mediterranean have an incidence on a g r e a t e r s c a l e . I t i s well known t h a t along many s h o r e s , there i s a c l e a r r e l a t i o n s h i p between t h e evolution with tiire of the " d a i l y mean sea l e v e l " ( p r a c t i c a 1 l y f r e e from sea t i d a l e f f e c t s ) and of the local atmospheric pressure. Often the l o c a l sea level r e a c t s as an "inverted barometer" : an increase of pressure of 1 mbar causes a decrease of about 1 cm of the sea l e v e l . This "inverted barometer" reaction i s f a i r l y well v e r i f i e d i n many Mediterranean harbors. T h e n , i f we admit t h a t t h i s "law" can be applied in the open s e a , i t i s seen t h a t a drop of t h e mean pressure o f 1 mbar i n one day over the whole Nediterranean corresponds t o an increase of about 1 cm f o r the sea l e v e l . AS the surface of t h e sea i s 2.5 l o 6 km2 (excluding the Black Sea) the volume of water
70
involved i s
2.5 10"
m3/ day, i e about 2.9 lo5 n3/s : t h i s i s o f t h e o r d e r o f
1 / 4 o f t h e mean f l u x e s i n t h e s t r a i t . One can t h u s e x p e c t i m p o r t a n t e f f e c t s on these f l u x e s . Another
approach nay be made : i n t h e presence o f C o r i o l i s f o r c e an i n c r e a s e
o f t h e i n c o n i n g c u r r e n t a t t h e s u r f a c e w i l l cause an e l e v a t i o n o f t h e sea l e v e l on t h e Southern shore o f t h e s t r a i t a n d / o r a decrease on t h e N o r t h e r n . f n t h a t l i n e we t r i e d t o r e l a t e t h e v a r i a t i o n s o f t h e d a i l y mean sea l e v e l on t h e two shores o f t h e s t r a i t t o t h e mean atmospheric p r e s s u r e o v e r t h e Mediterranean.
M. CREPON (1965) extended t h e s t u d y t o a number o f m o n t h l y p e r i o d s d u r i n g which t h e d i s t r i b u t i o n o f t h e a t m o s p h e r i c p r e s s u r e o v e r t h e l l e d i t e r r a n e a n showed 1arc;e v a r i a t i o n . S t u d y i n g t h e r e l a t i v e mean sea l e v e l on t h e South s h o r e (Ceuta) r e l a t i v e l y t o t h e N o r t h shore ( G i b r a l t a r ) * ,
he n o t e s t h e f r e q u e i t presence o f f a i r l y
good c o r r e l a t i o n between t h e r e l a t i v e mean sea l e v e l and mean atmospheric p r e s s u r e . As t h e s u r f a c e f l u x i s c l e a r l y r e l a t e d t o t h e t o t a l i n c o m i n g f l u x , i t i s a p p a r e n t t h a t l o w p r e s s u r e s t e n d t o i n c r e a s e t h e i n c o m i n g f l u x and c o n v e r s e l y h i g h p r e s s u r e s t e n d t o decrease i t . This simple q u a l i t a t i v e r u l e r a i s e s d i f f i c u l t i e s , i n p a r t i c u l a r i n r e l a t i o n w i t h t h e e q u a t i o n o f c o n t i n u i t y (CREPON 1965), b u t i t i s a s i m p l e , approximate guide. O f course, a r e l a t i o n o f t e n e x i s t s between t h e l o c a l w i n d regime and t h e gener a l regime o v e r t h e M e d i t e r r a n e a n : t h e l l e s t e r l i e s
blow o v e r t h e s t r a i t when
t h e p r e s s u r e i s l o w o v e r t h e W. E e d i t e r r a n e a n and t h e l o c a l e f f e c t s may f a v o u r t h e i n c r e a s e o f f l u x e s due t o t h e i n v e r t e d barometer r e a c t i o n s o f t h e sea l e v e l i n t h e Mediterranean.
IV
RELATIONS
OF THE REGIHE OF THE STRAIT VITH PHENOt!ENA PRESENT I N THE ADJACENT
SEAS EAST AND WEST These a r e t h e l l e s t e r n A l b o r a n Sea and t h e Bay o f Cadix. The a n t i c y c l o n i c g y r e
of t h e Llestern A l b o r a n Sea
-
a v e r y conspicuous and permanent f e a t u r e v i s i b l e on
s a t e l l i t e thermographs -which may be g e n e r a t e d b y t h e o b l i q u i t y o f t h e mean s u r f a c e j e t f l o w i n g t o t h e E a s t w i t h r e s p e c t t o t h e E-If a x i s o f t h e L e s t e r n A l b o r a n Sea
-
w i l l be c o n s i d e r e d b y o t h e r speakers
i n this
colloquium
(DONGUY (1962) NATO TR n o 2, o c t 1962, GROUSSON and FAROUX (1963), LANOIX 1972, 1974 ; LACOMBE 1977, P E T I T e t a l (1978) CHENEY and DOBLAR (1979).
"In t h e absence o f any l e v e l l i n g network l i n k i n g t h e two shores o f t h e s t r a i t , t h e l e v e l s have t o be r e f e r r e d t o an a r b i t r a r y datum and, so, o n l y t h e
m-
tions o f t h e i r difference
are accessible.
71
AS f o r t h e existence o f the “density c u r r e n t ” of lledi terranean water flowing Westward i n t h e thalweg of the submarine valley following the s t r a i t t o t h e blest, i t i s a remarkable example of t h e o b s t a c l e opposing tomixing between waters of small density d i f f e r e n c e s , despite the presence of superimposed strong c u r r e n t (LACORBE e t a1 1970, NATO TR n o 7,BOYUI.I G , IIADELAIN 1970).
CONCLUSION I n t h e s t r a i t of G i b r a l t a r a range of various phenomena occur which have a g r e a t i n t e r e s t f o r physical oceanography because they a r e typical examples f o r a number of them. I t i s a model s t r a i t . The r e l a t i v e l y g r e a t length of the s t r a i t , about 100 km from 6’40’ kf t o 5’20’ Irl permit the f u l l development of some processes which reach remarkable amplitude. Observation i s s t i l l , f o r the time being, our main source of information, because purely dynamical modelling i s i n a c c e s s i b l e , due t o t h e complexity o f t h e events present. lle know new program a r e envisaged t o be c a r r i e d out i n t h e area. This i s very f o r t u n a t e because, a f t e r t h e g r e a t e f f o r t during t h e 6 0 ’ , no important multiship work was made since then and we s t i l l need many informations t o t r u l y understand what happens. For instance s u f f i c i e n t c u r r e n t measurementsare s t i l l lacking on the s i l l i t s e l f . kle have very few information on t h e r o l e which may have, f o r the regime of t h e Eastern half of t h e s t r a i t the flow taking place near t h e N and S shores I.1 of T a r i f a . !Je do not know with s u f f i c e n t accuracy the fundamental data regarding the mean exchanged flows andtheirseasonal v a r i a t i o n s ; we have no c l e a r idea of the l a r g e i n t e r n a l waves on the Southern shores, w i t h respect t o those on the Northern.
ble hope t h a t these questions w i l l be elucidated by t h e planned f u t u r e observations, which may i n turn permit the building of a good numerical model of the strait.
12
REFERENCES Bethoux, J.P., 1980. Mean w a t e r f l u x e s across s e c t i o n s i n t h e Pediterranean Sea, e v a l u a t e d on t h e b a s i s of w a t e r and s a l t budgets and o f observed s a l i n i t i e s . Oceanol. Acta, 3, 76-88. Cavanie, A., 1972. Observations de f r o n t s i n t e r n e s dans l e d e t r o i t de G i b r a l t a r pendant l a campagne oceanographique OTAN 1970 e t i n t e r p r e t a t i o n des r e s u l t a t s p a r un nodele rnathematique. Elem. SOC. Roy. S c i . Liege, 6i.me s e r i e , 11, 27-41. Cavanie, A., 1973. Observations oceanographiques dans l e d e t r o i t de G i b r a l t a r pendant l a campagne PHYGIB ( s e p t . - o c t . 1971). Ann. Hydrogr., 5eme s e r i e , Vol. 1, fasc. 1, 75-84. Cheney R . E . , R.A. Doblar, 1979. Alboran Sea 1977 : P h y s i c a l c h a r a c t e r i s t i c s and a t m o s p h e r i c a l l y induced v a r i a t i o n s o f t h e oceanic f r o n t a l system, US Naval Oceanogr. O f f . , Techn. Note 3700-82-79, 24 p. Crepon M . , 1965. I n f l u e n c e de l a p r e s s i o n atmospherique s u r l e niveau moyen de l a Mediterranee o c c i d e n t a l e e t s u r l e f l u x a t r a v e r s l e d e t r o i t de G i b r a l t a r . P r e s e n t a t i o n d ' o b s e r v a t i o n s . Cah. Oceanogr., X V I I , 15-3; and Nato T.R. no 21 mars 1965. Donguy, J.R., 1962. H y d r o l o g i e en l l e r d ' A l b o r a n . Cah. Oceanogr. XIV.8 pp 573-578. F r a s s e t t o , R., 1960. A p r e l i m i n a r y survey o f t h e thermal m i c r o s t r u c t u r e i n t h e S t r a i t o f G i b r a l t a r . Deep-sea r e s . , 7, ( 3 ) , 152-163. F r a s s e t t o R . , 1964. S h o r t - p e r i o d v e r t i c a l displacements o f t h e upper l a y e r i n t h e S t r a i t o f G i b r a l t a r . S a c l a n t ASN Res. L e n t e r , Tech. Kep. no 30, p a r t 1 t e x t , p a r t 2 d i a g r a m s , Nov. 1964. Grousson K. e t J. Faroux, 1969. Measures des courants de s u r f a c e en Ver d'Alboran. Cah. Oc6anogr. X V , 10 pp 716-721 and Nato T.R. n o 10 f e b . 1964. Lacombe H., 1961. C o n t r i b u t i o n 8 l ' e t u d e du d e t r o i t de G i b r a l t a r , etude dynanique. Cah. Oceanogr. X I I , 2 pp 73-107. Lacombe H. e t C. Richez, 1961. C o n t r i b u t i o n 8 l ' e t u d e du d e t r o i t de G i b r a l t a r I 1 Etude hydrologique. Cah. Oceanogr., X I I I , 5 pp 276-291. Lacombe H., P. Tchernia, C. Richez & L. Gamberoni, 1964. Deuxieme c o n t r i b u t i o n 8 l ' e t u d e du regime du d e t r o i t de G i b r a l t a r (Travaux de 1960). Cah. Oceanogr. P a r i s X V I , P. 283-327 and Nato T.R. no 14 j u l y 1964. Lacombe H., F. rladelain, J.C. Gascard, 1968. Rapport s u r l a campagne " G i b r a l t a r I" du N/O "Jean Charcot", 7 av.-12 mai 1967. Cah oceanogr., XX, 102-107. Lanoix F, 1972, 1974. Etude hydrologique e t dynamique de l a mer d'Alboran, these I I I e m e c y c l e P a r i s V I , 28.VI.72 e t Kapp. Techn. OTAN n o 66 (mai 1974). Madelain F., 1970. I n f l u e n c e de l a topographie du fond s u r l ' e c o u l e m e n t m e d i t e r raneen e n t r e l e d e t r o i t de G i b r a l t a r e t l e Cap S a i n t - V i n c e n t . Cah. Oceanogr. X X I I , 43-61. Peluchon G., K. Bockel, 1962. Travaux oc@anographiques de 1 "Origny" dans l e d e t r o i t de G i b r a l t a r . l e r e p a r t i e : h y d r o l o g i e dans l e d e t r o i t . Cah. Oceanogr. X I V , 323-329. P e t i t !I., V . Klaus, R. G e l c i , F.Fusey, J . J . Thery, P. Bouly, J.T. Gallagher, 1978. Etude d ' u n t o u r b i l l o n oceanique d ' e c h e l l e moyenne en mer d ' A l b o r a n p a r emploi c o n j o i n t de techniques s p a t i a l e s e t oceanographiques. CR. Acad. S c i . P a r i s , v o l . 287 B, 215-218, 8 f i g . T i x e r o n t J., 1970. Le b i l a n h y d r o l o g i q u e de l a Her N o i r e e t de l a l l e d i t e r r a n e e . Cah. Oceanogr. 22, 227-237. Zenk I I . , 1975. On t h e Mediterranean o u t f l o w \ l e s t o f G i b r a l t a r . "Meteor" Forschungergebnisse n o 16 pp 23-34. Ziegenbein J., 1969. Short i n t e r n a l waves i n t h e S t r a i t o f G i b r a l t a r . Deep Sea Res., v o l . 16, 479-487. Ziegenbein J . , 1970. S p a t i a l observations o f s h o r t i n t e r n a l waves i n t h e S t r a i t of G i b r a l t a r . Deep Sea Res., v o l . 17, 867-875.
73
NATO Technical Reports ( T . R . ) du Sous-Comit.6 oceanographique T.R. n o 2
- P r o j e t G i b r a l t a r . Resultats des observations oceanographiques e f f e c tuees en mai e t j u i n 1 9 6 1 dans l a region du d e t r o i t de G i b r a l t a r .
Oct. 1962. Plosby H . , 1961-62. Hydrological observationa the tl/S "HellandHansen" near t h e S t r a i t of G i b r a l t a r . May-June 1961. AoDt 1Y62. 4 Current measurements, meteorological observations and soundings of the M/S "Helland-Hansen" near the S t r a i t 6 f G i b r a l t a r . May-June 1961. Tables. Nov. 1962. 7 - Boyum G . , 1963. Hydrology and c u r r e n t s i n the area West of G i b r a l t a r . Results from t h e "Helland-Hansen" Expedition Hay-June 1961. Flai 1963. 10 - P r o j e t G i b r a l t a r . Resultats des observations effectuees en mai e t j u i n 1 9 6 1 dans l a region du d e t r o i t de G i b r a l t a r . Fevrier 1964. 14 - P r o j e t G i b r a l t a r . Resultats des observations oceanographiques e f f e c tuees dans l a region du d e t r o i t de G i b r a l t a r . J u i l l . 1964. 2 1 - P r o j e t G i b r a l t a r . Resultats des observations oceanographiques e f f e c tuees dans l a region du d e t r o i t de G i b r a l t a r . Mars 1965. 30 - Can0 PI., 1966. Campagna oceanografica d e l l a nave " S t a f f e t t a " d e l l a marina m i l i t a r e n e l l e s t r e t t o di G i b i l t e r r a ( 8 maggio - 19 giuno 1Y51). Octobre 1966. 3 1 - P r o j e t G i b r a l t a r . Resultats des observations e f f e c t u e e s 1 bord du navire belge "Eupen" (mai-juin 1961). Decernbre 1966. 34 - Boyum G. Hydrological observations of t h e K / S "Helland-Hansen" in the area Hest of G i b r a l t a r . May 1965. Tables. Bergen. Feb. 1967. 35 - Boyum G. Current measurements of the FI/S "Helland-Hansen" in the area West o f G i b r a l t a r . Tables. Flay 1965. Bergen march 1967. 36 - Boyum G., 1967. Hydrology a n d currents i n the blest of G i b r a l t a r . Results from the "Helland-Hansen" expedition. May 1965. Bergen. April 1967.
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75
A REDUCED GRAVITY NUMERICAL MODEL O F CIRCULATION I N THE ALBORAN SEA
/
RUTH PRELLER
JAYCOR, 205 South Whiting S t r e e t , Alexandria, VA 22304, USA HARLEY E.
HURLBURT
Environmental Simulation Branch (Code 322), Naval Ocean Research and Development A c t i v i t y , NSTL S t a t i o n , MS 39529, USA I
ABSTRACT Oceanographic o b s e r v a t i o n s have shown t h e e x i s t e n c e of a l a r g e a n t i c y c l o n i c gyre i n t h e western Alboran Sea.
S a t e l l i t e imagery demonstrates t h e p e r s i s t e n c e
of t h e Alboran Gyre and suggests t h a t t h e d i r e c t i o n o f inflow through t h e S t r a i t of G i b r a l t a r p l a y s an important r o l e i n determining t h e s i z e and l o c a t i o n of t h e gyre.
S a t e l l i t e d a t a a l s o r e v e a l s more time varying, smaller s c a l e c i r c u -
l a t i o n p a t t e r n s i n t h e e a s t e r n Alboran Sea. The reduced g r a v i t y model of Hurlburt and Thompson (1980, J. Phys. Oceanogr.
10: 1611-1651) h a s been adapted t o t h e semi-enclosed b a s i n of t h e Alboran Sea. The model domain i s a r e c t a n g l e 600 km east-west by 160 km north-south.
The
S t r a i t of G i b r a l t a r i s modeled by a p o r t i n t h e western boundary and t h e e a s t e r n boundary i s e n t i r e l y open.
When t h e model i s forced by a northeastward inflow
through t h e p o r t i n t h e western boundary, it evolves t o a steady s t a t e which e x h i b i t s a meandering eastward c u r r e n t .
The f i r s t meander of t h i s c u r r e n t forms
t h e northern boundary of a s t r o n g a n t i c y c l o n i c gyre i n t h e western p a r t of t h e basin.
The dimensions and l o c a t i o n o f t h e model gyre a r e c o n s i s t e n t with t h e
p e r s i s t e n t gyre observed t o dominate t h e western Alboran Sea.
A weaker cyclonic
c i r c u l a t i o n i n t h e e a s t e r n Alboran i s a l s o p r e d i c t e d by t h e model.
This model
s o l u t i o n c l o s e l y resembles t h e o b s e r v a t i o n a l d a t a of Lanoix (1974, NATO Tech. Report 6 6 , B r u s s e l s ) .
The s o l u t i o n was obtained without i n c l u d i n g bottom
topography, c o a s t l i n e f e a t u r e s , o r winds which have been suggested a s important f a c t o r s i n determining t h e s i z e and l o c a t i o n of t h e Alboran Gyre.
A preliminary
i n v e s t i g a t i o n using t h e model i n d i c a t e s t h e importance of inflow angle, inflow v o r t i c i t y , and t h e l o c a t i o n of t h e S t r a i t of G i b r a l t a r .
This model does n o t
account f o r t h e v a r i a b i l i t y observed i n t h e c i r c u l a t i o n of t h e e a s t e r n Alboran Sea.
76
1.
INTRODUCTION
The Alboran Sea i s an a t t r a c t i v e semi-enclosed domain f o r t h e study o f hydrodynamic phenomena o f t e n observed i n l a r g e oceans.
These phenomena include
meandering c u r r e n t s , a p e r s i s t e n t g y r e , and t r a n s i e n t eddies.
Of p a r t i c u l a r
i n t e r e s t i s a p e r s i s t e n t and i n t e n s e a n t i c y c l o n i c gyre which dominates t h e c i r c u l a t i o n of t h e western Alboran Sea. p a t t e r n e x i s t s i n t h e e a s t e r n Alboran.
A more complex t i m e v a r y i n g . C i r c u l a t i o n
This paper r e p o r t s t h e preliminary s t a g e s
of an e f f o r t t o model t h e c i r c u l a t i o n of t h e Alboran Sea.
A highly i d e a l i z e d
numerical model has simulated t h e major f e a t u r e s of t h e upper l a y e r c i r c u l a t i o n , p a r t i c u l a r l y t h e a n t i c y c l o n i c gyre. The c i r c u l a t i o n of t h e Alboran Sea i s dependent on both A t l a n t i c and Mediterranean waters.
A t l a n t i c w a t e r flows through t h e nd;row (20 km wide) and
shallow (300 m deep) S t r a i t of G i b r a l t a r i n t o t h e Alboran Sea forming a 150-200 m deep s u r f a c e l a y e r .
(Ovchinnikov, 1966; Lanoix, 1974; Katz, 1972).
Mediterranean
water e n t e r s t h e Alboran a t i t s open e a s t e r n boundary and flows slowly westward i n t h e form of an i n t e r m e d i a t e and lower l a y e r .
I t has been suggested t h a t even
t h e deepest water can e x i t through t h e S t r a i t (Stomme1 e t a l , 1973; Gascard, 1978) 6 3 The l a r g e volume t r a n s p o r t of inflowing A t l a n t i c water, 1 t o 2 x 1 0 m /sec, (Lacombe, 1971; Bethow, 1979; Lacombe, 1982) r e t a i n s i t s
a s a narrow
(30 km wide) j e t with i n i t i a l speeds of 100 cm/sec n e a r t h e S t r a i t (Lacombe,
1961; Peluchon and Donguy, 1962; Grousson and Faroux, 1963; Lanoix, 1974; Cheney, 1977; P e t i t e t a l , 1978; and Wannamaker, 1979).
The j e t e n t e r s t h e b a s i n and
flows n o r t h e a s t t o approximately 4OW, curves southward and then s p l i t s (Fig. 1). P a r t of t h e j e t flows t o t h e west and is i n c o r p o r a t e d i n an a n t i c y c l o n i c g y r e ,
while t h e remainder f l o w s s o u t h e a s t t o Cape Tres Forcas and then along t h e African c o a s t forming t h e southern periphery of a cyclonic c i r c u l a t i o n . S a t e l l i t e i n f r a r e d imagery (Fig. 2 ) i n d i c a t e s v a r i a t i o n s i n t h e shape, l o c a t i o n and i n t e n s i t y of t h e p e r s i s t e n t a n t i c y c l o n i c gyre which dominates t h e western Alboran Sea.
Figure 2a shows t h e gyre occupying t h e m a j o r i t y of t h e
western Alboran b a s i n a s i n Fig. 1.
Figure 2b shows t h e gyre with a smaller
north-south e x t e n t and i n d i c a t e s a j e t through t h e S t r a i t o f G i b r a l t a r which flows almost due east.
Hydrographic d a t a and s a t e l l i t e i n f r a r e d images support
t h e year-round p e r s i s t e n c e of t h e g y r e , although i t s s i z e and l o c a t i o n v a r i e s (Stevenson, 1977; Cheney, 1978; Wannamaker, 1979; Burkov e t a l , 1979; Gallagher e t a l , 1981).
I n t h e e a s t e r n p o r t i o n of t h e Alboran Sea a g e n e r a l p a t t e r n of
a l t e r n a t i n g c y c l o n i c and a n t i c y c l o n i c c i r c u l a t i o n s has been observed (Cheney, 1978; Lanoix, 1974).
S a t e l l i t e imagery shows t h a t , compared t o t h e western
Alboran, t h i s c i r c u l a t i o n p a t t e r n i s f a r more v a r i a b l e and of smaller s c a l e . The purpose o f t h i s p r o j e c t i s t o s i m u l a t e observed c i r c u l a t i o n p a t t e r n s i n t h e Alboran Sea and t o i n v e s t i g a t e t h e i r dynamics.
I n t h i s paper w e r e p o r t
F i g . 1. 1962-
Dynamic topography of the surfaoe r e l a t i v e to 200 dbar for July-August
Overlaid rectangle 1s t h e modei Alboran Sea geometry.
(
~
~ 1974)~
i
~
,
78
Fig. 2 .
NOAA 6 i n f r a r e d s a t e l l i t e imagery view of the S t r a i t of G i b r a l t a r and
Alboran Sea.
Lighter shades i n d i c a t e c o l d e r s u r f a c e temperatures.
1980; b) December 1 4 , 1979.
a ) June 2 5 ,
79 on p r e l i m i n a r y r e s u l t s from t h e s i m p l e s t model capable of s i m u l a t i n g major f e a t u r e s of t h e c i r c u l a t i o n .
This i s a reduced g r a v i t y model i n a semi-enclosed,
I t i s e s s e n t i a l l y a model of t h e f i r s t b a r o c l i n i c mode and
r e c t a n g u l a r domain.
does n o t p e r m i t b a r o c l i n i c i n s t a b i l i t y o r t h e i n c l u s i o n of bottom topography. The model formulation and parameters a r e discussed i n Section 2 .
In Section
3 the model r e s u l t s a r e p r e s e n t e d i n t e r n s of a p i v o t a l experiment and some d e v i a t i o n s from it.
Section 3 . 1 d i s c u s s e s t h e p i v o t a l experiment.
which follow i n v e s t i g a t e t h e i n f l u e n c e s of location,
2.
The subsections
( 3 . 2 ) inflow angle, ( 3 . 3 ) p o r t
( 3 . 4 ) boundary e f f e c t s , and ( 3 . 5 ) inflow v o r t i c i t y .
THE MODEL A n o n l i n e a r reduced g r a v i t y model, developed f o r t h e G u l f of Mexico by
Hurlburt and Thompson (1980), has been adapted f o r t h e Alboran Sea.
The model
e q u a t i o n s a r e solved numerically using an economical semi-implicit scheme.
The
model c o n s i s t s of an a c t i v e upper l a y e r and a lower l a y e r which i s i n f i n i t e l y deep and a t r e s t .
I t i s s t a b l y s t r a t i f i e d and has a f i x e d d e n s i t y c o n s t r a s t
between two immiscible l a y e r s .
The model assumes a h y d r o s t a t i c , Boussinesq
f l u i d i n a r o t a t i n g right-handed coordinate system on a R-plane. i n t e g r a t e d model equations a r e
ah, + v
- +v1
at
= 0
where
+ V
1
-+
= h v
1 1
A
= h (u i
1
1
h
+
vlj)
The v e r t i c a l l y
80 and x and y a r e tangent-plane
C a r t e s i a n c o o r d i n a t e s with x d i r e c t e d eastward
and y northward, u1 and v1 a r e t h e eastward and northward v e l o c i t y components i n t h e upper l a y e r , h i s t h e upper l a y e r t h i c k n e s s , t i s t i m e , g i s t h e a c c e l 1 e r a t i o n due t o g r a v i t y , pi i s t h e d e n s i t y of seawater i n l a y e r i , f o and yo a r e t h e v a l u e s of t h e C o r i o l i s parameter and t h e y-coordinate
-+
boundary, T~
a t t h e southern
-L
i s t h e wind s t r e s s , and T 2 i s t h e i n t e r f a c i a l s t r e s s .
The
remaining parameters a r e defined i n Table 1.
TABLE 1
Model parametexs f o r t h e p i v o t a l experiment
Parameter
Definition
Value
A
eddy v i s c o s i t y
-1 250 m2sec
%
(df/dy) C o r i o l i s parameter
fO
9'
H1 H2 Lx Ax
"Y
x
At "1 i n
a tS
2 x 10-llm-lsec-l -5 -1 8 x 10 s e c
Ay
reduced g r a v i t y due t o s t r a t i f i c a t i o n
. 0 2 m sec-2
undisturbed upper l a y e r depth
200 m
undisturbed lower l a y e r depth
m
h o r i z o n t a l dimensions of t h e model domain
600 km x 160 km
h o r i z o n t a l g r i d spacing f o r each dependent variable
10 km x 5 km
time s t e p
1hr.
inflow v e l o c i t y
100 cm/sec
angle of inflow
21° n o r t h of e a s t
inflow s p i n up time constant
30 days
Figure 1 shows t h e model domain superimposed on a map of t h e Alboran Sea. This domain i s 603 km x 160 km with 10 km x 5 km g r i d r e s o l u t i o n f o r each dependent v a r i a b l e .
Forcing i s due s o l e l y t o p r e s c r i b e d inflow through t h e
western p o r t ( S t r a i t of G i b r a l t a r ) . through an open e a s t e r n boundary.
Inflow i s e x a c t l y compensated by outflow This i s accomplished by allowing normal flow
a t t h e e a s t e r n boundary t o be self-determined and by imposing an i n t e g r a l c o n s t r a i n t on t o t a l mass outflow (Hurlburt and Thompson, 1980).
Except a t t h e
inflow and outflow p o r t s , t h e boundaries a r e r i g i d and a no-slip
condition i s
p r e s c r i b e d on t h e t a n g e n t i a l flow. component i s s e t t o z e r o one-half
Along t h e e a s t e r n boundary t h e t a n g e n t i a l g r i d d i s t a n c e o u t s i d e t h e p h y s i c a l domain.
The model parameters f o r t h e p i v o t a l experiment a r e given i n Table 1. In t h i s experiment t h e western (inflow) p o r t i s centered 102 km from t h e southern boundary and 1 s 1 5 km wide, a width a p p r o p r i a t e f o r t h e S t r a i t of G i b r a l t a r
81 The s p e c i f i c a t i o n o f t h e model f o r c i n g i s accomplished
a t a depth of 100 m. i n e i t h e r of two ways.
1) by p r e s c r i b i n g v e l o c i t y
+
(vlin)
o r 2 ) by p r e s c r i b i n g
+ t r a n s p o r t (V
, ) and allowing t h e model t o determine t h e inflow v e l o c i t i e s . The lin The t o t a l inflow t r a n s p o r t used i n former is used i n t h e p i v o t a l experiment. 6 3 This value i s necessarv t h e model ( 2 . 5 x 10 m / s e c ) i s h i g h e r than observed.
+
-+
t o d r i v e a uniform inflow p r o f i l e f o r v1 o r V1 with speeds of given t h e p o r t width and upper l a y e r depth i n Table 1.
.
-
1 0 0 cm/sec,
The inflow i s spun up
with a time c o n s t a n t of 30 days t o minimize t h e e x c i t a t i o n of high frequency waves.
The angle of inflow w a s v a r i e d based on d i r e c t o b s e r v a t i o n s (Lacombe,
1961) and on i n f e r e n c e s from s a t e l l i t e imagery.
The standard inflow angle was
chosen t o be 21° n o r t h of e a s t based on t h e geometric o r i e n t a t i o n of t h e S t r a i t of G i b r a l t a r .
P o s s i b l y important wind forcir),g (Ovchinnikov e t a l , 1976; Mommsen,
1978) i s neglected t o allow focus on t h e c i r c u l a t i o n d r i v e n by flow through t h e S t r a i t of G i b r a l t a r . S u b s t a n t i a l e f f o r t was made t o assure t h a t unphysical a s p e c t s of t h e model such as t h e g r i d r e s o l u t i o n and t h e t i m e s t e p d i d not s i g n i f i c a n t l y i n f l u e n c e t h e model s o l u t i o n .
The open e a s t e r n boundary c o n d i t i o n was a s p e c i a l concern
and one important t e s t of i t s i n f l u e n c e i s discussed i n Section 3.4. The i n t e g r a l c o n s t r a i n t on t h e t o t a l mass f l u x through t h e e a s t e r n boundary r e s u l t e d i n plane wave r e f l e c t i o n of s u f f i c i e n t amplitude t o pose a s i g n i f i c a n t problem.
The eddy
v i s c o s i t y ( A ) chosen f o r t h e model i s t h e minimum value which p r e v e n t s any v i s i b l e o s c i l l a t i o n i n t h e s o l u t i o n due t o t h i s r e f l e c t i o n .
A n eddy v i s c o s i t y
2% t i m e s s m a l l e r y i e l d e d n e a r l y t h e same s o l u t i o n except f o r some unphysical
oscillations.
A viscous boundary l a y e r using a l i n e a r i n t e r f a c i a l s t r e s s w a s
a l s o a p p l i e d near t h e open e a s t e r n boundary i n an e f f o r t t o damp t h e o s c i l l a t i o n s due t o t h e i n t e g r a l c o n s t r a i n t .
The maximum v a l u e f o r t h e drag c o e f f i c i e n t was
s e c - l a t t h e e a s t e r n boundary.
It decreased e x p o n e n t i a l l y away from t h e
boundary with an e-folding width of 50 km. t h e r e f l e c t i o n from t h e i n t e g r a l c o n s t r a i n t .
This aided only s l i g h t l y i n damping Except f o r t h e viscous boundary
l a y e r , t h e i n t e r f a c i a l s t r e s s w a s zero.
3.
MODEL RESULTS
Over 40 numerical experiments were performed f o r the Alboran Sea.
Some
preliminary r e s u l t s w i l l be p r e s e n t e d i n terms of a p i v o t a l experiment and s e l e c t e d v a r i a t i o n s from it.
M o s t of the numerical s o l u t i o n s evolved t o a
steady s t a t e i n about one year.
3.1
The p i v o t a l experiment The p i v o t a l experiment uses t h e parameters i n Table 1.
Figure 3 shows t h e
steady s t a t e model s o l u t i o n (day 5 0 0 ) i n terms of the pycnocline anomaly ( P A ) .
82 The- P A i s t h e d e v i a t i o n of t h e i n t e r f a c e between t h e upper and lower l a y e r s from i t s i n i t i a l f l a t p o s i t i o n a t 200 m depth. (upper l a y e r t h i c k e r than i n i t i a l l y ) .
Downward d e v i a t i o n s a r e p o s i t i v e
The most s t r i k i n g f e a t u r e s a r e 1) a
meandering c u r r e n t which t r a v e r s e s t h e model domain f s o m west t o e a s t , 2 ) a s t r o n g a n t i c y c l o n i c gyre i n t h e western 2 4 0 k m of t h e b a s i n , and 3 ) a weak cyclonic c i r c u l a t i o n t o t h e eas t .
This p a t t e r n i s very s i m i l a r t o t h w tempera-
t u r e f i e l d shown i n a s a t e l l i t e image (Fig. 2a) and t o Lanoix's dynamic topography (Fig. 1).
Fig. 3 .
PA (pynocline anomaly) of t h e p i v o t a l case s o l u t i o n a t day 500.
Inflow
angle i s 21° n o r t h of e a s t .
S o l i d contours a r e p o s i t i v e (downward) d e v i a t i o n s .
Dashed contours a r e negative
(upward) d e v i a t i o n s .
Contour i n t e r v a l i s 1 0 m.
I n r o t a t i n g tank experiment, Whitehead and M i l l e r (1979) attempted t o simul a t e t h e Alboran Gyre using a d e n s i t y d r i v e n c u r r e n t .
They suggest t h a t t h e
dimensions of t h e gyre depend on a c o a s t l i n e f e a t u r e , Cape Tres Forcas.
I t has
a l s o been suggested by P o r t e r (1976) t h a t t h e dimensions of t h e gyre a r e d i r e c t l y r e l a t e d t o t h e bottom topography with Alboran I s l a n d a c t i n g a s t h e e a s t e r n boundary of t h e gyre.
Y e t t h e reduced g r a v i t y model i s a b l e t o simulate an
Alboran Gyre with r e a l i s t i c dimensions, while i n c l u d i n g n e i t h e r c o a s t l i n e i r r e g u l a r i t i e s nor bottom topography.
The model gyre i s a l s o a p e r s i s t e n t
r a t h e r than a t r a n s i e n t f e a t u r e of t h e flow, again i n accord with o b s e r v a t i o n s noted e a r l i e r .
3.2
The e f f e c t of inflow angle The c i r c u l a t i o n p a t t e r n i n t h e p i v o t a l experiment (Fig. 3 ) and s a t e l l i t e
imagery (Fig. 2 ) suggest t h a t t h e inflow angle may e x e r t an important i n f l u e n c e on t h e meandering c u r r e n t and t h e Alboran Gyre. were c a r r i e d o u t varying t h e i n f l o w angle.
Thus, a number of experiments
One experiment used t h e standard
parameters from Table 1 except t h a t t h e inflow e n t e r e d t h e model domain normal t o t h e western boundary.
In t h e s t e a d y s t a t e s o l u t i o n f o r t h i s case (Fig. 4),
t h e j e t e n t e r s t h e b a s i n flowing due e a s t , b u t q u i c k l y v e e r s southward.
The
83 a n t i c y c l o n i c gyre i n t h e western p a r t of t h e b a s i n i s r e s t r i c t e d t o a much s m a l l e r north-south e x t e n t t h a n i n t h e s t a n d a r d case.
The c y c l o n i c c i r c u l a t i o n
t o t h e e a s t i s i n t e n s i f i e d and a new a n t i c y c l o n i c flow appears i n t h e e a s t e r n 200 km.
This c i r c u l a t i o n p a t t e r n i s similar t o t h a t of t h e s e a s u r f a c e tempera-
t u r e seen i n t h e s a t e l l i t e i n f r a r e d imagery of Fig. 2b.
,.
600
IKMI Fig. 4.
PA of t h e p i v o t a l case a t day 500 but with due e a s t inflow.
Contour
i n t e r v a l i s 10 m.
3.3
Port location The n e x t s e t of experiments w a s designed t o observe t h e importance of t h e
north-south l o c a t i o n of t h e inflow p o r t .
I f t h e S t r a i t of G i b r a l t a r was l o c a t e d
south of t h e b a s i n c e n t e r , how would t h e c i r c u l a t i o n p a t t e r n be a f f e c t e d ?
Two
such experiments used t h e s t a n d a r d parameters of Table 1 except t h a t t h e p o r t was c e n t e r e d 7 km s o u t h o f t h e c e n t e r of t h e western boundary and t h e inflow angles were those of Fig. 3 ( s t a n d a r d 21° n o r t h of e a s t ) and Fig. 4 steady s t a t e s o l u t i o n s a r e p r e s e n t e d i n Fig. 5.
(OO).
The
Figure 5a, with t h e angled
inflow of the s t a n d a r d c a s e , shows 1 ) an a n t i c y c l o n i c gyre s m a l l e r than t h a t of the s t a n d a r d case i n t h e western p a r t of t h e b a s i n , 2) a s t r o n g cyclonic c i r c u l a t i o n i n t h e c e n t r a l p a r t , and 3 ) a weak a n t i c y c l o n i c c i r c u l a t i o n i n t h e e a s t e r n part.
When the inflow e n t e r s flowing due e a s t (Fig. 5b) t h e western gyre i s
even s m a l l e r than i n Fig. 5a and t h e two gyres t o t h e e a s t a r e s l i g h t l y s t r o n g e r . Clearly, t h e entrance of t h e A t l a n t i c water i n t h e northern h a l f of t h e Alboran Sea f a c i l i t a t e s t h e development of an Alboran Gyre of l a r g e north-south e x t e n t .
3.4
Boundary e f f e c t s The i n f l u e n c e of t h e domain s i z e and t h e open e a s t e r n boundary were a l s o
investigated.
A s described i n Section 2 , t h e p i v o t a l experiment i n c l u d e s a
viscous boundary l a y e r near t h e open e a s t e r n boundary.
One t e s t compared t h e
p i v o t a l experiment w i t h t h i s boundary l a y e r (Fig. 3 ) t o an i d e n t i c a l experiment without it ( n o t shown).
Except i n t h e region of t h e viscous boundary l a y e r , t h e
results were a l m o s t identical.
In t h e experiment without t h e boundary l a y e r ,
a4
600
(KMI
/
[KMI
600
P A of t h e p i v o t a l case a t day 500 b u t w i t h t h e p o r t c e n t e r e d 7 km south
Fig. 5.
o f t h e c e n t e r of t h e w e s t e r n boundary. b ) due e a s t i n f l o w .
a ) i n f l o w a n g l e d 21° n o r t h o f e a s t :
Contour i n t e r v a l i s 1 0 m.
t h e c u r r e n t m a i n t a i n e d i t s c r o s s - s e c t i o n a l s t r u c t u r e as it approached and p a s s e d t h r o u g h t h e open e a s t e r n boundary.
When it w a s i n c l u d e d , t h e PA c o n t o u r s s p r e a d
o u t i n t h e v i s c o u s boundary l a y e r and t h e j e t s t r u c t u r e d i s i n t e g r a t e d t o a more u n i f o r m flow ( s e e F i g .
3).
Numerical e x p e r i m e n t s were a l s o performed t o d e t e r m i n e if t h e open e a s t e r n boundary was s e r i o u s l y d i s t o r t i n g t h e s o l u t i o n .
critical test.
F i g . 6 shows t h e r e s u l t s of a
I t compares two s o l u t i o n s which d i f f e r o n l y i n t h e east-west
e x t e n t o f t h e model domain. t h e open e a s t e r n boundary.
I n e a c h c a s e t h e r e i s a v i s c o u s boundary l a y e r n e a r I n t h i s t e s t , c h a n g i n g t h e l o c a t i o n of t h e open
e a s t e r n boundary c a u s e d o n l y minor changes i n t h e s o l u t i o n i n t h e w e s t e r n 4 0 0 km
05 t h e model domain. i n Fig.
The e a s t e r n 100 km i n F i g . 6b d i f f e r s from t h e same r e g i o n
6 a , d u e f n o s t l y t o t h e v i s c o u s boundary l a y e r i n t h e v i c i n i t y of t h e open
boundary. The e f f e c t o f t h e n o r t h - s o u t h t h e y-dimension
e x t e n t of t h e b a s i n w a s examined by d o u b l i n g
of t h e s t a n d a r d e x p e r i m e n t ( F i g . 3 ) and k e e p i n g t h e p o r t l o c a t i o n
s l i g h t l y n o r t h of t h e b a s i n cen ter.
F i g u r e 7 shows t h e f l o w e n t e r i n g t h e b a s i n
85
800
0 Fig. 6.
(HM I
P A of t h e p i v o t a l case a t day 1 9 0 b u t with d i f f e r e n t dimensions
x 800 k m b a s i n ; b ) 180 km x 500 k m basin.
1:2.5.
500
Contour i n t e r v a l i s 1 0 m.
a) 180 km
Scale f a c t o r f o r t h e s e f i g u r e s x:y i s
86 a t t h e s t a n d a r d a n g l e o f 21° and t h e n c u r v i n g southward i n a manner s i m i l a r t o Fig.
5a.
Even t h o u g h t h e n o r t h - s o u t h
e x t e n t of t h e b a s i n h a s been d o u b l e d , t h e
n o r t h e r n and s o u t h e r n b o u n d a r i e s o f t h e domain s t i l l l i m i t t h e n o r t h - s o u t h of t h e c u r r e n t meanders. meanders i n F i g .
D e s p i t e a l a r g e i n c r e a s e i n t h e a m p l i t u d e of t h e
7 , t h e wavelengths i n Fig.
A s t r i k i n g f e a t u r e i n Fig.
meanders.
scale
5 a and F i g . 7 are almost t h e same.
7 i s t h e downstream a m p l i f i c a t i o n of t h e c u r r e n t
Less d r a m a t i c examples o f t h i s a p p e a r i n some o f t h e o t h e r f i g u r e s .
I t s h o u l d b e n o t e d t h a t t h i s and a l l t h e o t h e r s o l u t i o n s are s t e a d y and n o t
unstable.
- 0 F i g . 7.
600 P A a t day 600 o f an e x p e r i m e n t where t h e n o r t h - s o u t h
dimension of t h e
b a s i n h a s been e x t e n d e d t o 320 km, c o n t o u r i n t e r v a l i s 1 0 m. 3.5
Shear a t inflow I n a l l t h e e x p e r i m e n t s d i s c u s s e d s o f a r , t h e i n f l o w h a s been p r e s c r i b e d + ( ~ 1 ) .However, i n t h i s model t h e i n f l o w may a l s o be
as a velocity profile
p r e s c r i b e d i n terms of t r a n s p o r t
+
(V1).
I n t h e l a t t e r case, t h e model p a r t i a l l y
c o n t r o l s t h e i n f l o w v e l o c i t y p r o f i l e t h r o u g h t h e g e o s t r o p h i c tilt i n t h e i n t e r f a c e . Fig.
8 shows a s t e a d y s t a t e s o l u t i o n f o r a n e x p e r i m e n t s i m i l a r t o t h a t shown i n
+
-+
F i g . 5 b , e x c e p t t h a t V1 i s p r e s c r i b e d i n s t e a d of vl.
i s eastward.
In Fig.
I n b o t h cases t h e i n f l o w
8 t h e prescribed inflow t r a n s p o r t i s 2.5 x
lo6
m3/sec.
T h i s y i e l d s i n f l o w v e l o c i t i e s s i m i l a r t o F i g . 5b. b u t t h e g e o s t r o p h i c tilt i n t h e i n t e r f a c e i n t r o d u c e s a s h e a r ( w a y ) o f 1.54 x
sec
-1
a t inflow.
Without
t h e s h e a r ( F i g . 5b) t h e c u r r e n t t u r n s southward a f t e r i n f l o w , b u t w i t h t h e shear (Fig. 8) t h e c u r r e n t t u r n s northward.
I n a d d i t i o n , F i g . 8 shows a l a r g e r Alboran
Gyre which i s f u r t h e r t o t h e e a s t and a small cyclonic gyre i n t h e northwest corner.
The p o s s i b i l i t y t h a t v o r t i c i t y a t inflow t u r n s t h e incoming A t l a n t i c
water northward has been suggested by Nof (1978).
Fig. 8.
P A a t day 500 of a case i d e n t i c a l t o t h e case represented i n Fig. 5b
except t h a t t h e model i s forced w i t h a p r e s c r i b e d t r a n s p o r t .
4.
Contour i n t e r v a l i s 10
SUMMARY AND FUTURE WORK
A nonlinear; semi-implicit,
reduced g r a v i t y numerical model (Hurlburt and
Thompson, 1980) has been adapted t o study t h e c i r c u l a t i o n i n t h e Alboran Sea. Both hydrographic d a t a and s a t e l l i t e imagery i n d i c a t e t h e e x i s t e n c e of a permanent a n t i c y c l o n i c qyre i n t h e western Alboran.
This c i r c u l a t i o n appears t o be
driven by a j e t of A t l a n t i c w a t e r which e n t e r s through t h e S t r a i t of G i b r a l t a r . In t h e model t h e S t r a i t w a s r e p r e s e n t e d by a p o r t i n t h e western boundary and the e a s t e r n boundary w a s e n t i r e l y open.
Model r e s u l t s using an i d e a l i z e d rectan-
g u l a r geometry (600 km x 160 km), no topography and a northeastward inflow through
the S t r a i t of G i b r a l t a r show an a n t i c y c l o n i c qyre s i m i l a r i n s i z e , shape and l o c a t i o n t o t h e Alboran Gyre (Fig. 3 ) .
These r e s u l t s c l o s e l y resemble t h e dynamic
height contours o f Lanoix (Fig. 1) and suggest t h a t topography and p a r t i c u l a r c o a s t l i n e f e a t u r e s a r e n o t necessary t o c r e a t e a gyre with r e a l i s t i c dimensions and l o c a t i o n .
However, model r e s u l t s f o r t h e e a s t e r n Alboran show a s e r i e s of
cyclonic and a n t i c y c l o n i c c i r c u l a t i o n s of much l a r g e r s c a l e and s m a l l e r v a r i a b i l i t y than observed.
Additional numerical experiments showed t h e importance
of t h e inflow angle and inflow v o r t i c i t y i n determining t h e s i z e and l o c a t i o n of the Alboran Gyre. This paper has p r e s e n t e d preliminary r e s u l t s of an attempt t o model t h e Alboran Sea.
Future work w i l l i n c l u d e an i n v e s t i g a t i o n of the model dynamics,
more r e a l i s t i c models, and i n t e r a c t i o n with a f i e l d experiment.
The meandering
c u r r e n t observed i n t h e model s o l u t i o n s might be considered a standing Rossby wave with a highly d i s t o r t e d conservation of a b s o l u t e v o r t i c i t y t r a j e c t o r y (e.9. see H a l t i n e r and Martin, 1957).
The flow t r a j e c t o r y i s s t r o n g l y influenced by
t h e proximity of t h e northern and southern boundaries, t h e l a r g e amplitude v a r i a t i o n s i n t h e upper l a y e r depth, c r o s s - i s o b a r i c i n e r t i a l e f f e c t s , and p o s s i b l y by f r i c t i o n a l e f f e c t s .
Planned model refinements i n c l u d e more r e a l i s t i c
c o a s t l i n e geometry, an a d d i t i o n a l a c t i v e l a y e r , bottom topography, and winds. The i n f l u e n c e of each o f t h e s e f e a t u r e s on t h e Alboran Gyre w i l l be t e s t e d , b u t they w i l l a l s o be used i n an attempt t o o b t a i n a more r e a l i s t i c simulation of t h e c i r c u l a t i o n i n t h e e a s t e r n Alboran Sea.
We have a l r e a d y begun t o use t h e
model r e s u l t s i n t h e design of a NORDA (Naval Ocean Research and Development A c t i v i t y ) f i e l d experiment.
The intended r e s u l t i s a cooperative i n t e r a c t i o n
i n which t h e models a i d i n t h e i n t e r p r e t a t i o n of t h e observations and t h e o b s e r v a t i o n s l e a d t o more r e a l i s t i c model s i m u l a t i o n s .
ACKNOWLEDGEMENTS W e wish t o thank D r . J. Dana Thompson, George Heburn, and Thomas Kinder
f o r t h e i r h e l p f u l comments.
The f a s t , v e c t o r i z e d Helmholtz s o l v e r f o r t h e semi-
i m p l i c i t model was provided by D r . Daniel Moore of Imperial College, London. Some of t h e graphics software w a s provided by t h e National Center f o r Atmospheric Research which i s sponsored by t h e National Science Foundation.
Computations
w e r e performed on t h e two-pipeline Texas Instruments Advanced S c i e n t i f i c Computer a t t h e Naval Research Laboratory i n Washington, D.C.
P a r t i a l funding was provided
by t h e ONR Coastal Science Program c o n t r a c t N00014-81-AB-11-12.
REFERENCES Bethoux, J. P . , 1979. Budgets of t h e Mediterranean Sea. Their dependence on Oceanol. t h e l o c a l climate and on c h a r a c t e r i s t i c s of t h e A t l a n t i c waters. Acta. 2 , 2 : 137-163. Burkov, V. A . , Krivosheya, V. G., Ovchinnikov, I. M. and Savin, M . T . , 1979. Eddies i n t h e c u r r e n t system of t h e western Mediterranean Basin. Oceanology, 19: 9-13. Cheney, R. E . , 1977. Recent observations o f t h e Alboran Sea f r o n t . NAVOCEANO Technical Note 370-73-77, 24 pp. Cheney, R. E . , 1978. Recent o b s e r v a t i o n s of t h e Alboran Sea f r o n t a l system. J. Geophys. Res., 83: 4593-4597. Gallagher, J. J . , Fecher, M. and Goman, J . , 1981. P r o j e c t HUELVA oceanographic/ a c o u s t i c i n v e s t i g a t i o n of t h e western Alboran Sea. NUSC Technical Report 6023, 106 pp. Gascard, J. C . , 1978. Mediterranean deep water formation. Baroclinic i n s t a b i l i t y and oceanic e d d i e s . Oceanologica Acta 1 , 3 : 315-330. Grousson, R. and Faroux, J. 1963. Measure de courants de s u r f a c e en Mer d ' n l b o r a n . Cah. Oceanogr., 1 5 : 716-721. H a l t i n e r , G. J . and Martin, F. L., 1957. Dynamical and Physical Meteorology. McGraw-Hill, pp. 470. H u r l b u r t , H. E. and Thompson, J. D . , 1980. A numerical study of h w p Current J. Phys. Oceanogr., 10: 1611-1651. i n t r u s i o n s and eddy shedding. Katz, E . J . , 1972. The Levantine i n t e r m e d i a t e water between t h e S t r a i t of S i c i l y and t h e S t r a i t of G i b r a l t a r . Deep Sea Res., 19: 507-520. Lacombe, H . , 1961. Contribution A L'Etude du Regime du D e t r o i t de G i b r a l t a r . Cah. Oceanogr., XIII: 74-107.
89 Lacombe, H . , 1971. Le D e t r o i t de G i b r a l t a r . Note e t Memoires de Service Geologique du Maroc., No. 2 2 2 b i s , 111-146. Lacombe, H . , 1982. Regime of t h e S t r a i t of G i b r a l t a r and of i t s e a s t and west approaches. I n : J. C. J. Nihoul ( E d i t o r ) , Hydrodynamics of semi-enclosed s e a s . E l s e v i e r , Amsterdam, pp. 13-73. Lanoix, F . , 1974. P r o j e c t Alboran Etude Hydrologique Dynamique de l a Mer d'Alboran. Tech. r e p o r t 66, N. A t l . Treaty Org. B r u s s e l s , pp. 39. Momsen, D. B . , J r . , 1978. The e f f e c t of wind on s e a s u r f a c e temperature g r a d i e n t s i n t h e S t r a i t o f G i b r a l t a r and Alboran Sea. R e p d t from F l e e t Weather C e n t r a l , Rota, Spain, 18 pp. Nof, D . , 1978. On geostrophic adjustment i n Sea s t r a i t s and e s t u a r i e s : theory J. Phys. Oceanogr., and l a b o r a t o r y experiments. P a r t 11: Two-layer system. 8 : 861-872. Ovchinnikov, I. M . , 1966. C i r c u l a t i o n i n t h e s u r f a c e and i n t e r m e d i a t e l a y e r s of t h e Mediterranean. Oceanology, 6: 48-59. Ovchinnikov, I . M.. Krivosheya, V. G. and Maskalenko, L. V . , 1976. Anomalous f e a t u r e s of t h e water c i r c u l a t i o n of tl?e Alboran Sea during t h e summer of 1962. Oceanology, 15: 31-35. peluchon, G. and Donguy, J. R . , 1962. Travaux Oceanographiques d "1'OrignY" dans l e D e t r o i t de G i b r a l t a r . Compaigne i n t e r n a t i o n a l e - 15 mpi, 15 Juin 1961. Zemi p a r t i e . Hydrologie en Mer d'Alboran. Cah. Oceanogr., 1 4 : 573-578. P e t i t , M., Klaus, V. G e l c i , R., Fusey, F . , Thery, J. J. and Bouly, P . , 1978. Etude d'un t o u r b i l l o n oceanique d ' e c h e l l e moyenne en mer d'Alboran p a r C.R. Acad. Sci. emploi c o n j o i n t techniques s p a t i a l e s e t oceanographiques. 287: 215-218. Independent P o r t e r , D. L . , 1976. The a n t i c y c l o n i c gyre of t h e Alboran Sea. r e s e a r c h r e p o r t from M.1.T.-WHO1 j o i n t program, Woods Hole, M a , pp. 29. Stevenson, R. W . , 1977. Huelva Front and Malaga, Spain eddy chains a s defined by s a t e l l i t e and oceanographic d a t a . Deut. Hydrogr. A. 30, 2 : 51-53. Stommel, H . , Bryder, H. and Magelsdorf, P . , 1973. Does some of t h e Mediterranean outflow come from g r e a t depth? Pure and Appl. Geophysics. 105: 879-889. Ship s a t e l l i t e and h i s t o r i c a l data. Wannamaker, B . , 1979. The Alboran Sea G y r e : SACLANT ASW Research Centre Report SR-30, La Spezia, I t a l y , 27 pp. Whitehead, J . A. and M i l l e r , A. R., 1979. Laboratory simulation of t h e gyre i n t h e Alboran Sea. J. Geophys. Res. 84: 3733-3742.
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91
SURFACE TEMPERATURE FRONTS I N THE MEDITERRANEAN SEA FROM INFRARED S A T E L L I T E IMAGERY,
Michele PHILIPPE, LoYc HARANG.
1
-
.J
INTRODUCTION
I n t h e M e d i t e r r a n e a n S e a , , . t h e r m a l f r o n t s which o u t c r o p a t t h e s e a s u r f a c e c a n be e a s i l y observed u s i n g r a d i o m e t r i c s a t e l l i t e measurements i n t h e i n f r a r e d wavelength. Up t o now, e s p e c i a l l y t h e N a v i e s have been i n t e r e s t e d i n them, b e c a u s e of t h e p o s s i b l e i m p l i c a t i o n s o f s u c h f r o n t s i n t h e propag a t i o n o f s u b m a r i n e a c o u s t i c waves. Navy S t u d i e s a b o u t M e d i t e r r a n e a n f r o n t s had been a c h i e v e d by t h e U S Naval Oceanographic O f f i c e (Cheney, 19771, (Cheney, 1978), and by t h e SACLANT ASW R e s e a r c h C e n t e r ( B r i s c o e e t a l . , 1974), ( J o h a n n e s s e n and S m a l l e n b u r g e r , 1977), (Wannamaker, 1979) and by t h e U S Naval Underwater System C e n t e r ( G a l l a g h e r e t a l . , 1981)
.
I n F r a n c e , t h e m o n i t o r i n g o f f r o n t s i n t h e M e d i t e r r a n e a n Sea h a s been a c h i e v e d s i n c e 1978 a t t h e C e n t r e d e M e t 6 o r o l o g i e S p a t i a l e (C.M.S.) w i t h t h e p a r t i c i p a t i o n of F r e n c h Navy m e t e o r o l o g i s t s . The d a t a come from t h e p o l a r o r b i t i n g s a t e l l i t e s (TIROS N and NOAA 6), o p e r a t e d by t h e N a t i o n a l Oceanic and Atmospheric A d m i n i s t r a t i o n (U.S.A.)
and r e c e i v e d a t t h e C.M.S.
S e a s o n a l c h a n g e s o f s u r f a c e f r o n t s w e r e d e r i v e d and d i s c u s s e d from s a t e l l i t e d a t a c o l l e c t e d o v e r one y e a r ( A p r i l 1979-March 1980). These c h a n g e s w e r e i n f e r r e d from c h a r t s o f f r o n t s , drawn f o r e a c h month o f t h i s p e r i o d . These c h a r t s d i s p l a y t h e major f r o n t s o b s e r ved o v e r e a c h month and t h e o c e a n i c f e a t u r e s a s s o c i a t e d w i t h them : c u r r e n t s , e d d i e s , c o n v e r g e n c e and d i v e r g e n c e a r e a s , u p w e l l i n g s . A few c h a r a c t e r i s t i c s o f t h e i n t e r a n n u a l f r o n t v a r i a b i l i t y were also o b t a i n e d by comparing t h e c o n t o u r s o f t h e s u r f a c e f r o n t s f o r t h e same months o f two c o n s e c u t i v e y e a r s ( A p r i l 1979 t o March 1981).
2
-
DATA
2 . 1 DATA PROCESSING
Data a r e r e c o r d e d by AVHRR (Advanced Very High R e s o l u t i o n Radiometer) i n t h e 10.5 t o 11.5 pm w a v e l e n g t h r a n g e . Data from
92
b o t h TIROS N and NOAA 6 s a t e l l i t e s w e r e u s e d , when a v a i l a b l e . The AVHRR s c a n n e r h a s a s p a t i a l r e s o l u t i o n of
1.1 km a t t h e s a t e l l i t e
s u b p o i n t and a t e m p e r a t u r e s e n s i t i v i t y of l e s s t h a n 0.2'X
a t 300'K.
Raw d a t a a r e p r o c e s s e d t o a l l o w t h e optimum d e t e c t i o n of o c e a n i c t e m p e r a t u r e f r o n t s and t h e r e s u l t s a r e s t o r e d on n e g a t i v e f i l m s . T h i s computing p r o c e s s l e a d s t o a d j u s t t h e a v a i l a b l e d i s c r e t e s h a d e s of g r e y w i t h i n t h e r a n g e of s e a t e m p e r a t u r e s . The p r i n c i p l e of t h e
enhancement p r o c e s s i n g i s g i v e n i n f i g u r e 1. Warm w a t e r s a r e r e p r e s e n t e d u s i n g t h e d a r k e r t o n e s of g r e y and c o l d e r w a t e r s u s i n g l i g t h e r ones.
I
G
I
R
I
r----1
b
Tmin
TI T2
13
TEMPERATURES
T ma:
F i g . 1 . a C o n t r a s t enhancement c u r v e s . Example w i t h 8 s h a d e s of grey ( l = w h i t e c o l o r , 8=black c o l o r ) . ---- = w i t h o u t c o n t r a s t enhancement see F i g . l b . = w i t h c o n t r a s t enhancement. Curve b e t w e e n T3 and T 2 i s u s e d f o r s e a s u r f a c e t e m p e r a t u r e s and c u r v e between T2 and T i f o r c o l d e s t w a t e r s and some low l e v e l c l o u d s - see F i g . l c .
-
-
However, e s p e c i a l l y i n summer and autumn, when t h e p i c t u r e s show v e r y high temperature c o n t r a s t s , t h e g r e y s c a l e (16 shades each c o v e r i n g a t e m p e r a t u r e i n t e r v a l of 0.5'C)
i s n o t wide enough to
c o v e r t h e whole t e m p e r a t u r e r a n g e of t h e s e a s u r f a c e . Then
tempe-
r a t u r e g r a d i e n t s i n s i d e t h e c o l d e s t water m a s s e s a r e d i s p l a y e d
93
F i g . 1 b TIROS N image o f t h e L i g u r i a n s e a ( S e p t e m b e r , 7 t h , 1 9 8 0 ) v i s u a l i z e d w i t h o u t c o n t r a s t enhancement. F i g . 1c Same s c e n e a s i n f i g u r e lb b u t v i s u a l i z e d w i t h c o n t r a s t enhancement. A s i n a l l t h e images p r e s e n t e d below 1 6 s h a d e s of g r e y a r e u s e d . The c e n t e r of t h e L i g u r i a n d i v e r g e n c e ( c o l d w a t e r s ) i s r e p r e s e n t e d i n b l a c k which i s t h e f i r s t s h a d e of t h e second c u r v e of enhancement. u s i n g t h e g r e y s c a l e f o r a s e c o n d time ( a g a i n from b l a c k t o w h i t e t o n e s ) . Low l e v e l clouds are also displayed using t h i s second s c a l e d u e t o t h e i r t e m p e r a t u r e which i s v e r y c l o s e t o t h e t e m p e r a t u r e of t h e c o l d e s t w a t e r s (see F i g .
l c ) . The i m a g e s p r e s e n t e d i n t h i s t e x t
were r e a l i z e d u s i n g a g r e y s c a l e of 1 6 s h a d e s , e a c h s h a d e c o v e r i n g a t e m p e r a t u r e i n t e r v a l of 0 . 5 O C . From t h e a n a l y s i s of n e g a t i v e f i l m s , u s i n g a d e n s i t o m e t e r , t e m p e r a t u r e g r a d i e n t s b e t w e e n a n y c o u p l e of s e a p o i n t s c a n b e e v a l u a t e d , a t l e a s t i n a f i r s t o r d e r a p p r o x i m a t i o n , s i n c e atmosphe-
r i c absorption e f f e c t s a r e neglected. 2 . 2 VOLUME O F DATA
The r a d i o m e t e r s w a t h s o b t a i n e d f o r t w o c o n s e c u t i v e s a t e l l i t e p a s s e s a r e r e p r e s e n t e d i n f i g u r e 2 . Examining t h i s f i g u r e shows t h a t two o r t h r e e c o n s e c u t i v e p a s s e s ( d e p e n d i n g on t h e i r a s c e n d i n g n o d e s ) a r e n e c e s s a r y f o r t h e t o t a l s u r v e y of t h e M e d i t e r r a n e a n Sea, from West t o E a s t . Each d a y t h e b e s t o r b i t s w i t h r e g a r d t o t h e
94
F i g . 2 AVHRR swaths o b t a i n e d a f t e r two c o n s e c u t i v e p a s s e s of a TIROS N s a t e l l i t e o v e r t h e M e d i t e r r a n e a n S e a . c l o u d c o v e r o v e r t h e s e a , a r e s e l e c t e d and p r o c e s s e d . From A p r i l 1 9 7 9 t o March 1 9 8 1 , more t h a n 1 2 0 0 images w e r e produced. F i g u r e 3
shows t h e monthly d i s t r i b u t i o n of t h e images.
I n a given r e s t r i c t e d
a r e a l o c a t e d between t h e Alboran Sea and t h e I o n i a n S e a , a c l o u d f r e e s c e n e c a n be o b t a i n e d on a v e r a g e e v e r y 3 d a y s , on a n a n n u a l b a s i s . For t h e most e a s t e r n a r e a s t h e amount of a v a i l a b l e d a t a d e c r e a s e s b e c a u s e t h e s e a r e a s a r e l o c a t e d n e a r o r o u t s i d e t h e TIROS N a c q u i s i t i o n c i r c l e a t Lannion
(see Fig. 4 ) .
95
"1
60
1979
A
M
J
J
A S 1980
1980
O
N
D
J
F M 1981
F i g . 3 Monthly d i s t r i b u t i o n of t h e r m a l images of t h e M e d i t e r r a n e a n Sea from April 1 9 7 9 to March 1 9 8 1 .
96
F i g . 4 . TIROS N a c q u i s i t i o n c i r c l e a t C.M.S. e l e v a t i o n : --- 5' e l e v a t i o n .
__ 0'
2 . 3 METHOD OF FRONT ANALYSIS
The f o l l o w i n g d e f i n i t i o n o f f r o n t s was u s e d : a s u r f a c e temperat u r e f r o n t o c c u r s i n a r e a s where t h a n 1'C
g r a d i e n t s a r e equal t o o r g r e a t e r
w i t h i n a d i s t a n c e of a b o u t 5km. T h i s i s a r a t h e r l i r n i t a t i v e
d e f i n i t i o n i n view o f t h e v a l u e s g i v e n by o t h e r a u t h o r s ( J o h a n n e s s e n 1 9 7 5 ) . But t h e aim o f t h e s t u d y c o n c e r n i n g t h e whole M e d i t e r r a n e a n
Sea i s o n l y t o d e t e c t and m o n i t o r t h e main f r o n t s . F i g u r e 5 shows a t h e r m a l image of t h e L i g u r o - P r o v e n q a l b a s i n (see f i g u r e 8 f o r g e o g r a p h i c a l l o c a t i o n s ) . On t h i s image, t h e a r r o w s p o i n t o u t t h e f r o n t s d e t e c t e d a c c o r d i n g t o t h e above d e f i n i t i o n . The images a r e n o t g e o g r a p h i c a l l y c o r r e c t e d . The l o c a t i o n s of f r o n t s a r e r e t r i e v e d u s i n g 0.5'
x O.S'.latitude-longitude
grids.
97
F i g . 5.TIROS N image of t h e L i g u r o - P r o v e n q a l b a s i n . The a r r o w s i n d i c a t e t h e f r o n t s , according t o t h e d e f i n i t i o n given i n section 2 . 3 : g r a d i e n t s > loC/5km. T h e s e g r i d s a r e computed from t h e a v e r a g e o r b i t a l p a r a m e t e r s o f t h e s a t e l l i t e s . The a c c u r a c y of t h e l o c a t i o n r e t r i e v a l s r e a c h e s about 3 n a u t i c a l m i l e s near t h e s a t e l l i t e subtrack.
3
-
SEASONAL CHANGES OF FRONTS To s t u d y t h e s e a s o n a l c h a n g e s o f f r o n t s , t h e r e s u l t s of t h e
a n a l y s e s o f a l l t h e i m a g e s p r o d u c e d , b e t w e e n A p r i l 1979 and March
1980, w e r e u s e d t o d r a w m o n t h l y c h a r t s of f r o n t s . On s u c h c h a r t s (see F i g . 7, 12, 16 and 21) t h e g e n e r a l c o n t o u r s of a r e a s where f r o n t s w e r e d e t e c t e d d u r i n g t h e month a r e f i l l e d i n b l a c k . O t h e r i n d i c a t i o n s a r e a l s o g i v e n on t h e c h a r t s : t h e maximum g r a d i e n t m e a s u r e d d u r i n g t h e month i n e a c h f r o n t a l a r e a , t h e o c e a n i c f e a t u r e s associated with f r o n t s (divergences, convergences, upwellings). S i g n i f i c a n t a r e a s of c o l d o r w a r m w a t e r s a r e a l s o i n d i c a t e d . The a r r o w s g i v e a n i d e a of t h e assumed s u r f a c e c u r r e n t s n e a r f r o n t a l a r e a s . B e c a u s e no i n s i t u s i m u l t a n e o u s c u r r e n t measurements w e r e made, t h e s e a r r o w s m u s t o n l y b e c o n s i d e r e d a s i n d i c a t i o n s . F r o n t s i n t h e M e d i t e r r a n e a n Sea a r e l i n k e d u p w i t h s u r f a c e water c i r c u l a t i o n . Figure 6 g i v e s a surface c u r r e n t c h a r t calculated b y O v c h i n n i k o v (1966) u s i n g t h e g e o s t r o p h i c method. The main
98
F i g . 6 . Winter c h a r t of g e o s t r o p h i c s u r f a c e c u r r e n t (Ovchinnikov) xxxx d i v e r g e n c e l i n e : O o o 0 c o n v e r g e n c e l i n e ; 1 : c y c l o n i c c i r c u l a t i o n of t h e Liguro-Provenqal b a s i n : 2 : A f r i c a n c u r r e n t : 3 : Divergence of t h e s t r a i t s of B o n i f a c i o : 4 : A n t i c y c l o n i c c i r c u l a t i o n of t h e S y r t a g u l f : 5 : C y c l o n i c c i r c u l a t i o n of t h e A d r i a t i c Sea ; 6 : D i v e r g e n c e s o u t h w e s t of C r e t a ; 7 : Divergence s o u t h e a s t of Rhoda : 8 : C y c l o n i c c i r c u l a t i o n of t h e Aegean S e a . M e d i t e r r a n e a n s u r f a c e c u r r e n t i s t h e A f r i c a n c u r r e n t which r u n s a l o n g t h e A f r i c a n c o a s t and c a r r i e s " A t l a n t i c " waters from t h e
s t r a i t s of G i b r a l t a r t o t h e L e v a n t i n b a s i n . On t h e North of t h e African c u r r e n t develop l a r g e cyclonic c i r c u l a t i o n s . I n the c h a r t of f i g u r e 6 , t h e s e c y c l o n i c c i r c u l a t i o n s e x i s t i n a l l t h e b a s i n s l o c a t e d on t h e North of t h e A f r i c a n c u r r e n t . On t h e c o n t r a r y , on t h e S o u t h of t h e A f r i c a n c u r r e n t , a n t i c y c l o n i c e d d i e s and c i r c u l a t i o n s a p p e a r . The c h a r t i n f i g u r e 6 w a s computed f o r t h e w i n t e r p e r i o d . According t o i t s a u t h o r (Ovchinnikov, 19661, t h e summer c h a r t of s u r f a c e c u r r e n t s c o u l d be v e r y s i m i l a r t o t h e w i n t e r o n e , u n l e s s f o r t h e r a t e of c i r c u l a t i o n which s h o u l d be d i v i d e d by two. I n t e r p r e t a t i o n s of o c e a n i c phenomena, g i v e n h e r e u n d e r , w i l l be founded on t h e Ovchinnikov c h a r t b u t a l s o on t h e g l o b a l knowledge e x i s t i n g a b o u t t h e M e d i t e r r a n e a n oceanography. And, w e have t o q u o t e some of t h e most i m p o r t a n t p a p e r s w r i t t e n till now a b o u t t h e Medit e r r a n e a n Sea : i t s g e n e r a l h y d r o l o g y (Lacombe and T c h e r n i a , 1 9 6 0 1 , i t s r e g i o n a l oceanography : i n t h e Alboran Sea ( L a n o i x , 1 9 7 4 1 , i n western Mediterranean (Furnestin, 1960) (Ozturgut, 1 9 7 6 ) .
,
i n t h e Levantin basin
99 131 2
FLUXES AND T H E I R SEASONAL VARIATIONS The p r e s e n c e of a M a r i n e S t a t i o n a t V i l l e f r a n c h e s u r M e r h a s a l l o h
t h e f r e q u e n t t a k i n g of m e a s u r e m e n t s o f f Nice and a l o n g t h e Nice-Calv s e c t i o n , t h r o u g h t h e permanent c y c l o n i c c i r c u l a t i o n . T h i s c i r c u l a t i c c o n c e r n s t h e s u p e r f i c i a l w a t e r ( a b o u t 0-200m)
and i n t e r m e d i a t e w a t e r
(200-800rn). Two s t r e a m s o f m e r i d i o n a l waters f l g w up b o t h s i d e s of Co
s i c a , j o i n a t t h e N o r t h o f Cap C o r s e and form t h e L i g u r i a n c u r r e n t which l a p s t h e s h o r e s o f t h e I t a l i a n R i v i e r a and t h e F r e n c h C 6 t e d'A I n t h e case o f l a c k of d i r e c t m e a s u r e m e n t s , t h e knowledge of t h e c i r c u l a t i o n i s b a s e d on t h e c a l c u l a t i o n o f t h e g e o s t r o p h i c c u r r e n t a c r c t h e Nice-Calvi
s e c t i o n . D u r i n g t h e p a s t y e a r s , a growing number of
h y d r o l o g i c a l d a t a h a v e been e x p l o i t e d , ; ' and r e c e n t l y h y d r o l o g i c a l ave r a g e s h a v e been c a l c u l a t e d , b a s e d on t h e c o m p l e t e m e a s u r e m e n t s c a r r i o u t d u r i n g t h e p e r i o d o f 1950-1973 and s t o r e d i n t h e a r c h i v e s of t h e d a t a bank o f t h e BNDO-COB
i n B r e s t ( N y f f e l e r e t a l . , 1980). Among 2 2
h y d r o l o g i c a l s t a t i o n s i n t h e L i g u r i a n S e a , m o r e t h a n 9 0 0 , on t h e Nic C a l v i s e c t i o n , w e r e t h u s u s e d . The a v e r a g e a n n u a l f l o w s on t h i s sect i o n h a v e been c a l c u l a t e d a n d , t a k i n g i n t o a c c o u n t t h e w a t e r b u d g e t of t h e b a s i n , t h e f l u x e s t h r o u g h t h e C o r s i c a n c h a n n e l have been dedu t e d and compared t o p r e v i o u s e s t i m a t i o n s (Bethoux e t a l . , 1 9 8 0 ) . I n f i g u r e 1 and i n t a b l e 1 are p r e s e n t e d t h e mean f l o w s r e l a t i n g t o t h e s u p e r f i c i a l (SL) and i n t e r m e d i a t e (IL) l a y e r s , t h e
+
sign indicates
a SW/NE f l o w ( o f f C a l v i ) o r a S/N f l o w ( C o r s i c a n c h a n n e l ) , and t h e s i g n i n d i c a t e s a f l o w i n a NE/SW d i r e c t i o n ( 1 Sv = 1 0 6m 3 /set).
-
TABLE 1
Mean f l o w s i n t h e s u p e r f i c i a l (SL) and i n t e r m e d i a t e ( I L ) l a y e r s i n t h e L i g u r i a n Sea N i c e side
SL IL
-
-
Calvi side
1.4 s v 0.4
+ +
0.7 0.2
sv
Corsican channel
+
+
0.7 s v 0.2
T h e s e f l o w s a r e l a r g e , e s p e c i a l l y o f f N i c e , where t h e s t r o n g e s t c u r r e n t s s t a y c h a n n e l l e d i n t o a c o a s t a l band 2 0 t o 3 0 m i l e s wide. The s u r f a c e s p e e d s a r e between 2 0 t o 3 0 cm/sec and are below 5 cm/se from 250m downwards (see F i g . 2 ) .
I n t h e c e n t r a l zone t h e a v e r a g e geo
s t r o p h i c f l o w s are a l m o s t n u l l . T h e f l o w s on b o t h s i d e s of Cap Corse a r e , on an a v e r a g e , e q u a l , which shows t h e i m p o r t a n c e of t h e T y r r h e n i a n S e a o u t f l o w , p e r h a p s u n d e r e s t i m a t e d u p t o now. I t c o n s i s t s of w a r m p a t c h e s of w a t e r which a p p e a r i n b l a c k o n
100
Fig. 7 .
=
spatial envelope shape of frontal feature
warmwater
L"+'I
@
coldwater
-0-
-+ +
maximum gradient in OC/5lan measured accross the front.
cold core eddy o r circulation
warmcoreeddy supposed direction of the surfake current
""
F i g . 8. AS : A l b o r a n S e a ; AB : A l g e r i a n b a s i n ; BB : B a l e a r i c b a s i n ; PB : P r o v e n q a l b a s i n ; LS : L i g u r i a n S e a ; TS : T y r r h e n i a n S e a ; ASB : A f r o - S i c i l i a n b a s i n ; I S : I o n i a n sea ; ADS : A d r i a t i c S e a ; LB : L e v a n t i n b a s i n ; AES : Aegean Sea ; m : Majorca ; c : C o r s i c a ; s : S a r d i n i a s i : S i c i l y ; m : Malta ; k : Kerkennah ; d : D j e r b a ; c r : C r e t a ; r : Rhoda ; 1 : G i b r a l t a r ; 2 : straits of M e s s i n a ; 3 : CyrenaPca ; 4 : T r e s F o r c a c a p e ; 5 : A d v e n t u r e bank ; 6 : B o n i f a c i o s t r a i t s ; 7 : S a r d i n i a straits ; 8 : g u l f of L i o n ; 9 : g u l f o f S y r t a .
102
F i g . 9 a . TIROS N image of t h e e a s t e r n M e d i t e r r a n e a n sea o b t a i n e d on J u n e 28th, 1 9 7 9 .
103
F i g . 9b. P a r t of t h e same s c e n e v i s u a l i z e d u s i n g 0.25'C p e r s h a d e of g r e y i n s t e a d of 0 . 5 0 ' C . 1 : upwellings : 2 : wave-like f e a t u r e s ; 3 : e d d i.es. t h e i m a g e s . T e m p e r a t u r e g r a d i e n t s o n t h e b o u n d a r i e s of s u c h p a t c h e s a r e h i g h b u t n o t enough t o b u i l d f r o n t s a c c o r d i n g to t h e above
d e f i n i t i o n . An example o f s u c h warm p a t c h e s i s g i v e n i n f i g u r e 1 1 ( o b t a i n e d o n May 1 8 t h , 1979 o n t h e I o n i a n s e a ) . Such warm p a t c h e s a r e i n d u c e d by s t r o n g d i u r n a l h e a t i n g o c c u r i n g a t t h e s e a s u r f a c e i n calm wind a r e a s . T h e i r g e o g r a p h i c a l p s i t i o n s Change from day t o day f o l l o w i n g t h e c e n t e r s of sunny w i n d l e s s a r e a s . T h e s e warm p a t c h e s o b s c u r e t h e u n d e r l y i n g t e m p e r a t u r e s t r u c t u r e which i s r e p r e s e n t a t i v e of s u r f a c e w a t e r d y n a m i c s . Images w i t h warm p a t c h e s c a n n o t be used i n f r o n t a n a l y s i s .
104
Fig. 10. Image NOAA6 4892 obtained o n June 5th, 1980. 1 : filamentlike features : 2 : upwellings : 3 : Kerkennah shallows : 4 : Djerba shallows.
105
F i g . 11. TIROS N image of t h e A f r o - S i c i l i a n b a s i n o b t a i n e d on May 1 8 t h , 1 9 7 9 . 1 : warm p a t c h e s ; 2 : Kerkennah s h a l l o w s : 3 : D j e r b a shallows.
106
3.2 SUMMER: J U L Y , AUGUST, SEPTEMBER 1 9 7 9 The f r o n t c h a r t c h o s e n t o i l l u s t r a t e t h e summer p e r i o d i s t h e August c h a r t (see f i g u r e 1 2 ) .
/
The v e r t i c a l summer t e m p e r a t u r e s t r a t i f i c a t i o n of t h e water m a s s e s i s now w e l l formed and most of t h e f r o n t s d e t e c t e d a r e a s s o c i a t e d w i t h h o r i z o n t a l and v e r t i c a l water c i r c u l a t i o n s . Movements of w a t e r modify t h e s l o p e s , o f t h e i s o t h e r m a l l a y e r s . T h e r e f o r e , h o r i z o n t a l t e m p e r a t u r e g r a d i e n t s a p p e q r , which may o u t c r o p o n t h e sea s u r f a c e and create s u r f a c e t e m p e r a t u r e f r o n t s . O t h e r f r o n t s c o u l d b e i n d u c e d by t u r b u l e n c e e f f e c t s o c c u r i n g i n s t r a i t s o r above s h a l l o w s . These t u r b u l e n c e e f f e c t s mix t h e w a t e r s and weaken t h e s e a s o n a l t h e r m o c l i n e . The f r o n t s shown i n f i g u r e 1 2 a r e f i r s t l y c r e a t e d by t h e A f r i c a n c u r r e n t . Such f r o n t s a r e o b s e r v e d i n t h e A l b o r a n Sea, where t w o a n t i c y c l o n i c g y r e s a p p e a r e d i n August 1 9 7 9 . The most i m p o r t a n t of them i s o b s e r v e d W e s t o f t h e T r e s F o r c a c a p e and t h e second one E a s t of t h i s c a p e . The g y r e d i a m e t e r s r e a c h a b o u t 150 km. F r o n t s
a r e d e t e c t e d on b o t h s i d e s o f t h e c o l d t o n g u e s which e n c i r c l e t h e i r warm c o r e s . F i g u r e 1 3 shows a n image of t h e A l b o r a n Sea o b t a i n e d on August 2 0 t h , 1 9 7 9 . The a b o v e m e n t i o n e d g y r e s a p p e a r c l e a r l y on t h i s image. On August 2 0 t h and d u r i n g t h e p r e v i o u s d a y s , t h e wind w a s blowing from t h e E a s t i n t h e A l b o r a n S e a . C o n s e q u e n t l y , u p w e l l i n g s c a n be n o t i c e d o f f t h e A f r i c a n c o a s t and a warm c o u n t e r c u r r e n t r u n s a l o n g t h e S p a n i s h c o a s t s . F r o n t s d u e t o t h e A f r i c a n c u r r e n t a r e a l s o d e t e c t e d S o u t h of S i c i l y , e s p e c i a l l y above t h e A d v e n t u r e Bank and above t h e E a s t e r n s l o p e of t h e S i c i l o - M a l t e s e c o n t i n e n t a l s h e l f
(Malta f r o n t ) .
But, i n t h i s a r e a , t h e A f r i c a n c u r r e n t i n t e r a c t s w i t h c o a s t a l u p w e l l i n g s and c o n t i n e n t a l s h e l f e f f e c t s . C o n s e s u e n t l y , t h e f r o n t s i n t h i s area r e s u l t from s e v e r a l e f f e c t s i n c l u d i n g c u r r e n t , m i x i n g and u p w e l l i n g s . Other major f r o n t s a r e l i n k e d up w i t h c y c l o n i c c i r c u l a t i o n s . These f r o n t s a p p e a r a t t h e l i m i t between t h e c o l d c o r e s of t h e s e c i r c u l a t i o n s ( d i v e r g e n c e s ) and t h e warm waters r u n n i n g round them. The m o s t i m p o r t a n t f r o n t s a r e found i n t h e Liguro-ProvenGal
Fig. 12. Monthly c h a r t o f s u r f a c e t h e r m a l f r o n t s
spatial envelope shape of frontal feature
wazmwater coldwater
-
+
August 1 9 7 9 cold core eddy or circulation warm core eddy
* supposed direction of
@ maximum gradient in 0C/51an measured accross the front.
t h e surface current
108
F i g . 1 3 . NOAA6 image of t h e Alboran Sea o b t a i n e d on August 2 0 t h , 1 9 7 9 . 1 : warm c o r e of t h e a n t i c y c l o n i c eddy ; 2 : c o l d b o u n d a r i e s of a n t i c y c l o n i c e d d i e s ; 3 : u p w e l l i n g s ; 4 : w a r m c o a s t a l c o u n t e r current. basin
( f i g u r e 1 4 ) and South-East
of Rhoda ( f i g u r e 1 5 ) . A s m a l l e r ,
b u t e q u a l l y a c t i v e d i v e r g e n c e is d e t e c t e d E a s t of t h e B o n i f a c i o s t r a i t s ( f i g u r e 1 4 ) . O t h e r c i r c u l a t i o n s a r e i n t e r m i t t e r i i y observed i n t h e S a r d i n i a s t r a i t s ( f i g u r e 1 4 ) and W e s t of C r e t a ( f i g u r e 1 5 ) . A t h i r d t y p e of
f r o n t s i s induced by u p w e l l i n g s . F r o n t s mark
t h e o f f s h o r e l i m i t s of c o l d upwelled waters. Throughout summer, u p w e l l i n g s c a n be d e t e c t e d i n t h e E a s t of Aeqean Sea (see f i g u r e 1 5 ) . The u p w e l l i n g s a r e c a u s e d by s t r o n g n o r t h w i n d s , c a l l e d E t e s i a n winds o r M e l t e m i .
109
F i g . 1 4 . TIROS N image of t h e c e n t r a l M e d i t e r r a n e a n S e a o b t a i n e d on A u g u s t 2 2 t h , 1 9 7 9 . 1 : L i g u r o - P r o v e n @ divergence ; 2 : warm c u r r e n t : 3 : u p w e l l i n g s ; 4 : secondary c y c l o n i c d i v e r g e n c e s ; 5 : w a r m p a t c h e s due t o s t r o n g d i u r n a l h e a t i n g : 6 : mesoscale eddy.
110
F i g . 1 5 . TIROS N image of t h e E a s t e r n M e d i t e r r a n e a n o b t a i n e d on 5 t h , August 1 9 7 9 . 1 : c y c l o n i c d i v e r g e n c e s : 2 : u p w e l l i n g s d u e t o e t e s i a n winds ; 3 : warm c u r r e n t .
111 U p w e l l i n g s a l o n g t h e c o a s t of Albany a r e a l s o c a u s e d by n o r t h e r l y winds s i m i l a r t o t h e e t e s i a n w i n d s . Along t h e A f r i c a n and L y b i a n c o a s t s , winds o f t e n blow from t h e E a s t i n summer and u p w e l l i n g s a l s o a p p e a r . More i n t e r m i t t e n t u p w e l l i n g s d e v e l o p i n t h e g u l f of L i o n s . I n summer, f r o n t s c a u s e g r a d i e n t s which may r e a c h 3 o r 4 O C w i t h i n a d i s t a n c e of a b o u t 5 ?un. Such v a l u e s a r e r e a c h e d i n August and September i n t h e A l b o r a n S e a , t h e S o u t h of t h e P r o v e n q a l b a s i n and t h e M a l t a f r o n t . 3 . 3 AUTUMN : OCTOBER, NOVEMBER,
DECEMBER 1 9 7 9
The autumn f r o n t c h a r t p r e s e n t e d h e r e i s t h e November c h a r t (figure 1 6 ) . The d i s t r i b u t i o n of s e a s u r f a c e t e m p e r a t u r e s i n autumn i s r e p r e s e n t a t i v e of a t r a n s i t i o n a l p e r i o d . Some summer f r o n t s p e r s i s t on t h e autumn i n f r a r e d images. O t h e r f r o n t s a p p e a r , which w i l l a l s o b e o b s e r v e d d u r i n g t h e w i n t e r months. The r e m a i n i n g f r o n t s a r e t y p i c a l of t h e autumn p e r i o d . C o n s e q u e n t l y autumn i s t h e s e a s o n d u r i n g which t h e g r e a t e s t amount of f r o n t s c a n b e d e t e c t e d on t h e i n f r a r e d images. Major f r o n t s a r e s t i l l l i n k e d u p w i t h d i s t u r b a n c e s of t h e summer thermocline. C y c l o n i c d i v e r g e n c e s and a s s o c i a t e d f r o n t s a r e o b s e r v e d d u r i n g t h e autumn. I n November Provenqal b a s i n
(see f i g u r e 1 6 ) , t h e y appear i n t h e l i g u r o -
( f i g u r e 1 7 ) , E a s t o f t h e s t r a i t s of B o n i f a c i o and
S o u t h e a s t o f Rhoda ( f i g u r e 2 0 ) . F r o n t s a t t h e l i m i t of t h e i r c o l d c o r e s seem t o become more i n s t a b l e d u r i n g t h e autumn ( s e e f i g u r e 1 7 ) . A t t h e b e g i n n i n g of autumn,
t h e t e m p e r a t u r e s t r u c t u r e of t h e
A l b o r a n S e a i s d i s t u r b e d by t h e c h a n g e s o c c u r i n g i n t h e wind fluxes. I n summer, p r e v a i l i n g winds blow from t h e E a s t , w h e r e a s , t h e y come from t h e West i n w i n t e r . Such c h a n g e s i n t h e main wind d i r e c t i o n o c c u r e d i n 1 9 7 9 d u r i n g l a t e September and O c t o b e r . D u r i n g t h e s e months p e r i o d s of e a s t e r l y winds a l t e r n a t e d w i t h p e r i o d s of w e s t e r l y o n e s . I n November, w e s t e r l y winds a r e w e l l e s t a b l i s h e d i n t h e A l b o r a n Sea and a l o n g t h e c o a s t of A l g e r i a , h e n c e t h e g y r e s of t h e A l b o r a n Sea become c l e a r l y v i s i b l e a g a i n . The p a t h of t h e A f r i c a n c u r r e n t
112
Fig.
1 6 . Monthly c h a r t of s u r f a c e t e m p e r a t u r e frontal feature
November 1 9 7 9 . cold core eddy or circulation
m spatial envelope shape of warmwater
a coldwater @
A t
+
maximum gradient i n O C / ~ I m~ e a s u r e d accross the front.
warm core d d y m p p s e d direction of the surface current
113
Fig.
1 7 . NOAA6 I m a g e of t h e L i g u r o - P r o v e n q a l b a s i n a n d t h e b a l e a r i c : c o l d d i v e r g e n c e s of t h e Liguro-Provenqal c y c l o n i c c i r c u l a t i o n ; 2 : warm c o a s t a l c u r r e n t ; 3 : w a r m water i n c l u s i o n .
hasin o b t a i n e d o n 4 t h , November 1 9 7 9 . 1
114 o f f t h e A f r i c a n coast i s u n d e r l i n e d b y an i r r e g u l a r c o l d tongue. The image o f f i g u r e 1 8 o b t a i n e d o n November 2 8 t h , 1979 shows
s e r i e s of s m a l l a n t i c y c l o n i c e d d i e s ( a b o u t 25 t o 3 0 n a u t i c a l miles i n d i a -
t h a t t h i s c o l d t o n g u e f o l l o w s t h e N o r t h e r n b o u n d a r y of
m e t e r ) . These eddies d e v e l o p between t h e main c u r r e n t - p n d t h e A f r i c a n coast.
F i . 1 8 . NOAA6 image of t h e w e s t e r n M e d i t e r r a n e a n o b t a i n e d o n 2 8 t h , November 1 9 7 9 . 1 : e d d i e s o f t h e A l b o r a n S e a : 2 : p a t h o f t h e A f r i c a n c u r r e n t : 3 : warm w a t e r i n c l u s i o n . I n t h e Aegean S e a a n d i n t h e S o u t h o f t h e A d r i a t i c S e a , t h e n o r t h w e s t e r l y winds ( e t e s i a n winds) s t o p blowing a t t h e beginning of autumn. Wind f l u x e s become more i r r e g u l a r . B u t i n autumn, t h e p r e v a i l i n g w i n d s s e e m t o blow from t h e S o u t h ( S i r o c c o ) . W a r m w a t e r i n t r u s i o n s t a k e t h e p l a c e of summer u p w e l l i n g s i n t h e E a s t of t h e
115 Aegean S e a (see f i g u r e 1 9 ) . A s i m i l a r phenomenon o c c u r i n t h e A d r i a t i c S e a where a w a r m c u r r e n t c a n b e o b s e r v e d i n t h e p l a c e of t h e summer u p w e l l i n g s o f f t h e c o a s t s of Y u g o s l a v i a and Albany. T h i s warm c u r r e n t u n d e r l i n e s t h e e a s t e r n n o r t h w a r d b r a n c h of t h e g e n e r a l c y c l o n i c c i r c u l a t i o n i n t h e A d r i a t i c S e a . The w e s t e r n s o u t h w a r d b r a n c h i s e m p h a s i z e d by a n a r r o w s t r i p of c o l d c o a s t a l w a t e r s . These c o l d w a t e r s may o r i g i n a t e i n t h e n o r t h of t h e A d r i a t i c S e a where s h a l l o w waters u n d e r g o a s t r o n g w i n t e r c o o l i n g ( e f f e c t of Bora w i n d ) . F r o n t s a r e d e t e c t e d a l o n g t h e w e s t e r n s i d e of t h e w a r m w a t e r i n t r u s i o n a n d a l o n g t h e o f f s h o r e l i m i t of c o a s t a l w a t e r s ( s e e f i g u r e 2 0 ) . T h i s l a t t e r t y p e of f r o n t s w i l l p e r s i s t i n w i n t e r . S i m i l a r f r o n t s t y p i c a l of t h e w i n t e r p,eriod a p p e a r i n some p l a c e s
F i g . 1 9 . NOAA6 image of t h e Aegean S e a o b t a i n e d on 6 t h , November 1 9 7 9 . 1 : c o l d w a t e r s from t h e B l a c k S e a ; 2 : w a r m w a t e r i n t r u s i o n 3 : cyclonic divergence.
116 w h e r e c o l d c o a s t a l w a t e r s c a n be o b s e r v e d , d u e t o wind m i x i n g over c o n t i n e n t a l s h e l v e s and t o r i v e r o u t f l o w s ( g u l f o f L i o n s w i t h t h e RhBne r i v e r f o r i n s t a n c e ) .
F i g . 2 0 . NOAA6 image o f t h e A d r i a t i c S e a o b t a i n e d o n 5 t h , December 1 9 7 9 . 1 : c o l d c o a s t a l waters ; 2 : w a r m water i n t r u s i o n ; 3 : c e n t e r of one of t h e A d r i a t i c c y c l o n i c c i r c u l a t i o n c e l l ; 4 : runo f f of r i v e r ? Upwellings induced m a i n l y by n o r t h l y t o n o r t h w e s t e r l y winds are s t i l l v i s i b l e o n t h e i n f r a r e d i m a g e s . I n November 1 9 7 9 , u p w e l l i n g s
were observed w e s t o f S a r d i n i a and s o u t h o f S i c i l y . I n t h e Afro-Sicilian
b a s i n t h e temperature s t r u c t u r e of t h e
s u r f a c e i s v e r y i n t r i c a t e d a n d a g r e a t number of f r o n t s c a n be detected : upwelling f r o n t s , f r o n t s associated with t h e African c u r r e n t , f r o n t s d u e t o w i n t e r c o o l i n g o f s h a l l o w waters ( a r o u n d t h e
117 t h e i s l a n d s o f Djerba and K e r k e n n a h , f o r i n s t a n c e ) . An i n t e r e s t i n g phenomenon c a n b e o b s e r v e d i n autumn. I t c o n s i s t s o f w a r m n e a r l y c i r c u l a r p a t c h e s ( a b o u t 40 n a u t i c a l m i l e s i n diame-
t e r ) o f w a r m waters embedded i n c o l d e r c i r c u l a t i o n s . On t h e image of f i g u r e 18, s u c h w a r m i n c l u s i o n s c a n be s e e n n o r t h of Majorca ( B a l e a r i c b a s i n ) . F i g u r e 1 7 was o b t a i n e d o n M o G e m b e r 4 t h , 1 9 7 9 . The
image o f f i g u r e 19, o b t a i n e d more t h a n t h r e e weeks l a t e r , shows t h e
same w a r m p a t t e r n i n t h e same p l a c e . I t s b o u n d a r y h a s become i r r e g u l a r . S t r o n g g r a d i e n t s ( > 4'C/5km) c a n be m e a s u r e d a t t h e l i m i t b e t w e e n t h e s e w a r m waters a n d t h e c y c l o n i c c i r c u l a t i o n o f t h e provenqal basin. B u t o u t s i d e t h i s area g r a d i e n t s ih f r o n t s a r e weaker t h a n i n summer. They v a r y from 1 t o 2.5'C/5km.
W a r m i n c l u s i o n s may b e d u e
t o c h a n g e s o c c u r i n g d u r i n g autumn i n t h e g e n e r a l w a t e r c i r c u l a t i o n ( i n f l u e n c e o f wind f l u x e s )
.
3.4. WINTER : JANUARY, FEBRUARY, .?-IARCH 1 9 8 0 The summer t h e r m o c l i n e h a s b e e n d e s t r o y e d by t h e w i n t e r c o o l i n g and f r o n t s a s s o c i a t e d w i t h t h e dynamic d i s t u r b a n c e s o f s u b s u r f a c e i s o t h e r m a l l a y e r s have almost c o m p l e t e l y d i s a p p e a r e d (see t h e F e b r u a r y f r o n t c h a r t i n f i g u r e 21). An e x c e p t i o n c a n however b e f o u n d i n t h e L e v a n t i n b a s i n where t h e d i v e r g e n c e o b s e r v e d s o u t h e a s t o f Rhoda p e r s i s t s t i l l F e b r u a r y 1 9 8 0 . F r o n t s d e t e c t e d o n t h e t h e r m a l i m a g e s a r e now m a i n l y l i n k e d
u p w i t h c o l d w a t e r masses w h i c h n a y b e c a u s e d b y t h e c o o l i n g of s h a l l o w c o a s t a l waters, r i v e r r u n - o f f s t h e Aegean S e a )
.
or Black Sea outflow ( i n
Some o f t h e s e f r o n t s were a l r e a d y o b s e r v e d i n autumn, s u c h a s f o r i n s t a n c e , f r o n t s a t t h e o f f s h o r e l i m i t of I t a l i a n c o a s t a l
waters(see f i g u r e 24), i n t h e g u l f o f L i o n s ( s e e f i g u r e 23) o r a r o u n d t h e D j e r b a a n d Kerkennah s h a l l o w s . I n t h e Afro-Sicilian
b a s i n , f r o n t s develop i n t h e N o r t h o f t h e
S y r t a a n t i c y c l o n i c c i r c u l a t i o n . I n t h i s area, t h e A f r i c a n c u r r e n t and, p o s s i b l y waters from t h e North of t h e I o n i a n S e a , c o n t r a s t with t h e w a r m c e n t e r of t h e a n t i c y c l o n i c c i r c u l a t i o n (convergence area)
,
( s e e f i g u r e 24).
I n t h e Aegean S e a ( s e e f i g u r e 25), w a t e r s from t h e B l a c k S e a a r e c o l d b u t l i g h t e r t h a n t h e s u r r o u n d i n g Aegean w a t e r s . T h e r e f o r e t h e s e c o l d waters s p r e a d over t h e n o r t h w e s t e r n p a r t of t h e Aegean S e a d u e t o t h e C o r i o l i s e f f e c t . The t e m p e r a t u r e of w a t e r s i n t h i s
118
Fig. 21. Wnthly chart of surface temperature fronts. February 1980.
=
s p a t i a l envelope shape of f r o n t a l feature
warm water cold water
@ W i m u n ~gradient i n
-0- cold
core eddy or c i r c u l a t i o n
$- warn core eddy + supposed direction of the surface current
'C/Slan
m e a r u s e d accross the front.
119
F i g . 22. NOAAG image o f t h e A l b o r a n Sea o b t a i n e d on 8 t h , J a n u a r y 1980. 1 : a n t i c y c l o n i c eddy ; 2 : w a r m s u r f a c e i n f l o w o f A t l a n t i c w a t e r s ; 3 : p a t h of t h e A f r i c a n c u r r e n t . p a r t of t h e Aegean Sea i s a l s o lowered by t h e c o l d n o r t h e r l y wind, which o f t e n blows i n t h i s a r e a i n w i n t e r ( V a r d a r w i n d ) , and a l s o by r i v e r run-offs.
F r o n t s a p p e a r a t t h e limit between c o l d w a t e r s i n
t h e n o r t h w e s t o f t h e sea and w a r m e r waters i n t h e s o u t h e a s t . O u t s i d e t h e M e d i t e r r a n e a n a r e a s where f r o n t s c a n be d e t e c t e d , t h e t h e r m a l s e a s u r f a c e s t r u c t u r e i s smooth (see f i g u r e 23). I n t h e Alboran Sea a n i n t e r e s t i n g f e a t u r e c a n sometimes be o b s e r v e d : t h e w a t e r s c a r r i e d by t h e A f r i c a n c u r r e n t may b e warmer, n e a r t h e s u r f a c e t h a n t h e s u r r o u n d i n g M e d i t e r r a n e a n w a t e r s . These warmer w a t e r s a p p e a r a s a warm t o n g u e on t h e s a t e l l i t e images ( s e e f i g u r e 22). I n w i n t e r , g r a d i e n t s i n f r o n t a r e a s a r e of t h e same o r d e r of magnitude a s i n autumn : 1 t o 2.5'c/5km.
120
Fig. 23. T I R O S N Image of the Liguro-Provenqal basin obtained on 28th, February. 1 : cold coastal waters.
121
F i g . 2 4 . TIROS N image of I o n i a n Sea o b t a i n e d on 3 r d , F e b r u a r y 1 9 8 0 . 1 : Syrta anticyclonic c i r c u l a t i o n center ; 2 : cold c o a s t a l waters.
122
F i g . 2 5 . TIROS N image o f t h e Aegean S e a o b t a i n e d o n 7 t h , F e b r u a r y 1 9 8 0 . 1 : c o l d w a t e r i n f l o w from t h e B l a c k S e a . 4.
I N T E R ANNUAL VARIABILITY
To e m p h a s i z e t h e i n t e r a n n u a l v a r i a b i l i t y of M e d i t e r r a n e a n
s u r f a c e t e m p e r a t u r e f r o n t s , c h a r t s w e r e drawn by s u p e r i m p o s i n g t h e f r o n t a l envelope s h a p e s f o r t h e same months of two c o n s e c u t i v e y e a r s . From t h e a n a l y s i s of t h e t w e l v e m o n t h l y c h a r t s , a s i g n i f i c a n t s i m i l a r i t y c a n g e n e r a l l y b e o b s e r v e d b e t w e e n t h e l o c a t i o n s of f r o n t a l a r e a s d u r i n g b o t h y e a r s . F i g u r e 2 6 which shows t h e c h a r t of November 1 9 7 9 and November 1 9 8 0 , g i v e s a n example o f s u c h a s i m i l a r i t y . D u r i n g b o t h months m a j o r f r o n t s f i r s t a p p e a r e d i n t h e A l b o r a n S e a ( e d d i e s ) a n d a l o n g t h e p a t h of t h e A f r i c a n c u r r e n t . I n t h e l a t t e r area f r o n t a l e n v e l o p s h a p e s w e r e a l m o s t c o h c i d e n t . F r o n t s
Fig. 26. Superimposition of frontal envelope shapes. November 1979-November 1980.
123
124
associated with cyclonic circulations were also found during both months : Liguro-Provenqal basin, East of the Straits of Bonifacio, and South-East of Rhoda. Here the locations and extensions of frontal contours changed between 1979 and 1980, probably due to changes in general wind conditions. For instance, the cold center of the Bonifacio divergence was more extended in November 1980 than in November 1979. In the South of the Liguro-Provenqal basin, a greater number of frontal areas were detected during the second year of measurements. On the contrary, fronts of both years are nearly superimposed in the Adriatic Sea. In the Straits of Sardinia and in the Afro-Szcilian basin, fronts are complex during both months. If they are always related to the same oceanic features (African current, upwellings, Syrta circulation, topography of continental shelves), their contours are not well coincident outside the area of the Malta front. The image of figure 27 shows a scene taken above the central Mediterranean in November 1980. By comparing this image with the monthly chart of fronts of November 1979 (see figure 28), the similarities and differences described above appear clearly. The comparison between fronts observed in the Levantin basin and in the Aegean Sea, in 1979 and in 1980, shows a greater dispersion in the front distribution, perhaps because autumn is a transition period in the Aegean Sea (see section 3 . 3 above). The season during which the best coincidence between front areas observed during two consecutive years can be observed is winter. It is especially true for the fronts appearing at the offshore limits of coastal waters because they seem to be linked up with the bottom topography. The chart of figure 27 points out this fact for the months of February 1980-February 1981. 5. DISCUSSION Most of the phenomena observed on the thermal images above have been interpreted according to the general knowledge we have on the Mediterranean oceanography. The source of information was a bibliography which was mainly constituted from historical in situ measurements (see section 3 above). Other phenomena on which no bibliography was available were interpreted taking into account their analogies with the previously identified phenomena. A few phenomena such as warm water intrusions in autumn and filament-like features
w
r-
N
..
125
(u
.Em Q) -4 me
Fig. 27. NOAA6 image nr. 7210 obtained on November 15th, 1 9 8 0 . 1 : Liguro-Provenqal cyclonic divergence : 2 : divergence west of the straits of Bonifacio : 3 : divergence of the straits of Sardinia ; 4 : cold coastal waters : 5 : warm intrusion.
126
F i q . 28. S u p e . r i r n p o s i t i o n of front envelope s h a p e s . F e b r u a r y 1 9 8 0 - F e b r u a r y 1 9 7 9 .
127
i n s p r i n g a r e n o t y e t f u l l y u n d e r s t o o d . Taking t h e s e f a c t s i n t o a c c o u n t and c o n s i d e r i n g t h a t v e r y f e w i n s i t u measurements, o b t a i n e d s i m u l t a n e o u s l y w i t h s a t e l l i t e s images, are a v a i l a b l e , it i s l i k e l y t h a t some i n t e r p r e t a t i o n s o f phenomenon g i v e n i n t h i s t e x t a r e wrong. B u t , t h o u g h r e s u l t s a r e i m p e r f e c t , t h e y , however, improve t h e g e n e r a l knowledge of f r o n t s i n t h e M e d i t e r r a n e a n S e a . Some o f t h e r e s u l t s p r e s e n t e d i n s e c t i o n 3 i n d i c a t e t h a t t h e w i n t e r c h a r t of s u r f a c e c u r r e n t s g i v e n by Ovchinnikov ( s e e f i g u r e 5) i s n o t e v e r y w h e r e r e p r e s e n t a t i v e o f t h e summer c i r c u l a t i o n . F o r
i n s t a n c e , u p w e l l i n g s w h i c h a p p e a r i n summer i n t h e e a s t e r n Aegean Sea and o f f t h e c o a s t s o f Albany and A l g e r i a s e e m t o s t o p o r e v e n t o reverse the surface currents. Such c h a n g e s i n t h e s u r f a c e c i r c u l a t i o n a r e n o t s u r p r i s i n g however because s u r f a c e c u r r e n t s i n t h e M e d i t e r r a n e a n Sea a r e mainly induced by w i n d s and w i n d s u n d e r g o i m p o r t a n t s e a s o n a l c h a n g e s i n t h e a r e a s concerned. Another f a c t h a s t o b e p o i n t e d o u t : f r o n t s i n t h e Mediterranean Sea may b e s t r o n g . S u r f a c e g r a d i e n t s of 3 t o 4'C/5km
are often
e n c o u n t e r e d i n summer and autumn i n c e r t a i n a r e a s s u c h a s t h e A l b o r a n S e a and t h e P r o v e n q a l b a s i n .
6. CONCLUSION From two y e a r s of s a t e l l i t e i n f r a r e d d a t a o v e r t h e M e d i t e r r a n e a n S e a , i t was p o s s i b l e t o s t u d y t h e s u r f a c e t e m p e r a t u r e f r o n t s , t h e i r s e a s o n a l c h a n g e s and some c h a r a c t e r i s t i c s o f t h e i r i n t e r a n n u a l v a riability. S u r f a c e t e m p e r a t u r e f r o n t s i n t h e M e d i t e r r a n e a n Sea a r e s e a s o n a l . T h e i r d i s t r i b u t i o n f o l l o w s t h e a n n u a l c y c l e , summer heating
-
winter
c o o l i n g . I n s p r i n g , t h e s u r f a c e w a t e r s a r e w e l l mixed and o n l y a few f r o n t s a p p e a r . I n summer numerous f r o n t s a r e d e t e c t e d , a s s o c i a t e d w i t h dynamic d i s t u r b a n c e s o f t h e summer t h e r m o c l i n e . Autumn i s a t r a n s i t i o n p e r i o d d u r i n g which summer f r o n t s c a n b e o b s e r v e d t o g e t h e r w i t h w i n t e r o n e s . I n c e r t a i n a r e a s , such a s t h e Alboran Sea i n O c t o b e r , t h e A f r o - S i c i l i a n b a s i n and t h e Aegean S e a , f r o n t s seem t o be d i z o r g a n i s e d . I n w i n t e r f r o n t s a p p e a r a t t h e l i m i t o f waters of d i f f e r e n t o r i g i n s . They a r e m a i n l y d e t e c t e d on t h e o f f s h o r e l i m i t s of c o l d c o a s t a l w a t e r s , e x c e p t i n t h e n o r t h e a s t o f t h e Aegean S e a where o t h e r f r o n t s o c c u r , l i n k e d u p w i t h t h e c o l d i n f l o w o f B l a c k Sea w a t e r s . From o n e y e a r t o a n o t h e r t h e same s e a s o n a l e v o l u t i o n o f f r o n t s c a n b e o b s e r v e d o n t h e i n f r a r e d i m a g e s . Major s e a s o n a l f r o n t s a r e
128 detected, associated with the same oceanic features but their precise locations and their extensions may have changed. Associated with surface temperature fronts a great number of oceanic phenomena were detected and analysed. Some of them are not yet fully understood. Satellite teledetection gives numerous informtions about the Mediterranean oceanography but raises ,an equally important number of new questions about this oceanography. This study shows the interest of using infrared imagery from meteorological satellites for the monitoring of wide oceanic areas, specially in areas where the cloud cover is not important, such as over the Mediterranean Sea. Such satellite data are very useful for the study of mesoscale oceanic phenomena whit$, induce temperature gradients at the sea surface. But it can be assumed that the simultaneous use of in situ measurements, of infrared satellite data and also of data from other satellite sensors such as altimeters or synthetic aperture radars will improve such studies and enlarge it to phenomena with no temperature signature. REFEREIJCES Briscoe, M.G., Johannessen, O.M. and Vicenzi, S., 1974. The Maltese oceanic front : a surface description by ship and aircraft. Deep Sea Research, 21(4): 247-262; Cheney,R.E., 1977. Aerial observations of oceanic fronts in the western Mediterranean Sea. Technical Note, 3700-69-77. US Naval Oceanographic Office, Washington, DC. Cheney, R.E., 1978. Recent observations of the Alboran Sea frontal system. Journal of Geophysical Research, 83(C9):4593-4597. Furnestin, J., 1960. Hydrologie de la Mediterranee occidentale (golfe du Lion, mer Catalane, mer d'Alboran, Corse orientale). Revue des Travaux de 1'Institut des PQches Maritimes. 24(1):5-98. Gallagher, J.J., Fecher, M., Gorman,J., 1981. Project HUELVA. Oceanographic/Acoustic investigation of the western Alboran Sea. NUSC Technical Report 6023A. Naval Underwater Systems Center. Johannessen, O.M., 1975. A review of oceanic fronts. In Proceedings Conference SACLANTCEN on Oceanic Acoustic Modelling, 17(5). Johannessen, O.M., and Smallenburger, C., 1977. Observation of an oceanic front in the Ionian Sea during early winter in 1970. Journal of Geophysical Research, 82(9):1381-1391. Lacombe, H., and Tchernia, P., 1960. Quelques traits generaux de l'hydroloqie mediterraneenne. Cahiers Oceanographiques, 12(8) : 527-547. Lanoix, R., 1974. Projet Alboran : etude hydrologique et dynamique de la mer d'Alboran. Technical Report 66, NATO, Brussels, Belgium. Ovchinnikov, I.M., 1966. Circulation in the surface and intermediate layers of the Mediterranean.Oceanology, 6(1):48-58. Ozturgut, E., 1976. The sources and spreading of the Levantine intermediate water in the eastern Mediterranean. SACLANTCEN Memorandum, SM-92. Wannamaker, B., 1979. The Alboran Sea gyre : ship, satellite and historical data. SACLANTCEN Report, SR-30.
129
THE WATER CIRCULATION I N THE NORTH-WESTERN
MEDITERRANEAN SEA ,
ITS RELATIONS W I T H W I N D AND ATMOSPHERIC PRESSURE
J.P.
Bethoux(x!
L.
Prieur(x!
F. N y f f e l e r ( x x )
ABSTRACT Mean v a l u e s o f h y d r o l o g i c a l d a t a ( , r e l a t i n g t o t h e p e r i o d 1950-1973) are u s e d t o e v a l u a t e t h e c y c l o n i c f l u x e s i n t h e L i g u r i a n S e a , i . e . , through the Nice-Calvi
s e c t i o n a n d t h e C o r s i c a n c h a n n e l . A marked
s e a s o n a l c y c l e a p p e a r s o f f Nice a n d a l s o t h r o u g h t h e C o r s i c a n c h a n n e l w h e r e are c o n f i r m e d some p r e v i o u s d i r e c t m e a s u r e m e n t s o f t h e f l o w . The s t u d y o f wind a n d a t m o s p h e r i c p r e s s u r e shows t h a t t h e s e e x t e r n a l f o r c e s o n l y e x e r t a moderate e f f e c t on t h e w a t e r c i r c u l a t i o n w h i c h t h e r e f o r e s h o u l d be c h i e f l y t h e r m o h a l i n e . 1
INTRODUCTION The d i f f e r e n t b a s i n s of t h e N o r t h - W e s t e r n
Yediterranean, t h e Tyrrhe-
n i a n S e a , t h e L i q u r i a n S e a , t h e G u l f o f L i o n s and t h e C a t a l a n S e a a r e t h e s i t e o f g r e a t c y c l o n i c c i r c u i t s whose g e n e r a l o u t l i n e w a s s u g g e s t e d by N i e l s e n i n 1 9 1 2 . Most s t u d i e s o f t h e m a r i n e e n v i r o n m e n t a n d t h e n o d e l l i n g o f o b s e r v e d phenomena r e q u i r e a q u a n t i t a t i v e k n o w l e d g e of
w a t e r c i r c u l a t i o n . The w a t e r f l o w of t h e L i g u r i a n S e a f o r m s a n i m p o r t a n t l i n k i n t h e c i r c u l a t i o n of t h e W e s t e r n b a s i n , s i n c e it conn e c t s t h e Tyrrhenian Sea, t h e Algero-provenqal
b a s i n and t h e Gulf
of L i o n s . I n t h i s s t u d y , w e p r e s e n t f i r s t a d y n a m i c a l e v a l u a t i o n o f t h e water f l u x e s i n t h e L i q u r i a n Sea and o f t h e i r s e a s o n a l v a r i a t i o n s . B u t t h e d y n a m i c a l m e t h o d does n o t g i v e a n y i n f o r m a t i o n upon t h e ext e r n a l or i n t e r n a l f o r c e s w h i c h c r e a t e t h e m e a s u r e d d e n s i t y g r a d i e n t s . So, a f t e r , w e e x a m i n e w h a t may b e t h e r e s p e c t i v e e f f e c t s o f t h e ex-
t e r n a l f o r c e s , wind and a t m o s p h e r i c p r e s s u r e , on t h e d i f f e r e n t calculated fluxes. L a b o r a t o i r e de P h y s i q u e e t C h i m i e M a r i n e s , E r a CNRS, S t a t i o n M a r i n e , BP 8 , 06230 V i l l e f r a n c h e s u r M e r , F r a n c e . ( X x ) U n i v e r s i t 6 d e N e u c h a t e l , I n s t i t u t d e G E o l o g i e , 11 r u e E . A r q a u d , CH 2 0 0 0 N e u c h a t e l , S u i s s e .
130
44"
Ligurian Sea
43'
-
-
Strperficial Layer
,
.-...- P intermediate 7"
Layer
8"
9"
6 3 F i g . 1. Mean v a l u e s of f l u x e s ( i n 1 0 m / s e c , o r Sv) i n t h e s u p e r f i c i a l (0-200m) and i n t e r m e d i a t e (200-800m) l a y e r s , t h r o u g h t h e N i c e C a l v i s e c t i o n and t h e C o r s i c a n c h a n n e l .
131 2
FLUXES AND T H E I R SEASONAL VARIATIONS The p r e s e n c e of a M a r i n e S t a t i o n a t V i l l e f r a n c h e s u r M e r h a s a l l o w e d
t h e f r e q u e n t t a k i n g of m e a s u r e m e n t s o f f Nice and a l o n g t h e N i c e - C a l v i s e c t i o n , t h r o u g h t h e permanent c y c l o n i c c i r c u l a t i o n . T h i s c i r c u l a t i o n c o n c e r n s t h e s u p e r f i c i a l w a t e r ( a b o u t 0-200m)
and i n t e r m e d i a t e w a t e r
(200-800rn). Two s t r e a m s o f m e r i d i o n a l waters f l g w up b o t h s i d e s of Cor-
s i c a , j o i n a t t h e N o r t h o f Cap C o r s e and form t h e L i g u r i a n c u r r e n t which l a p s t h e s h o r e s o f t h e I t a l i a n R i v i e r a and t h e F r e n c h C 6 t e d'Azur. I n t h e case o f l a c k of d i r e c t m e a s u r e m e n t s , t h e knowledge of t h e c i r c u l a t i o n i s b a s e d on t h e c a l c u l a t i o n o f t h e g e o s t r o p h i c c u r r e n t a c r o s s t h e Nice-Calvi
s e c t i o n . D u r i n g t h e p a s t y e a r s , a growing number of
h y d r o l o g i c a l d a t a h a v e been e x p l o i t e d , ; ' and r e c e n t l y h y d r o l o g i c a l aver a g e s h a v e been c a l c u l a t e d , b a s e d on t h e c o m p l e t e m e a s u r e m e n t s c a r r i e d o u t d u r i n g t h e p e r i o d o f 1950-1973 and s t o r e d i n t h e a r c h i v e s of t h e d a t a bank o f t h e BNDO-COB
i n B r e s t ( N y f f e l e r e t a l . , 1980). Among 2 2 0 0
h y d r o l o g i c a l s t a t i o n s i n t h e L i g u r i a n S e a , m o r e t h a n 9 0 0 , on t h e N i c e C a l v i s e c t i o n , w e r e t h u s u s e d . The a v e r a g e a n n u a l f l o w s on t h i s sect i o n h a v e been c a l c u l a t e d a n d , t a k i n g i n t o a c c o u n t t h e w a t e r b u d g e t of t h e b a s i n , t h e f l u x e s t h r o u g h t h e C o r s i c a n c h a n n e l have been deduct e d and compared t o p r e v i o u s e s t i m a t i o n s (Bethoux e t a l . , 1 9 8 0 ) . I n f i g u r e 1 and i n t a b l e 1 are p r e s e n t e d t h e mean f l o w s r e l a t i n g t o t h e s u p e r f i c i a l (SL) and i n t e r m e d i a t e (IL) l a y e r s , t h e
+
sign indicates
a SW/NE f l o w ( o f f C a l v i ) o r a S/N f l o w ( C o r s i c a n c h a n n e l ) , and t h e s i g n i n d i c a t e s a f l o w i n a NE/SW d i r e c t i o n ( 1 Sv = 1 0 6m 3 /set).
-
TABLE 1
Mean f l o w s i n t h e s u p e r f i c i a l (SL) and i n t e r m e d i a t e ( I L ) l a y e r s i n t h e L i q u r i a n Sea N i c e side
SL IL
-
-
Calvi side
1.4 s v 0.4
+ +
0.7 0.2
sv
Corsican channel
+
+
0 . 7 Sv 0.2
T h e s e f l o w s a r e l a r g e , e s p e c i a l l y o f f N i c e , where t h e s t r o n g e s t c u r r e n t s s t a y c h a n n e l l e d i n t o a c o a s t a l band 2 0 t o 3 0 m i l e s wide. The s u r f a c e s p e e d s a r e between 2 0 t o 3 0 cm/sec and are below 5 cm/sec from 250m downwards (see F i g . 2 ) .
I n t h e c e n t r a l z o n e t h e a v e r a g e geo-
s t r o p h i c f l o w s are a l m o s t n u l l . T h e f l o w s on b o t h s i d e s of Cap Corse a r e , on an a v e r a g e , e q u a l , which shows t h e i m p o r t a n c e of t h e T y r r h e n i a n S e a o u t f l o w , p e r h a p s u n d e r e s t i m a t e d u p t o now.
132
500
10amB
800 .rn
i
1I
ZONE
14
15
10
NICE
\i
16
30
18
17
60
19
20
miles
8G
CALVI
F i g . 2. V e r t i c a l p r o f i l e s of c u r r e n t s t h r o u g h t h e Nice-Calvi (90 m i l e s , d i v i d e d i n t o 7 z o n e s numbered 1 4 t o 20).
section
133
For t h e s t u d y of t h e s e a s o n a l c y c l e s , based on h y d r o l o g i c a l c r i t e r i a and t a k i n g i n t o a c c o u n t t h e number of h y d r o l o g i c a l s t a t i o n s a v a i l a b l e e a c h month, t h e y e a r h a s been d i v i d e d i n t o 7 p e r i o d s which c o r respond t o t h e months : period : month :
1 I
2 I1
3
4 IV,V
I11
5 V1,VII
6 VIII;IX,X
7 X1,XII
The s e a s o n a l c y c l e s of t h e w a t e r f l o w s o f f Nice and C a l v i , and, f o r comparison, t h r o u g h t h e C o r s i c a n c h a n n e l , a r e shown i n f i g u r e 3 , f o r b o t h w a t e r l a y e r s examined. The flow on t h e h a l f s e c t i o n on t h e Nice s i d e shows a v e r y marked c y c l e , w i t h a n o t i c e a b l y h i g h r i s e between p e r i o d s 6 (August, September and O c t o b e r ) and 7 (November and December) from 1 . 4 t o 2.3 Sv. Near C a l v i , t h e " s e a s o n a 1 c y c l e of f l o w i s less marked and seems more i r r e g u l a r . I n comparison w i t h t h e two p r e c e d i n g c y c l e s , a c y c l e comparable t o t h a t found o f f N i c e i s found i n t h e Cors i c a n c h a n n e l , w i t h a v e r y marked f l u x i n c r e a s e between p e r i o d s 6 and 7 , when t h e t o t a l f l o w ( 0 - 4 0 0 m )
g o e s from 0 . 2 t o 1 . 8 Sv. On t h i s
graph concerning t h e flow through t h e Corsican channel, t h e d i r e c t measurements of S t o c c h i n o and T e s t o n i (1969) c a r r i e d o u t i n J u n e - J u l y 1966
(0.7 Sv) a r e shown t o g e t h e r w i t h t h o s e of LeFloch ( 1 9 6 3 ) performed
i n F e b r u a r y and i n August 1960 (1.5 and 0.4 Sv, r e s p e c t i v e l y ) . These d i r e c t f l o w measurements a g r e e w i t h o u r c a l c u l a t e d c y c l e and t h e geost r o p h i c c a l c u l a t i o n s . They a l s o c o n f i r m t h e c l e a r d e c l i n e of t h e f l o w between p e r i o d s 2 and 6. During p e r i o d 7, up t o about 30 m i l e s o f f N i c e , t h e a v e r a g e speed c a l c u l a t e d i s 2 8 cm/sec on t h e s u r f a c e and 3 cm/sec a t 3 0 0 m d e p t h . With r e g a r d t o p e r i o d 6 , t h e s p e e d s i n c r e a s e on a v e r a g e by 5 cm/sec between t h e s u r f a c e and 150m d e p t h . Moreover, o f f N i c e , a d e c r e a s e a p p e a r s i n t h e s a l i n i t y of t h e s u r f a c e up t o 300m, on a v e r a g e e q u a l t o 0.07°/oo
(see f i g u r e 4 ) . Such a v a r i a t i o n i n t h e s a l i n i t y cannot
be a r e s u l t of t h e s u r f a c e w a t e r budget
( t h e months of November and
December a r e r e l a t i v e l y r a i n y , b u t a t t h a t t i m e heavy e v a p o r a t i o n a l s o o c c u r s ) and t h e r e f o r e i t l e a d s t o t h e h y p o t h e s i s of t h e i n f l u x of l e s s s a l i n e w a t e r , o r i g i n a t i n g from t h e S o u t h . T h i s d e c r e a s e i n s a l i n i t y ,
i n e f f e c t , between p e r i o d s 6 and 7, can be e q u a l l y o b s e r v e d , i n t h e 0-1OOm
l a y e r , on b o t h s i d e s o f Cap Corse and even between weriod 5
and 6 off C a l v i . D i f f e r e n t a u t h o r s have s t u d i e d t h e e x t e r n a l f o r c e s e f f e c t s (wind, atmospheric p r e s s u r e
,
t i d e ) upon t h e s u p e r f i c i a l f l u x e s i n t h e Mediter-
r a n e a n . Among them, Crepon (1965) examined t h e e f f e c t s of t h e atmosp h e r i c p r e s s u r e v a r i a t i o n s on t h e s e a l e v e l , and E l l i o t t (1979) s t u d i e d
134
m3/s
f
lo6
CALVI
p l I
0 m3A
2.lo' CORSICA CHANNEL
Id
0
' 1 ' 2 ' 3 '
4
I
5
l
6
I
7
' 1 ' 2 ' 3 -
F i g . 3 . S e a s o n a l c y c l e s of f l u x e s o f f N i c e , o f f C a l v i and t h r o u g h t h e C o r s i c a n c h a n n e l . Direct m e a s u r e m e n t s of L e F l o c h (LF) and t h o s e of S t o c c h i n o and T e s t o n i (ST) t h r o u g h t h e C o r s i c a n c h a n n e l .
135
current speed
cmh
3
10
fi section periods 6and 7
20
30
m F i g . 4. V e r t i c a l p r o f i l e s of c u r r e n t s and s a l i n i t i e s , o f f N i c e , a t :’ p e r i o d 6 ( A u g u s t , S e p t e m b e r and O c t o b e r ) and 7 (November and December)
.
136 t h e wind e f f e c t on t h e sea l e v e l and c u r r e n t s i n t h e Gulf o f Genova, whereas Laevastu
( 1 9 7 2 ) shown t h a t a b o u t 1/4 o f t h e i n f l o w i n g A t l a n t i c
w a t e r s r e s u l t from t h e t i d a l e f f e c t s ( a m p l i t u d e d i f f e r e n c e a t o p p o s i t e e n d s of t h e s t r a i t s ) t h r o u g h t h e S t r a i t of G i b r a l t a r . S i n c e V i l l a i n ( 1 9 4 9 , 1 9 5 2 ) v e r y f e w s t u d i e s a b o u t M e d i t e r r a n e a n t i d e s h a v e been c a r r i e d o u t . So it i s n o t p o s s i b l e t o e s t i m a t e t i d e e f f e c t s upon t h e c i r c u l a t i o n i n s i d e t h e M e d i t e r r a n e a n . However, owing t o P u r g a e t a l . (19791, t i d e i s s y n c h r o n o u s i n t h e T y r r h e n i a n S e a , and s o , it may have a s t a -
t i c e f f e c t ( s u c h a s a t m o s p h e r i c p r e s s u r e ) on t h e sea l e v e l and on t h e superficial circulation. W e have l o o k e d f o r t h e p o s s i b l e c l i m a t i c e x t e r n a l c a u s e s of t h e i m -
p o r t a n t mean c a l c u l a t e d f l u x e s f i r s t , and t h e n ,of t h e s e a s o n a l c y c l e , by e x a m i n i n g t h e e f f e c t s of wind and o f a t m o s p h e r i c p r e s s u r e v a r i a t i o n s on t h e w a t e r c i r c u l a t i o n , on a m o n t h l y scale. 3
WINDS I N THE NORTH-WESTERN MEDITERRANEAN SEA
I n o r d e r t o make a c o m p a r i s o n w i t h h y d r o l o g i c a l a v e r a g e s ( r e f e r r i n g t o t h e y e a r s 1953-1973) w e have u s e d t h e wind a v e r a g e s r e l a t i v e t o t h e p e r i o d 1951-1960,
o b t a i n e d from t h e m e t e o r o l o g i c a l s t a t i o n s of
Cap BBar, S P t e , PomPgues, Cap C a m a r a t , Cap F e r r a t and Cap Corse (Darchen and DeBlock, 1 9 6 8 ) , which g i v e t h e s p e e d , t h e o r i g i n and t h e f r e q u e n c y of wind f o r e a c h month.
I t i s p o s s i b l e t o e v a l u a t e t h e con-
s e q u e n t d r i f t f l u x , F , a t 90° t o t h e w i n d , l i n k e d t o t h e s q u a r e of t h e wind s p e e d , V , by t h e e m p i r i c a l e q u a t i o n :
2
F =
K pa V 2 w s i n e pw
where p a and p w a r e a i r and w a t e r d e n s i t i e s . I f w e assume t h e adimens i o n a l f r i c t i o n c o e f f i c i e n t , K , be e q u a l t o 2 m3/sec/m
--
2.7
10-2
v2
t h e equation is:
m/sec
3 . 1 Wind a t N i c e (Cap F e r r a t ) T h e a v e r a g e s p e e d of wind a t Cap F e r r a t , from a l l d i r e c t i o n s , i s 2 . 1 m/sec.
However, a s a r e s u l t of d i f f e r e n t s e c t o r s , f r e q u e n c i e s and
s p e e d s of w i n d , t h e r e s u l t i n g a v e r a g e wind s p e e d , V , f a v o u r a b l e t o t h e f l o w (NE/SW) i s o n l y a b o u t 1 m/sec
( s e e F i g . 5 ) . On a h a l f s e c t i o n
4 5 m i l e s o f f N i c e , t h e a v e r a g e f l o w r e s u l t i n g from t h e wind i s a b o u t 2.2
103m3/sec,
t r o p h i c flow.
t h a t i s around one t h o u s a n d t h of t h e c a l c u l a t e d geosI n a d d i t i o n , t h e s e a s o n a l wind c y c l e e x p l a i n s n e i t h e r
q u a l i t a t i v e l y nor q u a n t i t a t i v e l y t h e f l o w c y c l e o f f N i c e .
137
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XI1 month-
F i g . 5. S e a s o n a l c y c l e of mean r e s u l t i n g w i n d , owing t o i t s s p e e d , f r e q u e n c y , o r i g i n and t o t h e mean l o c a l water c i r c u l a t i o n .
138 3 . 2 Wind o n e i t h e r s i d e o f Cap Corse
T h e c o n s e q u e n t average wind a t Cap Corse i s a l w a y s f r o m t h e N o r t h
o r West s e c t o r s , and it i s t h e r e f o r e a l w a y s u n f a v o u r a b l e t o t h e SW/NE c i r c u l a t i o n o f f C a l v i , a s w e l l a s t o t h e S/N c i r c u l a t i o n t h r o u g h t h e Corsican channel.
Its r e s u l t i n g annual averaqe i s -4.8
f l o w o f f C a l v i , and - 4 . 6
m/sec
m/sec f o r t h e f o r t h e f l o w coming f r o m tce T y r r h e n i a n
S e a . I n a d d i t i o n , t h e s e a s o n a l wind c y c l e h a s n o a p p a r e n t c o n n e c t i o n w i t h t h a t of t h e flows. 3 . 3 Wind i n t h e G u l f o f L i o n s
I n o r d e r t o s t u d y a p o s s i b l e e f f e c t o f t h e wind downstream o f t h e c u r r e n t s , w e e x a m i n e d t h e d a t a o n wind r e l a t i n g t o t h e s t a t i o n s o f t h e G u l f of L i o n s . A t Cap B & a r , S B t e and Porni5gueG t h e d o m i n a n t w i n d ,
a n o r t h w e s t e r l y w i n d , i s t h e r e f o r e f a v o u r a b l e to t h e c i r c u l a t i o n i n t h e o p e n sea (NE/SW). T h e r e s u l t i n g a v e r a g e wind s p e e d s a r e 6 m/sec
a t PomGgues, 1 . 9 m/sec a t S G t e and 9 m / s e c
a t Cap B B a r . F o r t h e l a t t e r
s t a t i o n , w h i c h c o r r e s p o n d s t o t h e m o s t f a v o u r a b l e case ( s e e f i g u r e 5 )
,
t h e NE/SW f l o w g e n e r a t e d b y t h e wind a l o n g a w i d t h o f 4 5 m i l e s i s about 0.2 Sv, which s t i l l o n l y r e p r e s e n t s n e a r l y a t e n t h of t h e geost r o p h i c water f l o w c a l c u l a t e d o f f N i c e . F u r t h e r m o r e a g a i n , t h e s e a s o n a l wind c y c l e d o e s n o t s e e m t o a c c o u n t f o r t h e w a t e r f l o w c y c l e . G a l e s p l a y a n i m p o r t a n t r o l e a s much o n t h e s u r f a c e f l o w ( a d v e c t i o n phenomena) a s o n t h e o c e a n - a t m o s p h e r e
interchanges,particularly i n
t h e Gulf o f L i o n s . But w i t h r e g a r d s t o t h e a v e r a g e c i r c u l a t i o n o f a c y c l o n i c t y p e i n t h e North-Western M e d i t e r r a n e a n , w i n d s c a n o n l y gene-
r a t e a b o u t a t e n t h of t h e c a l c u l a t e d f l o w s , i n t h e m o s t f a v o u r a b l e c a s e , i . e . i n t h e G u l f o f L i o n s . I n t h e Cap Corse s e c t o r , wind i s countrary t o t h e circulation, while off N i c e ,
it i s o n l y s l i g h t l y
f a v o u r a b l e . T h e r e f o r e t h e r e i s d e f i n i t e l y n o d i r e c t r e l a t i o n between t h e w a t e r f l u x e s and t h e w i n d s , on a m o n t h l y o r s e a s o n a l s c a l e , i n t h e North-Western Mediterranean. 4
ATMOSPHERIC PRESSURE I N THE WESTERN MEDITERRANEAN The a t m o s p h e r i c d i s t u r b a n c e s a b o v e . t h e M e d i t e r r a n e a n h a v e been
s t u d i e d i n p a r t i c u l a r by B e r e n g e r ( 1 9 5 5 ) . One p e c u l i a r i t y , d u e t o t h e g e o g r a p h i c p o s i t i o n and t h e m o u n t a i n o u s s u r r o u n d i n g s , i s t h a t 73% o f t h e d e p r e s s i o n s i n t h e M e d i t e r r a n e a n are formed a b o v e t h i s
sea, c h i e f l y i n t h e W e s t e r n b a s i n . I n t h i s b a s i n , t h e most f r e q u e n t a r e t h e G u l f o f Genova ( 5 0 % ) , t h e B a l e a r i c ( 2 5 % ) a n d t h e S a h a r a n d e p r e s s i o n s . T h e s e d i s t u r b a n c e s o c c u r p r i n c i p a l l y i n autumn
,
winter
139 and s p r i n g . T h e r e i s t h e r e f o r e a marked c o n t r a s t between summer and t h e other seasons. V a r i o u s a u t h o r s h a v e d e a l t w i t h t h e q u a l i t a t i v e l i n k a g e between a t m o s p h e r i c p r e s s u r e and sea l e v e l i n t h e M e d i t e r r a n e a n . L i s i t z i n (1954) s t u d i e d t h e s e a s o n a l v a r i a t i o n s i n t h e sea l e v e l i n d i f f e r e n t s p o r t s , where t h e s e a l e v e l u n d e r g o e s a g r e a t i n c r e a s e , i n O c t o b e r and November b e f o r e d e c r e a s i n g a t t h e beginning of t h e y e a r . T h i s c y c l e t h e r e f o r e p r e s e n t s remarkable analogies with t h e c u r r e n t wariations off N i c e , but, according t o P a t t u l l o et al.
(1955). a high sea l e v e l during t h e
f a l l ( a low s e a l e v e l d u r i n g s p r i n g ) i s a s s o c i a t e d w i t h t e m p e r a t u r e and s a l i n i t y f l u c t u a t i o n s i n . t h e u p p e r 1OOm ( s p e c i f i c volume f l u c t u a tions)
.
However, a t Monaco, M a r s e i l l e , , , and P o r t o - M a u r i z i o ,
Lisitzin
found q u i t e a good c o r r e l a t i o n between t h e m o n t h l y v a r i a t i o n s i n t h e s e a l e v e l and t h o s e o f t h e a t m o s p h e r i c p r e s s u r e . A c c o r d i n g t o Crepon (19651, t h e v a r i a t i o n s i n a t m o s p h e r i c p r e s s u r e , i n e f f e c t , a r e t h e e s s e n t i e l c a u s e of t h e v a r i a t i o n s i n t h e a v e r a g e l e v e l o f v a r i o u s p o r t s i n t h e W e s t e r n b a s i n . On t h e o t h e r h a n d , a c c o r d i n g t o Lacombe ( 1 9 6 0 ) , a l o w e r i n g o f t h e a t m o s p h e r i c p r e s s u r e upon t h e M e d i t e r r a n e a n i n v o l v e s an i n c r e a s e o f t h e i n f l o w (0-200111) t h r o u g h t h e S t r a i t s of G i b r a l t a r , i n c o u n t e r p a r t , a r i s e o f t h e o u t f l o w ( a t more t h a n 180m d e p t h ) w i l l accompany a rise o f t h e a t m o s p h e r i c p r e s s u r e . In order t o estimate t h e f l u x e s due t o t h e atmospheric v a r i a t i o n s of s e a l e v e l , w e s t u d i e d t h e M e d i t e r r a n e a n a t m o s p h e r i c p r e s s u r e v a r i a t i o n s a s a f u n c t i o n o f t h e s e a s o n s , whose e x a m p l e s a r e g i v e n i n f i g u r e 6.
-
The Gulf o f Genova b e i n g a low p r e s s u r e c e n t e r a l l a l o n g t h e y e a r ,
a h o r i z o n t a l g r a d i e n t o f p r e s s u r e e x i s t s from G i b r a l t a r t o Genova-The s e a s o n a l c y c l e of t h e f i g u r e 6 a , e s t i m a t e d from t h e d a t a i n 'Weather i n the Mediterranean'
-
(1962)
,
shows a jump between p e r i o d 6 and 7.
The f i g u r e 6 b i s a r e p r o d u c t i o n o f t h e a v e r a g e s e a s o n a l c y c l e of
t h e a t m o s p h e r i c p r e s s u r e a t N i c e , f o r t h e y e a r s 1951-1960
(Garnier,
1 9 6 6 ) . The a v e r a g e p r e s s u r e i s maximum d u r i n g p e r i o d 6 and minimum i n
F e b r u a r y o r March.
-
The l o c a l a t m o s p h e r i c p r e s s u r e shows a marked s e m i - d i u r n a l c y c l e ,
whose a m p l i t u d e a t N i c e ( f i g u r e 6 c ) v a r i e s from 0.7mb i n p e r i o d 6 t o a b o u t 0.9mb i n p e r i o d 7 . Owing t o t h e s e a s o n a l c y c l e s o f t h e a t m o s p h e r i c p r e s s u r e
(figures 6
a , b and c ) it i s p o s s i b l e t o f i n d q u a l i t a t i v e c o r r e l a t i o n s between f l u x e s and a t m o s p h e r i c p r e s s u r e v a r i a t i o n s o f f N i c e .
However, o n l y
t h e s e m i - d i u r n a l a t m o s p h e r i c p r e s s u r e v a r i a t i o n ( F i g . 6 c ) can p r o d u c e
140
m o r e o r l e s s p e r m a n e n t f l u x e s , on a m o n t h l y o r s e a s o n a l s c a l e . F o r t h e whole M e d i t e r r a n e a n ( a r e a a b o u t 2 . 5 1 0 1 2 r n 2 ) , a s e m i - d i u r n a l a m p l i t u d e of t h e a t m o s p h e r i c p r e s s u r e of a b o u t 0.8mb i n v o l v e s a maximum i n - o r - o u t
f l o w i n g f l u x e s o f 0 . 4 6 S v , t h a t i s a b o u t 3 0 % of t h e e s t i -
mated f l u x e s t h r o u g h t h e S t r a i t s of G i b r a l t a r ( B e t h o u x , l 9 7 9 ) . The f l u x e s o f f N i c e f o r m i n g a n i m p o r t a n t b r a n c h of t h e c i r c u l a t i o n i n t h e W e s t e r n b a s i n , it i s d i f f i c u l t t o know t h e i n f l u e n c e a r e a of t h e a t m o s p h e r i c p r e s s u r e v a r i a t i o n s . A s a rough e s t i m a t e , i f w e suppose t h a t t h e s t a t i c v a r i a t i o n s of t h e s e a l e v e l o f a b o u t h a l f of t h e Wes12 2 t e r n b a s i n ( 0 . 4 1 0 m ) a c t on t h e f l u x e s o f f N i c e , t h e a t m o s p h e r i c s e m i - d i u r n a l v a r i a t i o n s may p r o d u c e a b o u t 10% of t h e c a l c u l a t e d f l u x e s . S e m i - d i u r n a l v a r i a t i o n s o f t h e a t m o s p h e r i c p r e s s u r e may be an i m p o r t a n t cause of t h e Mediterranean c i r c u l a t i o n , s p e c i a l y through t h e S t r a i t s of G i b r a l t a r
(and S i c i l y ) . B u t , i n t h e L i g u r i a n S e a , t h e y d o n o t seem
t o i n v o l v e more t h a n 1 0 % o f t h e f l u x e s , and d o n o t e x p l a i n t h e i n c r e a s e o f t h e f l u x e s between p e r i o d 6 and 7.
A P(GIBRALTAR 3-
- GENOVA)
6a
2
c
P(NICE)
15t
6b
1 -
--
-
A P(NICE)
65
0.5
- 1
' 1 ' 2 ' 3 '
4
IV ' V
I
I
I
5 Vl
I
Vlf
I
VIiI
'
6 IX
1
7
I
period
X ' XI ' XI1 ' month
F i g . 6 . S e a s o n a l c y c l e of a t m o s p h e r i c p r e s s u r e d i f f e r e n c e s between G i b r a l t a r and Genova ( 6 a ) , o f mean a t m o s p h e r i c p r e s s u r e i n Nice ( 6 b ) and of i t s s e m i - d i u r n a l v a r i a t i o n s ( 6 c ) .
141 5
CONCLUSION
The u s e of a v e r a g e s , c a l c u l a t e d from a g r e a t number o f h y d r o l o g i c a l s t a t i o n s between N i c e and C a l v i , a l l o w s n o t o n l y t h e a v e r a g e a n n u a l v a l u e o f t h e f l o w s b u t a l s o t h e i r s e a s o n a l v a r i a t i o n s t o be o b t a i n e d . These r e s u l t s s h o u l d be u s e f u l i n d i f f e r e n t s t u d i e s i n dynamics, chem i s t r y o r marine biology. ,.
The L i g u r i a n Sea i s a n i m p o r t a n t l i n k i n t h e c i r c u l a t i o n o f w a t e r i n t h e N o r t h Western M e d i t e r r a n e a n , and i t s e e m s t o be n e c e s s a r y t o p r o v e t h e c a l c u l a t e d f l o w s by d i r e c t measurements on t h e s e c t i o n s o f t h e R i v i e r a - C o r s i c a and E l b a - C o r s i c a . The C o r s i c a n c h a n n e l a p p e a r s t o be one o f t h e key p o i n t s i n t h e u n d e r s t a n d i n g of t h e dynamics o f t h e Mediterranean. I The s t u d y o f m e t e o r o l o g i c a l d a t a o b t a i n e d on t h e North-West c o a s t s l e a d t o a t t r i b u t e a r e d u c e d e f f e c t on t h e a v e r a g e water f l o w s and on t h e i r s e a s o n a l v a r i a t i o n s by t h e m e c h a n i c a l a c t i o n o f wind. On t h e o t h e r hand, t h e s e m i - d i u r n a l v a r i a t i o n o f a t m o s p h e r i c p r e s s u r e may o n l y p r o d u c e a b o u t 10% o f t h e f l u x e s , and c a n n o t e x p l a i n t h e a n n u a l c y c l e of t h e c i r c u l a t i o n o f f N i c e . S i n c e t h e s e two e x t e r n a l f o r c e s , wind and a t m o s p h e r i c p r e s s u r e , e x e r t moderate e f f e c t s , t h e c i r c u l a t i o n should be c h i e f l y thermohaline. The i n i t i a l c y c l o n i c g y r e , c e r t a i n l y produced by t h e water d e f i c i t (Bethoux,l980)
,
i s a m p l i f i e d by t h e a r r i v a l a t t h e p e r i p h e r y o f t h e
b a s i n of waters coming from t h e s o u t h e r n r e g i o n s . These w a t e r s a r e r e l a t i v e l y warmer and l e s s s a l i n e t h a n t h o s e o f t h e c e n t r a l a r e a . S u c h a t h e r m a l a d v e c t i o n by t h e s u r f a c e w a t e r s i s s u e d from t h e T y r r h e n i a n S e a i s c l e a r l y v i s i b l e on t h e i n f r a - r e d
et a1.,1979).
s a t e l l i t e p i c t u r e s (Bethoux
The i n c r e a s e o f t h e c i r c u l a t i o n between p e r i o d 6 and 7
is d u e t o t h e d e n s i t y c o n t r a s t between t h e c o a s t a l and c e n t r a l waters. I n t h e c e n t r a l a r e a , t h e sea u n d e r g o e s t h e e f f e c t s o f t h e n e g a t i v e h e a t and w a t e r b u d g e t s w i t h t h e a t m o s p h e r e , w h i l e , i n t h e p e r i p h e r y a r e a , s u c h e f f e c t s a r e lowered by t h e r m a l a d v e c t i o n o f s o u t h e r n waters and by c o a s t a l r u n o f f .
Acknowledgements- T h i s work w a s s u p p o r t e d by CNEXO ( c o n t r a c t 79/2084) CNRS (GRECO 3 4 ) and Fonds N a t i o n a l S u i s s e d e l a Recherche S c i e n t i f i q u e [ p r o j e c t 2 . 2 8 0 . 0 7 9 ) . T h a n k s a r e due t o F. L o u i s , who d r a f t e d t h e f i g u r e s .
142 REFERENCES B e r e n g e r , M. ,1955. E s s a i d ' b t u d e m S t 6 o r o l o g i q u e d u b a s s i n m s d i t e r r a ngen. Mgmorial d e l a M 6 t C o r o l o g i e N a t i o n a l e , 4 0 , 42pp. Bethoux , J . P . , 1 9 7 9 . B u d g e t s o f t h e M e d i t e r r a n e a n S e a . T h e i r dependance on t h e l o c a l c l i m a t e and on t h e c h a r a c t e r i s t i c s of t h e A t l a n t i c waters. O c e a n o l . A c t a , 2 , 2 , 1 5 7 - 1 6 3 . Bethoux , J . P . ,1960. Mean w a t e r f l u x e s a c r o s s s e c t i o n s i n t h e M e d i t e r r a n e a n S e a , e v a l u a t e d on t h e b a s i s of water and s a l t b a g e t s and of o b s e r v e d s a l i n i t i e s . Oceanol. Acta,3,1,79-88. B e t h o u x , J . P . , P r i e u r , L. and A l b u i s s o n , M. ,1979. A p p o r t s d e l a t ' e l 8 d e t e c t i o n i n f r a - r o u g e Fi l a c o n n a i s s a n c e d e l a c i r c u l a t i o n s u p e r f ic i e l l e d a n s l a p a r t i e Nord-Est du b a s s i n O c c i d e n t a l . Rapp.Com. i n t . Mer M g d i t . , 25-26. B e t h o u x , J . P . , N y f f e l e r , F. and P r i e u r , L. ,1960. U t i l i s a t i o n d e moyennes hydrologiques pour l e c a l c u l d e s f l u x d'eau dans l e bassin Lig u r o - p r o v e n q a l , X X V I I C o n g r e s C I E S M , C a g l i a r i , 9 - 1 8 o c t o b r e 1980,4pp. C r e p o n , M.,1965. I n f l u e n c e d e l a p r e s s i o n a t m o S p h e r i q u e s u r l e n i v e a u moyen d e l a M g d i t e r r a n g e O c c i d e n t a l e e t s u r l e f l u x a t r a v e r s l e d 6 t r o i t d e G i b r a l t a r . C a h i e r s O c b a n o g r a p h i q u e s , XVII,1,15-32. D a r c h e n , J. and d e B l o c k , A. ,1968. Le v e n t s u r l e s c 6 t e s d e l a F r a n c e M 6 t r o p o l i t a i n e , M 6 d i t e r r a n G e . Monographies d e l a M E t 6 o r o l o g i e N a t i o n a l e , 6 2 ,2 ,9 7pp. E l l i o t t , A . J . , 1 9 7 9 . The e f f e c t of l o w f r e q u e n c y w i n d s on s e a l e v e l and c u r r e n t s i n t h e G u l f o f Genova. O c e a n o l . A c t a , 2 , 4 , 4 2 9 - 4 3 3 . Climatologie d e l a France, Elements d e l a v a r i a t i o n G a r n i e r , M.,1966. d i u r n e . Memorial d e l a M G t g o r o l o g i e N a t i o n a l e , 5 1 , 1 4 8 p p . Lacombe, H.,lY60. Note s u r l e r e g i m e du d d t r o i t d e G i b r a l t a r . Memoires e t T r a v a u x d e l a S.H.F.,11,136-143. L a e v a s t u , T. ,1972. R e p r o d u c t i o n o f c u r r e n t s and w a t e r e x c h a n g e i n t h e S t r a i t of G i b r a l t a r w i t h h y d r o d y n a m i c a l n u m e r i c a l model of Walter Hansen. I n : S t u d i e s i n P h y s i c a l Oceanography. A r n o l d L . G o r d o n , e d i t o r , Gordon and B r e a c h , 2 , 2 1 9 - 2 3 2 . L e F l o c h , J . ,1963. S u r l e s v a r i a t i o n s s a i s o n n i e r e s d e l a c i r c u l a t i o n s u p e r f i c i e l l e d a n s l e s e c t e u r Nord-Est d e l a M 6 d i t e r r a n 6 e Occident a l e . CRE0,5,1,5-10. L i s i t z i n , E . ,1954. L e s v a r i a t i o n s du n i v e a u d e l a m e r Fi Monaco,Compar a i s o n avec q u e l q u e s a u t r e s s t a t i o n s m a r 6 g r a p h i q u e s d e l a c6te f r a n qaise e t i t a l i e n n e . B u l l . Inst.Oc6an.Monaco,1040 ,24pp. Nielsen, J.N.,1912. Hydrography of t h e M e d i t e r r a n e a n and a d j a c e n t wat e r s . D a n i s h Oceanog.Exp.1908-1910,Rep.VI177-191. N y f f e l e r , F. , R a i l l a r d , J. and P r i e u r , L. ,1960. L e b a s s i n L i g u r o - p r o v e n q a l , E t u d e s t a t i s t i q u e des d o n n 6 e s h y d r o l o g i q u e s 1950-1973. Rapp o r t s s c i e n t i f i q u e s e t t e c h n i c y e s CNEX0,42,163pp. P a t t u l l o , J.,Munk, W . , R e v e l l e , R. and S t r o n g , E.,1955. The s e a s o n a l o s c i l l a t i o n s i n s e a l e v e l . J . o f Marine Research,14,1,88-123. P u r g a , N . , M o s e t t i , F . and A c c e r b o n i , E . ,1979. T i d a l harmonic c o n s t a n t s f o r some M e d i t e r r a n e a n h a r b o u r s . B o l l e t i n o D i G e o f i s i c a T e o r i c a Ed A p p l i c a t a , XXI,81,72-81. S t o c c h i n o , C. and T e s t o n i , A . , 1 9 6 9 . Le c o r r e n t i n e l canale d i Corsica e n e l l ' a r c h i p e l a g o Toscan0,C.N. R. , S e r . A,19,26pp. V i l l a i n , M . C . , 1 9 4 9 . S u r l a maree Fi A l g e r e t en M b d i t e r r a n b e Occident a l e . COEC ,9 ,1 6 - 1 9 . V i l l a i n , M.C. ,1952. L e s m a r 6 e s d e l a M b d i t e r r a n g e O r i e n t a l e . COEC, IV,3,92-103. Weather i n t h e Mediterranean,Meteorological o f f i c e , l 9 6 2 . H e r M a j e s t y ' s S t a t i o n e r y Off i c e , London, 3 62pp.
ANALYSIS O F UPWELLING I N T H E GULF O F LIONS MILLOT C l a u d e X
A B ST R A C T
The s a l i e n t f e a t u r e s i n a reference paper
of
1979).
(Millot,
infrared thermographies. surface layer,
t h e u p w e l l i n g phenomenon,
are f i r s t described with
Some h y p o t h e s i s
s u p p o r t e d by
already presented
a b o u t t h e dynamics of
the
t h e sea surface temperature distribution,
have been v e r i f i e d and completed by numerous i n s i t u measurements. Numerical and a n a l y t i c a l models have been performed, possible
t o e v a l u a t e t h e e f f e c t s of
l o c a l i s a t i o n of
the cool water
some p a r a m e t e r s on b o t h
source points,
h o r i z o n t a l c i r c u l a t i o n s . The dynamics
of
I-THE
t h e view
the Roussillon very d i f f e r e n t .
A t
a
l a r g e scale,
c o a s t and o f f Although
i n Millot
(1981)).
;
Antenne
2,
(fig 1);
t h e sea s u r f a c e t e m p e r a t u r e s
off
i s t h e most windy r e g i o n ,
t h e same t e m p e r a t u r e a s t h e o p e n s e a .
s u r f a c e waters are d r i f t e d
t o the south-
they a r e accumulated along t h e Roussillon c o a s t s
when u p w e l l i n g
BP
are strong north-westerlies
the Roussillon
Due t o t h e C o r i o l i s f o r c e ,
:
( a much m o r e d e t a i l e d
t h e Languedoc and Provence c o a s t s a r e
t h e coastal waters have n e a r l y
x
of
i n f i g 2 h a s been o b t a i n e d a b o u t one day a f t e r t h e o n s e t
t h e s e winds.
west
and t h e s t r u c t u r e of
THERMOGRAPHIES
The M i s t r a l and t h e Tramontane
of
the
u p w e l l i n g i n t h e Gulf
L i o n s s e e m s t o b e now c o r r e c t l y u n d e r s t o o d and complete a n a l y s i s i s p r e s e n t e d
and i t h a s been
(downwelling)
i s o b s e r v e d a l o n g t h e c o a s t s o f Languedoc and Provence.
du L a b o r a t o i r e d ' o c e a n o g r a p h i e
83501 La Seyne, F r a n c e .
P h y s i q u e d u Museum
144
Fig 1
:
The s t u d i e d a r e a .
SEA SURFACE TEMPERATURE DISTRIBUTION on 08-01-77 obout one day after the onset of a NW storm. Isotherm interval is 0.5OC and grey interval is l 0 C
Fig 2
:
The i n f r a r e d t h e r m o g r a p h y o b t a i n e d o n t h e
a t a b o u t 09 00 T U .
1 s t of August
1917,
145 t h e upwelling i s discontinuous
A t a smaller s c a l e ,
The b a t h y m e t r y i s r a t h e r s m o o t h a n d t h e w i n d f i e l d i s r a t h e r
in fig 2). homogeneous
i n t h e Camargue c o a s t a l a r e a
t i n u i t y i s an i n t e r e s t i n g observation. f r o m some u p w e l l i n g z o n e s .
; consequently,
The t o n g u e a s s o c i a t . e ? d w i t h z o n e A s u g g e s t s
isotherms i n t h e south-western I n some c o a s t a l a r e a s ,
p a r t of
b u t when o b s e r v e d ,
;
( %
the upwelling zones,
l°C/
t h e upwelling zones
a r e observed.
( i n t e n s i t y , dimension,
...I
I n order t o estimate the sea surface
temperature m a p observed during north-westerly
c h a r a c t e r i s t i c s of
some km)
t h e upwelled waters a r e l o c a t e d i n t h e zones A , . . . , F .
v a r y from one view t o t h e o t h e r .
15 p h o t o s .
the
wind i s n o t a l w a y s blowing o v e r t h e e n t i r e g u l f ,
The c h a r a c t e r i s t i c s o f
summed
correlatively,
t h e g u l f r e v e a l a n eddy s t r u c -
on t h e edge of
large alongshore temperature gradient: The n o r t h - w e s t e r l y
t h i s discon-
Cool s u r f a c e tongues extend
a c o o l seaward c u r r e n t t u r n i n g t o t h e r i g h t
ture.
(zones A-F
From t h e mean map
wind e v e n t s , w e h a v e
( f i g 3 ) , it appears t h a t the
t h e upwelling already described a r e very s i g n i -
ficant.
+,
Fig 3
:
UPWELLING IN T H E GULF OF LIONS The m w n distribution of the sea surface temperature is computed from the summatim of 15 infra red satellite views. Isotherm interval is 0.5%.
T h e mean d i s t r i b u t i o n o f
by s u m m a t i o n o f
15 p h o t o s .
t h e sea surface temperature obtained
146 2.-
THE I N S I T U M E A S U R E M E N T S The d a t a o b t a i n e d
the reference paper
in ;
1974,
1975, and 1977 have been p r e s e n t e d
i n
w e w i l l now d i s c u s s t h o s e o b t a i n e d i n 1 9 7 8
(fig 4 for instance).
To A
10m
To A
3Om
B
10m
To B
30m
To E
30m
To
TEMPERATURE.
I5
5 -
2
10
2
15
-C
IOm
A
SURFACE CURRENT u X c m r’ C
E
10m
BOTTOM CURRENT
10 c m s-’
Fig 4
:
The d a i l y w i n d s a n d c u r r e n t s a n d some t e m p e r a t u r e r e c o r d s
from September 4 t o
15,
1 9 7 8 . V e c t o r s a r e p l o t t e d i n s u c h a way t h a t
t h e v e r t i c a l a x i s is n o r t h - s o u t h .
147 2.1-
The t e m p e r a t u r e d a t a
During t h e g u s t s of wind,
t h e s e d a t a show t h a t t h e s t r a t i f i c a t i o n
i s much m o r e d i s t u r b e d b y a d v e c t i o n , waves a t t h e i n e r t i a l f r e q u e n c y
( M i l l o t and Crdpon,
The t e m p e r a t u r e r e c o r d s a t
mixing.
an upwelling at
78-A
up and downwelling,
10 a n d 3 0 m
and a downwelling a t 78-E.
the temperature is decreasing
surface,
v a l u e s o b s e r v e d b e f o r e t h e wind e v e n t t i o n of
1981)
(?ig
4)
A t
78-B
than by
c l e a r l y show near
the
and t h e n i n c r e a s i n g up t o t h e :
i s c l e a r l y due t o advec-
this
( r e v e a l e d b y t h e to?,gue)
i n the surface layer
The m a i n t e m p e r a t u r e s o v e r t h e w h o l e e x p e r i m e n t a t 78-B
only.
78-E
cool water
internal
and
a r e n e a r l y t h e same.
2 . 2 The s u r f a c e c u r r e n t d a t a These d a t a are i n s t r u c t i v e l a t i o n from t h e g e n e r a l one. supported by a s t a t i s t i c a l
i f we s e p a r a t e t h e w i n d i n d u c e d c i r c u The f e a t u r e s
a n a l y s i s o v e r t h e whole experiment
1 9 8 0 ) . F i g 5 shows t h a t d u r i n g t h e wind e v e n t s ,
( M i l l o t and Wald,
t h e mean s u r f a c e c u r r e n t a t 7 8 - B
to the N
(11 cm/s)
surface current When c o m p a r i n g
suggested i n f i g 4 are
a t 78-E.
A t
i s t o t h e SSE
78-E,
(21 cm/s)
t h e o b s e r v e d wind
t h e c u r r e n t a n d t e m p e r a t u r e d a t a a t 78-B
t h a t t h e characteristics of
t h i s northward
the coastal current presented
Millot
(1981).
L e t us mention
c u r r e n t are d i f f e r e n t from
i n a preceding paper
1 9 7 6 ) , a l t h o u g h b o t h a r e i n d u c e d by t h e w i n d . continental shelf
and 78-E,
a r e concerned with an a n t i c y c l o n i c
c i r c u l a t i o n i n d u c e d by t h e wind i n t h e s u r f a c e l a y e r .
t h e whole
induced
i s roughly opposed t o t h e t h e o r e t i c a l d r i f t c u r r e n t
it appears t h a t the 2 points
those of
when i t i s
(Millot,
The c i r c u l a t i o n o v e r
i s d e s c r i b e d w i t h much m o r e d e t a i l s
in
148
/
50 m
Meon surfoce currenlr ( thick orrows ) during
the whole 85
- day
experiment ( _ _ ) o l e seporoled
into mean currenls during 40.5 stormy days (
-
1
ond meon currenls during I h e rsmoining 44.5 days
For bollom currenls ( thin a r r o w s ) is
divided into periods of 20 doys (
, tho
i.,... 1.
6 9 - day eaperimenl (
-
) and 49 days (
__ )
...._.. ) respeClivelY.
Voluss ore in cm.r -I. Bollom mcasuremsnls ore mode a1 9 3 m ( B
Fig 5
:
38 m ( A )
D e p e n d e n c e o f mean s u r f a c e a n d b o t t o m c u r r e n t s u p o n t h e
occurrence of
2.3
ond
north-west
storms.
The b o t t o m c u r r e n t d a t a
These d a t a
( f i g 4 a n d 5 ) r e v e a l more homogeneous f e a t u r e s .
( 5 0 m) a n d a t 7 8 - B
(100 m)
,
5 cm/s
t o t h e NE
values
a r e observed a t 77-C
1979).
Then,
(A,.
along t h e isobaths
( M i l l o t and Wald,
( f i g 1 ) on t h e e d g e o f
t h e whole bottom
.., F ) .
78-A
t h e mean s p e e d i n d u c e d by t h e w i n d i s
layer
from t h e downwelling zone t o t h e N E , zones
A t
1980). Similar
the shelf
(Millot,
is a d v e c t e d by t h e n o r t h - w e s t e r l i e s and l o c a l l y t o t h e upwelling
149 3-INTERPRETATION 3.1
A N D MODELISATION
The d i s c o n t i n u i t y and t h e l o c a l i s a t i o n o f
The n o n - i n f l u e n c e
of
the spatial variability of both
stress applyes only t o zones A ,
and t h e wind
tends to be parallel t o the coast,
wind
upwelling
and
t h e bathymetry
. . . ,E
( i n zone F , t h e -* the continental shelf
i s r e d u c e d ) . Some h o u r s a f t e r t h e o n s e t o f
t h e wind,
water
along s t r a i g h t coastal
source points
appear a t t h e surface,
s e g m e n t s some t e n - t w e n t y
nautical m i l e s
while w a r m waters
spread out,
actual
cool
T h e s e cool a r e a s t h e n
long.
remain i n t h e v i c i n i t y of
capes and
small bays. In fact,
t h e u p w e l l i n g phenomenon i s l i n k e d t o a n o f f s h o r e d r i f t
surface water.
of off
a regular
This seaward d r i f t h a s a
coastline w e l l oriented with
because the d r i f t i n g of menon,
i.e.
all the particles
t h e upwelling.
an irregular coast,
respect t o t h e wind, results
i n t h e same pheno-
i s n o t t h e case i n t h e v i c i n i t y of
w h e r e d i f f e r e n t phenomena
downwelling) are induced gradients,
This
large spatial extension
i n adjacent places.
local circulations reducing
( f o r example up and Due t o l a r g e h o r i z o n t a l
the extension of
each pheno-
menon p r o b a b l y o c c u r . I t is difficult
of
t o model such a n e f f e c t b e c a u s e o f
the coastline features.
and Richez
( 1 9 8 1 ) a n d Hua
models which
Nevertheless, (1981)
Saint-Guily
( 1 9 8 0 ) , Crepon
have e l a b o r a t e d more o r less s i m p l e
confirm our interpretation
:
the spatial variability
t h e u p w e l l i n g i n t h e c o a s t a l zone i s mainly
Of
the small scale
dependent on
the
c o a s t l i n e drawing.
3.2
The t o n g u e s of
c o o l water
These f e a t u r e s r e v e a l then d r i f t e d
seaward,
t h e r e c o r d s a t 78-B
t h a t t h e water upwelled near
r o u g h l y i n t h e wind d i r e c t i o n .
(fig 4),
the coast is But
if
we c o n s i d e r
it i s clear t h a t l a r g e speeds a t a
10 m
cool and w a r m s u r f a c e water.
depth a r e associated with both reveals
the direction of
current
i s wider
of
than
an upwelling zone,
The tongue
t h e d r i f t c u r r e n t on a thermography,
t h e tongue.
The tongue i s a permanent
but
this
feature
i t s p o s i t i o n i s n o t w e l l d e f i n e d and so
but
i t may s w e e p a c r o s s a m o o r i n g p o i n t .
(as in fig 4 ) ,
3 . 3 The a n t i c y c l o n i c c i r c u l a t i o n One w e e k a f t e r t h e o n s e t o f
t h e wind,
we noticed
I f ye consider
s u r f a c e waters w e r e s t i l l d r i f t e d seaward.
is of
speed which
the order of
o b s e r v e d c a n n o t come f r o m t h e c o a s t a l As
cm/s,
some t e n s
a t 78-E
observed a t t h e 2 points
p o i n t 78-A.
now
t h e mean
a n d 78-E
which a r e
t h e r e i s a c o n t i n u i t y between t h e northward c u r r e n t
and t h e south-south
centered off
the current
zone.
t e m p e r a t u r e v a l u e s i n t h e s u r f a c e l a y e r a t 78-B the same,
that warm
the warm water
t h e i s o t h e r m s t r u c t u r e i n f i g 2 and by
s u g g e s t e d by
nearly
(fig 4)
are p a r t s of
the Roussillon L e t us
e a s t w a r d c u r r e n t a t 78-B.
The f l o w s
an anticyclonic circulation,
c o a s t s and which d o e s n o t c o n c e r n t h e
mention t h a t very s i m i l a r f e a t u r e s have been
observed i n the southern p a r t of
Lake Michigan
( B e l l a i r e and Ayers,
1967). Among t h e m e c h a n i s m s b y w h i c h the e f f e c t of
the spatial
has been studied
(Hua,
t h e wind
and temporal v a r i a b i l i t y
1981). I t has been
circulation only develops with
the gulf.
wind i n t h e v i c i n i t y o f variability Whatever
of
speed
conditions
:
t h e o n s e t must b e earlier i n t h e
(Millot,
t h e spreading of
the
1979), though t h i s s p a t i a l
t h e wind d i r e c t i o n i s p r o b a b l y
t h e most important meteorological
seaward c u r r e n t i s d r i f t e d
t h e wind
only
shown t h a t t h e a n t i c y c l o n i c
W e h a v e n o t modeled
zone A
of
specific meteorological
t h e speed must b e s t r o n g e r and/or central p a r t of
induces such an eddy,
from t h e u p w e l l i n g
important. parameters zone A
.
are, a large As
shown w i t h
observations
(Lamy, M i l l o t a n d M o l i n e s ,
1981), t h e d e f i c i t of t h e upwelled water. the upwelling
1981) and computations
i s n o t e n t i r e l y c o m p e n s a t e d by
surface water
Due t o t h e s t r o n g s t r a t i f i c a t i o n r e m a i n i n g o u t s i d e
zone d u r i n g a wind
event
(fig 4),
t h e c o n d i t i o n of from zone A t o be
c o n t i n u i t y i n e a c h l a y e r r e q u i r e s t h e d r i f t cu;rent compensated by c u r r e n t s o r i g i n a t e d dynamical process measured a t 78-E
(Hua,
from t h e edges of
e x p l a i n s both t h e c o n t i n u i t y of and 7 8 - B ,
and t h e f a c t t h a t wind
zone A .
This
the surface currents induced c u r r e n t s
can be opposed t o t h e l o c a l wind.
4-SYNTHESIS
O F THE
MAIN
RESULTS
The u p w e l l i n g phenomenon i n d u c e d by n o r t h - w e s t e r l y Gulf
of
winds i n t h e
Lions has t h e following s p e c i f i c f e a t u r e s .
The o b s e r v a t i o n s a n d t h e m o d e l s show t h a t t h e v e r t i c a l m i x i n g i s c l e a r l y d i s c e r n i b l e i n a few km n e a r t h e dynamics of
the shelf
the coast only
anywhere e l s e ,
:
w a t e r s d u r i n g summer i s t h o s e o f
a two-
l a y e r s y s t e m w i t h a c o u p l i n g b e t w e e n t h e two l a y e r s o n l y d u e t o pressure forces. A t a
wind.
large scale,
and it i s d i s c e r n i b l e n e a r
area.
the NE), A t a
a r e d r i f t e d t o t h e r i g h t of
The c o m p e n s a t i n g f l o w i n t h e b o t t o m
t h e wind, break
the surface waters
layer
i s t o t h e l e f t of
t h e bottom a s f a r a s t h e s h e l f
Upwelling s p r e a d s o u t over t h e 2/3 p a r t of
and downwelling o v e r t h e 1 / 3 p a r t
smaller scale,
t i c a l l y observed
:
s e g m e n t s some 2 0 - 4 0
the
the gulf
(in
( i n t h e SW).
a c t u a l s o u r c e p o i n t s of
c o o l water a r e systema-
they a r e l o c a t e d i n t h e c e n t e r of
straight coastal
km i n l e n g t h . U p w e l l i n g z o n e s a r e l i m i t e d b y
c a p e s a n d s m a l l b a y s i n t h e v i c i n i t y of w h i c h l a r g e a l o n g s h o r e temperature gradients a r e observed.
The s p a t i a l v a r i a b i l i t y o f
u p w e l l i n g i s m a i n l y d e p e n d e n t on t h e c o a s t l i n e drawing. Strong d r i f t currents
i s s u e d from t h e u p w e l l i n g zones a r e v i s u a l i z e d
152 by
tongues
of
cool surface waters,
o f warm w a t e r .
I n t h e v i c i n i t y of
b u t t h e y c a r r y away a l a r g e a m o u n t the upwelling zones,
c u r r e n t s a r e d i r e c t e d t o t h e s o u r c e p o i n t s of Off
t h e c o a s t of
Roussillon,
t h e bottom
cool water.
a n a n t i c y c l o n i c e d d y i s i n d u c e d by
w i n d from a r a t h e r complex mechanism.
First,
the
t h e s p a t i e d and temporal
t h e w i n d s t r e s s d e f i n e s t h e m a i n c h a r a c t e r i s t i c s of
v a r i a b i l i t y of
t h e u p w e l l i n g zone A and t h e a s s o c i a t e d d r i f t c u r r e n t . u p w e l l i n g zone t h e s t r a t i f i c a t i o n r e m a i n s s t r o n g ,
Outside the
and by c o n t i n u i t y
t h e d r i f t c u r r e n t i s a s s o c i a t e d with compensating flows i n t h e surface Due t o t h e s e m i c i r c u l a r s h a p e o f
layer.
w e l l i n g phenomenon i n this area,
t h e Gulf
occurs i n the south-western
of Lions,
p a r t of
a down-
the gulf
;
t h e dynamical s e a l e v e l i s h i g h e r t h a n it i s i n t h e
upwelling zone.
Consequently,
compensating flows opposed t o t h e
t h e o r e t i c a l d r i f t c u r r e n t d e v e l o p and c r e a t e t h e a n t i c y c l o n i c eddy.
REFERENCES Bellaire, Proc. Crdpon,
F.R.,
Ayers,
Hua,
Richez,
M.,
Lamy,
C.,
of A.,
1981.
C u r r e n t p a t t e r n s and l a k e s l o p e .
t h e Mem.
1981. A n o n - l i n e a r Lions. Millot,
pp.
251-263.
T r a n s i e n t u p w e l l i n g g e n e r a t e d by
This i s s u e of Molines,
C.,
S O C . Roy.
Sc.
Liege.
n u m e r i c a l model o f t h e Mem. J.M.,
l e v e l measurements i n t h e Gulf pp.
.
a t m o s p h e r i c f o r c i n g and v a r i a b i l i t y i n t h e c o a s t -
This i s s u e of
B.L.,
Gulf
1967
1 0 t h Conference G r e a t Lakes R e s . ,
two-dimensional line.
J.C.,
SOC.
upwelling i n the
Roy.
Sc.
Liege.
1981. Bottom p r e s s u r e and s e a
of L i 0 n s . J .
Phys.
Ocean.,
11, 3,
394-410.
Millot,
C.,
1976.
Specific features of
n e a r Cape L e u c a t e . Millot, shelf
C.,
of
Mem.
CrBpon, M . , t h e Gulf
S O C . Roy.
1981.
of Lions.
t h e sea-shore
S c . LiGge,
6,
circulation
10, pp.
227-245.
I n e r t i a l o s c i l l a t i o n s on t h e c o n t i n e n t a l Observations and theory.
J . Phys.
153 Ocean., Millot,
11,
C.,
5,
pp. 6 3 9 - 6 5 7 .
Wald, L . ,
1980
: Upwelling
i n t h e Gulf
Volume o n ” C o a s t a l U p w e l l i n g R e s e a r c h , Millot,
C.,
lings.
CUEA
1980”. To b e published.
1981. L a dynamique marine s u r l e p l a t e a u c o n t i n e n t a l
du G o l f e d u L i o n e n B t 6 . Saint-Guily,
of Lions.
B.,
XXVII
1980
.
ThSse d ‘ E t a t , Paris’VI-MusBum.
N o t e s u r l a s t r u c t u r e d i s c o n t i n u e d e s upwel-
Congr6s-Assembl6e
P l 6 n i 6 r e d e l a CIESM,
Cagliari.
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155
DISCONTINUOUS UPWELLING ALONG A RECTILINEAR COAST WITH A SERIES OF SMALL CAPES _, by Bernard SAINT-GUILY Muscum National d'Histoire Naturelle, Paris, and Laboratoire Arago, Banyuls sur Mer, France
Introduction Summer upwellings which occur in the Gulf of Lions, in the Mediterranean Sea, have a discontinuous shape. They are composed of several cold water sources fixed on certain places along the coast (Millot, 1979, 1981). The positions of these
source seem to be imposed by the coastal geometry. In addition the circulation in the surface layer is mainly advective with quasi slab motions. In the following pages the wind induced circulation along a rectilinear coast with small spitlike irregularities is studied. The theory shows that t h e presence of small capes gives necessarily birth to singular points, which are vortex points for a wind normal to the coast, and source or sink points for a wind parallel to the coast. This problem
is examined by regarding the superficial currents as irrotational and confined in a thin layer of constant depth. Afterwards a solution is obtained when currents are considered as linear in a baroclinic layer (reduced gravity layer).
I n e r t i a l and s t e a d y f l o w In the superficial (mixed) layer of constant depth h, the currents are consi-
dered as two-dimensional and irrotational. The circulation induced by a uniform wind stress is described by a stream function J, or a potential function c p , which are solutions of the Laplace equations
,
A J , = O
:
Alp
0
.
(1)
The components of the velocity u, V, are given by
and the pressure is obtained from the Bernoulli's equation p +
;(u'
+ v')
+
pfJ,
- r;1
(XTO
+
YTn)
=
c
(3)
156 where
f
=
2wSin 1 (w angular velocity of the earth, 1 latitude), and
T~
,
are the wind stress components respectively normal and parallel to the coast. Far from the rectilinear coast which is taken as oy axis, that is when x
+
m
,
the circulation tends to an Ekman drift. Then we have the condition 1
(G
+
pfh
hO+
YT;.;)
for x
-
-+
.
(4)
If there exists on the coast a series of small spitlike capes, regularly distributed at the points x
= 0
, y
(n=l,Z...), the boundary conditions
= % (2n-l)ka
for the normal and the tangential velocity are given by u = O ,
v =
0
for x = O ,
, for x
and
= 0
y
= ?
.
(2n-l)na
,
The stream function is the sum of two terms JI,
(G<:
(5)
, corresponding
to wind
stress components respectively normal and parallel to the coast. Taking B = x/2a,
p
=
y/2a as non-dimensional coordinates, and leaving out the tildes, the solu-
tion takes the following form
(Go
=
2a-r r pfh Lx -
(1
:
+ t Zy)thxl th'x J
tgzy
f
'
In these two terms, systems of singularities for the velocity appear between the capes at the points x
= 0
, y
= C nk, n = 0, 1, 2...,
(Betz, 1964). These
singularities are vortices (here anticyclonic) in the first term, for a wind normal to the coast (figure l), and sources in the second term, for a wind parallel to the coast (figure 2 ) . If the wind is making an angle of 45' with the coast, the singular points are composite (figure 3 ) , and the circulation shows an anticyclonic curvature. The potential function corresponding to ( 6 ) is given by 'P
'Po 'Pfc
'Po+'p*
ZaTL pfh
2a.r, pfh
3
r
- thzx)tgyl tgZy + th'x J
(I
Ly +
r
log ,-2
(Sin'y
,
(7)
1
+ Shzx)J
Inertial f l o w dependent on time If the motion in the superficial layer of constant depth h is dependent on
time, two-dimensional and irrotational, there are still stream and potential functions which are solutions of Laplace equations.
157
0
-x
Fig.1. Stream lines of the superficial circulation for a wind normal to the coast.
158
+TL:
.
-7t
Fig.2. Stream lines of the superficial circulation for a wind parallel to the coast.
159
3-K 2
x 2
0
--7L2
-7F
3-K -_ 2
\ Fig.3.
Stream lines of the superficial circulation for a slanting wind.
160 But the Bernoulli's equation is now
where the wind stress
T ~ ,T;,~,
depends on time. Far from the coast we must have an
Ekman regime. So we have the condition
where
So,*
-
To,$< =
f
fk
T ~ , ; , ~(t')
f
J:
T
~
(t') ,
,
Cosf(t-t')dt'
.
~ Sinf(t-t')dt' ~
If the wind stress is constant after the initial instan:
inertial oscillations with the period so,*
=
T
~
Sinft , ~
, ~ To,,
=
the boundary conditions are not modified following form
I
(t =
0)
we have simply
2r/f : T
;
~
(1,
- ~Cosft)
.
(11)
and the stream function takes the
:
I. + Y,>
,
where I+o, I+<: are the solutions(6). In the same manner the potential function is found to be @
where go
a,+@*
, gfC are
,
the solutions (7).
L i n e a r b a r o c l i n i c flow dependent on time We regard now the superficial layer as baroclinic with a variable depth h
;
and we suppose the flow linear, and the wind stress uniform and parallel to the coast. Then we have the following equations
:
161
E + f u at
at ah
+
where 6 = ( p ’ depth (at t =
- 6 g aah y
=
s
r&
avl ho L ax + a y , = o ,
p)/p’ 0).
is the relative density difference, and h, is the initial
Eliminating successively h and v we obtain first a system of
equations for u and v
r
a2 J 1 L ~a7- 6 g h , ~ v + r f a - 6 g h L at
L1~=0
axay J
I
aT
ph,
at
and then a wave equation for u
Let the axis oy be taken still along the rectilinear coast
;
supposing that there
is only one small spitlike cape at the point x = 0, y = a, the boundary conditions are u = O ,
for x = O ,
v = O ,
for x = O
and y = a .
(17)
Let the velocity be the sum of two terms
u = uo
+
U,?
,
v = vo +
V,$
,
(18)
where uoy vo represents the solution of the complete equations (15) which satisfies the first boundary condition (17), and u*, v* , the solution of the homogeneous equations (15) which satisfies the complementary conditions
u,~= 0 , for
x = 0
, vfc+
vo = 0 , for x = 0 and
y = a
. (19)
We consider first the case of a periodic wind stress T
-
T~
Sh u t
with a low frequency (u < f ) . The expressions of uo and vo are given by
(20)
162
-fTn
uo
=
vo
=
k
=,-
(Pho(fz-oz)
-kx (1-e )Sinot
TO
-
(phoo( f Z-az )
(f2
,
.-kx-uz ) c o s o t
,
r
We know that the terms uh and v~:must vanish far from the coast and be finite along the coast, except possibly at certain singular points. These terms are obtained in the following way. We note that if
cp
is a solution of the homogeneous wave
equation (16), the expressions of u9: and vg take the form
The appropriate solution rp has a singularity at the origin A bgh,
rp
Where K
x K, C o s o t r
= - - -
= K,(kr)
:
;
(23)
is the modified Bessel function of the first species, and
rz = xz + yz. Making use of the Bessel functions properties (Abramowitz and
Stagun, 19641, the following expressions for u* and v,:. are obtained
( 2 K,
vfc= A€
When
K,
=
o x K bgho r
1
K, (kr)
, KO
Sinot + A
= K,(kr)
r( r L+
2 - 3 2 )
+
krK,)
1
Cosot
(24)
(2 K1 + krKo)-
.
The first boundary condition (19) is satisfied, and the second one gives'the constant A
;
we have T,az
This result shows clearly that singularities are necessary to fulfil the boundary conditions on small capes. In general, the wind stress is not periodic and
-
we must have recourse to the Laplace transformation. Let w ( s ) be the transform of the function w(t)
:
163 The expressions of ,,;
, Go
are easily found. Then the second terms ;sc
, $:;
must
vanish far from the coast and be finite along the coast except possibly at certain singular points. The solution is constructed from the transform of the homogeneous wave equation (16)
the expressions of uJ:
-
-
-
, v*
of a solution q
:
are then given by (22). It is easy to write the explicit
forms of ug and v* , to verify that the first boundary condition (19) is satisfied and that A is determined by the second one. It is not necessary to proced further, to study the case of a row of small capes, and to engage into the problem of
.
It.'appears clearly that the addition obtaining the original functions u9< , vj: of small capes on a rectilinear coast entails the production of singularities in the resulting flow.
Conclusion We may observe that, in the first model, the flow is irrotational and non linear, and that the superficial layer is "rigid" the depth h being maintained constant. This advective and irrotational flow represents the main part of the superficial motion. And the source points appear between the capes, in agreement with the observations. But the slightly rotational motions associated with barotropic and baroclinic waves are obviously left out. This restraint is relaxed in the second model where the motion is linear. Nevertheless both these analyses lead to solutions with singularities. We must also note that in the first mode1,with a wind parallel to the coast, even in the absence of capes source points are necessarily present. The role of the coastal singularities is only to fix their distribution. Along a perfectly rectilinear coast the distance between the sources must depend on a characteristic length
;
and the most eligible one is the internal radius of
deformation. In the Gulf of Lions the distance 2Ta between the upwelling sources is about 37 km. And a = 6 km, a value which is equal to the local internal radius of deformation. In any case these theoretical considerations, with a permanent rigid layer and with a transient reduced gravity layer, plead in favour of a strong influence of coastal geometry on the sources distribution in the upwellings.
References AbramOWitZ, M. and Stegun, I.A., 1964. Handbook of Mathematical Functions. National Bureau of Standards, 1046 pp. Betz, A., 1964. Konforme Abbildung. Springer. 407 pp. Millot, C., 1979. Wind induced upwellings in the Gulf of Lions. Oceanologica Acta, 2 (3): 261-274. Millot, C., 1981. La dynamique marine sur le plateau continental du golfe du Lion en 6t6. These Mus6um National d'Histoire Naturelle, Paris.
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165
DEVIATIJN WITH XESPECT TO CORIOLIS PERIOD FOR GRAVITY-INERTIAL INTERNAL M V E S GEllERATED I N AN OCEAN BASIN BY AN IMPULSIOPIAL HIND . C
Dominique P. RENOUARD I n s t i t u t d e Xecanique d e S r e n o b l e
B.P.
53 X
F-38041 GRENJBLE-CEDEX France ABSTRACT Our aim i s t o s t u d y l a r g e a m p l i t u d e o s c i l l a t i o n s o f t h e season o f t h e r m o c l i n e o f p e r i o d c l o s e to t h a t o f t h e C o r i o l i s p e r i o d . I n some r e s p e c t , t h e y a r e t h e measurable t r a n s l a t i o n o f a g e o s t r o p h i c a d j u s b n e n t o c c u r r i n g a t t h e o n s e t o f , o r i m m e d i a t e l y a f t e r , a r a p i d v a r y i n g wind o r storm. Consequently, t h i s phenomenon i s observed o n l y d u r i n g some p e n d u l a r p e r i o d , a l t h o u g h a few o b s e r v a t i o n s made i n t h e X e d i t e r r a n e a n Sea have shown t h a t t h e y may e x i s t f o r a l m o s t two weeks ( c f . P e r k i n s , 1972). As f o r t h e p e r i o d , it i s 3 t o 20 % s h o r t e r t h a n t h e C o r i o l i s p e r i o d (cf.
Day and LJebster, 1965; Gonella, 1971; P e r k i n s , 1972; Fomin, 1975;
Kundu, 1976). These thermocl i n e o s c i l l a t i o n s a r e a s s o c i a t e d w i t h c u r r e n t s of maximum speeds o f o f 10 t o 20 cm/s, r o t a t i n g c l o c k w i s e w i t h t i m e i n t h e n o r t h e r n hemisphere. These c u r r e n t s have e x a c t l y t h e C o r i o l i s p e r i o d , and appear imnediat e l y a f t e r t h e o n s e t o f t h e wind. T h i s i n d i c a t e s a p r o p a g a t i v e phenomenon ( c f . Cr6pon e t a l . ,
1972; M i l l o t , 1931).
As j u s t i n d i c a t e d , t h e s e b a r o c l i n i c movements a r e t h e ocean's response t o a m o d i f i c a t i o n i n t h e g e o s t r o p h i c e q u i l i b r i u m . T h i s phenomenon has been t h e subj e c t o f numerous s t u d i e s reviewed, f o r i n s t a n c e , i n Blumen (1972), o r , more r e c e n t l y , Thorpe (1975) o r B r i s c o e (1975).
1 ANALYTICAL AND EXPERIMENTAL FOREGROUND 1.1 Among t h e numerous s t u d i e s d e v o t e d t o t h a t s u b j e c t , we have chosen t h a t o f Crepon (1969), f o r whom t h e n e a r C o r i o l i s o s c i l l a t i o n s o f t h e seasonal t h e r m o c l i n e f i r s t appear a t t h e c o a s t , a t t h e o n s e t o f a g u s t o f .wind, and t h e n propagate towards t h e open sea. The c o n c l u s i o n s o f t h i s model seem t o be i n good agreement w i t h o b s e r v a t i o n s made i n t h e G u l f o f L i o n s ( H e d i t e r r a n e a n Sea) ( c f . M i l l o t , 1931) b o t h f o r t h e g r a v i t y - i n e r t i a l waves and f o r t h e u p w e l l i n g generated by t h e conj u n c t i o n o f a l o c a l s t a t i o n a r y w i n d p e r t u r b a t i o n and a c o a s t ( c f . Crepon and Richez, 1931).
166 From t h e h y p o t h e s i s f i r s t adopted b y CrPpon (1969) - l o n g wave a p p r o x i m a t i o n ; momentum and mass c o n s e r v a t i o n e q u a t i o m l i n e a r i z e d c a l i n each l a y e r
-
and i n t e g r a t e d a l o n g a v e r t i -
we have developed a model, which i s an approximate s o l u t i o n o f
t h e p r o b l e m o f t h e g e n e r a t i o n o f such wave by an i m p u l s i o n a l wind, b l o w i n g o v e r a r e c t a n g u l a r ocean. Our main r e s u l t i s t h a t t h e p e r i o d s f o u n d f o r t h e g r a v i t y - i n e r t i a l o s c i l l a t i o n s l i n k e d t o t h e g e o s t r o p h i c a d j u s t m e n t , a r e c o n s t a n t with.'time,
in-
dependent f r o m t h e o b s e r v a t i o n p o i n t , depending on t h e dimensions o f t h e b a s i n and o f t h e parameters c h a r a c t e r i z i n g t h e s t r a t i f i c a t i o n . They a r e g i v e n by:
T (m,n)
where :
f
= 2n/~~(m,n)
i s t h e C o r i o l i s parameter, c2'
= g.hlh2/(hl
t h2). A P / P
i s the
b a r o c l i n i c phase speed (hi b e i n g t h e t h i c k n e s s o f t h e upper ( i = 1) and l o w e r ( i = 2) l a y e r s , A P / P
t h e buoyancy ), a and b t h e dimensions o f t h e b a s i n .
411 t h e s e p e r i o d s t e n d towards t h e i n e r t i a l p e r i o d when t h e two h o r i z o n t a l dimensions o f t h e b a s i n become l a r g e . I t may b e n o t e d t h a t , from t h e same equat i o n s , b u t u s i n g a n o t h e r way t o s o l v e them, Csanady (1973) had proposed, and v e r i f i e d b y measurements, a s o l u t i o n n e x t o f o u r s , f o r o b l o n g l a k e s . Though, f o r i t s c a l c u l a t i o n s , t h i s a u t h o r c o n s i d e r e d t h e l a k e as i n f i n i t e l y l o n g . Our s o l u t i o n does n o t s a t i s f y t h e c o n d i t i o n o f nu1 1 mass t r a n s p o r t a c r o s s every s i d e o f t h e b a s i n . However, a t l e a s t f o r t h e b e g i n n i n g o f t h e modement, f o r a s u f f i c i e n t l y l a r g e b a s i n , thus mass t r a n s p o r t w i l l be weak, and we w i l l c o n s i d e r o u r s o l u t i o n as a n a p p r o x i m a t e one, and t h e e x p e r i m e n t s w i l l have t o v e r i f y t h e 1 e g i t i m i t y o f t h i s p o i n t o f view.
1.2
I n o r d e r t o s t u d y t h e i n t e r n a l waves g e n e r a t e d by t h e wind i n a r e c t a n g u -
l a r t a n k i n r o t a t i n g a x i s we have b u i l t , o n t h e l a r g e r o t a t i n g p l a t f o r m , 14 cm d i a m e t e r , o f t h e G r e m b l e ' s U n i v e r s i t y , a channel (8 x 2 x 0,6 m) f i t t e d w i t h a wind-tunnel. We a r e a b l e t o o b t a i n winds r e a c h i n g t h e i r e q u i l i b r i u m v a l u e , a t e v e r y p i n t
i n the a i r t e s t section,
i n l e s s t h a n 1.2 s, which i s a t i m e s h o r t e r t h a n a l l
t h e c h a r a c t e r i s t i c p e r i o d s of t h e observed phenomena. So t h a t we c a n say t h a t we have a w i n d q u a s i - i m p u l s i o n a l w i t h t i m e . I n p r a c t i c e , a wind-speed o f V = 5.5 m/s i s used i n q u i t e a l l o u r e x p e r i m e n t s . I n o r d e r t o r e c o r d i n t e r f a c e h e i g h t v a r i a t i o n s w i t h time, a t a n y g i v e n p o i n t , s o - c a l l e d " i n t e r f a c e f o l l o w e r s " a r e used. There c o n s i s t o f c o n d u c t i v i t y m e t e r s equipped w i t h a sensor s l a v e d t o f o l l o w a l a y e r o f g i v e n r e s i s t i v i t y . I t has been v e r i f i e d t h a t , d u r i n g a n e x p e r i m e n t t h e t h i c k n e s s o f t h e i n t e r f a c e i s
167
n 20s Y,I.
m
I
P
1
-1
1 ") -1
Y-2.
m
F i g . 1. I n t e r f a c e h e i g h t v a r i a t i o n s , a l o n g f i v e l o n g i t u d i n a l l i n e s a t d i f f e r e n t t i m e s , a f t e r t h e o n s e t o f t h e wind. I n t h i s experiment hl = h 2 = 26 cm ; = 0 , 9 9 8 7 ; p,= 1,0168; T r o t = 50.4 S . 01
168 s p a t i a l l y u n i f o r m and does n o t v a r y two much w i t h t i m e . Thus we c a n say t h a t , as a f i r s t a p p r o x i m a t i o n , t.be s u c c e s s i v e r e c o r d i n g s o b t a i n e d d u r i n g a n experiment, a r e r e p r e s e n t a t i v e o f t h e s e w h i c h would have been o b t a i n e d i n a s i n g l e g u s t o f wind.
2
GENERAL DESCRIPTION OF THE PHENOYEM OCCURRINS I N THE TANK A S TkE WIND BLOWS
I f t h e v a r i a t i o n s i n the i n t e r f a c e h e i g h t w i t h time a r e considered a t a given p o i n t , t h e f o l l o w i n g movements w i l l b e observed s t a r t i n g f r o m r e s t : a The v a r i a t i o n i n t h e mean l e v e l o f t h e i n t e r f a c e , f r o m a s t a t i c e q u i l i S b r i u m l e v e l c o r r e s p o n d i n g t o t h e i n t e r f a c e a t r e s t ( a 2 ) t o a dynamic e q u i l i b r i u m l e v e l , w i t h wind
(0;).
T h i s v a r i a t i o n ' c a n b e b r o k e n down i n t o two p a r t s :
t h e f i r s t , and most i m p o r t a n t , i s due t o t h e s l o p e t h a t t h e w i n d g i v e s t o t h e f r e e s u r f a c e ; t h i s e x i s t s i n d e p e n d e n t l y o f t h e r o t a t i o n . The second p a r t of t h i s v a r i a t i o n r e s u l t s from t h e r o t a t i o n : t h i s can be c a l l e d a geostrophic adjustment i n t h e channel due t o t h e c u r r e n t s generated by t h e wind. I t i s t h i s p a r t of t h e mean l e v e l v a r i a t i o n o f t h e i n t e r f a c e which i s accompanied b y t h e g r a v i t y - i n e r t i a l waves l o o k e d f o r . But, t h e e x p e r i m e n t s have p o i n t e d o u t t h a t i f t h e l a t t e r p a r t o f t h i s v a r i a t i o n o f t h e mean l e v e l f i r s t appear a l o n g a l l t h e s i d e s o f t h e tank, and t h e n propagates towards t h e i n s i d e o f it, t h e f o r m e r f i r s t appear a t t h e upstream and downstream%nds o f t h e b a s i n , as K e l v i n - t y p e u p w e l l i n g o r downwell i n g t h e n p r o p a g a t i n g a l o n g t h e s i d e s o f t h e t a n k t h e y l e a v e a t t h e r i g h t of t h e i r d i r e c t i o n o f p r o p a g a t i o n (sense of f ) ( c f . f i g . 1).
b
An o s c i l l a t i o n of p e r i o d c l o s e t o : T2 = 2a/c,
which i s t h e n a t u r a l l o n g i t u d i n a l b a r o c l i n i c o s c i l l a t i o n o f t h e t a n k ( o r d e r o f magnitude 120 s ) .
T h i s a l s o e x i s t s w i t h o u t r o t a t i o n which o n l y a f f e c t s i t s
shape : w i t h o u t r o t a t i o n , t h i s o s c i l l a t i o n i s a p l a n e swash whereas, w i t h m'otat i o n , i t becomes a P o i n c a r e - K e l v i n amphidromy, b u t w i t h t h i s d i f f e r e n c e t h a t t h e D d e n i v e l l a t i o n s a r e t o be measured f r c m ( a , ) and n o t f r o m t h e p l a n e z = - h l ( c f . f i g . 2 ) . So i t seems p r e f e r a b l e t o speak o f a " p s e u d o - P o i n c a r e - K e l v i n amp hidromy" .
c
An o s c i l l a t i o n o f p e r i o d c l o s e t o : TI
= 2a/cl
(cl
= g(hl
+ h,))
which i s t h e n a t u r a l l o n g i t u d i n a l barotropic o s c i l l a t i o n o f t h e tank (order o f magnitude 7 s ) . T h i s o s c i l l a t i o n has t h e same shape as t h e b a r o c l i n i c one. I t i s o b v i o u s t h a t because t h e t a n k i s o n t h e r o t a t i n g p l a t f o r m , t h e phase speed o f t h e b a r o c l i n i c and b a r o t r o p i c modes a r e m o d i f i e d ; and as t h e t a n k i s a c l o s e d b a s i n , t h e phase speeds a r e , i n f a c t , weaker t h a n c i so t h a t t h e n a t u r a l p e r i o d s a r e l o n g e r t h a n Ti by some p e r c e n t ( ' ~ 5 % ) .
.x
Upstream and downstream w i t h r e s p e c t t o t h e w i n d f l o w .
169
D F i g . 2. Level l i n e s o f t h e dynamic e q u i l i b r i u m l e v e l , w i t h wind ( 0 2 ) o f t h e i n t e r f a c e (a), and l i n e s o f equal amplitude ( b ) , and equal phase ( c ) o f t h e peudo-Poincar6K e l v i n amphydromy. The experimental c o n d i t i o n s a r e those g i v e n i n f i g . 1 ; h e i g h t s are i n m, phases i n degrees.
170
3
ESTABLISH.4ENT OF THE GRAVITY INERTIAL WAVE LINKED TO THE IMPULSIONAL CHAZACTER 3F THE WIND F o r a n experiment,
i.e.
f o r a g i v e n t o t a l depth, t h i c k n e s s and d e n s i t y o f each
l a y e r , and r o t a t i o n speed, s e v e r a l wind g u s t s were made, each c o r r e s p o n d i n g t o what w i l l be c a l l e d a t e s t . F o r each o f t h e s e t e s t s , a r e c o r d i n g o f i n t e r f a c e h e i g h t v a r i a t i o n s i s o b t a i n e d a t f i v e d i f f e r e n t p o i n t s . A s p e c t r a l a n a l y s i s has been c a r r i e d o u t on each o f t h e s e p o i n t s , a f t e r h a v i n g e l i m i n a t e d f h e v a r i a t i o n s i n mean l e v e l o f t h e i n t e r f a c e . The s p e c t r a o b t a i n e d show peaks c o r r e s p o n d i n g t o t h e l o n g i t u d i n a l b a r o c l i n i c and b a r o t r o p i c p e r i o d s ; i n t h e s e experiments, t h e harmonics o f t h e s e p e r i o d s , l i k e t h e p e r i o d s o f t h e t r a n s v e r s e b a r o c l i n i c and b a r o t r o p i c o s c i l l a t i o n s , do n o t genera 11y appear. However, t h e s p e c t r a l a n a l y s i s always shows t h e exis'tence o f a s i g n i f i c a n t peak a t a p e r i o d s h o r t e r t h a n t h e C o r i o l i s p e r i o d o f 8 t o 21 %.The d i f f e r e n c e between t h e observed and t h e C o r i o l i s f r e q u e n c y i s always g r e a t e r t h a n a t l e a s t two f r e q u e n c y spectrum c a l c u l a t i o n s t e p s . T h i s d i f f e r e n c e appears s y s t e m a t i c a l l y when t h e wind blows suddenly. I n o r d e r t o check t h a t t h i s d i f f e r e n c e between t h e C o r i o l i s p e r i o d and t h e observed p e r i o d i s due t o t h e suddenly a p p l i e d wind,
the wind establishment time
i s g r a d u a l l y i n c r e a s e d and i t i s f o u n d t h a t when t h i s t i m e i s g r e a t e r t h a n approx-
imately h a l f t h e C o r i o l i s period, then the d i f f e r e n c e disappears. I n o r d e r t o g a i n a c l e a r e r u n d e r s t a n d i n g o f t h i s d i f f e r e n c e , t h e two t y p e s of mean s p e c t r a were computed, each spectrum c o r r e s p o n d i n g t o a g i v e n experiment. I n t h e f i r s t , t h e mean o f t h e s p e c t r a o b t a i n e d i n t h e v a r i o u s t e s t s was computed, t h e i n t e r f a c e f o l l o w e r s h a v i n g been i n v a r i o u s p l a c e s i n t h e channel d u r i n g t h e experiment. The r e s u l t s o f a number o f experiments a r e g i v e n i n t a b l e 1. I t i s n o t i c e a b l e t h a t t h e s e mean s p e c t r a always show o n l y one s i g n i f i c a n t peak
f o r a g i v e n value lower than the C o r i o l i s period. I n t h e second computation, f o r each experiment, t h e i n t e r f a c e
f o l l o w e r s were
n o t moved and s e v e r a l g u s t s o f wind were s i m u l a t e d ( s e v e r a l t e s t s ) . The mean spectrum was t h e n computed f o r t h e e x p e r i m e n t f o r each i n t e r f a c e f o l l o w e r , and f o r t h e experiment as a whole c o n s i d e r i n g a l l t h e sensors t o g e t h e r , as i n t h e f i r s t mean t y p e .
The f o l l o w i n g o b s e r v a t i o n s were made r e g a r d i n g t h e l a s t two types o f mean spectra : The s i g n i f i c a n t peak n e a r e s t t h e C o r i o l i s p e r i o d corresponds t o a p e r i o d a t h a t i s c l e a r l y d i f f e r e n t frm, and always s h o r t e r than, t h e C o r i o l i s p e r i o d . T h i s peak corresponds t o t h e same p e r i o d f o r a l l t h e i n t e r f a c e f o l l o w e r s b t h e n t h i s p e r i o d appears t o be independent o f t h e o b s e r v a t i o n p o i n t , a f a c t t h a t was t o b e expected because t h e f i r s t t y p e o f mean s p e c t r a a l s o shows o n l y one s i g n i f i c a n t peak f o r t h e s e p e r i o d s .
171
J
20
a it/
J 15
.
20
20
b
Fig. 3. Comparison between the experimentally measured period, and the period calculated by the "chequerboard" model, ( a ) for the mean spectra corresponding t o each experiment, ( b ) for the mean spectra corresponding to each interface-followers, for the experiments in which they were a t a fixed point throughout the experiment.
172 I f t h e r e l a t i v e d i f f e r e n c e between t h i s p e r i o d and t h e C o r i o l i s p e r i o d i s p l o t t e d o n l o g - l o g paper a g a i n s t t h e i n t e r n a l r a d i u s o f d e f o r m a t i o n
(XD
= C 2 / f ) which i s
a parameter i n t e g r a t i n g t h e p h y s i c a l c h a r a c t e r i s t i c s o f t h e experiment, i t c a n be seen t h a t t h e p o i n t s a r e l o c a t e d o n a s t r a i g h t l i n e o f s l o p e equal t o two. I f t h e e x p e r i m e n t a l l y f o u n d p e r i o d i s compared w i t h t h e p e r i o d computed u s i n g
t h e "chequerboard" model, i . e . ,
TTH = 2 n / B 2 (m = 0, n = 0) v e r y good agreement
i s f o u n d between them ( c f . f i g . 3 ) . Moreover, t h e d i f f e r e n c e s f o u n d between t h e observed and p r e d i c t e d p e r i o d s , f o r some experiments, can b e v e r y w e l l e x p l a i n e d by e x p e r i m e n t a l measurement e r r o r s , f o r example,
i n t h e determination o f thick-
nesses ( h = ? 3 mn) w h i c h l e a d s t o a n e r r o r i n t h e p r e d i c t e d p e r i o d . N e v e r t h e l e s s , i t i s t o be n o t e d t h a t t h i s d i f f e r e n c e between t h e observed and p r e d i c t e d f r e q u e n -
c y i s never g r e a t e r t h a n one f r e q u e n c y s p e c t r u n c a l c u l a t i p n s t e p . The same comparison was made between t h e p e r i o d c o r r e s p o n d i n g t o a s i g n i f i c a n t peak i n t h e e x p e r i m e n t a l spectrum i m m e d i a t e l y s h o r t e r t h a n t h e g r a v i t y i n e r t i a l wave p e r i o d , and t h e p e r i o d g i v e n b y t h e "chequerboard" model f o r T~~ (m = 0, n
=
= 2n/B2
1). The r e s u l t s a r e n o t i n such good agreement as p r e v i o u s l y , c o r r e s -
ponding t o v e r y small amp1 i t u d e s , b u t t h e agreement n e v e r t h e l e s s seems s i g n i f i c a n t I t s h o u l d b e noted t h a t t h e "chequerboard" model p r e d i c t e d t h a t t h e p e r i o d s do
n o t depend o n t h e p o s i t i o n o f t h e measurenent p o i n t , and t h i s has been v e r i f i e d i n t h e tank experiments. I n o r d e r t o see whether t h e p e r i o d f o u n d e x p e r i m e n t a l l y changes w i t h time, each r e c o r d i n g was c u t i n t o two o r f o u r equal p a r t s and t h e spectrum o f each o f t h e s e p a r t s was c a l c u l a t e d s u c c e s s i v e l y ( b y p a r t i a l s p e c t r a l a n a l y s i s ) .
In all
t h e s p e c t r a c a l c u l a t e d , t h e s i g n i f i c a n t peak n e a r e s t to t h e C o r i o l i s p e r i o d was e i t h e r e x a c t l y i n t h e same p l a c e o r a t t h e c o m p u t a t i o n p o i n t o f t h e p a r t spectrum n e a r e s t t h e p o i n t f o u n d f o r t h e s i g n i f i c a n t peak o n t h e spectrum o f t h e whole r e c o r d i n g . No change i n peak p o s i t i o n was n o t e d as t i m e i n c r e a -
ses and i t t h e r e f o r e seems r e a s o n a b l e t o say t h a t t h e p e r i o d f o u n d f o r t h e g r a v i t y i n e r t i a l wave l i n k e d t o t h e i m p u l s i o n a l wind i s c o n s t a n t w i t h time. I t should
b e added t h a t ,
i n r e a l l i f e , such a change i n p e r i o d o f t h e g r a v i t y i n e r t i a l
wave has never been evidenced,
a t l e a s t t o t h e a u t h o r ' s knowledge. T h i s l a s t
p o i n t i s i n agreement w i t h t h e "chequerboard" model c o n c l u s i o n .
As a l r e a d y demonstrated i n t h e "chequerboard" model, t h e p e r i o d depends o n t h e t a n k dimensions. Experiments have been made w i t h d i f f e r e n t t a n k l e n g t h s , and
i t has been found t h a t t h e agreement between t h e observed and p r e d i c t e d p e r i o d s i s good a s l o n g as t h e l e n g t h of t h e t a n k i s l a r g e r t h a n t h e w i d t h o f t h e channel.
Ift h e s e two dimensions a r e equal, t h e p r e d i c t e d d i f f e r e n c e between t h e "chequerb o a r d " model and t h e C o r i o l i s p e r i o d i s g r e a t e r t h a n t h e e x p e r i m e n t a l d i f f e r e n c e .
Ifc o n s i d e r a t i o n i s now g i v e n t o t h e c r o s s - s e c t i o n o f t h e tank, i t i s found t h a t a t m i d - l e n g t h ( x = 4 m) ( c f . f i g . 4)
2)
t h e r e i s a time i n t e r v a l o f about
7 s near t h e s i d e s , between t h e o n s e t of t h e w i n d and t h e t i m e a t which t h e
173
Y=1.25rn
-1 L
I X=4m
F i g . 4. I n t e r f a c e h e i g h t v a r i a t i o n , w i t h time, f o r d i f f e r e n t p o i n t s o f t h e t r a n s v e r s a l s e c t i o n , i n t h e m i d d l e o f t h e channel ( X = 4 m) f r o m t o p t o bottom, c l o s e t o t h e s i d e s , and a t d i s t a n c e s o f 25 cm, $0 cm, and 7 5 cm f r o m t h e s i d e s . The d o t t e d l i n e s i n d i c a t e h e i g h t s 0 , l cm. The p r o p a g a t i o n t i m e c o r r e s p o n d i n g t o a v e l o c i t y o f about 10 cm/s, whi.ch i s the o r d e r o f magnitude o f t h e b a r o c l i n i c phase speed f o r t h i s experiment, i s i n d i c a t e d b y t h e dashed l i n e .
-
174 i n t e r f a c e h e i g h t v a r i a t i o n s r e a c h a n a m p l i t u d e o f 1 mm, and
b)
above a l l , as
r e g a r d s t h e t i m e r e q u i r e d t o o b t a i n a h e i g h t v a r i a t i o n o f 1 mm, t h e r e i s an i n t e r f a c e h e i g h t v a r i a t i o n p r o p a g a t i o n t i m e f r o m t h e s i d e s t o t h e c e n t r e o f t h e channel. T h i s corresponds t o a p r o p a g a t i o n v e l o c i t y o f t h e same o r d e r o f magnitude as t h e b a r o c l i n i c wave phase speed f o r t h e experiment c o n s i d e r e d . As p r e v i o u s l y s a i d ( c f . f i g . 3 ) t h e l o n g i t u d i n a l b a r o c l i n i c o s c i l l a t i o n s f i r s t appear i n o n l y two p a r t i c u l a r p o i n t s , namely, t h e r i g h t upstream ( x = 0, y = 0) and l e f t downstream ( x = 8 m, y = 2 m) c o r n e r s and t h e n p r o p a g a t e from t h e r e a l o n g t h e l o n g i t u d i n a l s i d e s . The t i m e r e q u i r e d f o r such b a r o c l i n i c o s c i l l a t i o n s t o r e a c h t h e c e n t r a l s e c t i o n o f t h e t a n k i s g r e a t e r t h a n t h a t measured f o r t h e i n t e r f a c e h e i g h t v a r i a t i o n t o become g r e a t e r t h a n 1 mm a t x = 4 m, y = 1.25 m . Consequently, t h e propag a t i o n noted i n f i g u r e 8 i s t h a t o f t h e g e o s t r o p h i c a d j d s t m e n t i n t h e channel and o f t h e g r a v i t y i n e r t i a l waves accompanying i t . These waves f i r s t appear near t h e s i d e s on t h e i r who1 e 1 e n g t h and t h e n p r o p a g a t e towards t h e a x i s o f t h e channel. T h i s p o i n t a l s o seems t o be f o u n d i n r e a l l i f e ( c f . i h n d u , 1 9 7 6 ) and i s a l s o i n agreement w i t h t h e "chequerboard" model. C o n s i d e r i n g now t h e a m p l i t u d e o f t h i s g r a v i t y i n e r t i a l wave, computed by spect r a l analysis,
i t c a n be seen t h a t f o r a g i v e n experiment, t h e a m p l i t u d e reaches
i t s maximum v a l u e when t h e d u r a t i o n o f t h e wind i s h a l f t h e p e r i o d p r e d i c t e d f o r t h i s e x p e r i m e n t by t h e "chequerboard" model. The r a t i o between t h e a m p l i t u d e o f t h e g r a v i t y i n e r t i a l wave and t h a t o f t h e l o n g i t u d i n a l b a r o c l i n i c wave g e n e r a t e d by t h e same g u s t o f w i n d i s a t i t s maximum, and a l m o s t equal t o one, f o r g u s t s o f v e r y s h o r t d u r a t i o n ,
then r a p i d l y
decreases a s t h i s d u r a t i o n i n c r e a s e s and r e m a i n s a t a v a l u e o f a b o u t 0 . 1 as soon a s t h e d u r a t i o n i s equal t o or g r e a t e r t h a n t h e C o r i o l i s p e r i o d .
4 s regards t h e i n t e r f a c e height v a r i a t i o n s a t d i f f e r e n t times a f t e r the onset o f t h e wind a l o n g t h e l o n g i t u d i n a l channel, i t was f o u n d t h a t ,
immediately a f t e r
t h e w i n d s t a r t s t o blow, t h e v a r i a t i o n i s q u i t e independent o f t h e measurement p o i n t , e x c e p t near t h e t w o p r e v i o u s l y mentioned c o r n e r s . I t can t h u s be deduced t h a t , as soon a s t h e wind s t a r t s blowing, t h e g e o s t r o p h i c a d j u s t m e n t appears and t h e a m p l i t u d e o f t h e mean v a r i a t i o n i n i n t e r f a c e l e v e l r e s u l t i n g f r o m t h i s a d j u s t ment i s independent o f t h e x - a x i s ,
a s c a l c u l a t e d i n t h e "chequerboard" model
( c f . f i g . 1).
I f one l o o k s a t t h e c u r r e n t s generated by t h e wind, i n t h e upper l a y e r , immed i a t e l y a f t e r i t s t a r t s t o blow,
i t c a n be n o t i c e d t h a t ,
i n a t h i n l a y e r , near
t h e f r e e s u r f a c e , i t appears a n o s c i l l a t i o n a t e x a c t l y t h e C o r i o l i s p e r i o d ( 2 a / f ) and t h a t , under t h i s l a y e r and above t h e i n t e r f a c e , two o s c i l l a t i o n s o f t h e c u r r e n t a r e to be d i s t i n g u i s h e d : one a t t h e C o r i o l i s p e r i o d , and one a t t h e g r a v i t y i n e r t i a l one
[ h / B (0.0)l.
T h i s l a s t one b e i n g more and more i m p o r t a n t as
2
we a r e nearer t h e i n t e r f a c e meanwhile t h e f i r s t one d i s a p p e a r s a t 3 o r 4 cm f r o m t h e f r e e s u r f a c e . I n t h e l o w e r l a y e r t h e v e l o c i t i e s a r e too weak t o be measured.
175 CONCLUSI3N So, e v i d e n c e seems t o have been c l e a r l y g i v e n o f t h e e x i s t e n c e o f a g r a v i t y i n e r t i a l wave l i n k e d t o t h e i m p u l s i o n a l c h a r a c t e r o f t h e wind i n t h e e x p e r i m e n t a l channel f i t t e d w i t h a wind t u n n e l , and t h i s f o r v a r i o u s experimental c o n d i t i o n s . I t has a p e r i o d c o n s t a n t w i t h t i m e and g i v e n , w i t h a v e r y good a p p r o x i m a t i o n , by t h e model we have imagined. T h i s wave accompanies t b e v a r i a t i o n i n mean l e v e l o f t h e i n t e r f a c e r e s u l t i n g o f t h e g e o s t r o p h i c a d j u s t m e n t i n t h e channel. I t i s a p r o g r e s s i v e wave, f i r s t a p p e a r i n g a l o n g t h e s i d e s and t h e n p r o p a g a t i n g towards t h e i n s i d e o f t h e channel. I t s a m p l i t u d e depends o n t h e wind speed, and, f o r a g i v e n wind o f i t s d e v i a t i o n ; i t i s independent o f t h e x - a x i s a l o n g t h e l o n g i t u d i n a l sides. I n a d d i t i o n , i t i s shown t h a t t w p r i v i l m e d c o r n e r s e x i s t f o r t h e appearance o f K e l v i n - t y p e p e r t u r b a t i o n s of t h e i n t e r f a c e which then g i v e p l a c e t o t h e mean l e v e l v a r i a t i o n o f t h e i n t e r f a c e due t o t h e s l o p e imposed by t h e wind a t t h e f r e e s u r f a c e , and t o t h e l o n g i t u d i n a l b a r o c l i n i c o s c i l l a t i o n (pseudo-Poincare-Kelvin amphidromy) which i s l i n k e d t o t h i s v a r i a t i o n . These t w o r e s u l t s a r e i n good agreement w i t h t h e a n a l y t i c a l developments o b t a i ned f r o m t h e h y p o t h e s i s f i r s t adopted by Crepon (1969) and t h u s j u s t i f y t h e n a p o s t e r i o r i . And t h e y show t h e i m p o r t a n c e and u s e f u l n e s s o f a p h y s i c a l model t o s t u d y n a t u r a l phenomena which would o t h e r w i s e be d i f f i c u l t t o understand, and t o check t h e o r e t i c a l h y p o t h e s i s more e a s i l y t h a n by sea-measurements.
REFERENCES Blumen, W., 1972. G e o s t r o p h i c a d j u s t m e n t . Rev. Geophys. Space Phys., 10: 435-528. B r i s c o e , M.G., 1975. I n t e r n a l wave i n t h e ocean. Rev. Geophys. Space Phys., 13: 591-598. .._ ~ . - . Crepon, M., 1969a. Hydrodynamique m a r i n e en regime i m p u l s i o n n e l . Cah. Oceanogr. 21: 333-355. Crepon, PI., 1969b. Hydrodynamique marine en regime i m p u l s i o n n e l . Cah. Oceanogr. 21: 363-877. Crepon, M., Gonella, J . , Lacombe, H . and S t a n i s l a s , G., 1972. P a r t i c i p a t i o n f r a n c a i s e I? l a campagne COFRASOV I , Rpt. CNEXD No. 04, 156 pp. Crepon, M. and Richez, C., 1981. T r a n s i e n t u p w e l l i n g generated by two dimensional a t m o s p h e r i c f o r c i n g and by s h o r e v a r i a b i l i t y . P a r t I.A n a l y t i c a l model ( i n p r e s s ) . Csanady, G.T., 1973. T r a n s v e r s e i n t e r n a l s e i c h e s i n l a r g e oblong l a k e s and m a r g i n a l seas. J . Phys. Oceanogr., 3: 439-447. Day, G.G. and Webster, F., 1965. Some c u r r e n t measurements i n t h e Sargano Sea. Deep-sea Res., 12: 805-314. Fomin, L.M., 1975. I n e r t i a l o s c i l l a t i o n i n a h o r i z o n t a l l y un-homogeneous c u r r e n t v e l o c i t y f i e l d . I z v . A t m . Oceanic Phys., 9: 37-40. Gonella, J . , 1971. A l o c a l s t u d y o f i n e r t i a l o s c i l l a t i o n s i n t h e upper l a y e r o f t h e ocean. Deep-sea Res., 18: 775-789. Kundu, P.K., 1976. An a n a l y s i s o f i n e r t i a l o s c i l l i a t i o n s observed n e a r Oregon c o a s t . J . Phys. Oceanogr., 6: 879-393. Thorpe, S.A., 1975. The e x c i t a t i o n , d i s s i p a t i o n and i n t e r a c t i o n o f i n t e r n a l waves i n t h e deep ocean. J . Geophys. Res., 30: 329-333.
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177
HYDRODYNAMICS OF THE ADRIATIC SEA 3 P. MALANOTTE RIZZOLI 1 and A. BERGAMASCO-
Istituto per lo Studio della Dinamica delle Grandi Ma<;e, 2
C.N.R.,Venezia (Italy)
Scientific Collaborator, ISDGM-CNR, Venezia (Italy)
ABSTRACT Two extreme average situations characteriz: the Adriatic Sea. The first one, typical of seasonal conditions of autumn-winter, with a complete homogeneity of the vertical distribution of the water physical properties (temperature,salinity, hence density); the second one, relative to the seasonal conditions of springsummer, with a very strong vertical stratification. The relevant models of the Adriatic Sea circulation so far construzted are summarized. The first one has been developed to study the relative importance of air-sea thermal and evaporative fluxes, wind stress, horizontal advection and diffusion and the dense,deep water formation process. The second, a multilevel model, satisfies two basic flexibility criteria of being applicable to basins of quite different geometries and capable of describing quite different phenomenological situations. Results are shown and discussed. 1
PHENOMENOLOGY From the phenomenological point of view, two extreme average situations can
be distinguished in the Northern Adriatic.
The first one, typical of the season-
al conditions of late autumn-winter, is characterized by essentially complete homogeneity of the vertical distribution of the water physical properties (temperature, salinity, hence density) north of the sill of Pelagosa, with the exclusion of the only southernmost, deepest part in communication with the Ionian Sea (Cruises Najade-Ciclope 1911-1914; Trotti, 1966; Franco, 1970, 1972 a,b; Malanotte Rizzoli, 1977).
This vertical homogeneity is complete down to depths of
about 200 m, characteristic of the mid-Adriatic (Jabuka) pit, at the breaking point of the continental shelf, which constitutes all the northern half of the basin. As well-known, the Northern Adriatic Sea is one of the three Mediterranean sites of dense deep water formation.
This mechanism, lasting from 10 to 20 days,
occurs in wintertime, at the outbreaks of cold, dry air of Euro-Asiatic origin blowing directly onto the Northern Adriatic. The evaporation fluxes at the airsea interface are then
so
intense as to produce a quick overturning of the water
column, with vertical mixing down to the bottom of the basin, accompanied by the formation of a mass of water of remarkably high density (ot>29.4) in the interior region (Trotti, 1970; Hendershott and Rizzoli, 1976, Figs. 1 , 2 ) .
Fig. 1. Surface distribution of density anomaly for the period January-February 1972 (from Malanotte Rizzoli, 1977).
38 37
36
35
34
33
32
m O
10 20 -
30
-
40
-
50 60 70 80
-
Fig. 2 Vertical distribution of density onomaly Winter 1972 cross-section from Porto Civitanova to Isola Grossa (from Malanotte Rizzoli, 1977).
179 The second average situation is the one relative to the seasonal conditions of late spring-summer, characterized by a very strong vertical stratification, with pycnoclines rising to the very surface in the northernmost, shallowestpart of the basin.
A further fundamental characteristic of the Adriatic Sea is the major outflow of fresh, light water along the northwestern Italian sid?, due to the runoff of the rivers, the most important of which is the Po. This river runoff constitutes one of the basic driving forces of the horizontal circulation, producing very intense horizontal density gradients with the salty water mass of the interior of Ionian origin.
This river outflow forms a narrow boundary region elongated a-
long the Italian (western) coastline, colder in winter, warmer in summer relative to the interior mass. 2
THE MODELS We summarize now the relevant models of the Adriatic Sea circulation so far
constructed. For the late autumn-winter condition, a numerical model has been developed to study the relative importance of some of the physical processes (such as river inflow, air-sea thermal and evaporative fluxes, wind stress, horizontal advection and diffusion, exchange with the Southern Adriatic) in determining the winter fields of density and horizontal transport (Hendershott and Rizzoli, 1976). The basic conservation equations are adimensionalized using the characteristic length scales of the Northern Adriatic Sea, typical values for its average velocities and values for the eddy viscosity and eddy diffusivity used in the literature for basins of its size.
The model's primary idealization, corresponding
to the above discussed phenomenological evidence, is that vertical mixing ofheat and salt is always complete, the density field depending essentially only upon horizontal variables. The model is constituted by
a
geostrophic interior and
two top and bottom, Ekman layers of small thickness relative to the total depth. Considering average, seasonal evolutions, one does not allow for sea level variations, but rather impose a rigid lid on the sea surface. Thus, both the momentum and the density equations are vertically integrated to obtain two coupled equations in the density field and the transport streamfunction, with complex interactions with the bottom topography. A series of numerical experiments was performed solving the model equations for two winter situations (1966-1972) and the theoretical predictions were found to tie in good agreement with experimental results for the main interior part of the Adriatic basin (Hendershott and Rizzoli, 1976; Malanotte Rizzoli and Dell'Orto, 1981). In Fig. 3, the evolution of the transport streamfunction and density fields are shown at successive steps of the time integration. The formation processis
180 a3
a2
bl
b2
Fig. 3. Time evolution of transport streamfunction (al,a2,a3) and density ( b l , b2,b3) both in dimensionless units, multiplied by 100: streamfunction contours may be interpreted as dimensional transports in units of lo-‘ m2/s while density contours are increments of 2ut in units of a1,bl = time step 5 , corresponding to 3,46 days ’’ , 11 17,38 a2,b2 = time step 25, ” 1 ” 31,14 ” a3,b3 = time step 4 5 , (1
quite well reproduced of the dense water pool centered in the northern part of the basin stretching southward in a characteristic tail which follows isobath contours.
The transport streamfunction shows
a
typical circulation gyre of ther-
mohaline origin, determined by the strong gradients between light water of river runoff along the boundaries and the dense water of the interior. The gyre iscompletely disconnected from the forcing condition given at the southern, open boundary.
181 The model cannot describe the flow near the Italian coastline due to its basic assumption of complete vertical mixing.
In fact, near this coastline, river
induced vertical stratification is observed to persist very intensely all the year long.
An analytical treatment has been developed for this density boundary
layer adjacent to the Italian coastline, in which the vertical density stratification is maintained.
This treatment is based upon boundary layer analysis, em-
phasizing therefore the importance of cross-boundary density gradients and diffusion processes in determining the nearcoastal circulation (Malanotte Rizzoli and Gazzillo, 1976; Malanotte Rizzoli and Dell'Orto, 1 9 8 1 ) . The previous models describe and reproduce the wintertime seasonal evolution of the circulation and density field. A much more flexible model is necessary
for the Adriatic Sea if one wants to satisfp'the following requirements: 1 ) Capability to reproduce, describe and predict phenomenological situations as
widely different as late autumn-winter and spring-summer seasons. In these last ones a very strong pycnocline is present throughout the basin under average meteorological conditions. 2) Capability to represent phenomena with time scales ranging from the seasonal
one down to the time scales typical of the tidal circulation (about 1 day).
3) Capability to be applied to the whole Adriatic Sea or to subportions of it. 4) Capability to include all necessary driving forces for the circulation (thermohaline and wind driven).
The wind can be an important driving force for
the Adriatic Sea, for instance scirocco inhibits Adriatic outflow along the western coast (Italy) and forces inflow along the eastern one (Yugoslavia), on the tine scales typical of storm surges.
Such a model has been constructed (Malanotte Rizzoli and Bergamasco, 1 9 8 1 ) . Fig.
4 shows its schematic representation.
Fig. 4. Schematic representation of model.
182 The model gives the space-time evolution of sea level; total mass transport (integrated over the total depth); mass transport in each layer (integrated over the layer thickness); vertical velocities at the layer interfaces; horizontaldistributions of temperature, salinity, density anomaly for each layer. The model accepts as input the wind stress field Z and the thermal-evaporation fluxes q at the air-sea interface; the coastal river runoff at coa,?tal boundaries. The model equations can be sythesized as follows:
A(V
k
)
ADk :-fU k - 7 @
aw z-
LDk-&$-
k+l dz + D(Vk)
+
ZY
k
-3
the horizontal momentum equations for each layer k , integrated over the layer depth.
the thermodynamical equations for the temperature T and salinity S of each layer k.
is the equation of state for the density in each layer k. Where is the k-layer thickness
ADk
is Coriolis parameter, considered constant
f r
horizontal transport components for each layer k
barotropic pressure, with pSur the surface pressure and the mean density baroclinic pressure
is the surface sea level
183 i s t h e t a n g e n t i a l s t r e s s a t t h e ( k + l ) upper i n t e r f a c e of the k-layer t h e wind s t r e s s , a t t h e f r e e s u r f a c e i s t h e s t r e s s a t t h e k - l a y e r lower i n t e r f a c e of t h e k-layer
t h e bottom s t r e s s a t t h e bottom.
with
a a(@)= st+
u@+
a dv@+ aY aZ w@
the advection operator
f
with
n(@)= cHV@+ 2
cvdZz
the diffusion operator
w i s t h e v e r t i c a l v e l o c i t y f o r each l a y e r k.
a r e t h e s o u r c e f u n c t i o n s of h e a t and s a l t i n each l a y e r k , t h a t i s t h e v e r t i c a l fluxes a t t h e k-layer i n t e r f a c e s .
A s an a p p l i c a t i o n o f t h e model, a n u m e r i c a l s i m u l a t i o n h a s been c a r r i e d o u t f o r t h e n e a r c o a s t a l s t r i p a l o n g t h e I t a l i a n l i t t o r a l i n t h e p e r i o d September 15October 1 6 , 1978.
For t h i s p e r i o d a s e t o f d a t a e x i s t s , namely time s e r i e s of
c u r r e n t r e c o r d s a t a c u r r e n t s i t e 6 km from t h e c o a s t and v e r t i c a l s e c t i o n s of t e m p e r a t u r e , s a l i n i t y and d e n s i t y a l o n g two t r a n s e p t s , e x t e n d i n g 20 km i n t o t h e s e a , measured e v e r y week, n o r t h e r n and s o u t h e r n b o u n d a r i e s of t h e t e s t a r e a . These d a t a have been used f o r comparison and c a l i b r a t i o n o f t h e model.
The mod-
el was c o n s i d e r e d i n i t s two-layer v e r s i o n ( s u r f a c e l a y e r 7 m t h i c k n e s s ) .
A re-
a l i s t i c bottom topography d i s t r i b u t i o n w i t h 1 km2 s p a c e r e s o l u t i o n was g i v e n as input.
O t h e r i n p u t s were t i m e s e r i e s o f t h e s e a l e v e l a t t h e b o u n d a r i e s ; sur-
f a c e wind stress and a i r - s e a i n t e r f a c e t h e r m a l e v a p o r a t i o n f l u x e s , a s computed by m e t e o r o l o g i c a l d a t a r e c o r d e d a t c o a s t a l s t a t i o n s . Comparing t h e F i g u r e s 5 and 6 we can see t h e c o o l i n g o c c u r r e d a t t h e a i r - s e a interface during the simulation period.
I n f a c t t h e temperature i n f r o n t of the
Po R i v e r d e l t a d e c r e a s e s from 22O-23OC t o 18°-190C.
We can see moreover t h e
t r e n d o f t h e u n d e r c o a s t a l r i v e r w a t e r ( B r e n t a , Adige, Po) t o extend southward al o n g t h e c o a s t i n a t o n g u e - l i k e movement. T h i s t r e n d i s shown even b e t t e r i n t h e s u r f a c e s a l i n i t y d i s t r i b u t i o n s o f Figu r e s 7 and 8 .
I n t h e s e l a s t maps i t i s a l s o c l e a r t h e i n t r u s i o n o f t h e s a l t y
w a t e r mass o f s o u t h e r n o r i g i n p r o t r u d i n g northward i n t h e i n t e r i o r of t h e b a s i n .
184
i F i g . 5. S u r f a c e t e m p e r a t u r e d i s t r i b u t i o n o n S e p t . 15, 1978, 12:OO hours.
F i g . 6. S u r f a c e t e m p e r a t u r e dist r i b u t i o n on O c t . 16, 1978, 12:OO hours.
185
Fig. 7. Surface s a l i n i t y d i s t r i b u t i o n a s i n F i g . 5.
F i g . 8. S u r f a c e s a l i n i t y d i s t r i b u t i o n as i n F i g . 6.
186 F i g u r e 9 shows t h e d e n s i t y d i s t r i b u t i o n i n t h e s u r f a c e l a y e r .
This i s essen-
t i a l l y d e t e r m i n e d by t h e s a l i n i t y d i s t r i b u t i o n , as e v i d e n t from t h e s t r o n g c o r r e l a t i o n of t h e c o r r e s p o n d i n g maps.
hours.
The n u m e r i c a l p r e d i c t i o n s a r e g i v e n every 2
S u b s e q u e n t l y , t h e y are averaged o v e r 24 h o u r s , t o e l i m i n a t e t h e t i d a l
component and o b t a i n t h e a v e r a g e d a i l y e v o l u t i o n .
The maps shown i n F i g u r e s 5
t o 9 a r e i n very good agreement w i t h t h e c o r r e s p o n d i n g e x p e r i m e n t 3 1 d i s t r i b u t i o n s r e l a t i v e t o t h e same p e r i o d .
Fig. 9.
Density d i s t r i b u t i o n a s i n F i g . 8.
REFERENCES F r a n c o , P . , 1970. Oceanography of Northern A d r i a t i c S e a . 1 . H y d r o l o g i c f e a t u r e s : c r u i s e s July-August and October-November 1965. Arch. Oceanogr. L i m n o l . , Suppl. 16: 1-93. F r a n c o , P . , 1 9 7 2 a . Oceanography o f Northern A d r i a t i c Sea. 2 . H y d r o l o g i c f e a t u r e s : c r u i s e s January-February and April-May 1966. Arch. Oceanogr. L i m n o l . , Suppl. 17: 1-97. F r a n c o , P . , 1972b. Oceanography o f Northern A d r i a t i c S e a . 3. D i s t r i b u t i o n of t h e w a t e r t r a n s p a r e n c y : c r u i s e s July-August and October-November 1965, JanuaryF e b r u a r y and April-May 1966. Arch. Oceanogr. Limnol., S u p p l . 17: 1-14. H e n d e r s h o t t , M . C . and R i z z o l i , P . , 1976. The w i n t e r c i r c u l a t i o n o f t h e A d r i a t i c S e a . Deep Sea Res., 23: 353-370. M a l a n o t t e R i z z o l i , P . and G a z z i l l o , D . , 1976. On t h e i n f l u e n c e o f t h e v e r t i c a l d e n s i t y s t r u c t u r e on t h e dynamics o f s m a l l b a s i n s , w i t h s p e c i f i c a p p l i c a t i o n t o t h e A d r i a t i c Sea. Ann. G e o f i s . , X X I X , i 4 : 247-275. M a l a n o t t e R i z z o l i , P . , 1977. Winter o c e a n o g r a p h i c p r o p e r t i e s o f Northern Adria t i c S e a . C r u i s e January-February 1972. Arch. Oceanogr. Limnol., 19, 1 : 1-45. M a l a n o t t e R i z z o l i , P. and D e l l ' O r t o , F . , 1981. C o a s t a l boundary l a y e r s i n ocean m o d e l l i n g : an a p p l i c a t i o n t o t h e Adriatic Sea. I1 Nuovo Cimento, Marzo-Aprile, Serie 1, 4C: 173-220. M a l a n o t t e R i z z o l i , P . andBergamasco A . , 1981. A m u l t i l a y e r model o f t h e c i r c u l a t i o n i n small b a s i n s . I n p r e p a r a t i o n . M o s e t t i , F. and L a v e n i a , A . , 1969. R i c e r c h e o c e a n o g r a f i c h e i n A d r i a t i c o n e l per i o d o 1966-1968. B o l l . G e o f i s . Teor. A p p l . , X I , 43: 191-218. T r o t t i , L . , 1970. C r o c i e r e Mare A d r i a t i c o . CNR, R a c c o l t a d a t i o c e a n o g r a f i c i , S e r i e A , No. 29. Zor6-Amanda, M . , 1963. Les masses d ' e a u d e l a m e r A d r i a t i q u e . Acta A d r i a t i c a , 10:
5-85. Zorh-Armanda,M., 1968. The s y s t e m o f c u r r e n t s i n t h e A d r i a t i c s e a . E t u d . R e v . , 3 4 : 1 - 4 2 .
187
CURRENT CIRCULATION I N THE LIGURIAN SEA /
A. ESPOSITO
L a b o r a t o r i o per l o S t u d i o d e l l ' A m b i e n t e Marino, F i a s c h e r i n o (La Spe-
C.N.E.N.
zia), I t a l y
G. MANZELLA C.N.R.
I s t i t u t o per l o S t u d i o d e l l a Oinamica d e l l e Grandi Masse, Stazione Ocea-
nografica, San Terenzo (La Spezia), I t a l y
ABSTRACT
Observation o f t h e c i r c u l a t i o n i n t h e L i g u r i a n Sea have g e n e r a l l y been i n f e r red i n d i r e c t l y from t h e f i e l d o f mass, w h i l e few o b s e r v a t i o n a l data gathered by moored currentmeters can be found i n t h e l i t e r a t u r e . The c y c l o n i c c i r c u l a t i o n seems t o be f o r c e d by t h e wind s t r e s s t h a t imparts v o r t i c i t y ( c u r l o f t h e wind s t r e s s ) t o t h e sea.
I n p a r t i c u l a r , a s o u t h e r l y wind seems t o cause a c o a s t a l
c o u n t e r c u r r e n t i n t h e G u l f o f Genova.
A s p e c i a l a t t e n t i o n deserves t h e i n t e r -
a c t i o n between t h e L i g u r i a n Sea and t h e Tyrrhenian Sea, since t h e data c o l l e c t ed on t h e s h e l f d u r i n g Spring 1979 showed a s i g n i f i c a n t coherence o f t h e alongshore c u r r e n t o n l y a t about 1 cpd.
INTRODUCTION The L i g u r i a n Sea i s an abyssal depression d e l i m i t e d by t h e shallow water s h e l f o f t h e Tuscan Archipelago toward t h e south-east and l a r g e l y open toward the Western Mediterranean.
The c o n t i n e n t a l s h e l f i s narrow and steeps deeply
(see F i g . 1 ) . I t i s w e l l known t h a t t h e L i g u r i a n Sea i s a c y c l o g e n e t i c area and t h a t t h e
c y c l o g e n e t i c a c t i v i t y i s more f r e q u e n t from October t o May (Gleeson, 1954).The seasonal v a r i a t i o n s o f t h e atmospheric motions i n f l u e n c e t h e dynamics o f t h e basin.
A s t a t i s t i c a l a n a l y s i s o f t h e wind measured a t Genoa shows t h a t i n
w i n t e r t h e winds are g e n e r a l l y n o r t h o r n o r t h - w e s t e r l y , so t h a t they r e i n f o r c e
188
Fig. 1
The L i g u r i a n Sea. the currents.
The s c a t t e r p l o t s show t h e d i f f e r e n c e between
189 t h e g e n e r a l c y c l o n i c c i r c u l a t i o n o f t h e L i g u r i a n Sea.
I n summer t h e p r e v a i l i n g
winds a r e s o u t h e r l y and t e n d t o m o d i f y t h e g e n e r a l c y c l o n c c i r c u l a t i o n i n t h e G u l f o f Genoa. The L i g u r i a n Sea c i r c u l a t i o n has been i n f e r r e d i n d i r e c l y from t h e f i e l d o f mass ( S t u c c h i n o and T e s t o n i , 19771, w h i l e few o b s e r v a t i o n a l d a t a f r o m moored c u r r e n t m e t e r s were g a t h e r e d i n t h e deep b a s i n .
They do n o t c o n s t i t u t e s u f f i -
c i e n t l y l o n g - t e r m t i m e s e r i e s i n o r d e r t o a t t a i n a s i g n i f i c a n t s t a t i s t i c a l analysis. A n a l y z i n g t h e Genoa and Leghorn s e a - l e v e l s E l l i o t t (1978) f o u n d t h a t t h e c o h e r e n t m o t i o n s i n t h e L i g u r i a n Sea a r e a t 33, 3.6 and 1-2 hours.
The o s c i l l a -
t i o n s a t 3.6 and 1-2 h o u r s were s t u d i e d by Papa (1977) and a r e a s s o c i a t e d w i t h t h e s e i c h e motions, w h i l e t h e o r i g i n o f t h e 33 h o u r s o s c i l l a t i o n i s n o t r e a l l y known. About t h e l o w e r f r e q u e n c y m o t i o n s t h e c i r c u l a t i o n p a t t e r n s g i v e n by c l i m a t o l o g i c a l averages, s e v e r a l s y n o p t i c s t u d i e s and a g r e a t number o f s a t e l l i t e images suggest an annual c y c l e o f t h e h o r i z o n t a l dynamics. The o b s e r v a t i o n s o f t h e l o w - f r e q u e n c y m o t i o n s were l i m i t e d t o some r e s t r i c t ed areas, so t h a t i t i s n o t known o v e r what a l o n g s h o r e d i s t a n c e i s t h e f l o w coherent. I n o r d e r t o s t u d y t h e annual e v o l u t i o n o f t h e s h e l f c i r c u l a t i o n a l o n g t e r m c u r r e n t o b s e r v a t i o n was programmed.
I t c o n s i s t e d i n t h e mooring o f t h r e e
Aanderaa RCM-4 c u r r e n t m e t e r s a t 15, 50 and 95 m d e p t h on t h e 100 m i s o b a t h i n f r o n t o f S e s t r i Levante.
Because o f t h e a n t i c i p a t e d c o n c l u s i o n o f t h e expe-
r i m e n t , o n l y c i r c a 10 months (September 24, 1978
-
J u l y 12, 1979) l o n g t e r m
c u r r e n t o b s e r v a t i o n s a r e a v a i l a b l e . The winds r e c o r d e d a t Genoa, Pisa, C i v i t a v e c c h i a ( n e a r Rome), Ponza i s l a n d , O l b i a ( S a r d i n i a ) , C a l v i and N i c e were p r o vided.
S i n c e t h i s paper i s concerned w i t h a p a r t i c u l a r study, o n l y t h e L i g u -
r i a n area w i n d d a t a were examined and t h e c u r r e n t measured d u r i n g A p r i l 1979 were analyzed.
-
May
I n t h i s p e r i o d a second a r r a y w i t h a c u r r e n t m e t e r a t 50 m
was moored i n f r o n t o f P o r t o v e n e r e ( L a S p e z i a ) on t h e 100 m i s o b a t h .
THE ATMOSPHERIC MOTIONS The i m p o r t a n c e o f t h e w i n d as f o r c i n g was u n d e r l i n e d by many a u t h o r s b u t i t s e f f e c t on t h e c i r c u l a t i o n as w e l l as t h e e f f e c t of t h e boundary c o n d i t i o n s have y e t t o be q u a n t i f i e d .
An a n a l y s i s o f t h e winds measured a t Genoa, Pisa, C a l v i
190 and N i c e f r o m September 1978 t o March 1979 showed t h a t t h e y a r e i n f l u e n c e d by t h e orography as can b e seen i n F i g u r e 2.
T h e r e f o r e t h e coherence a n a l y s i s o f
t h e p r i n c i p a l components showed t h a t a l l t h e winds were c o h e r e n t a t 14-18 days and a t 42 days. Peaks a t 6, 8 and 17 days were p r e s e n t i n t h e wind s p e c t r a . The f i r s t two v a l u e s a r e c l o s e t o t h e c y c l o g e n e t i c c h a r a c t e r i s t i c t i m e s c a l e . The a t m o s p h e r i c p r e s s u r e p r e s e n t e d some t y p i c a l p a t t e r n s .
The s p e c t r a a t
Genoa, C a l v i and N i c e has t h e same peaks a t 5 and 14 days, f u r t h e r m o r e t h e coherence between t h e p r e s s u r e measured a t t h e s e s t a t i o n s was v e r y h i g h f o r per i o d s g r e a t e r t h a n 2 days.
The p r e s s u r e peak a t 5 days can be r e l a t e d t o t h e
same p e r i o d i c i t y o s c i l l a t i o n a f f e c t i n g t h e M e d i t e r r a n e a n r e g i o n (Gupta and Sing, 1977).
THE GENERAL CIRCULATION The measurements d e s c r i b e d by De Maio e t a l .
(1977) showed t h a t t h e c y c l o n i c
c i r c u l a t i o n a f f e c t s t h e w a t e r mass f r o m t h e s u r f a c e t o 1000 m depth. l y s i s o f c u r r e n t n i e t e r d a t a g a t h e r e d a t l o c a t i o n 44"11'80"N
-
The ana-
8O59'00"E
on t h e
1000 rn i s o b a t h showed t h a t t h e EW component decreased r e a c h i n g a v a l u e c l o s e t o z e r o a t a 600
in
depth.
The c o u n t e r c l o c k w i s e c u r r e n t v e e r i n g was f i t t e d by t h e
empirical formula9=363.58 downward
-
-
0 . 1 5 ~ 2 ( 8 i n degrees and Z i n meters, p o s i t i v e
S t o c c h i n o p r i v a t e communication).
B u t t h e v e e r i n g was p r o b a b l y r e -
l a t e d t o t h e p a r t i c u l a r morphology o f t h e area, t h a t i s t h e presence of two deep canyons i n f r o n t o f Genoa. A c o a s t a l c o u n t e r c u r r e n t i s p r e s e n t d u r i n g summer i n t h e G u l f o f Genoa, t h e i n n e r p a r t o f t h e L i g u r i a n Sea.
I t i s a s s o c i a t e d t o a s o u t h e r l y w i n d and can
b e e x p l a i n e d as a d r i f t c u r r e n t whose c h a r a c t e r i s t i c depends on t h e c o a s t a l curvature.
T h i s c o u n t e r c u r r e n t was p r e d i c t e d by Bossolasco and Dagnino (1957);
a n u m e r i c a l model was c o n s t r u c t e d b y Papa ( 1 9 8 0 ) . The coherence a n a l y s i s of w i n d s t r e s s and sea l e v e l a t Genova showed t h a t f o r p e r i o d s g r e a t e r t h a n 10 days t h e y a r e o u t o f phase, i . e . toward t h e c o a s t corresponded a l o w e r i n g o f t h e sea l e v e l .
?it a w i n d b l o w i n g T h i s phenomenon was
m o d e l l e d by E l l i o t t (1980) who showed t h a t i t was r e l a t e d t o a f l o w g o i n g f r o m t h e L i g u r i a n Sea t o t h e T y r r h e n i a n Sea.
From t h e o b s e r v a t i o n a l data, E l l i o t t
e s t i n i a t e d t h a t a 16 i d s w i n d s h o u l d cause a r e d u c t i o n o f t h e sea l e v e l o f c i r c a
20 crn i n t h e Gulf o f Genoa.
C o n t i n u i t y reasons r e q u i r e d a r e t u r n f l o w of t h e
s u r f a c e w a t e r near C o r s i c a .
From t h i s model one s h o u l d e x p e c t a t lower f r e -
191
GENOVA
CALVI
Fig. 2
a PlSA
NICE
The w i n d r o s e s a t Genoa, Pisa, N i c e and C a l v i . I t is p o s s i b l e t o see t h e o r o g r a p h i c a l o r i e n t a t i o n .
192 quencies a coherent response o f t h e c o a s t a l c u r r e n t along t h e e a s t e r n L i g u r i a n continental shelf.
One month-long o b s e r v a t i o n a l data o f A p r i l
-
May 1979 show-
ed t h a t t h e i n t e r a c t i o n between t h e L i g u r i a n and T y r r h e n i a n Seas i s v e r y complic a t e d s i n c e a f r o n t and meanders were p r e s e n t j u s t n o r t h o f t h e Elba I s l a n d ( S e e F i g s . 3a,b).
THE INTERACTION BETWEEN THE LIGURIAN AND TYRRHENIAN SEAS
The a n a l y s i s of c u r r e n t d a t a gathered on t h e 100 ni i s o b a t h i n f r o n t o f Ses t r i Levante f r o m September 1978 t o J u l y 1979 (Bruschi. and Manzella, 1980; Espos i t o and Manzella, 1981) d e a l t w i t h c o n c l u s i o n s d i f f e r e n f f r o m E l l i o t t ' s (1981).
The non l o c a l winds seemed t o p l a y a non r e l e v a n t r o l e on t h e continen-
t a l s h e l f c i r c u l a t i o n , t h a t seemed f o r c e d by t h e c i r c u l a t i o n i n t h e i n t e r i o r . The d i f f e r e n t c o n c l u s i o n s can be b e t t e r evidenced by examining t h e d a t a b o t h a t S e s t r i Levante and Portovenere.
The hodograph e l l i p s e s were c a l c u l a t e d and t h e
r e s u l t s a r e presented i n Table 1 (see a l s o F i g s . 1 and 4).
TABLE 1 The hodograph e l l i p s e parameters
lr
v
u U'+v V' '
Sestri
3.16
8.21
0.02
0.93
134.74
Portov.
3.58
8.52
0.09
5.02
147.03
g
A
B
A/B
u'v'
19.93
6.76
1.25
23.80
6.18
7.56
The mean values i n d i c a t e d t h e presence o f a more e n e r g e t i c c u r r e n t i n f r o n t o f S e s t r i Levante ( t h e mean alongshore components were V=29 cm/s a t S e s t r i and
V=20 cm/s a t Portovenere).
It i s v e r y s u r p r i s i n g t o see t h a t a t t h e two s i t e s ,
whose d i s t a n c e i s c i r c a 20 nini, t h e alongshore c u r r e n t s were n e i t h e r c o r r e l a t e d (r=0.12 w h i l e t h e 95% s i g n i f i c a n t l e v e l i s 0.14) nor coherent a t lower f r e quencies ( s e e F i g . 5 ) . coherence.
Only f o r p e r i o d s of about 1 day t h e r e was a s i g n i f i c a n t
T h i s c o u l d be caused by t h e thermal f r o n t shown i n F i g u r e s 3a, b,
due t o t h e meeting o f t h e T y r r h e n i a n and L i g u r i a n Seas.
Large meanders c o u l d
i n d i c a t e an i n f l o w of v o r t i c i t y producing a l o c a l u p w e l l i n g a c t i v i t y . I n some sense one can t h i n k t h a t t h e L i g u r i a n water was f u n n e l l e d approximately by t h e
193
APRIL 1979
\
13.7
\\'
14.1
APRIL 1979
LA SPEZIA
Fig. 3
The teriiperature pattern observed during April 1979. Integral between 5-20 m depth ( a ) and between 40-60
111
depth ( b ) .
194
0s
OF
s/ w3
u L u
c
01
01-
.,
L O
W D
cro
ulx @+I
L u l
E
a .V
W
,--
L O +-0
* w
W
E
c x @ + P -00 W
E U 0
O nL L o
1
-3
c u
w x
0
% E -
s3pI
In 4 4
a,
E L
wro
c
c 4 w=r.
In-0 @ C
LL:
3
=+I ’-
v
W
L-u
o w
In3
-cL
w
W L
mul r 4 o w -5 E W
s
I-3
0 7
=r
I&
.r
195
1
00-J d
W
-i
?O ? JI I
0.00
I
I
I
0.20
I 0.40
I
I 0.6 0
I
I
I
0.80
FREQUENCY ( C P D ) Fig. 5
The coherence squared between the alongshore currents measured a t Sestri Levante and Portovenere.
I 1.00
196 500 m i s o b a t h .
I n t h e e x i s t i n g l i t e r a t u r e t h i s phenomenon i s f o u n d i n T r o t t i
(1954). I n o r d e r t o s t u d y t h e i n f l u e n c e o f t h e w i n d on t h e c o a s t a l c i r c u l a t i o n t h e v a r i a n c e a t v a r i o u s f r e q u e n c i e s was f o u n d b y p e r f o r m i n g a F o u r i e r a n a l y s i s on 300 h o u r s o v e r l a p p i n g b l o c k s d a t a .
T h i s method causes a l o s s o f d a t a (150 ,.
h o u r s ) a t t h e b e g i n n i n g and a t t h e end o f t h e r e c o r d s .
T h i s a n a l y s i s was p e r -
formed a f t e r a p p l y i n g a 30 h o u r s lowpass f i l t e r t o t h e r e c o r d s . t h e t i d a l and s t r o n g b r e e z e s i g n a l s were removed.
I n t h i s way
From F i g u r e 6a one can see
t h a t t h e l a r g e amount o f S e s t r i c u r r e n t v a r i a n c e was a f t e r A p r i l 26 f o r p e r i o d i c i t i e s comprised between 8-11 days.
The P o r t o v e n e r e c u r r e n t had t h e maximum
v a r i a n c e a t l o w e r f r e q u e n c i e s f r o m A p r i l 2 2 t o 25.
About t h e winds one can
see i n F i g u r e 6b t h e v a r i a n c e p a t t e r n s o f Genoa, P i s a and Ponza; t h e l a s t one was used i n o r d e r t o v e r i f y E l l i o t t ' s (1981) c o n c l u s i o n s on t h e c o a s t a l c i r c u l a t i o n forcings.
I n e f f e c t a t l o w e r f r e q u e n c i e s t h e p a t t e r n was s i m i l a r f o r
t h e P o r t o v e n e r e a l o n g s h o r e c u r r e n t and t h e Ponza w i n d i f one c o n s i d e r s a d e l a y o f more t h a n one day between t h e t w o t i m e s e r i e s .
U n f o r t u n a t e l y t h e c u t s due
t o e i t h e r t h e f i l t e r i n g o r t h e F o u r i e r d e c o m p o s i t i o n reduced enormously t h e time series.
A MODEL
I t can be s a i d t h a t t h e l a c k o f a c l e a r f o r c i n g a c t i o n o f t h e winds on t h e L i g u r i a n s h e l f c i r c u l a t i o n was due t o t h e e f f e c t o f t h e m o t i o n i n t h e deep basin.
I n o r d e r t o approach t h e problem, we m o d i f i e d A l l e n ' s model ( A l l e n , 1976)
c o n s i d e r i n g i t s a p p l i c a t i o n t o t h e L i g u r i a n Sea.
O t h e r a u t h o r s (Buchwald and
Adams, 1968; A d a m and Buchwald, 1969; G i l l and Schumann, 1974) p r e v i o u s l y s t u d i e d t h e s h e l f waves b u t one o f t h e i r fundamental h y p o t h e s i s was t h e cond i t i o n V=O f o r t h e a l o n g s h o r e v e l o c i t y a t t h e s h e l f - i n t e r i o r j u n c t i o n .
This i s
c o r r e c t f o r f r e e s h e l f waves, b u t needs m o d i f i c a t i o n f o r f o r c e d s h e l f waves.
On t h e o t h e r hand t h e above h y p o t h e s i s i s v e r y u s e f u l because i t p e r m i t s t o u n c o u p l e t h e m o t i o n i n t h e s h e l f from t h a t . i n t h e i n t e r i o r .
A l l e n corrected
t h e h y p o t h e s i s and d e a l t h w i t h t h e p r o b l e m by u s i n g a p e r t u r b a t i v e method. T h i s o n l y r e q u i r e s t h a t t h e w i d t h o f t h e s h e l f W and t h e l e n g t h o f t h e whole b a s i n o f f s h o r e s a t i s f y t h e c o n d i t i o n W/L=l,
L = 150 km.
A l l e n used t h e h y p o t h e s i s
i s n o t necessary.
az
i n t h e p r e s e n t case W = 20 km and = 0 but t h i s r e s t r i c t i v e imposition
The h y d r o s t a t i c h y p o t h e s i s i s more r e a l i s t i c and does n o t
197
c5
n
Q V v
LL
Por t o w n c re
1 I
I 20
1
I
I
I
I
21
I
22
23
24
25
I
'26
27
1 28
DAYS Fig.6a
The v a r i a n c e a t v a r i o u s f r e q u e n c i e s vs. t h e t i m e f o r t h e alongshore currents.
198
Pisa
0.7
Ponra
3-
5-
I
rr)
a0
aOD
Q1
20
1
21
1
22
1
23
1
24
~
25
1
26
27
1
28
DAYS Fig. 6b As i n Figure 6a for t h e winds resolved i n t h e alongshore d i r e c t i o n .
1
199 m o d i f y t h e c a l c u l a t i o n s , so t h a t i t can b e m a i n t a i n e d .
By n e g l e c t i n g t h e non
l i n e a r teriiis one o b t a i n s f o r t h e stream f u n c t i o n t h e e q u a t i o n
where
v : ( hax. a
k f (.Q;O;l1
8
The above e q u a t i o n can be b e t t e r t r e a t e d i n non d i m e n s i o n a l form.
The f l u i d i s
c o n t a i n e d i n a r e c t a n g u l a r b a s i n X=O,1 and Y=O,L.
We a l s o assume t h a t t h e w i n d
s t r e s s component v a r i a t i o n s on t h e X , Y s c a l e s a r e
O(1).
The d e p t h has an expo-
n e n t i a l b e h a v i o u r on t h e s h e l f and i s c o n s t a n t i n t h e i n t e r i o r :
The e q u a t i o n r e q u i r e s a d i f f e r e n t t r e a t m e n t i n t h e i n t e r i o r and i n t h e s h e l f regions.
A p a r t i c u l a r a t t e n t i o n needs t h e c o n d i t i o n a t t h e j u n c t i o n .
c o n t i n u i t y o f t h e f l u x across t h e j u n c t i o n
c o n t i n u i t y of t h e p r e s s u r e a l o n g t h e j u n c t i o n
where
i s t a n d s f o r i n t e r i o r and
s stands f o r s h e l f .
A t l o w e s t o r d e r t h e e q u a t i o n s on t h e i n t e r i o r and on t h e s h e l f a r e :
200
a
where I = t W ; C = X / W and”&’lbs-Cd
(see A l l e n , 1976).
The e q u a t i o n f o r
‘f
can be s o l v e d i n terms of t h e e i g e n f u n c t i o n expansion
where t h e Fn a r e t h e f r e e s h e l f waves e i g e n f u n c t i o n s ( G i l l and Schumann, 1974; G i l l and C l a r k ,
1974, S e c t . 1 0 ) .
The s t r e a n i f u n c t i o n 9 ,
can be expanded i n s i n e
The r e s u l t i n g e q u a t i o n i s an o r d i n a r y d i f f e r e n t i a l
and c o s i n e t i m e s e r i e s .
e q u a t i o n i n t h e Y v a r i a b l e whose s o l u t i o n i s o b t a i n e d n u m e r i c a l l y .
We regarded
o n l y t h e f i r s t mode and i n v e s t i g a t e d t h e s o l u t i o n f o r a t m o s p h e r i c m o t i o n s havi n g a t a l l f r e q u e n c i e s a iiiagnitude g i v e n by t h e mean v a l u e s o f t h e observed data.
The w i n d s t r e s s c u r l a c t i n g on t h e deep b a s i n was computed u s i n g t h e 3 Genoa, C a l v i and N i c e w i n d d a t a , t h e mean v a l u e was 0.3X10-5dynlcm On t h e 2 s h e l f an a l o n g s h o r e w i n d s t r e s s w i t h a mean v a l u e o f -4.8X10-2dynlcni was
.
I n Table 2 t h e r e s u l t s i n
a p p l i e d ( t h e minus means a n o r t h w a r d w i n d s t r e s s ) .
terms o f s i n e and c o s i n e a r e shown f o r some p e r i o d i c i t i e s .
The comparison i s
made w i t h t h e w e i g h t e d means o b t a i n e d f r o m t h e seasonal data, t h e w e i g h t i s g i v e n by t h e l e n g t h o f t h e r e c o r d i n each season.
TABLE 2 Comparison between t h e model and t h e o b s e r v a t i o n s
PEKIOOICITY
MODEL
(days)
OBSERVATIONS
cos
sin
20.0
-16.8
6.5
-0.72
2.27
10.0
- 4.9
4.8
-3.09
1.20
-
2.4
2.4
-3.62
1.37
1.1
1.1
-3.34
2.58
5 .O 2.5
cos
sin
The model t e n d s t o o v e r e s t i m a t e t h e c u r r e n t a t l o w e r f r e q u e n c i e s anu t o u n d e r e s t i m a t e t h e c u r r e n t a t h i g h e r f r e q u e n c i e s , t h e b e s t r e s u l t b e i n g a t 5 days.
201
0
m
I
I
1 ' 1 I! I
h
c
I u) v
az
0
Q W
I v)
0
m I
Fig. 7
I
FEE.
I
I
I
MAR.
APR.
MAY.
The shear computed by using t h e data gathered i n f r o n t of S e s t r i Levante f r o i n February 1 2 t o May 30, 1979.
202
DISCUSSION The a n a l y s i s o f t h e d a t a suggest t h a t t h e c i r c u l a t i o n o f t h e L i g u r i a n Sea depends on t h e a t m o s p h e r i c m o t i o n s and on t h e unknown boundary c o n d i t i o n s .
In
p a r t i c u l a r t h e s h e l f c i r c u l a t i o n seems f o r c e d by t h e deep b a s i n c i r c u l a t i o n and a l o c a l wind.
I t can be
The i n t e r a c t i o n w i t h t h e T y r r h e n i a n Sea i s n o t c l e a r .
seen f r o m T r o t t i (1954) t h a t t h e r e i s a s t r o n g seasonal v a r i a t i o n o f t h e phys i c a l s t r u c t u r e i n t h e a r e a j u s t n o r t h o f t h e Tuscan A r c h i p e l a g o . An a t t e m p t t o i n v e s t i g a t e t h e w i n d f o r c e d m o t i o n was made by u s i n g a f o r c e d s h e l f wave model.
T h i s was a p p l i e d w i t h a v e r y c r u d e a p p r o x i m a t i o n , s i n c e we
d i s r e g a r d e d t h e a d v e c t i v e terms.
The i m p o r t a n c e of t h e ? d v e c t i v e terms can be
q u a l i t a t i v e l y appreciated b y analysing t h e data gathered i n f r o n t o f S e s t r i L e v a n t e d u r i n g t h e w i n t e r season. The v e r t i c a l shear o f t h e c u r r e n t was computThe v a l u e s o f
ed by f i l t e r i n g t h e d a t a b y means o f a 80 h o u r s lowpass f i l t e r .
t h e shear e v a l u a t e d f r o i n t h e d i f f e r e n c e between t h e 15 m and 50 ni c u r r e n t s and t h a t o f t h e 50 m and 95 m i s shown i n F i g u r e 7.
The shear was sometimes u n i -
A l a r g e v a l u e o f t h e s u r f a c e shear p o i n t s
f o r m i n d i c a t i n g a d v e c t i v e processes.
o u t t h e i m p o r t a n c e o f l o c a l f o r c i n g a f f e c t i n g t h e s u r f a c e w a t e r motion.
REFERENCES Adam, J.K., and Buchwald, V.T., waves.
The g e n e r a t i o n o f c o n t i n e n t a l s h e l f
J . F l u i d Mech., 35: 815-826.
A l l e n , J.S.,
1976.
On f o r c e d
J . Phys. Ocean.,
6: 426-43
Bossolasco, M. and Dagnino, I Genova.
1969.
G e o f i s . Pura Appl
B r u s c h i , A. and M a n z e l l a , G.,
l o n g c o n t i n e n t a l s h e l f waves on f - p l a n e .
, ,
1957.
Sulle correnti costiere nel Golfo d i
30: 123-140.
1980.
Wind and c u r r e n t autumnal d a t a s e r i e s
a n a l y s i s on t h e L i g u r i a n c o n t i n e n t a l s h e l f . Buchwald, V.T. waves.
and Adams, J.K.,
1968.
I 1 Nuovo Cimento,3C:
151-164.
The p r o p a g a t i o n o f c o n t i n e n t a l s h e l f
Proc. Koy. SOC. London, A305: 235-250.
De Maio, A.,
M o r e t t i , M.,
Sansone, E.,
Spezie, G. and V u l t a g g i o ,
M., 1975.
Su l a c i r c o l a z i o n e s u p e r f i c i a l e e p r o f o n d a n e l G o l f o d i Genova. U n i v . Nav. N a p o l i , Vol. X L I I I - X L I V : E l l i o t t , A.J.,
1978.
1st.
97-112.
The response o f t h e c o a s t a l w a t e r s o f Northwest I t a l y .
S a c l a n t c e n t Memo. SM 117, La Spezia, 14 pp.
203
E l l i o t t , A.J.,
1980.
The e f f e c t o f l o w f r e q u e n c y winds on sea l e v e l and Oceanol. Acta, 2: 429-433.
c u r r e n t s i n t h e G u l f o f Genova. E l l i o t t , A.J., of Italy.
1981.
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 o f f t h e west c o a s t
Oceanl. Acta, 4: 47-55.
E s p o s i t o , A. and M a n z e l l a , G., circulation. G i l l , A.E.
wind.
and C l a r k , A.J.,
1974.
J. Phys. Ocean.,
Geo. Bio., Gupta, B.R.
1954.
Wind induced u p w e l l i n g , c o a s t a l c u r r e n t
Deep Sea Res.,
and Schumann, E.H.,
Gleeson, T.A.,
An a n a l y s i s o f t h e L T g u r i a n s h e l f
Tech. Rep. CNEN R T / F I ( 8 1 ) 3 , 101 pp.
and sea l e v e l changes. G i l l , A.E.
1981.
1974.
21: 325-345.
The g e n e r a t i o n o f l o n g s h e l f waves by
4: 83-90.
Cyclogenesis i n t h e Mediterranean region.
Arch. Meteo.
A 6 ( 2 ) : 153-171. and Sing, G.,
1977.
A power spectrum a n a l y s i s o f t h e mean d a i l y
p r e s s u r e o v e r t h e M e d i t e r r a n e a n and neighborhood d u r i n g November 1967 t o A p r i l 1968. Papa, L.,
T e l l u s , 29: 382-384.
1977.
H-N method. Papa, L.,
The f r e e o s c i l l a t i o n o f t h e L i g u r i a n Sea computed by t h e Deutsche H y d r o g r a f . Z e i t . ,
1980.
o f Genoa.
A numerical v e r i f i c a t i o n o f a clockwise c i r c u l a t i o n i n t h e Gulf
App. Math. Model. 4: 313-315.
S t o c c h i n o , C . and T e s t o n i , A.,
1977.
d e l l e c o r r e n t i n e l Mar L i g u r e . T r o t t i , L.,
30: 82-90.
1954.
Nuove o s s e r v a z i o n i s u l l a c i r c o l a z i o n e
1 s t . I d r o g r . Mar. M i l i t a r e , Genova, 39 pp.
R e p o r t on t h e oceanographic i n v e s t i g a t i o n s i n t h e L i g u r i a n
and N o r t h T y r r h e n i a n Seas.
Cent. T a l a s s o g r a f . T i r r e n . ,
Genova, 21 pp.
This Page Intentionally Left Blank
205
NON-TIDAL
FLOW I N THE NORTH CHANNEL OF THE IRISH S EA
M. J . HOWARTH
I n s t i t u t e o f Oceanographic S c i e n c e s , B i d s t o n O b s e r v a t o r y , B i r k e n h e a d , M e r s e y s i d e , England
ABSTRACT The e n t r a n c e t o a s e m i - e n c l o s e d s e a forms a c o n s t r i c t e d c o n n e c t i o n between two d i f f e r e n t w a t e r masses and s o p r o c e s s e s t h e r e w i l l s i g n i f i c a n t l y a f f e c t t h e dynamics o f t h e s e a . Across t h e e n t r a n c e t h e r e a r e l i k e l y t o b e l a r g e d e n s i t y and e l e v a t i o n g r a d i e n t s which w i l l d r i v e e a s i l y m e a s u r a b l e c u r r e n t s . Measurements have b e e n r e c o r d e d i n t h e N o r t h C h a n n e l , t h e n a r r o w e r of two e n t r a n c e s t o t h e I r i s h S e a . F o r a y e a r c o a s t a l e l e v a t i o n s and v o l t a g e s i n d u c e d i n a c r o s s - c h a n n e l t e l e p h o n e c a b l e were r e c o r d e d a n d , a s w e l l , f o r 45 d a y s i n summer, c u r r e n t s and o f f - s h o r e sea b e d p r e s s u r e s . The f l o w s w e r e dominated by s t r o n g t i d a l c u r r e n t s ( i n e x c e s s o f 1 m/s) which c a u s e d s t r o n g m i x i n g . During t h e 45 day e x p e r i m e n t t h e c u r r e n t and CTD o b s e r v a t i o n s showed a w e l l d e f i n e d c i r c u l a t i o n p a t t e r n which had l a r g e s p a t i a l g r a d i e n t s and w i t h c u r r e n t s i n e x c e s s of 0.05 m / s . T h e r e w e r e a l s o wind d r i v e n e v e n t s which c a u s e d u n i f o r m c u r r e n t s a l o n g t h e c h a n n e l w i t h a magnitude comparable t o t h a t of t h e c i r c u l a t i o n . The 45 d a y s e x p e r i m e n t h a s e n a b l e d t h e p h y s i c s of t h e l o w f r e q u e n c y f l o w s i n t h e c h a n n e l t o be i n v e s t i g a t e d i n d e t a i l and a n i n d i c a t i o n o f t h e i r v a r i a b i l i t y h a s been g a i n e d from t h e y e a r l o n g measurements. INTRODUCTION I n s t u d i e s o f t h e dynamics o f s e m i - e n c l o s e d s e a s i t i s o f t e n c o n v e n i e n t t o i s o l a t e t h e s e a by making a n e n t r a n c e a boundary where c o n d i t i o n s a r e measured o r assumed t o b e known, f o r example i n t i d e and s u r g e n u m e r i c a l models o r when e s t i m a t i n g t h e f l u s h i n g
or r e s i d e n c e t i m e o f t h e s e a . F u r t h e r u n d e r s t a n d i n g o f t h e s e a ' s r e s p o n s e c a n o f t e n b e g a i n e d by c o n s i d e r i n g t h e s h e l f s e a combined w i t h t h e a d j a c e n t ocean. Since the entrance is a constriction between t h e two w a t e r masses any exchange between them s h o u l d g e n e r a t e t h e r e l a r g e c u r r e n t o r p r e s s u r e g r a d i e n t s i g n a l s which c a n b e e a s i l y measured e i t h e r d i r e c t l y by d e p l o y i n g i n s t r u m e n t s i n t h e s e a o r r e m o t e l y from t h e l a n d o r s k y .
The f i r s t approach
206
i s e x p e n s i v e b o t h b e c a u s e t h e equipment h a s t o b e r o b u s t and r e l i a b l e i n a h o s t i l e environment and a l s o b e c a u s e a s h i p i s needed f o r deployment and r e c o v e r y .
I n a d d i t i o n , t h e equipment
i s v u l n e r a b l e and d a t a l o s s e s can b e s i g n i f i c a n t and a r e of unknown e x t e n t u n t i l r e c o v e r y i s a t t e m p t e d . These measurements a r e u s u a l l y l o c a l s o t h a t , i n o r d e r t o g a i n an a d e q u a t e s p a t i a l c o v e r a g e , many i n s t r u m e n t s must be d e p l o y e d .
The s e c o n d , remote,
approach i s o f t e n c h e a p e r s i n c e t h e equipment i s less v u l n e r a b l e , e a s i e r t o i n s t a l l and c h e a p e r t o check and r e p a i r i f f a u l t y . g e n e r a l , t h e measurements a r e i n t e g r a t e d .
In
However, c a l i b r a t i o n
of t h e s y s t e m i s o f t e n u n s u r e , p a r t i c u l a r l y f o r z e r o flow c o n d i t i o n s , and t h e measurements can be s u s c e p t i h l e t o i n s t r u mental d r i f t . The approaches can b e combined by d e p l o y i n g c u r r e n t meters and p r e s s u r e r e c o r d e r s i n t h e s e a f o r one month t o p r o v i d e t h e d a t a t o c a l i b r a t e and v a l i d a t e t h e s h o r e b a s e d measurements which a r e t h e n r e c o r d e d f o r l o n g e r . experiment t o study
T h i s was t h e d e s i g n of an
a s e m i - d i u r n a l t i d a l amphidrome i n t h e
North Channel o f t h e I r i s h Sea and t h e r e g i o n ' s low f r e q u e n c y ( l e s s t h a n 1 cpd) dynamics.
The o f f s h o r e c u r r e n t and s e a bed
p r e s s u r e measurements w e r e made i n August and.September 1 9 7 9 w h i l s t o n s h o r e e l e v a t i o n and t e l e p h o n e c a b l e measurements were r e c o r d e d from J u l y 1 9 7 9 t o J u l y 1 9 8 0 .
This paper contains a
b r i e f d e s c r i p t i o n o f t h e p h y s i c a l oceanography of t h e a r e a and
of t h e e x p e r i m e n t f o l l o w e d by a p r e l i m i n a r y d i s c u s s i o n o f t h e low f r e q u e n c y r e s u l t s l o o k i n g a t b o t h t h e measuring systems and t h e dynamics o f t h e North Channel, I r i s h Sea and Malin S h e l f Sea.
DESCRIPTION O F THE NORTH CHANNEL A r e g i o n of i n t e r - c o n n e c t e d s e a s which loop from t h e A t l a n t i c
Ocean t h r o u g h t h e I r i s h Sea back t o t h e A t l a n t i c Ocean e x i s t s o f f t h e w e s t c o a s t of B r i t a i n .
The s o u t h e r n arm of t h e l o o p i s
formed by t h e C e l t i c Sea (which i s a l s o t h e e n t r a n c e t o t h e E n g l i s h and B r i s t o l Channels) and t h e S t . G e o r g e ' s Channel; n o r t h e r n arm by t h e North Channel and t h e Malin S h e l f S e a , Figure l a .
the
t
10
F i g u r e 1. a ) Map of w e s t c o a s t of B r i t a i n
207
b ) B a t h y m e t r i c map of N o r t h C h a n n e l _ _ _ - 100 m : . . .... 2 0 0 rn c o n t o u r s
208 D e p t h s i n t h e l o o p s l o p e g e n t l y from 2 0 0 m a t t h e C e l t i c S e a s h e l f e d g e t o a b o u t l O O m i n t h e S t . G e o r g e ' s C h a n n e l and w e s t e r n I r i s h S e a ( t h e e a s t e r n I r i s h S e a i s s h a l l o w e r , l e s s t h a n 55m). The g r e a t e s t d e p t h s i n t h e l o o p o c c u r i n l o c a l i z e d d e p r e s s i o n s i n t h e North Channel
-
t h e d e e p e s t b e i n g 280m i n a n a r r o w t r o u g h
o f f t h e Mull o f G a l l o w a y , F i g u r e l b .
The a v e r a g e d e p t h o f t.he
N o r t h C h a n n e l i s b e t w e e n 1 2 0 m and 1 4 0 m b u t t h e r e i s a s i l l o f d e p t h 4 0 m b e t w e e n I s l a y and M a l i n Head f o l l o w e d b y a g e n t l e s l o p e down t o t h e s h e l f e d g e .
The n a r r o w e s t p a r t o f t h e l o o p
o c c u r s i n t h e N o r t h C h a n n e l (20km b e t w e e n T o r r Head and t h e M u l l o f K i n t y r e ) and a l s o t h e s m a l l e s t c r o s s - s e c t i o n a l
4 x
lo6 m3
compared w i t h 6 x
lo6
area (about
m3 f o r t h e n a r r o w k s t p a r t o f
t h e S t . G e o r g e ' s Channel. The d o m i n a n t p h y s i c a l p r o c e s s i n t h e a r e a i s t h e s e m i - d i u r n a l t i d e which p r o p a g a t e s from t h e A t l a n t i c Ocean i n t o t h e I r i s h S e a t h r o u g h b o t h arms of t h e l o o p and i s r e f l e c t e d by t h e E n g l i s h c o a s t , f o r m i n g a s t a n d i n g wave i n t h e I r i s h S e a (Doodson and Corkan, 1 9 3 2 ) .
I n t h e North Channel t h e i n c i d e n t and r e f l e c t e d
waves combine t o make a n amphidrome i n t h e r e g i o n b e t w e e n t h e M u l l o f K i n t y r e , I s l a y and T o r r Head.
The n e t f l u x o f s e m i -
d i u r n a l t i d a l energy t h r o u g h t h e North Channel i s s m a l l ( T a y l o r , 1919;
Robinson, 1 9 7 9 ) ,
n o r t h e r n arm.
implying n e a r p e r f e c t r e f l e c t i o n f o r t h e
B e c a u s e o f t h e amphidrome t i d a l e l e v a t i o n s a r e
s m a l l i n t h e North Channel b u t c u r r e n t s ( a n d hence t i d a l mixing)
are l a r g e
-
t h e M2 a m p l i t u d e b e t w e e n t h e Mull o f K i n t y r e and
T o r r Head e x c e e d s 1 m / s
-
and t h e p h a s e o f t h e c u r r e n t v a r i e s
l i t t l e t h r o u g h o u t t h e North Channel. F o r a v e r a g e c o n d i t i o n s a t any t i m e t h e s u r f a c e w a t e r i n t h e
s o u t h e r n p a r t o f t h e N o r t h C h a n n e l i s t h e f r e s h e s t and c o o l e s t i n t h e w h o l e l o o p , i g n o r i n g r e g i o n s c l o s e t o t h e s h o r e s and i n t h e e a s t e r n I r i s h Sea.
Throughout t h e y e a r t h e r e i s a s a l i n i t y
d i f f e r e n c e of approximately 1 . 3 x
between t h e s u r f a c e w a t e r
o f t h e A t l a n t i c Ocean and t h e N o r t h C h a n n e l (ICES, 1 9 6 2 ) .
The
c o r r e s p o n d i n g t e m p e r a t u r e d i f f e r e n c e v a r i e s b e t w e e n 2OC, f o r m o s t o f t h e y e a r , and O°C,
i n October and November.
Hence t h e
d e n s i t y d i f f e r e n c e for t h e s u r f a c e w a t e r i s s m a l l ( a b o u t 0 . 8 3 Kg/m ) w i t h t h e N o r t h C h a n n e l w a t e r l i g h t e r t h a n t h e A t l a n t i c
water.
Because o f s t r o n g t i d a l mixing t h e w a t e r i n t h e North
C h a n n e l i s v e r t i c a l l y homogeneous t h r o u g h o u t t h e y e a r .
However,
t i d a l c u r r e n t a m p l i t u d e s d e c r e a s e r a p i d l y away from t h e N o r t h
209
C h a n n e l and a s e a s o n a l p y c n o c l i n e o c c u r s i n t h e M a l i n S h e l f S e a . I n t h e r e g i o n b e t w e e n t h e homogeneous and s t r a t i f i e d w a t e r s ( b e t w e e n M a l i n Head and I s l a y ) a f r o n t i s formed which i s v i s i b l e i n summer i n s a t e l l i t e i n f r a - r e d
et al.,
1 9 7 8 , Simpson e t a l . ,
photographs
(Pingree
1979).
The o v e r a l l c i r c u l a t i o n of t h e N o r t h C h a n n e l r'egion
i s weak
b u t w e l l d e f i n e d , a c c o r d i n g t o p r e v i o u s measurements by d r i f t e r s ( B a r n e s and G o d l e y , 1 9 6 1 ) and by t r a c e r s s u c h a s s a l i n i t y (Bowden, 1 9 5 0 ) a n d C a e s i u m 137 ( W i l s o n , 1 9 7 4 ; 1981a).
McKinley e t a l .
Both Bowden a n d W i l s o n c a l c u l a t e d from t h e d i s t r i b u -
t i o n o f t h e i r t r a c e r s a n e t n o r t h w a r d f l o w b e t w e e n D u b l i n and Holyhead o f 0 . 0 0 3 5 m / s
-
e q u i v a l e n t , b y ' c o n t i n u i t y , t o 0.01 m / s
t h r o u g h t h e n a r r o w e s t p a r t o f t h e North Channel.
This northward
f l o w i s c l e a r l y shown i n t h e d i s t r i b u t i o n o f t h e w a s t e o u t p u t from t h e n u c l e a r r e - p r o c e s s i n g p l a n t a t W i n d s c a l e . includes radio-active
The w a s t e
T r i t i u m and Caesium 134 and 1 3 7 , e a c h o f
which a p p e a r s t o r e m a i n i n t h e w a t e r column.
The u s e f u l n e s s o f
T r i t i u m a s a tracer i s reduced because o f a l a r g e atmospheric i n p u t b u t m o n i t o r i n g of Caesium 1 3 7 , i n p a r t i c u l a r , h a s shown t h a t t h e f l o w from W i n d s c a l e e x t e n d s t o t h e N o r t h C h a n n e l ( t i m e t a k e n t o r e a c h i t a b o u t 6 m o n t h s ) , n o r t h w a r d a r o u n d S c o t l a n d and i n t o t h e N o r t h S e a (McKinley e t a l . ,
1981b;
Kautsky e t a l . ,
1980). The s a l i n i t y d i s t r i b u t i o n ( C r a i g , 1 9 5 9 ;
Lee,
1960;
Slinn,
1 9 7 4 ) and p l a n k t o n d i s t r i b u t i o n s ( W i l l i a m s o n , 1956) show t h a t t h e n o r t h w a r d f l o w i s n o t u n i f o r m a c r o s s t h e N o r t h Channel b u t t h a t t h e r e i s a f l o w o f A t l a n t i c w a t e r i n t o t h e I r i s h Sea c l o s e t o t h e I r i s h c o a s t , which i s p r o b a b l y i n t e r m i t t e n t .
This flow
was a l s o o b s e r v e d i n c u r r e n t meter r e c o r d s from t h e S k u l m a r t i n Lightvessel
( a t t h e s o u t h e r n e n d of t h e N o r t h C h a n n e l c l o s e t o
t h e I r i s h s h o r e ) which l a s t e d 1 3 months and h a d an o v e r a l l mean of 0.008 m / s
towards t h e s o u t h - e a s t
(Proudman, 1 9 3 9 ) .
S u p e r i m p o s e d on t h i s c i r c u l a t i o n p a t t e r n a r e more e n e r g e t i c h i g h e r f r e q u e n c y ( 0 . 1 t o 1 c p d ) c u r r e n t s d r i v e n by s t o r m s . t h e N o r t h C h a n n e l a r e a t h e s e h a v e b e e n s t u d i e d i n two ways
In
-
by
n u m e r i c a l models and by t h e v o l t a g e s i n d u c e d i n a c r o s s c h a n n e l telephone cable.
Heaps a n d J o n e s
(1975 and 1 9 7 9 ) h a v e u s e d two-
and t h r e e - d i m e n s i o n a l n u m e r i c a l models t o s t u d y s t o r m s u r g e s w i t h i n t h e I r i s h S e a , t a k i n g t h e North Channel a s a boundary. They h a v e shown t h a t t h e e x t e r n a l s u r g e p r o p a g a t i n g t h r o u g h t h e
210
North Channel i s , f o r most a r e a s of t h e I r i s h S e a , more i m p o r t a n t than the l o c a l l y generated surge.
A two-dimensional
numerical
model of t h e s h e l f s e a s around t h e B r i t i s h I s l e s by P i n g r e e and G r i f f i t h s (1980) p r e d i c t s t h a t u n i f o r m winds w i l l n o t g e n e r a t e a p p r e c i a b l e e l e v a t i o n g r a d i e n t s , e i t h e r a l o n g o r a c r o s s t h e North Channel, and t h a t t h e maximum flow t h r o u g h t h e North Channel w i l l b e g e n e r a t e d by winds blowing a l o n g i t . The l a t t e r p r e d i c t i o n i s s u p p o r t e d by t h e c a b l e measurements of Bowden and Hughes ( 1 9 6 1 ) and P r a n d l e ( 1 9 7 6 ) .
S i n c e sea w a t e r
i s an e l e c t r i c a l c o n d u c t o r which moves t h r o u g h t h e E a r t h ' s
m a g n e t i c f i e l d an e . m . f .
i s generated.
For f l o w t h r o u g h a
c h a n n e l t h e e . m . f . becomes a p o t e n t i a l d i f f e r e n c e " between t h e two s i d e s of t h e c h a n n e l which can b e measured v i a a c o n d u c t i n g c a b l e a c r o s s t h e channel.
The r e l a t i o n s h i p between c a b l e
v o l t a g e and flow v a r i e s a c c o r d i n g t o t h e f l o w p a t t e r n (Robinson, 1 9 7 6 ) s o t h a t a c a l i b r a t i o n made w i t h t i d a l c u r r e n t measurements w i l l n o t n e c e s s a r i l y h o l d f o r c i r c u l a t i o n . Another problem, e s p e c i a l l y f o r c i r c u l a t i o n e s t i m a t e s , i s t h a t t h e c a b l e h a s an unknown c o n s t a n t p o t e n t i a l d i f f e r e n c e , a r i s i n g from i t s p r o p e r t i e s and i t s e a r t h i n g a r r a n g e m e n t . The measurements
showed a good c o r r e l a t i o n between t h e wind r e s o l v e d a l o n g t h e c h a n n e l and c a b l e v o l t a g e ( c o e f f i c i e n t o f 0 . 7 f o r t h e whole y e a r , s m a l l e r i n summer, l a r g e r i n w i n t e r ) and t h a t t h e v o l t a g e l a g g e d t h e wind by a b o u t 2 h o u r s .
Therefore water flows through t h e
North Channel i n t o o r o u t o f t h e I r i s h Sea i n r e s p o n s e t o winds from t h e n o r t h - w e s t o r s o u t h - e a s t w i t h v e r y l i t t l e d e l a y . MEASUREMENTS AND COMPARISONS The topography o f t h e North Channel i s r e l a t i v e l y s i m p l e and some of t h e dynamics a t f r e q u e n c i e s l e s s t h a n 1 c . p . d . s t o r m d r i v e n and c i r c u l a t i o n
-
-
b r o a d l y known, a s i n d i c a t e d above.
The p u r p o s e of t h e e x p e r i m e n t was t o s e e if t h e s e dynamics c o u l d be q u a n t i f i e d i n agreement w i t h t h e e q u a t i o n s of motion by means o f a c c u r a t e o f f s h o r e and s h o r e b a s e d o b s e r v a t i o n s , t o measure t h e r e s p o n s e i n more d e t a i l and t o d e t e r m i n e t h e d r i v i n g f o r c e s f o r e l e v a t i o n s and c u r r e n t s .
The measurements would a l s o e n a b l e
t h e c a l i b r a t i o n of t h e c a b l e a t both t i d a l and, f o r t h e f i r s t t i m e , low f r e q u e n c i e s .
570
56'
*
MET STATION
OJ
55.
ATLANTIC OCEAN
540
Figure 2 .
Map of s t a t i o n pmsiticms. T i d e g a v s at B A - B a l l y a i t s t l e , LB-Larne, MA-NacbrilP&~h, M H - M a l i n H e a d , PE-RDrt E l l e n , T H - T o n Bead, M e t . s t a k i a s at & - U * v V e n PR+YeSAriCk3r, TI-Tiree.
c.
CL
212 The o b s e r v a t i o n s w e r e s h o r e b a s e d measurements l a s t i n g 1 3 m o n t h s , from J u l y 1 9 7 9 t o J u l y 1980 ( s e a s u r f a c e e l e v a t i o n , v o l t a g e i n a c r o s s c h a n n e l c a b l e , a t m o s p h e r i c p r e s s u r e , wind s p e e d and d i r e c t i o n ) and o f f s h o r e m e a s u r e m e n t s l a s t i n g 4 5 d a y s , from August t o S e p t e m b e r 1 9 7 9 ( s e a b e d p r e s s u r e , c u r r e n t and s e a w a t e r d e n s i t y ) , see F i g u r e 2 f o r a map. The r e s u l t s d i s c u s s e d i n t h i s p a p e r h a v e a l l b e e n low pass f i l t e r e d , u n l e s s o t h e r w i s e s t a t e d , by a B u t t e r w o r t h s q u a r e d f i l t e r w i t h h a l f power p o i n t a t 0 . 7 1 6 4 cpd and N=9
(see f o r
i n s t a n c e Hamming 1 9 7 7 , pp 189-195 o r Thomson and Chow, 1 9 8 0 ) . I t s r e s p o n s e , F i g u r e 3 , i s m o n o t o n i c , a t 0 . 6 cpd i s 0 . 9 6 and
a t 0 . 9 cpd i s 0.01, s o t h a t a l l d i u r n a l and s e , m i - d i u r n a l t i d e s , a s w e l l a s i n e r t i a l c u r r e n t s , have b e e n c o m p l e t e l y s u p p r e s s e d . The B u t t e r w o r t h
f i l t e r i s r e c u r s i v e a n d was a p p l i e d t w i c e
( f o r w a r d s t h e n b a c k w a r d s ) s o t h a t no p h a s e l a g s w e r e i n t r o d u c e d . The d a t a w e r e r e - s a m p l e d e v e r y 3 h o u r s and t o r e d u c e r i n g i n g 1% d a y s w e r e d e l e t e d f r o m t h e b e g i n n i n g and e n d o f e a c h r e c o r d .
AMPLITUDE SQUARED RESWNSE BUTTERWORTH FILTER N.9, CUT OFF P€RlOD=33*5h
Ibo 50 3 3 2 5 2 0
Figure 3 .
hours
PERIOD
Response o f low p a s s f i l t e r .
213 Shore b a s e d measurements Sea s u r f a c e e l e v a t i o n
Pneumatic t i d e gauges w e r e i n s t a l l e d a t
M a c h r i h a n i s h , P o r t E l l e n , B a l l y c a s t l e a n d T o r r Head.
The
d i f f e r e n c e b e t w e e n t h e p r e s s u r e a t a p o i n t f i x e d below l o w e s t s e a l e v e l and a t m o s p h e r i c p r e s s u r e was m e a s u r e d by a D i g i q u a r t z ( q u a r t z c r y s t a l ) p r e s s u r e t r a n s d u c e r and r e c o r d e d by an Aanderaa l o g g e r ( B r o w e l l and Pugh, 1 9 7 7 ) .
The p r e s s u r e t r a n s d u c e r
s t a b i l i t y was good
-
b e w i t h i n 100 Pa.
The r e c o r d s from P o r t E l l e n and T o r r Head
i t was c h e c k e d e v e r y 4 months a n d f o u n d t o
were c o m p l e t e b u t a t M a c h r i h a n i s h t h e a i r p i p e was c u t and 30 d a y s l o s t b e t w e e n 1 7 December 1 9 7 9 and 1 5 J a n u a r y 1980.
At
B a l l y c a s t l e t h e p r e s s u r e p o i n t was n o t . s t a b l e f o r t h e p e r i o d of o f f s h o r e measurements s o i t s r e c o r d h a s n o t been c o n s i d e r e d further.
Measurements from s t i l l i n g w e l l t i d e g a u g e s a t L a r n e
and M a l i n Head w e r e o b t a i n e d froin t h e a p p r o p r i a t e a u t h o r i t i e s . T h a t from L a r n e c o n t a i n e d 5 g a p s t o t a l l i n g 35 d a y s d u r i n g t h e 1 3 m o n t h s , w h i l s t t h a t from Malin Head w a s good f o r t h e p e r i o d
of o f f s h o r e m e a s u r e m e n t s b u t a f t e r t h a t t h e gauge s i l t e d u p . The h y d r o s t a t i c e q u a t i o n i s assumed t o h o l d s o t h a t t h e s e a bed p r e s s u r e p i s g i v e n by
were p i s t h e s e a w a t e r d e n s i t y , g t h e a c c e l e r a t i o n due t o g r a v i t y , 5 t h e s e a s u r f a c e e l e v a t i o n , h t h e mean w a t e r d e p t h ,
P t h e a t m o s p h e r i c p r e s s u r e a n d P t h e mean a t m o s p h e r i c p r e s s u r e , taken t o be 1 . 0 1 2 x
lo5
Pa.
The a t m o s p h e r i c p r e s s u r e a t e a c h
t i d e g a u g e s i t e was c a l c u l a t e d by l i n e a r i n t e r p o l a t i o n from t h r e e s e t s o f o b s e r v a t i o n s , see below.
The p n e u m a t i c t i d e
gauges r e c o r d e d d i f f e r e n t i a l p r e s s u r e (p-p) and s o t h e s e a s u r f a c e e l e v a t i o n was e a s i l y c a l c u l a t e d .
The s e a bed p r e s s u r e ,
p , i s a more u s e f u l p a r a m e t e r when c o n s i d e r i n g t h e dynamics of t h e s e a a n d t h i s , t o o , was c a l c u l a t e d f o r e a c h s i t e . T o i n v e s t i g a t e w h e t h e r t h e o b s e r v a t i o n s conformed t o an
' i n v e r t e d b a r o m e t e r ' , where an i n c r e a s e i n a t m o s p h e r i c p r e s s u r e of 100 Pa c a u s e s a d e c r e a s e i n e l e v a t i o n o f 0 . 0 0 9 9 m , t h e e l e v a t i o n s m u l t i p l i e d by pg w e r e c o r r e l a t e d w i t h t h e a t m o s p h e r i c p r e s s u r e a t e a c h s i t e , T a b l e 1.
The c o r r e l a t i o n s a r e h i g h l y
s i g n i f i c a n t and t h e m a g n i t u d e s of t h e s l o p e s of t h e l e a s t s q u a r e s l i n e a r f i t s a r e s l i g h t l y g r e a t e r t h a n t h e e x p e c t e d v a l u e o f 1.
214 T h i s i s common f o r t h e w e s t c o a s t o f t h e B r i t i s h I s l e s , w h e r e a s f o r t h e e a s t c o a s t t h e m a g n i t u d e of t h e s l o p e i s n o r m a l l y less t h a n 1 (Thompson, 1 9 8 0 ) .
The d i f f e r e n c e s a r e p r e s u m a b l y b e c a u s e
o f wind stress s e t u p / s e t down a s s o c i a t e d w i t h a t m o s p h e r i c pressure systems.
Two common w e a t h e r p a t t e r n s f o r t h e B r i t i s h
Isles a r e f i r s t a d e p r e s s i o n moving e a s t w a r d t o t h e n o r t h ,of S c o t l a n d accompanied by winds v e e r i n g from s o u t h e r l y t o n o r t h w e s t e r l y and s e c o n d a s t a t i o n a r y h i g h p r e s s u r e o v e r S c a n d a n a v i a accompanied by w i n d s from t h e e a s t .
I n b o t h p a t t e r n s t h e wind
s e t u p / s e t down a g a i n s t t h e w e s t c o a s t o f B r i t a i n w i l l r e - i n f o r c e t h e adjustment of t h e s e a s u r f a c e t o t h e atmospheric p r e s s u r e . The s t a n d a r d d e v i a t i o n s of t h e e l e v a t i o n r e c o r d s l e r e a p p r o x i m a t e l y 1 7 0 0 Pa and f o r t h e sea b e d p r e s s u r e r e c o r d s
w e r e 1150 P a , a r e d u c t i o n i n v a r i a n c e by 5 4 % . TABLE 1
L e a s t s q u a r e s l i n e a r f i t b e t w e e n s e a s u r f a c e e l e v a t i o n and atmospheric pressure.
I
Site
I
Correlation coefficient
T o r r Head Port Ellen Machrihanish
-0.74 -0.77 -0.76 -0.71 -0.77
Larne M a l i n Head
I
Slope of f i t
1
-1.11 -1.17 -1.11 -1.06 -1.04 I
Telephone c a b l e v o l t a g e
The v o l t a g e i n d u c e d by t h e f l o w of w a t e r
t h r o u g h t h e s o u t h e r n p a r t of t h e N o r t h C h a n n e l was r e c o r d e d on a d a t a l o g g e r b e t w e e n J u l y 1979 and J u l y 1980 u s i n g t h e P o r t p a t r i c k t o Donaghadee t e l e p h o n e c a b l e , which i s a p p r o x i m a t e l y 35 Km l o n g . Maximum r e c o r d e d v o l t a g e s were 2 1 v o l t . T w o g a p s , one of 1 2 h o u r s and one o f 2 d a y s , b o t h a t t h e b e g i n n i n g o f August 1 9 7 9 , were i n t e r p o l a t e d by s y n t h e s i z i n g t h e t i d e s from a h a r m o n i c a n a l y s i s o f t h e r e s t of t h e r e c o r d and making a n a l l o w a n c e f o r t h e r e s i d u a l s a t t h e e n d s of t h e i n t e r p o l a t i o n s . Meteorological
H o u r l y wind s p e e d and d i r e c t i o n and 3 h o u r l y
a t m o s p h e r i c p r e s s u r e r e a d i n g s from T i r e e , P r e s t w i c k and A l d e r g r o v e w e r e o b t a i n e d from t h e B r i t i s h M e t e o r o l o g i c a l O f f i c e a n d h o u r l y wind s p e e d and d i r e c t i o n from M a l i n Head from t h e
215 I r i s h Meteorological Office.
A l l d a t a w e r e low p a s s f i l t e r e d .
From t h e a t m o s p h e r i c p r e s s u r e s a g e o s t r o p h i c wind was c a l c u l a t e d and compared w i t h t h e o b s e r v e d w i n d s , T a b l e 2 .
The s p e e d
c o r r e l a t i o n is highly s i g n i f i c a n t a t a l l sites, p a r t i c u l a r l y f o r t h e more e x p o s e d s t a t i o n s a t T i r e e e and Malin Head.
A s expected,
t h e g e o s t r o p h i c wind was s t r o n g e r t h a n t h e o b s e w e d and was r o t a t e d clockwise r e l a t i v e t o it.
A l s o shown i n T a b l e 2 a r e
v a l u e s o b t a i n e d by H a s s e a n d Wagner ( 1 9 7 1 ) from l i g h t v e s s e l s i n t h e German B i g h t f o r n e u t r a l s t a b i l i t y c o n d i t i o n s .
Their
o b s e r v e d s u r f a c e wind s p e e d s a r e s l i g h t l y l a r g e r i n comparison w i t h t h e g e o s t r o p h i c wind b u t t h e d i r e c t i o n d e v i a t i o n i s t h e same.
S i n c e i t w a s n o t known how r e p r 6 s e n t a t i v e t h e o b s e r v a -
t i o n s from t h e s h o r e s t a t i o n s w e r e f o r t h e e s t i m a t i o n of wind
s t r e s s o v e r t h e N o r t h C h a n n e l , t h e g e o s t r o p h i c wind c a l c u l a t e d from t h e o b s e r v e d p r e s s u r e s was u s e d and c o n v e r t e d t o s u r f a c e wind w i t h t h e v a l u e s o f Hasse and Wagner.
The wind s t r e s s ,
T,
i s g i v e n by T
=
cpu2
where p i s t h e d e n s i t y o f t h e a i r , U t h e wind s p e e d and C t h e d r a g c o e f f i c i e n t g i v e n by C = 0.0015 +0.00104
-1
(1 + e x p ( - U + 1 2 . 5 ) / 1 . 5 6 ) The wind s t r e s s t i m e
(Amorocho a n d D e V r i e s , 1 9 8 0 ) .
s e r i e s w a s then l o w pass f i l t e r e d . TABLE 2
Comparison between g e o s t r o p h i c and o b s e r v e d wind.
E i t f o r wind s p e e d i n m / s Station
Correlation coefficient
M
I
0.42 0.24 0.26 0.40 0.56 I
2.4 1.9 1.6 3.2
2.4
c
Observed-geostrophic
C ~~
0.80 0.57 0.70 0.74
+
Direction
Speed
Tiree P r e stwick Aldergrove Malin Head Hasse a n d Wagner
Least squares
i s : - Observed = M x G e o s t r o p h i c
~
-
20 -16 -26 -26 -20
216 O f f s h o r e measurements The o f f s h o r e measurements of sea bed p r e s s u r e and c u r r e n t w e r e made by d e p l o y i n g i n t e r n a l l y r e c o r d i n g i n s t r u m e n t s . and r e c o v e r y c r u i s e s e a c h l a s t e d a f o r t n i g h t
The launch
( a t t h e beginning
o f August and end of September 1 9 7 9 , r e s p e c t i v e l y ) and were s e p a r a t e d by one month.
During e a c h c r u i s e s e a s u r f a c e ,
t e m p e r a t u r e and c o n d u c t i v i t y w e r e c o n t i n u o u s l y m o n i t o r e d and CTD p r o f i l e s r e c o r d e d .
Sea bed p r e s s u r e
I n s t r u m e n t s were d e p l o y e d a t s t a t i o n s B , E l D
and J , T a b l e 3 and F i g u r e 2 .
Those a t s t a t i o n s B and D w e r e
f i t t e d w i t h D i g i q u a r t z q u a r t z c r y s t a l p r e s s u r e t r a n s d u c e r s and
a t s t a t i o n s E and J w i t h s t r a i n gauges.
Thesepressure
t r a n s d u c e r s , w h i l s t p r i m a r i l y d e s i g n e d t o measure t i d e s , a r e r e a s o n a b l y s t a b l e s o t h a t low f r e q u e n c y p r e s s u r e s a r e a l s o measured.
The agreement between t h e s h o r e b a s e d and o f f s h o r e
gauges f o r l o w f r e q u e n c y p r e s s u r e i s v e r y good, f o r i n s t a n c e F i g u r e 4 , b u t i t w i l l be shown t h a t i t i s d i f f i c u l t t o d i f f e r e n t i a t e between r e a l g r a d i e n t s and i n s t r u m e n t a l problems when c o n s i d e r i n g p r e s s u r e d i f f e r e n c e s of less t h a n 1000 P a . TABLE 3
Station positions
1
Station
Latitude N 54O 4 9 ' 54O 5 8 ' 54O 5 8 ' 55O 5 2 ' 55O 2 8 ' 55O 2 5 ' 55O 31' 55O 5 3 ' 55O 00'
Longitude W 5O 3 8 '
5O 36' So 1 4 ' 5O 4 5 ' 6 O 10' 7O 31' 6O 5 1 ' 6 O 33' 00'
loo
Depth below l o w e s t w a t e r l e v e l (m) 195 155 54
120 110
55 60 45 125'
217 Pacah 2000
0
PORT ELLEN
0
STATION E
- 2000 5
I5
25
Figure 4 .
Currents
4
SEPTEMBER
WWST
14 1979
24
Low f r e q u e n c y bottom p r e s s u r e o b s e r v a t i o n s from a s h o r e b a s e d gauge ( P o r t E l l e n ) and an o f f s h o r e gauge ( s t a t i o n E) , as r e c o r d e d .
1 9 Aanderaa RCM4 c u r r e n t meters and 3 v e c t o r
a v e r a g i n g c u r r e n t meters m a n u f a c t u r e d by A M F (henceforward r e f e r r e d t o a s AMF VACM) w e r e d e p l o y e d i n 9 r i g s a t t h e p o s i t i o n s g i v e n i n T a b l e 3.
(There w e r e two r i g s a t s t a t i o n D
where an Aanderaa w a s d e p l o y e d i n a bottom frame:
a l l the
o t h e r r i g s were s u p p o r t e d by s u b - s u r f a c e buoyancy a b o u t 5 m above t h e t o p c u r r e n t meter.
N o c u r r e n t measurements were
made a t s t a t i o n J). A l l t h e meters w e r e r e c o v e r e d and r e c o r d l e n g t h s a r e g i v e n i n T a b l e 4. 7 7 % o f p l a n n e d d a t a was o b t a i n e d ; two major f a i l u r e s were seaweed o b s t r u c t e d t h e r o t o r i n t h e bottom frame a t s t a t i o n D and t h e t a p e h e a d f e l l o f f t h e t o p m e t e r a t s t a t i o n I d u r i n g deployment.
218
TABLE 4
Current m e t e r ~ - 2 t a i l s . A S t a ti o n
Meter type
-
Aanderaa, V- AMF
Meter h e i g h t above s e a f l o o r (m)
CM
Low p a s s f i l t e r r e c o f d StartEnd Length ( h ) 0 9 0 0 7/8 0000 15/8 0 9 0 0 7/8
1800 0600 1800
20/9
0000 0000 0000
7/8 7/8 7/8
2100 1260 0000
20/9 2/9 8/9
0600
7/8 7/8 7/8
1500 2100 0000
3 1/8
19/8 2 1/9
0600 0600
8/8
2100
21/9
8/8
2100
21/9
1074 1074
6
1200
8/8
0300
22/9
1074
30
1200 1200 0900
9/8
28 11
1800 0300 1800
2 4/9 2 1/9 2 4/9
1113 102 6 1116
V A A A
39 37 27 11
0600 0600 0600 0600
9/8
9/8
2100 2100
1170 1170
9/8 9/8
0000 2100
26/9 2 6/9 5/9 26/9
A A
26 11
0000 13/8
0300
2 7/9
1086
70 45
A A A
20
A A A
110 60 20
V A A
33 31
0900
10
0600
A A
81 41
A V A A
A
-
9/8 9/8
-
-
8/9 20/9
106 8 585 1068 1080 639 771
588 303 1077
-
645 1170
-
-
S i n c e i n t e r c o m p a r i s o n s have h i g h l i g h t e d problems w i t h Aanderaa meters i n s h e l f s e a s , p a r t i c u l a r l y i n t h e measurement o f low f r e q u e n c y c u r r e n t s ( e . g . B e a r d s l e y e t . a l . , 1 9 7 7 ) AMF VACMs
w e r e d e p l o y e d c l o s e t o t h e Aanderaa meters a t t h e t o p of r i g s C,
F and G a s a check on t h e i r o p e r a t i o n .
The f u l l a c c o u n t o f
t h e comparison h a s been p r e s e n t e d e l s e w h e r e (Howarth, 1981) b u t t h e main c o n c l u s i o n was t h a t t h e r e . w a s no s i g n i f i c a n t d i f f e r e n c e between t h e low f r e q u e n c y r e c o r d s o f t h e two meter t y p e s , see T a b l e s 5 and 6 f o r comparisons of t h e low p a s s f i l t e r e d r e c o r d s and o v e r a l l means.
T h i s was p r o b a b l y b e c a u s e t h e m e t e r s were
n o t deployed c l o s e t o t h e s e a s u r f a c e , because t h e t i d a l c u r r e n t s
were s t r o n g and b e c a u s e t h e r e c o r d s w e r e o b t a i n e d when wave
219 These t h r e e f a c t o r s combined s o
a c t i v i t y was l i k e l y t o b e low.
t h a t f o r o n l y a s m a l l f r a c t i o n of t h e r e c o r d l e n g t h was m o t i o n w i t h a p e r i o d s h o r t e r t h a n t h e sample i n t e r v a l , f o r i n s t a n c e wave o r b i t a l m o t i o n , s i g n i f i c a n t compared w i t h t h e measured velocity.
The o n l y m a j o r d i f f e r e n c e b e t w e e n t h e r e c o r d s
o c c u r r e d f o r t h e o v e r a l l means r e c o r d e d a t s t a t f o n C , where t h e
AMF VACM a p p e a r e d t o h a v e a m a l f u n c t i o n .
A n o t h e r c o n c l u s i o n was
t h a t i n f a s t t i d a l c u r r e n t s , a t s t a t i o n G t h e M2 a m p l i t u d e was 1 m/s,
meters w h i c h a r e moored d i r e c t l y i n t o t h e m e t e r w i r e w i l l
e x p e r i e n c e p r o b l e m s c a u s e d by t h e i n c l i n a t i o n o f t h e meter w i r e and t h e m e t e r d u e t o t h e d r a g . TABLE 5
Least
s q u a r e s f i t s f o r low p a s s f i l t e r e d s p e e d s . AMF VACM
S t a ti o n
=
+
M x AANDERAA
Slope-M
c
Correlation coefficient
Intercept-C
m/s
2
Degrees of freedom
C
0.864
5
0.046
0.004
0.006
0.99
8
F
0.950
0.021
0.003 f 0 . 0 0 2
0.99
29
G
0.915
_+ -+
0.047
0.000
_+
0.96
33
0.004
TABLE 6
Mean v e l o c i t i e s r e c o r d e d by Aanderaa The d i r e c t i o n a l s t a b i l i t y i s
( A ) and AMF VACM ( V ) meters.
( V e c t o r mean s p e e d / s c a l a r mean
s p e e d ) x 100. Station
Record length(h)
C
3 03
F
1026
G
1170
Speed (m/s) Mean S.e.
Direction Mean Stability
V A
0.093 0.105
0.005 0.005
163 198
93 95
V
0.048 0.048
0.003
A
0.003
63 64
73 72
V A
0.065 0.071
0.002 0.002
110 101
82 82
Meter type
I
220
Cable calibration The voltage recorded via the cross channel telephone cable was calibrated against the observed currents at stations A , B and
C for both tidal and low frequencies. Details will be presented elsewhere and only the conclusions described here. The cable voltages have been monitored intermittently since Bowden and Hughes (1961) started in 1955.
Their paper contains the only
previous calibration, 1 volt is equivalent to 1.35 m/s, based on several days of tidal stream observations. It also includes an estimate of the M2 amplitude and phase from one month's harmonic analysis of voltages recorded in 1955 which has been compared with a similar estimate for the same month in 197'9. The amplitude had changed by less than 1% and the phase by less than lo, indicating that at tidal frequencies the cable observations had not changed significantly in 24 years. The current meter records and cable voltages were harmonically analysed for the same 29 day period to give a calibration of 1 volt is equivalent to 1.21 m/s at M2, which also held for all tidal frequencies higher than and including diurnal, 0.1
I
0 VOLTS
-0.05
0.4
0.2
0
t
TRANSVERSE FLOW
Figure 5.
Comparison between low frequency cable voltage and observed flow.
221 The o b s e r v e d low f r e q u e n c y f l o w a l o n g t h e c h a n n e l was c a l c u l a t e d by r e s o l v i n g t h e c u r r e n t m e t e r r e c o r d s i n t h e d i r e c t i o n of t h e M2 c u r r e n t s a t e a c h s t a t i o n , which i n c i d e n t a l l y a l s o minimized t h e variance i n t h e c a l c u l a t e d transverse flow, Figure 5 . p e r i o d when a l l t h e c u r r e n t meters f u n c t i o n e d
-
1 5 . 0 0 3 1 A u g u s t , 585 h o u r s l o n g Flow i n m / s
= (Cable v o l t a g e
-
-
a l e a s t squa-s
0.005
_+
For t h e
0 9 . 0 0 7 August t o
l i n e a r f i t gave:-
0.004)x(2.259
_+
0.431)
(1)
There w e r e 1 7 d e g r e e s of freedom and t h e c o r r e l a t i o n c o e f f i c i e n t was 0 . 7 9 .
Hence t h e l o w f r e q u e n c y c a l i b r a t i o n i s 1 v o l t i s e q u i v a -
l e n t t o 2.26 m/s,
l a r g e r t h a n f o r t i d a l c u r r e n t s and s u p p o r t e d by
c o m p a r i s o n s a t a f o r t n i g h t l y f r e q u e n c y , , and a t mean f l o w s , assuming t h e above v a l u e o f 0 . 0 0 5 V a t z e r o f l o w .
The c a l i b r a t i o n s f o r
t i d a l a n d low f r e q u e n c i e s a r e d i f f e r e n t p r e s u m a b l y b e c a u s e t h e i r f l o w p a t t e r n s a r e d i f f e r e n t ( R o b i n s o n , 1 9 7 6 1 , see more below. P r e v i o u s e s t i m a t e s f o r t h e c a b l e v o l t a g e a t z e r o flow have ranged from
-
0.030 V t o 0 . 0 1 9 V ( P r a n d l e , 1 9 7 9 ) w h i l s t t h e p r e s e n t
e s t i m a t e , 0.005 V,
i s n o t s i g n i f i c a n t l y d i f f e r e n t from z e r o .
The
mean v o l t a g e f o r t h e 1 3 month p e r i o d was 0.010 V , e q u i v a l e n t t o a n o r t h w a r d f l o w 0.01 m / s
by e q u a t i o n 1.
T h i s compares f a v o u r a b l y ,
and f o r t u i t o u s l y , w i t h t h e e s t i m a t e s o f t h e mean f l o w t h r o u g h t h e I r i s h S e a g i v e n by Bowden ( 1 9 5 0 ) and W i l s o n ( 1 9 7 4 ) . RESULTS Low f r e q u e n c y dynamics The v e r t i c a l l y i n t e g r a t e d e q u a t i o n s of m o t i o n g o v e r n i n g low f r e q u e n c y f l o w i n a c o a s t a l s e a whose dynamics a r e dominated by t h e t i d e s a r e , a s s u m i n g t h a t t h e t i d a l e l e v a t i o n i s s m a l l compared w i t h t h e w a t e r d e p t h , h :-
a (hu) +
at
a (hv) at
+
Kxhu
+
non-linear t i d a l t e r m s
(2)
+
non l i n e a r t i d a l t e r m s
(3)
K hv
Y
222
where all variables have been low pass filtered and (u, v ) is the depth mean current, Kx and Kg friction coefficients based on the tidal current and a square low for bottom friction, f the coriolis
-
5 the law frequency equilibrium tide, ( Fx, F ) Y the wind stress and A the coefficient of horizontal eddy viscosity (Heaps, 1 9 7 8 , equations 85-87). The equations are linear in u, v and 5 since the convective acceleration terms are,’zero
parameter,
because the tidal elevation is small compared with the water depth, Equation 4 is the equation of continuity;
equations 2 and 3 are
the equations of motion in the x and y directions respectively with terms representing, from left to right, acceleration, bottom friction, Coriolis, pressure gradient, wind stress and horizontal friction. Since the assumption that the tidal elevations are small compared with the water depth is valid for the North Channel and since the observed low frequency and mean currents were barotropic, these equations can be applied directly.
All the
variables were measured so the importance of the various terms in the equations can be calculated and the accuracy of the measurements assessed from discrepancies in balancing the equations. However, the absolute values of the cable voltage and the sea surface elevation were not known to sufficient accuracy so that, initially, each quantity was calculated relative to its mean. The x axis was taken along the North Channel, positive towards the Atlantic Ocean, so that v ,
the transverse
component, was small, Figure 5, and was taken to be zero. Since the sea area is small the low frequency equilibrium tide can be neglected as can the horizontal friction terms which are small compared with the bottom friction terms. The non-linear tidal terms in equations 2 and 3 were also small, approximately 0.8 x m2/s2 ,for the m 2 /s2 compared with maxima greater than other terms.
The longitudinal speed,
u, was calculated from the
cable voltage since, as has been shown, it measured the low frequency flow well and since its record was longer than the current meter observations. The M2 constituent dominates the tidal currents in the North Channel and is rectilinear parallel to the channel’s axis. Hence the friction coefficients Kx and K~ are given by:-
223
K,
=
4Ka
Ti
and
K Y
=
0.5
Kx
where a is the M2 current amplitude and K the coefficient of bottom friction in a square law for tidal currents (taken as 0.0026, Heaps, 1978). For the North Channel a = 0.7 m/s and h = 120 m so that K, = 2 x s-'. Both the friction coefficient, Kx, and the non-linear tidal terms might be expected to vary with the spring-neap cycle; K, by a factor of two and the non-linear tidal terms between approximately 0.4 x m2/s2 but both have been taken to be and 1.5 x constant. Equation 2, the longitudinal momentum equation, has four major terms - acceleration, bottom friction, pressure gradient and wind stress (the Coriolis term is zero because V = 0 ) . The acceleration was calculated by subtracting low pass filtered currents 6 hours apart and the pressure gradient from the low pass filtered sea bed pressures from Malin Head and Larne (120 Km apart). Time series of the four terms from 5 August to 28 September 1979 are shown in Figure 6. This 55 day period is coincident with the period of offshore measurement and also enables the terms to be studied in detail. The amplitude of the variations in each of the terms is of a similar magnitude but the pressure gradient term has the largest variance - 6.2 x 4 m /s4 compared with 2.3 x m4/s4 f o r the wind stress and m4/s4 for both the acceleration and friction terms. 1.5 x The sum of the four terms (with due regard to sign) and the difference between the friction and wind stress terms are also shown in Figure 6. Equation 2 appears not to balance satisfactorily - there is a noise level of about 2 x 10-4 m2/s2 as well as periods of larger inbalance. However, for most of the time the -4 2 2 10 m /s friction and wind stress terms balance to within Moreover, when the wind stress and friction terms do differ, their
.
difference is largely balanced by the pressure gradient term. Previous studies of the cable voltages (Bowden and Hughes, 1961; Prandle, 1976 and 1979) also found a high correlation between the longitudinal wind stress and the cable voltages. For the present data set (3098 values, 1 July 1979 - 22 July 1980) the correlation coefficient between wind stress and cable voltage had a maximum value of 0.69 when the wind stress was resolved
224
along 298O and the voltage lagged the wind stress by 2.4 hours. Then the least squares linear fit had a slope of 0.11 Vm 2/N which is of the same order as the theoretical value from equation 2 of 2 0 . 1 9 Vm /N. Possible causes for the difference, the theoretical value is larger, are that the wind stress was over-estimated or that the friction coefficient or cable calibration were too, small. The difficulty in estimating the wind stress is the conversion from geostrophic to sea surface wind so the factor of 0 . 5 6 by Hasse and Wagner might be too large. This is corroborated by the comparisons in Table 2, although the shore based observations under-estimate the wind speed over the sea. The friction coefficient would be increased if a larger tidal current were representative - higher values than 0.7 m/s were recorded elsewhere in the North Channel. The observations were split into two groups and correlation coefficients between wind stress and cable voltage calculated. When the wind was from the north-west, 1 6 9 9 observations, the correlation coefficient was 0 . 6 9 whereas when the wind was from the south-west, 1 3 9 9 observations, the coefficient was smaller, 0.51. These findings agree with those from the earlier studies in which the wind stress was calculated from observations at shore stations around the Irish Sea. The slopes of the least squares fits were larger in these cases (between 0 . 1 9 and 0 . 3 6 2 Vm /N) perhaps implying weaker calculated wind stresses. A l s o the wind stress directions for maximum correlation were more northerly, possibly because their wind stresses were calculated from winds within the Irish Sea whereas the winds covered the North Channel and its north-west approaches in the present study. However, the correlation coefficient showed only a weak dependence on wind stress direction - it was greater than 0 . 6 5 for wind stresses between 280° and 320°. The longitudinal wind stress and cable voltage were correlated month by month. There was a small seasonal variation, the correlations being slightly weaker in summer when the wind stress was smaller, but all the values, except one, were between 0.55 and 0.85. The exception occurred for August 1 9 7 9 , part of the period of offshore measurement, when the correlation was very low, 0 . 2 4 . During this month the winds were weak and on at least two occasions the wind stress differed significantly from the cable voltage,Figure 6.
225
M2/S2
ACCELERATION
AUGUST
Figure 6.
SEPTEMBER 1979
T i m e series of t h e f o u r major terms i n t h e low f r e q u e n c y l o n g i t u d i n a l e q u a t i o n of motion from 5 August-28 September 1 9 7 9 .
226
One weather pattern caused most of the large wind stress events. A depression moved eastward across the Atlantic passing to the south of Iceland and to the north of Scotland accompanied by winds which veered from southerly to north-westerly first driving water out of the Irish Sea through the North Channel and then, as the wind veered, into it. The depression usually covered A large part of the Atlantic Ocean so that nearly uniform winds blew over the area and generated an almost instanteneous current response in the Irish Sea and North Channel with no elevation gradients created within the North Channel. Winds blowing along the North Channel appear not only to generate currents *long the North Channel (which is too narrow for the Earth's .Gotation to deflect the currents) but are also in the right direction, in an Ekman sense, to push water into or out of the Irish Sea through the St. George's Channel giving the system a unified response, This is supported by Pingree and Griffiths' (1980) numerical model which predicted that the maximum flow through the St. George's Channel would be generated by winds from 140°/3200. The paths of a few storms usually secondary depressions, were more southerly, although they still travelled generally eastward, and crossed Ireland and/or Scotland. These storms were smaller in size and were accompanied by non-uniform winds over the region. The response of the sea was not uniform and sea bed pressure gradients were created in the North Channel. For instance, on 14 August 1979 a storm travelled north-eastward across southern Ireland and the Irish Sea. Water flowed out of the Irish Sea through the North Channel against the wind stress because a sea bed pressure gradient had arisen with water in theIrish Sea higher than that in the Malin Shelf Sea, Figure 6. Storms like this occurred several times in August 1979 which led to the poor correlation between the wind stress and the cable voltage. Hence the response of the Irish Sea and North Channel area subject to wind stress depends on whether the wind stress over the area is spatially uniform. If it is, the wind stress along the North Channel is balanced by linear friction whilst if it is not, the wind stress is balanced by linear friction and a sea bed pressure gradient. This is conjecture since the acceleration and, to some extent, pressure gradient terms have been ignored. If the acceleration term is included in the balance between wind stress and friction the correlation is poorer and so the estimate for
221
this term is doubtful. A l s o , whilst the sea bed pressure gradient largely balances the gross differences between friction and wind stress when these occur, it is the noisiest term and at times is large when the wind stress and friction terms agree well. The magnitude of the pressure gradient along the North Channel, both estimated from the difference between frietion and wind stress and observed, varied between 10- 3 and Pa/m (equivalent to an elevation gradient of 0.01 to 0.1 m in 100 Km), Figure 6. The larger elevation differences should certainly have been measurable with well maintained conventional tide gauges - the noise level of the observed pressure gradient suggests that the low frequency records from the gauges'at Malin Head and Larne had an uncertainty of about 0.02 m - so what are the possible causes for the larger discrepancies. First, one of the tide gauges could have been faulty; however nothing else indicates this. Second, local pressure gradients close to the tide gauge sites could have corrupted the measurements. This is unlikely because the local gradients would have to be very large, because of their small length scale, to generate elevations large enough to affect the measurements. No data supports this hypothesis. Third, other large scale sea bed pressure gradients could have been included in the measurements, generated by, for instance, the wind stress parallel to the west coasts of Ireland and Scotland, or the transverse Coriolis force from flow through the North Channel or the tides, particularly MSf. The sea bed pressures measured by all five shore based and three offshore gauges in the North Channel region were highly correlated (correlation coefficients between 0.91 and 0.99 for a common period of 37 days) indicating that the pressure field there was predominantly uniform. The pressure field was correlated with the north-east/south-west wind stress - the 13 month long records of wind stress and sea bed pressure at Port Ellen had a maximum correlation coefficient of 0 . 1 5 when the wind stress was resolved along 033O/213O and when the pressure lagged the wind by 6 hours. This suggests the .following dynamics - the wind stress parallel to the Atlantic coasts of Ireland and Scotland generates a current parallel to the coast (by friction) which combines with the Earth's rotation to create a pressure gradient across the shelf. If the pressure variations are small at the shelf edge the pressures at the coast will be correlated
228
with the alongshore wind stress. A pressure recorder was deployed near the shelf edge at station J , Figure 2. Its record was correlated with those from the North Channel (correlation coefficient of 0 . 3 6 , which is significant at the 95% level, with the pressure at Port Ellen and the latter lagging by about 1 hour) and had 10% of the variance. , The North Channel sea bed pressure records differed by up to 5 x 103 Pa from their mean during the 13 month period, which corresponds to a cross shelf gradient of 3 x Pa/m and a longshelf current of 0.3 m/s, according to the suggested dynamics.(For the period shown in Figure 6 , the maximum gradient was 10- 2 Pa/m). The slope of the least squares linear fit between the wind stress and sea bed pressure was used to estimate the friction coefficient - 4 x 1 015s-1 - which whilst of the right order of magnitude is probably too large and suggests that as well as the frictional flow the wind stress is balanced by a longshore pressure gradient. Secondly, a sea bed pressure gradient will balance the transverse (Coriolis) force from the flow through the North Channel. For the 55 day period of Figure 6 the largest flow recorded by the cable was 0.2 m/s leading to a gradient of 1.7 x lo-’ Pa/m and elevation differences of 0.1 m in.40 Km (the width of the channel at the cable). This is discussed in more detail below. Thirdly, there are tidal sources. The gradients arising from the low frequency astronomic tides will be less than Pa/m and can be ignored. However, non-linear interaction between the major tidal constituents can generate low frequency motion with shorter length scales and therefore larger gradients, the most significant being between M2 and S 2 to generate MSf which often occurs where there is a change in topography. Estimates for MSf elevations are given in Table 7, showing that the largest amplitude occurs at Torr Head, where the North Channel changes direction For the tide gauges listed in Table 7 the maximum elevation -2 difference is 0 . 0 6 m and the maximum gradient 1.4 x 10 Pa/m. However, near Torr Head the gradients will be larger since the above gradients were calculated for tide gauges separated by more than 3 0 Km.
229
TABLE 7
Tide gauge Malin Head Port Ellen Machrichanish Torr Head Larne
Amplitude (m) 0.007 0.017 0.026 0.060 0.021
,.
Phase 273 205 219 216 259
Hence pressure gradients of approxjmately equal magnitude arise in the North Channel from four different sources. The tidal, MSf, contribution is easy to determine since it is periodic but it varies spatially within the North Channel. The others - the along channel gradient from equation 2, the across channel gradient balancing the Coriolis force and the across shelf generated by the along shelf wind stress, are approximately spatially uniform within the North Channel. Although the gradients from these three sources are of the same order, the across shelf gradient acts over the longest distance and so dominates the sea bed pressure records (producing elevations which vary between t 0.2 m during 5 August 2 8 September 1979, compared with 2 0.1 m for the other sources). This is one reason for the difficulty, referred to earlier, in measuring the pressure gradient term in equation 2 since we are trying to measure a signal in the presence of others of the same size or larger. The pressure gradient was estimated from the records from Malin Head and Larne but other combinations were available - Port Ellen and Machrihanish, Malin Head and Torr Head, Torr Head and Larne and station E and station B. The various estimates do not agree well, see Figure 7 for three. The distance between Port Ellen and Machrihanish is 37 Km and between Torr Head and Larne is 39 Km so that the maximum elevation difference would be 0.03 m, near the limit the systems are capable of measuring so that neither estimate would be reliable. Although the drift in sea bed pressure records has greatly reduced recently so that both tides and low frequencies can be measured, it is highlighted by estimating the low frequency pressure gradient between two gauges.
230
FdKm
10
I A -
5
C
PRESSURE GRADIENT
5
a
C !
C
-t
-K
IS
5 AUGUST
Figure 7.
4
14 SEPTEMBER 1979
24
T i m e s e r i e s of l o n g i t u d i n a l s e a bed p r e s s u r e
gradient observations. a ) Malin Head-Larne b) P o r t E l l e n - M a c h r i h a n i s h c ) S t a t i o n Es t a t i o n B , w i t h t r e n d removed.
231
The gauges at stations E and B had overall drifts of approximately 0.06 m and 0.21 m respectively for their period of operation, both in the same sense, which dominated the pressure gradient signal. The drift, which can be discontinuous, has many possible sources, both from within the pressure sensor and from the relation of the frame to the sea floor. Hence it cannot be accurately removed although an attempt was made by fitting a straight line to the difference between the records from stations E and B. The problem at Torr Head is the large MSf signal, which was removed, but cannot be accurately calculated even from a year's data. Hence, the Malin Head - Larne gradient was used since it should have been most accurately measurable because the gauges were furthest apart. Figure 7 also shows that the background noise level was higher in the Malin Head - Larne signal, both stilling well tide gauges, compared with the Port Ellen - Machrihanish signal, pneumatic gauges one quarter the distance apart. The offshore measurement, station E - station B, had a lower noise level than either of these presumably since it was less affected by local nearshore gradients. Much of this discussion of the longitudinal equation of motion for the North Channel (equation 2) is relevant to the transverse equation (equation 3 ) . The three largest terms - Coriolis, pressure gradient and wind stress - and their sum have been plotted in Figure 8. The acceleration and friction terms are small since the transverse velocity, v , is small and the magnitude of the wind stress term is less than that of the Coriolis and pressure gradient terms which have the largest magnitude of any in the equations of motion. Their correlation coefficient is 0.50 and although this is significant at the 1% level it is not as high as might be expected. The variance of the Coriolis term is twice as large as that of the pressure gradient term and it is apparent in Figure 8 that the magnitude of the varitions in the Coriolis term are larger than those in the pressure gradient term. Once again the equation has not balanced as well as anticipated, either because an important factor has been omitted or because of errors in the flow or pressure measurements. There was no obvious problem with the flow measurement in the longitudinal equation and certainly no suggestion it had been over-
232
M2/S2 0002
0.001
0.0
0.001
0.0
0001
0.0
0 001
0.0
-o.ool~,v ,.,,,,,,,
i,$ V>,,Iy,,; ,*,,
I
v
,(,, ,,,.,,,,,
Y
,,,,,
V
-0~002
5
15 AUGUST
Figure 8.
25
4
14
24
SEPTEMBER 1979
T i m e s e r i e s of t h e t h r e e m a j o r t e r m s i n t h e low f r e q u e n c y t r a n s v e r s e e q u a t i o n of m o t i o n f o r t h e N o r t h C h a n n e l , 5 August-28 September 1 9 7 9 .
233 estimated.
There a r e , however, a t l e a s t t w o p o s s i b l e problems i n
m e a s u r i n g t h e p r e s s u r e g r a d i e n t s i g n a l b o t h o f which h a v e a l r e a d y F i r s t , T o r r Head a n d M a c h r i h a n i s h a r e s e p a r a t e d
been mentioned.
by 3 3 Km s o t h a t t h e maximum e x p e c t e d l e v e l d i f f e r e n c e i s o n l y 0 . 0 6 m.
However, t h e p n e u m a t i c p r e s s u r e r e c o r d e r s i n s t a l l e d a t
both s i t e s should b e capable of r e s o l v i n g d i f f e r e h c e s of t h e o r d e r of
-+
0.01 m and so s h o u l d have measured a t l e a s t t h e extreme
events.
Second, t h e MSf
s i g n a l a t T o r r Head i s l a r g e and t h e
a t t e m p t t o remove it c o u l d a l s o h a v e a f f e c t e d t h e p r e s s u r e g r a d i e n t s i g n a l s i n c e t h e frequencies overlap. To sum up, i n t h e f r e q u e n c y r a n g e 0 . 5 t o 0 . 1 cpd t h e wind s t r e s s /
i s t h e m a j o r d r i v i n g f o r c e f o r t h e dynamics o f t h e N o r t h C h a n n e l . 0
The l o n g i t u d i n a l wind s t r e s s ( a l o n g 118O/298 ) i s i m m e d i a t e l y b a l a n c e d by a f r i c t i o n a l f l o w t h r o u g h t h e N o r t h C h a n n e l and I r i s h S e a w h i l s t t h e t r a n s v e r s e w i n d stress
0
( a l o n g 033O/213 ) g e n e r a t e s
a n a l o n g s h o r e p r e s s u r e g r a d i e n t and c u r r e n t i n t h e M a l i n S h e l f Sea.
The c u r r e n t c r e a t e s a c r o s s s h e l f
(Coriolis) pressure
g r a d i e n t which d o m i n a t e s t h e sea b e d p r e s s u r e f i e l d i n t h e N o r t h C h a n n e l and l a g s t h e wind stress by a b o u t 6 h o u r s .
The f l o w
t h r o u g h t h e N o r t h C h a n n e l a l s o s e t s up a t r a n s v e r s e
(Coriolis)
pressure gradient there.
I n a d d i t i o n , i f t h e s c a l e of t h e weather
p a t t e r n i s s m a l l , a p r e s s u r e g r a d i e n t can b e g e n e r a t e d along t h e F o r a d e p r e s s i o n moving e a s t w a r d a c r o s s t h e
North Channel.
A t l a n t i c Ocean t h i s i m p l i e s t h a t w a t e r w i l l f i r s t f l o w o u t of t h e I r i s h S e a t h r o u g h t h e N o r t h C h a n n e l and t h e n r e v e r s e and f l o w i n t o
i t as t h e d e p r e s s i o n p a s s e s , w h i l s t e l e v a t i o n s i n t h e North Channel r i s e , b o t h from t h e i n v e r s e b a r o m e t e r e f f e c t and t h e wind s t r e s s , and t h e n f a l l a f t e r t h e d e p r e s s i o n h a s p a s s e d .
This description
i s i n a c c o r d a n c e w i t h t h e e q u a t i o n s of m o t i o n b u t t h e measurements d i d n o t b a l a n c e a s w e l l as h a d b e e n h o p e d , i n p a r t i c u l a r t h e a c c e l e r a t i o n and p r e s s u r e g r a d i e n t t e r m s p r e s e n t e d problems. Mean c u r r e n t s Of t h e t h r e e f r e q u e n c y b a n d s commonly m e a s u r e d w i t h r e c o r d i n g current m e t e r s (1- 0 . 1 c . p . d . )
-
i n e r t i a l and t i d a l ( 1 2 - 1 c . p . d . ) ,
storm driven
and c i r c u l a t i o n ( l e s s t h a n 0 . 1 c . p . d . )
l o w e s t i s t h e most s u s c e p t i b l e t o e r r o r s .
-
the
In continental shelf
s e a s t h e c i r c u l a t i o n i s u s u a l l y weaker t h a n t h e t i d a l and s t o r m d r i v e n c u r r e n t s s o t h a t any f a u l t s i n t h e m e t e r ' s d e s i g n , o p e r a t i o n o r i n i t s i n t e r a c t i o n w i t h i t s mooring c a n a l i a s e n e r g y t o
234
t h e l o w e s t f r e q u e n c i e s , swamping t h e s i g n a l and p a r t i c u l a r l y causing erroneous d i r e c t i o n s .
However, t h e mean r e c o r d e d c u r r e n t s
d u r i n g August and S e p t e m b e r 1 9 7 9 h a d h i g h s p e e d s ( m o s t b e t w e e n 0 . 0 5 and a t m o s t s i t e s were b a r o t r o p i c
and 0 . 1 2 5
m/s)
Table 8.
A l s o Aanderaa and AMF VACM meters d e p l o y e d c l o s e t o g e t h e r
r e c o r d e d s i m i l a r mean c u r r e n t s , a s shown e a r l i e r .
( t o within 15O), The c u r r e n t s
formed a n u n u s u a l l y c o h e r e n t and s t a b l e p a t t e r n ( s m a l l s t a n d a r d e r r o r s f o r t h e s p e e d s and d i r e c t i o n a l s t a b i l i t y c l o s e t o 100) w h i c h was l a r g e l y s u p p o r t e d by CTD o b s e r v a t i o n s and p r e v i o u s ( L a g r a n g i a n ) measurements.
( I n t h e N o r t h Channel E u l e r i a n ( c u r r e n t
meter) and L a g r a n g i a n measurements s h o u l d b e c o m p a r a b l e b e c a u s e t h e Stokes d r i f t due t o t h e s e m i - d i u r n a l t i d e i s sma,ll s i n c e t h e t i d e i s a standing wave).
A l l t h i s suggests t h a t the observations
w e r e a r e l i a b l e e s t i m a t e of t h e c i r c u l a t i o n s f o r t h a t p e r i o d . TABLE 8
Mean c u r r e n t s f o r t h e p e r i o d s g i v e n i n T a b l e 4.
Directional
s t a b i l i t y i s ( v e c t o r mean s p e e d / s c a l a r mean s p e e d ) x 100.
Station
Meter h e i g h t above s e a f l o o r (m) ~
V e c t o r mean Speed Direction
~~
0.123 0.093 0.080
134 150
60 20
70
I
:;::7
Direction stability
141
0.002 0.003 0.002
99 99 95
0.041 0.005 0.012
215 297 222
0.002 0.002 0.002
63
33 31 10
0.091 0.105 0.052
172 198 173
0.002 0.002
94 95 a2
81 41
0.079 0.076
89 63
0.002 0.002
94 91
6
0.053
319
0.002
87
30 28 11
0.046 0.048 0.021
64 66 76
0.003 0.003 0.002
12 73 45
39 37 27
110
11
0.065 0.071 0.050 0.067
116
0.002 0.002 0.002 0.002
82 82 73 85
11
0.050
351
0.002
80
45 20
110
101 93
0.005
13 31
235
The most o b v i o u s i n t e r p r e t a t i o n o f t h e mean c u r r e n t s i n T a b l e 8
i s t h a t t h r o u g h o u t t h e two months w a t e r flowed towards t h e I r i s h Sea b o t h c l o s e t o t h e I r i s h s h o r e ( a t s t a t i o n s F , G and A ) and a l s o c l o s e t o t h e Mull o f Galloway ( a t s t a t i o n C ) and flowed away from t h e I r i s h Sea c l o s e t o I s l a y ( a t s t a t i o n s E and I ) . s t r o n g southward f l o w s n e a r t h e s h o r e s a t t h e s & t h e r n
The
end of t h e
North Channel ( a t s t a t i o n s A and C ) d i d n o t o c c u r i n t h e middle ( a t s t a t i o n B) where t h e t o p meter r e c o r d e d a mean a c r o s s t h e c h a n n e l and t h e middle and bottom meters r e c o r d e d weak means.
At
s t a t i o n F t h e mean c u r r e n t s were a l s o weaker and more v a r i e d i n d i r e c t i o n , p e r h a p s b e c a u s e i t was t h e o n l y s t a t i o n i n s t r a t i f i e d w a t e r and f o r p a r t o f t h e t i m e was c l o & t o t h e f r o n t s e p a r a t i n g s t r a t i f i e d and homogeneous w a t e r which a p p e a r e d from t h e CTD o b s e r v a t i o n s and t h e s a t e l l i t e i n f r a - r e d photographs t o be a d v e c t e d towards t h e North Channel d u r i n g August and September 19 79. A s i m p l e a t t e m p t t o q u a n t i f y t h e f l o w i n t o and o u t of t h e North Channel b a s e d on t h i s c i r c u l a t i o n p a t t e r n and t h e r e c o r d s from
s t a t i o n s A , B , C , E , F and G f a i l e d s i n c e i t showed a n e t l o s s of w a t e r which was n o t b a l a n c e d by a change i n s e a l e v e l .
10 day
a v e r a g e s of t h e low f r e q u e n c y c u r r e n t s w e r e c a l c u l a t e d which showed t h a t t h e southward flow a t s t a t i o n s A and C v a r i e d v e r y l i t t l e b u t t h a t a t s t a t i o n s B , E l F and G a change o c c u r r e d about 5 September.
B e f o r e t h e n t h e flow a t s t a t i o n B had a northward
component s o t h a t t h e flow a t s t a t i o n s F and G i n t o t h e North Channel was b a l a n c e d by a f l o w o u t o f t h e North Channel a t s t a t i o n s A, B and C t o t h e region.
0.8 x
(-
westward a t s t a t i o n E
lo5 m 3 / ) .
5 3 1 . 3 x 10 m / s )
(-
Hence t h e flow n o r t h represented a net loss
A f t e r 5 September t h e flow a t s t a t i o n B was
southward, t h e f l o w s a t s t a t i o n s F and G i n c r e a s e d and E (and I ) decreased.
However, t h e f l o w southward a t s t a t i o n s A , B and C 5 3 ( - 2 . 2 x 10 m / s ) was now g r e a t e r t h a n t h e flow i n a t s t a t i o n s
F and G by a b o u t 0 . 4
5
a b o u t 1 . 2 x 10
m 3/s
x
.
lo5
m3/s
and t h e r e was a g a i n a n e t loss o f
(The change i n flow p a t t e r n was caused by
t h e l o n g i t u d i n a l wind stress which was s t r o n g e r towards t h e I r i s h Sea a f t e r 5 S e p t e m b e r ) . The a t t e m p t e d b a l a n c e was v e r y c r u d e b u t t h e s i z e o f t h e d i s a agreement i m p l i e s t h a t changing t h e c r o s s - s e c t i o n a l a r e a c o r r e s p o n d i n g t o each m e t e r w i l l n o t s u b s t a n t i a l l y improve t h e calculation.
An a l t e r n a t i v e e x p l a n a t i o n f o r t h e imbalance i s
236
t h a t t h e mean c u r r e n t a t s t a t i o n E i n s t e a d o f r e p r e s e n t i n g a f l o w o u t of t h e N o r t h C h a n n e l was p a r t o f a c l o c k w i s e g y r e i n t h e Sound of J u r a which i n c l u d e d s t a t i o n D , w h e r e t h e mean c u r r e n t was l a r g e and t r a n s v e r s e t o t h e s o u n d .
A s i m i l a r , b u t o s c i l l a t i n g , gyre i n
t h e Sound of J u r a would e x p l a i n t h e q u a s i - f o r t n i g h t l y
currents
r e c o r d e d a t s t a t i o n s D , E , F a n d G I T a b l e 9 , w h e r e t h e cur-rents a t s t a t i o n E w e r e 180° o u t of p h a s e w i t h t h o s e a t s t a t i o n s D, F and G.
The mean g y r e w a s s t r o n g e r t h a n t h e f o r t n i g h t l y g y r e whose
d r i v i n g f o r c e s i n c l u d e b o t h wind and t i d a l , MSf, S O t h a t t h e c o m b i n a t i o n a l w a y s r o t a t e d c l o c k w i s e b u t w i t h a s p e e d which v a r i e d w i t h f o r t n i g h t l y and m o n t h l y p e r i o d s . TABLE 9
Q u a s i - f o r t n i g h t l y c u r r e n t e l l i p s e s f r o m a h a r m o n i c a n a l y s i s of a common 2 9 day p e r i o d .
A m p l i t u d e s are i n m/s
and t h e s e n s e o f
r o t a t i o n i s g i v e n by t h e s i g n o f t h e minimum a m p l i t u d e ( + a n t i - c l o ckw i s e )
S t a ti o n
ve
.
Meter h e i g h t above t h e s e a floor(m)
maximum amplitude
Minimum amplitude
Phase
Direction
81 41
0.051 0.057
-0.015 0.003
41 43
56 31
6
0.013
-0.001
213
132
30 28 11
0.020 0.019
0.007
90 92 113
105 107
39
0.016
37
0.020
-0.003 -0.003
IJ.
0.023
0.005
0.013
0.009 -0.003
81 72 55
107
141 139 178
On t h i s i n t e r p r e t a t i o n t h e c i r c u l a t i o n of t h e N o r t h C h a n n e l f o r A u g u s t and S e p t e m b e r 1 9 7 9 was:-
c o n s t a n t flows towards t h e I r i s h
S e a b o t h by t h e M u l l o f Galloway a n d by t h e I r i s h C o a s t from Malin Head t o L a r n e , a v a r i a b l e f l o w i n t h e c e n t r e o f t h e N o r t h C h a n n e l d e p e n d i n g on t h e l o n g i t u d i n a l w i n d , a c l o c k w i s e g y r e i n t h e Sound of J u r a and a n o r t h w a r d f l o w i n t h e Malin S h e l f S e a b y p a s s i n g t h e e n t r a n c e o f t h e N o r t h C h a n n e l , s c h e m a t i c a l l y shown i n F i g u r e 9 . The f l o w t h r o u g h t h e s o u t h e r n end o f t h e N o r t h C h a n n e l was a l w a y s t o w a r d s t h e I r i s h S e a and w a s , t h e r e f o r e ,
a t y p i c a l s i n c e Caesium
231
1 3 7 o u t p u t from Windscale c l e a r l y shows a mean f l o w o u t of t h e
I r i s h Sea t h r o u g h t h e North Channel (McKinley e t a l . 1981a, b ) .
WW
Figure 9 .
4.W
7.W
Scheme o f mean flow a s r e c o r d e d by c u r r e n t meters The d i r e c t i o n d u r i n g August and September 1 9 7 9 . o f t h e flow i n t h e middle o f t h e North Channel depends on t h e w i n d ' s d i r e c t i o n .
This c i r c u l a t i o n p a t t e r n has a l a r g e r s p a t i a l v a r i a b i l i t y than t h e t i d a l and s t o r m d r i v e n c u r r e n t s , which w e r e e i t h e r uniformly towards o r away from t h e I r i s h S e a .
However, a t most meters t h e
mean s p e e d s w e r e s o h i g h t h a t t h e y dominated t h e low f r e q u e n c y r e c o r d s and s t o r m d r i v e n flow r e v e r s a l s o c c u r r e d o n l y f o r s h o r t p e r i o d s . Hence t h e c a b l e c a l i b r a t i o n f o r 'low f r e q u e n c y flows r e f l e c t s t h e c i r c u l a t i o n p a t t e r n and i s d i f f e r e n t from t h e t i d a l calibration.
I f t h e c i r c u l a t i o n p a t t e r n changed s o might t h e low
f r e q u e n c y c a b l e c a l i b r a t i o n (Robinson, 1 9 7 6 ) .
S i n c e t h e flow i s
n o t uniform a c r o s s t h e North Channel and s i n c e t h e c a b l e measures
238 t h e a v e r a g e f l o w t h r o u g h t h e c h a n n e l , c a b l e measurements on t h e i r own w i l l n o t d e t e r m i n e t h e s p a t i a l v a r i a t i o n s i n t h e c i r c u l a t i o n p a t t e r n and so c a n n o t b e u s e d t o e x t e n d t h e c u r r e n t m e t e r r e c o r d s . From t h e p r e v i o u s s e c t i o n t h e wind stress i s a major d r i v i n g f o r c e f o r t h e f l o w s i n t h e North Channel and t h e Malin S h e l f S e a . For b o t h p e r i o d s August t o September 1 9 7 9 and J u l y 1 9 7 9 t o 5 u l y 1980 t h e mean wind stress was a p p r o x i m a t e l y t r a n s v e r s e t o t h e North Channel
(0.105 N/m2
towards 045O and 0 . 0 9 4 N / m 2
towards
018O r e s p e c t i v e l y ) s u g g e s t i n g t h a t t h e r e was a mean c u r r e n t n o r t h w a r d t h r o u g h t h e Malin S h e l f S e a , a s o b s e r v e d p r e v i o u s l y by McKinley e t a1 ( 1 9 8 1 b ) .
The component o f t h e mean,wind stress
a l o n g t h e North Channel (118O/298O) w a s 0 . 0 3 1 N/m2'
towards t h e
I r i s h Sea f o r August t o September 1 9 7 9 and 0 . 0 1 6 N/m2 t h e I r i s h Sea f o r J u l y 1 9 7 9 t o J u l y 1980. v o l t a g e s f o r t h e c o r r e s p o n d i n g p e r i o d s were which c o r r e s p o n d t o mean c u r r e n t s of
-
away from
The mean c a b l e
-
0.013V and 0.010 V
0.041 m/s
and 0.011 m / s
r e s p e c t i v e l y , assuming e q u a t i o n 1 i s v a l i d f o r mean c u r r e n t s . The former v a l u e compares w e l l w i t h an e s t i m a t e o f from t h e c u r r e n t m e t e r measurements.
-
0.035 m/s
This suggests t h a t t h e
wind s t r e s s i s a l s o i m p o r t a n t i n d e t e r m i n i n g t h e mean flow t h r o u g h t h e North Channel. CONCLUSIONS The low f r e q u e n c y dynamics of t h e I r i s h S e a , North Channel and Malin S h e l f S e a a r e l a r g e l y c o n t r o l l e d by t h e wind. storm driven frequency range,
1-0.1 c . p . d . ,
In the
t h e wind stress a l o n g
t h e North Channel i s b a l a n c e d by a f r i c t i o n a l flow t h r o u g h t h e I r i s h Sea and North Channel (and sometimes by a p r e s s u r e g r a d i e n t a l o n g t h e North Channel i f t h e s t o r m ' s s i z e i s s m a l l ) . The wind stress t r a n s v e r s e t o t h e North C h a n n e l , which i s a l s o p a r a l l e l t o t h e w e s t c o a s t s of I r e l a n d and S c o t l a n d , i n d i r e c t l y f o r c e s t h e s e a b e d p r e s s u r e f i e l d a t t h e c o a s t , w i t h a l a g of
6 hours. The mean wind stress i s a l s o i m p o r t a n t f o r t h e l o n g t e r m f l o w a l o n g t h e Malin S h e l f S e a and t h r o u g h t h e North Channel. During t h e o f f s h o r e measurements t h e r e was a w e l l d e f i n e d c i r c u l a t i o n p a t t e r n w i t h i n t h e North S e a , F i g u r e 9 . The d y n a m i c s w e r e o b s e r v e d by a 45 day l o n g p e r i o d o f o f f s h o r e measurement and a 1 3 month l o n g p e r i o d of s h o r e b a s e d measurement.
The c o m b i n a t i o n e n a b l e d t h e c a l i b r a t i o n o f t h e
c r o s s c h a n n e l t e l e p h o n e c a b l e by comparison w i t h t h r e e r e c o r d i n g c u r r e n t meter r i g s which showed d i f f e r e n t c a l i b r a t i o n s f o r t i d a l
2 39
( 1 . 2 1 Vs/m)
and low f r e q u e n c y c u r r e n t s ( 2 . 2 6 V s / m ) ,
reflecting the circulation pattern.
the l a t t e r
The v o l t a g e f o r z e r o flow
(0.005V) was n o t s i g n i f i c a n t l y d i f f e r e n t from z e r o .
There w e r e
d i f f i c u l t i e s i n measuring t h e a c c e l e r a t i o n , p r e s s u r e g r a d i e n t and wind stress w i t h i n t h e North Channel
-
the pressure gradient
b e c a u s e t h e g r a d i e n t s w e r e s m a l l and b e c a u s e o f d r i f t i n t h e o f f s h o r e measurements and t h e wind stress b e c a u s e no o f f s h o r e measurements were a v a i l a b l e and s o t h e g e o s t r o p h i c wind had t o be converted t o t h e s u r f a c e
wind.
The e x t e n d e d s h o r e b a s e d
measurements o f c a b l e v o l t a g e e l e v a t i o n and a t m o s p h e r i c p r e s s u r e e n a b l e d t h e m o n i t o r i n g of much of t h e dynamics
-
t h e storm driven
f l o w s i n t h e North Channel and Malin ShLlf S e a s and a l s o t h e s p a t i a l l y a v e r a g e d mean f l o w s b u t n o t t h e v a r i a t i o n s w i t h i n t h i s s p a t i a l average.
F u r t h e r and l o n g e r o f f s h o r e measurements a r e
r e q u i r e d t o s t u d y t h e l a t t e r and t o c o n f i r m some o f t h e above points.
REFERENCES Amorocho, J. and D e V r i e s , J . J . , 1980. A new e v a l u a t i o n of t h e wind stress c o e f f i c i e n t o v e r w a t e r s u r f a c e s . J o u r n a l o f G e o p h y s i c a l R e s e a r c h , 85 ( c l ) : 433-442. B a r n e s , H.
and Goodley, E.F.W., 1 9 6 1 . The g e n e r a l hydrography of P a r t 1: d e s c r i p t h e Clyde Sea a r e a , S c o t l a n d . t i o n o f t h e a r e a : d r i f t b o t t l e and s u r f a c e s a l i n i t y d a t a . B u l l e t i n s o f Marine Ecology, 5 ( 4 3 ) : 112-150.
Beardsley, R.C.,
B o i c o u r t , W., H u f f , L . C . and S c o t t , J . , 1 9 7 7 C M l C E 7 6 : a c u r r e n t meter i n t e r c o m p a r i s o n e x p e r i m e n t o f f Long I s l a n d i n February-March, 1976. Woods Hole Oceanographic I n s t i t u t i o n , T e c h n i c a l R e p o r t , WHOI-77-62, 123 pp. (Unpublished manuscript)
.
Bowden, K.F.,
Bowden, K.F.
1950. P r o c e s s e s a f f e c t i n g t h e s a l i n i t y o f t h e I r i s h S e a . Monthly n o t i c e s o f t h e Royal A s t r o n o m i c a l S o c i e t y , g e o p h y s i c a l supplement 6 ( 2 ) : 63-90. and Hughes, P . , 1 9 6 1 . The flow of w a t e r t h r o u g h t h e Geophysical I r i s h Sea and i t s r e l a t i o n t o wind. J o u r n a l of t h e Royal A s t r o n o m i c a l S o c i e t y , 5: 265-291.
240
and Pugh D . T . , 1 9 7 7 . F i e l d t e s t s o f t h e Aanderaa p r e s s u r e l o g g e r w i t h p n e u m a t i c t i d e g a u g e s , and t h e d e s i g n of a s s o c i a t e d p n e u m a t i c c o n t r o l circuits I n s t i t u t e o f Oceanographic Sciences, R e p o r t 37, 11 pp. (Unpublished m a n u s c r i p t ) .
Browell, A.
.
Craig, R.E.,
1959. Hydrography o f S c o t t i s h C o a s t a l w a t e r s . Marine R e s e a r c h , 2 : 1-30. / and Corkan, R . H . , 1932. The p r i n c i p a l c o n s t i t u e n t o f t h e t i d e s i n t h e E n g l i s h and I r i s h C h a n n e l s . P h i l o s o p h i c a l t r a n s a c t i o n s o f t h e Royal S o c i e t y o f London, A , 231: 29-53.
Doodson, A . T .
Xamming, R.W.,
Hasse, L . ,
1977.
Digital f i l t e r s . 2 2 6 pp.
P r e n t i c e Hall, New J e r s e y ,
and Wagner, V . , 1 9 7 1 . On t h e r e l a t i o n s h i p between g e o s t r o p h i c a n d s u r f a c e wind a t s e a . Monthly w e a t h e r r e v i e w , 9 9 : 255-260.
Heaps, N.S.
1978.
Linearized vertically-integrated equations f o r residual circulation i n coastal seas. 31 ( 5 ) : Deutsche Hydrographische Z e i t s c h r i f t 147-169.
,
Heaps, N.S.
a n d J o n e s , J . E . , 1975. Storm s u r g e c o m p u t a t i o n s f o r t h e I r i s h Sea u s i n g a t h r e - d i m e n s i o n a l n u m e r i c a l model. Mgmoires de l a S o c i d t e ' r o y a l e d e s S c i e n c e s de LiSge, 6 s e r . , 7 : 289-333. and J o n e s J . E . , 1979. Recent s t o r m s u r v e s i n t h e I r i s h Sea. I n J . C . J. Nihoul ( E d i t o r ) I Marine f o r e c a s t i n g . E l s e v i o r , Amsterdam, pp. 285-319.
Heaps, N.S.
Howarth, M . J . ,
1981. An i n t e r c o m p a r i s o n of AMF VACMs and Aanderaa RCM4s i n a t i d a l l y dominated c o n t i n e n t a l s h e l f s e a . I n t e r n a t i o n a l c o u n c i l f o r t h e E x p l o r a t i o n of t h e s e a (Unpublished m a n u s c r i p t ) . c.m. 1981/c : 31 : pp. 1 2 .
I.C.E.S.
1962. Mean monthly t e m p e r a t u r e and s a l i n i t y of t h e s u r f a c e l a y e r o f t h e North Sea and a d j a c e n t w a t e r s from 1905-1954. C h a r l o t t e n l u n d S l o t , Denmark.
Kautsky, H . ,
L e e , A.J.,
J e f f e r i e s , D.F. and S t e e l e , A . K . , 1980. R e s u l t s o f t h e R a d i o l o g i c a l North Sea Programme RANOSP 1 9 7 4 t o 1976. Deutsche H y d r o g r a p h i s c h e Z e i t s c h r i f t , 33 ( 4 ) : 152-1 5 7 . 1960. Hydrographical i n v e s t i g a t i o n s i n t h e I r i s h Sea, January-March 1953. F i s h e r y i n v e s t i g a t i o n s , London, 2 S e r . , 2 3 ( 2 ) : 1-25.
McKinley, I . G . , B a x t e r , M.S. and J a c k , W . , 1981a. A s i m p l e model o f r a d i o c a e s i u m t r a n s p o r t from Windscale t o t h e Clyde Sea a r e a . E s t u a r i n e , C o a s t a l and S h e l f S c i e n c e , 1 3 : 59-67. McKinley, I . G . , Baxter, M.S., E l l e t t , D . J . and J a c k , W . , 1981b. T r a c e r a p p l i c a t i o n s o f r a d i o c a e s i u m i n t h e Sea o f t h e Hebrides. E s t u a r i n e , C o a s t a l and S h e l f S c i e n c e , 1 3 : 69-82.
241 P i n g r e e , R . D . , H o l l i g a n , P . M . a n d M a r d e l l , G.T., 1978. The e f f e c t s of v e r t i c a l s t a b i l i t y on 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 i n t h e summer on t h e n o r t h w e s t European S h e l f . kepS e a R e s e a r c h , 25 : 1011-1028. P i n g r e e , R.D.
P r a n d l e , D.
P r a n d l e , D.
and G r i f f i t h s , D . K . , 1980. C u r r e n t s d r i v e n by a s t e a d y u n i f o r m wind s t r e s s o n t h e s h e l f s e a s a r o u n d t h e B r i t i s h I s l e s . O c e a n o l o g i c a A c t a , 3(2) : 227-236.
,
1976. Wind-induced f l o w t h r o u g h
Proudman, J . , 1939. On c u r r e n t s i n t h e N o r t h C h a n n e l o f t h e I r i s h Sea. Monthly n o t i c e s o f t h e Royal A s t r o n o m i c a l S o c i e t y , g e o p h y s i c a l s u p p l e m e n t , 4 : 387-403. R o b i n s o n , I . S . , 1976. A t h e o r e t i c a l a n a l y s i s o f t h e u s e of submarine cables a s electromagnetic oceanographic f l o w m e t e r s . P h i l o s o p h i c a l T r a n s a c t i o n s o f t h e Royal S o c i e t y of London, A , 280(1297) : 355-396. R o b i n s o n , I . S . 1979. The t i d a l dynamics of t h e I r i s h and C e l t i c Sea. G e o p h y s i c a l J o u r n a l of t h e Royal A s t r o n o m i c a l S o c i e t y , 56 (1) : 159-197. Simpson, J . H . , E d e l s t e n , D . J . , Edwards, A . , M o r r i s s , N . C . G . and T e t t , P . B . , 1979. The I s l a y f r o n t : physical s t r u c t u r e and 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 . Estuarine and c o a s t a l Marine S c i e n c e , 9 : 713-726. Slinn, D.J.,
1974. Water c i r c u l a t i o n and n u t r i e n t s i n t h e n o r t h w e s t I r i s h S e a . E s t u a r i n e and C o a s t a l Marine S c i e n c e , 2 : 1-25.
Taylor, G . I . ,
1919. T i d a l f r i c t i o n i n t h e I r i s h S e a . P h i l o s o p h i c a l T r a n s a c t i o n s o f t h e Royal S o c i e t y of London, A , 220 : 1-93.
Thompson, K . R . , 1980. An a n a l y s i s o f B r i t i s h monthly mean sea l e v e l . G e o p h y s i c a l J o u r n a l of t h e Royal A s t r o n o m i c a l S o c i e t y ,
63(1) : 57-73.
.
Thomson, R . E . and Chow, K . Y . , 1980 B u t t e r w o r t h and Lanczoswindow c o s i n e d i g i t a l f i l t e r s : w i t h a p p l i c a t i o n t o d a t a p r o c e s s i n g on t h e Univac 1106 computer. Pacific Marine S c i e n c e R e p o r t 80-9, 6 0 p p . I n s t i t u t e of Ocean S c i e n c e , Canada. (Unpublished m a n u s c r i p t )
.
Williamson, D . I . ,
1952.
The p l a n k t o n i n t h e I r i s h S e a , 1951 and B u l l e t i n s of Marine E c o l o g y , 4(31) : 87-114.
1956.
1974. Caesium-137 a s a w a t e r movement t r a c e r i n W i l s o n , T.R.S., N a t u r e , 248 : 125-127. S t . George's Channel.
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243
THE DYNAMICS OF THE LOOP CURRENT AND SHED EDDIES I N A IlUMERICAL MODEL OF THE GULF
OF M E X I C O
HARLEY E . HURLBURT and J . DAidA THOMPSON Environmental S i m u l a t i o n Branch (Code 3221, Naval Ocean Research and Development A c t i v i t y , NSTL S t a t i o n , MS 39529
USA
ABSTRACT The dynamics o f t h e c i r c u l a t i o n i n t h e G u l f of Mexico have been i n v e s t i g a t e d u s i n g s i m p l e , e f f i c i e n t n u m e r i c a l models t a p a b l e o f s i m u l a t i n g c o n s i s t e n t l y observed dynamical f e a t u r e s , i n c l u d i n g t h e Loop C u r r e n t and t h e shedding o f l a r g e a n t i c y c l o n i c eddies f r o m t h e Loop.
Over 150 model experiments were
i n t e g r a t e d t o s t a t i s t i c a l e q u i l i b r i u m , t y p i c a l l y 3-5 y e a r s . One p o p u l a r h y p o t h e s i s h o l d s t h a t t h e Loop C u r r e n t sheds a n t i c y c l o n i c cddies i n response t o annual v a r i a t i o n s i n t h e i n f l o w t h r o u g h t h e Yucatan S t r a i t s . However, a s t r i k i n g r e s u l t f r o m t h e models i s t h e i r a b i l i t y t o s i m u l a t e t h e observed q u a s i - a n n u a l eddy shedding p e r i o d w i t h
~2t i m e v a r i a t i o n s i n t h e i n f l o w .
The m o d e l - p r e d i c t e d eddy d i a m e t e r s , a m p l i t u d e s , and westward p r o p a g a t i o n speeds are a l s o r e a l i s t i c .
The dominant i n s t a b i l i t y mechanism i n t h e eddy shedding i s
a h o r i z o n t a l s h e a r i n s t a b i l i t y of t h e f i r s t i n t e r n a l mode, a b a r o t r o o i c r a t h e r than a b a r o c l i n i c i n s t a b i l i t y .
T h e r e f o r e , a r e d u c e d - g r a v i t y model w i t h one
w r t i c a l mode i s a b l e t o s i m u l a t e t h e b a s i c dynamics o f t h e Loop C u r r e n t - e d d y system.
Rossby-wave t h e o r y and a c o n s e r v a t i o n o f a b s o l u t e v o r t i c i t y t r a j e c t o r y
a n a l y s i s were used t o e x p l a i n t h e b e h a v i o r o f t h e Loop C u r r e n t , i n c l u d i n g i t s n o r t h w a r d p e n e t r a t i o n i n t o t h e G u l f , t h e l a t i t u d e o f westward bending, t h e shcdding p e r i o d f o r t h e e d d i e s , as w e l l as t h e i r diameter, and t h e i r westward p r o p a g a t i o n speed. A regime diagram f o r t h e r e d u c e d - g r a v i t y model was c o n s t r u c t e d i n terms o f t h e Reynolds number Re and t h e b e t a Rossby number
RB
= vC/RLp2, where vc i s t h e
v e l o c i t y a t t h e c o r e o f t h e c u r r e n t , Lp i s h a l f t h e p o r t s e p a r a t i o n d i s t a n c e and
B i s differential rotation.
Eddy shedding can be p r e v e n t e d b y r e d u c i n g Re o r
b y i n c r e a s i n g RB. Bottom r e l i e f a c t s t o i n h i b i t b a r o c l i n i c i n s t a b i l i t y , y i e l d i n g s o l u t i o n s more c l o s e l y r e s e m b l i n g t h o s e f r o m t h e reduced-gravi t y model than t h e t w o - l a y e r f l a t - b o t t o m model.
Topography a l s o i n f l u e n c e s t h e p a t h s o f t h e shed e d d i e s and,
i n t h e presence o f s u f f i c i e n t deep w a t e r i n f l o p / t h r o u g h t h e Yucatan S t r a i t s , p r e v e n t s Loop C u r r e n t p e n e t r a t i o n , westward bending, and eddy shedding.
In
e f f e c t , t h e West F l o r i d a S h e l f a c t s t o reduce t h e p o r t s e o a r a t i o n , i n c r e a s e
RB, and s h i f t t h e Loop C u r r e n t i n t o a s t a b l e regime.
244
The s i g n a t u r e s o f b a r o t r o p i c and b a r o c l i n i c i n s t a b i l i t i e s i n t h e t w o - l a y e r G u l f o f Mexico model were s t u d i e d u s i n g upper and l o w e r l a y e r p r e s s u r e f i e l d s and eddy-mean e n e r g e t i c s .
Both i n s t a b i l i t y processes t e n d t o d r i v e a deep f l o w
c h a r a c t e r i z e d by m o d o n l g e n e r a t i o n and t h e y e x h i b i t s i m i l a r v e r t i c a l phase r e l a t i o n s h i p s . However, i n t h e s e e x p e r i m e n t s t h e westward p r o p a g a t i o n speeds a s s o c i a t e d w i t h b a r o c l l n i c i n s t a o i l i t y a r e t y p i c a l l y two t o t h r e e t i m e s f a s t e r . 'For
convenience and i n t h e s p i r i t o f S t e r n ' s (1975) a p p l i c a t i o n t o o b s e r v a t i o n s
we have g e n e r a l i z e d t h e t e r m "modon" t o r e f e r t o any c o u n t e r - r o t a t i n g v o r t e x p a i r i n t h e lower l a y e r generated by a s i n g l e v o r t e x i n t h e upper layer. 1.
II4TRODUCTION Semi-enclosed seas a r e a t t r a c t i v e domains f o r ocean m o d e l i n g p a r t l y because
t h e y a l l o w t h e use o f n u m e r i c a l g r i d s t h a t r e s o l v e s t r o n g meandering c u r r e n t s and a s s o c i a t e d e d d y i n g phenomena a l s o found i n m a j o r ocean b a s i n s .
The G u l f o f
Mexico i s p a r t i c u l a r l y a t t r a c t i v e because i t c o n t a i n s a m a j o r c u r r e n t system t h a t sheds e n e r g e t i c a n t i c y c l o n i c e d d i e s which a r e comparable i n s i z e t o warmc o r e G u l f Stream r i n g s .
T h i s system i s i l l u s t r a t e d i n F i g . 1 by t h e d e p t h o f
t h e 22OC i s o t h e r m i n t h e e a s t e r n G u l f o f Mexico based on a h y d r o g r a p h i c survey b y L i e p p e r (1970).
I t shows t h e Loop C u r r e n t e n t e r i n g f r o m t h e s o u t h t h r o u g h
t h e Yucatan S t r a i t s and e x i t i n g t o t h e e a s t t h r o u g h t h e F l o r i d a S t r a i t s . mean t r a n s p o r t t h r o u g h t h e s t r a i t s i s
-
30 m3/s (Idowlin, 1972).
The
I n Fig. 1 a
l a r g e a n t i c y c l o n i c eddy i s about t o b r e a k - o f f f r o m t h e Loop C u r r e n t , as c o n f i r m e d b y subsequent o b s e r v a t i o n s ( E l l i o t t , 1979).
The Loop C u r r e n t oene-
t r a t e s i n t o t h e G u l f and sheds t h e s e l a r g e a n t i c y c l o n i c e d d i e s w i t h a q u a s i annual p e r i o d .
The e d d i e s have a t y p i c a l r a d i u s o f 180 km and t r a n s l a t e i n t o
t h e w e s t e r n G u l f a t a mean speed o f 2.4 cm/s
( E l l i o t t , 1979).
I n t h i s paper we p r e s e n t some b a s i c dynamical i d e a s and n u m e r i c a l r e s u l t s
c o n c e r n i n g t h e b e h a v i o r o f t h e Loop Current-eddy system.
The dynamical
t o p i c s i n c l u d e 1) t h e n a t u r e o f t h e i n s t a b i l i t y a s s o c i a t e d w i t h t h e eddy shedding, 2 ) t h e e x t e r n a l and/or i n t e r n a l f a c t o r s which d e t e r m i n e t h e eddy shedding p e r i o d , 3 ) t h e t r a j e c t o r y dynamics o f t h e Loop C u r r e n t and how t h e y a f f e c t t h e p e n e t r a t i o n o f t h e Loop i n t o t h e G u l f , t h e eddy shedding, and t h e d i a m e t e r o f t h e e d d i e s , 4 ) t h e e x i s t e n c e o f d i f f e r e n t regimes f o r t h e Loop C u r r e n t , 5) two i m p o r t a n t r o l e s of topography i n t h e dynamics, and 6 ) t h e d i s t i n c t i v e s i g n a t u r e s o f b a r o t r o p i c and b a r o c l i n i c i n s t a b i l i t y i n t h e f l o w and i n t h e e n e r g e t i c s .
Over 150 n u m e r i c a l experiments have been performed t o
e x p l o r e t h e model parameter space, b u t more i m p o r t a n t l y t o a i d i n t h e formul a t i o n and t e s t i n g o f dynamical hypotheses.
T h i s paper i s b o t h a d i s t i l l a t i o n
and an e x t e n s i o n of H u r l b u r t and Thompson (1980), h e r e a f t e r r e f e r r e d t o as HT. That paper d i s c u s s e s t h e o n l y p r e v i o u s n u m e r i c a l model o f t h e G u l f o f Mexico w h i c h was i n t e g r a t e d t o s t a t i s t i c a l P s u i l i b r i u m o r w h i c h s i m u l a t e d t h e b a s i c r e p e t i t i v e f e a t u r e s o f t h e eddy shedding by t h e Loop C u r r e n t .
245
F i g . 1. Topography of t h e 2 2 O C i s o t h e r m a l s u r f a c e , 4-18 August 1966 ( A l a m i n o s c r u i s e 66-A-11) f r o m L e i p p e r ( 1 9 7 0 ) . Subsequent d a t a ( E l l i o t , 1379) i n d i c a t e s t h a t an a n t i c y c l o n i c eddy s e p a r a t e d f r o m t h e Loop C u r r e n t w i t h i n s e v e r a l months.
2.
DESIGN OF THE NUMERICAL MODELS AND NUMERICAL EXPERIMENTS The t h r e e n u m e r i c a l models o f HT a r e used t o e l u c i d a t e t h e Loop C u r r e n t -
eddy shedding dynamics.
These models were designed t o be as s i m p l e as p o s s i b l e
w h i l e r e t a i n i n g t h e a b i l i t y t o s i m u l a t e t h e b a s i c phenomena o f i n t e r e s t . t h r e e models a r e 1 ) reduced g r a v i t y , 2 ) b a r o t r o p i c , and 3 ) t w o - l a y e r .
The
The
f i r s t two a r e m a t h e m a t i c a l l y i d e n t i c a l e x c e p t f o r parameter v a l u e s , p a r t i c u l a r l y the g r a v i t a t i o n a l acceleration.
The reduced g r a v i t y model i s designed t o
r e p r e s e n t t h e f i r s t i n t e r n a l mode and c o n t a i n s an upper a c t i v e l a y e r and a l o w e r l a y e r which i s i n f i n i t e l y deep and a t r e s t .
I n t h e reduced g r a v i t y
and t w o - l a y e r models t h e p y c n o c l i n e i s r e p r e s e n t e d by an i n m i s c i b l e i n t e r f a c e between two l a y e r s w i t h a p r e s c r i b e d d e n s i t y c o n t r a s t .
I n t h e reduced g r a v i t y
model b o t t o m topography and b a r o c l i n i c i n s t a b i l i t y a r e n o t p e r m i t t e d .
Two
a c t i v e l a y e r s i s t h e minimum t o a l l o w b a r o c l i n i c i n s t a b i l i t y and t o a l l o w c o e x i s t e n c e o f topography and t h e p y c n o c l i n e .
The b a r o t r o p i c and reduced
g r a v i t y models demonstrate t h e b e h a v i o r o f t h e i n d i v i d u a l modes and p r o v i d e
246
They a l s o a l l o w t h e
i n s i g h t i n t o how t h e y i n t e r a c t i n t h e t w o - l a y e r model. i n v e s t i g a t i o n o f some phenomena i n t h e s i m p l e s t c o n t e x t .
The models a r e p r i m i t i v e e q u a t i o n on a O-plane and r e t a i n a f r e e s u r f a c e . Using t h e h y d r o s t a t i c and Boussinesq a p p r o x i m a t i o n s and a r i g h t - h a n d e d C a r t e s i a n c o o r d i n a t e system, t h e v e r t i c a l l y i n t e g r a t e d model e q u a t i o n s a r e c
a
\vi
r-+ ( v - \Vi
+
\Vi
-v
h
\vi
+
k x f \Vi = -hiVPi
ahi
at +V.\Vi = o where i = 1,2 f o r t h e t w o - l a y e r model, i = l f o r t h e b a r o t r o p i c and reduced g r a v i t y models and
See Appendix A f o r symbol d e f i n i t i o n s .
I n t h e reduced g r a v i t y model t h e l o w e r
l a y e r momentum e q u a t i o n i s gVq = g'Vhl. F i g . 2 shows t h e model domain superimposed on a t o p o g r a p h i c map o f t h e G u l f o f Mexico. neglected.
The 20° c o u n t e r - c l o c k w i s e r o t a t i o n o f t h e model domain i s
The n u m e r i c a l models were d r i v e n f r o m r e s t by p r e s c r i b e d i n f l o w
t h r o u g h t h e Yucatan S t r a i t s ( s o u t h e r n p o r t ) compensated b y o u t f l o w t h r o u g h t h e F l o r i d a S t r a i t s (eastern p o r t ) .
Except a t t h e p o r t s t h e b o u n d a r i e s a r e
r i g i d and i n a l m o s t a l l cases t h e n o - s l i p c o n d i t i o n i s used. a t the southern ( i n f l o w ) p o r t . used f o r Vi.
\Vi i s p r e s c r i b e d
I n most cases a p a r a b o l i c i n f l o w p r o f i l e i s
Due t o t h e g e o s t r o p h i c t i l t i n t h e i n t e r f a c e across t h e p o r t ,
t h e v e l o c i t y maximum i s west o f t h e c e n t e r o f t h e i n f l o w p o r t .
A t the eastern
( o u t f l o w ) p o r t t h e normal f l o w i s s e l f - d e t e r m i n e d u s i n g t h e f u l l x-momentum equation.
A t i n f l o w p o i n t s t h e boundary c o n d i t i o n i s u,=O.
p o i n t s t h e c o m p u t a t i o n a l boundary c o n d i t i o n i s uxx=O. upstream d i f f e r e n c i n g f o r t h e (Uu),
A t outflow
The l a t t e r r e s u l t s i n
term, w h i c h i s l a g g e d i n t i m e i n t h i s case.
The normal p r e s s u r e g r a d i e n t i s assumed u n i f o r m across t h e p o r t and i s determined by an i n t e g r a l c o n s t r a i n t r e q u i r i n g t h e n e t o u t f l o w t h r o u g h t h e e a s t e r n p o r t t o
247
compensate t h e i n f l o w t h r o u g h t h e s o u t h e r n p o r t . ponent a t t h e domain.
T h i s weak o v e r s p e c i f i c a t i o n e l i m i n a t e s t h e p o s s i b i l i t y o f oUtfloW a t
u n r e a l i s t i c angles.
O u t f l o w t h r o u g h a channel modeling t h e F l o r i d a S t r a i t s i s
a more r e a l i s t i c approach. effect.
The t a n g e n t i a l v e l o c i t y com-
p o r t s i s u s u a l l y s e t a t zero 1 / 2 g r i d d i s t a n c e o u t s i d e t h e p h y s i c a l
T h i s was done i n a few cases, b u t w i t h n e g l i g i b l e
The s e m i - i m p l i c i t n u m e r i c a l models o f HT a r e u s e f i n t h i s s t u d y .
The
i m p l i c i t t r e a t m e n t o f t h e e x t e r n a l and i n t e r n a l g r a v i t y waves a l l o w s much l o n g e r t i m e s t e p s i n t h e n u m e r i c a l i n t e g r a t i o n t h a n comparable e x p l i c i t p r i m i t i v e equat i o n models w i t h a f r e e s u r f a c e .
See HT f o r f u r t h e r d i s c u s s i o n o f t h e n u m e r i c a l
model s.
30 '
20'
F i g . 2. Bathymetry of t h e G u l f o f Mexico based on U. S . Coast and Geodetic Survey C h a r t 1007 and soundings on f i l e a t t h e Dept. o f Oceanography, Texas A&M U n i v e r s i t y . From N o w l i n (1972). The r e c t a n g l e shows t h e approximate domain o f t h e n u m e r i c a l model. I n f l o w and o u t f l o w p o r t s a r e a l s o i n d i c a t e d . Table 1 p r e s e n t s t h e parameters of t h e p i v o t a l experiment f o r each n u m e r i c a l model.
These parameters i m p l y a maximum upper l a y e r i n f l o w v e l o c i t y o f 70-75
cm/s and an i n t e r n a l r a d i u s o f d e f o r m a t i o n , h = ( g ' h 1 ) ' / 2 / f
= 45 km, about f o u r
times l e s s t h a n t h e observed r a d i u s o f m a j o r eddies shed by t h e Loop C u r r e n t . I n t h e t w o - l a y e r model t h e v a l u e o f g ' i n t h e t a b l e i s m u l t i p l i e d
248
b y (Hl+H2)/H2
t o y i e l d t h e same i n t e r n a l values f o r t h e g r a v i t y wave speed as
i n a reduced g r a v i t y model.
The i n f l o w t r a n s p o r t i s spun up w i t h a t i m e
c o n s t a n t o f 30 days t o m i n i m i z e t h e e x c i t a t i o n o f h i g h f r e q u e n c y waves.
Potent i a l l y i m p o r t a n t w i n d d r i v i n g i s n e g l e c t e d t o a l l o w f o c u s on t h e L o o p - d r i v e n c i r c u l a t i on. TABLE 1 Model parameters f o r s t a n d a r d case
A
~ ~ ~ c m ~ s e c - ~
f0
5
P
1 gm cm-3
g
980 cm sec-‘
gi
0
g’
3 cm sec-2
Ax
20 km*
H1
200 m 2800 m
Ay
18.75 km*
At
1.5 h r
H2
B
~x~~-’~cm-’sec-~
Domain S i z e , xL by yL
1600 x 900 km
Southern P o r t Width, L p w
160 km
E a s t e r n P o r t Width, Le
150 km
Center o f s o u t h e r n p o r t a t x
1200 km
P
Center o f e a s t e r n p o r t a t y
75 km
Lower Layer I n f l o w T r a n s p o r t
20 x 1 0 ~ m ~ s e c - ’ - ( 2 0s v ) 10 x 106m3sec-’ (10 s v )
P Upper L a y e r I n f l o w T r a n s p o r t * *
Angle o f i n f l o w f r o m x - a x i s ,
goo
01
Inflow spin-up time constant
30 days ~
~
~~~~
F o r t h e b a r o t r o p i c model t h e i n i t i a l maximum d e p t h i s H=3000 m and t h e i n f l o w t r a n s p o r t i s 30 Sv.
* for a ** a l s o
given v a r i a b l e f o r t h e s t a n d a r d reduced g r a v i t y model
H o r i z o n t a l f r i c t i o n p r o v i d e s t h e o n l y d i s s i p a t i o n i n t h e models. Because Lap1 a c i an f r i c t i on is a crude parameterization, f o r convenience AhiV&i
was r e p l a c e d by AV2\Vi
viscosity
(A)
( w i t h minimal e f f e c t ) .
The s t a n d a r d eddy
i s g r e a t e r t h a n r e q u i r e d f o r s t a b l e i n t e g r a t i o n o f t h e models.
HJ showed t h i s v a l u e y i e l d s a c o n s t a n t eddy-shedding p e r i o d f o r t h e Loop Current.
S m a l l e r values i n t r o d u c e d some i r r e g u l a r i t y i n t o t h e p e r i o d w i t h o u t
s u b s t a n t i a l l y a l t e r i n g t h e l o n g - t e r m mean.
A l t h o u g h l o w e r eddy v i s c o s i t i e s
a r e u t i l i z e d i n some experiments, most employ t h e l a r g e r v a l u e t o reduce t h e l e n g t h o f t h e i n t e g r a t i o n r e q u i r e d t o o b t a i n s t a b l e s t a t i s t i c s , and t o f a c i l i t a t e the analysis of the results.
F i g . 3 s h o w t h e i d e a l i z e d G u l f o f Mexico
249
topography used i n some o f t h e n u m e r i c a l experiments.
T y p i c a l l y t h e models
were i n t e g r a t e d f i v e y e a r s t o s t a t i s t i c a l e q u i l i b r i u m .
900
[KMI
0 0
1600
IKM)
F i g . 3. B a t h . m e t r v of t h e i d e a l i z e d G u l f o f Mexico model. The deeoest w a t e r i s - a t 3000 m a n d t h e s h a l l o w e s t topography i s 400 m deep. The c o n t o u r i n t e r v a l i s 250 m. (From HT).
3.
AN ATTEMPT TO SIMULATE THE EDDY SHEDDING BY THE LOOP CURRENT Our f i r s t g o a l was t o d e t e r m i n e which, ifany, of t h e models c o u l d demon-
s t r a t e eddy shedding w i t h a r e a l i s t i c eddy diameter, a m p l i t u d e , shedding p e r i o d , and p r o p a g a t i o n .
W i t h i n t h e framework o f t h e t w o - l a y e r model, t h e
f i r s t s i m u l a t i o n was made as r e a l i s t i c as p o s s i b l e i n c l u d i n g t h e i d e a l i z e d topography shown i n F i g . 3.
A l o n g s t a n d i n g h y p o t h e s i s (Cochrane, 1965)
m a i n t a i n s t h a t t h e Loop C u r r e n t e x h i b i t s an aanual eddy shedding c y c l e due t o seasonal v a r i a t i o n s i n t h e f l o w t h r o u g h t h e Yucatan S t r a i t s which a f f e c t t h e p e n e t r a t i o n d i s t a n c e o f t h e Loop C u r r e n t . i s presumed t o occur.
When t h e Loop r e t r e a t s , eddy shedding
D e s p i t e t h i s h y p o t h e s i s , t h e model was f i r s t d r i v e n by
a s t e a d y i n f l o w t o see i f t h e l o o p C u r r e n t would shed eddies due t o p u r e l y i n t e r n a l mechanisms.
This might then e s t a b l i s h a n a t u r a l frequency f o r t h e
eddy shedding. The f i r s t e x p e r i m e n t u t i l i z e s t h e parameters o f Table 1 and t h e topography o f F i g . 3 e x c e p t t h a t t h e u p p e r l a y e r i n f l o w t r a n s p o r t i s 25 Sv, t h e l o w e r l a y e r
5 Sv.
F i g . 4 i l l u s t r a t e s an eddy shedding c y c l e f r o m t h i s experiment u s i n g a
sequence of f o u r s y n o p t i c maps o f t h e p y c n o c l i n e anomaly (PA).
The PA i s t h e
9001
1
'
I
'
"
'
1
'
1
1
'
'
1
'
1
9001
"
'
I
'
'
I
'
'
'
"
-_.._
............................ .............. ................-.
I
'
,I 1
lKMl
0 0
IKMI
IKMI
1600
900
1600
900
_.____... - - - -.............. IKM1
IKMI
0
0 0
(KMI
1600
0
(KMI
1600
Fig. 4. Sequence of synoptic maps of P A a t 70-day i n t e r v a l s showing t h e l i f e cycle of an eddy s t a r t i n g a t day 2210. The contour i n t e r v a l i s 20 m. I n a l l t h e ' f i g u r e s dashed contours a r e negative. PA i s p o s i t i v e downward. ..The case shown here uses the parameters of Table 1 and the topography of Fig. 3 except t h a t the upper l a y e r inflow transport i s 25 S v , the l w e r layer 5 Sv. (From H T ) .
N u1 0
251 d e v i a t i o n o f t h e i n t e r f a c e between t h e l a y e r s from i t s i n i t i a l f l a t e l e v a t i o n and i s p o s i t i v e downward ( u p p e r l a y e r t h i c k n e s s g r e a t e r t h a n i n i t i a l ) .
Fig.
4a shows t h e Loop C u r r e n t has p e n e t r a t e d i n t o t h e G u l f and i s b e g i n n i n g t o form an a n t i c y c l o n i c eddy.
I n F i g . 4b t h e Loop C u r r e n t has b e n t westward and
an eddy i s about t o b r e a k o f f .
F i g . 4c shows t h e Loop C u r r e n t and an eddy
j u s t a f t e r an eddy-shedding event.
I n F i g . 4d t h e eddy Gas d r i f t e d westward
w h i l e t h e Loop C u r r e n t has p e n e t r a t e d f u r t h e r i n t o t h e G u l f .
F i g . 4a, b shows
t h a t when an eddy reaches t h e w e s t e r n boundary, i t d r i f t s n o r t h w a r d w i t h f i n a l decay i n t h e n o r t h w e s t c o r n e r o f t h e b a s i n . The c y c l e o f Loop C u r r e n t p e n e t r a t i o n i n t o t h e G u l f , westward bending and eddy shedding i s r e p e a t e d w i t h a p e r i o d o f a b o u t 290 days, c l o s e t o t h e q u a s i annual p e r i o d observed.
C o n t r a r y t o the p o p u l a r h y p o t h e s i s , t i m e v a r i a t i o n s
of t h e i n f l o w a r e n o t r e q u i r e d f o r t h e model Loop C u r r e n t t o e x h i b i t r e a l i s t i c q u a s i - a n n u a l eddy shedding, a s t r i k i n g r e s u l t f i r s t n o t e d by HT.
The model
a l s o p r e d i c t s a r e a l i s t i c eddy d i a m e t e r , a m p l i t u d e , and westward p r o p a g a t i o n speed.
I n subsequent experiments
HT found t h a t r e a l i s t i c t i m e v a r i a t i o n s i n
t h e upper l a y e r i n f l o w can have a s i g n i f i c a n t i n f l u e n c e on t h e eddy shedding. However, t h e eddy shedding i s dominated by t h e n a t u r a l p e r i o d , n o t t h e p e r i o d o f t h e f o r c i n g , a t o p i c we s h a l l n o t pursue here.
I n S e c t i o n 7 we do examine
an i m p o r t a n t e f f e c t o f topography and l o w e r l a y e r i n f l o w t h r o u g h t h e Yucatan S t r a i t s on t h e eddy shedding.
4.
A SIMPLE TEST FOR THE INSTABILITY MECHANISM The r e m a i n i n g s e c t i o n s a r e designed t o p r o v i d e some i n s i g h t i n t o t h e
dynamics o f t h e Loop Current-eddy system.
We m i g h t be tempted t o u n d e r t a k e a
s t a b i l i t y a n a l y s i s t o f i n d i n s t a b i l i t y mechanisms, u n s t a b l e wavelengths, and growth r a t e s , b u t we would a n t i c i p a t e t h a t t h e c o n f i g u r a t i o n o f t h e c u r r e n t would be troublesome.
However, t h e r e a r e more f r u i t f u l approaches t h a n t h i s .
N e v e r t h e l e s s , we w i l l s t a r t w i t h one s i m p l e t e s t f o r t h e p r i m a r y i n s t a b i l i t y mechanism b y u s i n g t h e reduced g r a v i t y model.
I f i t produces r e s u l t s s i m i l a r
t o t h e t w o - l a y e r model, t h e n we have e l i m i n a t e d b a r o c l i n i c i n s t a b i l i t y as an e s s e n t i a l element o f t h e dynamics, and t h e p r i m a r y i n s t a b i l i t y mechanism
is a h o r i z o n t a l s h e a r i n s t a b i l i t y o f t h e i n t e r n a l mode, a b a r o t r o p i c i n s t a b i l i t y .
252
F i g . 5 compares ( a ) t h e e x p e r i m e n t w i t h topography d i s c u s s e d i n S e c t i o n 3, ( b ) a t w o - l a y e r f l a t - b o t t o m e x p e r i m e n t u s i n g t h e s t a n d a r d parameters from Table
1, and ( c ) a reduced g r a v i t y e x p e r i m e n t u s i n g a p p r o p r i a t e parameters f r o m T a b l e 1.
Shown i s a l a t i t u d e vs. t i m e ( y vs. t ) p l o t o f PA a t a l o n g i t u d e 190 km
west o f t h e c e n t e r o f t h e s o u t h e r n p o r t .
I n a l l t h r e e cases t h e PA shows a
r e g u l a r p r o g r e s s i o n o f d i s c r e t e e d d i e s w i t h s i m i l a r eddy d i a m e t e r , a m p l i t u d e , and shedding p e r i o d .
However, t h e e x p e r i m e n t w i t h topography ( F i g . 5a) d i d n o t
b e g i n t o shed e d d i e s f o r a l m o s t t h r e e y e a r s , a p o i n t addressed i n S e c t i o n 7. With s t a n d a r d parameters t h e b a r o t r o p i c model e v o l v e d t o a s t e a d y s t a t e w i t h o u t shedding e d d i e s , a m a t t e r d i s c u s s e d i n S e c t i o n 6. The r e s u l t s shown i n F i g . 5 l e a d us t o conclude t h a t ’ a h o r i z o n t a l shear i n s t a b i l i t y o f t h e i n t e r n a l mode i s dominant.
The t w o - l a y e r model w i t h F i g . 3
topography, t h e t w o - l a y e r f l a t - b o t t o m model, and t h e reduced g r a v i t y model do n o t agree i n a l l t h e parameter space we e x p l o r e d (see S e c t i o n 8), b u t t h e y do agree f o r a regime i n a c c o r d w i t h observed f e a t u r e s o f t h e Loop Current-eddy system.
S i n c e t h e reduced g r a v i t y model i s t h e s i m p l e s t o f t h e models t o p r o v i d e
a r e a l i s t i c s i m u l a t i o n , i t i s used i n much o f o u r a n a l y s i s .
The q u e s t i o n o f
b a r o t r o p i c vs. b a r o c l i n i c i n s t a b i l i t y i s addressed f u r t h e r i n S e c t i o n 8 u s i n g eddy-mean e n e r g e t i c s and o t h e r s i g n a t u r e s o f t h e i n s t a b i l i t y mechanisms. 5.
CAY TRAJECTORIES AND ROSSBY WAVE THEORY ELUCIDATE THE LOOP CURRENT
-
EDDY
SHEDDING DYNAMICS Constant a b s o l u t e v o r t i c i t y (CAV) t r a j e c t o r i e s and Rossby wave t h e o r y a r e u s e f u l a i d s i n u n d e r s t a n d i n g t h e dynamics o f t h e Loop C u r r e n t and t h e eddy shedd i n g i n c l u d i n g t h e p e n e t r a t i o n o f t h e Loop C u r r e n t i n t o t h e G u l f and t h e eddy d i a m e t e r , shedding p e r i o d , and westward p r o p a g a t i o n .
5.1
CAV t r a j e c t o r y a n a l y s i s CAV t r a j e c t o r i e s a r e based on c o n s e r v a t i o n o f p o t e n t i a l v o r t i c i t y on a
B-plane and on s t e a d y , f r i c t i o n l e s s , g e o s t r o p h i c a l l y b a l a n c e d f l o w .
I n the
reduced g r a v i t y model t h i s i m p l i e s t h a t c o n t o u r s o f upper l a y e r depth a r e s t r e a m l i n e s , and t h u s a b s o l u t e v o r t i c i t y i s a l s o conserved.
The CAV
263
F i g . 5. Time v a r i a t i o n s o f PA 190 km west o f t h e c e n t e r o f t h e i n f l o w p o r t f o r t h r e e cases: ( a ) case shown i n F i g . 4 which i n c l u d e s topograDhy, ( b ) s t a n d a r d t w o - l a y e r f l a t - b o t t o m case u s i n g parameters f r o m Table 1, and ( c ) s t a n d a r d reduced g r a v i t y case u s i n g a p p r o p r i a t e parameters f r o m Table 1. A r e g u l a r p r o g r e s s i o n o f e d d i e s t h r o u g h t h e n o r t h - s o u t h c r o s s s e c t i o n i s shown i n each case. The c o n t o u r i n t e r v a l i s 30 m. (From HT).
254
t r a j e c t o r i e s are c a l c u l a t e d from
where 0 i s t h e a n g l e o f t h e c u r r e n t w i t h r e s p e c t t o t h e p o s i t i v e x - a x i s , v c i s t h e v e l o c i t y a t t h e c o r e o f t h e c u r r e n t , r o i s t h e r a d i u s o f curvature;
and t h e
s u b s c r i p t , 0, i n d i c a t e s a v a l u e a t t h e o r i g i n o f t h e t r a j e c t o r y c a l c u l a t i o n see HT; Reid, 1972; H a l t i n e r and M a r t i n , 1 9 5 7 ) .
(e.g..
F i g . 6 shows CAV t r a j e c t o r i e s superimposed on t h e model domain f o r v c =
75 un/s,
ro=m
and s i x d i f f e r e n t values of 0,.
S i n c e ro=m, t h e o r i g i n i s t h e
f i r s t i n f l e c t i o n p o i n t a f t e r i n f l o w (see F i g . 4 ) , and n o t ,the i n f l o w p o r t as i m p l i e d by t h e f i g u r e . l o o p back on i t s e l f .
As
Oo i n c r e a s e s , t h e t r a j e c t o r y i n c r e a s i n g l y t e n d s t o
When O0=13Oo,
t h e CAV t r a j e c t o r y i n t e r s e c t s i t s e l f a t t h e
o r i g i n , a p h y s i c a l l y impossible s i t u a t i o n f o r a steady flow.
Thus, when 0,
becomes l a r g e some p h y s i c a l i n s t a b i l i t y o f t h e Loop C u r r e n t can be a n t i c i p a t e d . I n F i g . 6 Oo i s v a r i e d t o s i m u l a t e t h e f o r m a t i o n o f an eddy, b u t i t r e a l l y r e p r e s e n t s a sequence o f s t e a d y s t a t e s o l u t i o n s t o ( 4 ) .
A l t h o u g h t h e eddy-
shedding Loop C u r r e n t i s n o t steady, i t s e v o l u t i o n i s s u f f i c i e n t l y s l o w t o c o n s i d e r i t i n i s o s t a t i c a d j u s t m e n t w i t h r e s p e c t t o CAV t r a j e c t o r i e s .
I n the
t i m e a f l u i d p a r t i c l e i n t h e Loop moves f r m t h e w e s t s i d e t o t h e e a s t s i d e , t h e Loop bends westward o n l y 5 t o 10% o f t h e Loop d i a m e t e r .
5.2
I n f l u e n c e o f Rossby waves
How does t h e model LOOPC u r r e n t bend westward when t h e a n g l e o f i n f l o w t h r o u g h t h e Yucatan S t r a i t s i s n o t v a r i e d ? We can g a i n some i n s i g h t i n t o t h i s by examining t h e c o n t i n u i t y e q u a t i o n , ( 2 ) .
If t h e mass d i v e r g e n c e i s g e o s t r o -
p h i c , i t w i l l propagate westward as a n o n d i s p e r s i v e i n t e r n a l Rossby wave. (Note t h e converse i s n o t t r u e n e a r t h e e q u a t o r ) .
where V
9
F o r g e o s t r o p h i c d i v e r g e n c e ( 2 ) becomes
i s t h e g e o s t r o p h i c m e r i d i o n a l t r a n s p o r t and
i s t h e n o n d i s p e r s i v e i n t e r n a l Rossby wave speed. The i m p o r t a n c e o f n o n d i s p e r s i v e Rossby wave p r o p a g a t i o n can b e a n t i c i p a t e d f r o m a p p r o p r i a t e i s o l a t e d v o r t e x t h e o r y (McWilliams and F l i e r l , 1979), because
1) r/X=4 where r i s t h e eddy r a d i u s and A i s t h e i n t e r n a l r a d i u s o f d e f o r m a t i o n , and 2 ) t h e b e t a Rossby number, R s = v c / ( B r Z ) = l f o r t h e eddies.
From t h e l i n e a r
E L
m
0
0
m
O
0
m
2 ==
T O
O
E O r
EO
0 0
m 0
EO
0
.
""U
.""I
and 0, = ( a ) 70°, ( b ) 90°,
(c) llOo,
( d ) 130°, ( e ) 150°,
( f ) 170'.
a,
vc = 75 cn/s,
255
F i g . 6,
CAV t r a j e c t o r i e s superimposed on t h e model domain wit:? ro =
256
phase speed f o r Rossby waves 2 2 -2 cr=R/(k +I +A
(7)
where k and L a r e zonal and m e r i d i o n a l wavenumbers, r e s p e c t i v e l y , t h e d i s p e r s i v e and n o n d i s p e r s i v e c o n t r i b u t i o n s a r e equal f o r c i r c u l a r e d d i e s when r/X=.rri 2.22.
@=
Hence, we a l s o e x p e c t a s i g n i f i c a n t b u t secondary c o n t r i b u t i o n from
d i s p e r s i v e Rossby wave p r o p a g a t i o n . and t h e g e o s t r o F i g . 7 compares t h e i n s t a n t a n e o u s mass d i v e r g e n c e (V.\V,) ah f o r t h e s t a n d a r d reduced g r a v i t y e x p e r i m e n t a t p h i c mass d i v e r g e n c e ( - c i r $) two d i f f e r e n t s t a g e s i n t h e eddy shedding c y c l e .
The usef,ulness o f t h e i n s t a n -
taneous mass d i v e r g e n c e f i e l d s must be q u e s t i o n e d , s i n c e t h e y a r e e a s i l y domin a t e d b y r a p i d o s c i l l a t i o n s and c o m p u t a t i o n a l n o i s e .
The absence o f t h e s e con-
t a m i n a t i o n s was v e r i f i e d by showing t h a t t h e i n s t a n t a n e o u s mass d i v e r g e n c e and t h e 20-day mean a r e v i r t u a l l y i d e n t i c a l . d e t e r m i n e d from t h e change i n hl
From ( 2 ) t h e 20-day mean can be
i n 20 days.
Near t h e p o r t s and n e a r t h e western boundary t h e mass d i v e r g e n c e i s f a r from geostrophic.
Note p a r t i c u l a r l y i n F i g . 7e t h e a g e o s t r o p h i c mass conver-
gence i n t h e s o u t h e a s t e r n p a r t o f t h e b a s i n a s s o c i a t e d w i t h t h e n o r t h w a r d penet r a t i o n o f t h e Loop C u r r e n t .
A l s o n o t e t h a t mass convergence o c c u r s a t t h e
c e n t e r o f t h e eddy d u r i n g i t s f o r m a t i o n (an a n t i c y c l o n i c i n f l o w ) , w h i l e mass d i v e r g e n c e occurs a t t h e c e n t e r ( a n t i c y c l o n i c o u t f l o w ) a f t e r t h e eddy separates f r o m t h e Loop and s l o w l y decays.
However, i n t h e westward bending Loop and i n
t h e r e c e n t l y shed eddy t h e t o t a l mass d i v e r g e n c e and t h e g e o s t r o p h i c mass divergence are q u i t e s i m i l a r .
T h i s c l e a r l y demonstrates an i m p o r t a n t c o n t r i b u -
t i o n o f n o n - d i s p e r s i v e i n t e r n a l Rossby wave p r o p a g a t i o n t o t h e westward bending
o f t h e Loop C u r r e n t and t h e westward p r o p a g a t i o n o f t h e eddies.
Other c o n t r i -
b u t i o n s such as n o n l i n e a r and d i s p e r s i v e Rossby wave p r o p a g a t i o n a r e n o t accounted f o r h e r e .
S t i l l , we have i d e n t i f i e d an i m p o r t a n t mechanism w h i c h
a c t s t o bend t h e Loop C u r r e n t westward.
Thus, i t a l s o produces a c o u n t e r -
clockwise r o t a t i o n o f t h e c u r r e n t a t the f i r s t i n f l e c t i o n p o i n t a f t e r i n f l o w ( s e e F i g . 4).
T h i s i n t u r n produces changes i n t h e CAV t r a j e c t o r y ( F i g . 6 )
w h i c h l e a d s us t o a n t i c i p a t e t h e f o n n a t i o n and shedding o f an eddy.
5.3
Two t i m e s c a l e s a s s o c i a t e d w i t h t h e eddy shedding Note t h a t westward b e n d i n g of t h e c u r r e n t and t h e tendency f o r i t t o l o o p
back on i t s e l f can be u n d e r s t o o d w i t h o u t i n v o k i n g an i n s t a b i l i t y mechanism. An i n s t a b i l i t y mechanism appears e s s e n t i a l o n l y t o e x p l a i n t h e s e p a r a t i o n o f t h e eddy f r o m t h e Loop.
Thus, two t i m e s c a l e s a r e a s s o c i a t e d w i t h t h e eddy
shedding p e r i o d : 1) t h e l o n g t i m e s c a l e f o r t h e Loop C u r r e n t t o p e n e t r a t e i n t o t h e G u l f and bend westward i n t o an u n s t a b l e c o n f i g u r a t i o n , and 2 ) t h e much s h o r t e r t i m e s c a l e f o r t h e growth o f t h e i n s t a b i l i t y as t h e eddy separates f r o m
257
900.
]
.
.
I
,
,
.
,
. .
1
,
I
.
,
,
0
.
'
"
"
"
"
400.
'
'
000.
1200. "
,
1600J
KM
DRY=1080
-BrCP-HrHX/FmrZ
gnu.
600. L r
r S 300.
0.
0
1200.
KM
1600.
KM
Fig. 7. Shows ( a , d ) t h e PA f o r t h e standard reduced g r a v i t y experiment, which uses t h e p e r t i n e n t parameters from Table 1, and compares t h e associated V1) and ( c , f ) geostrophic mass divergenct (b,e) instantaneous mass divergence (V (-cirah/ax). Two d i f f e r e n t s t a g e s of an eddy cycle a r e i l l u s t r a t e d a t days 990 cm/s ( l e f t ) and 1080 ( r i g h t ) . The contour i n t e r v a l s a r e 20 m f o r PA and f o r mass divergence.
-
258
t h e Loop C u r r e n t .
T h i s suggests a r e p e a t e d s p i n - u p o f t h e Loop C u r r e n t w h i c h
e v e n t u a l l y becomes u n s t a b l e .
A l t h o u g h i t may, i t i s n o t c l e a r t h a t t h e Loop
C u r r e n t must s a t i s f y any c r i t e r i o n f o r i n s t a b i l i t y d u r i n g much o f t h e eddy c y c l e . 5.4 The CAV t r a j e c t o r y a n a l y s i s , Rossby wave t h e o r y , and t h e v o r t i c i t y e q u a t i o n can be used t o f o r m u l a t e a number o f q u a n t i t a t i v e hypotheses c o n c e r n i L g t h e n o r t h w a r d p e n e t r a t i o n o f t h e Loop C u r r e n t i n t o t h e G u l f , t h e l a t i t u d e a t which t h e westward b e n d i n g occurs, and t h e eddy diameter, shedding p e r i o d , and westward p r o p a g a t i o n .
We w i l l f o r m u l a t e t h e a p p r o p r i a t e s c a l e s and t h e n t e s t them
as hypotheses f o r t h e dynamics g o v e r n i n g t h e Loop Current-eddy system p r e d i c t e d by t h e reduced g r a v i t y n u m e r i c a l model.
The v o r t i c i t y e q u a t i o n f o r t h e reduced
g r a v i t y model i s
where c=v -u X
5.5
Y
i s the r e l a t i v e v o r t i c i t y .
Eddy d i a m e t e r , Loop C u r r e n t p e n e t r a t i o n , and l a t i t u d e of westward bending.
The b e t a Rossby number, RB, i s t h e r a t i o o f r e l a t i v e t o p l a n e t a r y v o r t i c i t y a d v e c t i o n , and R B = ~ p r o v i d e s a minimum i n e r t i a l l e n g t h s c a l e , LBI=(vc/R) 1/2 , o v e r w h i c h 13 i s i m p o r t a n t .
We h y p o t h e s i z e t h a t t h i s determines t h e l a t i t u d e a t
w h i c h t h e Loop C u r r e n t bends westward.
B i s i m p o r t a n t , L,F=(A/B)1/3,
The f r i c t i o n a l l e n g t h s c a l e o v e r w h i c h
i s much s m a l l e r .
o u r s t a n d a r d reduced g r a v i t y e x p e r i m e n t .
LBI=191
km and LBF=37 km f o r
This i m p l i e s t h a t i n e r t i a w i l l prevent
Rossby wave a c t i o n from bending t h e Loop C u r r e n t westward a t a h i g h e r l a t i t u d e than f r i c t i o n . We a l s o f i n d t h a t RB=l and r = ( v c / 3 ) 1 / 2
are appropriate values f o r t h e
r a d i u s o f t h e e d d i e s formed by t h e Loop C u r r e n t .
However, w i t h o u t f u r t h e r
a n a l y s i s i t i s n o t c l e a r why t h e eddies f r o m t h e Loop C u r r e n t s e l e c t t h i s s c a l e . McWilliams and F l i e r 1 (1979) have s t u d i e d p e r s i s t e n t i s o l a t e d e d d i e s w i t h RB>>l and n o t e t h a t t y p i c a l l y R B > l f o r G u l f Stream r i n g s . For i n s i g h t i n t o t h e s c a l e s e l e c t i o n by t h e Loop C u r r e n t e d d i e s , we t u r n t o t h e CAV t r a j e c t o r y a n a l y s i s and p r e s e n t a d i s c u s s i o n s i m i l a r t o HT.
Inte-
g r a t i o n o f ( 4 ) assuming v c = c o n s t a n t a l o n g a s t r e a m l i n e a t t h e c o r e o f t h e current yields cos0 = cos0,
+ - yR
2
-y/ro
2VC
This neglects the p o i n t t h a t vc # constant along a streamline, v a r i a t i o n s i n radius o f curvature.
i f there are
The n o r t h - s o u t h d i a m e t e r o f an eddy between
259 speed maxima can be e s t i m a t e d by s e t t i n g Oo=n a t t h e southernmost e x t e n t ( t h e o r i g i n ) and O=O a t t h e n o r t h e r n m o s t e x t e n t .
Then f o r
ro=m,
( 9 ) becomes
where d i s t h e d e s i r e d d i a m e t e r , a n o r t h - s o u t h "dimension" f o r " s t a t i o n a r y p l a n e t a r y e d d i e s " n o t e d b y Rossby (1940, p. 82).
T h i s im{lies
t h a t RB=vc/(Br2)=1
f o r t h e Loop C u r r e n t e d d i e s . The n o r t h e r n m o s t p e n e t r a t i o n of t h e c o r e o f t h e c u r r e n t , b, from t h e l a t i t u d e o f 0, can be e s t i m a t e d f r o m ( 9 ) b y s e t t i n g 0=0 a t t h e n o r t h e r n m o s t e x t e n t . This y i e l d s
For ro=m, (11) reduces t o b = d sin+@, Thus, w i t h ro=m t h e maximum a m p l i t u d e f o r a CAV t r a j e c t o r y o c c u r s when 0, T h i s i s what (10) r e a l l y r e p r e s e n t s , s i n c e i n t h i s case t h e CAV t r a j e c t o r y loops back on i t s e l f n o r t h w e s t o f t h e o r i g i n ( s e e F i g . 6 ) .
F o r 00=1300 t h e CAV t r a j e c -
t o r y l o o p s back on i t s e l f a t t h e o r i g i n i n a f i g u r e 8 (Fig. 6d) and s i n $ O o ~ . 9 . We m i g h t a n t i c i p a t e t h a t t h e h o r i z o n t a l s h e a r i n s t a b i l i t y would o c c u r when t h e f i r s t i n f l e c t i o n p o i n t o f t h e c u r r e n t a f t e r i n f l o w r o t a t e s counterclockwise t o
-
I n t h e n u m e r i c a l s o l u t i o n s where t h e f l o w i s n o t steady, p o t e n t i a l
130'.
v o r t i c i t y i s n o t p e r f e c t l y conserved, and o t h e r c o n d i t i o n s o f t h e CAV a n a l y s i s a r e n o t p e r f e c t l y met, we f i n d t h a t eddy s e p a r a t i o n occurs when t h i s a n g l e i s somewhat > 130° (see F i g . 4). I n t h i s case a CAV t r a j e c t o r y w o u l d l o o p back on i t s e l f northwest o f t h e f i r s t i n f l e c t i o n p o i n t a f t e r i n f l o w .
However, a c o l i s
c o n f i g u r e d such t h a t eddy s e p a r a t i o n a c t u a l l y occurs s o u t h e a s t o f t h i s i n f l e c t i o n From t h e s t a n d p o i n t o f e s t i m a t i n g t h e a m p l i t u d e o f t h e CAV t r a j e c t o r y
point.
( w i t h ro=m) and t h u s t h e eddy d i a m e t e r , t h e v a l u e o f 0, when t h e eddy separates f r o m t h e Loop C u r r e n t i s n o t c r i t i c a l , s i n c e sin40,
v a r i e s o n l y 10% f r o m Oo=13O0
t o Oo=a. 5.6
Tests of some dynarnical hypotheses
T e s t s o f some hypotheses c o n c e r n i n g t h e dynamical b e h a v i o r of t h e Loop C u r r e n t a r e summarized i n T a b l e 2. I m m e d i a t e l y a p p a r e n t i s t h e p e r v a s i v e r o l e of d i f f e r e n t i a l r o t a t i o n B. The r e s u l t s a r e based on 35 reduced g r a v i t y e x p e r i ments ( 3 4 f o r LB1 and L n d f r o m T a b l e 2 of HT, t h e same ones t h e y used i n s i m i 1a r h y p o t h e s i s t e s t i n g .
260
TABLE 2 Tests o f some dynami c a l hypotheses f o r t h e Loop C u r r e n t e d d y system.
% bias
1.
Standard reduced g r a v i t y case numerical theoretical
Eddy r a d i u s 6
2.
correlation
87
186 km
131 km
D i s t a n c e f r o m t h e s o u t h e r n boundary t o t h e l a t i t u d e o f westward b e n d i n g b y t h e Loop C u r r e n t .
L~~ = ( V c / ~ ) ' "
3.
= r
-7
.75
201 km
-1
.77
201 km
186 km 191 km
Maximum n o r t h w a r d p e n e t r a t i o n o f t h e Loop C u r r e n t . Lnp = L B I + b = 3r
-2
4
.99 -89
4. Westward p r o p a g a t i o n speed o f t h e e d d i e s . 2 2 40 .99 cir = BX = Bg'hl/f c
=
B/(k2+L2+A-2)
574 km 574 km
560 km 573 km
3.21 cm/s
4.57 cm/s
-2
.97
3.21 cm/s
3.49 cm/s
-
.95 .96
327 days 327 days
359 days 338 days
5. Eddy shedding p e r i o d . p e = A,
?-
+ Alr(l+cosOI) '/ce
The % b i a s and t h e l i n e a r c o r r e l a t i o n a r e s t a t i s t i c s f o r t h e t h e o r e t i c a l p r e d i c t i o n v s . t h e v a l u e s observed i n t h e reduced g r a v i t y n u m e r i c a l model. They a r e based on 34 t o 35 n u m e r i c a l experiments f r o m Table 2 o f HT, the same ones t h e y used i n t h e i r h y p o t h e s i s t e s t i n g f o r s i m i l a r q u a n t i t i e s . The % b i a s 5 ((mo-mp)/mo) where mo and mp a r e t h e means o f t h e observed and p r e d i c t e d v a l u e s , r e s p e c t i v e l y . The two r i g h t m o s t columns p r e s e n t t h e r e s u l t s observed and p r e d i c t e d f o r t h e s t a n d a r d reduced g r a v i t y e x p e r i m e n t which uses t h e p e r t i n e n t parameters f r o m T a b l e 1. R e s u l t s f r o m two t e s t s a r e p r e s e n t e d f o r LBI, Lnp and Pe. On t h e upper l i n e v a l u e s of r and Ce observed i n t h e n u m e r i c a l model, were used i n t h e p r e d i c t o r . On t h e l o w e r l i n e t h e t h e o r e t i c a l v a l u e s were used f o r r and ce ( i . e . cr f o r c e ) . I n e s t i m a t i n g r, L B I , and Lnp t h e maximum speed a t i n f l o w was used f o r vc. O n e - h a l f t h e n o r t h - s o u t h d i a m e t e r between speed maxima was used f o r t h e eddy r a d i u s from t h e reduced g r a v i t y n u m e r i c a l model.
The d i s t a n c e from t h e s o u t h e r n
boundary t o t h e s o u t h e r n end o f t h e eddy d i a m e t e r was used f o r LBI
and f r o m t h e
s o u t h e r n boundary t o t h e n o r t h e r n end o f t h e d i a m e t e r f o r L These were nP' measured as t h e eddy c e n t e r passed a l o n g i t u d e 110 km w e s t o f t h e w e s t e r n boundary o f t h e i n f l o w p o r t .
T h i s was a l s o c l o s e t o t h e i n f l e c t i o n p o i n t w h i c h
261 e x h i b i t e d a l a r g e a n g l e a t t h i s t i m e (see F i g s . 4 & 7 ) . e s t i m a t e o f b was s i m p l i f i e d b y s e t t i n g O0=v and
rO=m.
Thus, t h e t h e o r e t i c a l This y elds b=2r.
The agreement between t h e t h e o r e t i c a l e s t i m a t e s o f r, LBI v a l u e s c a l c u l a t e d f r o m t h e n u m e r i c a l model i s remarkably good. t h e agreement f o r r was w i t h i n 5%.
and Lp and t h e I n most cases
However, a t l o w Reynolds numbers and low
l a t i t u d e s , (10) o v e r e s t i m a t e d t h e model v a l u e by > lo%,
I n t h e experiments w i t h
low Reynolds numbers downstream a t t e n u a t i o n o f t h e c u r r e n t appears t o e x p l a i n this.
A t l o w l a t i t u d e s t h e assumption o f i s o s t a t i c a d j u s t m e n t w i t h r e s p e c t t o
CAV t r a j e c t o r i e s i s n o t as good due t o an i n c r e a s e d westward p r o p a g a t i o n speed. A l s o r / h i s l e s s , so t h e Loop and t h e e d d i e s a r e more s u b j e c t t o d i s p e r s i o n . v a l u e s o f r f r o m t h e n u m e r i c a l model were used f o r nP’ t h e upper l i n e and t h e o r e t i c a l v a l u e s f o r t h e l o w e r l i n e . I n e s t i m a t i n g LBI
and L
I n e s t i m a t i n g A , he f r o m T a b l e 2 of HT was used f o r hl and t h e v a l u e of f a t t h e l a t i t u d e o f t h e eddy c e n t e r was used.
The c o r r e l a t i o n between cir
and
t h e westward p r o p a g a t i o n speed o f shed e d d i e s i s e x t r e m e l y h i g h , b u t t h e t h e o r e t i c a l speed i s 40% g r e a t e r t h a n observed i n t h e reduced g r a v i t y n u m e r i c a l model.
When t h e d i s p e r s i v e c o n t r i b u t i o n i s i n c l u d e d , t h e mean Rossby wave
speed and t h e mean observed westward p r o p a g a t i o n speed d i f f e r by 2%. The 2 2 v a l u e o f k +L was e s t i m a t e d b y assuming c i r c u l a r e d d i e s and u s i n g t h e t h e o r e t i c a l values f o r r. I n Table 2 a r e g r e s s i o n e q u a t i o n i s used t o t e s t t h e h y p o t h e s i s t h a t t h e eddy shedding p e r i o d i s a m u l t i p l e o f t h e t i m e r e q u i r e d f o r an eddy t o move one eddy r a d i u s westward. current, OI.
The m u l t i p l e depends on t h e a n g l e o f i n f l o w f o r t h e
The upper l i n e p r e s e n t s t h e r e s u l t s when v a l u e s measured f r o m t h e
n u m e r i c a l model a r e used f o r r and c e ( t h e westward p r o p a g a t i o n speed).
On
t h e l o w e r l i n e t h e o r e t i c a l v a l u e s ( c r and ce and (10) f o r r ) a r e used.
The
r e g r e s s i o n c o e f f i c i e n t s a r e A0=45.1 days and A1=4.67 f o r t h e upper l i n e and Ao=-.2
days and A1=5.34 f o r t h e l o w e r l i n e .
The r e g r e s s i o n c o e f f i c i e n t , 4A1,
i s a k i n d o f i n v e r s e S t r o u h a l number ( n o n d i m n s i o n a l p e r i o d ) i f we t a k e t h e eddy d i a m e t e r , d, as t h e a p p r o p r i a t e diameter, and t h e westward p r o p a g a t i o n speed o f t h e e d d i e s ( r a t h e r t h a n t h e i n j e c t i o n v e l o c i t y ) as t h e a p p r o p r i a t e velocity.
The S t r o u h a l numbers (S=2/A1) i m p l i e d b y t h e two r e g r e s s i o n r e s u l t s
a r e .43 f o r t h e upper l i n e and .37 f o r t h e l o w e r l i n e .
I f d was t h e h a l f -
wavelength f o r a c o n t i n u o u s w a v e t r a i n , t h e n t h e S t r o u h a l number would be S=.5. The eddy shedding p e r i o d a l s o e x h i b i t s a weak dependence on t h e eddy v i s c o s i t y A, p r i m a r i l y because t h i s a f f e c t s t h e amount o f e n t r a i n m e n t o r d e t r a i n m e n t downstream.
The r e s u l t i s an eddy-shedding p e r i o d w h i c h i n c r e a s e s
w i t h i n c r e a s i n g Reynolds number,
Re=vc.L/A where
vci
i s t h e maximum v e l o c i t y
a t i n f l o w and L i s h a l f t h e i n f l o w ( s o u t h e r n ) p o r t w i d t h .
A t h i g h Reynolds
numbers, secondary c i r c u l a t i o n s o f t h e Loop-eddy system become s i g n i f i c a n t and i n t r o d u c e some i r r e g u l a r i t y i n t o t h e eddy shedding p e r i o d .
262
k! 6.1
REGIMES FOR THE LOOP CURRENT I N THE REDUCED GRAVITY MODEL The eddy-shedding regime (E) The p r e c e d i n g s e c t i o n examined some o f t h e dynamics o f t h e eddy shedding
by t h e Loop C u r r e n t and demonstrated t h e u s e f u l n e s s o f CAV t r a j e c t o r y a n a l y s i s I t a l s o demonstrated t h e i m p o r t a n t
and Rossby waves i n e x p l a i n i n g t h e b e h a v i o r . role o f differential rotation
( B ) i n most aspects o f t h e eddy-shedding dynamics.
We w i l l c a l 1 t h e eddy-shedding regime t h e E regime.
6.2
The s t e a d y westward s p r e a d i n g regime ( W ) T h i s s e c t i o n i n v e s t i g a t e s t h e e x i s t e n c e o f o t h e r f l o w regimes i n t h e
n e i g h b o r i n g parameter space.
One such regime was f o u n d by r e d u c i n g t h e Reynolds
number, Re = vCL/A, where L i s t h e h a l f - w i d t h o f t h e p o r t . damp
This acts both t o
p h y s i c a l i n s t a b i l i t i e s i n t h e c u r r e n t and t o decrease p o t e n t i a l v o r t i c i t y
c o n s e r v a t i o n , t h u s r e d u c i n g t h e tendency o f t h e c u r r e n t t o l o o p back on i t s e l f . The r e s u l t i s a s t e a d y s o l u t i o n w i t h a westward b e n d i n g Loop C u r r e n t as shown i n F i g . 8a.
We w i l l c a l l t h i s t h e W
regime.
F i g . 8a was o b t a i n e d by i n c r e a s i n g
t h e eddy v i s c o s i t y ( A ) f r o m 107 t o 3x10 7 cm2 /s i n t h e s t a n d a r d reduced g r a v i t y model.
Steady l i n e a r v i s c o u s s o l u t i o n s (where R v ~ = A V ~
s o l u t i o n s b e l o n g t o t h e W regime.
As mentioned i n S e c t i o n 5, t h e l a t i t u d e of westward bending a f t e r i n f l o w i s d e t e r m i n e d by t h e l a r g e r o f L E I and LBF. AS n o t e d by HT, t h e mean o f t h e s t a n d a r d reduced g r a v i t y e x p e r i m e n t o v e r an eddy T h i s i m p l i e s t h a t i n t h e mean t h e eddies d r i v e
c y c l e i s v e r y s i m i l a r t o F i g . 8a.
a n o r t h w a r d - f l owi ng w e s t e r n boundary c u r r e n t . Between t h e E and W regimes t h e r e i s a t r a n s i t i o n regime ( T ) w i t h eddies superimposed on a westward bending Loop C u r r e n t .
T h i s i s i l l u s t r a t e d i n F i g . 8b 7 2 Experiu s i n g t h e s t a n d a r d reduced g r a v i t y model e x c e p t t h a t A=2.5 x 10 cm /s.
ments t h a t e x h i b i t e d b o t h eddy shedding and an unbroken, westward bending z e r o c o n t o u r ( l i k e F i g . 8 b ) were a s s i g n e d t o t h e 6.3
T
regime.
Steady s o u r c e - s i n k regime ( N )
A t h i r d m a j o r regime we c a l l t h e N regime i s f o u n d by i n c r e a s i n g t h e b e t a Rossby number, RB=vC/(BL:),
where
o f t h e i n f l o w and o u t f l o w p o r t s .
L i s h a l f t h e distance separating t h e centers
P The N regime occurs when RB,>~.
l o w Reynolds numbers t h e t r a n s i t i o n between t h e
A t sufficiently
N and W regimes i s determined
3
by t h e b e t a Ekman number, EB=A/(BLp ) , as d i s c u s s e d i n t h e n e x t s u b s e c t i o n .
In
e i t h e r case t h e N regime i s c h a r a c t e r i z e d b y a steady s o u r c e - s i n k f l o w w i t h no westward bending by t h e Loop C u r r e n t .
I t i s i l l u s t r a t e d i n F i g . 9 b y two v a r i -
a t i o n s on t h e s t a n d a r d reduced g r a v i t y experiment.
I n F i g . 9a R=O and R B ' ~ .
Note t h a t p 0 i s e s s e n t i a l f o r t h e westward b e n d i n g o f t h e Loop C u r r e n t and t h e eddy shedding shown i n F i g s . 4 and 7. some i n s t a b i l i t y t o o c c u r i n t h e
W i t h Re s u f f i c i e n t l y h i g h , we would e x p e c t
s o u r c e - s i n k c u r r e n t , b u t n o t t h e quasi-annual
eddy shedding e x h i b i t e d by t h e Loo:,
Current.
263
0
IKM)
0
IKMl
1600
1600
Fig. 8. I l l u s t r a t i o n o f ( a ) steauy reaine W an3 ( b j time-dependent regime T. The standard parameters f o r t h e reduced g r a v i t y model were used except t h a t i n ( a ) A = 3 x l o 7 cm2/sec and i n ( b ) A = 2.5 x l o 7 cm2/s. The contour interval i s 20 rn. In regime W the Loop Current bends weshard and i s steady. I n regimr! T eddy shedding i s superimposed on a westward bending loop instead o f being d i s c r e t e as i n Fig. ? a , d.
264
G
Fig. 9.
lKHl
1600
lKMl
I600
I l l u s t r a t i o n of t h e steady regime N f o r the standard reduced gravity
experiment except t h a t B = 0 and ( b ) a s e c t i o n of land was added t o approximate t h e west Florida s h e l f . Steady mixed regime M i s shown i n ( c ) with parameters chosen t o approximate those of Mellor and Blumberg (1981), including Re = 10.8 and R B = 1.19.
266
I n a second e x p e r i m e n t t h e p o r t s e p a r a t i o n was reduced by i n s e r t i n g a l a n d In
mass w h i c h approximates t h e l o c a t i o n o f t h e West F l o r i d a S h e l f ( F i g . 9b). t h i s case Lp was measured u s i n g a p o r t c e n t e r e d 75 km s o u t h o f t h e w e s t e r n
thus t h e beta From S e c t i o n 5 r=LBI=(vc/B)’, 2 2 Rossby number can a l s o be expressed as R g = ( r / L p ) o r RB=(LBI/Lp) . Since the N regime occurs f o r R ~ 2 2 , t h i s i m p l i e s a c r i t i c a l p o r t s e p p r a t i o n 2Lpc= @r = @LBI
boundary o f t h e i n s e r t e d l a n d mass.
From t h e d e f i n i t i o n o f RB, b o t h B and Lp p l a y a s i m i l a r r o l e i n d e t e r m i n i n g t h e N regime.
Otherwise, t h e i r r o l e s a r e n o t s i m i l a r .
As l o n g as RB i s s m a l l
enough f o r eddy shedding t o o c c u r , t h e E regime i s q u i t e i n s e n s i t i v e t o L
but
P’
most aspects o f t h e dynamics a r e v e r y s e n s i t i v e t o 6. The N regime o c c u r s when t h e Loop C u r r e n t reaches a s t e a d y s t a t e before From (12) and F i g . 6d a
p e n e t r a t i n g f a r enough i n t o t h e G u l f t o bend,,westward.
CAV t r a j e c t o r y w i t h rO=- can p e n e t r a t e i n t o t h e G u l f w i t h no westward bending a d i s t a n c e b = $r
= @LaI
( t h e same as t h e c r i t i c a l p o r t s e p a r a t i o n ) .
Using
t h i s as an e s t i m a t e o f t h e maximum p o s s i b l e Loop C u r r e n t p e n e t r a t i o n i n t h e N regime i s c o n s i s t e n t w i t h o u r p r e s e n t n u m e r i c a l r e s u l t s (see HT f o r f u r t h e r discussion). The t r a n s i t i o n between regimes N and E i s q u i t e a b r u p t and a t r a n s i t i o n regime has n o t been found i n any o f o u r n u m e r i c a l experiments. between regimes N and W i s broader.
The t r a n s i t i o n
I n t h i s mixed regime (M) t h e westward
s p r e a d i n g o f t h e Loop C u r r e n t i s s i g n i f i c a n t l y l e s s t h a n i t would be i f t h e p o r t s e p a r a t i o n were i n f i n i t e .
The n u m e r i c a l s i m u l a t i o n o f t h e Loop C u r r e n t by
Blumberg and M e l l o r (1981) b e l o n g s t o t h i s M regime.
F i g . 9c shows a reduced
g r a v i t y a n a l o g o f t h a t e x p e r i m e n t u s i n g o u r e s t i m a t e s o f a p p r o p r i a t e parameters, i n c l u d i n g Re=10.8 and R ~ = 1 . 1 9 (See Appendix B f o r o t h e r parameters used). C o n s i d e r i n g o u r n e g l e c t o f t h e 20’
counterclockwise r o t a t i o n o f t h e basin, our
p a t t e r n f o r t h e Loop C u r r e n t i s r e m a r k a b l y s i m i l a r t o t h a t f r o m t h e much more c o m p l i c a t e d and expensive model o f Blumberg and M e l l o r (1981).
Experiments were
a s s i g n e d t o t h e M regime i f t h e c e n t r a l c o n t o u r on i n f l o w e x h i b i t e d any westward bending, b u t t h e a m p l i t u d e o f t h e Loop PA was < 30% o f t h e maximum a d i s t a n c e L ( v C i / B ) * w e s t o f t h e c e n t e r o f t h e i n f l o w , where v c i i s t h e maximum v e l o c i t y a t inflow. 6.4
S t a b i l i t y regime diagram Three nondimensional parameters from t h e v o r t i c i t y e q u a t i o n (Eq. ( 8 ) ) p l a y
an i m p o r t a n t r o l e i n d e t e r m i n i n g t h e s t a b i l i t y regimes f o r t h e Loop C u r r e n t i n t h e reduced g r a v i t y and f l a t - b o t t o m b a r o t r o p i c models. They a r e t h e Reynolds number (Re), t h e b e t a Rossby number (RB), and t h e b e t a Ekman number (EB). two o f t h e s e a r e independent.
Only
P r o v i d e d t h e same s c a l e s a r e used, EB=RB/Re.
F i g . 10 shows t h e parameter space occupied b y t h e v a r i o u s regimes on a s t a b i l i t y diagram o f Re vs. RB.
Eddy shedding occurs f o r R&
and Re125 f o r t h e reduced
-..
;$zN zuu E-.... .... ........ .... .... 150
100
50
1
i
E
E EE
E
E E E
E
EE
.... .... .... .... .... .... .... ........ .... .... .... .... .... .... ........ .... .... ....... .... ... ....... ... .... ... .... ... .... ... E ,::. ,.... ;:;: N .... .... .... ........ .... ..... .... ..... .... ....
20
W
N
2
F i g . 10.
Regime diagram f o r t h r e e s t a b i l i t y regimes and t r a n s i t i o n regimes between them f o r a reduced g r a v i t y model of t h e
Gulf of Mexico.
The axes a r e t h e Reynolds number (Re) and t h e b e t a Rossby number (RBI.
( F i g s . 5c and 7a, d ) , ( W ) steady westward s p r e a d i n g ( F i g . 8 a ) ,
E and W u i t h eddy shedding superimposed on a mean
1000
The regimes a r e ( E ) eddy shedding
(N) steady s o u r c e - s i n k ( F i g . 9a, b ) , ( T ) t r a n s i t i o n between
( F i g . 8b) and (M) t r a n s i t i o n between steady
regimes
and
(Fig.9c)
N Q, Q,
261
g r a v i t y model, Re240 f o r t h e f l a t - b o t t o m b a r o t r o p i c model ( n o t shown). A p p a r e n t l y , t h e d i s p e r s i v e n a t u r e o f Rossby waves i n t h e b a r o t r o p i c model i s a c a t a l y s t which l e a d s t o a h i g h e r c r i t i c a l Reynolds number (Rec). The t r a n s f e r o f energy t o t h e l o w e r l a y e r i n t h e t w o - l a y e r models seems t o have a s i m i l a r e f f e c t on Re,. A t l o w Reynolds number t h e t r a n s i t i o n between regimes N and W depends upon EB=RBL/(ReLp).
The c o r r e c t i o n f a c t o r L/Lp i s r e q u i r e d because we have n o t used
Lp i n o u r d e f i n i t i o n o f Re.
T h i s t r a n s i t i o n i s c l e a r l y d e f i n e d on o u r s t a b i l i t y
d i a g r a m o n l y i f L/Lp i s f i x e d .
From S e c t i o n 5.5 RB and EB can be expressed i n
terms o f t h e l a t i t u d e o f westward bending b y t h e Loop C u r r e n t , i . e . RB=(LBI/Lp) and EB=(LBF/Lp)3.
2
Whether RB o r EB determines t h e t r a n s i t i o n t o t h e N regime
depends upon t h e r e l a t i v e i m p o r t a n c e o f LBF, t h e f r i c t i o n a l l e n g t h s c a l e , and LBI,
t h e i n e r t i a l l e n g t h s c a l e , i n d e t e r m i n i d j t h e l a t i t u d e o f westward bending
by t h e Loop C u r r e n t .
From t h e regime diagram, t h e t r a n s i t i o n between t h e s e two
c r i t e r i a o c c u r s when 2.5 LBF=LBI/
fl.
O t h e r parameters n o t accounted f o r h e r e such as i n f l o w a n g l e , b a s i n geometry, and b a s i n o r i e n t a t i o n may a l s o have some i n f l u e n c e on t h e regime selection.
A d d i t i o n a l i n f l u e n c e s i n t h e t w o - a c t i v e - l a y e r model a r e d i s c u s s e d
i n t h e n e x t two s e c t i o n s .
7.
PREVENTION OF EDDY SHEDDING BY TOPOGRAPHY AND DEEP-WATER INFLOW THROUGH
THE YUCATAN STRAITS
I n t h i s s e c t i o n t h e t w o - l a y e r model i s used t o demonstrate a d r a m a t i c e f f e c t o f topography on t h e eddy-shedding b y t h e Loop C u r r e n t when t h e r e i s s u f f i c i e n t deep-water i n f l o w t h r o u g h t h e Yucatan S t r a i t s . F i g . l l a shows t h e domain-averaged upper l a y e r ( u p p e r c u r v e ) and l o w e r l a y e r k i n e t i c energy vs. t i m e f o r a t w o - l a y e r e x p e r i m e n t t h e same as shown i n Fig. 4, e x c e p t t h a t d u r i n g t h e f i r s t s i x y e a r s o f model i n t e g r a t i o n t h e l o w e r l a y e r i n f l o w was z e r o . i n c l u d e s t h e topography o f F i g . 3.
This
A t t h e beginning o f year 7 t h e lower l a y e r i n f l o w While t h e lower l a y e r
was i n c r e a s e d t o 10 Sv w i t h a t i m e c o n s t a n t o f 30 days.
i n f l o w was z e r o , eddy shedding o c c u r r e d i n a manner s i m i l a r t o t h a t shown i n F i g . 4.
The s i g n a t u r e o f t h e eddy shedding c y c l e i s d e p i c t e d i n t h e upper l a y e r
energy c u r v e o f F i g . l l a .
When t h e l o w e r l a y e r i n f l o w was i n c r e a s e d , t h e eddy
shedding ceased and t h e s o l u t i o n e v o l v e d t o a s t e a d y s t a t e as shown i n F i g . l l a . T h i s s t e a d y s o l u t i o n i s shown i n F i g . l l b , c i n . t e r m s o f t h e PA ( F i g . l l b ) and t h e l o w e r l a y e r p r e s s u r e , p 2 ( F i g . l l c ) . The P A d e p i c t s a s o u r c e - s i n k f l o w l i k e regime N , w h i l e t h e f l o w i n t h e l o w e r l a y e r f o l l o w s t h e f / h c o n t o u r s o f t h e topography.
HT uses a k i n e m a t i c a n a l y s i s t o i l l u m i n a t e t h e dynamics o f t h i s
phenomenon.
From t h e c o n t i n u i t y e q u a t i o n ( 2 ) , t h e d i v e r g e n c e t e r m h l V
b a l a n c e d b y t h e a d v e c t i v e t e r m wl-Vhl n e a r l y geostrophic,
wl"Jhl
i n a steady s t a t e .
\v1 i s
Since the f l o w i s
= w l g - V h l = \ ~ 2 ~ - V hwhere ~, wig
i s t h e geostrophic
268
lo
8 i
3 t
3
4
5
6
7
8
T I M E I N YEARS
0
LKMl
1600
F i g . 11. Results f o r t h e bottom topography experiment shown i n Fig. 4 except t h a t T1 = 25 Sv and T2 = 0 u n t i l y e a r 6 when T2 increases t o 10 Sv. ( a ) domainaveraged upper l a y e r ( t o p curve) and lower l a y e r k i n e t i c energy, (IC = 1 . 5 ) . ( b ) Nearly steady PA a t day 2887. The contour i n t e r v a l i s 23 m. ( c ) Lower l a y e r pressure normalized by density (p2) a t day 2880. The contour i n t e r v a l i s . 2 5 m 2 /s 2 .
269
v e l o c i t y component i n l a y e r i. The magnitude o f w 2 g * V h l i s g r e a t e s t when r e l a t i v e l y s t r o n g l o w e r l a y e r c u r r e n t s f l o w a t l a r g e angles t o c o n t o u r s o f hl. Comparison of F i g . l l b and l l c shows t h a t t h i s o c c u r s where t h e Loop C u r r e n t i n t e r s e c t s a c u r r e n t f o l l o w i n g t h e f / h c o n t o u r s o f t h e West F l o r i d a S h e l f . t h e l o w e r l a y e r c u r r e n t i s s t r o n g enough f o r t h e a d v e c t i o n t o balance t h e
If
d i v e r g e n c e i n (2) a s s o c i a t e d w i t h t h e approaching Loop, fhen t h e i n t e r f a c e deepening and Loop C u r r e n t p e n e t r a t i o n i n t h i s r e g i o n a r e h a l t e d . Thus, t h e West F l o r i d a S h e l f a l o n g t h e e a s t e r n boundary o f t h e domain (see F i g . 3 ) and l o w e r l a y e r f l o w a c t i n c o n j u n c t i o n t o e f f e c t i v e l y reduce t h e p o r t s e p a r a t i o n by l o c a l l y l i m i t i n g t h e n o r t h w a r d p e n e t r a t i o n o f t h e Loop C u r r e n t . Ift h i s r e s u l t s i n R&2, when we measure 2L as t h e d i s t a n c e between t h e c e n t e r P of t h e i n f l o w p o r t and t h e p o i n t where t h e u w e r and l o w e r l a y e r c u r r e n t s i n t e r -
sect, then t h e upper l a y e r c u r r e n t e x h i b i t s t h e source-sink f l o w c h a r a c t e r i s t i c of t h e N regime d e s c r i b e d i n S e c t i o n 6.
T h i s i s i l l u s t r a t e d by comparing F i g . l l b
w i t h F i g . 9b, t h e reduced g r a v i t y e x p e r i m e n t w i t h a l a n d mass i n t h e l o c a t i o n o f t h e West F l o r i d a S h e l f . I n t h e e x p e r i m e n t shown i n F i g . 11 t h e Loop C u r r e n t had a l r e a d y p e n e t r a t e d f a r i n t o t h e G u l f and shed e d d i e s when t h e l o w e r l a y e r i n f l o w was i n c r e a s e d . When t h i s i n c r e a s e o c c u r r e d , a c u r r e n t f o l l o w i n g t h e , f / h c o n t o u r s developed i n t h e l o w e r l a y e r and t h e a d v e c t i o n t e r m ( wl.Vhl)
began t o exceed t h e d i v e r g e n c e
t e r m i n t h e c o n t i n u i t y e q u a t i o n where t h e Loop C u r r e n t c r o s s e d t h e s h e l f s l o p e , c a u s i n g hl
t o decrease t h e r e .
Thus, t h e Loop C u r r e n t r e t r e a t e d southward u n t i l
an e q u i l i b r i u m o c c u r r e d n e a r t h e s o u t h e r n end o f t h e s h e l f . I n terms o f v o r t i c i t y dynamics, t h e n o r t h w a r d p e n e t r a t i o n o f t h e Loop C u r r e n t i s h a l t e d when t h e i n t e r a c t i o n between t h e topography o f t h e West F l o r i d a S h e l f and t h e p r e s s u r e f i e l d r e s u l t s i n a n e a r balance between t h e p r e s s u r e t o r q u e s and t h e n o n l i n e a r terms i n t h e mass t r a n s p o r t v o r t i c i t y equation.
HT d i s c u s s and document t h i s t o p i c i n more d e t a i l .
The r e s u l t s i n t h i s s e c t i o n suggest t h a t c e r t a i n t i m e v a r i a t i o n s i n t h e deep f l o w t h r o u g h t h e Yucatan S t r a i t s may have a g r e a t e r e f f e c t on t h e Loop C u r r e n t t h a n f l u c t u a t i o n s i n t h e upper ocean c u r r e n t t h r o u g h t h e S t r a i t . e f f e c t s of t h e l a t t e r a r e d i s c u s s e d b y HT b u t n o t i n t h i s paper.
The
270
8.
OF TOPOGRAPHY
MROTROPIC VS. BAROCLINIC INSTABILITY AND THE IMPORTANT ROLE
In
S e c t i o n 6 examined s t a b i l i t y regimes f o r t h e reduced g r a v i t y model.
S e c t i o n 7 we s t u d i e d a steady regime f o r t h e two- a y e r model w h i c h r e s u l t s f r o m a p a r t i c u l a r c o m b i n a t i o n o f topography and deep f ow f o l l o w i n g f / h c o n t o u r s . I n t n i s s e c t i o n we w i l l i n v e s t i g a t e a d d i t i o n a l regimes of t h e two a c t i v e l a y e r model, c o n f i n i n g o u r s e l v e s t o unsteady regimes w i t h eddies.
I n p a r t f c u l a r we
w i l l s e a r c h f o r cases o f b a r o t r o p i c , b a r o c l i n i c , and m i x e d i n s t a b i l i t y . The reduced g r a v i t y and b a r o t r o p i c models can e x h i b i t b a r o t r o p i c , b u t n o t baroclinic instability.
The reduced g r a v i t y model has demonstrated an eddy
shedding regime w i t h a h o r i z o n t a l shear i n s t a b i l i t y o f t h e f i r s t i n t e r n a l mode ( a " b a r o t r o p i c " i n s t a b i l i t y ) w h i c h produces a remarkable s i m u l a t i o n o f observed f e a t u r e s o f t h e Loop C u r r e n t
-
eddy shedding system.
We i n o w f r o m S e c t i o n 4
t h a t i n some cases t h e two a c t i v e l a y e r model e x h i b i t s s i m i l a r r e s u l t s w i t h I n t h i s s e c t i o n we w i l l i n v e s t i g a t e t h e p o t e n t i a l importance
s i m i l a r parameters.
o f b a r o c l i n i c i n s t a b i l i t y and t h e r o l e o f topography i n d e t e r m i n i n g i t s importance.
8.1
Eddy-mean e n e r g e t i c s We b e g i n t h i s i n v e s t i g a t i o n by s u r v e y i n g t h e eddy-mean e n e r g e t i c s f o r t h e
seven n u m e r i c a l e x p e r i m e n t s l i s t e d i n Table 3.
We t h e n i l l u s t r a t e some charac-
t e r i s t i c f e a t u r e s o f t h e d i f f e r e n t regimes u s i n g s y n o p t i c maps o f upper and l o w e r l a y e r p r e s s u r e ( p i and p 2 ) and curves o f domain-averaged'energy shows t h e eddy-mean e n e r g e t i c s i n terms o f energy box diagrams. t h e energy t r a n s f e r s .
F i g . 12
vs. t i m e .
F i g . 12a l a b e l s
See Appendix A f o r symbol d e f i n i t i o n s and Appendix C f o r
t h e energy t r a n s f e r i n t e g r a l s .
A l l o f t h e model domain was used i n c a l c u l a t i n g
t h e e n e r g e t i c s e x c e p t t h e p a r t s w i t h i n 100 km o f t h e e a s t e r n boundary and 37.5 km o f t h e s o u t h e r n boundary.
Thus, t h e e a s t e r n and s o u t h e r n b o u n d a r i e s o f t h e
e n e r g e t i c s c a l c u l a t i o n s a r e open.
K i n e t i c energy and p r e s s u r e work f l u x e s
t h r o u g h t h e s e open b o u n d a r i e s a r e r e p r e s e n t e d by arrows a t t h e t o p ( b o t t o m ) o f t h e K1 (K2) boxes.
I n a l l cases most o f t h e energy f l o w s i n t o
El.
I n some
cases t h e r e i s s i g n i f i c a n t e f f l u x f r o m K i , b u t always must less than t h e transfer.
Fl+Ki
The arrows p o i n t i n g o u t w a r d f r o m t h e s i d e s r e p r e s e n t d i s s i p a t i o n o f
a p a r t i c u l a r t y p e o f energy due t o L a p l a c i a n h o r i z o n t a l f r i c t i o n .
Arrows between
t h e boxes r e p r e s e n t c o n v e r s i o n s o f energy f r o m one t y p e t o a n o t h e r as i n d i c a t e d by t h e d i r e c t i o n o f t h e arrow. F i g . 12b shows t h e eddy-mean e n e r g e t i c s f o r Experiment 1 on T a b l e 3, a twol a y e r f l a t - b o t t o m e x p e r i m e n t u s i n g t h e s t a n d a r d parameters g i v e n i n T a b l e 1. The
';1+Ki
energy c o n v e r s i o n i s c h a r a c t e r i s t i c o f a b a r o t r o p i c i n s t a b i l i t y .
The
p o t e n t i a l energy t r a n s f e r i s a c t u a l l y r e v e r s e d w i t h eddy p o t e n t i a l energy ( P ' ) f e e d i n g t h e mean. A n g l i n g t h e i n f l o w 27'
west o f normal i n t h e s t a n d a r d t w o - l a y e r f l a t - b o t t o m
model (Experiment 2 ) produced a d r a m a t i c change i n t h e eddy-mean e n e r g e t i c s which
271 TABLE 3 Model experiments d i s c u s s e d i n S e c t i o n 8 Exp f!
Differences from standard two-layer f l a t - b o t t o m e x p e r i m e n t i n Table 1
F i g u r e s i n HT f r o m t h e s e experiments (HT F i g . # )
1
None
F i g s . 5b, l l b , 14a F i g s . 12, 13a, 14d
2 3
Reduced g r a v i ty , Yucatan and F l o r i d a S t r a i t s added t o model, domain
4
A
6 2 3 x 10 cm / s ,
Sv2 = 0
5
5 2 A = 3 x 10 cm /s, F i g . 3 topography
Sv2 = 0
6
Svl
= 25, Sv2 = 0
7
Svl
= 25, Sv2 = 0,
=
F i g s . 20a, 21a, HT T a b l e 2 case RG32 Experiment i n HT F i g s . 10, l l a , 14c e x h i b i t s s i m i l a r behavior
F i g s . 24b, 25b
F i g . 3 topography
F i g s . 24c, 25c
Sv, i s t h e i n f l o w i n l a y e r i i n 10
6
3 m /s o r Sv.
(The l o w e r l a y e r i n f l o w was a l s o reduced t o zero, b u t
i s shown i n F i g . 12c.
o t h e r experiments show t h i s has a r e l a t i v e l y m i n o r r o l e i n a l t e r i n g t h e e n e r g e t i c s i n t h i s case).
F i g . 12c i l l u s t r a t e s a c l a s s i c s i g n a t u r e of b a r o c l i n i c i n s t a b i l i t y
i n t h e eddy-mean e n e r g e t i c s w i t h
F+Pi d o m i n a t i n g t h e mean t o eddy energy
t r a n s f e r and f e e d i n g t h e upper and l o w e r l a y e r s a l m o s t e q u a l l y . a r e v e r s e cascade i n t h e k i n e t i c energy
(Ki+Kl)
There i s even
w i t h eddies f e e d i n g t h e mean
flow. The eddy-mean e n e r g e t i c s f o r t h e reduced g r a v i t y model (Experiment 3 and F i g . 12d) i l l u s t r a t e s a p u r e b a r o t r o p i c i n s t a b i l i t y , s i n c e t h i s model excludes baroclinic instability. is
K+Ki.
I n t h i s case t h e dominant mean t o eddy energy t r a n s f e r
Even though t h i s i s a p u r e b a r o t r o p i c i n s t a b i l i t y , t h e r e i s a n e t
t r a n s f e r from %PI.
Thus, t h e e x i s t e n c e o f such a t r a n s f e r does n o t n e c e s s a r i l y
i m p l y any c o n t r i b u t i o n f r c m b a r o c l i n i c i n s t a b i l i t y .
21 2
qySo iyk 15.8
T
T
4.2
.. 5.0
.6
H 6.8
11.6
19.2
F i j . 12.
9.6
20.9
4.4
I 28.2
*
5.7
It.
I
1-91
2-l
1.3
1.7
1.5
A
Eddy-mean tiilerqetics for t h e experiments l i s t e d i n Table 3 :
( a ) labels
f o r t h e energy pathways and energy r e s e r v o i r s , ( b ) e n e r g e t i c s f o r Experiment 1, standard flat-bottom case, ( c ) Experiment 2 , f l a t bottom with non-normal inflow,
( d ) Experiment 3 , reduced g r a v i t y , ( e ) Experiment 4 , f l a t bottom with low
273
.3
I
15.4
+-J
-2
1.1
.2 0.0
0.0
(f) 120.3
32.01 31.4
2.74
+.I
11.9 1.5
.l
I
12.5
12.5
r
I
I
3.5
v i s c o s i t y , ( f ) Experiment 5 , same as t h e preceding b u t w i t h topography, ( g ) ExJeriment 6 , f l a t bottom, ( h ) Experiment 7 , same as preceding b u t with topography. The energy r e s e r v o i r s a r e i n u n i t s o f lOI5 j o u l e s and t h e energy t r a n s f e r s a r e i n units of lo8 j o u l e s / s .
274
F i g . 12e i s p a r t i c u l a r l y i n t e r e s t i n g because i t i l l u s t r a t e s a mixed i n s t a b i l i t y and because i t demonstrates t h e v a l u e o f s e p a r a t i n g t h e k i n e t i c energy i n t o u p p e r and l o w e r l a y e r components.
These r e s u l t s were o b t a i n e d p r i m a r i l y
b y r e d u c i n g t h e eddy v i s c o s i t y i n t h e t w o - l a y e r f l a t - b o t t o m model by a f a c t o r o f t h r e e (Experiment 4 ) .
If K1 and K2 were combined t o produce a 4-box diagram,
t h e r e s u l t s would l o o k much l i k e t h o s e f o r t h e reduced g r a v i t y model and we m i g h t c o n c l u d e t h a t t h i s i s a case o f b a r o t r o p i c i n s t a b i l i t y . 6-box diagram ( F i g . 1 2 e ) i l l u s t r a t e s a s t r i k i n g r e s u l t . energy c o n v e r s i o n
(K,+Ki)
I n contrast, the
Although a b a r o t r o p i c
i s dominant i n t h e u p p e r l a y e r , t h e l o w e r l a y e r eddies
a r e f e d a l m o s t e q u a l l y by t r a n s f e r s f r o m
F+P'
and Ki+P'.
I n v i e w o f t h e reduced
g r a v i t y r e s u l t s , t h i s i s i n s u f f i c i e n t e v i d e n c e f o r an i m p o r t a n t c o n t r i b u t i o n f r o m b a r o c l i n i c i n s t a b i l i t y t o t h e lower l a y e r eddies.
A d d i t i o h l evidence f o r t h i s
w i l l be p r o v i d e d s h o r t l y . F i g s . 12e and 12f compare t h e r e s u l t s f o r Experiments 4 and 5.
The e x p e r i -
ments a r e i d e n t i c a l e x c e p t t h a t Experiment 4 ( F i g . 1 2 e ) has a f l a t b o t t o m and Experiment 5 ( F i g . 1 2 f ) i n c l u d e s t h e i d e a l i z e d G u l f o f Mexico topography shown
i n F i g . 3.
The topography s t r o n g l y suppresses any b a r o c l i n i c i n s t a b i l i t y .
With
t h e topography added, t h e e n e r g y box diagram ( F i g . 1 2 f ) i n d i c a t e s a s t r o n g b a r o topic instability
(Kl+Ki) and a s t r o n g r e v e r s e p o t e n t i a l energy f l u x (P'+p).
F i g s . 129 and 12h a g a i n compare experiments w i t h and w i t h o u t t h e topography
o f F i g . 3 (Experiments 6 and 7 ) .
They d i f f e r f r o m t h e p r e c e d i n g by a t h r e e - f o l d
i n c r e a s e i n t h e eddy v i s c o s i t y and a 25% i n c r e a s e i n t h e upper l a y e r i n f l o w . The e x p e r i m e n t w i t h t h e topography ( F i g . 12h) e x h i b i t s e s s e n t i a l l y t h e same e n e r g y pathways as t h e p r e v i o u s frame w i t h t h e same topography ( F i g . 1 2 f ) . r e v e r s e p o t e n t i a l energy t r a n s f e r (P'+p) i s even s t r o n g e r . eddy energy makes a complete c i r c u i t .
The
Almost 1/3 o f t h e
Although t h i s reverse t r a n s f e r i s c l e a r l y
augmented by t h e topography, i t i s n o t r e s t r i c t e d t o e x p e r i m e n t s w i t h topography (see F i g . 12b).
W i t h o u t t h e b e n e f i t o f t h e e n e r g e t i c s a n a l y s i s , HT c o r r e c t l y
i d e n t i f i e d t h e b a r o c l i n i c a l l y u n s t a b l e case ( F i g . 1 2 c ) and a m i x e d i n s t a b i l i t y case s i m i l a r t o F i g . 12e.
However, t h e y a l s o c o n j e c t u r e d t h a t Experiment 6
( F i g . 1 2 9 ) i s a case o f m i x e d i n s t a b i l i t y . domair: i n t e g r a t e d eddy-mean e n e r g e t i c s .
T h i s i s n o t c o r r o b o r a t e d by t h e Eddies i n b o t h l a y e r s a r e f e d b y energy
215
conversions appropriate f o r a b a r o t r o p i c i n s t a b i l i t y , t h e lower l a y e r f e d i n d i r e c t l y v i a energy t r a n s f e r f r o m t h e upper l a y e r .
I n t h i s case, i n c r e a s i n g
t h e eddy v i s c o s i t y has suppressed t h e c o n t r i b u t i o n f r o m b a r o c l i n i c i n s t a b i l i t y . Experiment 6 ( F i g . 129) d i f f e r s f r o m Experiment 1 ( F i g . 12b) by h a v i n g 25% g r e a t e r i n f l o w i n t h e upper l a y e r and none i n t h e l o w e r l a y e r .
The energy
pathways i n t h e two experiments a r e s i m i l a r , b u t F i g . 129,shows more energy t r a n s f e r t o t h e l o w e r l a y e r and l a c k s t h e r e v e r s e (PI*)
t r a n s f e r o f t h e standard
f l a t - b o t t o m e x p e r i m e n t ( F i g . 12b). The energy t r a n s f e r s i n a l l t h e s e experiments a r e s t r o n g l y inhomogeneous i n space.
Thus, as s t r e s s e d b y H a r r i s o n and Robinson (1978), energy t r a n s f e r s
averaged o v e r t h e model domain may n o t be c h a r a c t e r i s t i c o f any i m p o r t a n t subregion. 8.2
K i n e t i c energy vs. t i m e I n t h e f o l l o w i n g d i s c u s s i o n , we w i l l i l l u s t r a t e f e a t u r e s o f t h e f l o w w h i c h
a r e c h a r a c t e r i s t i c o f t h e t h r e e regimes i d e n t i f i e d i n t h e eddy-mean e n e r g e t i c s w i t h b a r o t r o p i c , b a r o c l i n i c , and m i x e d i n s t a b i l i t i e s .
W e w i l l u t i l i z e the four
experiments w h i c h do t h i s most s i m p l y and c l e a r l y , ( a ) Experiment 1 f o r b a r o t r o p i c i n s t a b i l i t y w i t h a f l a t bottom, ( b ) Experiment 7 f o r b a r o t r o p i c i n s t a b i l i t y w i t h topography,
( c ) Experiment 2 f o r b a r o c l i n i c i n s t a b i l i t y , and ( d ) Experiment 4
f o r mixed i n s t a b i l i t y .
F i g . 13 shows t h e curves o f K1 and K2 vs. t i m e f o r t h e s e
f o u r experiments. F i g . 13a, b r e p r e s e n t s t h e b a r o t r o p i c a l l y u n s t a b l e experiments and c l e a r l y shows a r e l a t i v e l y l o n g p e r i o d f o r t h e eddy shedding c y c l e , 273 days f o r E x p e r i ment 1 ( F i g . 13a) and 250 days f o r Experiment 7 ( F i g . 13b).
F i g . 13c shows a
much f a s t e r 57 day o s c i l l a t i o n f o r t h e b a r o c l i n i c a l l y u n s t a b l e experiment, Experiment 2.
The c o r r e s p o n d i n g reduced g r a v i t y e x p e r i m e n t ( n o t shown), i n
w h i c h b a r o c l i n i c i n s t a b i l i t y i s n o t p e r m i t t e d , has a 284 day p e r i o d .
The p e r i o d
i n F i g . 13c i s v e r y s i m i l a r t o t h a t found by H o l l a n d and L i n (1975) f o r midl a t i t u d e mesoscale e d d i e s i n a t w o - l a y e r model w i t h b a r o c l i n i c i n s t a b i l i t y . They a l s o n o t e d a s i m i l a r maximum i n K 1 n e a r t h e o n s e t o f b a r o c l i n i c i n s t a b i l i t y which i s f o l l o w e d b y a r i s e i n K2.
W e have n o t f o u n d t h i s t y p e o f s i g n a t u r e i n
any o f o u r b a r o t r o p i c a l l y u n s t a b l e experiments.
F i g . 13d shows K1 and K2 v s . .
t i m e f o r Experiment 4, t h e e x p e r i m e n t f o r which t h e eddy-mean e n e r g e t i c s ( F i g . 12e) suggest a mixed i n s t a b i l i t y .
Two p e r i o d s w h i c h a r e n o t h a r m o n i c a l l y r e l a t e d =re
c l e a r l y i n d i c a t e d , a l o n g p e r i o d o f 300 days, w h i c h i s t y p i c a l o f b a r o t r o p i c a l l y u n s t a b l e e x p e r i m e n t s , and a much s h o r t e r 56 day p e r i o d s i m i l a r t o t h a t f o r t h e b a r o c l i n i c a l l y u n s t a b l e experiment. K2 l a g g i n g t h e maximum i n K1.
Also notable are t h e dramatic spikes i n
T h i s resembles t h e b e h a v i o r o f K2 a t t h e o n s e t
o f b a r o c l i n i c i n s t a b i l i t y shown i n F i g . 13c.
276
3
2
T I M E IN YERRS
0
I
2
3
T I M E I N YE(IRS
4
5
6
7
*
5
TIME I N YERRS
5
0
1
z 3 TIME I N E R R S
Fig. 13. Average k i n e t i c energy over the rectangular domain (upper curve f o r upper l a y e r ) f o r ( a ) Experiment 1, t h e standard two-layer flat-bot,tom case, ( b ) Experiment 7 , with t h e topography o f Fig. 3, ( c ) Experiment 2 , with non-normal inflow, and ( d ) Experiment 4 , i d e n t i c a l t o Experiment 1 b u t with A = 3 x 106 cm2 / S and Sv2 = 3. The value o f IC i s ( a ) - 5 , ( b ) 1 . 0 , ( c ) .55, ( d ) . 7 .
217
8.3
Modon g e n e r a t i o n i n t h e b a r o t r o p i c a l l y u n s t a b l e experiments We b e g i n examining t h e c h a r a c t e r i s t i c f e a t u r e s o f t h e f l o w i n d i f f e r e n t
regimes by s t u d y i n g two experiments where t h e eddy-mean e n e r g e t i c s i n d i c a t e barotropic instability.
One e x p e r i m e n t has a f l a t bottom, and t h e o t h e r i n c l u d e s
t h e i d e a l i z e d G u l f o f Mexico topography shown i n F i g . 3.
The two experiments
which i l l u s t r a t e t h e b a s i c f e a t u r e s o f t h i s f l o w i n t h e s i m p l e s t and c l e a r e s t f a s h i o n a r e Experiment 1 w i t h F i g . 12b e n e r g e t i c s ( t h e s t a n d a r d f l a t - b o t t o m e x p e r i m e n t ) and Experiment 7 w i t h topography and F i g . 12h e n e r g e t i c s . F i g . 1 4 shows s y n o p t i c views o f p i and p2 f o r Experiment 1.
A t day 1710,
p1 ( F i g . 14a) shows t h e Loop C u r r e n t p e n e t r a t i n g i n t o t h e b a s i n and b e g i n n i n g t o bend westward.
An eddy shed e a r l i e r l i e s i n t h e w e s t e r n G u l f .
A characteristic
f e a t u r e o f t h e b a r o t r o p i c a l l y u n s t a b l e experimehts i s t h e g e n e r a t i o n o f a modon i n t h e l o w e r l a y e r as t h e Loop C u r r e n t begins t o f o r m an eddy ( F i g . 14b).
The
r e l a t i o n s h i p between p1 and p2 can be seen c l e a r l y b y superimposing t h e f i e l d s . The modon i n t e n s i t y tends t o f o l l o w t h a t o f t h e g e n e r a t i n g eddy i n t h e upper layer.
The a x i s o f t h e modon i s o r i e n t e d c l o s e t o t h e d i r e c t i o n o f p r o p a g a t i o n
by t h e upper l a y e r v o r t e x w i t h t h e a n t i c y c l o n i c member l e a d i n g and t h e c y c l o n i c member t r a i l i n g .
The o r i e n t a t i o n o f t h e modon g e n e r a t e d h e r e i s q u i t e d i f f e r e n t
f r o m t h a t f o u n d by McWilliams and F l i e r l (1979) f o r i s o l a t e d , n e a r l y c i r c u l a r v o r t i c e s , b u t t h e tendency o f t h e eddy i n t h e upper l a y e r t o propagate toward t h e member o f t h e modon w i t h l i k e r o t a t i o n i s s i m i l a r .
However, i n t h i s case
t h e westward p r o p a g a t i o n speed o f t h e modon s l i g h t l y exceeds t h a t o f t h e upper layer vortex.
Thus t h e f l o w a c t u a l l y becomes more b a r o c l i n i c and i n F i g . 14a, b
we see t h e a n t i c y c l o n i c eddy i n t h e upper l a y e r s i t u a t e d o v e r t h e c y c l o n i c member
o f t h e modon. ments.
T h i s b e h a v i o r i s comnon b u t n o t u n i v e r s a l i n o u r n u m e r i c a l e x p e r i -
It i s q u i t e u n l i k e t h e coupled behavior o f t h e i s o l a t e d b a r o c l i n i c
v o r t e x and b a r o t r o p i c modon s t u d i e d by McWilliams and F l i e r l (1979).
In their
r e s u l t s t h e modon member w i t h r o t a t i o n u n l i k e t h e b a r o c l i n i c v o r t e x e v e n t u a l l y b r o k e away and t h e b a r o t r o p i c and b a r o c l i n i c v o r t i c e s tended t o become superimposed and t o approach a s t a t e o f deep compensation (no s i g n a t u r e o f t h e v o r t e x i n t h e lower l a y e r ) .
When t h e u p p e r l a y e r v o r t e x reaches t h e w e s t e r n boundary
and propagates n o r t h w a r d ( F i g . 14c), i t i s a g a i n a s s o c i a t e d w i t h a modon i n t h e l o w e r l a y e r ( F i g . 14d) and a g a i n t h e modon i s o r i e n t e d i n t h e d i r e c t i o n o f p r o p a g a t i o n w i t h t h e l i k e ( a n t i c y c l o n i c ) member l e a d i n g and t h e o p p o s i t e member trailing. F i g . 14b, d shows an a d d i t i o n a l i n t e r e s t i n g phenomenon which occurs i n t h e lower layer.
I f t h e l o w e r l a y e r were i n t e g r a t e d s e p a r a t e l y as a b a r o t r o p i c
model, t h e s o l u t i o n would e v o l v e t o a steady, westward-bending Loop C u r r e n t as i n regime W.
The s o l u t i o n would be s i m i l a r t o F i g . 8a b u t t h e l o o p would bend
westward a t a l o w e r l a t i t u d e because (vc/B)+ i s much l e s s (see S e c t i o n 5.5). The l o w e r l a y e r i n f l o w v e l o c i t y a t t h e c o r e o f t h e c u r r e n t i s o n l y 3.35 cm/sec.
0 0)
0
P
0
L
; 0
mo 0
0
2
0
0
N
mY
op;
C
Q
0
( a ) p1 and ( b ) p2 a t d a j 1710 and ( c ) p1 and (d) p2 a t day 1800 f o r 2 2 Experiment 1. The contour i n t e r v a l i s .5 m /s f o r p1 and -05 m2/s2 for p2. F i g . 14.
279
In t h i s experiment w i t h two a c t i v e l a y e r s , the lower l a y e r flow i s q u i t e d i f f e r e n t from t h e b a r o t r o p i c prediction.
During t h e formation of t h e modon, t h e Loop Current i n t h e lower l a y e r e x h i b i t s a source-sink flow ( F i g . 14b). The modon i s t h e dominant flow and prevents the natural westward bending of t h e Loop. When t h e modon moves away (Fig. 14d), the lower layer Loop bends f a r t o the west and sheds a weak eddy almost i n phase w i t h t h e upper laye? (Fig. 14c). I n t h e mean (Fig. 15) b o t h t h e upper and lower layers e x h i b i t a westward-bending loop l i k e t h e W regime. As predicted by ( v , / B ) ~ and t h e higher inflow velocity i n the upper l a y e r , the mean loop i n the upper l a y e r bends westward a t a higher l a t i t u d e . The lower l a y e r a l s o e x h i b i t s c o u n t e r r o t a t i n g and zonally elongated mean gyres north of t h e loop. These a r e d r i v e n by downward flux of eddy energy from t h e upper l a y e r and may a l s o influence ti& l a t i t u d e of the mean Loop Current in t h e lower layer. Fig. 16 shows a synoptic view of p1 and p2 a t day 1760 f o r a barotropically unstable experiment w i t h Fig. 3 topography (Experiment 7 w i t h Fig. 1 2 h e n e r g e t i c s ) This experiment e x h i b i t s coupled upper l a y e r vortex, lower l a y e r modon behavior s i m i l a r t o t h e f l a t bottom experiment, except t h a t t h e modon i s mostly confined t o t h e abyssal p l a i n . Another d i f f e r e n c e i s t h a t t h e upper l a y e r vortex remains between t h e modon p a i r . The modon i s p a r t i a l l y steered by t h e topography. Apparently, t h e back i n t e r a c t i o n from the modon t o t h e upper l a y e r i s s u f f i c i e n t t h a t the t r a j e c t o r y of the upper l a y e r vortex i s a l s o modified by t h e topography.
Fig. 17 compares upper l a y e r eddy t r a j e c t o r i e s f o r Experiments 6 and 7 , two experiments with no flow through the ports i n t h e lower layer. The experiments a r e i d e n t i c a l except t h a t Experiment 6 has a f l a t bottom and Experiment 7 includes Fig. 3 topography. Because Experiment 7 includes no flow through t h e ports i n the lower l a y e r , t h e r e i s no c u r r e n t following t h e f/h contours, unlike F i g . l l c .
The addition of such a current had no major e f f e c t on the modon, provided the current was weak enough t o permit the normal eddy shedding t o occur. Although eddy a c t i v i t y i n the lower l a y e r modified t h e propagation of t h e upper l a y e r vortex, t h e propagation of both the upper l a y e r vortex and t h e associated modon was dominated by i n t e r n a l Rossby wave propagation in b o t h the reduced g r a v i t y and two a c t i v e l a y e r experiments which exhibited d i s c r e t e eddy shedding and a horizontal s h e a r ( b a r o t r o p i c ) i n s t a b i l i t y of t h e i n t e r n a l mode.
As we w i l l s e e s h o r t l y , t h i s i s not the case i n the experiment w i t h a b a r o c l i n i c instability.
280
900
600 KM
300
0 0
400
800
1200
1600
400
BOO XM
1200
1600
KM
600 KM
300
0 -
0
F i g . 15. Time mean of ( a ) p1 and ( b ) p 2 f o r Experiment 1 . i s .2 m2/ s 2 for p1 and .02 m2/s 2 for p2.
The contour interval
281
0
400
0
400
800
1200
800
1200
[KMI
1600
900
600 [KMI
300
0 1600
[KMI
Fig. 16. ( a ) p1 a n d ' ( b ) p2 a t day 1760 f o r Experiment 7. is .5 rn2 /s 2 f o r p1 and .05 m 2 /s 2 f o r p2.
The contour i n t e r v a l
N N
W
006 0
009 1
0
F i g . 17. Shows t h e e f f e c t o f bottom topography on eddy t r a j e c t o r i g s f o r i d e n t i c a l experiments except t h a t Experiment 6 (upper t r a j e c t o r y ) had a f l a t bottom and Experiment 7 ( l o w e r t r a j e c t o r y ) included t h e topography o f F i g . 3 which i s used as background i n t h i s f i g u r e . The t r a j e c t o r i e s are d o t t e d a t 3'3 day i n t e r v a l s .
283
8.4 F i g . 18 shows a s y n o p t i c view o f p1 and p2 f o r Experiment 2 where t h e upper l a y e r i n f l o w i s a n g l e d 27’ west o f normal and t h e r e i s n o f l o w t h r o u g h t h e p o r t s i n t h e lower l a y e r .
The eddy-mean e n e r g e t i c s ( F i g . 1 2 c ) i n d i c a t e t h e occurrence
of baroclinic instability.
T h i s experiment e x h i b i t s m o d o n - l i k e g e n e r a t i o n s i m i l a r However, t h e eddies
t o t h a t e a r l i e r associated w i t h a b a r o t r o p i c i n s t a b i l i t y .
t e n d t o be s m a l l e r and t h e g r e a t e r p o p u l a t i o n o f e d d i e s tends t o mask t h e modon c h a r a c t e r o f t h e eddy g e n e r a t i o n .
The upper and l o w e r l a y e r e d d i e s n e a r t h e
e a s t e r n p a r t o f t h e Loop b e a r a phase r e l a t i o n s h i p which i s s i m i l a r t o t h e The modon a x i s i s o r i e n t e d c l o s e t o t h e
b a r o t r o p i c a l l y u n s t a b l e experiments.
d i r e c t i o n o f p r o p a g a t i o n of t h e a n t i c y c l o n i c eddy i n t h e upper l a y e r , w i t h t h e a n t i c y c l o n i c modon member l e a d i n g and t h e cye’lonic one t r a i l i n g . i s t h a t t h e modon a x i s i s s o u t h o f t h e upper l a y e r v o r t e x .
One d i f f e r e n c e
Thus, t h e l o w e r l a y e r
eddies t e n d t o be s t r o n g e s t under t h e w e s t w a r d - f l o w i n g a m o f t h e Loop C u r r e n t as expected f o r a b a r o c l i n i c i n s t a b i l i t y ( G i l l , e t a l , 1974; P h i l a n d e r , 1976). L a t e r , i n t h e c e n t r a l b a s i n t h e l e a d i n g modon member s h i f t s northward, away f r o m t h e westward p r o p a g a t i n g v o r t e x i n t h e upper l a y e r . under t h e westward branch o f t h e Loop. w i t h the d i r e c t i o n o f propagation.
The t r a i l i n g v o r t e x remains
Thus t h e modon a x i s i s no l o n g e r a l i g n e d
I n g e n e r a l , t h e l o w e r l a y e r eddies t e n d t o
be e l o n g a t e d m e r i d i o n a l l y i n t h e e a s t e r n p a r t o f t h e b a s i n where t h e y o r i g i n a t e arid z o n a l l y i n t h e w e s t e r n p a r t o f t h e b a s i n where t h e y decay.
I n the western
p a r t o f t h e b a s i n t h e eddies a l s o show some tendency t o w a r d b a r o t r o p y .
Except
f o r the i n i t i a l meridional elongation, these tendencies are consistent w i t h r e s u l t s p r e s e n t e d by Rhines (1977). The m o s t d r a m a t i c d i f f e r e n c e between t h e e x p e r i m e n t s w i t h b a r o t r o p i c and I n the
b a r o c l i n i c i n s t a b i l i t y l i e s i n t h e p r o p a g a t i o n speed o f t h e eddies.
b a r o t r o p i c a l l y u n s t a b l e e x p e r i m e n t s w i t h d i s c r e t e eddies t h e i n t e r n a l Rossby wave speed a s s o c i a t e d w i t h t h e upper l a y e r v o r t e x e x e r t s p r i m a r y c o n t r o l on t h e propagation i n both layers.
Even though t h e eddies i n t h e b a r o c l i n i c a l l y
u n s t a b l e case a r e s m a l l e r , t h e y p r o p a g a t e westward a t
-
10 cm/sec, t y p i c a l l y
2 t o 3 t i m e s f a s t e r t h a n i n t h e b a r o t r o p i c a l l y u n s t a b l e experiments. Although i t i s d i f f i c u l t t o e s t i m a t e an a p p r o p r i a t e s h e a r v e l o c i t y , t h e p r o p a g a t i o n speeds
i n o u r n u m e r i c a l model a r e q u i t e c o n s i s t e n t w i t h t h o s e f o r b a r o c l i n i c i n s t a b i l i t y i n a l i n e a r i z e d t w o - l a y e r model w i t h a h o r i z o n t a l l y u n i f o r m b a s i c f l o w ( P e d l o s k y , 1979).
284
900
600 [ KM
300
0 0
400
800
1200
1600
IKM)
Fig. 18. ( a ) p1 and ( b ) p2 a t day 2450 f o r Experiment 2. 2 2 2 2 i s .5 m /s f o r p1 and .05 m /s f o r p2.
The c o n t o u r i n t e r v a l
285 G i l l , e t a1 (1974) have suggested t h e upper t o l o w e r l a y e r ohase s h i f t as a means o f d e t e c t i n g b a r o c l i n i c i n s t a b i l i t y .
I n o u r r e s u l t s we f i n d t h i s i s n o t
v e r y u s e f u l because t h e b a r o t r o p i c i n s t a b i l i t y which occurs i n t h e upDer l i y e r generdtes a modon i n t h e l o w e r l a y e r w i t h u p p e r - l o w e r l a y e r phase r e l a t i o n s h i p s which a r e much l i k e t h o s e o f t h e b a r o c l i n i c i n s t a b i l i t y .
I n our results the
westward p r o p a g a t i o n speed o f t h e eddies i s a much c l e a r e r d i s t i n p u i s ' i i n g characteris t i c .
8.5
Flow c h a r a c t e r i s t i c s o f a mixed i n s t a b i l i t y F i g . 19 shows t w o s y n o p t i c views of p1 and p 2 f o r Experiment 4 which has a
f l a t bottom, no i n f l o w i n t h e l o w e r l a y e r , and o n e - t h i r d t h e eddy v i s c o s i t y o f t h e experiments d i s c u s s e d i n S e c t i o n s 8.3 and 9.4.
The eddy-mean e n e r g e t i c s
( F i g . 12e) suggest t h a t a mixed i n s t a b i l i t y occurs i n t h i s experiment. Since t h e r e i s no f l o w t h r o u g h t h e p o r t s i n t h e l o w e r l a y e r , a l l t h e energy i n t h e l o w e r l a y e r i s r e c e i v e d f r o m t h e upper l a y e r .
Apart from t h i s t h e flows i n t h e
two l a y e r s a r e much more independent t h a n t h o s e d i s c u s s e d i n t h e two p r e c e d i n g subsections. Eddies i n t h e l o w e r l a y e r propagate westward a t a p p r o x i m a t e l y t h e e x t e r n a l Rossby wave speed (- 10 cm/sec), and those w i t h l i k e r o t a t i o n pass a g i v e n p o i n t w i t h a p e r i o d i c i t y o f a b o u t 60 days.
U n l i k e t h e experiments d i s c u s s e d i n
S e c t i o n s 8.3 and 8 . 4 t h e r e i s n o c l e a r phase r e l a t i o n s h i p between t h e eddies i n t h e l o w e r l a y e r and t h e eddy w h i c h forms on t h e Loop C u r r e n t i n t h e upper layer.
T h i s i s t r u e d u r i n g most, b u t n o t a l l , o f t h e eddy-shedding c y c l e of t h e
Loop C u r r e n t .
I n t h i s e x p e r i m e n t t h e eddy-shedding p e r i o d i s about 300 days and
i s d e p i c t e d as a s l o w o s c i l l a t i o n i n K1 ( F i g . 1 3 d ) .
There i s a back i n t e r a c t i o n
f r o m t h e l o w e r l a y e r e d d i e s t o t h e Loop C u r r e n t i n t h e upper l a y e r which causes a s t r o n g u n d u l a t i o n o f t h e Loop w i t h a p p r o x i m a t e l y a 60 day p e r i o d . d e p i c t e d i n F i g . 13d as t h e h i g h f r e q u e n c y o s c i l l a t i o n i n K1.
This i s
Except f o r t h i s
u n d u l a t i o n , t h e Loop C u r r e n t p e n e t r a t e s i n t o t h e G u l f , bends westward and begins t o f o r m an eddy s t r u c t u r e j u s t as i n the b a r o t r o p i c a l l y u n s t a b l e experiments, b u t near t h e t i m e an eddy would break o f f ( F i g . 19a) i n a b a r o t r o p i c a l l y u n s t a b l e experiment, something q u i t e d i f f e r e n t occurs.
The Loop C u r r e n t suddenly shoots
f a r t o t h e west a t a speed a p p r o p r i a t e f o r b a r o c l i n i c i n s t a b i l i t y and breaks i n t o a s e r i e s o f s m a l l e r eddies.
D u r i n g t h i s process l o w e r l a y e r eddies under
t h e s o u t h s i d e o f t h e Loop s t r e n g t h e n d r a m a t i c a l l y and t h e upper and l o w e r l a y e r eddies d e v e l o p d i s t i n c t phase r e l a t i o n s h i p s .
An a n t i c y c l o n i c eddy i n t h e l o w e r
l a y e r l e a d s t h e westward advance on t h e Loop C u r r e n t .
A t t h i s s t a g e phase
r e l a t i o n s h i p s i n t h e upper and l o w e r l a y e r s a r e v e r y s i m i l a r t o t h o s e f o r t h e b a r o c l i n i c a l l y u n s t a b l e case, and t h e y e x h i b i t t h e same d i f f e r e n c e s from t h e b a r o t r o p i c a l l y u n s t a b l e experiments.
These phase r e l a t i o n s d i s i n t e g r a t e as soon
as t h e r a p i d westward advance o f t h e Loop C u r r e n t i s h a l t e d .
Thus we have a
286
F i g . 19.
( a ) p1 and ( b ) o2 a t day 1720 and (c) p1 and ( d ) p:, a t day 1750 f o r
Ex?eriment 4.
2
The c o n t o u r i n t e r v a l i s . 5 m / s
2
f o r p1 and
.i m2/s2
f o r p2.
p i c t u r e o f e p i s o d i c b a r o c l i n i c i n s t a b i l i t y a s s o c i a t e d w i t h a s m a l l p a r t o f each 300 day eddy-shedding c y c l e o f t h e Loop Current.
T h i s i n s t a b i l i t y i s s t r o n g enough t o
show up i n t h e domain-averaged eddy-mean e n e r g e t i c s ( F i g . 12e) and t o p r o v i d e a sharp s p i k e i n t h e c u r v e o f
K2 vs. t i m e ( F i g . 13d).
Day 1720 ( F i g . 19b) i s
n e a r t h e f o o t o f t h e l a s t s p i k e and day 1760 ( F i g . 19d) i s n e a r t h e t o p o f i t .
The much weaker coupling f o r the t w o layers than found i n e i t h e r t h e b a r o t r o p i c a l l y o r b a r o c l i n i c a l l y u n s t a b l e e x p e r i m e n t s i s e x p l a i n e d i n p a r t by t h e p e c u l i a r e p i s o d i c n a t u r e o f t h e b a r o c l i n i c i n s t a b i l i t y i n Experiment 4 and i n p a r t by t h e 3 t i m e s l o w e r eddy v i s c o s i t y .
Because t h e eddies i n t h e l o w e r
l a y e r a r e governed by e x t e r n a l Rossby wave p r o p a g a t i o n , t h e y a r e d i s p e r s i v e i n nature.
W i t h t h e l o w e r eddy v i s c o s i t y t h e y aye n o t d i s s i p a t e d as soon a f t e r
g e n e r a t i o n and have g r e a t e r o p p o r t u n i t y t o d i s p e r s e and f i l l t h e b a s i n .
The
importance o f d i s p e r s i o n i n s p r e a d i n g t h e eddy p o p u l a t i o n i n t h e l o w e r l a y e r has been n o t e d by Rhines (1977) and i n t h e s t u d y of i s o l a t e d v o r t i c e s by McWilliams and F l i e r 1 (1979).
A comparison of F i g . 16 ( f o r t h e experiment w i t h i d e a l i z e d G u l f o f Mexico topography) and F i g . 19 ( f o r t h e f l a t - b o t t o m experiment w i t h a mixed i n s t a b i l i t y ) i n d i c a t e s how t h e topography can suppress t h e episodes o f b a r o c l in i c i n s t a b i 1it y found i n t h e l a t t e r case.
When t h e topography of F i g . 3 i s p r e s e n t , t h e eddies
i n the lower l a y e r a r e m o s t l y confined t o t h e abyssal p l a i n .
Lower l a y e r eddy
generation o v e r t h e s t r o n g l y s l o p i n g topography i s p r e v e n t e d because t h e eddy flow would have t o
C ~ Q S St h e
c l o s e l y packed f / h c o n t o u r s a t l a r g e angles,
b e h a v i o r n o t a n t i c i p a t e d i n g e o s t r o p h i c a l l y balanced f l o w which conserves potential vorticity.
The s t r o n g eddies i n F i g . 19d which form under t h e westward-
f l o w i n g branch o f t h e Loop C u r r e n t l i e o v e r t h e r e g i o n o f t h e Campeche Bank and t h e s l o p e of t h e bank.
Thus, t h e y a r e p r e v e n t e d f r o m f o r m i n g when t h e topography
of F i g . 3 i s i n c l u d e d .
We can now a p p r e c i a t e why t h e t w o - l a y e r model w i t h topo-
graphy produces r e s u l t s more l i k e t h e reduced g r a v i t y model t h a n does t h e twol a y e r f l a t - b o t t o m model.
Ift h e westward branch o f t h e Loop C u r r e n t were t o
flow o v e r t h e a b y s s a l p l a i n , we m i g h t e x p e c t t h e model t o e x h i b i t eoisodes o f b a r o c l i n i c i n s t a b i l i t y even when t h e topography i s i n c l u d e d .
288
9.
SUMMARY AND CONCLUSIONS I n t h i s paper we have demonstrated t h e a b i l i t y o f s i m o l e n u m e r i c a l models t o
p e r f o r m remarkable s i m u l a t i o n s o f t h e Loop C u r r e n t Mexico.
-
eddy system i n t h e G u l f of
Tne models were designed f o r c o m p u t a t i o n a l e f f i c i e n c y and s i m p l i c i t y ,
r e t a i n i n g o n l y t h e e s s e n t i a l p h y s i c s and c h a r a c t e r i s t i c s o f t h e G u l f r e q u i r e d s i m u l a t e t h e b a s i c dynamical b e h a v i o r o f t h e system.
t G
The s i m p l i c i t y d t h e models
f a c i l i t a t e d t h e a n a l y s i s o f t h e system dynamics and t h e c o m p u t a t i o n a l e f f i c i e n c y a l l o w e d us t o p e r f o r m o v e r 150 m u l t i - y e a r i n t e g r a t i o n s .
The e f f i c i e n c y a l s o
a l l o w e d us t o u s e h o r i z o n t a l r e s o l u t i o n adequate t o i n v e s t i g a t e i n t e r e s t i n g r e g i o n s o f t h e parameter space. r e g i o n s where t i m e dependent e d d i e s dominated the circulation. The numerous n u m e r i c a l experiments e x p l o r e d t h e model p i r a m e t e r soace and a i d e d i n t h e f o r m u l a t i o n and t e s t i n g o f dynamical hypotheses.
The most s a l i e n t
r e s u l t s f r o m t h e model a r e summarized i n t h e seven p o i n t s which f o l l o w .
1) The s i m p l e models were a b l e t o s i m u l a t e t h e a n t i c y c l o n i c eddy shedding by t h e Loop C u r r e n t and t o s i m u l a t e e d d i e s w i t h r e a l i s t i c d i a m e t e r s , a m p l i t u d e s , and westward p r o p a g a t i o n ( F i g s . 1,4).
Most s t r i k i n g was t h e a b i l i t y o f t h e models
t o s i m u l a t e t h e observed quasi-annual p e r i o d o f t h e eddy shedding w i t h
no t i m e
v a r i a t i o n s i n t h e i n f l o w t h r o u g h t h e Yucatan S t r a i t s ( s o u t h e r n p o r t ) .
This i s
c o n t r a r y t o t h e p o p u l a r h y p o t h e s i s t h a t t h e Loop C u r r e n t sheds eddies i n response t o annual v a r i a t i o n s o f t h e i n f l o w .
2 ) The reduced g r a v i t y model p r o v e d t o be t h e s i m p l e s t model a b l e t o sirnulace t h e b a s i c dynamics o f t h e Loop C u r r e n t and t h e eddy shedding ( F i g . 5). T h i s i n d i c a t e s t h a t b a r o c l i n i c i n s t a b i l i t y i s n o t an e s s e n t i a l element o f t h e dynamics. I n s t e a d a h o r i z o n t a l s h e a r i n s t a b i l i t y of t h e f i r s t i n t e r n a l mode ( a b a r o t r o p i c i n s t a b i l i t y ) i s t h e dominant i n s t a b i l i t y mechanism.
3) We have demonstrated t h e u s e f u l n e s s o f CAV t r a j e c t o r y a n a l y s i s and i n t e r n a l Rossby waves i n e x p l a i n i n g t h e eddy-shedding b e h a v i o r o f t h e Loop C u r r e n t , i n c l u d i n g t h e eddy d i a m e t e r , t h e Loop C u r r e n t p e n e t r a t i o n i n t o t h e G u l f , t h e l a t i t u d e of westward b e n d i n g by t h e Loop C u r r e n t , t h e westward speed o f eddy p r o p a g a t i o n , and t h e eddy shedding p e r i o d (see T a b l e 2 ) . i s pervasive.
The r o l e o f d i f f e r e n t i a l r o t a t i o n ( 8 )
T h i s t h e o r y a l s o showed t h a t i t i s n o t necessary t o i n v o k e an
i n s t a b i l i t y mechanism t o e x p l a i n t h e westward b e n d i n g o f t h e Loop C u r r e n t , n o r t h e tendency f o r i t t o l o o p back on i t s e l f .
T h i s suggests t h a t an i n s t a b i l i t y
m a y b e e s s e n t i a l o n l y t o e x p l a i n t h e f i n a l eddy s e p a r a t i o n f r o m t h e Loop C u r r e n t .
4 ) Two s t e a d y regimes were found i n t h e p a r a m e t e r space n e i g h b o r i n g t h e eddy shedding regime. The parameter space o c c u p i e d by each regime was d e p i c t e d on a regime diagram f o r t h e reduced g r a v i t y model ( F i g . 10).
5 ) I n t h e presence o f s u f f i c i e n t deep w a t e r i n f l o w t h r o u g h t h e Yucatan S t r a i t s , t h e F l o r i d a S h e l f topography may p r e v e n t Loop C u r r e n t p e n e t r a t i o n , westward bending and eddy shedding by e f f e c t i v e l y r e d u c i n q t h e p o r t s e p a r a t i o n .
This s h i f t s the
289
Loop C u r r e n t i n t o one o f t h e s t a b l e regimes ( S e c t i o n 7).
Certain time varia-
t i o n s i n t h e deep f l o w t h r o u g h t h e Yucatan S t r a i t s may have a g r e a t e r e f f e c t on t h e Loop C u r r e n t t h a n f l u c t u a t i o n s i n t h e upper l a y e r flow t h r o u g h t h e s t r a i t .
6 ) Bottom topography p l a y s a n o t h e r i m p o r t a n t r o l e by i n h i b i t i n g b a r o c l i n i c Thus t h e reduced g r a v i t y s o l u t i o n s were more l i k e t w o - l a y e r s o l u t i o n s
instability.
w i t h t h e i d e a l i z e d G u l f o f Mexico topography ( F i g . 3 ) t h a n t w o - l a y e r f l a t - b o t t o m solutions. upper
The topography a l s o demonstrated some a b i l i t y t o s t e e r eddies i n t h e
ocean t h r o u g h back i n t e r a c t i o n f r o m eddies i n t h e l o w e r l a y e r w h i c h were
mostly confined t o the abyssal p l a i n .
7 ) F i n a l l y , we examined t h e c h a r a c t e r i s t i c s i g n a t u r e s o f b a r o t r o p i c and b a r o c l i n i c i n s t a b i l i t y i n t h e p r e s s u r e f i e l d s o f b o t h l a y e r s and i n t h e eddymean e n e r g e t i c s .
I n b o t h cases t h e r e was a Ybndency f o r eddies i n t h e upper
l a y e r t o d r i v e a modon i n t h e l o w e r l a y e r .
The upper and l o w e r l a y e r phase
r e l a t i o n s were s u r p r i s i n g l y s i m i l a r f o r b o t h t y p e s o f i n s t a b i l i t y , b u t t h e westward p r o p a g a t i o n speeds a s s o c i a t e d w i t h b a r o c l i n i c i n s t a b i l i t y were t y p i c a l l y two t o t h r e e t i m e s f a s t e r . ACKNOWLEDGEMENTS We e x t e n d o u r a p p r e c i a t i o n t o D r . L . B. L i n , who developed much o f t h e a n a l y s i s and d i s p l a y s o f t w a r e , i n c l u d i n g t h e eddy-mean e n e r g e t i c s .
We thank
Ruth P r e l l e r , John H a r d i n g , Monty P e f f l e y , M a r l a Burson and C y n t h i a Seay f o r a s s i s t i n g us i n v a r i o u s aspects o f m a n u s c r i p t p r e p a r a t i o n .
D r . D a n i e l Moore o f
I m p e r i a l C o l l e g e , London p r o v i d e d t h e f a s t v e c t o r i z e d H e l m h o l t z s o l v e r s f o r b o t h r e c t a n g u l a r and i r r e a u l a r domains.
D r . Donna Blake.
The CAV t r a j e c t o r y program was p r o v i d e d by
Some o f t h e g r a p h i c s s o f t w a r e was s u p p l i e d by t h e N a t i o n a l
Center f o r Atmospheric Research, which i s sponsored by t h e N a t i o n a l Science Foundation.
Computations were p e r f o r m e d on t h e t w o - p i p e l i n e Texas I n s t r u m e n t s
Advanced S c i e n t i f i c Computer a t t h e Naval Research ' L a b o r a t o r y i n Washington, D.C. We thank Charlene P a r k e r f o r t y p i n g t h e m a n u s c r i p t . APPENDIX A L i s t o f Symbols
A
h o r i z o n t a l eddy v i s c o s i t y
'i r
n o n d i s p e r s i v e i n t e r n a l 3ossby wave speed i n t e r n a l Rosshy wave speed ' i n c l u d i n g d i s p e r s i o n
3
) P C o r i o l i s parameter; f o t a k e n a t s o u t h e r n boundary ( y o )
b e t a Ekman number, A/(BL
a c c e l e r a t i o n due t o g r a v i t y reduced g r a v i t y , g(p,
-
pl)/p
i n i t i a l thicknesses o f the l a y e r s instantaneous l o c a l thickness o f t h e layers
290
Ki
-
, Ki, K;
k , .L L Lt3F
k i n e t i c energy % ( u L + v L ) ; o f t h e mean f l o w ; mean o f t h e eddy f l o w , r e s p e c t i v e l y , f o r l a y e r i. zonal and m e r i d i o n a l wave numbers, r e s p e c t i v e l y h a l f w i d t h o f the southern p o r t minimum f r i c t i o n a l l e n g t h s c a l e o v e r w h i c h B i s i m p o r t a n t ,
( A/R) LBI
minimum i n e r t i a l l e n g t h s c a l e o v e r w h i c h B i s i m p o r t a n t , (VC/B)+
Lnp LP P, B, P '
P1 p2 Pe
maximum n o r t h w a r d p e n e t r a t i o n o f t h e Loop C u r r e n t h a l f the p o r t separation distance p o t e n t i a l energy +p(gq: +g'q:); t h e eddy f l o w , r e s p e c t i v e l y .
o f t h e mean f l o w ; mean of
upper l a y e r d e n s i t y - n o r m a l i z e d p r e s s u r e , 9171. l o w e r l a y e r d e n s i t y - n o r m a l i z e d P r e s s u r e , 9n1 b e t a Rossby number, vc/BL
r
eddy r a d i u s
t
ti me
Reynolds number, vCL/A
2 P
At
time increment i n t h e numerical i n t e g r a t i o n
ul' u2
x - d i r e c t e d components o f c u r r e n t v e l o c i t y
vC
g'lhl-H1)
eddy shedding p e r i o d
RB Re
'ci
-
maximum i n f l o w speed speed a t t h e core o f t h e c u r r e n t geostrophic meridional t r a n s p o r t
vg \v1, \v2
h i ~ 1 h2 , ~2
x, Ys
t a n g e n t p l a n e C a r t e s i a n c o o r d i n a t e s : x p o s i t i v e eastward, y p o s i t i v e n o r t h w a r d , z p o s i t i v e upward e a s t - w e s t and n o r t h - s o u t h domain s i z e h o r i z o n t a l g r i d increments d i f f e r e n t i a l r o t a t i o n , df/dy
5
- u Y f r e e s u r f a c e anomaly; h e i g h t o f t h e f r e e s u r f a c e above i t s i n i t i a l u n i f o r m e l e v a t i o n ; n l = h l + h2 - H1 - H2 r e l a t i v e v o r t i c i t y vx
n 2 = H1 + n1
-
h1 = h 2
-
H2 = -PA
angle o f i n f l o w w i t h respect t o the p o s i t i v e x-axis i n t e r n a l radius o f deformation d e n s i t i e s o f sea w a t e r x and y d i r e c t e d t a n g e n t i a l s t r e s s e s a t t h e t o p ( i ) and b o t t o m ( i + 1) o f l a y e r i
291
B
APPENDIX
Nev\r Reduced G r a v i t y Experiments f o r t h e Regime Diagram ( F i g . 10) L
Experinienr
vci
L
A
Lz,
a
Re
155
54.4
80
4.0
227.1
2.0
10.9
157
54.1 73.4
80
4.0
150.3
1.19
80
2.0
203.5
2.0 2.0
10.8
158
29.4
.89
153
73.2
80
2.5
203.5
2.0
23.4
16D
40.3
80
7.3
203.5
16 1
41.4
80
203.5
162
41.2 40.5
80 80
1.6 1.6 4.6 4.6
.43 .537
233.5 203.5
.69 1.21"
.88 1.93 1.86 1.44
163
40.8
164
80
.69
203.5 7
4.4 20.7 20.6
v
.81
7.1
1.43
2
w i d t h and h a l f - p o r t s e p a r a t i o n , r e s p e c t i v e l y .
w
.527
7.0
i n cm/s; L, L i n km; A i n 10 cm /s; B i n ci P See Appendix A f o r symbol d e f i n i t i o n s . N o t e t h a t L and L
units:
Regime
RB
-1
Cm
SeC
-1
are the half-port P The o t h e r parameters a r e t h e
same as i n Table 1 e x c e p t t h a t (1) i n Experiments 155 and 157 a l a n d mass was i n s e r t e d i n t h e l o c a t i o n o f t h e West F l o r i d a S h e l f (See F i g . 9b, c ) a n d t h e c e n t e r o f t h e e a s t e r n p o r t was t a k e n t o be 75 km s o u t h o f t h e w e s t e r n end o f t h i s l a n d mass, ( 2 ) t h e s o u t h e r n p o r t was c e n t e r e d a t xp = 1000 km i n Experimeni = 1160 krn i n Experiment 1 5 7 , and ( 3 ) t h e i n f l o w t r a n s D o r t vias P 14 Sv i n Experiments 155 and 157, and 10 Sv i n Experiments 160-164.
155 and a t x
APPENDIX C D e r i v a t i o n of Eddy-mean E n e r g e t i c s f o r a Two-layer,
Free-surface, P r i m i t i v e -
e q u a t i o n Model w i t h Open Boundaries C o n s i d e r t h e momentum f o r m o f t h e p r i m i t i v e e q u a t i o n s f o r a t w o - l a y e r f l u i d with a free surface:
arll at + V -+ V at
*
(hl \vl
+ h2 \v2) = 0
(h2 \v2) = 0
292
where i=1,2 and n l and q 2 are the deviations of the free surface and the interface, respectively (see Appendix A). Also,
Note i n (Cl) t h a t we have used the traditional form of Laplacian f r i c t i o n N o w define the kinetic and potential energies as
( u 2i + v 2i )
K i = +phi
P
2
where i = 1 , 2
2
= 15P (gnl + 9 ' Q 2 ) .
Multiplying (Cl) by p h i \vi ( i = 1 , 2 ) and using (C2) and (C3) we obtain the kinetic energy equations :
Note that i n deriving (C6) we have assumed g ' V n l << gml and q = O f o r i=1,2,3. The potential energy equation i s formed by multiplying ( C 2 ) by pgnl and (C3) by p g ' q 2 and sumning the r e s u l t s :
Now define mean and perturbation quantities f o r u , v, h, and (-)
sto +
I
= T
t0
(
)dt
Q
such t h a t
293 and
where T i s a s u i t a b l e t i m e i n t e r v a l .
A l s o d e f i n e t h e k i n e t i c energy o f t h e mean
f l o w p e r u n i t a r e a as
and t h e mean k i n e t i c energy of t h e eddy f l o w p e r u n i t area as
K;
- Ki.
+ vi2)
= +phi(ui2
S i m i l a r l y , f o r t h e p o t e n t i a l e n e r g y o f t h e mean f l o w
and f o r t h e mean p o t e n t i a l energy o f t h e eddy f l o w
SIT)
P' = L,p(gT+ The
Fl
equation i s obtained by m u l t i p l y i n g
where f o r l a y e r i
The Ki
equation i s
aKi = - [V at
' -\
(c5)-
-
(C12) o r
v
-
(
FIK1)li.y1
(c1)w i t h
i = l by p K l q l :
294
Similarly, f o r
K2
and
K; we o b t a i n
and
aKi = at
The
P
(
[V
\qy- v -
( \v2K2)1 + Y2
equation i s obtained by mu t i p l y
and sumning t h e r e s u l t s :
By s u b t r a c t i n g (C16) from
+ pg?ilV
-
( h i \v; +
(n), we o b t a i n t h e
h;)
P ' equation
295 When t h e terms i n t h e energy e q u a t i o n s a r e c a l c u l a t e d f r o m a model s o l u t i o n i n s t a t i s t i c a l e q u i l i b r i u m and a s u i t a b l e t i m e average i s used, t h e tendency terms a r e n e g l i g i b l e .
Regional energy budgets can be o b t a i n e d , i f (C12)
are also integrated spatially.
- (C17)
I n t e g r a t e d over a closed basin the divergence
terms v a n i s h , b u t i n an open domain t h e y must be r e t a i n e d .
The energy balances
a r e c o n v e n i e n t l y d i s p l a y e d u s i n g an energy box diagram such as F i g . 12a.
Each
t e r m i s r e p r e s e n t e d by an a r r o w i n o r o u t o f t h e box f o r t h e energy r e s e r v o i r associated w i t h t h a t equation.
When i d e n t i c a l terms w i t h o p p o s i t e s i g n appear
i n two e q u a t i o n s , t h e y r e p r e s e n t a c o n v e r s i o n o f energy from one t y p e t o another. The energy t r a n s f e r s shown i n F i g . 12a were c a l c u l a t e d from t h e s p a t i a l l y i n t e g r a t e d terms i n t 1 2 )
-
(C17) as shown below.
K1 terms
K i term:
2 V \vl
-
- -
2 hl \vl V \vlIdxdy
296
-Kz
terms
291
I n o u r r e s u l t s (Kl K i I >> Thus, any c o n t r o v e r s y o v e r t h e f o r m u l a t i o n o f t h e s e terms
The b r a c k e t n o t a t i o n i s dropped i n S e c t i o n 8. lKiF
-+
Ki
f
PW
+
KiI.
+
( H a r r i s o n and Robinson, 1978) s h o u l d n o t c l o u d t h e i n t e r p r e t a t i o n o f t h e b a s i c r e s u l t s i n F i g . 12.
Also, t h e d i f f e r e n c e between t h e f r i c t i o n a l f o r m u l a t i o n i n t h e models and t h e e n e r g e t i c s d i d n o t r e s u l t i n any s e r i o u s imbalances i n t h e
energy e q u a t i o n s . REFERENCES Blumberg, A. F. and G. L . MeTlor, 1981: A n u m e r i c a l c a l c u l a t i o n o f t h e c i r c u l a t i o n i n t h e G u l f of Mexico. D y n a l y s i s o f P r i n c e t o n Rept. No. 66. Prepared f o r D i v i s i o n o f S o l a r Technology. U.S. Dept. o f Energy., 159 pp. Cochrane, J . D., 1965: The Yucatan C u r r e n t and e q u a t o r i a l c u r r e n t s o f t h e western A t l a n t i c , U n p u b l i s h e d r e p o r t , Dept. of Oceanography, Texas A&M U n i v e r s i t y , Ref. (65-17T), 20-27. E l l i o t t , B. A., 1979: A n t i c y c l o n i c r i n g s and t h e e n e r g e t i c s o f t h e c i r c u l a t i o n of t h e G u l f of Mexico. Ph.D. t h e s i s , Dept. o f Oceanograohy, Texas A&M U n i v e r s i t y , 188 pp. G i l l , A. E . , J . S. A. Green, and A. J . S i m o n s , 1974: Energy p a r t i t i o n i n t h e l a r g e - s c a l e ocean c i r c u l a t i o n and t h e p r o d u c t i o n o f mid-ocean eddies. DeeDSea Research, 21, 499-528. H a l t i n e r , G . J . , and F. L. M a r t i n , 1957: Dynamical and P h y s i c a l M e t e o r o l o g y , McGraw-Hill, 470 D, .P . H a r r i s o n , D. E., and A. R. Robinson, 1978: Energy a n a l y s i s o f open r e g i o n s of t u r b u l e n t flows-mean eddy e n e r g e t i c s o f a n u m e r i c a l ocean c i r c u l a t i o n e x p e r i ment. Dyn. Atmos. Oceans, 2 , 185-211. H o l l a n d , W. R., and L. 6 . L i n , 1975: On t h e g e n e r a t i o n o f mesoscale eddies and t h e i r c o n t r i b u t i o n t o t h e oceanic g e n e r a l c i r c u l a t i o n . I . A p r e l i m i n a r y n u m e r i c a l e x p e r i m e n t . J . Phys. Oceanogr., 5, 642-657. H u r l b u r t , H. E. and J . D. Thompson, 1980: A n u m e r i c a l s t u d y o f Loop C u r r e n t i n t r u s i o n s and eddy shedding. J . Phvs. Oceanogr., 10, 1611-1651. L e i p p e r , D. F., 1970: A sequence o f c u r r e n t p a t t e r n s i n t h e G u l f o f Mexico. J. Geophys. Res., 75, 637-657. M c ' d i l l i a m s , J . C., and G. R. F l i e r l , 1979: On t h e e v o l u t i o n o f i s o l a t e d , n o n l i r i e a r v o r t i c e s . J . Phys. Oceanogr., 9, 1155-1182. N o w l i n , W. D., 1972: W i n t e r c i r c u l a t i o n p a t t e r n s and p r o p e r t y d i s t r i b u t i o n s . C o n t r i b u t i o n s on t h e P h y s i c a l Oceanography o f t h e G u l f o f Mexico, V o l . 11, L. R. A. Capurro and J . L. Reid, Eds., G u l f P u b l i s h i n g Co., 3-51. Pedlosky, J . , 1979: Geophysical F l u i d Dynamics, S p r i n g e r - V e r l a g . 624 pp. P h i l a n d e r , S. G. H., 1976: I n s t a b i l i t i e s of zonal e q u a t o r i a l c u r r e n t s . J . Geophys. Res., 81, 3725-3735. Reid, R. O., 1972: A s i m o l e dynamic model o f t h e Loop C u r r e n t . C o n t r i b u t i o n s on t h e P h y s i c a l Oceanography o f t h e G u l f o f Mexico, Vol. 11, L. R. A. Capurro and J . L. Reid, Eds., G u l f P u b l i s h i n g Co., 157-159. Rhines, P., 1977: The dynamics o f unsteady c u r r e n t s . The Sea, V o l . 6, E . 0. Goldberg, I . N. McCave, 3. J . O ' B r i e n and J . H. S t e e l e , Eds., W i l e y I n t e r s c i e n c t 189- 318. Rossby, C. G., 1940: P l a n e t a r y f l o w p a t t e r n s i n t h e atmosphere. Q u a r t . J . Roy. Meteor. SOC., 66 ( S u p p l . ) , 68-87. S t e r n , M. E., 1975: M i n i m a l p r o p e r t i e s o f p l a n e t a r y eddies. J. Mar. Res.,
33, 1-13.
This Page Intentionally Left Blank
299
A NUMERIC=
G.W.
MODEL OF EDDY GENERATION IN THE SOUTHEASTERN CARIBBEAN SEA
HEBURN
Science Applications, Inc., T.H.
KINDER and J.H.
2999 Monterey-Salinas Highway, Monterey, CA, USA
WENDER
Physical Oceanography Branch (Code 331). Naval Ocean Research and Development Activity, NSTL Station, l4.S H.E.
39529
HURLBURT
Environmental Simulation Branch (Code 322), fiaval Ocean Research and Development Activity, NSTL Station, M S
39529
ABSTRACT Previous oceanographic observations in the southeastern Caribbean suggested high levels of mesoscale variability.
Because of the strong westward mean flow
and because the Caribbean is a semi-enclosed sea, this variability must be formed locally.
A joint observational and numerical modeling study of
mesoscale variability in the southeastern Caribbean Sea was therefore initiated. Satellite-tracked drifters have shown that the variability in the southeastern Caribbean is dominated by mesoscale (about 100 which originate close to the Lesser Antilles passages.
)an
diameter) eddies
The models of Hurlburt
and Thompson (1980, J. Phys. Oceanogr. 10:1611-1651) were adapted to the southeastern Caribbean basin (720 km x 720 km model domain).
The two-layer
model, forced by inflow through the three southern passages and with the most realistic parameters, produced eddies similar to those observed.
A one-mode
reduced gravity model produced nearly identical results, demonstrating the negligible effect of bottom topography on eddy generation and that the eddies form by a horizontal shear instability.
Comparisons between these model
results and linear instability theory were in satisfactory agreement.
1.
INTRODUCTION Semi-enclosed seas such as the Caribbean (Fig. 1 1 , exhibit hydrodynamical
phenmena similar to oceans, but their partial isolation causes differences that are both interesting and useful.
A natural laboratory for the study of
fluid flow exists where strong flows enter seas through narrow passages. Inflow is restricted to a small part of the boundary where it is often concentrated into a narrow and well-defined jet.
At the same time, the partial
300
Figure 1. The Caribbean Sea. Much of t h e flow comprising t h e westward Caribbean Current o r i g i n a t e s i n t h e narrow passages of t h e Lesser A n t i l l e s such as Grenada and S t . Vincent. enclosure of a sea prevents t h e entrance of large eddies from t h e a d j a c e n t ocean.
Strong inflow through t h e narrow passages of t h e southern Lesser
A n t i l l e s (Fig. 2 ) forms such a n a t u r a l l a b o r a t o r y i n t h e s o u t h e a s t e r n Caribbean Sea, where w e have been u s i n g numerical modeling and f i e l d experiments t o study t h e mesoscale (about 100 km) v a r i a b i l i t y t h a t i s generated t h e r e . Flow in t h e Caribbean has long i n t e r e s t e d oceanographers.
Wust ( 1 9 6 4 )
t r a c e d cores of hydrographic p r o p e r t i e s t o d e f i n e a westward flowing Caribbean
c u r r e n t concentrated i n t h e southern t h i r d of t h e sea and e x i t i n g a t t h e Yucatan S t r a i t .
H e used d a t a t h a t w e r e widely s e p a r a t e d s p a t i a l l y and
temporally, b u t t h e g r o s s p a t t e r n t h a t he i n f e r r e d has been confirmed by others.
Gordon (1967) used h i s t o r i c a l hydrographic d a t a from t h r e e d i f f e r e n t
y e a r s and t h e dynamic method t o c o n s t r u c t 5 meridional s e c t i o n s of v e l o c i t y . I n t h e e a s t e r n Caribbean he showed westward speeds of 0.4 t o 0.5 m / s e c a t t h e
core of t h e Caribbean Current, b u t t h e r e w a s some eastward flow i n a l l sections.
Roemmich (1981) used i n v e r s e techniques on h i s t o r i c a l hydrographic
d a t a and obtained a s t r o n g Caribbean c u r r e n t .
H i s a n a l y s i s a l s o suggested
s t r o n g e r s p a t i a l v a r i a b i l i t y near inflow passages t h a n f a r t h e r downstream. Recent a p p l i c a t i o n s of t r a d i t i o n a l methods have used more synoptic data. Febras-Ortega and Herrera (1976) used August 1972 hydrographic d a t a t o i n f e r geostrophic flow i n t h e s o u t h e a s t e r n Caribbean and a d j a c e n t A t l a n t i c Ocean. They noted a meridional a l t e r n a t i o n of eastward and westward flow, superimposed on mean westward c u r r e n t , which they a t t r i b u t e d t o meanders o r countercurrents.
301
Figure 2. The Southeastern Caribbean Sea. me numerical model was designed to simulate the generation of mesoscale variability. in this region. Depths are in meters.
They further conjectured that the complex flow patterns resulted from lee effects of the Lesser Antilles manifest as cyclonic and anticyclonic gyres. Morrison (1977) used meridional sections across the Caribbean to define two branches of the westward-flowing Caribbean Current and two eastward-flowing countercurrents which he believed lie to the north of each westward branch.
Other i n v e s t i g a t o r s concentrated d i r e c t l y oh t h e v a r i a b i l i t y .
Wyrtki,
Magaard and Hager (1976) used s h i p d r i f t measurements from 1900-1972 t o i n f e r mean and eddy k i n e t i c energy of s u r f a c e flow.
Their l o x l D square averaged
r e s u l t f o r t h e North A t l a n t i c showed l a r g e v a l u e s (0.1 m 2 / s e c 2 )
maximum of eddy k i n e t i c energy i n t h e s o u t h e a s t e r n Caribbean.
in a local E a r l i e r Leming
(1971) had used expendable bathythermographs t o suggest t h a t eddies form w e s t of S t . Vincent Passage.
H e suggested t h a t a n t i c y c l o n i c eddies form n o r t h of
t h e passage and cyclonic eddies t o t h e south.
Based on o b s e r v a t i o n s of two
e d d i e s he reported t h a t t h e eddies were confined near t h e s u r f a c e ( 7 5 and 3 0 0
m ) , t h a t they were mesoscale (about 110 km d i a m e t e r ) , and t h a t they formed i n about two weeks.
More r e c e n t l y Molinari e t a l .
(1981) have used s a t e l u t e -
tracked d r i f t e r s t o demonstrate t h a t eddies a r e p r e s e n t over much of t h e Caribbean, i n c l u d i n g t h e southeast.
We e l a b o r a t e on t h e i r most p e r t i n e n t d a t a
i n a l a t e r s e c t i o n on observations.
W e believe t h a t t h e s e o b s e r v a t i o n s and analyses suggest t h a t t h e southe a s t e r n Caribbean i s a region with abundant mesoscale flow v a r i a b i l i t y .
Inter-
p r e t a t i o n of flow f e a t u r e s v a r i o u s l y d e s c r i b e d a s c o u n t e r c u r r e n t s , g y r e s , eddies, and meanders probably r e f e r t o o b s e r v a t i o n s of v a r i o u s s t a g e s of t h e
s a m e process measured with d i f f e r e n t r e s o l u t i o n .
A t l e a s t some of t h e s e
f e a t u r e s were defined s u f f i c i e n t l y t o show t h a t they were too l a r g e (about 100
km) t o have come through t h e passages (less t h a n 4 0 km), b u t must have formed locally.
Apparently many of them formed c l o s e t o t h e passages.
This s u g g e s t s
t h a t t h e eddies a r e p r i m a r i l y a consequence of flow i n s t a b i l i t i e s of t h e c u r r e n t s downstream from t h e A n t i l l e s passages.
Because of t h e geography of
t h e region and because of t h e s t r o n g mean westward flow, w e have t h e advantage of studying t h e formation of t h e mesoscale v a r i a b i l i t y without contamination from e i t h e r t h e North A t l a n t i c (narrow passages) o r t h e western Caribbean ( s t r o n g westward mean), and with t h e f u r t h e r advantage of knowing approximately where formation repeatedly occurs. A combination of numerical modeling and f i e l d experiments has been used t o
address a number of d e s c r i p t i v e and dynamical q u e s t i o n s .
For example, how w e l l
can a simple numerical model s i m u l a t e mesoscale eddies observed i n t h e e a s t e r n Caribbean i n terms of generation l o c a l e , propagation, d i s t r i b u t i o n , diameter, amplitude, p e r i o d , v e r t i c a l s t r u c t u r e , and sense of r o t a t i o n ?
Are t h e eddies
an important component of t h e flow i n t h e o b s e r v a t i o n s and i n t h e models?
What
p h y s i c a l i n s t a b i l i t y mechanisms a r e involved i n t h e formation of t h e eddies? A r e t h e model r e s u l t s c o n s i s t e n t with l i n e a r i n s t a b i l i t y theory?
What i s t h e
i n f l u e n c e of t h e flow through t h e A n t i l l e s passages and of dramatic topographic f e a t u r e s , such a s t h e Aves r i d g e ( F i g . 2 1 , on t h e eddy formation and propagation?
What i s t h e importance of inflow angle and of time-varying inflow
through t h e passages?
What are t y p i c a l l i f e c y c l e s of t h e eddies?
To what
303 e x t e n t do they behave l i k e i s o l a t e d eddies? How nonlinear i s t h e i r propagation?
sive?
p e r s i s t e n t t r a d e winds?
A r e they d i s p e r s i v e o r nondisper-
What i s t h e l o c a l importance of t h e
P a r t i a l answers have been obtained f o r some questions,
while some answers await work t h a t i s i n progress.
In t h i s paper w e concen-
t r a t e on t h e success of t h e model i n generating mesoscale eddies t h a t resemble observations. For t h e numerical modeling, w e use t h e Hurlburt and Thompson (1980) Gulf of
Mexico model adapted f o r use i n t h e Caribbean. b r i e f l y described i n s e c t i o n 2.
These adapted models are
In s e c t i o n 3, w e p r e s e n t s a t e l l i t e - t r a c k e d
d r i f t e r data which show t h e e x i s t e n c e of mesoscale eddies within t h e e a s t e r n Caribbean.
These o b s e r v a t i o n s a r e l a t e r ,'compared with t h e numerical r e s u l t s .
In s e c t i o n s 4 and 5 w e examine t h e r e s u l t s of simulations with one and two a c tive layers. ocean.
We give p a r t i c u l a r a t t e n t i o n t o eddy generation i n t h e upper
The r e s u l t s from t h e s e t w o s i m u l a t i o n s are inter-compared and also
compared t o t h e d r i f t e r t r a c k s .
The p h y s i c a l c h a r a c t e r i s t i c s of t h e eddies
such a s diameter, wavelength, and p e r i o d are examined.
W e then compare t h e s e
c h a r a c t e r i s t i c s q u a l i t a t i v e l y with t h o s e p r e d i c t e d by l i n e a r s t a b i l i t y theory f o r a h o r i z o n t a l shear flow.
Molinari e t a l .
(1981) suggest t h a t topographic
f o r c i n g i s important f o r t h e generation of eddies i n t h e e a s t e r n Caribbean Sea. We p r e s e n t h o r i z o n t a l shear i n s t a b i l i t y of a zonal j e t a s an a l t e r n a t i v e hypothesis.
2.
APPLICATION OF THE NUMERICAL MODEL The numerical models used f o r t h i s p r o j e c t a r e v a r i a n t s of t h e Hurlburt and
Thompson (1980) Gulf of Mexico models.
Hurlburt and Thompson showed t h a t t h e s e
models a r e u s e f u l t o o l s i n studying t h e dynamics of t h e Loop Current and eddy shedding i n t h e Gulf.
These models a r e e f f i c i e n t , and e a s i l y adaptable t o
o t h e r semi-enclosed sea such as t h e Alboran Sea ( P r e l l e r and Hurlburt,
1982)
and t h e Caribbean Sea. The b a s i c assumption f o r t h e use of a model with one or two a c t i v e l a y e r s is t h a t t h e dynamics of t h e flow can be represented by t h e b a r o t r o p i c and f i r s t b a r o c l i n i c modes.
The r e l a t i v e l y s t r o n g s t r a t i f i c a t i o n i n t h e Caribbean Sea
s u g g e s t s t h a t it i s amenable to such i d e a l i z a t i o n s .
The models used here
n e g l e c t thermodynamics and assume t h a t l a y e r s with d i f f e r i n g d e n s i t i e s a r e immiscible.
The h y d r o s t a t i c , Boussinesq and
@-plane approximations are used,
b u t t h e p r i m i t i v e equations and a f r e e s u r f a c e are r e t a i n e d .
Using a r i g h t -
handed coordinate system t h e v e r t i c a l l y i n t e g r a t e d model equations a r e :
a$
+
+
-
f
-
+ (v-vi + Vi-V)vi + kxfGi
= -hiVPi
+ e i + V - V = ~ 0,
+
+
p - l (Ti
-
+ Ti+l)
+
AV2SiI
(1)
304 ,where i = 1 , 2 f o r t h e two-layer model, i = 1 f o r t h e b a r o t r o p i c and reduced g r a v i t y models and
v
a : a: ax + -] ay
= -1
+ -+ Vi = h . v . = h. (uii h
1
1 1
9' = g ( P z
f= f ,
-
PI)P
+
(3)
-1
+ B(Y - Yo)
See Appendix A f o r symbol d e f i n i t i o n s . The reduced g r a v i t y model i s e s s e n t i a l l y a model of t h e f i r s t b a r o c l i n i c mode.
It assumes an a c t i v e upper l a y e r , b u t a lower l a y e r which i s i n f i n i t e l y
deep and a t rest.
Thus, i n t h e reduced g r a v i t y model t h e l o w e r l a y e r momentum
equation degenerates t o gVrl =g'Vhl. For a more complete d e s c r i p t i o n of t h e 1 models and t h e i r numerical formulation, t h e r e a d e r is d i r e c t e d t o t h e o r i g i n a l Hurlburt and Thompson (1980) paper. 2.1
Model domain and boundary c o n d i t i o n s
The domain covered by t h e model extends from t h e Venezuelan s h e l f t o Puerto R i c o (11.5 t o 18ON) and from t h e A n t i l l e a n Arc t o t h e c e n t r a l Venezuelan Basin ( 6 1 . 1 t o 67.6OW)
(see Fig. 1 ) .
The northern,
of t h e model domain have n a t u r a l analogues. S t . Vincent and Grenada passages.
southern, and e a s t e r n boundaries
Flow e n t e r s through t h e St. Lucia,
The western boundary through t h e c e n t r a l
Venezuelan Basin is completely open.
Normal flow a t t h i s boundary i s
self-determined with t h e i n t e g r a l c o n s t r a i n t t h a t t h e n e t mass t r a n s p o r t out from each l a y e r match t h e t o t a l inflow through t h e A n t i l l e s passages.
Any
phenomena o r i g i n a t i n g a t t h e western boundary a r e induced or r e f l e c t e d a r t i f i c i a l l y by t h e open western boundary condition.
Various formulations f o r t h i s
boundary c o n d i t i o n were t e s t e d and it w a s found t h a t f o r our a p p l i c a t i o n ' t h e use of a weak damping boundary l a y e r w a s t h e most e f f e c t i v e a t reducing t h e s e unwanted phenomena.
The f r i c t i o n a l boundary l a y e r employs a l i n e a r drag law
proportional t o velocity.
The drag c o e f f i c i e n t v a r i e s e x p o n e n t i a l l y from zero
a t 150 km from t h e western boundary t o a maximum of
a t t h e boundary.
Because t h e flow i s a r t i f i c i a l l y modified i n t h e westernmost 150
)an
of t h e
b a s i n , t h e s o l u t i o n s i n t h i s region are u n r e a l i s t i c and w i l l not be included i n t h e discussions.
The kinematic and no-slip boundary c o n d i t i o n s a r e a p p l i e d a t
t h e r i g i d boundaries (heavy s o l i d l i n e s , Fig. 3 ) .
305
C
720
1KP1
Figure 3. Caribbean Model Basin and Bottom Topography. Contour i n t e r v a l is 2 0 0 m. The v a l u e s shown are h e i g h t s above a r e f e r e n c e l e v e l ( t h e f l o o r of t h e Venezuelan Basin a t 5000 m d e p t h ) . The heavy l i n e s denote s o l i d boundaries while t h e narrow l i n e s denote open boundaries. 2.2
Inflow boundary c o n d i t i o n s
The inflow through t h e e a s t e r n ports i n t h e model i s s p e c i f i e d based on o b s e r v a t i o n a l data.
The St. Lucia, S t . Vincent and Grenada Passages provide a t
l e a s t h a l f t h e volume t r a n s p o r t t o t h e Caribbean Current and they a r e t h e most important Caribbean passages f o r flow and water p r o p e r t i e s i n t h e upper 1 0 0 0 m (Wust, 1964; Gordon, 1967; S t a l c u p and Metcalf, 1972; Mazeika, Burns and Kinder,
1980a).
Flow through t h e s e t h r e e southern passages profoundly a f f e c t s
t h e flow t o t h e w e s t and t h e s e inflows a r e used t o provide t h e f o r c i n g i n t h e model.
Passages f a r t h e r n o r t h (e.g.
Dominica) and w e s t (e.g.
Mona) a r e
u n l i k e l y t o i n f l u e n c e t h e flow i n t h e s o u t h e a s t e r n Caribbean and a r e not included i n t h e model. The inflow boundary c o n d i t i o n s a r e steady except f o r a spin-up with a time c o n s t a n t of 30 days and a r e based on a review of e x i s t i n g measurements. Experiments with f l u c t u a t i n g inflow w i l l be reported i n a l a t e r paper.
Direct
c u r r e n t measurements have been made by moored c u r r e n t meters, by c u r r e n t meters lowered from s h i p s , and by f r e e - f a l l
(dropsonde) instruments over p e r i o d s from
1 t o 280 days ( S t a l c u p , Metcalf and Zemanovic,
Brooks,
1978; Mazeika, Burns and Kinder,
1971; Burns and Car, 1975;
1980b).
The model inflows were
designed t o produce speeds and volume t r a n s p o r t s compatible with published values.
The mean outflow through t h e Yucatan S t r a i t i s well-established
by t h e
work of N i i l e r and Richardson (1973) (assuming mean Yucatan S t r a i t t r a n s p o r t and mean F l o r i d a S t r a i t t r a n s p o r t a r e e q u a l ) a t 30 x lo6 m3/sec.
I t has
not been e s t a b l i s h e d , however, how t h e matching inflow is shared among t h e v a r i o u s passages.
W e follow Mazeika, Burns and Kinder (1980a) who reviewed
306 t h e l i t e r a t u r e on t r a n s p o r t estimates near t h e Lesser A n t i l l e s and suggested t h a t t h e mean t r a n s p o r t through t h e t h r e e southern passages i s only 15 x lo6 This value i s much lower than t h e S t a l c u p and Metcalf (1972) value
m3/sec.
of 26 x lo6 m3/sec based on lowered c u r r e n t meters, b u t it i s c l o s e t o their free-fall
(dropsonde) measurements (about 15 x
(1981) estimated 22 x lo6 m 3 / s e c
lo6 m3/sec).
f o r a l l passages e a s t of 64OW.
Roemmich W e also
examined direct c u r r e n t measurements f o r speed and d i r e c t i o n , s i n c e t h e k i n e t i c energy and shear depend on v e l o c i t y and not d i r e c t l y on t r a n s p o r t .
Table 1
shows t h e mst r e p r e s e n t a t i v e speeds and d i r e c t i o n s s y n t h e s i z e d from t h e v a r i o u s measurements.
TABLE 1.
Pass age
INFLOW BOUNDARY CONDITIONS
Observations
Model
SPEED DIRECTION (106m3/sec) (m/sec) (OT)
TRANSPORT
TRANSPORT (106m3/sec)
SPEED DIRECTION (m/sec) (OT)
St. Lucia Upper l a y e r Lower l a y e r
1.5 1.5
0.30 0.20
270 270
1.1 .9
0.28 0.10
270 270
S t . Vincent Upper l a y e r Lower l a y e r
3 3
0.60 0.15
310 310
3.6 2.0
0.50 0.15
310
Grenada Upper l a y e r Lower l a y e r
3 3
0.50 0.20
270 270
3.1
1.8
0.27 0.20
270 270
12.5
--
---
Total
15
--
---
The inflow angle i n t h e Grenada and S t . Lucia passhges w a s taken as due
310
West
(2700T), b u t c u r r e n t measurements i n S t . Vincent Passage i n d i c a t e d a flow n o r t h of w e s t ( a s i n g l e exception is a c u r r e n t meter r e c o r d taken w i t h i n 30 m of t h e bottom).
These not only included t h e moored c u r r e n t meters, lowered c u r r e n t
meters, and dropsondes, b u t a l s o d r i f t e r t r a c k s j u s t w e s t of t h e Passage ( F i g s . 4-6).
W e o f f e r no explanation f o r t h i s p e r s i s t e n t northward flow component,
b u t n o t e t h a t it may s i g n i f i c a n t l y i n f l u e n c e t h e r e s u l t i n g flow downstream. The a c t u a l model inflow c o n d i t i o n s w e r e s e l e c t e d by assuming t h a t upper l a y e r v e l o c i t y was most c r i t i c a l , followed by t o t a l t r a n s p o r t .
The h o r i z o n t a l
p r o f i l e a t t h e port w a s s p e c i f i e d as uniform because a c t u a l p r o f i l e s a r e n o t well-known
( e s p e c i a l l y i n S t . Vincent Passage) and because t h e model has few
g r i d p o i n t s to d e f i n e t h e p r o f i l e i n t h e p o r t s .
Work t o examine t h e e f f e c t of
t h e p r o f i l e , which Nof (1978) a r g u e s is important, i s planned.
Because t h e
model port geometry was s e l e c t e d independently t o match t h e passage geometry, s e l e c t i n g t h e upper l a y e r v e l o c i t y and t o t a l t r a n s p o r t t h u s s p e c i f i e d v e l o c i t y and t r a n s p o r t i n both l a y e r s f o r each port ( d i r e c t i o n s were t h e same i n both The maximum model speeds a r e a l i t t l e lower than t h e o b s e r v a t i o n s
layers).
because t h e o b s e r v a t i o n s tended t o be near t h e higher speed core of t h e inflow. Our t r a n s p o r t s are s e l e c t e d towards t h e lower e s t i m a t e s because t h i s permits
numerical s t a b i l i t y a t longer t i m e s t e p s and reduces t h e c o s t of t h e computations.
2.3
Bottom topography
I d e a l i z e d bottom topography was used i n t h e two-layer
experiments.
The
bottom topography f o r t h e r e c t a n g u l a r model domain,.described above was d i g i t i z e d a t about a 10-20 km i n t e r v a l from Naval Oceanographic O f f i c e c h a r t s , i n t e r p o l a t e d t o 7.5 km, and smoothed t o e l i m i n a t e two-grid-length The r e s u l t i n g model topography i s shown i n Fig.
3.
variations.
The algorithm used f o r t h e
numerical s o l u t i o n does not allow i s l a n d s , so t h e A n t i l l e s a r e represented a s t h e minimum model depth (500 m )
.
We j u s t i f i e d t h e "sunken i s l a n d s " a
p o s t e r i o r i by n o t i n g t h a t t h e t o t a l flow over t h e s e regions of minimum depth was a small f r a c t i o n of t h e t o t a l flow i n t h e model.
W e made no attempt t o
i n c l u d e r e a l i s t i c topography i n t h e western t h i r d of t h e model domain.
Depth
contours t h e r e w e r e purposely s t r a i g h t e n e d t o reduce t h e e f f e c t s of t h e open boundary.
2.4
Model v a l i d a t i o n tests
Before t h e v a l i d i t y of t h e model r e s u l t s can be accepted, t h e s e n s i t i v i t y of t h e model t o changes i n t h e numerical design (e.9.
s e n s i t i v i t y t o changes i n
such non-physical parameters a s t h e t i m e s t e p , g r i d spacing, east-west b a s i n e x t e n t , spin-up time, open boundary condition s p e c i f i c a t i o n , and eddy v i s c o s i t y ) must be t e s t e d .
A series of experiments was conducted t o determine
t h e parameters f o r our s t a n d a r d c a s e s and t o determine t h e parameter range f o r which reasonable changes i n t h e numerical design d i d not s i g n i f i c a n t l y a l t e r t h e physical solutions.
Table 2 lists t h e most s i g n i f i c a n t model v a l i d a t i o n
experiments and c o n t a i n s b r i e f comments on t h e r e s u l t s . The parameters f o r t h e p i v i t o l experiment w e r e s e l e c t e d following t h i s
series of experiments and are presented i n Table 3.
The values of g'
and H1
w e r e chosen based on an envelope of d e n s i t y p r o f i l e s derived from CTD d a t a taken i n t h e Grenada Basin (Teague, 1979). S e l e c t i o n of t h e eddy v i s c o s i t y r e q u i r e d p a r t i c u l a r care.
For our purpose,
t h e eddy v i s c o s i t y must be l a r g e enough t o c o n t r o l t h e enstrophy cascade, b u t small enough so t h a t t h e damping t i m e s c a l e f o r t h e primary eddies i s much longer than t h e t i m e f o r them t o develop and propagate a c r o s s t h e model domain.
308
TRBLE 2 .
MODEL VALIDATION EXPERIMENTS
PARAMTER DIFFERENCES
FROH TABLE 3
TO TEST EFFECT OF:
COIMENTS
1
(Standard Case)
Standard Case
R e a l i s t i c eddies. no r e f l e c t e d (eastward p r o p a g a t i n g ) waves. Minimal s m a l l s c a l e v a r i a b i l i t y . Generally ! acceptable r e s u l t s .
2
No F8L ( F r i c t i o n a l Boundary Layer). tspin-up =10 days. A-200
Changer i n spin-up tme
S o l u t i o n s contaminated by r e f l e c t e d waves ( u n a c c e p t a b l e ) .
3
No FBL, A=200
Open boundary condition with d i f f e r e n t values of eddy v i s c o s i t y
G e n e r a l l y good o v e r a l l r e s u l t s w i t h only s l i g h t indication of r e f l e c t e d naves. S o l u t i o n s a c c e p t a b l e b u t not completely satisfactory.
4
N
5
No FBL. A=50
Increased v e f l e c t e d wave a m p l i t u d e over Cases X3 L 0 So1u t i on m a r g i n a l l y acceptable.
6
No FBL. A.25
S i g n i f i c a n t r e f l e c t e d waves. S o l u t i o n contaminateb.
J
No FBL *ester;
8
No FBL. A-200.
9
No FBL. A-200. XL=9M) km tspin.up=10 days
TASE
0
Same as Case X3
FBL
A=200 bounddry
tsp,n.up=10
-0
at
YL=900km
days, A=200,
B~ =90 km = km
Change i n s p e c i f i c a t i o n of t a n g e n t i a l v e l o c i t y d t open boundary
S i g n i f i c a n t r e f l e c t e d waves a f t e r 90-100 days Solutions contaminated.
I n c r e a s i n g E-W extent
R e s u l t s same as Case X3 i n cornon b a s i n a r e a Results S ~ M as Case X2 i n common b a s i n a ~ e a
F r i c t i o n a l boundary l a y e r S h o r t spin-up
S i g n i f i c a n t r e d u c t i o n of r e f l e c t e d nave over Case 6 2 . R e s u l t s s i m i l a r t D Case X3.
FBL W i t h v a r i o u s values o f eddy v i s c o s i t y and boundary l a y e r (EL) t h i ckness
Low t o moderate a m p l i t u d e r e f l e c t e d waves p r e s e n t . S o l u t i o n s contaminated.
11
A-25. B,
12
1\=25
FBL w i t h v a r i o u s v a l u e s o f eddy viscosity
S i g n i f i c a n t r e d u c t i o n of r e f l e c t e d waves i i v w Case 111. No apparent c o n t a m i n a t i o n due 10 e a s t u a i d p r o p a g a t i n g naves. R e s u l t s s i m i l a r t o Case X I b u t w i t h sow i n d 7 c a t i o n of small s c a l e V a r l a b i 1 1 t y .
13
1.50
FBL With v a r i o u s v a l u e r o f eddy visrosity
Same a s Case Y12 b u t w i t h a r e d u c t i o n i n small s c a l e variabi I i t y .
Chanqe i n draO rwffirient
No s i g m f i c a n t d i f f e r e n c e f r m Case 113.
CD-? 0 x 10.'
14
A.50.
15
X L ~ 1 5 0 0 kill. 4.50
lnrrearlnq E - h extent
R e s u l t s same as Care b13 I " cormion h a s i n are3 D i i t r l d e FBL.
Df
309
PARAMETER DIFFERENCES
casr
FROM TABLE 3
16
XL.900
17
XL=900 km
R e s u l t s same a s Case 4 1 I " c m o n b a r i n w e d outride o f FBL.
18
XL=IMO h
Results
19
YL=36O km")
20
YL-360 h( 't-314 h r
TO
TESl EFFECT OF:
km, PI-50
CONMCNTS R e s u l t s same as Case 113 i n commn b a s i n area O u t s i d e of FBL .
same as Care # I I n c m n b a s i n area outside o f
FBL.
11)
".
bx*by=3.75 km.
A
G e n e r a l l y r e s u l t s similar t o Case # I . b u t w t h s l i g h t l y s m a l l e r d i a m e t e r eddies. s l i g h t l y faster p r o p a g a t i o n speeds and only t h e n a r t h e i n a n t i - c y c l o m c and c e n t r a l cyclonic eddies present.
Reducing g r l d s p a c i n g and time step
R e s u l t s S a m ar Case 119
N o r t h I S o u t h e x t e n t of b a s i n c e n t e r e d on central port.
I n f l o w t h r o u g h c e n t r a l p o r t only.
TABLE 3 .
Reducing N-S e x t e n t . Compare w i t h Case #20.
MODEL PARAMETERS FOR STANDARD CASE
R = 2 . 2 4 x 10-1 m-ll sec
= 100 m2 sec-l
fo
-
4
= 9 . 8 m sec-2
4'
= 0.03
Hl
= 250 m
b y = 7.5 km 11)
H2
= 4750 m
A t = 1.5 h r
tspin-up V0"tflC.W
~
sec-l
2.9
m sec-'
bX
by YL
o
= 7.5 km ( I '
BL = 150 km
30 days
XL
= lo3 kq m-'
:=
cD
= 0 121
Domain S i z e ,
D
=
=
IO-'
7 2 0 x 7 2 0 km
11) For each dependent variable 12) 1 / 2 g r i d point outside t h e o u t f l o w boundary
310 The value of t h e eddy v i s c o s i t y was v a r i e d from A = 25 t o 200 m2/sec. Although t h e model w a s s t a b l e a t values a s low a s A = 25 m2/sec,
w e found
t h a t below A = 100 m2/sec h o r i z o n t a l f e a t u r e s s m a l l e r than t h e design Also, t h e t e s t s
r e s o l u t i o n of t h e g r i d (approximately 10 Ax) were p r e s e n t .
revealed t h a t even with A = 2 0 0 m2/sec t h e f e a t u r e s with h o r i z o n t a l l e n g t h s c a l e a t o r above t h e design r e s o l u t i o n s c a l e were not s i g n i f i c a n t l y d i f f e r e n t Therefore, A = 100 m2/sec was chosen a s
from those with A = 1 0 0 m2/sec.
t h e standard value f o r t h e eddy v i s c o s i t y . The standard d u r a t i o n of a model experiment was one year.
The model
r e q u i r e d approximately four t o f i v e months t o reach a quasi-steady r e g u l a r eddy shedding ( s e e Fig.
10).
s t a t e with
A one year model i n t e g r a t i o n allowed a t
l e a s t s i x eddy shedding c y c l e s a f t e r t h e model reached s t a t i s t i c a l equilibrium. The reduced g r a v i t y s t a n d a r d case was run f o r an a d d i t i o n a l year t o v e r i f y t h a t s t a t i s t i c a l e q u i l i b r i u m was achieved a f t e r s i x months.
3.
OBSERVATIONS OF EDDIES BY D R I F T I N G BUOYS D r i f t i n g s u r f a c e buoys which follow shallow c u r r e n t s have been used i n t h e
s o u t h e a s t e r n Caribbean.
These s u r f a c e buoys were l o c a t e d by s a t e l l i t e and
t h e i r t r a c k s showed shallow c u r r e n t f e a t u r e s with p e r i o d s exceeding two days and with s i z e s l a r g e r than about 2 0 km.
S p a t i a l s c a l e s and v a r i a b i l i t y
p a t t e r n s derived from d r i f t e r t r a c k s were used t o check model v a l i d i t y . D r i f t e r s were deployed both by R.
Molinari of t h e National Oceanic and
Atmospheric Administration ( N O A A ) and by us ( N O R D A ) and t h e techniques used were e s s e n t i a l l y i d e n t i c a l .
A small s u r f a c e buoy w a s t r a c k e d by t h e Random
Access Measurement System of t h e NIMBUS-G
satellite.
Windowshade drogues
centered a t e i t h e r 3 0 m ( N O A A ) or 100 m (NORDA) depth ensured t h a t t h e d r i f t e r c l o s e l y followed water motion.
This s y s t e m provided about two u s e f u l p o s i t i o n s
d a i l y with an accuracy of about 5 km, so t h a t t h e d a i l y speeds of t h e d r i f t e r s were a c c u r a t e t o about 0.05 m/sec.
E d i t i n g removed t h e worst p o s i t i o n s (based
on a c r i t e r i o n of excess speed, 2.5 m/sec f o r NOAA and 2.0 The NOAA d a t a were a l s o smoothed. Molinari e t a l .
m/sec
f o r NORDA).
(1981) r e p o r t on t h e i r e n t i r e
d a t a s e t , d e s c r i b e t h e technique more completely, and list s e v e r a l r e f e r e n c e s t h a t d i s c u s s windage and o t h e r e r r o r sources. A t o t a l of
15 d r i f t e r s were r e l e a s e d near t h e passages i n 3 d i f f e r e n t
deployments during October 1975, January 1976, and November 1977.
A l l but one
d r i f t e r continued transmission u n t i l leaving t h e a r e a ( a r b i t r a r i l y defined a s p a s s i n g westward of 64% o r northward of 16%).
D r i f t e r s remained w i t h i n
t h e a r e a f o r p e r i o d s ranging from 3 t o 76 days and moved with s c a l a r speeds of
0 . 2 t o 0.9 m/sec.
Speeds were higher during t h e w i n t e r (January 1976)
deployment t h a n during t h e two f a l l (October 1975 and November 1977) deployments ( a s c a l a r mean of 0.6 m/sec versus 0.3 m/secl,
b u t part of t h i s
d i f f e r e n c e may have been caused by t h e d i f f e r e n t drogue depths.
Eddies
encountered by t h e d r i f t e r s s t r o n g l y a f f e c t e d d r i f t e r v e l o c i t i e s , and an eddy was encountered during each deployment (Table 4 ) .
TABLE 4.
EDDIES OBSERVED BY DRIFTERS I3j
Number of D r i f t e r r i n Eddy
Deploynmt
Number o f Loops Around Eddy
Sense o f Rotation
Diametb:'
Drift
(km)
(m/sec.'T)
(41 Swirl
(mlrecj
October 25-26 1 9 7 5 NOAA 4 drifters (I) 30 m drogues
3
5.5
anticyclonic
60
0.1. 230
0.3
January 20-23 1976 NORA 6 drifters 30 m drogues
1
1
cyclonic
90
O.?.
0
Novem~er 12-15 1977 NORDA 4 drifters 100 m drogues
1
11)
Buoy
ID 343
4
330
2.5
anticytlonic
KO
0.1.
0.2
290
f a i l e d a f t e r 4 days and I S n o t i n c l u d e d .
(il E q t i l v a l e n t diameter d e f i n e d as t w i c e t h e square r o o t of t h e p r o d u c t of t h e major and semi-minor axes of t h e l a r g e s t d r i f t e r l o o p . e s t i m a t e because o f d r i f t e r k i n e m a t i c s .
(3)
Speed and d i r e c t i o n o f eddy movment
ICI
S c a l a r speed o f d r i f t e r w h i l e e n t r a i n e d in eddy
Semi-
T h i s i s orobably a mimnum
During t h e October 1975 deployment t h r e e d r i f t e r s encountered an anticyc l o n i c eddy about 200 km northwest of S t . Vincent Passage (Fig. 4 ) .
Drifter
1417 ( d r i f t e r s a r e i d e n t i f i e d by t h e i r assigned s a t e l l i t e channel) completed
only h a l f a circumference, b u t 1421 c i r c l e d t h e eddy once and 1450 made four complete loops and w a s still i n t h e eddy when it passed 64%.
Because of i t s
entrainment i n t h e eddy, buoy 1450 had t h e l o n g e s t residence time ( 4 2 days) but h i g h e s t s c a l a r speed ( 0 . 9 m/sec) of t h e deployment.
312
Figure 4. Buoy t r a j e c t o r i e s during NOAA October 1975 deployment. Note t h e a n t i c y c l o n i c eddy near 15ON 62.5OW, e s p e c i a l l y t h e t r a c k of buoy 1450. Underlined numbers a r e buoy i d e n t i f i c a t i o n s and t h e o t h e r numbers along t h e t r a c k s a r e J u l i a n days.
Buoy 610, launched i n January 1976, a l s o d e t e c t e d an eddy with one c y c l o n i c loop south of t h e S t . Vincent Passage inflow (Fig. 5).
The buoy may have
remained i n t h e eddy u n t i l it reached t h e 64OW meridian, but t h i s i s u n c e r t a i n . This buoy had t h e l o n g e s t residence t i m e (23 days) b u t , u n l i k e buoy
313
Figure 5. Buoy trajectories during NOAA January 1976 deployment. Note the cyclonic eddy near 1 4 O N 62.5OW. Underlined numbers are buoy identifications and the other numbers along the tracks are Julian days.
1450 in October, this buoy also had the lowest scalar mean (0.4 m/sec) of the deployment.
The relatively low scalar mean occurred in part because the other
buoys were apparently located near the core of a westward current through one of the passages.
Buoys 516, 626, and 1126 downstream of the St. Vincent and
St. Lucia passages averaged nearly 0.5 m/sec.
Buoys 657 and 1161 downstream of
314 t h e Grenada p a s s a g e a v e r a g e d almost 0.7 m/sec. During t h e November 1977 deployment buoy 1600 c o m p l e t e d t w o l o o p s a r o u n d a n a n t i c y c l o n i c eddy s o u t h w e s t of S t . V i n c e n t I s l a n d ( F i g . 6).
Along w i t h buoy
610 i n J a n u a r y , t h i s buoy had t h e l o n g e s t r e s i d e n c e time ( 7 6 d a y s ) and l o w e s t
scalar mean (0.17 m / s e c ) o f t h e deployment.
F i g u r e 6. Buoy t r a j e c t o r i e s d u r i n g NORDA November 1977 deployment. Note t h e a n t i c y c l o n i c eddy n e a r 1 3 O N 62OW. U n d e r l i n e d numbers are buoy i d e n t i f i c a t i o n s and t h e o t h e r numbers a l o n g t h e t r a c k s are J u l i a n days.
316 The two m o s t e n e r g e t i c eddies, t h e a n t i c y c l o n i c eddy north of t h e S t . Vincent Passage inflow ( F i g . 4 ) and t h e cyclonic eddy south of t h e S t . Vincent Passage inflow (Fig. 5 ) were c o n s i s t e n t with Leming's ( 1 9 7 1 ) hypothesis t h a t a n t i c y c l o n i c ( c y c l o n i c ) e d d i e s form n o r t h ( s o u t h ) of t h e passage.
The northern
a n t i c y c l o n i c eddy appeared t o be more e n e r g e t i c than t h e inflow through S t . Lucia and S t . Vincent Passages, while t h e southern cyclonic eddy seemed s l i g h t l y less e n e r g e t i c .
The a n t i c y c l o n i c eddy revealed i n 1977 (Fig. 6 ) was not
c l e a r l y a s s o c i a t e d with an inflow c u r r e n t , and a l l four 1977 d r i f t e r s showed low speeds.
Taken t o g e t h e r , t h e d r i f t e r d a t a suggest t h a t mesoscale eddies a r e
common i n Grenada Basin ( t h r e e of t h r e e d r i f t e r deployments d e t e c t e d an eddy), and t h a t t h e presence of an eddy profouhdly i n f l u e n c e s t h e shallow flow.
4.
'IWO-LAYER 4.1
SIMULATION
Two-layer model r e s u l t s
W e begin our d i s c u s s i o n of t h e case s t u d i e s by p r e s e n t i n g t h e r e s u l t s of t h e
most r e a l i s t i c model p o s s i b l e w i t h i n t h e framework of t h e two-layer system. T h i s i s t h e two-layer model with t h e i d e a l i z e d bottom topography ( F i g . 3 ) and t h e b e s t e s t i m a t e s of t h e inflow through t h e e a s t e r n passages (Table 1 ) . parameters f o r t h i s case are shown i n Table 3.
The
Following t h e a n a l y s i s of t h e s e
r e s u l t s we w i l l examine t h e r e s u l t s of simpler models with one v e r t i c a l mode and use them t o e l u c i d a t e t h e dynamics i n t h e two-layer model.
This f i r s t case
w i l l be r e f e r r e d t o a s t h e "Two-layer Standard Case", and i t w i l l be t h e experiment t o which a l l o t h e r s a r e compared.
The inflow t r a n s p o r t f o r t h i s
case i s steady except f o r a spin-up with a 30-day time constant. I n Fig.
7, we p r e s e n t a sequence of synoptic views of t h e pycnocline height
anomaly a t 8-day i n t e r v a l s .
The pycnocline h e i g h t anomaly (PHA) i s t h e
d e v i a t i o n of t h e l a y e r i n t e r f a c e from i t s f l a t p o s i t i o n
a t 250 m depth.
The
contour i n t e r v a l f o r t h e PHA i s 5 m and p o s i t i v e contours r e p r e s e n t downward d e v i a t i o n s ( i n c r e a s e d t h i c k n e s s of t h e upper l a y e r ) .
This sequence d e p i c t s a
t y p i c a l eddy shedding c y c l e with t h e following s a l i e n t f e a t u r e s :
a meandering c u r r e n t emanating from t h e S t . Vincent passage, a meandering c u r r e n t emanating from t h e Grenada passage, a n t i c y c l o n i c eddies forming i n t h e northern Grenada Basin which propagate westward, cyclonic eddies forming south of t h e S t . Vincent inflow c u r r e n t which propagate west-southwestward, a n t i c y c l o n i c eddies forming i n t h e southeastern Grenada Basin which propagate west-northwestward
and merge with t h e northern
a n t i c y c l o n i c eddies, and a suggestion of a boundary c u r r e n t along t h e e a s t e r n and n o r t h e r n boundaries.
316
Figure 7. Pycnocline Height Anomaly (FHA) for the two-layer standard case. The contour interval is 5 m and the time interval between synoptic views is 8 days. This sequence shows a typical eddy shedding cycle starting at day 230.
317 W e a l s o note t h a t when t h e eddies f i r s t develop, t h e i r diameters a r e comparable t o t h e r a d i u s of deformation, Q , i n t h e model. = ( 9‘H)‘/f,
Rossby r a d i u s ,
The i n t e r n a l
v a r i e s from about 97 km a t t h e l a t i t u d e of
Grenada Passage t o about 8 0 km a t S t . Vincent based on t h e parameters i n Table 3. The upper and lower l a y e r p r e s s u r e f i e l d s ( n o t shown) demonstrate t h a t t h e e d d i e s observed i n t h e synoptic views of PHA a r e p r e s e n t i n t h e upper l a y e r but a r e absent from t h e lower l a y e r .
Also t h e meandering westward c u r r e n t s (from
S t . Vincent and Grenada passages) a r e not v i s i b l e i n t h e lower l a y e r but a r e confined t o t h e upper l a y e r .
In t h e lower l a y e r a mean boundary c u r r e n t flows
along t h e s l o p e near t h e e a s t e r n and nork’hern boundaries (Fig. 8 ) . also Basin.
There i s
evidence of a cyclonic c i r c u l a t i o n i n t h e lower l a y e r of t h e Grenada A b a r o t r o p i c experiment developed a s t e a d y - s t a t e
to t h e l o w e r l a y e r mean i n t h e two-layer model.
flow which was s i m i l a r
Roemmich (1981) i n f e r r e d a
s i m i l a r deep cyclonic c i r c u l a t i o n f o r t h e Venezuelan Basin ( w e s t of t h e Aves Ridge) based on hydrographic data.
The deep c i r c u l a t i o n appears t o follow t h e
f / h contours of t h e topography a s expected from conservation of p o t e n t i a l vorticity.
0
IKNl
720
Figure 8 . Lower Layer Mean P r e s s u r e anomaly ( P ) bas d on a six-month p e r i o d (days 180 t o 3 6 0 ) . The contour i n t e r v a l i s 0.035 1i/m
9.
4.2
Comparison of model r e s u l t s t o d r i f t e r observations
Examining Fig. 7 more c l o s e l y we can r e l a t e t h e eddies observed i n t h e model s o l u t i o n s t o t h e eddies observed with t h e s a t e l l i t e tracked d r i f t e r s . In Fig. 4
318 w e see an a n t i c y c l o n i c eddy northwest of S t . Vincent passage ( i n t h e Figure 7a, shows t h e development of
northwestern p a r t of t h e Grenada Basin). an a n t i c y c l o n i c eddy i n t h e s a m e area.
Both t h e observed and t h e model eddies
d r i f t westward. The cyclonic eddy which forms j u s t south of t h e c u r r e n t emanating from t h e S t . Vincent passage ( F i g . 7 a , b ) and t h e c y c l o n i c eddy d e t e c t e d by buoy 610 i n Fig.
5 , a l s o have s i m i l a r p o s i t i o n s and d i r e c t i o n s of propagation.
The model
eddy has a diameter of approximately 75 t o 100 km which i s comparible t o t h e observed eddy (see Table 4).
The a n t i c y c l o n i c eddy i n t h e s o u t h e a s t e r n Grenada
Basin d e l i n e a t e d by t h e d r i f t i n g buoy 1600 (Fig. 6 ) a l s o has a comparable analogue in t h e numerical s o l u t i o n (Fig. 7 c , d , f ) .
4.3
I n s t a b i l i t y mechanism
A preliminary a n a l y s i s of t h e e n e r g e t i c s f o r t h e upper and lower l a y e r flow
f i e l d s revealed no evidence of b a r o c l i n i c i n s t a b i l i t y f o r t h e s t a n d a r d case parameters.
The dominant energy t r a n s f e r was from k i n e t i c energy of t h e mean
flow t o eddy k i n e t i c energy and occurred i n t h e upper l a y e r .
This suggests
t h a t t h e eddies r e s u l t from a h o r i z o n t a l shear i n s t a b i l i t y of t h e f i r s t i n t e r n a l mode, a "barotropic" i n s t a b i l i t y . The upper and lower l a y e r flows i n t h i s experiment are n e a r l y decoupled. T h i s suggests t h a t t h e simpler and l e s s expensive models with a s i n g l e v e r t i c a l mode should be u s e f u l t o i n v e s t i g a t e t h e dynamics of t h e flow.
In p a r t i c u l a r
w e use t h e reduced g r a v i t y model t o study t h e eddy shedding downstream of t h e passages because t h e eddies are trapped near t h e s u r f a c e and not s u b s t a n t i a l l y influenced by t h e topography.
The low c o s t of t h i s model p e r m i t s us t o conduct
numerous numerical experiments with d i f f e r e n t model parameters and e x t e r n a l forcing.
5.
REDUCED GRAVITY SIMULATIONS
5.1
Model r e s u l t s
The reduced g r a v i t y model is used t o s i m u l a t e t h e f i r s t b a r o c l i n i c mode.
It
c o n t a i n s an a c t i v e upper l a y e r and a lower l a y e r which i s i n f i n i t e l y deep and quiescent. I n Fig. 9 w e p r e s e n t s y n o p t i c views of t h e PHA f o r a t y p i c a l eddy shedding c y c l e from t h e reduced g r a v i t y standard c a s e (based on a p p r o p r i a t e parameters from Table 3).
Here t h e PHA can be used d i r e c t l y t o i n f e r t h e upper l a y e r flow
f i e l d , s i n c e t h e lower l a y e r i s quiescent. Comparing Fig.
9 t o Fig. 7, w e see t h e same upper l a y e r f e a t u r e s a s
described f o r t h e two l a y e r simulation.
Although t h e match i s n o t p e r f e c t , t h e
i n t e n s i t i e s , l o c a t i o n s of eddy formation, d i r e c t i o n s of propagation, and eddy shedding p e r i o d s a r e s i m i l a r , l e n d i n g credence t o t h e hypothesis t h a t t h e
319
Fi’qure 9 . Pycnoclfne Height Anomaly (PHA) for the reduced gravity standard case. The contour interval is 5 m and the time interval between synoptic views is 8 days. This sequence shows a typical eddy shedding cycle starting at day 310.
reduced g r a v i t y model can be used t o e l u c i d a t e t h e dynamics of t h e dominant mesoscale phenomena. Figure 9a c l e a r l y shows t h e t h r e e primary t y p e s of eddies ( t h e n o r t h e r n and southern a n t i c y c l o n i c eddies and t h e cyclonic eddy forming south of t h e S t . Vincent passage).
Figure 9b shows t h a t t h e two a n t i c y c l o n i c eddies have
propagated westward and t h e southern eddy appears t o be merging with t h e Also in t h i s s y n o p t i c view a c y c l o n i c eddy i s about t o s e p a r a t e
n o r t h e r n one.
from t h e e a s t e r n boundary.
Figure 9c r e v e a l s t h a t t h e cyclonic eddy has
detached and i s propagating west-southwestward
m/sec.
Figures 9d and e show t h e
a t a speed of approximately 0.1
development of t h e n e x t set of a n t i c y c l o n i c
eddies and t h e beginning of t h e next cyclonic eddy.
F i n a l l y , i n Fig."9f,
we
see t h e next cyclonic eddy about t o be shed. Figure 10 shows north-south c r o s s - s e c t i o n s of PHA
VS.
t i m e a t three
d i f f e r e n t l o n g i t u d e s 40, 120, and 360 km w e s t of t h e e a s t e r n boundary. months a r e r e q u i r e d f o r t h e model t o reach s t a t i s t i c a l equilibrium.
Six
The
i n i t i a l Rossby wave f r o n t can e a s i l y be t r a c k e d a c r o s s t h e b a s i n and it i s apparent t h a t well-defined westward c u r r e n t s e x i s t only a f t e r t h e passage of t h i s front.
The meandering of t h e s e c u r r e n t s and t h e a s s o c i a t e d eddies a r e
e v i d e n t f i r s t i n t h e western b a s i n and l a t e r i n t h e e a s t e r n basin.
This
i n d i c a t e s t h a t t h e f i r s t p e r t u r b a t i o n s on t h e stream grow more slowly a s they propagate downstream than do those which follow them.
This i s evidence t h a t
meanders downstream i n c r e a s e t h e growth rate of new ones forming upstream, an important f i n i t e amplitude e f f e c t i n t h e s e r e s u l t s .
Figure 1Oa i s a
north-south c r o s s - s e c t i o n 4 0 km w e s t of t h e inflow boundary.
Here w e see
n e a r l y s t e a d y c u r r e n t s j u s t downstream from t h e t h r e e a c t i v e passages, although
w e see clear evidence of t h e formation of t h e c y c l o n i c eddies south of t h e St. Vincent inflow.
T h i s f i g u r e a l s o suggests t h e presence of a weak permanent
a n t i c y c l o n i c c i r c u l a t i o n between t h e southern (Grenada) and c e n t r a l ( S t . Vincent) inflow ports. Figure 10b i s a s e c t i o n through t h e c e n t e r of Grenada Basin ( 1 2 0 km w e s t of t h e inflow boundary).
It shows t h e presence of a l l t h r e e types of e d d i e s and
permits a good estimate of t h e eddy shedding p e r i o d , which i s approximately 35 days.
W e a l s o note t h a t t h e two northernmost c u r r e n t s , (i.e.
t h e weak one
emanating from St. Lucia passage and t h e s t r o n g one from S t . Vincent passage) have merged i n t o one c u r r e n t . F i n a l l y i n Fig.
10c. a s e c t i o n through t h e c e n t e r of t h e model b a s i n (360 km
w e s t of t h e inflow boundary), w e s e e t h a t t h e two a n t i c y c l o n i c eddies have merged and t h a t t h e northern one has continued to i n t e n s i f y . has propagated west-southwestward northward (see Fig. 9 ) . t h e c e n t r a l current.
The c y c l o n i c eddy
and has d e f l e c t e d t h e southernmost c u r r e n t
Furthermore, t h e southernmost c u r r e n t has merged with
321
7
720
1
I
I
l
l
I
I
[KMI
0 0 I 2 3 4 5 6 7 8 9 1011 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 M0N
,
I
,
[<Mi
0 0 1 2 3 4 5 6 7 8 9 l o l l 12131415161718192021222324 MON
IKHI
G
0 i 2 3 4 5 6 7 8 9 lO11121314151617l8192021222324 M0N
Figure 10. North-south cross-sections PHA VS. time for reduced gravity standard case: a) 40 )an downstream of the inflow ports, b) through the center of the Grenada Basin ( 1 2 0 km downstream of the inflow boundary), and c) through the center of the model basin (360 km downstream of the inflow boundary). The contour interval is 5 m.
322 Wust (19641, Gordon ( 1 9 6 7 ) and Roemich ( 1 9 8 1 ) i n f e r r e d a westward flowing Caribbean c u r r e n t concentrated i n t h e southern t h i r d of t h e basin.
Figure 10
s u p p o r t s t h e i d e a of a s i n g l e c u r r e n t but shows s t r o n g v a r i a b i l i t y i n t h e flow. A six-month
mean of t h e upper l a y e r flow ( F i g . 1 1 ) shows a merger of t h e
inflows i n accord with t h e t r a d i t i o n a l image.
.... .. . . ., . .. :, :, ,.., '., .. . . .. ., . . ... . ... . ... . .. .
~
I
. I
I
. . .: ..: :.. ,
.
. .
I
: :
.. . :.
............... .
. . ....... ... ..............................
.......
...
1
(KMI
0
720
Figure 11. Upper Layer Mean P r e s s u r e Anomaly ( P I ) based on a six-month p e r i o d (days 180 to 3 6 0 ) . The contour i n t e r v a l i s 0.07 N/m2 and t h e contour l a b e l s a r e s c a l e d by l o 3 .
5.2
Comparison t o l i n e a r s t a b i l i t y of a h o r i z o n t a l s h e a r flow
I t i s c l e a r l y e v i d e n t , from Figs.
9 and 10 t h a t t h e eddies are growing spa-
t i a l l y and temporally a s they propagate downstream.
These eddies a p p a r e n t l y
form as a r e s u l t of h o r i z o n t a l s h e a r i n s t a b i l i t i e s , as i n d i c a t e d by t h e s i m i l a r i t y of t h e s o l u t i o n s f o r t h e reduced g r a v i t y model and f o r t h e upper l a y e r of t h e two-layer model, and by t h e type of mean t o eddy energy t r a n s f e r , 2.e. k i n e t i c energy of t h e mean flow t o k i n e t i c energy of t h e eddies. I n s t a b i l i t i e s of c u r r e n t s i n t h e ocean and atmosphere have been i n v e s t i g a t e d f o r decades.
W e attempt t o relate some of t h e r e s u l t s from t h e s e i n v e s t i g a -
t i o n s , based on l i n e a r , normal-mode
results.
s t a b i l i t y a n a l y s i s , to t h e p r e s e n t model
Early s t u d i e s of i n s t a b i l i t i e s i n t h i s c o n t e x t w e r e done by Kuo
(19491, Charney ( 1 9 4 7 ) and Eady ( 1 9 4 9 ) .
Numerous o t h e r s t u d i e s have followed,
and Killworth (1980) has published a more o r less u n i f i e d treatment of barot r o p i c and b a r o c l i n i c i n s t a b i l i t y i n u n i d i r e c t i o n a l , of t h e s e s t u d i e s s h a r e a common foundation. on quasigeostrophic dynamics (e.g.
Most
geophysical flows.
The r e l e v a n t e q u a t i o n s are based
Pedlosky, 1964).
An unbounded flow
is
assumed along t h e a x i s of t h e mean c u r r e n t .
The s t a b i l i t y of t h e system t o
plane wave p e r t u r b a t i o n s as a f u n c t i o n of various nondimensional parameters i s t h e n determined.
Unstable modes a r e t h o s e which grow exponentially i n time a l l
along t h e a x i s of t h e flow.
For t h e moment w e adopt t h e viewpoint t h a t t h e S,t. Vincent inflow i s a westward j e t i n a r o t a t i n g , s t r a t i f i e d flow.
From both t h e two-layer and reduced
g r a v i t y model r e s u l t s it is clear t h a t e d d i e s amplify downstream by feeding on t h e mean flow, t h a t i s , w e have s p a t i a l l y growing disturbances.
Gaster ( 1 9 6 2 )
has shown t h a t t h e r e l a t i o n s h i p between s p a t i a l l y growing and temporally growing d i s t u r b a n c e s i n homogeneous shear flow i s simple and involves only t h e group v e l o c i t y provided t h e amplificatiQn r a t e s of t h e d i s t u r b a n c e s a r e small. Thus, w e proceed (without f u r t h e r j u s t i f i c a t i o n ) t o look f o r s i m i l a r i t i e s between our numerical r e s u l t s and published r e s u l t s from l i n e a r s t a b i l i t y analyses f o r temporally growing waves.
For two l a y e r flows, t h r e e non-dimensional analyses: 6 ,
parameters a r i s e i n t h e s e
t h e r a t i o of t h e upper t o t h e lower l a y e r depth:
A ,
t h e r a t i o of
t h e l e n g t h s c a l e (L) of t h e h o r i z o n t a l shear t o t h e i n t e r n a l r a d i u s of deformation, RD; and t h e r a t i o of t h e p l a n e t a r y v o r t i c i t y t o t h e v o r t i c i t y of t h e flow,
f3* = f 3 ~ ~ / Uwhere ~ , Uo i s a c h a r a c t e r i s t i c speed.
l a y e r depths i s small h e r e ( 6 = 0 . 1 )
a s discussed above.
i s no unique c h o i c e f o r t h e c h a r a c t e r i s t i c s c a l e s .
The r a t i o of t h e Unfortunately, t h e r e
A p a r t i c u l a r choice f o r t h e
h o r i z o n t a l length s c a l e i s L = 20 km, h a l f t h e width of t h e model p o r t t h a t r e p r e s e n t s S t . Vincent Passage.
On t h e o t h e r hand t h e views of t h e PHA
discussed above suggest t h a t t h e s c a l e of t h e h o r i z o n t a l shear i s approximately 50 km.
S i m i l a r l y , t h e c h a r a c t e r i s t i c speed based on inflow i n t h e upper l a y e r
i s about Uo = -0.5
m/sec.
However, t h i s speed might be a s low a s -0.20
m/sec
i f w e consider t h e speed a t t h e c o r e of t h e c u r r e n t around t h e model eddies. The 8-ef f e c t appears t o be q u i t e small i n any case because -0.28 u s i n g t h e previous range of s c a l e s . well-known,
The r o l e of
* 5
-0.02,
a s a r e s t o r i n g force is
though, and w e cannot discount i t s e f f e c t on l a r g e r scales without
f u r t h e r experiments. The length s c a l e (L) of t h e h o r i z o n t a l shear i s small compared t o t h e deformation r a d i u s ( 0 . 2
5% 5
0 . 6 ) and according t o Killworth ( 1 9 8 0 ) each
l a y e r of t h e system may be u n s t a b l e without t h e o t h e r i n t h i s s i t u a t i o n . Charney ( 1 9 6 3 ) h a s a l s o noted t h i s decoupling ,in e q u a t o r i a l systems where RD
i s r e l a t i v e l y large.
I f w e r e g a r d t h e perturbed flow a s O ( 1 ) i n t h e upper
l a y e r , a much w e a k e r flow of O( h2) arises i n t h e lower layer.
Thus, w e
should expect p r i m a r i l y h o r i z o n t a l shear i n s t a b i l i t i e s i n our model ocean.
The
e n e r g e t i c f e a t u r e s i n t h e reduced g r a v i t y model r e s u l t s and t h e upper l a y e r of t h e two-layer r e s u l t s are indeed s i m i l a r a s shown above.
The l i n e a r theory
seems t o confirm t h e u t i l i t y of t h e reduced g r a v i t y model i n t h e p r e s e n t
situation. The wavelength and p e r i o d of t h e f a s t e s t growing p e r t u r b a t i o n s p r e d i c t e d by l i n e a r theory are s e n s i t i v e t o t h e c h a r a c t e r i s t i c s c a l e s and t o t h e p r o f i l e of t h e j e t perpendicular to i t s a x i s .
I f on t h e one hand w e choose t h e l a r g e r
speed and smaller l e n g t h s c a l e s , t h e n r e s u l t s from Fig.
1 of Killworth ( 1 9 8 0 ) ,
suggest t h a t t h e p r e f e r r e d wavelength and p e r i o d ( f o r a zonal j e t with a sech’
p r o f i l e i n t h e north-south
d i r e c t i o n ) are about 140 km and 7 days.
If
on t h e o t h e r hand w e choose t h e smaller speed and t h e l a r g e r length scale, t h e n r e s u l t s from Fig.
7 of Kuo ( 1 9 7 3 ) suggest t h a t t h e p r e f e r r e d wavelength and
p e r i o d are about 310 km and 35 days, r e s p e c t i v e l y .
This l a t t e r wavelength and
p e r i o d a r e i n good agreement with t h e numerical model (e.g. 10).
see Figs.,, 9 and
In f u t u r e work we plan t o make f u r t h e r comparisons between t h e model
r e s u l t s and l i n e a r s t a b i l i t y t h e o r y , when w e vary t h e p e r t i n e n t nondimensional parameters
6.
.
SUMMARY
W e have b r i e f l y p r e s e n t e d t h e r e s u l t s of our s t a n d a r d case experiments using
t h e two-layer and reduced g r a v i t y models.
These experiments used t h e m o s t
r e a l i s t i c model c o n f i g u r a t i o n and parameters f o r t h e s o u t h e a s t e r n Caribbean Sea based on our b e s t estimates f r a n t h e o b s e r v a t i o n a l data. I n t h e upper l a y e r of t h e two-layer model and i n t h e reduced g r a v i t y model eddies are generated which compare favorably t o t h e NOAA and NORDA d r i f t e r observations.
The upper l a y e r mean flow showed a westward flowing c u r r e n t i n
t h e southern p o r t i o n of t h e model b a s i n which i s c o n s i s t e n t with t h e i d e a s d e r i v e d from h i s t o r i c a l hydrography (Wust, 1964; Gordon, 1967; Roemmich, 1981). Febres-Ortega and Herrera (1976) and Morrison ( 1 9 7 7 ) used meridional s e c t i o n s t o i n f e r t h e westward-flowing Caribbean c u r r e n t and eastward-flowing counter currents.
By t a k i n g a p p r o p r i a t e c r o s s - s e c t i o n s through s e l e c t e d f i e l d s from
t h e numerical model, e.g.
u ( x , y , t ) , t h e s a m e i n t e r p r e t a t i o n could be made, i f
t h e t o t a l h o r i z o n t a l p i c t u r e were not a v a i l a b l e .
Furthermore, t h e apparent
c o r r e l a t i o n between meanders and loops i n d r i f t e r t r a c k s and t h e topography may be f o r t u i t o u s r a t h e r than c a u s a l , c o n t r a r y t o t h e hypothesis advanced by Molinari e t a l .
(1981).
W e have demonstrated t h a t r e a l i s t i c eddies can be
generated i n t h e reduced g r a v i t y model which does not have bottom topography. The reduced g r a v i t y r e s u l t s suggest t h a t h o r i z o n t a l s h e a r i n s t a b i l i t i e s are t h e
primary cause of eddy generation i n t h e s o u t h e a s t e r n Caribbean Sea.
The
primary energy t r a n s f e r i n both t h e reduced g r a v i t y and two-layer c a s e s i s b a r o t r o p i c , i.e. eddies.
k i n e t i c energy of t h e mean flow t o k i n e t i c energy of t h e
This t r a n f e r s u p p o r t s t h e h o r i z o n t a l shear i n s t a b i l i t y hypothesis.
Further evidence f o r t h i s hypothesis i s t h a t t h e wavelengths and p e r i o d s observed i n t h e model are c o n s i s t e n t with r e s u l t s from l i n e a r i n s t a b i l i t y
,
325 t h e o r y f o r a reasonable choice of s c a l i n g parameters.
W e have a l s o shown i n t h e two-layer case t h a t t h e l a y e r s a r e n e a r l y decoupled and t h a t t h e primary e f f e c t s of topography i n t h e model a r e confined t o t h e lower l a y e r .
As expected i n a g e o s t r o p h i c a l l y balanced flow which
conserves p o t e n t i a l v o r t i c i t y , t h e flow i n t h e lower l a y e r tends t o follow t h e f / h contours of t h e topography.
The r e s u l t i s a northward c u r r e n t along t h e
topographic contours of t h e A n t i l l e s and a westward c u r r e n t following t h e topographic contours near t h e northern boundary.
There i s a l s o a weak cyclonic
gyre following t h e topographic contours of t h e Grenada Basin.
Furthermore, i f
w e had d a t a on t h e deep flow along t h e Venezuelan Slope, w e could s p e c i f y a lower l a y e r inflow near t h e southern end of t h e western boundary.
Then w e
might a l s o see a c y c l o n i c c i r c u l a t i o n i n t h e lower l a y e r of t h e Venezuelan Basin s i m i l a r to t h a t found by Fbemmich ( 1 9 8 1 ) . W e have presented t e n t a t i v e answers t o some of t h e q u e s t i o n s posed a t
t h e o n s e t of t h i s paper, b u t t h e r e is c o n s i d e r a b l e work s t i l l t o be done before d e f i n i t e answers are found. 1)
Work t h a t i s now i n progress includes:
an i n v e s t i g a t i o n of time-dependent
inflow (speed and
direction), 2)
a s t a b i l i t y a n a l y s i s of i d e a l zonal c u r r e n t s for various
values of t h e C o r i o l i s parameter ( f ) and d i f f e r e n t i a l r o t a t i o n
(B),
and f o r a c t u a l zonal c u r r e n t p r o f i l e s derived from model
results, 3)
f u r t h e r i n v e s t i g a t i o n of t h e e f f e c t of bottom topography,
4)
an i n v e s t i g a t i o n of t h e e f f e c t of changing lower l a y e r inflow,
5)
an a n a l y s i s of t h e eddy-mean e n e r g e t i c s f o r key model
6)
an i n v e s t i g a t i o n of t h e e f f e c t of both steady and t i m e
experiments, and
dependent t r a d e winds. T h i s p r e s e n t study i s a f i r s t s t e p i n t h e use of numerical modeling i n a j o i n t modeling and o b s e r v a t i o n a l program t o examine t h e c i r c u l a t i o n i n t h e e a s t e r n Caribbean Sea.
W e are o p t i m i s t i c t h a t t h e r e s u l t s from t h e i n i t i a l
modeling e f f o r t can be used t o formulate improved o b s e r v a t i o n a l s t u d i e s and t h a t t h e data from o b s e r v a t i o n s can be used t o r e f i n e t h e modeling e f f o r t .
ACKNOWLEDGEMENTS We thank Robert Molinari, I r v i n g Brooks and Carol Duckett f o r providing t h e NOAA d r i f t e r data.
A l b e r t Green and Donald Burns deployed t h e NORDA d r i f t e r s
and provided preliminary d a t a processing. manuscript and typed many rough d r a f t s . model Setup.
Joyce Ford prepared t h e f i n a l J a n i c e Boyd c o n t r i b u t e d t o t h e i n i t i a l
This i s NORDA Contribution # J A 320:026:81.
326 APPENDIX A
L i s t of Symbols f o r Model Equations A
h o r i z o n t a l eddy v i s c o s i t y
D
h e i g h t of bottom topography above a r e f e r e n c e l e v e l
f
C o r i o l i s parameter
9
a c c e l e r a t i o n due t o g r a v i t y
4'
reduced g r a v i t y , g ( p 2
-
PI)/
p
i n s t a n t a n e o u s l o c a l t h i c k n e s s of t h e l a y e r s
hl h 2 H1,H2(x,y) i n i t i a l t h i c k n e s s of t h e l a y e r s
t
time x - d i r e c t e d components of c u r r e n t v e l o c i t y
?nU2
V1'12
3, 'V2 XlYlZ
y-directed
+
components of c u r r e n t v e l o c i t y
+
h v ,h v 1 1 2 2 tangent p l a n e C a r t e s i a n c o o r d i n a t e s : x p o s i t i v e eastward, y p o s i t i v e northward, z p o s i t i v e upward
B
d i f f e r e n t i a l r o t a t i o n , df/dy
At
time increment i n t h e numerical i n t e g r a t i o n
Ax, AY
h o r i z o n t a l g r i d increments
'I1 n2 p,p1,p2 Ti
I
Ti
f r e e s u r f a c e anomaly; height of t h e f r e e s u r f a c e above i t s i n i t i a l uniform e l e v a t i o n ; r)l = h l + h 2 - H1 Ti2 = H1 + n l - h = h - n2 = -PHA d e n s i t i e s of s e a water x and y d i r e c t e d t a n g e n t i a l s t r e s s e s a t t h e t o p ( i l and bottom (i+l)of l a y e r i
REFERENCES
Brooks, I . N . , 1970. Transport and Velocity Measurenpnts i n S t . Lucia Passage of t h e Lesser A n t i l l e s , EOS 59: 1102 ( A b s t r a c t o n l y ) . Burns, D.A. and M . Car. 1975. Current Meter Data Report f o r t h e E a s t e r n p a r t of t h e Caribbean Sea, Naval Oceanographic O f f i c e T N 6110-6-75, impp. Charney, J . G . , 1947: The dynamics of long waves i n a b a r o c l i n i c w e s t e r l y c u r r e n t , J. Meteorol.: 4 . 135-163. , 1963: A note on l a r g e - s c a l e motions i n t h e t r o p i c s . J. Atmos. S c i . , 20: 607-609. Eady, E.T., 1949: Long waves and cyclone waves. T e l l u s , 1: 33-52. Febres-Ortega, G. and L.E. Herrera 1976. Caribbean Sea c i r c u l a t i o n and water mass t r a n s p o r t s near t h e Lesser A n t i l l e s . Biol. I n s t . Oceanogr. Univ. Oriente 15 ( 1 ) : 83-96. Gaster, M . , 1962: A note on t h e r e l a t i o n between temporally i n c r e a s i n g and s p a t i a l l y i n c r e a s i n g d i s t u r b a n c e s i n hydrodynamic s t a b i l i t y . J. F l u i d Mech., 14: 222-224. Gordon, A.L. 1967. C i r c u l a t i o n of t h e Caribbean Sea. J. Geophys. Res. 72 (24):
6207-6223.
Hurlburt, H.E. and J.D. Thompson, 1980: A Numerical Study of Loop Current I n t r u s i o n s and Eddy Shedding. J. Phys. Oceanog., 10: 1611-1651.
327 Killworth, P.D., 1980: Barotropic and b a r o c l i n i c i n s t a b i l i t y i n r o t a t i n g s t r a t i f i e d fluids. Dyn. Oce. and Atmos., 4: 143-184. 1949: Dynamic i n s t a b i l i t y of two-dimensional non-divergent flow i n Kuo, H.L., a b a r o t r o p i c atmosphere. J. Meteorol., 6 : 105-122. Kuo, H.L., 1973: Dynamics of quasigeostrophic flows and i n s t a b i l i t y theory. Adv. Appl. Mech., 13: 247-330. Leming, T.D. 1971. Eddies w e s t of t h e southern Lgsser A n t i l l e s . In Symposium on I n v e s t i g a t i o n s and Resources of t h e Caribbean Sea and Adjacent Regions. UNESCO, P a r i s . 113-120. Mazeika, P.A., D.A. Burns and T.H. Kinder, 1980a. Mesoscale c i r c u l a t i o n e a s t of t h e southern Lesser A n t i l l e s . J. Geophys. R e s . 8 5 ( 6 5 ) : 2743-2758. Mazeika, P.A., D.A. Burns, and T.H. Kinder, 1980b. Measured flow i n St. Vincent and Grenada Passages i n 1977. Naval Ocean Research and Development A c t i v i t y Technical Note 6 2 , 52 pp. Molinari, R.L., M. S p i l l a n e , I. Brooks, D. Atwood and C. Duckett, 1981: Surface c u r r e n t s i n t h e Caribbean Sea a s deduced from Lagrangian observations. J. Geophys. Res. 86(C7):6537-6542. Morrison, J.M., 1977: Water Mass P r o p e r t i e s Used as Flow I n d i c a t o r s Within t h e Ph.D. E a s t e r n Caribbean Sea During t h e Winter of 1972 and t h e F a l l of 1973. D i s s e r t a t i o n , Texas A&M University, College S t a t i o n , TX, 75 pp. Seasonal v a r i a b i l i t y of t h e F l o r i d a N i i l a r , P.P. and W . S . Richardson, 1973. Current. J. M a r . Res. 3 1 ( 3 ) : 144-167. Nof, D., 1978: On geostrophic adjustment i n sea s t r a i t s and wide e s t u a r i e s : theory and l a b o r a t o r y experiments. P a r t I1 - two l a y e r system. J. Phys. 861-872. Oceanogr. 8 ( 5 ) : Pedlosky, J., 1964: The s t a b i l i t y of c u r r e n t s i n t h e atmosphere and t h e ocean. P a r t I. J. A t m o s . Sci., 2 1 , 201-219. Hurlburt, 1982: A reduced g r a v i t y model of t h e P r e l l e r , R. and H.E. c i r c u l a t i o n i n t h e Alboran Sea. In: J.C.J. Nihoul ( E d i t o r ) , Hydrodynamics of Semi-Enclosed Seas. E l s e v i e r , Amsterdam,75-89. C i r c u l a t i o n of t h e Caribbean Sea: a well-resolved inverse Roemmich, D., 1981: J. Geophys. Res., i n press. problem. Current Measurements i n t h e Passages of Stalcup, M.C. and W.G. Metcalf, 1972: J. Geophys. Res. 77 ( 6 ) : 1032-1049. t h e Lesser A n t i l l e s . W.G. Metcalf, and M. Zemanovic, 1971: Current Measurements i n S t a l c u p , M.C., t h e Lesser A n t i l l e s . Woods Hole Oceanographic I n s t i t u t e Technical Report 71-51, 14 pp. F i g u r e s , Tables. Unpublished manuscript. Teague, W.J., 1979: CTD measurements i n t h e e a s t e r n Caribbean Sea, August 1978. Naval Oceanographic O f f i c e Technical Note TN 3431-2-79, 2 4 pp. S t r a t i f i c a t i o n and C i r c u l a t i o n i n t h e Antillean-Caribbean Wust, G., 1964: Basin. Columbia University P r e s s , N e w York, 2 0 1 pp. Wyrtki, K., L. Magaard and J. Hager, 1976: Eddy Energy i n t h e Oceans. J. Geophys. Res. 8 1 ( 1 5 ) : 2641-2646.
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329
A MODEL FOR FRONTAL UPWELLING C.L.
TANG
BEDFORD INSTITUTE OF OCEANOGRAPHY, DARTMOUTH, NOVA SCOTIA, CANADA
ABSTRACT To i n v e s t i g a t e t h e mechanism o f f m p t a l u p w e l l i n g ,
a l i n e a r time-independant
a n a l y t i c a l model f o r t h e c i r c u l a t i o n below a f r o n t a l l a y e r i s developed.
The r o l e
o f t h e f r o n t a l l a y e r i n t h e model i s t o p r o v i d e a d r a g a t t h e l o w e r boundary o f t h e f r o n t a l l a y e r t o d r i v e a m o t i o n below.
The ambient f l u i d i s viscous w i t h
c o n s t a n t v e r t i c a l and h o r i z o n t a l eddy c o e f f i c i e n t s .
An Ekman t r a n s p o r t beneath
t h e f r o n t a l l a y e r i s generated by t h e a l o n g - f r o n t movement o f t h e f r o n t a l l a y e r . T h i s Ekman t r a n s p o r t i s i n a d i r e c t i o n away f r o m t h e f r o n t and draws f l u i d i n a v e r t i c a l i n t e r n a l s h e a r l a y e r d i r e c t l y below t h e f r o n t upward, upwelling.
The t h i c k n e s s of t h e i n t e r n a l s h e a r l a y e r i s E'L,
t h e Ekman number and t h e h o r i z o n a l S t e w a r t s o n l a y e r s o f t h i c k n e s s ?L The v e r t i c a l
the frontal
layer.
Two o u t e r
f e e d t h e i n t e r n a l shear l a y e r and a l s o serve as
r e t u r n channels f o r t h e u p w e l l e d f l u i d . i s geostrophic.
scale o f
t h u s c r e a t i n g an where E and L are
O u t s i d e t h e Stewartson l a y e r s , t h e m o t i o n
v e l o c i t y i s determined by t h e d i v e r g e n c e o f t h e
i n t e r f a c i a l and b o t t o m Ekman t r a n s p o r t s and i s independent o f depth. s t r a t i f i c a t i o n i n t h e ambient f l u i d a r e discussed.
Effects of
Width o f t h e u p w e l l i n g l a y e r
i s c a l c u l a t e d and compared w i t h o b s e r v a t i o n s i n t h e G u l f o f S t .
Lawrence f r o n t a l
zone. INTRODUCTION
1.
A recent study o f t h e temperature-salinity o f St.
s t r u c t u r e o f the northwestern G u l f
Lawrence r e v e a l e d t h e e x i s t e n c e o f a sharp s a l i n i t y / d e n s i t y f r o n t near t h e
e n t r a n c e t o t h e S t . Lawrence E s t u a r y , and s t r o n g evidence o f u p w e l l i n g a l o n g t h e f r o n t (Tang, 1980, h e r e a f t e r r e f e r r e d t o as T). f l o w o f l m s a l i n i t y w a t e r f r o m t h e estuary. s e c t i o n a l view o f t h e front i s shown i n Figs.
T h i s f r o n t i s formed by t h e out-
The s p a t i a l s t r u c t u r e and t h e cross1 and 2.
The low s u r f a c e tempera-
t u r e and t h e hump i n t h e i s o t h e r m s j u s t o u t s i d e t h e f r o n t a l l a y e r a r e s i g n a t u r e s o f u p w e l l i n g o f c o l d sub-surface water.
The p o s s i b i l i t y o f s t r o n g v e r t i c a l m i x i n g
c a u s i n g t h e l m s u r f a c e t e m p e r a t u r e can be r u l e d out by a c l o s e examination o f t h e v e r t i c a l p r o f i l e s ( n o t shown).
I n c o n s i s t e n c e w i t h t h e T/S measurements,
a fila-
ment o f c o l d s u r f a c e w a t e r a l o n g t h e f r o n t can o f t e n be seen i n s a t e l l i t e imagery. M o t i v a t e d by t h e s e o b s e r v a t i o n s , we c o n s t r u c t t h i s u p w e l l i n g model t o i n v e s t i g a t e
088 O€
.00.99
,O€
,00.L9
,O€ (0%)
.oo.a9
Ap~ipsa q m g
Fig. 1.
Surface salinity in the northwestern Gulf o f S t . Lawrence
Fig. 2. Salinity and temperature sections (east-west) across the front.
331
the p o s s i b i l i t y t h a t the along-front
movement o f a d e n s i t y f r o n t can d r i v e a
v e r t i c a l c i r c u l a t i o n below and draw w a t e r t o t h e surface. The dynamics o f oceanic f r o n t s have been reviewed by Mooers (1978) and Joyce (1978).
Mooers e t al.
(1976) analysed t h e dynamical s t r u c t u r e o f a f r o n t a l zone
and emphasized t h e importance o f cross-front
flow.
Kao e t a l .
i n t r u s i o n numerically.
comprehending tb d i f f u s i v e mechanism t o t h e
(1978) s o l v e d a t i m e dependent problem o f f r o n t a l
T h e i r r e s u l t s show how a f r o n t i s formed f r o m a f r e s h
w a t e r source, advances i n p o s i t i o n w i t h t i m e and f i n a l l y a s t e a d y - s t a t e dominated by a s t r o n g a l o n g - f r o n t g e o s t r o p h i c f l o w i s reached.
I n t h e i r model, t h e cross-
f r o n t f l o w i s c o n t r o l l e d by s p e c i f i e d upstream and downstream boundary c o n d i t i o n s . A consequence o f t h i s i s t h a t t h e f l o w ,,is f o r c e d t o c r o s s t h e i n t e r f a c e t o con-
As we s h a l l see,
s e r v e mass.
o u r model employs a d i f f e r e n t boundary c o n d i t i o n
r e s u l t i n g i n a completely d i f f e r e n t f l o w pattern. An i m p o r t a n t i n g r e d i e n t f o r t h e model i s t h e concept o f t u r b u l e n t i n t e r f a c i a l l a y e r along t h e f r o n t a l interface.
Csanady (1978) examined t h e experimenta
dence o f it and suggested (Horne e t al.,
p r o v i d e a channel f o r t h e f l u i d beneath t h e f r o n t a l l a y e r t o move a l o n g t h e face.
evi-
1978) t h a t such a f r i c t i o n a l l a y e r c o u l d nter-
From t h e p o i n t o f view o f m o d e l l i n g , t h e e x i s t e n c e o f an i n t e r f a c i a l l a y e r
i s a consequence o f t h e assumption o f small and c o n s t a n t eddy c o e f f i c i e n t .
Since
such a t u r b u l e n t i n t e r f a c i a l l a y e r has a l l t h e c h a r a c t e r i s t i c s o f a s u r f a c e Ekman l a y e r , we s h a l l c a l l i t an i n t e r f a c i a l Ekman l a y e r . A n o t h e r element o f t h e model i s t h e i n t e r n a l s h e a r l a y e r . d i s c o n t i n u i t y o f d e n s i t y a t t h e surface,
v e r t i c a l l i n e below t h e d i s c o n t i n u i t y (Csanady, t h e shear.
An i n t e r n a l
e f f e c t s a r e important.
A f r o n t , due t o t h e
c r e a t e s a sharp h o r i z o n t a l shear a l o n g a 1971).
shear l a y e r i s a v e r t i c a l
F r i c t i o n a c t s t o weaken l a y e r i n which f r i c t i o n a l
K i l l w o r t h (1973) analyzed t h e l a y e r s t r u c t u r e around a
c u r r e n t d i s c o n t i n u i t y caused by a sudden change i n bottom s l o p e and found t h a t more t h a n one i n t e r n a l s h e a r l a y e r were needed i n o r d e r t o s a t i s f y a l l c o n t i n u i t y requirements.
The l a y e r s t r u c t u r e o f t h e ambient f l u i d i n t h i s model i s t h e same
as t h a t o f K i l l w o r t h . assumption.
I t s h o u l d be emphasized t h a t t h e l a y e r s t r u c t u r e i s n o t an
I t i s a consequence o f p a r a m e t r i z i n g t h e h o r i z o n t a l t u r b u l e n t m i x i n g
by a c o n s t a n t eddy c o e f f i c i e n t , solution.
and i t s e x i s t e n c e i s independent o f t h e method o f
I f no i n t e r n a l s h e a r l a y e r i s f o u n d i n nature,
t h e c o n c l u s i o n we can
draw i s t h a t o u r c h o i c e f o r t h e f o r m o f t h e h o r i z o n t a l t u r b u l e n t m i x i n g t e r n i n t h e momentum e q u a t i o n s i s i n c o r r e c t .
The same argument h o l d s f o r t h e i n t e r f a c i a l
Ekman l a y e r . W i t h t h e concept o f boundary l a y e r s d i s c u s s e d above, i t was suggested i n
T that
a mechanism s i m i l a r t o t h a t f o r c o a s t a l u p w e l l i n g c o u l d produce f r o n t a l u p w e l l i n g . C o a s t a l u p w e l l i n g i s caused by a wind-generated Ekman t r a n s p o r t s u c k i n g a compensa t i n g f l o w from below t h r o u g h a c o a s t a l boundary l a y e r . front,
I n t h e case o f a d e n s i t y
t h e i n t e r f a c i a l Ekman f l o w on t h e l o w e r s i d e o f t h e i n t e r f a c e d r i v e n by
332
the along-front vertical shear always moves in a direction away from the front. If there i s no significant flow across the interface, the f l u i d t h a t flows into the interfacial Ekman layer has t o be drawn from the ambient fluid. I t cannot be drawn from near the surface or directly from the i n t e r i o r since t h i s would require a strong vertical shear near the surface o r a high along-front pressure gradient,, both of which do not exist in the absence of an external forcing. The flow transported out of the interfacial Ekman layer can be replenished by a vertical transp o r t of subsurface f l u i d t o the surface through an internal shear layer, and thus an upwelling i s created. In t h i s paper, the cross-front circulation just described will be obtained from a model with the following basic assumptions: a. time independent and two-dimensional motion, b. slab-like structure f o r the frontal layer, c. constant density, vertical and horizontal eddy coefficients f o r the lower layer, d. l i n e a r dynamics f o r the lower layer, e. a prescribed along-front velocity f o r the frontal layer, f. no motion a t i n f i n i t y on both sides of the front in e i t h e r layer, g. no flow across the interface. The governing equations we shall use are basically the same as those in Mooers (1978) and Kao e t al. (1978). To solve the equations analytically, the standard boundary layer technique will be employed. The e n t i r e cross-section i s divided into different regions (layers) according t o the momentum balance i n each region. The equations are solved in each region separately and then joined together by matching boundary conditions. I n the following section, we define the mthemat i c a l problem and discuss the division o f the regions. The s o l u t i o n s are obtained in the next three sections. From the solutions, several streamline patterns are calculated i n section 6. A s u n a r y and discussion i s given in the l a s t section. The density front i n T will be used as an example t o make order of magnitude estimates. The parameter values appropriate f o r t h i s front are: L=3okm, the cross-front length scale the along-f ront velocity s c a l e u = 20 cm 5-1, H = 300 m, the water depth Before proceeding t o the development of the model, we wish t o emphasize t h a t ( a ) t h i s model i s not a frontogenisis model and we are n o t concerned w i t h how the front i s f o n e d . The existence of the front i s assumed and i t s along-front motion i s given. We a r e here dealing with the small second order cross-front motion induced by the f i r s t order frontal movement. ( b ) While the dynamics of the frontal layer i t s e l f are of great i n t e r e s t t o ocean0 graphers, our purpose here i s t o study the motion o f the ambient f l u i d below the
333
frontal layer. Because of t h i s , the frontal layer in t h i s model i s highly simplified and only serves as a moving boundary t o drive the fluid below i t . The circulation within the frontal layer i t s e l f i s not resolved.
Fig.
3.
Layer structure of the model and orders of velocity components and
pressure in each layer and region.
GOVERNING EQUATIONS AND STRUCTURE OF THE MODEL We consider a frontal layer of negligible thickness embedded in a fluid of constant density in the f-plane moving in the negative y direction, where the coordinate system i s x i n the cross-front, y i n the along-front and z i n the upward direction as shown in Fig. 3. The motion in the ambient fluid i s governed by the following set of equations:
2.
(2.la)
(2.lb)
(2.lc)
-a u+ - av + - =awI )
ax
ay
where v2 =a2 neglected, %d
(2.ld)
az
_.
+a 2
afl
The nonlinear terms in the momentum equations have been the variables have been non-dimensionalized by the following
2
334
s c a l ings (x*, Y*) = L (XPY) z* = Hz (u*, W*
u
v*) =
(u,v)
= (HU/L)W
p* = PULf P where t h e a s t e r i s k s i n d i c a t e dimensional v a r i a b l e s . scale, H i s t h e w a t e r depth,
p
L i s the horizontal length
i s t h e d e n s i t y and f i s t h e C o r i o l i s parameter.
Three d i m e n s i o n l e s s parameters appear i n t h e equations.
Ev = 2AV/(fH2),
t h e v e r t i c a l Ekman number
Eh = 2Ah/(fL2),
t h e h o r i z o n t a l Ekman number
6 = H/L,
t h e aspect r a t i o
They a r e
where AV and Ah a r e t h e v e r t i c a l and h o r i z o n t a l eddy c o e f f i c i e n t r e s p e c t i v e l y . The f i r s t o r d e r s o l u t i o n o f (2.1)
without t h e f r i c t i o n t e n s i s a geostrophic
a l o n g - f r o n t flow w i t h a d i s c o n t i n u i t y a t x=O. continuity.
F r i c t i o n s act t o eliminate the dis-
T h i s i s acheived by adding c o r r e c t i o n t e n s t o t h e g e o s t m p h i c s o l u -
t i o n i n t h e i n t e r n a l s h e a r l a y e r s around t h e d i s c o n t i n u i t y . cannot make a l l components o f t h e v e l o c i t y continuous. thlckness
E3
i n v (Veronis,
A s i n g l e shear l a y e r
A Stewartson l a y e r o f
on each s i d e o f t h e d i s c o n t i n u i t y can smooth out t h e d i s c o n t i n u i t y
1970).
l a y e r o f t h i c k n e s s Eh’
Between t h e two Stewartson l a y e r s ,
there exist a thinner
i n which u can be made continuous.
An even t h i n n e r l a y e r
o f t h i c k n e s s 6 serves t o match w across x=O (Pedlosky, 1968).
Since t h e 6 l a y e r
c a r r i e s a t r a n s p o r t s m a l l e r t h a n t h e t r a n s p o r t i n o t h e r l a y e r s by a f a c t o r o f
we s h a l l n e g l e c t t h i s l a y e r i n t h e s o l u t i o n . The o n l y consequence o f c i r c u l a t i o n is a d i s c o n t i n u i t y i n t h e slope o f
6/Ehk,
t h i s m i s s i o n t o the cross-front t h e s t r e a m l i n e s a t x=O.
Beneath t h e f r o n t a l
l a y e r and above t h e bottom,
an
i n t e r f a c i a l Ekman l a y e r and a b o t t o m Ekman l a y e r a r e developed, b o t h o f t h i c k n e s s
EVk.
They a r e r e q u i r e d t o s a t i s f y t h e n o - s l i p c o n d i t i o n a t t h e bottom and t h e
interface. To s i m p l i f y physics,
t h e mathematics
we assume Ev = Eh =E.
without
a t the time destroying the underlying
The c o n d i t i o n E << 1 i s r e q u i r e d t o a l l o w us
t o use t h e boundary l a y e r method t o s o l v e t h e equation.
The l a y e r s t r u c t u r e and
t h e o r d e r o f magnitude o f t h e c o r r e c t i o n terms i n each l a y e r a r e shown i n Fig. 3. The t o t a l v e l o c i t y and p r e s s u r e i n a g i v e n l a y e r a r e t h e sum o f t h e c o r r e c t i o n t e r n as g i v e n i n t h e s e c t i o n s d e a l i n g w i t h t h e i n d i v i d u a l regions.
335
We s h a l l use t h e s u b s c r i p t s 0, 1, 2 , 3 and 4 t o denote t h e f r o n t a l l a y e r , t h e 0 ( 1 ) r e g i o n , t h e E4 l a y e r and t h e E% l a y e r r e s p e c t i v e l y . The overhead symbols " - " and
"-"
r e f e r t o t h e i n t e r f a c i a l and t h e bottom Ekman l a y e r s r e s p e c t i v e l y .
Vari-
a b l e s w i t h o u t an overhead symbol denote t h e i n t e r i o r , which i s d e f i n e d t o be t h e r e g i o n between t h e two Ekman l a y e r s f o r x < 0, and fhe r e g i o n above t h e bottom f o r x > 0. THE 0 ( 1 ) REGION
3.
T h i s i s t h e r e g i o n o u t s i d e t h e Stewartson l a y e r s . i s g e o s t r o p h i c and independent o f z.
I n t h e i n t e r i o r , t h e motion
The e q u a t i o n s o f m o t i o n a r e
-v1+ap1=0 ax
(3.la)
(3.lb)
(3.1~)
aw,=O
(3.ld)
az
E".
To o r d e r E%, t h e r e i s no h o r i z o n t a l flow.
The v e r t i c a l v e l o c i t y i s o f o r d e r
and i s determined by t h e d i v e r g e n c e i n t h e two Ekman l a y e r s .
v e l o c i t y i s o f o r d e r 1 and i s r e l a t e d t o t h e p r e s s u r e g r a d i e n t .
The a l o n g - f r o n t B u t because o f
t h e n o n - s l i p boundary c o n d i t i o n , v1 can be f i x e d by mass c o n s e r v a t i o n alone. The b o t t o m boundary l a y e r s o l u t i o n s w i t h n o - s l i p c o n d i t i o n can be o b t a i n e d by s t a n d a r d technique,
and a r e g i v e n by
u1 = -vl
exp (-E%)
v 1 = -vl
exp (-E'
s i n (E%) z) cos
(E'z)
(3.2a) (3.2b)
The c r o s s - f r o n t mass t r a n s p o r t i s
u',
=
7 ijl dz
(3.3)
0
The v e r t i c a l v e l o c i t y a t z=O i s , by c o n t i n u i t y ,
-1 -av, 2 ax
(3.4)
3 36
The c o n d i t i o n o f no normal v e l o c i t y a t t h e b o t t o m d e t e r m i n e s t h e i n t e r i o r v e r t i c a l velocity:
Wl(X,Z)
= w1(x,o)
=
-
Wl(X.0)
=
1 av 1 2 ax
(3.5)
The s o l u t i o n s i n t h e i n t e r f a c i a l Ekman l a y e r a r e s i m i l a r t o t h o s e i n t h e b o t t o m Ekman l a y e r except t h a t i n s t e a d o f t h e no s l i p c o n d i t i o n t h e a l o n g - f r o n t v e l o c i t y a t t h e i n t e r f a c e i s equal t o t h e f r o n t a l v e l o c i t y , i.e.,
where v o i s t h e v e l o c i t y o f t h e f r o n t a l l a y e r .
We t h e n have a h o r i z o n t a l v e l o c i t y
of
il =
-(vo-vl)
exp[E-’(l-z)I
s i n [E-’(l-z)]
(3.7a)
a c r o s s - f r o n t mass t r a n s p o r t o f
Gl
1 Gl
=
dz =
’ -1 E5(vo-vl)
-0I
(3.8)
2
and a v e r t i c a l v e l o c i t y o f
The c o n d i t i o n o f z e r u normal v e l o c i t y a t z = l g i v e s Wl(X,L)
= Wl(X,l)
=
-
Wl(X,l)
=
-1 2
a(vo-vl)
For t h e a l o n g - f r o n t c u r r e n t s t o s a t i s f y b o t h (3.10) be i n d e p e n d e n t l y s p e c i f i e d .
1 vo v1 = 2
(3.10)
ax and (3.5),
vo and v1 cannot
They a r e r e l a t e d by
(3.11)
We n o t e t h a t with (3.11) t h e mass t r a n s p o r t s i n t h e two Ekman l a y e r s a r e equal i n magnitude and o p p o s i t e i n sign, a necessary consequence o f mass c o n s e r v a t i o n .
331
I n d e r i v i n g (3.11), t h e boundary c o n d i t i o n o f no m o t i o n a t x = S i n c e v o e x i s t s o n l y i n x < 0, we have v 1 = w1 = 0, Eqs.
(3.2),
region.
for x > 0 (3.5),
(3.7)
To summarize,
horizontal velocity.
and (3.11)
fm
has been used.
(3.10) completely specify t h e motion i n t h e 0(1)
t h e i n t e r i o r m o t i o n i s g e o s t r o p h i c w i t h no c r o s s - f r o n t
The a l o n g - f r o n t f l w i s d r i v e n by t h e f r o n t a l m o t i o n w i t h a
v e l o c i t y equal t o h a l f o f t h e f r o n t a l v e l o c i t y .
The shear across t h e i n t e r f a c e
and t h e a l o n g - f r o n t
and a
flow
i n d u c e an i n t e r f a c i a l
bottom Ekman t r a n s p o r t
The excess mass r e s u l t i n g f r o m t h e d i v e r g e n c e o f t h e i n t e r f a c i a l
respectively.
Ekman t r a n s p o r t moves s t r a i g h t downward and i s r e c e i v e d by t h e b o t t o m Ekman l a y e r .
THE
4.
&
LAYER
A f u n c t i o n o f t h i s l a y e r i s t o smooth v1 across x=O.
This requires t h e correc-
S i m i l a r t o the 0(1) region, t i o n v t o be o f t h e same o r d e r o f magnitude as vl. t h e F". l a y e r can be d i v i d e d v e r t i c a l l y i n t o t h r e e regions. 4.1
The i n t e r i o r The v e l o c i t y components and p r e s s u r e a r e decomposed as
.... .... v2
L
u = E 4 up + v = v1
w
=
i-
@ w1
(4.la) (4.lb)
-+
+ EL w2 +
....
(4.1~) (4.ld)
and obey ( V e r o n i s , 1970)
- ap2 +
v2 = 0
(4.2a)
ac
(4.2b)
(4.2~)
338
(4.2d)
From these equations, we immediately see t h a t u p , vg and p2 a r e independent o f z. up and w2 as f u n c t i o n s o f v z a r e g i v e n by
where 5 = E-'
up
x.
-- -1- a2v2 2
(4.3a)
ac2
Z
wg(x
=
J ?2! o
ac
dz + w 2 ( ~ , 0 ) =
2
1
w,(x>O,z)
=
a3v2 - -1 z + wp(E.0)
J % dz z ac
1
= - (1-2)
(4.3b)
ac3
a3v2 -
(4.3c)
ac3
2
The i n t e r i o r v e l o c i t y f i e l d can o n l y be determined a f t e r t h e s o l u t i o n s i n t h e Ekman l a y e r s are found. 4.2
The bottom Ekrnan l a y e r The dynamical v a r i a b l e s can be expanded as
u
=
i1 +
v = v1 +
E4 u2 +
v1
i2 +
....
+ vg + vz +
....
The equations o f motion i n t h e s t r e t c h e d c o o r d i n a t e system 5 = E-'X,
(4.4a)
(4.4b)
5 = E-%z
are
(4.5a)
(4.5b)
339 (4.5c)
(4.5d)
The s o l u t i o n s are (4.6a)
(4.6b)
(4.6~)
A t 5'0,
t h e v e r t i c a l v e l o c i t y i s given by
The two unknowns B and C a r e t o be determined from t h e boundary c o n d i t i o n s a t z=O, 1.
F o r x < 0, t h e n o - s l i p c o n d i t i o n a t t h e bottom gives
c=o
(4.8a)
vg+B=O
(4.8b)
+
wp(c.0)
l a - (B-C)
=
(4.8~)
0
2 ac
corresponding t o t h e u,v
from (4.8).
avp ac
and w components o f t h e v e l o c i t y .
E l i m i n a t i n g B and C
we o b t a i n an equation f o r vp:
2 wp(c,O)
= 0,
c<
0
A s i m i l a r equation l i n k i n g vp and wp(E.0) i n t e r f a c i a l Ekman l a y e r .
(4.9)
w i l l be d e r i v e d when we consider t h e
340
F o r x > 0, t h e c o u n t e r p a r t o f (4.9) does n o t have a t e n c o r r e s p o n d i n g t o t h e i n t e r i o r v e r t i c a l v e l o c i t y s i n c e t h e r e i s no Ekman l a y e r a t z = l . U s i n g t h e nos l i p condition,
a (-a2 ac;
(4.3d),
( 4 . 6 ) and (4.7),
1) v2 = 0,
we o b t a i n
(4.10)
5 ' 0
aE2
t h e r e a r e t h r e e general s o l u t i o n s f o r (4.10) t i o n t h a t vanishes as 5
+
m
b u t o n l y one i s bounded.
is
where
D i s a c o n s t a n t t o be determined by m t c h i n g vp a t
4.3
The i n t e r f a c i a l Ekman l a y e r The v a r i a b l e s
The s o l u -
i n t h i s l a y e r obey a s i m i l a r s e t
F, =
0.
o f e q u a t i o n as t h e b o t t o m
boundary l a y e r and t h e s o l u t i o n s have t h e same form as ( 4 . 6 ) .
Continuity of
v e l o c i t i e s a t z = 1 leads t o t h e equation
a a2 (ac ac2
-
1) vp -2w2(5,0)
c<
= 0,
E l i m i n a t i n g w p ( ~ , O ) = 0 f r o m ( 4 . 1 2 ) and (4.9),
a (- a2 ac
ac2
-
(4.12)
0
we get
2) vp =
The bounded s o l u t i o n o f (4.13)
is
L
v 2 = F e ~ p ( 25).~
(4.14)
5< 0
The two c o n s t a n t s i n t h e s o l u t i o n s f o r vp,
D and F, can be determined f r o m t h e
v1 + v2, and i t s f i r s t The r e s u l t s o f t h e c a l c u l a t i o n a r e
condition o f continuity of the t o t a l along-front velocity, d e r i v a t i v e , a(v,+v,)/ac,
a t 5 = 0.
(4.15a) (4.15b) where K = 0.5/(1+2%)
and ',v,
is av,/ax
e v a l u a t e d a t x = 0.
Having o b t a i n e d v2, we can e a s i l y c a l c u l a t e ug and wp as w e l l as t h e v e l o c i t i e s i n t h e boundary l a y e r f r o m (4.3) and (4.6). I n p a r t i c u l a r , up i s g i v e n by (4.3a).
341 and (4.13):
(4.10)
up =
1 vp,
(4.16a)
5 > 0
2
(4.16b)
up i s i n general d i s c o n t i n u o u s a t 5 = 0. x
T h i s n e c e s s i t a t e s a t h i n n e r l a y e r around
smooth o u t t h e d i s c o n t i n u i t y as w i l l
= 0 to
be d i s c u s s e d i n t h e f o l l o w i n g
section. The t o t a l c r o s s - f r o n t mass t r a n s p o r t ” i n t h e i n t e r f a c i a l and t h e bottom Ekman and
layer,
c,
a r e g i v e n by
(4.17a)
(4.17 b )
2
0
vp
drives
an
interfacial
and
a
bottom t r a n s p o r t s
of
equal
magnitudes
and
d i r e c t ions. To recap o u r f i n d i n g s i n t h i s s e c t i o n , flow,
a c o u n t e r c u r r e n t i n t h e EL
developed,
t o smooth t h e a l o n g - f r o n t
geostrophic
l a y e r on b o t h s i d e s o f t h e d i s c o n t i n u i t y i s
which i n t u r n d r i v e s a bottom Ekman t r a n s p o r t on both s i d e s and an
i n t e r f a c i a l Ekman t r a n s p o r t i n x < 0. t h e i n t e r i o r o f t h e EL
The two Ekman f l o w s a r e connected t h r o u g h
l a y e r giving rise t o a cross-front circulation.
However,
t h e h o r i z o n t a l v e l o c i t y so generated i s d i s c o n t i n u o u s a t x=O.
5.
THE
E5 LAYER
The h o r i z o n t a l v e l o c i t y i s made c o n t i n u o u s i n t h i s l a y e r . c o r r e c t i o n t e r m f o r u be o f o r d e r E*. o r d e r 1.
This requires the
The v e r t i c a l v e l o c i t y i s , by c o n t i n u i t y , o f
Because o f t h e l a r g e v e r t i c a l v e l o c i t y , we can i d e n t i f y t h i s l a y e r as
t h e upwelling layer.
The s t r u c t u r e o f t h e dynamical v a r i a b l e s i n t h e i n t e r i o r
r e g i o n on t h i s l a y e r can be r e p r e s e n t e d by u = E+ up +
E”2
v = v 1 + vp
+ E$
w = EL2 w 1 + Ek
u3 +
wp
....
v3 +
....
+
+
w3
....
342
The v a r i a b l e s a r e governed by
(5.la)
-
+2 3
u3
a d
= 0
(5.lb)
(5.1~)
(5.ld)
where
=
i-,
'-E
X.
A complete s o l u t i o n o f (5.1)
r e q u i r e s t h e s p e c i f i c a t i o n of boundary c o n d i t i o n s
a t z = 0.1, which can be found o n l y i f t h e s o l u t i o n s i n t h e two known.
E% x
E'5
boxes a r e
However, w i t h o u t knowing t h e d e t a i l e d s t r u c t u r e o f t h e v e l o c i t y f i e l d ,
it
i s s t i l l p o s s i b l e t o c a l c u l a t e t h e t r a n s p o r t i n an o u t o f t h e E% l a y e r t h r o u g h the continuity relations.
We t h u s s h a l l not a t t e m p t t o s o l v e t h e d i f f i c u l t two-
dimensional problem i n t h e two c o r n e r boxes. The volume o f f l u i d t h a t u p w e l l s t o t h e f r o n t a l zone, W,
i s equal t o t h a t f l o w -
i n g out o f t h e i n t e r f a c i a l Ekman l a y e r a t x=O, and is g i v e n by, fm (4.16b)
and
(4.17a).
W = -U(O)
=
(5.2a)
=
-
1 - E% [vo(O) 2
-
Vl(0)
-
(5.2a)
v~(O)]
-K E% (vg + ELv0')/2
(5.2b)
s t a t e s t h a t t h e upward mass t r a n s p o r t i s 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 s h e a r
a t the front.
F o r a f r o n t which has c r o s s - f r o n t g e o s t r o p h i c balance, v o t a k e s an
e x p o n e n t i a l f o r m and i s n e g a t i v e (Csanady, 1971). c a t i n g an u p w e l l i n g . zone, E4,
We t h u s have a p o s i t i v e W i n d i -
The upward mass t r a n s p o r t and t h e w i d t h o f t h e u p w e l l i n g
i n c r e a s e w i t h f r i c t i o n , w h i l e t h e v e r t i c a l v e l o c i t y remains o f o r d e r 1.
The u p w e l l i n g f l u i d i s sucked i n t o t h e i n t e r f a c i a l Ekman l a y e r and moves i n t h e negative x d i r e c t i o n .
I t l e a v e s t h e i n t e r f a c i a l Ekman l a y e r by s i n k i n g t o t h e
i n t e r i o r o f t h e EL l a y e r and t h e 0 ( 1 ) region. Ekman l a y e r ,
and t h e n f l o w s towards t h e Ei
A p o r t i o n o f i t reaches t h e b o t t o m layer.
A l o n g t h e way,
it
is f o r c e d
343
upward by t h e d i v e r g e n c e o f t h e b o t t o m Ekman t r a n s p o r t .
The f l u i d can a l s o move
d i r e c t l y f r o m t h e i n t e r f a c i a l Ekman l a y e r t o t h e E4 l a y e r t h r o u g h t h e i n t e r i o r o f t h e Eg l a y e r . Ekman l a y e r ,
The volume o f f l u i d t h a t feeds t h e E4 l a y e r by way o f t h e bottom Ub,
and t h r o u g h t h e i n t e r i o r ,
Ui,
can be c a l c u l a t e d f r o m (4.17b)
and ( 4 . 1 6 b ) .
(5.4)
We n o t e t h a t t h e sum of servation.
Ub and U i i s equal t o W,
a consequence o f mass con-
v2 i s t h e c o r r e c t i o n t e r m t o t h e a l o n g - f r o n t g e o s t r o p h i c f l o w t o e l i m -
i n a t e t h e d i s c o n t i n u i t y a t x=O.
I t s magnitude i n c r e a s e s w i t h t h e sharpness o f t h e
f r o n t a l velocity. v2 d r i v e s a c i r c u l a t i o n c e l l c o u n t e r t h e one d r i v e n by v1 and p a r t i a l l y cancels t h e f l ow i n t h e lower p a r t o f t h e & layer. Thus t h e l a r g e r v2
is, t h e h i g h e r t h e c i r c u l a t i o n c e l l i s s i t u a t e d .
However, unless t h e t o t a l along-
f r o n t v e l o c i t y i s zero, t h e r e i s always f l u i d a t t h e b o t t o m t h a t r i s e s t o t h e surface.
I n r e a l i t y , we do n o t expect t h a t a s u r f a c e f r o n t i n t h e open ocean can
draw w a t e r from t h e deep bottom.
The reason t h a t t h e bottom w a t e r a l s o p a r t i c i -
p a t e s i n t h e c i r c u l a t i o n i n o u r model i s t h a t we have assumed a homogeneous l o w e r l a y e r , hence no energy i s r e q u i r e d t o l i f t t h e f l u i d f r o m t h e bottom t o t h e upper ocean.
T h i s s i t u a t i o n can change i n a model w i t h s t r a t i f i c a t i o n i n t h e l o w e r
layer,
i n which c o n s e r v a t i o n o f energy would make t h e c i r c u l a t i o n c o n f i n e t o t h e
u p p e r p a r t o f t h e ocean. The
E4
l a y e r i n t h i s model i s needed t o e l i m i n a t e t h e d i s c o n t i n u i t y c r e a t e d by
t h e f r o n t a t x=O.
I n t h e Ocean i f t h e l e n g t h s c a l e o f t h e zone o f h i g h s u r f a c e
d e n s i t y g r a d i e n t i s g r e a t e r t h a n E4, t h e n an Ek l a y e r i s n o t required.
A l l the
sunk f l u i d i s r e t u r n e d t o t h e s u r f a c e t h r o u g h t h e EL l a y e r . 6.
NUMERICAL EXAMPLES We d e f i n e a stream f u n c t i o n , '?, by
(6.la) (6.lb)
344
Outside the EL' layer, the t o t a l velocity in any given region i s the sum of a l l the i n t e r i o r and the,boundary layer solutions. The stream function can be obtained by integration of the vertical velocity over x: for x
<
0
(6.2a)
and f o r x
0
>
=
1 2
(1-2)
-
a2v 1 vp 2 ag2
F(5)
(6.2b)
2
where 5 = $ 2 , 5 ' = E-%(I-z) and F ( 5 ) = (sinr; + cosr;) exp ( - 5 ) . F ( 5 ) and F ( g ' ) have non-zero values only in the bottom and interfacial Ekman layer respectively. The structure of the cross-front circulation i s now clearly exhibited i n these simple expressions. the i n t e r i o r stream functions represented by the f i r s t terms o f (6.2a) and (6.2b) have a l i n e a r z-dependence, implying a constant u. The second t e r m give the bottom Ekman transport which i s proportional t o the alongfront i n t e r i o r velocity. The interfacial Ekman transport given by the t h i r d term o f (6.2a) i s determined by the shear between the frontal and the lower layers. Fig. 4 shows the contours of E-%Y calculated from the following s e t s of parameters: ( a ) E = 0.01, vo = -exp(x) ( b ) E = 0.1, v o = -exp(x) and (c) E = 0.01, vo = -2exp(2x). The frontal velocity, vo, and the i n t e r i o r along-front velocity, v = v l + v i , a r e shown above and below the circulation diagrams respectively. Since the solution (6.2) i s valid only i n the EL layer and the 0(1) region the streamlines within the E4 layer are hand-interpolated. From Fig. 4(a) t o 4 ( c ) , we can see how the circulation patterns change w i t h the frontal velocity and the f r i c t i o n . The interfacial and b o t t a n Ekman layers i n ( a ) and (c) can be identified by the crowed streamlines and have a thickness of E3 =
345
X 0':
-10
-0 5
05
0
I
0,
-,D
X
-0 I
0
05
10
06
z 0 .
02
-,5
-10
I . 1 -0, X
0
05
Fig. 4. Contours of E-' Y calculated from the parameter sets: (a) E = 0.01, V = -exp(x) (b) E = 0.1, V = -exp(x) and (c) E = 0.01, V = -2exp(Zx). Vo and the interior along-fr8nt velocity, V , are shown abov& and below the cgrculation diagrams respectively. Contour intervals are 50 for the dotted lines, and 100 for the solid lines.
346
0.1.
I n t h e 0(1) region, t h e r e i s no h o r i z o n t a l v e l o c i t y and t h e v e r t i c a l veloc-
i t y i s independent o f z.
The i s most evident i n (a).
The consequences o f a
sharper f r o n t a l v e l o c i t y can be seen by comparing (a) and (c). t i v e l y l a r g e r t r a n s p o r t i n t h e !? l a y e r (Ek = 0.32)
There i s a r e l a -
and t h e c i r c u l a t i o n c e l l i s
c l o s e r t o t h e surface i n (c). The l a r g e r Ekman number i n (b) gives rise t o t h i c k e s t boundary l a y e n (E% = 0.32), which are not i d e n t i f i a b l e i n t h e contour p l o t . The s t r e a m l i n e p a t t e r n i s almost symmetrical
about z = 0.5.
The a l o n g - f r o n t
1 vo i f t h e r e were no E’-h layer. v e l o c i t y i n t h e lower l a y e r , v, would be equal t o 2 The $ l a y e r serves t o smooth out t h e d i s c o n t i n u i t y a t x = 0. I t can be seen f r o m t h e p l o t s o f v t h a t t h e d i s t a n c e over which v changes fm a (negative) maximum value t o zero i n x > 0 i s g r e a t e s t f o r (b). The absolute value o f t h e maximum i s c o n t r o l l e d by t h e maximum o f vo as can be seen by a comparison o f (a) and (c). As we noted i n t h e i n t r o d u c t i o n , a s i g n i f i c a n t d i f f e r e n c e between t h i s model and t h a t o f Kao e t al. flow at x =
+,
(1978) i s t h a t we impose t h e c o n d i t i o n o f no c r o s s - f r o n t the cross-front flow originates f r o m the
w h i l e i n Kao e t al.,
frontal layer at x =
--, which
and then moves on t o x =
01.
by c o n t i n u i t y has t o cross t h e f r o n t a l i n t e r f a c e ,
T h i s d i f f e r e n c e i n t h e boundary c o n d i t i o n r e s u l t s i n
q u i t e d i s s i m i l a r c i r c u l a t i o n patterns.
SUMMARY AND DISCUSSION
7.
We have developed a model f o r the c i r c u l a t i o n be1ow.a f r o n t a l l a y e r . F r i c t i o n and t h e C o r i o l i s f o r c e p l a y a dominant r o l e i n t h e dynamics. I n t h e absence o f f r i c t i o n , t h e system i s i n geostrophic balance w i t h a f l o w i n the a l o n g - f r o n t d i r e c t i o n w i t h a d i s c o n t i n u i t y i n t h e water column below t h e f r o n t . F r i c t i o n a l e f f e c t s c r e a t e several Ekman and i n t e r n a l shear l a y e r s . An i n t e r f a c i a l Ekman l a y e r beneath the f r o n t a l i n t e r f a c e channels a t r a n s p o r t o f o r d e r E g i n a d i r e c t i o n away from t h e f r o n t . A compensating f l o w w i t h a v e r t i c a l v e l o c i t y o f o r d e r 1 upwells t o t h e surface through a t h i n v e r t i c a l i n t e r n a l shear l a y e r of t h i c k n e s s E h around t h e d i s c o n t i n u i t y . The f l u i d i n the E 3 l a y e r i s drawn from a t h i c k e r Stewartson l a y e r o f t h i c k n e s s E * , which a l s o serves as a r e t u r n channel f o r the upwelled f l u i d . A f r o n t maintains i t s sharpness by the movement of surface ambient water t o wards t h e f r o n t .
Our r e s u l t s i n d i c a t e t h a t t h i s surface convergence i s achieved
through upwelled water being sucked underneath t h e f r o n t a l transport.
l a y e r by t h e Ekman L
The distance over which t h e surface convergence occum i s E 2 f r o m t h e
front. The e f f e c t o f s t r a t i f i c a t i o n i n t h e ambient f l u i d t o t h e c i r c u l a t e d can be understood by drawing analogy Pedlosky,
from coastal
1967; Hsueh and Ou. 1975).
upwelling
( B a r c i l o n and
We s h a l l r e s t r i c t our discussion t o h o r i -
zontal and v e r t i c a l Ekmans o f equal order o f magnitude. c a t i o n parameter by S = (N s/f)‘,
problems
where
L e t us d e f i n e a s t r a t i f i -
N i s t h e Brunt-VZisa’ila frequency.
For a
347 weak s t r a t i f i c a t i o n , US < E, where u i s t h e P r a n d t number, t h e f l u i d i n t h e l o w e r l a y e r behaves e s s e n t i a l l y as i f i t were homogeneous. range E < US <
$,
by t h e s t r a t i f i c a t i o n .
The i n t e r n a l shear l a y e r around t h e d i s c o n t i n u i t y c o n s i s t s
o f an i n n e r l a y e r o f t h i c k n e s s (US)% t h e i n n e r layer.
The (US)%
f l u i d with a vertical
(E/uS)*.
For stratification i n the
t h e development o f an i n t e r f a c i a l Ekman l a y e r i s not a f f e c t e d and two Stewartson l a y e r s on both s i d e s o f
l a y e r assumes t h e r o l e o f t h e E 4 i n t h e homogeneous
t r a n s p o r t o f o r d e r Ec’ and a v e r t i c a l
v e l o c i t y of order
I n comparison w i t h u p w e l l i n g i n a homogeneous l o w e r l a y e r , t h e v e r t i c a l
v e l o c i t y i s smaller,
t h e w i d t h o f t h e u p w e l l i n g zone i s g r e a t e r and t h e v e r t i c a l
t r a n s p o r t i s t h e same. homogeneous case.
The S t e w a r t s o n l a y e r s have t h e same f u n c t i o n as i n t h e
We t h u s see t h a t the., b a s i c mechanism o f u p w e l l i n g i s unchanged
i n a weakly s t r a t i f i e d f l u i d .
I f US i s i n c r e a s e d beyond E4,
no i n t e r f a c i a l Ekman
l a y e r e x i s t s and t h e dynamics a r e governed m a i n l y by d i s s i p a t i v e processes. We now use t h e o b s e r v a t i o n s i n t h e G u l f o f S t . some o r d e r o f m g n i t u d e estimates. below t h e f r o n t a l l a y e r . we need a v e r t i c a l
Lawrence f r o n t a l zone t o o b t a i n
From t h e CTD data,
S i s a p p r o x i m a t e l y 0.27
F o r t h e r e s u l t o f t h e homogeneous case t o be a p p l i c a b l e
eddy c o e f f i c i e n t E > US, which corresponds t o an i n t e r f a c i a l
Ekman l a y e r o f a t h i c k n e s s o f 150 m o r g r e a t e r (assuming u = 1). e n t l y t o o l a r g e s i n c e t h e w a t e r depth i s o n l y 300 m. r e s u l t f o r weak s t r a t i f i c a t i o n , i.e., and t h e w i d t h o f t h e u p w e l l i n g zone, 0.07 AX =
E 0.27 (uS)+L = u N H / f
E < US < AX,
E*.
T h i s i s appar-
Consequently,
we use t h e
The c o r r e s p o n d i n g range f o r E
a r e g i v e n by
<
=
15 km
A l t h o u g h t h e u p w e l l i n g w i d t h i s d i f f i c u l t t o d e f i n e and determine f r o m t h e data,
f r o m t h e w i d t h o f t h e zone o f c o l d s u r f a c e w a t e r i n Fig. 2, t h e u p w e l l i n g zone appears t o be 10 t o 20 km wide, which i s c o n s i s t e n t w i t h t h e c a l c u l a t e d width. The v e r t i c a l v e l o c i t y o f t h e u p w e l l i n g l a y e r i n t h e s t r a t i f i e d case i s o f o r d e r U s i n g (7.1),
(E/uS)*.
we o b t a i n a v e r t i c a l v e l o c i t y o f 0.1 t o 0.2
cm s - l .
This
r e p r e s e n t s a v e r y s t r o n g v e r t i c a l m o t i o n and s h o u l d be a b l e t o d e t e c t with a v e r t i c a l c u r r e n t meter. An a l t e r n a t i v e i n t e r p r e t a t i o n o f t h e r e s u l t s i s t o i d e n t i f y t h e x > 0 h a l f o f t h e EL
l a y e r as t h e u p w e l l i n g l a y e r .
As we n o t e d e a r l i e r ,
required i f t h e r e i s a d i s c o n t i n u i t y i n t h e f r o n t a l velocity.
t h e E%
layer i s
I n a f r o n t a l zone,
t h e r e a r e h i g h h o r i z o n t a l g r a d i e n t s o f a l o n g - f r o n t v e l o c i t y across t h e f r o n t , b u t t h e d i s t a n c e o v e r which t h e r a p i d change i n v e l o c i t y occurs my not be s m a l l e r Sinking Under such circumstances, t h e r e does n o t e x i s t an E4 l a y e r . t h a n E4
.
t a k e s p l a c e i n t h e I?
l a y e r and t h e O ( 1 )
r e g i o n below t h e f r o n t a l
u p w e l l i n g t a k e s p l a c e on t h e o t h e r s i d e o f t h e EL l a y e r .
We t h u s have
layer,
and
348
Ax = EL L = ( A h / f ) + L4
Using 15 km f o r Ax,
we get Ah = 5x107 cm2 s-’.
low sea under normal c o n d i t i o n s .
T h i s value i s l a r g e f o r a shal-
But i n a f r o n t a l zone,
vigorous m i x i n g caused by
s m a l l - s c a l e processes such as double d i f f u s i o n and i n t e r l e a v i n g can d r a s t i c a l l y i n c r e a s e t h e value o f Ah. value o f E. 2.5~10‘~.
The v e r t i c a l v e l o c i t y i n t h e E L l a y e r depends on t h e
Assuming an i n t e r f a c i a l Ekman l a y e r o f 15 m t h i c k ,
T h i s g i v e s a v e r t i c a l v e l o c i t y o f t h e o r d e r EL 6U = 0.04
we have E = cm s - l , which
i s one o r d e r o f magnitude s m a l l e r than o u r p r e v i o u s e s t i m a t e and appears t o be a more reasonable number. ACKNOWLEDGEMENTS The a u t h o r wishes t o thank Dr. C.N.K.
Mooers f o r reading t h e manuscript and f o r
o f f e r i n g u s e f u l comments. REFERENCES B a r c i l o n , V. and Pedlosky, J., 1967. A u n i f i e d l i n e a r t h e o r y o f homogeneous and s t r a t i f i e d r o t a t i n g f l u i d . Journal o f F l u i d Mechanics, 29: 609-621. 1971. On t h e e q u i l i b r i u m shape o f t h e t h e r m o c l i n e i n a shore zone. Csanady, G.T., Journal o f P h y s i c a l Oceanography, 1: 263-270. Csanady, G.T., 1978. T u r b u l e n t i n t e r f a c e layer. Journal o f Geophysical Research, 83: 2329-2342. Home, E.P.W., Bowman, M.J. and Okubo, A., 1978. C r o s s - f r o n t m i x i n g and cabbelM.J. Bowman and W.E. Esaias ( E d i t o r s ) , Oceanic f r o n t s i n c o a s t a l ing. In: processes. Spring-Verlag, B e r l i n Heidelberg New York, pp. 105-113. Hsueh, Y. and Ou, H., 1975. On t h e p o s s i b i l i t i e s o f c o a s t a l , mid-shelf and s h e l f break upwelling. Journal o f Physical Oceanography, 5: 670-682. Joyce, T.M., 1978. Dynamics o f oceanic f r o n t s . American Geophysical Union Transaction, 5: 490-491 Kao, T.W., Pao, H. and Park, C., 1978. Surface i n t r u s i o n s , f r o n t s and i n t e r n a l waves : a numerical study. Journal o f Geophysical Research, 83: 4641-4650. K i l l w o r t h , P.D., 1973. A two-dimensional model f o r t h e f o r m a t i o n o f A n t a r t i c bottom water. Deep-sea Research, 20: 941-971. 1978. F r o n t a l dynamics and f r o n t a l genesis. I n : M.J. Bowman and Mooers, C.N.K., W.E. Esaias ( e d i t o r s ) , Oceanic f r o n t s i n c o a s t a l processes Spring-Verlag. B e r l i n Heidelberg New York, pp. 16-22. Mooers, C.N.K., C o l l i n s , C.A. and Smith, R.L., 1976. The dynamic s t r u c t u r e o f t h e f r o n t a l zone i n t h e c o a s t a l u p w e l l i n g region o f f Oregon. Journal o f P h y s i c a l Oceanography, 6: 3-21. An overlooked aspect o f wind-driven oceanic c i r c u l a t i o n . Pedlosky, J., 1968. Journal o f F l u i d Mechanics, 32: 809-821. Tang, C.L., 1980. M i x i n g and c i r c u l a t i o n i n t h e northwestern G u l f o f St. Lawrence: a study o f a buoyancy d r i v e n c u r r e n t system. Journal o f Geophysical Research, 95: 2787-2796. Veronis, G., 1970. The analogy between m t a t i n g and s t r a t i f i e d f l u i d . Annual Review o f F l u i d Mechanics, 2: 37-66.
349
IIU?lCRICAL T I D A L S7PlUIATTONS IJITRTH TIIT: HAURAKI GULF, NEV ZEAL4ND
MALCOLPI .J
. BOVTIAN
Marine S c i e n c e s R c s r . i r c h C e n t r r , S t a t e l l n i v r r s i t y o f llrw York, S t o n y B r o o k , Nrw York, 1 1 7 9 4 , U.S.A.
STEPREN 71.
CllTSWELL
P h y s i c s D e p n r t m e n t , U n i v e r s i t y of A u c k l n n d , k i c k l a n d , New Zealand."
ABSTRACT The a p p l i c a t i o n o f a n o n l i n e a r n u m e r i c a l t i d a l m o d r l t o t h e Hniiraki G u l f , ;L
s e m i - e n c l o s e d s h e l f s e ? on t h r r n s t -east of t h e N o r t h I s l a n d ,
i s drscribcd.
I t his p r o v i d e d a p r e l . i m i n ? r y a s s e s s m e n t of t i d a l e l e v i t i o n s and r u r r r n t s ,
o v e r t i d e s , t i d a l residual. c u r r e n t s , v o r t i c i t y , e n e r g y d i s s i p : ~ t i o n r n t e s n n d t h e s t r a t i f i ca t i o n i n d e x . The X 2 t i d e c l o s i i l y a p p r o x i m i t e s a s t a n d i n g wave.
As t h r r e s o n i n t t i d a l
p e r i o d a l o n g t h e l o n g i t u d i n a l a x i s o f t h e G u l f i s -5.2 n o n l i n r a r 112:1.14 i n f l u e n c e of
resonnnt i n t e r a c t i o n is expected.
t i d a l scouring ind
hoiirs, s i g n i f i c a n t
The m o d r l s u g q c s t s
m i x i n g on s ~ d i m c n tdeposition
:ind
in
the
i n t c b n s i t y o f summer w a t e r c o l u m n s t r a t i f i c a t i o n .
INTRDDUCTION AND SIGNIFICANCE OF R E G I O N The 1 I . i u r a k i G u l f
is a semi-enclosed
shallow
se.1
o f .area -5,O')O
km2
b o u n d e d by t h e c i a s t e r n s h o r c o f t h e ?Jew Z r a l a n r l m a i n l n n r l n o r t h o f A u n k l n n d CiLy, (Figs.
t h e w e s t e r n s i d e of
1 and 2).
t h r Corom:indel
I t i s a c o n t i n u a t i o n of
P e n i n s u l n nnrl G r e a t l3:irric.r I s l a n d R
downfnulted r i f t v a l l e y whlch
a p p a r e n t l y e x t e n d s f r o m t h e F i r t h o f T h a m e s t o t h e C o l v i l l e C h a n n e l ;it t h e n o r t h e r n t i p of t h e Coromandel Peninsiiln. H ; i r b o u r (t.r. " s p a r k l i n g w . i t e r s " ) s e d i m c n t s of I l i o c e n e Age (15-25 :ictive s e i s m i c a c t i v i t y .
Tamnki Strali t and t h r \ . l n i t e m a t a
a r e drowned r i v e r v a l l r y s r u t i n m i r i n e
x 106 y e n r s ,?go).
The r e s i o n h a s a h i s t o r y of
A u c k l a n l C i t y i s b u i l t a r o u n d 50 e x t i n c t v o l c a n o r s .
The m o s t r e c e n t , the i s l a n d o f R i n g i L o t o ( t r . " b l o o d red sky") l i r s ;it t h r e n t r a n c e t o I J a i t c m a t n 11arbour and
WAS
a c t i v e some ? 5 0 y e n r s a e o d u r i n g t h e
e a r l y H : i o r i o c c u p a t i o n of N e w Z e a l a n d (r.
*
Prescnt .iffil iotion:
1100 AD
- ).
Mirine Sciences Rrscnrch Centrr.
350
165' I
170'E
175'
180'
I
I
1
NORTH CAPE
35' REAT BARRIER
EAST
TASMAN SEA
C
40's
CAPE FAREW
45'
SOUTH PAC/ N C BOUNTY ISLANDS
STEWART ISLAND
I
I
Fig. 1.
Locator
m?D
I
I
o f N r w Zriland and t h e h a u r o k i G u l f .
Of t h c t o t a l a r r a , a b o u t 5% .7re s h a l l o w t i d a l l i n r b o r i r s ,
40% s h o n l w a t e r s
l e s s t h i n 20 m i n d e p t h , 70% w i t e r s of d e p t h 29 t o 40 m , a n d 25X w a t e r s d e e p e r t h a n 4 0 m ( P a u l , 1968). Gulf
is n e a r T1i:tmrs
The m n j o r s o u r s e of f r c s h w a t e r d i s c h a r g e i n t o t h e
f r o m t h e W;iihou R i v e r ( F i g .
2) whicli d r - i i n s a l a r g e
p o r t i o n of the f e r t i l e lliuraki P l a i n s t o t h e south.
The G u l f i s e x p o s e d t o
t h e S o u t h P a c i f i c O r e n n o n l y a l o n g i t s n o r t h e r n a p p r o n c h e s w h i r h su@,:rsLs
the
o r i g i n s of i t s M-aori n'arnc "11.3u" rnenning w i n d a n d "rnki" rnerlning n o r t h . T h e s u b t r o p i r n l E a s t A u c k l n n d C u r r e n t f 1 0 , ~ ss o u t h w a r d s d o w n t h e N o r t h Island east
CO\IS~,
i s d e f l e c t e d i n d s w e p t s o u t h e a s t w n r d s by t h r s h e l v i n g
b o t t o m 'ir.ross t h e e n t r a n c e t o t h c G u l f ( R r o d i e ,
1960).
Currents
r o . a c h 1.5 m
5 - l a t t i m e s n e a r G r e n t I3arric:r I s l a n d ( A d m i r a l t y H y d r o g r ~ p h i cD e p a r t m e n t ,
1958). Idinds i r e m o s t f r e q u e n t f r o m t h e w s s t e r l y o r s o u t h w e s t e r l y q u : i r t c r ,
351
H4URMl WlF
NQUTICQL M I L E S
D'
Fig.
2. D e p t h c o n t o u r s i n m e t r r s , t i d c ~ , n u g e1 o r : i t i o n s ( o p e n c i r c l e s ) 3nd S e o g r n p h i c i l l o c a t i o n s . A
Auck1:ind
P I P o n u i Ts1:ind
C
Caromandel H a r b o u r
PJ P o r t Jackson
CC C.ipc C o l v i 1 I . e
R1 R a n y i t o t o T s l . i n d
"11 H a h u r , i n g i l l n r b o u r
R 2 Rocky P o i n t
Fll 1lurr:iys B:iy
RC Rqngi toto Cbi.inncl
F12 M n t l a t i n Rny
SC S e r g c . i n t Ch i n n e 1
H7 T1.m O'W,ir
h y
N4 Y o t u t i p i i I s l . i n d
T
T i r i T i r i 1 l . i t a n g i Is
1J
Weiti River
w i t h m o s t g a l e f o r c e w i n d s coining f r o m t h e n o r t h e a s t . T h e s e m i - d i u r n n l t i d e o v e r t h e :Jew Z c o l a n d c o n t i n e n t a l s h e l f f o r m s n
r e s o u . i n t t r a p p e d w.ive w h i c h r o t a t e s c o u n t e r c l o c k w i s e w i t h n 12.42 h o u r p e r i o d (Rye and H e a t h .
1375).
T h e New Z e a l a n d l n n d m n s s i s t h u s c e n t r e d o n a
degenerate .intinmphidrone (Heath,
1977).
of t h e N o r t h Tslnnd, i n t o t h e h u r n k i G u l f
The t i r l i l wave s w e e p s u p t h e c o n s t
and p r o g r e s s r s n o r t h w n r d t o N o r t h
Cape. Plany i n l e t s a n d e m b n y m e n t s a r e l o c a t e d a l o n g t h e w e s t e r n a n d s o u t h e r n
352 shoreline,
w i t h t h c Waitfmotn K i r b o u r s e r v i n ? ;is New Ze:ll:ind’s
.ind t h e f o c a l p o i n t of Anckland C i t y (pop. New Z e o l a n d Navy a r c l o c a t e d h e r e , commerci:-\l f i s h i n g c e n t r e .
-8 x
In5).
mnjor s e a p o r t
F i c i l i t i e s of t h e Royal
a n d t h e h a r b o u r i s a l s o :in i m p o r t a n t
Niimeroiis i s l a n d s w i t h i n t h e Gulf n e a r t h e Harbour
e n t r a n c e t o g c t h e r w i t h e i s i l y navijiab1.e w;iterw:iys p r o v i d e Eood she1 t e r a n d brrthiige f o r l a r g c s h i p s . I
From t i m e t o t i m c ,
t h e p o s s i b i l i t y of c o n s t r u c t i n g
s e a l e v e l c a n a l . i c r o s s t h e A u c k l a n d I s t h m u s (minimum w i d t h - 2 I c m ) t o l i n k Thc Hsur;iki Gulf i s a l s o
t h e P a c i f i c Ocean i n d T:ismin Se.1 h a s b e e n proposed. :I
r e g i o n of gre:it n a t u r a l b e a u t y a n d a m . n j o r r e c r e a t i o n s 1 a r e a f o r bo:iting,
f i s h i n g and swimming. A s a c o n t r i b u t i o n t o t h e o c e a n o g r n p h y o f t h e G i ~ l f ,2nd t o provi’dc i n p u t
t o w i s e d e c - i s i o n making f o r munici.pal, commercial 2nd r e c r e a t t o n a l development a r o u n d i t s p e r i m e t e r , t i d . 3 1 s i m u l a t i o n s w e r e performexd w i t h a n o n l i n e a r n u m e r i c a l m o d e l w h i c h h a s a l r c x d y b e e n s u c c e s s f u l l y a p p l i e d t o a n u q b r r of o t h e r a r e a s (e.g.,
Rowmnn e t 31, 19RO).
T h i s modcl i s a b l e t o s c c u r . i t e l y
p r e d i c t t i d a l c l e v x t i o n s and c u r r e n t s ; tlic n o n l i n e a r t e r m s i n t h e model l e n d t o t h e g e n e r a t i o n o f r e s i d u a l ( m e a n ) t i d a l f l o w s and h i g h e r o r d e r h a r m o n i c ti.dcs.
Energy d i s s i p a t i o n r a t e s and t h e i n f l u e n c e of
t i d a l m i x i n g o n summer
w n t r r column s t r a t i f i c a t i o n c:in q l s o be e s t i m : i t e d from t h o model r c s u 1 . t ~ .
THE MODEL The m o d e l i s
&I
v e r t i c a l l y i n t e g r a t e d , two dimension71, n o n l i n e q r .
d i f f e r e n c e m o d e l b a s e d o n t h e a l g o r i t h m s o f L e e n d r r t s e (1967).
finite A grid
d i m e n s i o n of 0.326 km (0.5 n a u t i c 3 1 m i l e ) v n s chosen t o g i v e n d e q u i t e s p i t i a l rcsolution.
The m o d e l c o n t a i n e d 7 7 4 2 a c t i v e c e l l s .
W a t e r d e p t h s were
d i g i t i z e d from Royal Ncw Z e a l 7 n d Navy N a v i g a t i o n C h a r t s Nos. N2532 and N2533. The m o d e l r a n w i t h o u t i n s t a b i l i t y w i t h n t i m e s t ~ opf 124.2 s p c o n d s ( 2 l u n i r minutes).
I n t h e J b s e n c e of o p e n s e a t i d e g a u g e d a t a , t h e a m p l i t u d e s
and p h a s e s a l o n g t h e n o r t h e r n m o d e l b o u n d a r y w e r e d e r i v p d f r o m l i n e a r i n t e r p o l a t i o n s of
t h e M 2 s e m i d i u r n i l t i d a l p r e d i c t i o n s a v a i l a b l e from necirby
c o a s t a l t i d a l s t . i t i o n s (R. G i l l b q n k s , RVZN Hydrographic O f f i c e ; p e r s comm).
T h e model c a l c u l a t e d t i d a l e l e v a t i o n i n d v e l o c l t y components i n e a c h i n t e r i o r c e l l f o r every time step. s t a t e ( t r a n s i e n t decay t i m e -6
I t was c i l i b r a t e d by r u n n i n g t o a s t e a d y
t i d a l p e r i o d s ) and a d j u s t i n g bottom f r i c t i o n
f o r a n o p t i m a l f i t between p u b l i s h e d i n d model p r e d i c t i o n s . t i d a l harmonics
Of4,
P16,
The
and
Other
c t c ) g e n e r a t e d by n o n l i n e q r e f f e c t s wrre e v a l u a t e d
w i t h F o u r i e r a n a l y s e s of t h e t i d e s nnd c u r r e n t s f o r e.ich c e l l . The l o c a t i o n s of t i d a l s t a t i o n s i n t h e G u l f are shown i n Fig. 2; of t h e s p o n l y Auckland m a i n t a i n s
a permanent s t a t i o n .
The r e m a i n d e r r e p r e s e n t
l o c a t i o n s wherr a t e m p o r a r y t i d e gauge hns a t some t i m e been i n s t a l l e d .
These
p e r i o d s have been of v a r y i n g d u r a t i o n and hence p r e d i c t i o n s a r e of v a r y i n g and
353
30'
40'
37-
00
NAUTICAL MILES
in'
F i g . 7.
Amplitude of H2 t i d e (cm).
sometimes u n c e r t a i n a c c u r a c y .
TIDAL ANPLITUDES AND PHASES The t i d e d e r i v e d from t h e i n o d r l w i t h i n t h e Gulf c l o s e l y Ypproximites s t a n d i n g wave where t h e 3 m p l i t u d e i n c r e a s e s t o w a r d s t h e head (i.e.,
1
F i r t h of
Tlinmes), r i s i n g f r o m a minimum of 9 5 cm a t P o r t J a c k s o n t o o v e r 1 2 0 cm n e a r t h e c i t y of Tlinmes ( F i g . 3 ) .
C o t i d a l l i n e s ( F i g . 4 ) show t h a t h i g h t i d e s a r e
\ilmost synchronous ( t o w i t h i n a few m i n u t e s ) 0vc.r t h e e n t i r e r e g i o n w i t h t h e s o u t h e r n F i r t h l a q g i n g by -7'
due to f r i c t i o n a l r e t a r d a t i o n of t h e t i d a l
wve. Table 1 l i s t s model versus t i d a l s t a t i o n HZ p r e d i c t i o n s f o r a m p l i t u d ? nnd phase r e l a t i v e t o Auckland. d a t a of d u b i o u s a c c u r a c y ,
Values w i t h q u e s t i o n marks i n d i c a t r i t i d e gauge d e s i g n 3 t e d a s s u c h by 1 i r g e d i s c r e p i n c i e s from t h e
model and by d e p a r t u r e s f r o m r e g i o n a l t r e n d s a l o n g t h e c o a s t l i n r .
Stations
l o c a t e d o n t h e o p e n c o a s t u s u a l l y show murh b e t t e r a g r e e m e n t w i t h m o d e l r e s u l t s th,n Harbour).
t h o s e l o c a t e d n e a r r i v e r m o u t h s o r h a r b o u r s (e.q.,
Elnhur3ngi
By u s i n g a l l d a t a from Table J ( e x c l u d i n g borindlry s t a t i o n s ) t h e
354
Fig. 4 .
P h i s e t i d e of T12 t i d e ( d e g . ts.r.t.
high t i d r a t A u c k h n d ) .
r o o t mean sqiiare (rms) c r r o r s i n a m p l i t u d c nnc! p h i s e ar't? 54.5 .ind t8.G'
(9 s t ? t i o n s ) .
cm ( 3 s t a t i o n s )
If q u e s t i o n ? b l e v a l u e s ire d e l e t e d , tht= r n s e r r o r i n
i m p l i t u d t , i s 22.9 crn ( 7 s t a t i o n s ) a n d p h a s e i 6 . K o
(7 st3tions).
I t n 3 y be
p o s s i b l e t o rc.rlrire t h e s e ~ r r o r sby f u r t h e r a d j n s t m e n t of bottom f r i c t i o n , 1
huL
c a r e f u l assessment of t i d a l s t I t i o n data q u i l i t y i s needed before attemptin:
qny f i n e r t u n i n g of t h r model.
The t i d a l
WIVC
alono, t h c
xis o f
r l o s e l y resembles a c o - o s r i l l n t i n g
tlrc e a s t e r n G u l f and F i r t h (745'T)
tide.
I g n o r i n g r o t a t i o n a l ,ind f r i c t i o n a l
e f f e c t s , p r e d i c t e d e l e v a t i o n s niid c u r r r n t s d r e (Meumcinn ind P i e r s o n ,
1966):
c o s kx n ( x ) = r l ( L ) c o s kL c o s w t
-
U(x) = q(L) ( g / h )S s i n kx s i n w t c o 6 kL whcre wnvenumbrr
k = w(gh)-'
,
t h e o r i g i n i s taken a t t h e s o u t h end of t h e
F i r t h 3nd Lhe p o s i t i v e x d i r e r t i o n i s 345'T. U s i n g N a r i r a k i G u l f v a l u e s of L = 8 x 1 0 4 m , h = 70 m , n ( L ) = .95 m ( s e e
355
TABLE I Comp\irisons of m o d e l -im, ind t i t l n l s t a t i o n a t s , nmpli t u l l r nncl p'l.ise of :I2t i d r . .
1
Locn t i o n
% i h i i r i n g i Ilbr T i r i Tiri H a t : i n f i i Is. \ J e i t j River Vurrnys R i y I l n t a i t i Ray Pl,in O'War Biy Rocky Point C o r o m i n d r l Hbr Port Jackson
9
m - a ts
>k p
in
Its
cm
rm
rm
dez
11
t
t.
-7
T
Sym bo 1
0 R?
?ll
107 95? l P 5 ,'
tl2 ii3
in5 1!4?
K
129
n
C PJ
101
5 -0.5
w
91.5
111
A i i ck 1:in d
116
Rm
"tS
-7 -2
-2
-1
-2
-2
-8?
-2
n n -3
-5
0
d??
9, - E l s rll=r:
n
-1 6 2
-9 -4
-I!+? -5
13:
-6 -14? -6 -1 1
4 147 6
0
7
9
sc t
*
w i t h r e s p e c t t o Aucklnnd -i not a v a i l a b l e
TA?LE TI C o a p T r i s o n s o € model qnd p u b l i s h e d c i i r r m t strengths and dirertions.
direction
Location
A
R C
D E
F G H
1
J K L M N 0 P
\lode1
Chart
0.2 3 0.23 0.1 5
0. l o ? ? 0.51 0.51 0.4 1 0.77 n.51
0.05? n.74 n.16 0.23
0.14 0.10 3.25 n.'17 0.26 0.20
0.09 0.26 0.28
Q
0.3 1
R
0.27 n.irl
s
Ratio
'lodrl
2.?'1? 0.45
in3 I no
0.2~
057
n.122? n.44
150 014
0.31
ng?
0.1 5? 0.27
1.53?
no4
0.61
n 70
0.31 0.5 i 36
n.
O.R1 0.73 9.72
-
-
-
0.51 0.5 I 0.64 0.77 i.n7?
-
0.51 0.55 0.45 n.75 0.1 5 5 ?
043 747 020 751 015
on6 720 351 34.3 346 315
(OT)
A R
100? 77
5 -6 67? 29 7 -22 -1 7
n 1
-5 71 0 16 17 11 -1 5
356 F i g s . 2 and 7),
find
wr7
and
These compnre f n v o u r n b l y w i t h t h e model p r e d i c t i o n s (Figs. 3 and 9).
TIDAL CURRENTS
F o u r v c c t o r p l o t s o f h o u r l y t i d a l c i i r r ~ n t sa r e p r e s e n t e d .
These have
b e e n s c l e c t e d t o c o v e r e b b t i d a l s t r e a m s a t 0 , 1 , 3 , :ind 5 s o l a r h o u r s a f t e r h i g h t i d e a t Auckland. ebb.
F l o o d t i d a l p c t t t e r n s a r e e s s e n t i a l l y t h c r e ' v e r s e of
To n c c o m o d a t c a w i d e d y n q m i c r i n g e i n c u r r c n t s , t i d a l s t r e a m v c c t o r s
were s c a l c d n o n l i n e a r l y by p r e s c r v i n g t h e i r d i r c c t i o n s b u t p l o t t i n g a m p l i t u d e s p r o p o r t i o n a l t o t h e s q u a r c r o o t of t h e c u r r e n t .
The t r u e c u r r e n t s t r e n g t h s
a r e e a s i l y o b t a i n e d by u s i n g t h e n o n l i n e a r s c a l e on each c h a r t .
0 h o u r s ( F i g . 5) --
S l a c k w a t e r o c c u r s o v e r t h e s o u t h e r n ha1.f of t h e G u l f .
A
s o u t h w a r d c u r r e n t f l o w s down t h e n o r t h w e s t e r n n n r g i n o f t h e G u l f t h r o u g h Wh:inp,aparaos Bay and s w e e p s a c r o s s t h e o p e n r e a c h e s a n d n o r t h w a r d a r o u n d Coromandel P e n i n s u l a a s a narrow j e t o v e r t h o r e l a t i v e l y deep Cnpe C o l v i l l e Chnnne 1.
+I hour --
(Fig. 6 )
Ebb c u r r e n t s fl.ow t o w a r d s t h e o p e n s e a o v e r t h e e n t i r e
r e g i o n e x c e p t i n t h e n o r t h w e s t e r n nppronch where c u r r e n t s f 1 ow s o u t h e a s t w a r d . S t r o n g f l o w s a r e found
i n t h c R a n g i t o t o Channel a s W?ltrmatn Harbour
d i s c h a r g e s , bctween Yototnpu and Woihcke I s l ? n d s ( S e r g e a n t Chnnncl). cind e a s t T h i s i s n conscquence of t h e w a t e r i n Tamiki S t r a i t
of Walheke I s l a n d .
e b b i n g , d i v e r g i n g snd f l o w i n g a r o u n d Waiheke I s l a n d .
+D h o u r s --
(Fig. 7 )
F l o w s i n t e n s i f y .is e b b c i i r r ~ n t sp e a k o v e r t h e G u l f .
A
s t r o n g conver,sencc f o r m s n o r t h of Waiheke I s l s n d as t h e f l o w s meet from around
i t s w e s t e r n and e a s t e r n e x t r e m i t i e s .
+5 h o u r s --
(Fig.
8)
N o s t of t h e Gulf c o n t i n u e s t o ebb,
C o l v i l l e where flood t i d e commences.
e x c e p t n e a r Cape
E l s e w h e r e most c u r r c n t s arc d i r e c t e d t o
t h e n o r t h e r l y qiiarter. Noximum t i d a l s t r e a m s a r e c o n t o u r e d i n F i g .
9.
Highest values a r e
l o c a t e d I n t h e c o n s t r i c t e d R a n g i t o t o and Serge;int Channels (-50 and 6 5 cm sr e s p e c t i v e l y ) and i n t h e C o l v i l l e Channel ( - 6 0 r m s - ' ) .
1
,
E l s e w h e r e i n t h e Gulf
c u r r e n t s a r e t y p i c a l l y -20 cm s-'. T i d a l . c u r r e n t e l l i p t i c i t i e s and m a j o r a x i s o r i e n t a t i o n s a r e p l o t t e d i n Fig.
10.
Again t h e c u r r e n t s w e r e s c a l e d w i t h a s q u a r e r o o t law.
In the
r e l a t i v e l y open seas of t h e n o r t h e r n a p p r o a c h e s c u r r e n t s a r e r o t a r y i n t h e e x p e c t e d a n t i c l o c k w i s e s e n s e f o r t h e s o u t h e r n hemisphere.
In c o a s t a l areas
and i n most of t h e s o u t h e r n Gulf t i d a l s t r e a m s are e s s e n t i a l l y r e c t i l i n e a r ,
357 e x c e p t n e a r i s l a n d s .and he:tdlanrls where i n e r t i a l e f f e c t s i n rcgions of sh.irp curvnture
C B I I S ~f l o w
s e p a r a t i o n inrl hence g r n c r a t c rotLition
t.he ~ h abn d
RS
f l o o d c u r r e n t s f o l l o w s l i q h t l y d i f f e r e n t p,iths. T a b l e I T p r e s e n t s compArisions of model. p r e d i c t i o n s w i t h h i s t o r i c a l t i d a l c u r r e n t m e a s u r e m e n t s ( R N Z N N a v i g a t i o n C h a r t s Nos. N7.532 nntl N2533). L o c a t i o n s of t h e s e measurements a r e p l o t t e d i n Fig.
The
10.
Although no d e t a i l s on e x p e r i m e n t , i l p r o c c d u r e o r i n i l y s i s methods were a v a i l a b l e a t t h e t i m e o f w r i t i n g , we h a v e a s s u m e d t h a t p u b l i s h e d v a l i i c s represent surf,ice s p r i n g t i d l 1 streams.
An a p p r o p r i a t e r n t i o of s p r i n g l n e a p
c u r r e n t s f o r t h e G u l f i s 1.35 (Rye and H c a t h .
1Q75).
We r e d u c e d s u r f a c e
c u r r e n t s Us t o depth-mean c u r r e n t s U fro'm thr. e m p i r i c a l power law
The sh.ipe of t h e v e l o c i t y d i s t r i b u t i o n i n ttd.11 r p g i o n s c i n be q u i t e v i r i i b l e w i t h r e p o r t e d v a l u e s of t h e exponent ct l y l n y between 1 / 5 a n d 1 / 1 1 (Van Vcpn, 1936).
For a t y p i c a l v.ilue of
CL = 1 / 7 (Dronkers,
T h i s compares w l t l i a v a l u e of 0.52
1364)
IJC
found
k0.17 o b t a i n e d from Table I T .
The q u e s t i o n marks i n column 2 r e p r e s e n t c u r r e n t speed d a t a t h . i t a p p e a r o f d u b i o u s q u a l i t y o r a r e i n f l u e n c e d by r i v e r r u n o f f ( v i z . .
s t a t l o n S, Fia.
F o r e x a m p l e , p r o x i m a t e s t a t i o n s A and B w o u l d be e x p e c t e d t o p o s s e s s
10).
s i m i l a r t i d a l s t r e a m s , as might s t a t i o n s G and E. D i f f e r e n c e s between p r e d i c t e d and o b s e r v e d c u r r e n t d i r e c t i o n s a r e a l s o p r e s e n t e d i n T a b l e 11.
6.0'
E x c l u d i n g q u e s t i o n m a r k e d v a l u e s , t h e mean e r r o r i s
which i s i n good agreement g i v e n t h e a p p r o x i m n t i o n s i n h e r e n t i n
f16.5',
t h e model and t h e d i f f i c u l t i e s of making a c c u r a t e c u r r e n t measurements i n shallow water. :ind F.
The two m a j o r d i s c r e p a n c i e s i n d i r e c t i o n are from s t a t i o n s B
These :ire b o t h l o c a t e d i n r e g i o n s of l o w e l l i p t i c i t y a n d d i f f i c . u l t i e s
i n e s t a b l i s h i n g t h e d i r e c t i o n of t h e s e m i m a j o r a x e s f r o m l i m i t e d d u r a t i o n d a t a would be expected. A map o f M 2 t i d a l v o r t i c i t y i s p r e s e n t e d i n F i g .
11.
These c o n t o u r s
conform t o e x p e c t e d p a t t e r n s where h i g h e s t v a l u e s ;ire a s s o c i a t e d w i t h r e g i o n s of
flow
i n t e n s i f i c a t i o n and
peninsulas.
curvatur.e around
V o r t i c i t y v a l u e s -3
x
s-l
the various
and
1 x
i s l a n d s and s-l
roughly
c o r r e s p o n d t o t h o s e i n t e r i s l a n d c h a n n e l s where t i d a l c u r r e n t s peak n e a r 40 a n d 2 0 cm s - l r e s p e c t i v e l y (Fi.g. 9).
I t i s n o t y e t known w h e t h e r v o r t i c i t y
g e n e r a t e d i n t h e s e r e g i o n s h;is a n y i n f l u e n c e o n o f f s h o r e t i d a l s a n d b a n k format ion.
P i n g r e e ( 1 9 7 8 ) nnd P i n g r e e a n d Mnrldock ( 1 9 7 9 ) h a v e c o n d u c t e d
i n t e r e s t i n g n u m e r i c a l e x p e r i m e n t s n e a r some h e a d l a n d s on t h e s o u t h c o a s t of D o r s e t and Devon, E n g h n d , which s u g g e s t a s y m m e t r i c f o r m n t i o n of s u b m a r i n e
358
30'
40'
50'
37:
00 S
NAUTICAL MILES
0
10
5
0
10
20
15 I
I
20 KILOMETERS
I
30
10'
I
40' Fig.
5.
50'
175'00'E
T i d a l currents ;it time of h i g h t i d e a t kickland.
359
_ _ _ _ ____<,,,.,..* ................. ................. .,,,.
_ * _ _ _ _ - - - l , , , , . l . _ _ _ _ _ . _ _ <
n . .
..._._...l. . . . . . . . . . .. .. .. .. .. .. .. .0. .. .._................. _ _ _ _ _ _ _ < _ A , , , , . , .
.......................... ........................ .... _-...... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
,a:::
. _ _ _ ........................
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1
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................ ............
............ ..-- - - - ..___
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............
40'
.,
37" 00' S
,,,,,<
-
5
0
NAUTICAL MILES I0 15 I
I
I0
0
20 KILOMETERS
20 I
30
10' -
40' Fi;.
5.
50'
175'00'E
T i i l i l c u r r e n t s 1 tiour a f t e r h i z h t i r l r n t Aiiclilnnd.
362
NAUTICAL MlLES
5
0
to
0
10 20 KILOMETERS
15
20
30
10'
40' Fiq. 7.
50'
175"OO'E
T i d a l c u r r e n t s 3 hours after hiqh t i d e
Auckl n ~ d .
It
363
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i
.:
,
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364
30'
40'
50'
37"
00' S
NAUTICAL MILES
5
0 0
15
10 I
I
20
10
20 I
30
KILOMETERS
lo'
40' F i g . 8.
50'
175'00'E
T i d a l c u r r e n t s 5 hours after h i g h t i d e a t Aucklnnd.
366
3 S NAUTICAL MILES
KILOMETERS
F i g . 9.
T i d n l c u r r e n t s p r e d s a l o n g semi-m?jor
axrs ( c m s - ~ ) .
b.inks n e a r t h e s e p r o q o n t o r i e s u n d e r t l i P i n f l u e n r e of p l a n e t a r y a n d r c l n t i v e vorticity.
C u r r e n t s a r o u n d t h e i s l a n d s of t h e Gtilf a r e o f t h e o r d e r of o n e
t h i r d o f t h o s e i n t h r E n g l i s h C h a n n e l and t h u s b o t t o m s t r e s s e s a r e ? b o u t o n e tcntli.
TIDAL RESZDUAL CIJRRENTS N o n l i n e n r t e r m s i n t h e model e q u a t i . o n s of m o t i o n and c o n t i n u i t y g e n e r a t e r e s i d u a l f l o w s ( E u l e r i n n t i d a l stre.ims a v e r a g e d o v e r a t i d a l c y c l e ) e v e n when t h e n o r t h e r n boundary i s d r i v e n p u r e l y a t t h e H2 frequency. E d d i e s i n t h e r e s i d u a l f l o w a r e g e n e r a t e d by t h e t r a n s f e r of v o r t i c i t y f r o m t h e t i d a l t o t h e mean f l o w a s n c o n s e q u e n c e o f t h e f i e l d a c c e l c r n t i o n
terms i n t h e e q u a t i o n o f m o t i o n .
These e f f e c t s a r e often associated with
s t r o n g o s c i l l a t o r y f l o w s a r o u n d p r o m o n t o r i e s ( P i n g r c r . a n d ?laddock.,
Mnddock and PI.i,;rec?,
1978; Tee,
Thc proper procedure f o r computing t i d a l r e s i d u a l s i s controversy.
1977;
1976, 1977). R
m n t t c r o f snme
N i h o u l ( 1 9 7 5 ) 2nd N i h o n l qnd R u n f o l n (1981) claim t h a t
t h e r e s i d u a l t i d a l s i g n a l t o n u m e r i c a l n o i s e r a t i o i s o f t h e o r d e r one i n many
367 r c s i o n s i.c., itself.
t h e c o m p i i t n t i o n : i l p r r o r i s c o m p n r ; l b l r t o t l i c r r 5 i d r i : i l rrirrvrit
Nitioul
i , q r i a t i o n s of
rlaims
motion,
level or currents.
ex;impIe,
t1i:it
i s necessary
On t h e o t h e r h a n d ,
h a v e prodricerl
:ipp;irently
i t
re:ilistic
with
plots
n o r t h w e s t e r n European s h e l f wind d r i v v n s o l u t i o n s . comput:ition r e l . i t r s
to first
t i m e nver:ryc
a n d a p p l y t h e s e w i t h known b o u n d a r y v i l r i r s of mt1;in
:I
of
P i n g r r e nnd GriffiLlis (13RO),
v e r y larc.,c f i n i C e d i f f e r r n c r model wind
driven
residual
c.iirrents
ovrr
thc
sr;i
for some the
by c o m p u t i n g E u l e r i n n a v e r a ~ , p sof t h e t i d i l p l u s
Anoth#!r p r o b l e m w h i c h a f f e c t s e i t h e r method of
t o t h e c o r r e c t s p e c i f i c a t i o n of
tlic boiindary comii t l o n s .
S m a l l c.hnnges i n . I n p l i t r i d e nnd p h a s e a l o n g t h c b o u n d a r y c a n c n i i s r s i g n i f i c n n t
changes i n r e s i d u a l c u r r e n t p a t t e r n s in”the model i n t e r i o r . As
an
initial
approach
t o t h r s t u d y of
mein
circulations
we
h:ive
c a l c u l a t e d t h e E u 1 e r i : i n t i d a l r r s i d u n l c u r r t = n t f r o m t h c ti.d:il s o l i i t i o n s ,
-
=
+
at,
T 0
r ~ h e r eT i s t h e t i d a l p p r i o d a n d v e l o c i t y vector.
t h r instantnneous v e r t i c a l l y avcragcd
One m e a s u r e o f s i i c c c s s i n s e p n r i t i n t : t h r s i g n - 1 1 f r o m t h e
n o i s e i s t h e a p p a r e n t s p a t i a l c o h e r e n c y of t h e r e s i d u a l s , a l t h o u g h s u b t l ? p r o b l e m s c a n nppenr.
F o r e x a m p l e , ? r i d s c a l e e d d i e s g r , n p r a t e d by :ihrupt r l r p t h
c h ? n p , e s :ind c ~ r n e re f f ~ c t sm u s t conccntrntcd attention
he
on m c s o s c n l e
ronsideri?d suspicious. f r . i t u r e s of
the
We h a v e
residu.11 flow ind
v o r t i c i t y n r o r i n d t h e L s l a n r l s i n d h e a d l a n d s w h e r e s i m i l a r e f f e c t s hnvi, h c e n d o c u m e n t e d i n o t h e r s h . i l l o w seas. F i g . 12 i s n p l o t of r e s i d u a l c i r c r i l . i t i o n compriterl i n t h e : i b s e n c e of w i n d stress. i)
Sever.?l f e a t u r e s rmergc:
A broad w e s t w n r d d r i f t o c c u r s o v e r t h e n o r t h e r n Gulf which p a s s e s b o t h
s i d e s of T i r i T i r i H;it.ingi I s l i n d i n d s w e e p s i n t o Whnngnparao.? nay. ii)
A number o f
c o u n t e r r o t a t i n g c d d i e s f o r m . i r o r i n d t h e m.ijor i s l : i n d Zrorips.
These a r e p a r t i c u l a r l y well developed o f f Island,
whcre
ii
t h r n o r t h e . ~ s t c r n r o r n r r of \J,iiliekp
strong o f f s h o r e ( ~ n s t w i r d )n e t f l o w r e s i i l t s .
A n o t h r r p , i i r of
e d d i e s i s l o c a t e d n o r t h i n d s o u t h of w e s t e r n Wniheke Tsland r p s i i l . t i n g i n a n o r t h w a r d f l o w n o r t h e ’ i s t o f f t h e i s l a n d and a s o u t h w a r d f l o w t o w a r d s t h e northern coast.
T h e s e e d d y i n g m o t i o n s i l s o become a p p a r e n t
v o r t i c i t y m,qp ( F i g .
17).
A l . t e r n ~ t i n qr e g i o n s of
in the residual
posi.tive and negative
v o r t i c i t y ;ire l o c a t e d r i t h e r s i d e of t h e v a r i o u s h e a d l . i n t l s and i s 1 : i n d s of t h e Gulf.
T h e r e l a t i v e v o r t i c i t y o f t h e s t r o n g e s t e d d y i s --0.4f
and i s l o c a t e d
[ i f f t h ? n o r t h e a s t e r n c o r n r r of I J ; i i h ~ k eI s l a n d w h i c h l i e s i n t h e p a t h o f t h e d i s c h a r g e f r o m b o t h t h e Tamaki S t r a i t and t h e F i r t h of T l w m e s .
368
30t . ....... .......... ,
F... .................... I II 1
p...................... : : I :::: ::: 1 1 1 1 11
......................
, 1 l , , , , l , r r l , , l l , ~ , , . ~
'"i
...................... ...................... ,
r
,
l
r
,
,
r
l
,
,
l
l
,
l
l
,
l
~
(
'
4
...... ............ ...... ,,,,,I
,....... . . . .
I . . . . .
.
I , , . . . .
.
.
50' ............
. ............ ............
'I
NAUTICAL MILES
0
5I
10 I
I
0
10
20
1I5
20 I
30
KILOMETERS
10'
40' F i z . 10.
50'
175°00'E
T i d ; i l c u r r e n t s p e e d s and e l l i p t i c i t i e s . L e t t e r s A through S represent locations where c u r r e n t dnt.) a r c n v a j l n b l e .
369
I
\ i \
i
I I I I I
10'
20'
30'
370
Fip,. 11.
Amplitudes of PI2 t i d a l v o r t i c i t y
s-').
IIIGHER T I D A L 1 I A R ' l O N I C S W h i l e t h e 'I2
t i d a l s o l u t i o n d e p e n d s o n l y w e a k l y on t l i e n o n l i n r n r t e r m s i n
t h c g o v e r n i n g e q u a t i o n s , tliese t e r m s s t i l l g e n e r a t e t i d a l hnrmonics i n tlie model i n t e r i o r .
The ? I 4 h a r m o n i c w i t h p e r i o d 6.21
h o r i r s is gener:itf?d by t h o s e
t e r m s wliirh c o n t a i n p r o d u c t s of v a r i a b l e s o s c i l l a t i n g n t t h e N2 f r e q u e n c y
( v ~ z . , t h e . i d v e c t i v e t e r m s ___ e t c . , The f r i c t i o n a l t e r m
and t h p c o n t i n n i t y t e r m s - (aH U )
ax
UlUl c a n b e , i p p r o x i n f l t c d f o r
etc.).
n co-oscill,Iting
tide
with zrro r e s i d u i l current as
llcncr,
qu t d r ~ t i cf r i c t i o n g e n e r a t e s o n l y o d d h n r m o n i r s ('16,
'Ilo,
etr.).
l l o w w c r , when d i v i d e d by t h r t i m e v a r y i n g d e p t h
H(x,y,t) f r i c t i o n genPratixs
,I
sm-111
= h(x,y) + rl(x,Y,t). contribution to
the
'1'
nccrler~tion.
For
371 rrctilinenr
flow i n
s t a n d i n g wave p i t t e r n ,
I
it
br s h o w n t h a L Lhe
can
r c s p c c t i v c c o n t r i b u t i o n s t o t h e P14 a c c e l e r a t i o n s a r e ( P i n t r e r 2 n d 'lnrlrlock,
1978) 4 g U , 2 b /3mC2h2
'L
f r i rtion
\.lit11 U o - .2 m s
-1
, no
+
+
kU:/2
k2gbU0/w
advert ion
rontinrii t y
1.0 m , h = 7 0 m iind k = 8.2 x l o - '
=
t h e r e l a t i v e m n g n i t u d e s i n g c n e r 2 t i n g :I4
m-]
o s c i l l a t i o n s i r r -1:7:20.
t h e n o n l j n e n r i t i e s i n t h e c o n t i n u t t y e q u a t i o n dominntc*, term being t h e smnllest.
Locilly,
Clearly
with t h e friction.11
w h r r e , ' r . o n s i d r r n b l e cu-rvntiirc e x i s t s i n t h e
n c i g h b o u r h o o d of p r o m o n t o r i e s and i . s l a n d s , t h e a d v e c t i v c t e r m s may d o m l n : i t r .
I n s u c h ,areas, t h e i n s h o r e l o w c r i n p , of sen I e v c l by c r n t r i f u g n l e f f r c t s d u r i n g hoth ebb and flood streaming gener.ites o s c i l l a t i o n s nt frequency as w e l l a s
:i
t-wicr t h e t i d ? l
l o w e r i n g of m r a n srn s u r E a c e t o p o q r i p h y .
To c o r r e c t l y s i m r i l a t r 1.14 t i d e s a n d c u r r e n t s i n t l i P model i n t e r i o r i t i s necess;iry t o a c c u r n t e l y s p e c i f y M 4 t i d a l o s c i l l n t i o n s g c n r r n t r r i r x t r r n i l l y and p r o p n ga t c d t Ii r o u g h t lie n o r t h e r n b o u n d a r y .
Un f o r t un:i t e 1y n o pub 1i s h e d d a t .7
~ i c r ca v n i l a b l c a n d s o t h i s c o n t r i b u t i o n c o u l d n o t h r c b v n l u n t c d .
We t h u s
i n v e s t i g a t e d o n l y t h e p r e s e n c e of h i g h e r h a r m o n i c s w i t h i n t h e m o d r l i n l e r i o r (Figs.
14 a n d 1 5 ) .
The r e s o n i n t l e n g t h L f o r t h e s e c o n d h a r m o n i c (?IL)
L = (gh/8)' where
B =
gUoT/2nhC2
'L
T[(1
+ B2/4)%
t i d e i s ( K r c i s s , 1357)
- l]'/B
.12 f o r h = 30 m and U .
9 6 km = 0.2 m s
-1
T h i s i s c l o s r t o t h e l e n g t h of l l i u r n k i G u l f , i l o n p , i t s n o r t h - s o u t h a x i s a n d h r n c c w e m i g h t c'xpect s i g n i f i c a n t n o n l i n r n r rc'sonant i n t c r n c t i o n .
I n siich
c a s e s .in e s t i m a t e o f !14 t o 'I2 c u r r e n t s r - ~ t i oi s
'L
. 4 5 for
no
= 1.2 m , h = 2 m , B
'L
4.34
T h i s c o m p n r t ? ~w e l l w i t h ,a m o d e l l e d v a l u e o f U4/U, = - 6 0 a t l o c a t i o n s S ( F i g . 10) i n t h e s h a l l o w s n e n r t h e c i t y of Thames.
U4/U,
= .054
However,
t h e m o d e l l e d v a l u e of
i n t h e d r e p r r c e n t r a l F i r t h w a t e r ( l o c a t i o n J ; h = 7 1 m) i s
c o n s i d e r a b l y l e s s t h x n K r e i s s ' p r e d i c t i o n of
0.35.
T h e :.I4 t i d e g c n c r a t e d b y t h e d i v e r g e n c e t e r m V q U
i n the continuity
I
e q u a t i o n p r o d u c e s a n n s s y m e t r y i n t h e t i d a l wave n e a r t.hc. head of embayments such t h a t t h e s t r o n g e r f l o o d t i d e i s of s!iorter d u r a t i o n t h i n tlie l o n g r r but w e a k e r e b b t i d e ( F i g . 16).
At location S , f o r oxnnple, currents flood f o r
5
372
a 30'
&.,,.,......... ,.. ... ................
... . .....& ......... .....,............ ..................
... ..................I ....................................... Wqf:::::::::::::::::: .;4,sI I
I , , , .
I I
\ I
- ? r r I I w
4 4 .
\
40'
50'
37"
00' S
0
5
NAUTICAL MlLES 10 15
1
0
10
20
I
I
20
30
K I LOMETE R S
10'
40' Fig.
12.
50' 'Tid:il ri.sirlu?l currents.
175'00'E
373
I
1
374
Fin.
13.
T i d a l rfsirlri?l v o r t i c i t y
s-l).
h o u r s 10 m i n u t e s , p e a k i n g .it 2 1 cm s - ’ , w h i l c e b b c u r r e n t s f l o w f o r 7 h o u r s 1 5 mi.nrites, ,i
;in3 p r a k
;it
17 ern s-’.
Sincr? s h c n r s t r e s s e s n e a r t h e s e n bed f o l l o w
s q u a r e l n w , t h i s c i n p r o d u c e s e d i m e n t t r . l n s p o r t t o w n r d s t h e h e a d of t!ie b ? y ,
althouzti i t I s d o u b t f u l i f El2
-
\ I 4 i n t e r n r t i o n s h i v e much e f f r c t ovpr most o f
ttic F i r t h .
The t16 2 n d h i g h e r 11-irmonics w e r e o f v p r y s n n l l a m p l i t u d e (<2 em)
OVCK
the
G u l f , 1 s werc d e v i a t i o n s i n m e ? n s e a surf;ice t o p o g r i p h y ( a r o u n d Wnihekr? I s l a n d mean s e n topogr:rphy d r o p p e d -1
BOTTO!l STRESS
em).
.AND E W R G Y DISSIPATION RATES
The mean b o t t o m f r i c t i . o n n 1 s t r e s s d u r i n g n t i d a l c y c l e i n t e r e s t i n s e d i m e n t r e s u s p e n s i o n and r1rposj.t i o n . correspond w i t h :ravel
Pg/c’.(Ul
i s of
l l i g h stress r e q i o n s shorild
o r b o i i l t l r r b o t t o m :in1 l o i ~s t r e s s r e g i o n s w i t h mud o r
clay.
N h r n p1.otted on l o q n r i t h a i c s c a l r s c o n t o u r s o f t h e e n e r g y d i s s i p 7 t i o n r a t e pg/ C 2’ 1vI latter
? r e simil.ir t o t h o s e of
:ire p l o t l e d
(Fig.
17).
hottom stress.
1liShcst
Accordingly only th?
d i s s i p a t i o n r.ates o c c u r
in
thc
375
II
NQUTICAL MILES
KILOMETERS
10'
Fig.
14.
Amplitude of !I4 t i d e (cm).
R:tnSitoto 2nd S c r g e r i n t C h a n n e l s ond a r o u n d t h r n o r t h e r n t i p of t h e Corom:lndel
Peninsula 0 1 0 0 e r g P e n i n s u 1 . i (<0.1
s-').
erg
p e r i m e t e r of t h c Gulf.
cm
-'
cm-2
L o w e s t v a l u e s a r e f o u n d n o r t h o f Wii;inp,apilrnon
s-'),
Lind i n s h e l t e r e d e m b a y m e n t s a r o u n d t h e
A b r o a d b
- 100 erg
s - l ) l i e s alonp, t h e e a s t e r n G u l f e x t e n d i n g s o u t h i n t o t h e F i r t h o f
Thamcs
.
A s i m p t i f f e d i n t e r p r e t a t i o n of bottom s e d i m e n t s (domin.int c o n p o n e n t s ) is
g i v e n i n Fig.
1 8 ( a f t e r C a r t c r and Ende,
1980).
R e n t o n s of c a l c . a r e n u s : r a v e l
(>502 c a l c i u m c a r b o n a t e i n Z r ; i v e l f r a c t i o n ) a r e l o c a t e d in t h e s o u t h e r n F i r t h , a r o u n d C a p e C o l v i l l e a n d s o u t h of T i r i T i r i > f a t ? n g i I s l a n d a n d i n S e r g e a n t Channel. beds,
Some of
but
Cape
dissipation.
these mntcrials Colvillr
and
nrp probably a s s o c i l t e d w i t h s h r l l f i s h i n g
Sergeant
Ch;?nnel
are
r e g i o n s of
elevated
A bro:irl band of s a n d y s e d i m e n t l i e s a c r n s s t h e n o r t h e r n G u l f and
t h i s a p p e a r s t o l i e b e t w e e n t h e 1 and 2 c o n t o u r s .
? l u d d y s e d i m e n t s ,are
g e n e r a l l y f o u n d i n r e g i o n s w i t h d i s s i p a t i o n l e s s t h a n 1 ( 1 0 e r g cm-* s - l ) * a l t h o u g h t h e s o u t h e r n F i r t h w i t h i t s c l a y b.ank d o c s n o t c o n f o r m t o t h i s interpretaton.
I t i s p o s s i b l e thrlt a n upstream (f.e.,
southerly) estuarine
376
Fio,.
15.
P h ~ s eTILl
t i d e ( d i ’ . ~ . w.r.t.
P12
h i g h t i d e a t kucklnnd).
+ 5 0 crn s-l n 0
s LL
I
0 m m
lT
’J
W
- 50 crn s-I Fig. 1 6 .
T i d a l c u r r ~ n tciirves f o r l o c a t i o n s J and S ( s c c F i g . 10).
377
NAUTICAL MILES I0
i
20
30
20 KILOMETERS
10,
Fig. 17.
-2
Energy d i s s i p a t i o n r a t e s ( e r g cm
s
-1
).
f l o w a t d e p t h r e c i r c u 1 : a t e s nnrl t r a p s f i n e s e d i m e n t s o r i g i n ; l t i n g f r o m t h e Wnihou R i v e r w i t h i n t h e s o u t h e r n F i r t h . A s t r o n g c o r r e l a t i o n between s e d i m e n t g r a d e a n d bottom s t r e s s wou1.d be
e x p e c t e d o n l y i f -in i n i t i a l . m i x o f s e d i m e n t a r y t y p e s were u n i f o r m l y s p r e : t d o v e r t h e e n t i r f r e g i o n ,lnrl subsequent i n l l y reworked by bottom c u r r e n t s .
Fines
would be d e p o s i t e d i n low s t r e s s r e g i o n s nnrl c o n r s e r s a n d s i n h i g h e r
strc?ss
regions.
Boulder sized g r n v e l would t h c n e x i s t i n t h e h i g h e r s t r e s s r c i i o n s
3 s t i d a l s c o u r i n s removed a l l s m a l l e r p a r t i c l e s . m o r e complex.
The r e a l s i . t u n t i o n i s much
F i n e s e d i m e n t s a r e brought down by r i v e r s nnd s t r e a m s e m p t y i n s
i n t o the b a s i n , c a l c a r e o u s s e d i m e n t s a c c u m u l a t e i n s h e l l f i s h i n g beds,
lah?rs
( v o l c a n i c mud f l o w s ) a n d d e b r i s f r o m R a n g i t . o t o and o t h e r A u c k l . l n d l s c h m u s v o l c a n o e s h?ve undoubtedly a f f e c t e d t h e Gulf. last
glaciation (-lo4
years
ago)
and
.
Ch?nginz sea l e v e l s s i n c e t h e
sedinent
accumulation i n
local
d e p r e s s i o n s e a c h have a n i n f l u e n c e on t h e p r e s e n t d n y s e d i m e n t s t r u c t i i r e . l J e v e r t h e l e s s , t h a m o d e l d e m o n s t r a t e s ?n i n f l u e n c e of t i d a l s t r e a m i n % o n reworking 2nd d i s t r i b u t i n g s e d i m e n t s .
378
Fig.
18.
T)omin:int s e d i m r n t t y p e s x c o r d i n g t o C a r t e r a n d E . i d e ( 1 9 8 0 ) ) .
SUMX R STRATIF I C A T T DN
S i m p s o n a n d H u n t e r ( 1 9 7 4 ) d e r i v e d a " s t r a t i f i c a t i o n index" h / U "
(vhere 'I
i s w a t e r d e p t h and U i.s t h e s u r f a c e c u r r e n t a m p l i t u d e f o r s p r i n g t i d e s ) a s measure of t h e i n t r ? n s i t y o f summer w q t e r c o l u m s t r ; i t i f i c n t i o n .
1
High v x l u e s
of h / U 7 o f t e n c o r r e l a t e w i t h r e g i o n s o f s t r o n g s t r n t i f i c n t i o n , v h e r e r l s l o w v a l u e s c o r r e s p o n d t o r e g i o n s w!iicli (-30
-
100 m - ' s - ?
r e m : i i n w e l l mixed.
I n t e r m e d i a t e v.ilu;?s
d e p e n d i n g p a r t l y on l n t i t i i d e ) h a v e been 1 s s o c i : i t e d w i t h
f r o n t a l s t r u c t u r e s p r o d u c e d by t i d a l s t i r r i n g v n r t a t i o n s i n t h e shelf s e a s of G r e a t B r i t a i n (e.g.,
Simpson, 1976; S i n p s o n e t a l , 1977, 1079; P i n g r e e and
G r i f f i t h s 1 9 7 8 ) , Ray o f F u n d y ( G a r r e t t e t n l , 1 0 7 8 ) , Long I s l a n d S o u n d , New
York ( B o w m a n .and E s n i a s , 1 9 8 1 ) q n d Cook S t r a i t , N e w Z e n l a n d (Rowman e t ~ 1 1 , 1980).
The a l m o s t f i x e d p o s i t i o n s o f t h e s e f r o n t s , a s d e t e c t e d by s n t c l l i t i ? ,
. ., p h y t o p 1.nn k t o n
h y d r o g r ilph i c o r b i o 1o g i c :i 1 m e;i s ti r em e n t s ( c g
c o n c e n t r n t i on s
;irc o f t e n w e l l p r e d i c t e d by t h e r.ontours of h/U'.
Fig. 19 i s
(uis., . .
3
p l o t of t h e i n v e r s e o f e n e r g y d i s s i p n t l o n r a t e p e r u n i t mass 8 [ T 3 L-']), w h i c h i s p r o p o r t i o n a l . t o h / U 3 ( a p : l r t
Czh/(glLl13) =
from s m a l l v a r i a t i o n s i n C w h i c h i n t u r n is w e a k l y d e p e n d e n t on d e p t h ) .
379
Fio,.
17.
Str:itific:ition
inrlrx s = !
o C21?/gU3. ~ ~
~
A c c o r d i n g t o t h e s e p r r d i c t i o n s m o s t of tli" G u l f i s e s p r r t r d t o s t r i t i f y i n srimmrr
ui.t11 l o c a l i - ; . e d
.nixed r i . q i o n s
loc.itrd
Cii:inn(.ls, a n d t h e s n u t h e r n r e I c h e s of front:il
zonc,
s
-
i n Riny,i t o t o a w l Scrp,r'ant
t.hc F i r t h .
4 m;Irqin;ll l y s t r : i t i f i r ? d
1.5 c o n c e n t r a t i o n s i s a l s o p r e d i c t r , d n r ' i r t.lv n o r t . h c r n t i p
of Coronnnrlel P c n j n s u l ? w'ierr s t r o n :
t i < ! a l r i p s :Ire p r c s c n t
(2.7..
Fig.
1:esu L t s f roni I i y d r o ~ r a p l l i r s u r v e y s g e n t ? r a l l y c o n f i r m ~ h e s rp r c r l i r t i o n s .
5). Thz
c e n t r a l Gu1.f s u s t a i n s .a m o d e s t s r n s o n n l t h e r m o c l i n e ( F i o , . 2 0 ) w i t h m : i x i m u m t t i m p e r . i t l i r l i c o n t r a s t s o f : I b o u t 4'
o r c u r r i n s i n t h e sprinz.
l n y c r d e e p e n s i n summer u n t i l i t
i n t e r s e c t s t h e bottom
Tlic s u r f a c e n i x e d :it
$0 rn
p a i - t i r u 1 , t r l o c n ~ i o n . A weak t e m p e r a t u r c inversion o c c u r s i n w i n t e r , c o m p e n s n t r d by
s\irf.{ce t o 75.6;:
;I
a t depth (Cassic,
fiirly
uniform
n e a r 14.5"
-0.1
- ..0.4X
-
a t the
1960).
w?ter
colum?
i l I u s t r , i t r ? d w i t h ,qn e x n m p l e f r o m l a t e s p r i n g ( F i g .
i n d i c a t o r of s t r c l t i f i c n t i . o n .
this
dcnsity
c o r r e s p o n d i n g i n c r e : i s c o f s a l i n i t y i r o n n h o l l t ,347;
The s p 7 t i q l d i s r r i b u t i o n o f wc'rc
.it
1i.O'
strntification 21).
is
1<(?11
Rotlom ti.mpei-.itiirrs
s o s u r f - 1 r . c c o n t o u r s were
:I
good
( T o p and b o t t o m s a l i n i t y c o n t r a s t s t y p i c 1 1 l y a r c
i n .lanrl.iry; C i s s i c ,
1360).
S u r f i c c t r m p e r n t u r p s n v c r m u c h of t h e
380
Fio,. 2 0 .
S r ~ s o n ~ it rl m p r r - i t i i r r r o n t o u r s f o r
I
mid Gulf
p r o f i l c ( n f t r r P?111, 1 0 6 5 ) .
F i g . 21.
D i s t r i b u t i o n of s t i r f a r ? t i ? m p ? r i t u r e (Novcmhrr 2 2
nerembcr
In,
1965;
a f t e r P-iul, 1968).
-
381
Cu1.f Lay i n t l i r r a n g e 1 7 O occurring
:IS ,I
-
w i t h s t r o n g r s t s t r a t i f i c : q t i i o n (AT
18’C,
- 4OC),
s1i:illow t h e r m o c l i n r w i t h i n a n e l l i p t i c a l p a t c h i n the‘ o f f s h o r e
w3Lers of t h e F i r t h .
t o t h e 1.5 r.ontorir,
A r e g i o n of
- lac\,
c o l d , m i x r d w i i t r r (AT
corrPspondin:,
was l o c a t e d o f f C i p ~C o l v i l l r , , w h i r h may b r a c o n s c q u r n c r
of t i d a l m i x i n g a n d / o r c e n t r i f i i g a l u p w ~ l l i n : :e r f r r t s ( G a r r e t t a n d Loucks,
1976).
T h i s i s a l s o an a r e ? of i n c r e a s e d t i i r b i d f t y ( P a u l ,
m:iy bc r e l n t e d t o p h y t o p l a n k t o n blooms. :I
F1argin:il
1968) some of whir11
s t r a t i f i c . Y t j o n , roiiplrd w i t 1 1
f a v o u r : i b l c l i g h t regi-mi? o f t p n f o s t e r e n h a n r e d p r i m a r y prod11cti.on i n s u c h
‘ireas.
T h e m i i o r d < s r r ( ~ p n n c yt o b r
observations
lirs
cxp1;iinrd
i n t h r southcrn’ Firth.
between
T t may be
crri:itctl by \ J i i h o i i R i v r r d i s c l i . i r y ?
str:itificition
p r e d i c t i o n s and that
salinity
n d d s s r i f f i T i t 3 n t buoyancy
fl.ux t o p r e v e n t s t r a t i f i c a t i o n b r r n k d o w n by t i d a l s t i r r i n g .
CONCLUS! DNS T l i i a p p l i r n t i o n of
provided
:I
a n o n 1 i n e : i r t i d n l mo!el
t o t h v I I a u r - i k i Crllf l i l s
p r e l i m i n a r y a s s e s s m e n t of tid.31 r l r v : i t i o n s , t i d a l a n d rcsirluTl
c u r r t ’ n t s , v o r t i c i t y , o v e r t irlr a e n e r n t i o n , b o t t o m s t r ~ s s r, n c r g y d i s s i p . i t i o n r a t e s a n d t h e s t r . i t i f i c n t ion indcx.
d a t n i s encourqging.
The a g r c e m r i i t w i t h a v a i l a h l r r x p c r i m e n t n l
1lopcful.ly t h i s m o d e llin g e f f o r t wi l l . stimu1:itc f u r t h r r
f i c s l d e f f o r t s t o i n v e s t i g a t e t i d a ? . and r u r r r n t c l i i r i c t a r i s t i c s .
?lc;isllremrnts
o f e l e v a t i o n i n + c u r r e n t s a l o n g t h e n o r t h e r n o p r n b o u n d a r y worllrl b e (!sprci-11l y a s s o c i a t r d w i t h our : i s s i i m p t t o n s of l i n e a r
u s e f u l i n r v . i l u : i t l . n g p o s s i b l t ! C’rors pli3st! a n d ampl.itiide g r a d i e n t s .
T h e s r d a t i would a l s o bc h r l p f u l i n n r r i i r n t c l y
m o d e l l . i n ~ t h e p r o p a q n t i o n of h i g h e r t i d n l h i r m o n i r s f r o m tlir e x t r r i o r r e n , i o n i n t o t!ie m o d e l .
Bott-om s c d i . m r n t s , a m p l c s Laken i n arr:is of h i s h r P s i d r i i ?
v o r t i c i t y m i g h t d r t c r m i n e i f p r e f e r p n t i a l o f f s h o r r sand b:lnk f o r m n t i o n o r c u r s . A good p l a c e t o s t . i r t l o o k i n g w o u l d be i n t h r r c g i o n of n e g : i t i v v
v o r t i c i t y o f f t h e n o r t l i e : a s t e r n c o n s t of Wai!ieke inti p L n n r t a r y
v o r t i c i t y hnvc t h r
same
residri~l.
Ts1:inrl f o r t h e r r , b0t.h r c l a ~ i v e
s i ~ ns n d
henre
s t r o n ~ r rb o t t o m
c o n v e r g c n c r s and s r d i m e n t a c r u m u l n t i o n n a y r c s u l t .
ACKNDWLEDCEXEFITS T h i s p r o j c c t was c o n r ( , i v r d :ind i n i t i a t e d when t h e a u t h o r s were w i t h t h e l’llysics
Department,
University
K i b b l e w l i i t e f o r l i i s h e l p :ind
of
Auclclnnd.
\de
r n c o i i r ; i ~ i r m e n t . !lr.
thanked f o r h i s computing a s s i s t a n c e .
think
Professor
A.C.
Grtorge C a r r o l l . i s a l s o
S u p p o r t w a s p r o v i d c r l by t h e S t l i t e
U n i v e r s i t y o f Mew York a n d t h e U n i v e r s i t y o f h u c k l n n d , f a c i l i t n t e d by t h e :lemorandum of Undt7rstnnding i.n m n r i n e s c i e n c e b e t w e e n tlie t w o i n s t i t u t i o n s .
C o n L r i b u t i o n 293 of t h e X i r i n c , S c i e n c e s R e s r a r c l l C e n t r r .
382 APPEND IX
Tlie d i f f e r e n t i . 1 1 c q u 7 t i o n s o f m o l i o n 1114 c o n : i n u i t y
are
x momentum
y momentum
continuity
$ + a,(HU) a
+ aa( H V )
= 0
Y
Chezy f r i c t j o n r o e f f i c i e n t :
thr Chezy c o . ? f f i c i e n t
is relatrt! t o t h e
Planning c o e f f i c i e n t N by ( i n 'lKS u n i t s )
4 c o n s t : i n t v a 1 . u ~of '1 = 0 . 0 2 8 was u s c d a s a model
Corio1i.s p a r a m e t e r - - ~ . 7 5
x
s - l ,?t 37'5
a c c e l c r n t i o n of g r a v i t y * 081 r m s-2 t o t a l w a t r r d e p t h = 11
-I-
rl
d e p t h o f v i t c r at. mciin s e a l e v e l h o r i z o n t a l wnvcnumber
k = W(gh)-'
l e n g t h s c : i l r of Gulf s t r n t i f i c n t i o n index !12
ti.dnl. p e r i o d = 1 2 . 4 2 h r
t imc
d c p t l i - n v c r n y d ve l o c i t y ronponents i n d i r e c t ion x.y amplitude of t i r l 3 l c u r r e n t i n I l i r e c t i o n x x c o s p o n e n t o f v c l o c i t y n t d e p t h z ( z me:isiirprl v e r t i c a l l y i i p w . i r d s
from s e n f l o o r )
o n g u l n r f r e q i i e n c y o f PI2 t i d r = 2 n /T
r a t i o of t i d a l p e r i o d t o f r i c t i o n r i l l t i m e s c . i l c s e a s u r f n r r c l e v n t i o n w i t h r e s p e c t t o menn
semidiurnal, qiiarter diiirnal tidi.s
SCR
level
383 REF EXEPJCES A d m i r a l t y Iiydroo,rxpliic Dep:*i-tment. soo p p .
1358.
N e w Ze.3l:in.l
Pilot,
1 2 t h ed. London.
Rowm.in, X.J., 4.C. K i b b 1 . e w h i t r , an4 D.E. Ash. 19(39. >12 t i d . 1 1 e f f e c t s i n 7 r e a t c r Cook S t r i i t , Ncv % - n l : i n d . J . G e o p h y s . Res. 85:27?Y-274?.
;[.is a n d W.E. E s a i : i s . 1 C ) R I . I s l a n d :tnd 5Jlock Tsl : i d S o u n d s .
Bowman,
F r o n t s , s t r ; i t . i f i c ; i t i o n .ind n i x l n g i n Lonq J . C,?ophys. R r s . RO:h2C)?-4?54.
B r o d i e , .J.W. 1969. C o i s t n l s u r f ; i c c c u r r e n t s ;irorind T1t.i~ Z r . i l n n d . G r o l . f~ Geoophys. 1 : ? 3 5 - 2 5 2 . ] % y e , J.A.T. n n d R.A. H r c i t h . ;Ihr. R E S . 3 7 : 4 ? 3 - h 4 2 .
1975.
T h e N e w Zea1:inr.l
semi.-dirirn~tl r i d ? .
C a r t e r , L. a n d J . V . E i d c . 1080. X x n r ; i k i S ( ? d i m e n t s , tJ.7.. Ctxirt, Co.ist:il S e r i r s I 3 2 0 0 8 3 0 . C;issir, R.!l.
1060.
llyrlrolop,y o f 11iiir;iki G u l f .
N.Z.
11.Z.
Orcsanogr.
E c o l . SOC.
J.
.I.
Tnst.
1 :40-47.
D r o n k r r s , J.J. 1964. T i d a l c o n p i i t n t ' , o n s i n r i v e r s a n d r o u t 1 1 w,ti>rs. I l o l l a n d ? u b l i s h i . n g Co. A m s t e r d m . 518pp.
North
G a r r e t t , C.J.R., J.R. K c e l e y ; i n d D . A . G r e e n b c r p , . 1378. T i d a l m i x i n g v e r s u s Atmospheret t i e r m i l stratific-it ion i n t h e Rny of Fiindy :ind Giilf o f ' I i i n c i . 0ce:in. 1 6 :403 - 4 2 7 .
Cnrrett, :IOV.I
Ilenth,
C.J.R. . i n d R.H. L o u c k s . 1375. Upwcll.ing :ilon;: Scotia. J . F i s l i . Rcs. Ro:ird C?n. 37:116-117. R.A.
Zralclnd.
K r c s i s s , 11. c!iannrls.
1977. Phase d i s t r i b u t i o n of t i d ; i l N . Z . J. l l n r . F r e s h w . Rcs. 11:787-?92.
1357. Tellus.
S o m c r;.mnrks !?:5y-h8.
about
t h o Ynrmoiith shorr of
c o n s t i t r i t x n t s n r o i i n d Ncii
nonlincbnr o s c i 1 I : i t i o n s
in tidil
L c e n d c r t s c , J.J. 1967. A s p v c t s o f s c o m p u t n t i o n ; i l m o d e l f o r lonp, p e r i o d wiiter wave p r o p n g n t i o n . Men. RIl 5294-PR, Rand C o r p o r n t i o i i , S 1 n t . i : l o n t c a , Cilif. H - i d d o c k , I,. a n d ?..D. P i n g r e e . 1978. Niineric:il s i m u l a t i o n of t h P P o r t l ? n d tidill eddies. E s t u a r i n e C o ; i s t . Har. S c i . 6:350-367. P r e n t i c c ? - l l a 1 1 T.nc., N c w J e r s e y . 565pp.
N i h o u l , J.C.J. 1q7.5. E f f r r t o f t h e t i d a l s t r e s s o n r e s i d u a l c i r c u l a t i o n a n d mud d e p o s i t i o n i n t h e S o u t h e r n R i g h t o f t h e N o r t h S e n . P:iqcioph. 1 1 7 : 5 7 7 -
581. Ilihoul, J.C.J. a n d R u n f o l a , Y. 1981. The r e s i d u a l c i r c u l a t i o n i n t h e N o r t h S e a . I n : J . C . J . N i h o u l ( E d i t o r ) , Ecohydrodynamics.'Elsevier, Amsterdam, 219-271. P a u l , L.J. 1 0 6 8 . Some s o n s o n n l w a t e r t e m p e r a t u r e p a t t r r n s i n t h e I I iu r n k i G u l . f , New Ze:iland. N.Z. J . b h r . F r e s h w . Res. 2 : 5 7 5 - 5 5 8 . P i n g r e e , R.D. 1 9 7 8 . T h e f o r m a t i o n o f t h e s h , i m b l ~ sn n d o t h e r b i n k s b y t i d a l s t i r r i n g o f t h e s p a s . ,I. N3r. R i o l . Ass. U.K. 58:711-726. P i n g i - e r , R.D. i n d D.K. G r i f f i t l i s . 1378. Tidil f r o n t s o n t h r s l i ~ l f s r i s a r o u n d tlie B r i t i s h I s l c s . J . Gcophys. Res. 8 3 : b h 1 5 - 4 5 2 2 .
384 P i n g r e e , R.D. and D. K. G r i f f i t 1 i . j . 1980. C i i r r p n t s d r i v r n by ? s t c n d y r i n i f o r m w i n d s t r e s s o n t h e s h r l f r , ~ i sn r o u i i d t h r R r i t i s l i Tsles. O c r n n o l . A c t 3. 3 : ?27-2?5. P i n g r c e , R.D. nnil L. :liddock. 1 3 7 7 . T i r l n l r r s i d i i 7 l s i n t h e E n g l i s h Ch. inne 1. J . I h r . Riol. Ass. U.K. 57:379-154.
P t n g r e e , R.D. a n d I,. : I d d o c k . 1 9 7 9 . T h e tirl:il. p h y s i c s o f h e a d l n n d f l o w s 2 n d o f f s h o r e t i d a l b:ink f o r m a t i o n . Yar. Geol. 72:269-289. E s t u a r i n r Co,ist Mir. S r i . G:71-31. S i m p s o n , J.11. a n d J . R . 2 50 :40 4 - 4 0 6 .
!luntcr.
1974.
F r o n t s i n t h r ? I r i s h Sea.
N.-~tiire.
S i m p s o n , J.11.. D.G. l l u ~ h ~.inti s M.C.G. Ilorris. 1977. The r e l n t i o n of seasonal s t r : a t i f i c a t i o n t o t i ~ l a m l i x i n % on t h e C o n t i n e n t a l S h r M . Deep Sea. Res. 24:127-740. S i m p s o n , J.H., C.El. A l l e n .ind N.C.G. I l o r r i s . S h e l f . J . C e o p hys. Rcs. 83: 4hn7-&614.
197R
F r o n t s on t h e C o n t i n e n t n l
T c e , K.T.
1 3 7 6 . T i d r - i n d u c e d r c s i d u i l c u r r e n t , n 2-D n o n l i n r n r ntinneric;il t i d a l model. J . '1;ir. Res. 3 4 : h n l - O 2 R .
T e e , K.T. model.
1977. Ti4e-inrluct:d resirlull current J . Phys Occ?.inogr. 7 : '196-4OZ.
.
-
Vert f i c a t i o n of
R
niimerlcal
V c e n , J. Van. 1976. n n d p r z o e k i - n g e n i n c1p H o o f d c n ( I l c n s u r e m e n t s i n t h e S t r a i t s of Dover, 2nd t h e i r r r l n t i o n t o t h e N e t h e r l a n d s c o a s t s ; E n g l i s h nnrl F r e n c h surnm.iry) ( L n n d s d r i i k k e r i j , The Il,iguc). 152pp.
385
THE SENSITIVITY OF THE BALTIC SEA
M NATURAL
AND M?A-.WE
IMPACT
EL. BOPEDERSEN
ABSTRACT Hydrographic observations i n the Baltic Sea during nearly a century have shown
the picture of a highly non-steady system.
The two m j o r sources f o r these varia-
tions a r e t h e b a r m t r i c pressure (the yind) and the r i v e r runoff.
As the wind
speed i s only k n m by visual judgement, and, i n t o the bargain, by a large numThis has h e n overcome by correlating t h e monthly man wind sped squared t o the m n t h l y ber of observers, no reliable secular variation of the wind i s known.
peak to peak value of the barometric pressure a t Copenhagen, t h e l a s t one being
known with high accuracy since 1873. As the natural variations show a high correlation
between the wind and the run-
o f f , it i s hard to separate t h e e f f e c t on f o r instance the s a l i n i t y from the variat i o n i n the wind and i n the runoff, respectively, unless one makes use of a mthe-
mtical m x k l , which i s based on knmledge of t h e hydrcdynamics of the system. A f i r s t s t e p (steady-state) &el has been outlined and used to investigate the e f f e c t on the Baltic Sea from a diversion of part of the r i v e r Neva. The calcul a t i o n s s h m that i f a 25% r i v e r diversion had been executed i n the beginning of t h i s century, a 30 to 40% higher salinity-variation m u l d have been encountered
i n t h e Baltic Sea
-
compared t o the actual variations during this century.
IiVIlWWCTION
The growing concern f o r our aquatic environment and the expansion of our agric u l t u r a l and i n d u s t r i a l a c t i v i t i e s quite often r e s u l t i n a p o l i t i c a l conflict. When we are dealing w i t h a semi-enclosed sea, such a s the Baltic Sea, this conf l i c t may even a t t a i n international dimensions, due t o the large n&r
tries bordering the Sea.
of coun-
This w a s the case i n 1978 i n connection with the Danish
project of building a bridge across the Great Belt (Bo Pedersen, 1978), and it w i l l be the case, i f the Fussian plans f o r r i v e r diversions w i l l involve the r i v e r kva.
Before this s o r t of major interference with nature i s decided upon, a qual-
i f i e d estimate of t h e long-term environmental consequences ought t o be evaluated
and cckrment.ed/agreed upon by a l l the concerned countries. The f i r s t condition f o r such a procedure is an extension of the international laws/conventions. The second c o n d i t i o n i s the developmsnt of a predictive mathematical d e l , i.e. a mdel reasonably representative f o r the dynamics of the sea. The t h i r d condition
386
is a knowledge of the natural variations i n t h e external forces of major importance f o r t h e system (such a s runoff, wind, t i d e , etc.) t o be used a s input to calibrate the mathendtical &el,
and f u r t h e m r e a s input and reference data i n the
simulation run of t h e man-mde interference.
The fourth condition is the a b i l i t y
to estimate the e n v i r o m n t a l impact, when the hydrcdynamic changes are knm. The fulfilment of condition no.1 - the international laws f o r making an e f f o r t i n regard to the other tasks
-
,,
is not necessary
- on t h e contrary,
a mathemtical
mde.1 w i l l create a growing understanding of the s e n s i t i v i t y t o a local interference of the whole system, and, hence, m y a c t a s a catalyzer f o r f u r t h e r develof the highly needed international conventions.
o-nt
In the f o l l m i n g , we s h a l l
f i r s t give a brief description of the Baltic Sea estuary system with fpcus on the dynamics and the t i m e scales i n r e l a t i o n to the establishmnt of a long-term predictive mathendtical &el.
Next, we s h a l l comoent on the fundammtal difference
i n the response of t h e Baltic Sea to a natural and t o a man-mde variation of the external forces, exemplified by a diversion of 25% of t h e discharge of t h e river Neva.
Finally, we shall discuss the problem of establishing a reliable secular
tims series of t h e wind force, which i s one of t h e mst important external forces i n the Baltic Sea, and which has h i t h e r t o been unknown. A STEADY-STATE W D E L OF THE BALTIC SPA
In Figure 1 i s shown a schematic longitudinal cross-section of the Baltic Sea estuary system, which comprises e i g h t sub-areas,
chosen i n such a way t h a t a rea-
sonably simple dynamic description can be given f o r each region (Bo Pedersen
&
W l l e r , 1981). This &el
w a s developed f o r the consequence analysis of the poss i b l e diversion of part of t h e r i v e r Neva. A t t h a t time no reliable time series
of the wind power was available, and hence it was only possible t o consider an a r t i f i c i a l , *layer
steady-state situation.
For each sub-area steady-state continuity equations f o r mass and volm were established.
The mixing across the interface c o n s t i t u t e s the dynamic contribu-
t i o n to these equations.
This mixing i s due t o the generation of turbulence by
the external forces, which primicily originate f m the wind, as w i l l be explained i n t h e following.
The wind is a highly non-steady force, and hence a proper dynam-
i c transformation from the non-steady t o the steady system has t o be p e r f o m d .
., According
to the author's (1980) romprehensive analysis of t h e mixing processes
f o r a large class of -layer
s t r a t i f i e d f l m s , a universal relationship e x i s t s
between t h e eneryy available f o r the turbulence production and the energy gained (potential as well a s turbulent k i n e t i c energy) owing t o the entrained mass. Hence the proper transformation from t h e non-steady to the steady system i s obtained by applying a dynamic mean veZocity V , r e f l e c t i n g t h e e n e q y production, -lY
387
where T i s tile averaging time scale and u is t h e mean velocity. The kinematic mean v e l o c i t y i n the continuity eqyations i s the simple mean veloc i t y and n o t the v e l o c i t y defined by E q . 1. The problem of obtaining consistency i n the dynamic balance a s well as i n the mss-balance was solved by introducing
a circulation-velocity w i t h no n e t t r a n s p o r t i n s i d e some of the sub-areas. Before the r e s u l t s of the a n a l y s i s are ccmnented upon, it i s convenient t o swmarize our knwledge of the system.
THE SHORT-TEIW
DYNmlICS OF THE m T I C SEA
A b r i e f supplement to the d e s c r i p t i o n of t h e normal, o v e r a l l dynamics of the
B a l t i c Sea, given by S.Kullenberg (page 399),
can most conveniently start from
Fig. 2 , which shows a typical time series of Lie measured discharge through the G r e a t Belt.
The f i g u r e illustrates the highly
non-steady in-and o u t f l w of huge
The flow i s caused by a water-level d i f f e r -
amounts of s t r a t i f i e d brackish w a t e r .
ence between Katteqat and the Arkona Basin, mainly due to the wind setup/setdown. The varying wind f i e l d i s created by the nearly c y c l i c passage over the area by
high/low a i r pressure.
I n the Kattegat region, this nearly c y c l i c mvenent i s
r e f l e c t e d i n a similar pendling forward/ba&ard f r o n t i n t h e upper layer.
governed by the energy input marily t h e wind
-
movement of the i(atteqat/Skagera!
The o v e r a l l mixing i n the two s h a l l w sub-areas
-
is
i . e . i n accordance w i t h the above-mntioned, p r i -
and the s t a b i l i t y
-
i.e. the f r e s h w a t e r content.
This fresh
water content i s i n t u r n determined by the n e t s e a w a r d t r a n s p o r t of the river runoff, which amounts to, say, only 10% of the t y p i c a l amplitude i n the nearly c y c l i c varying discharge. The G r e a t B e l t and the Sound are separated frcm the Arkona Basin by two s h a l l w s i l l regions.
The high mixing rate i n the s h a l l w t r a n s i t i o n area, combined with
a n e t outward d i r e c t e d flaw i n the upper l a y e r , creates a high longitudinal s a l i n -
i t y (and hence density) gradient, which mans t h a t part of the inward flowing w a t e r i s trapped by the sills as it, due to the density excess, plunges dawn and descends as a dense, e n t r a i n i n g bottcm c u r r e n t i n t o the lower l a y e r of the Bornholm Basin.
The residence time here (volm[discharge)
is about 4 months, which
means t h a t the main part of the i n t e r m i t t e n t l y i n f l w i n g dense w a t e r continues
as a delayed, nearly steady dense bottcan c u r r e n t through the Stolpe Channel i n t o the lower l a y e r of the Central B a l t i c , while a minor part i s entrained i n the
upper l a y e r due to wind-induced mixing.
The balance between the l m r layer dis-
charge i n p u t and t h e r a t e of upwards d i r e c t e d entrainment i n the Central B a l t i c govern the p o s i t i o n of the i n t e r f a c e there.
Again, the fresh water input (pri-
388
marily the r i v e r r u n o f f ) , the dense water input i n t o the 1-r
layer (primarily
caused by the wind) and t h e energy input (again the wind) are the most important external forces of the Baltic Proper.
The tine s c a l e f o r t h e Central Baltic
(volume/discharge) is of the order of magnitude of decades. No r u l e s without exceptions.
Under very severe wind conditions the inwards
directed flow may p r s i s t f o r so long a tixe t h a t huge amounts of highly s a l i n e
water pass the sills.
These w a t e r masses may then renew the deepest p a r t s of the
succeeding basins, creating a nearly stagnant bottom layer.
The long-term e f f e c t
of the major inflows i s the formation of stagnant mean deserts, suffering f m oxygen deficience. I n sumnary: the most important factors governing the hydrcyraphy OFthe B a l t i c Sea estuary system a r e the r i v e r runoff, the wind, and the gecinetry o f , especially, the shallow t r a n s i t i o n region, including t h e sills.
The order of magnitude of the
discharges, the s a l i n i t i e s , and the depths is indicated on the table i n Figure 1. THE LONGTERM DYNAMICS OF THE BALTIC SEA
The overall decrease i n oxygen content i n the deep waters, the overall increase in s a l i n i t y and temperature, and the rise of the halccline are some of the general
trends encountered i n the Baltic Sea during t h i s century, the causes of which have not found their f i n a l solution.
I n Figures 3 and 4 a r e shown some long-term time
series representative of this evolution. The correlations between a l l the parameters are evident, although the runoff has been subject t o man's interference (agriculture, industry, water power d e v e l o p n t ) .
mtharatical &el
As a long-term non-steady
f o r the Baltic Sea has not y e t been developed, a d e t a i l e d
analysis of the tine series cannot be given.
One general trend concerning the
forcing functions is obvious, namsly a decrease i n t h e r i v e r runoff as w e l l as i n the wind, probably because both are correlated to the b a r m e t r i c pressure. The wind/barometric pres-
Tfie r u n o f f / b a r m t r i c pressure correlation i s unknm.
sure correlation i s elaborated upon belaw.
THE DETUEKE OF NA?URAL AND MAN-MADE IMF'ACT ON THE BALTIC SEA As denonstrated on Figure 4 , a natural change i n the runoff has always been
associated w i t h a change i n the wind force also. Hence the e f f e c t of a m a n - d e change o f , f o r instance the runoff, can not be extracted frcm the observed natural changes;
it has t o be evaluated by use of a mathemtical rodel.
I n 1978 the
author developed such a type of consequence analysis model f o r estimating the
influence on the Baltic Sea from the building of a bridge with large embanlanents across t h e Great Belt.
The c r u c i a l r o l e of t h e mixing i n t h e shallow t r a n s i t i o n
(the Great Belt) w a s d m n s t r a t e d above, and the consequence analysis c l e a r l y showed t h a t a measurable change of the hydrography of t h e Baltic Sea w u l d have
3 89
been t h e r e s u l t , i f t h e bridge had been b u i l t i n accordance w i t h t h e p r o p s e d design. The two other important f a c t o r s f o r the hydrography of t h e Baltic Sea estuary system are the runoff and the wind.
I t i s therefore natural to investigate the
e f f e c t of a m - m d e change of the runoff
-
especia,lly because t h e USSR's Council
of Ministers i n t h e i r 5-year plan 1976-80 has i n i t i a t e d the preliminary planning f o r diverging up t o 2000 m3/s frcm t h e river Ob (which drains t o the Arctic Sea)
to the river Volga i n order t o meet the increasing water demand f o r i r r i g a t i o n a l purposes i n the dry regions north of the Caspian Sea and Lake Aral.
From an
engineering point of view the r i v e r Neva is a l s o a t t r a c t i v e a s a source f o r this As the r i v e r Neva qontributes about 20% of the runoff t o the
i r r i g a t i o n project.
Baltic Sea, any decrease i n i t s discharge would have a g r e a t bearing on the hydro-
graphy of the Baltic Sea and on the Danish inland waters. Hence a steady-state rrcdel was developed which gave an overall quantitative description of the B a l t i c estuary system as it behaves under the present average msteorologic and hydrographic conditions.
I f it i s assumed t h a t the man-made
changes have a minor e f f e c t on t h e msteorological conditions, then the governing equations s h a l l be s a t i s f i e d by the conditions a f t e r mn-made changes.
-
a s w l l a s before
-
the
Hence, by introducing the new parameters (discharges, depths,
and s a l i n i t i e s ) equal to the previously used ones w i t h an added minor correction,
the 22 highly non-linear equations i n the Wva analysis could be transforfwd t o a set of 22 l i n e a r equations i n t h e correction terms, which could then be solved directly. In order to quantify the consequences a hypothetical runoff reduction of 25 % of the r i v e r Neva discharge was investigated.
This corresponds t o an only 5 %
reduction of the t o t a l average runoff to t h e Baltic. w i l l be s i g n i f i c a n t .
Nevertheless, the influences
A detailed discussion of a l l the calculated hydrographic
e f f e c t s can be found i n t h e papers referred to. The mst s t r i k i n g difference
i s mst c l e a r l y i l l u s t r a t e d i n the runoff and i n the Baltic upper layer s a l i n i t y time series, Fig. 3.
between the response t o a natural and to a man-mde *act
The man-mde reduction i n the t o t a l runoff m u n t s to only 15 % of the natural
runoff variations encountered i n this century.
Nevertheless, the associated
s a l i n i t y change in the upper layer of the Baltic Proper (SF75) was c a l c u l a t d t o This large
be nearly 50 % of the natural s a l i n i t y variation i n t h e same period.
difference i n response may have two explanations.
The yearly runoff to the Baltic
Sea munts t o only 2 % of the total volmw, which mans that any response to non-steady external forces a s the runoff o r the wind w i l l be highly damped and delayed due to the l a r g e response time of the system (the so-called reservoir e f f e c t ) . A permanent change i n t h e runoff w i l l on the contrary a f t e r about half a century yield a pennanent, undamped change i n t h e response.
Another factor
-
390 not taken i n t o account i n the calculation performed amplifying e f f e c t of a variable wind.
-
i s the possible damping/
I t i s most probable t h a t the e f f e c t w i l l
be even mre pronounced than the calculated e f f e c t , because the reduced s t a b i l i t y
of the estuary system w i l l make the system mre s e n s i t i v e t o t h e inevitable changes i n the wind forces, which w e r e held constant i n the calculations. A LQNGTERM WIND DATA SERIES
The general a p p l i c a b i l i t y of the outlined mathematical &el
i s restricted,
mainly due t o lack of knowledge of the t i n = series f o r the important wind force. Without this time series a l o t of questions concerning the Baltic Sea remains unanswered, such as: What has caused the general trend i n the hydrqrabhy of the Baltic Sea as damnstrated i n Figure 3?
How long time w i l l elapse from the stop-
ping of a c e r t a i n pollution source till the e f f e c t can be recognized i n the various
parts of the estuary system? The long-term variations of mst oceanographic parameters i n the Baltic Sea’are r e l a t i v e l y well-known,
but not t h e very important wind data.
In Denmark, f o r
instance, the wind force and t h e w i n d direction have systematically been observed
a t several locations since the foundation of the Danish Neteorological I n s t i t u t e i n 1872.
Nevertheless, these observations a r e not reliable i n long-term t i m e
series, p a r t l y because they have been obtained by visual judgment (not by an a n m t e r ) , and p a r t l y because a time series covering a century must comprise
the observations of a large number of individual observers.
Hence, the importance
of the wind data series makes it necessary t o seek f o r new, untraditional data treahnt.
The following approach i s a f i r s t approximation to obtain a secular
time series f o r the wind. CHOICE OF TIME STEP
The tim s t e p chosen i n a mathematical &el
has a g r e a t bearing on the formu-
l a t i o n of the equations and of course on the computer cost. that s i g n i f i c a n t changes may take place within days.
Figure 2 i l l u s t r a t e d
Figures 5 and 6 i l l u s t r a t e
accordingly t h a t the seasonal variations of the wind p e r and tile temperature
are s i g n i f i c a n t , although the response of the water i s damped due to the reservoir e f f e c t (damping and delaying a s t e p i n p u t ) .
Finally Figure 4 shows t h a t even the
secular variations are pronounced, and, moreover, t h a t they themselves show
trends which mean t h a t they are only p a r t of an even longer varying time series. The existence of systexatic meteorological and hydrographical observations
since the l a s t half of the 19th century makes it obvious t o deal w i t h a tim horizon of a century.
The choice of a reasonable time s t e p is, according t o the
above-mentioned, not as obvious.
The s m r - t h e m l i n e f o m t i o n i n the Baltic
a c t s as a l i d over the halocline and thus prevents the wind from eroding the
halocline during the period .Yay
-
October (see Figure 6).
Hence, a model repre-
s e n t a t i v e f o r t h e dynamics of the sea cannot operate w i t h time s t e p s l a r g e r than h a l f a year.
A s h o r t e r time step, on t h e o t h e r hand, increases the mmplexity
of t h e model s i g n i f i c a n t l y , because i f the time s t e p becomes less than the typical
time-scale of a sub-area, then the non-steady terms have t o be retained f o r t h a t area. I n the present approach the s m r and the winter period, i . e . half a year has been chosen as the time s t e p i n the t i n e series f o r t h e wind.
As the response
time f o r the Central B a l t i c i s of the order of decades, this implies t h a t this region has t o be t r e a t e d as non-steady.
For a l l t h e o t h e r sub-areas the response
time i s less than half a year, and hen& they w i l l a t t a i n a steady-state condition before the lapse of each time step.
As w i l l be demonstrated below, a time s t e p
of a m n t h could have been used, b u t then t h e Bornholm Basin and probably the Kattegat region would be non-steady.
Especially a non-steady Katteqat/Skaqe.rak
f r o n t would be extremely d i f f i c u l t t o handle i n a mathmatical model.
Finally,
a time s t e p of less than a m n t h is n o t possible w i t h t h e present approach. WIND VELOCITY OR SPEED The superior r o l e of t h e Danish S t r a i t s i n governing the hydrography of the
B a l t i c Sea is demonstrated above.
The c h a r a c t e r i s t i c flow pattern here is e i t h e r
an inwards o r an outwards d i r e c t e d flow, which makes it reasonable t o operate with only two types of wind, one c r e a t i n g inflow, the o t h e r c r e a t i n g outflow.
As the
B a l t i c Sea i s a semi-enclosed basin, the n e t long-term outflow m u s t be equal to t h e n e t f r e s h water input.
Hence, i f the strength of the wind contribution t o
the in- and outflow, r e s p e c t i v e l y , are taken equal ( i n the simple, long-term
mdel), a non-accumulation condition i s ensured.
This i s a parallel to a semi-
enclosed sea connected to an ocean w i t h t i d e of varying strength. time (the &el
I f the averaginc
tim s t e p ) i s w e l l above the time s c a l e of t h e p h e n m n a , only
one parameter i s needed t o c h a r a c t e r i z e the force, n m l y t h e average wind s p e d or
-
i n the o t h e r example
-
t h e tidal amplitude.
WINE-AIR PRESSURE CORRELATION
By physical reasoning the average wind must depend on t h e air-pressure gradient. This m y either be evaluated i n a Lagrangian frame, f o r instance from two separate observation s t a t i o n s , or i n an Eulerian frame, from a s i n g l e observation s t a t i o n ,
located a t a p i n t where t h e lows and the highs pass by.
The l a t t e r is chosen
here, w i t h the stAtion a t the Danish Meteorologic I n s t i t u t e i n Copenhagen a s reference.
This does n o t man t h a t t h e conditions a t this p a r t i c u l a r s t a t i o n i s
r e p r e s e n t a t i v e of the wind force f o r the whole Baltic Sea system;
the s t a t i o n i s
merely chosen f o r convenience's sake, i n order t o d m n s t r a t e the basic approach.
392 By dinensional reasoning the wind speed must be proportional t o the square root of the representative barometric pressure, which is taken a s the monthly peak-topeak value.
In order t o test the value of this sixple hypothesis, the m n t h l y
wind speed observed a t Christians@Light Tower (the Bornholm Basin) has i n Figure 7 been plotted against the square root of the peak-tc-peak
sure i n Copenhagen.
value of the a i r pres-'
The wind speed i s converted from the Beaufort scale (B) to
a mtric value (V [m/sl)by use of the o l d (before 1931) conversion formula:
= (0.5
+ 2 BC) iO0.5[m/s1
The weak e l l i p t i c d i s t r i b u t i o n of t h e mnth-to-mnth values a r e probably caused by the seasonal variations i n the wind pattern.
I f we take the s m r (May to
October) and the winter (November to April) average values respectively, this minor e f f e c t disappears.
F m Figure 7 we conclude t h a t the variation i n the
m n t h l y peak-to-peak values of t h e b m m t r i c pressure is representative f o r the variations i n the monthly m a n wind.
As the b a r m t r i c pressure a t Copnhagen
has been measured without interruption s i n c e 1873, we are able t o o u t l i n e the c r u c i a l secular tim series f o r the wind.
Figure 8 shows a ten-year gliding m a n
of the wind squared, calculated by use of the a i r pressure.
In the same figure
i s shown the time series of the three-year gliding m a n of the wind speed t o the t h i r d power from Gedser Reef observations, referred t o by Kullenberg (1977).
The
three separate observation series resemble the calculated secular time series, while the general trend of t h e wind i s t o t a l l y d i f f e r e n t , due to the above-men-
tioned problem of having individual observers. A preliminary s e n s i t i v i t y test by t h e author, i n which the wind force and the
runoff have been assumed correlated (see Figure 41, gives further support to the v a l i d i t y of the calculated wind force tim series. SUPNARY AND CONCLUSIONS
Semi-enclosed seas - such a s the Baltic - a r e bordered by a large n&r countries.
of
This calls f o r an active international environmental policy based on
a d e t a i l e d knowledge of how the meteorology, the oceanography, the biology, the industry, the agriculture etc. are influencing one another. For the Baltic Sea two examples of these types of consequence analysis have been mentioned, namely i n connection w i t h the Danish p r o j e c t of building a bridge with embankmats across the Great Belt, and the (possible?) Russian project of diverting p a r t of the r i v e r Wva.
Both wamples i l l u s t r a t e t h a t "minor" man-made
changes have "major" e n v i r o m n t a l consequences. In an attempt t o develop a m a t h m t i c a l consequence model f o r the B a l t i c Sea,
393 which takes i n t o account t h e non-steadiness of the external forces (temperature, wind, runoff), a secular t h e series f o r the major external force (the wind) has been established.
This has been demonstrated by c o r r e l a t i n g the wind speed to
the monthly peak-to-peak
barometric pressures a t copenhagen.
When t h i s tim series i s known, a l o t of h i t h e r t o unanswered questions concerning the n a t u r a l long-term v a r i a b i l i t y of the hydrcgraphy of t h e B a l t i c Sea
can be answered. To this end the set of governing equations has t o be supplemented with the non-steady t e r m s , and the flaw i n t h e system has t o be expressed as functions of the wind f i e l d . Furthermore, this non-steady mathematical &el can be used to p r e d i c t the response of the Baltic Sea t o a major man-made i n t e r ference, and hence acts as a necessary t601 i n an a c t i v e environmental @icy f o r the B a l t i c Sea.
REFERENCES
BJ Pedersen, F l . , 1978. On t h e influence of a bridge across the Great Belt on t h e hydrography of the B a l t i c Sea. 11th Conference of the Baltic OceanographersRostock, DDR. Eb Pedersen, F l . , 1980. A mnograph on turbulent e n t r a i m n t and f r i c t i o n i n twol a y e r s t r a t i f i e d flaw. Series Paper, No. 25, I n s t i t u t e of Hydrodynamics and Hydraulic Engineering, T e c h n i c a l University of Denmark. Eb Pedersen, F1. and W l l e r , J . S . , 1981. Diversion of the r i v e r Neva - how w i l l it influence the B a l t i c Sea, the Belts and the Cattegat. Nordic Hydrology, 12:1-20 Danmarks R l i m a . Belyst ved tabeller og kort. [The climate of Denmark]. PUbl.by t h e Danish Meteorologic I n s t i t u t e . Copenhagen 1933. ( I n Danish) Fonselius,S.H., 1969. Hydrqraphy of t h e B a l t i c deep basins 111. Fishery board of Sweden, S e r i e s hydrography, Report no. 23. H e l a , I . , 1966. Secular changes i n the s a l i n i t y of the upper waters of the northern Baltic Sea. Comrrentationes Physicu-Plathematicae, Vo1.31, no.14. Helsingfors. 1977. Observations of the mixing i n the B a l t i c t h e m - and Xullenberg, G.E.B., halocline layers. Tellus, 29:572-587 National Agency of E n v i r o m n t a l Protection, Denmark, 1976. The Belt project. Interim r e p o r t on the Danish B e l t project. NiljDstyrelsen, Kampmannsgade 1, DK-1604 Copenhagen. ( I n Danish) Nilsson,H. and Svansson,A., 1974. IOng term v a r i a t i o n s of oceanographic parameters i n the Baltic and adjacent w a t e r s . Wddelande f r h Havsfiskelaboratoriet, Lysekil, no.174
.
394
s lkml
1500
lo00
R
500
0
d 7
Fig. 1. The Baltic e s t u a r y system divided i n t o e i g h t subareas. The s p e c i f i c c h a r a c t e r i s t i c s of the s i x o u t e m s t subareas are sunsnarized i n the table. From BO Pedersen and W l l e r , 1981.
20 KM’IDAY 10
10
20
1.0 M 0.5 20.0
-0.5 -1.0 Fig. 2. Typical time series of the measured outward ( p o s i t i v e ) and inward d i s charge through the Great Belt. From Bo Pedersen, 1978.
395
1900
1950 500 m S s
RVUOKSI
max
700 21%a
min
2O'lm.
,
'
i
I
SANHOLT NORD
7.5 %a 'F75
min
I
I
-4-
max
-.
0
/
H
7.0 %o
- --.-' 75 m
y00
Fig. 3. The secular changes in the Baltic Sea estuary i l l u s t r a t e d by the tenyear gliding mean of the runoff frmn the r i v e r Vuoksi (Nilsson and Svansson, 1 9 7 4 ) , the surface s a l i n i t y a t Anholt Nord (Nilsson and Svansson, 1974), the upper layer s a l i n i t y a t Station F75 ( t h e Central Baltic, Hela 1 9 6 6 ) , the u p p r layer depth i n t h e Central Baltic (Fonselius, 1 9 6 9 ) . I n the c o l m diagram t o the l e f t is shown the min/max values observed and the changes calculated f o r a 25% reduction of the r i v e r N e v a ' s runoff. F m Bo Pedersen and Mller, 1981.
1880
1900
1950 7°C
TCHRo
8
64 mrnHg
A p surnrner.winter
60
-VCHR 2 o
56
18= -----RVuoks,
.7.6-
14
5-
-RTotal
10 Fig. 4.
The secular variations of the ten-year gliding mean values of T
the a i r t a p r a t w e a t Christians@ (the Bornholm Basin),
CHW = winter -
Apsmr the sum of the s m r and winter average of m n t h l y peak-to-peak barcmetric pressure, proportional t o the wind speed squared a t Christians@, = the dis+
rGuOksi
charge of the Vuoksi river,
Tm,'Psumrer + winter Institute. Project.
%oksi,
STotal = the t o t a l fresh water runoff to the Baltic,
based on data published by the Danish 14=teorolOgic
f r m Nilsson and Svansson, 1974.
STOtal,
from the B e l t
396 0 2 4 6 8 1 0
20 m/s
0
0 0
0 0
0 Smer
0
0 0 0 0 0
0 0
-
0 0
0
0 Winter 0
0 0 0
0 0
0
0
Year
20 Ms
0 2 4 6 8 1 0
Fiq. 5. The m n t h l y ard annual wind sped p r o b a b i l i t y curves a t Anholt lighttower (the Kattegat region). The half-peak p r o b a b i l i t i e s are indicated to i l l u s t r a t e the seasonal v a r i a t i o n . From Danmarks Klima, 1933.
a) Mean= 1-
Period 1886-1925
-.--
,
J
F
Win-
M
A
M
J
J
Summer
A
S
O
N
,
ter
D
,
Fig. 6. a) The seasonal v a r i a t i o n of the a i r temperature (Tc),the wind power (Ap3''% (wind speed) 3 , and b) the water t a p r a t u r e i n the Bornholm Basin for a nearly continuous supply of dense water t o the deep w a t e r . yH = halocline depth, yt = t h e m l i n e depth; water tempsrature in 'C. Figure a) 1886-1925;
b) 1949-1961.
391
Winter (NoV- Ap) Summer
standard deviation
Fig. 7.
The m n t h l y 50 years average wind speed Vc[m/s] a t Christians@ l i g h t t m e r
(the Bornholm Basin) versus the square root of the monthly peak-to-peak a i r presswe a t Copenhagen [mn Hgl averaged over the s50 years period, namely 1876-1925. Original data taken from "Dmmrks Klirm", 1933.
1880
1900
1950
Apsummer. winter -v&R 0
3
~~~VGEDSER Fig. 8. Secular tim series of the calculated ten-year gliding man of the w i n d s@ squared ccxtpred w i t h the three-year gliding mean of third of the observed wind speed fran Gedser Rev lightvessel. The opposite trend in the individually observed timz series is obvious. V2- present calculations
v3Ged~ f m KullenhXg, 1977.
64mm "g 60
56
This Page Intentionally Left Blank
399
M I X I N G I N THE BALTIC SEA AND IMPLICATIONS FOR THE ENVIRONMENTAL CONDITIONS
GUNNAR KULLENBERG
I n s t i t u t e of P h y s i c a l Oceanography U n i v e r s i t y of Copenhagen H a r a l d s g a d e 6 , 2200 Copenhagen N , Denmark
ABSTRACT The B a l t i c Sea i s a s e m i - e n c l o s e d se*’with narrow and s h a l l o w c o n n e c t i o n s t o t h e open o c e a n and a n a n n u a l r i v e r r u n o f f amounting t o a b o u t 2 % of i t s volume. I n some r e s p e c t s t h e B a l t i c Sea c a n b e r e g a r d e d a s a s e r i e s of e s t u a r i e s . mean c y c l o n i c c i r c u l a t i o n i s v e r y weak and t h e wind-generated ting.
T h e r e i s a marked permanent s t r a t i f i c a t i o n ( h a l o c l i n e ) a t 50
and a summer t h e m c l i n e a r o u n d 2 0 m.
The
motion i s domina-
-
70 m d e p t h ,
The mean r e s i d e n c e t i m e i s a b o u t 30 y e a r s .
The B a l t i c Sea is s u b j e c t t o c o n s i d e r a b l e human i n f l u e n c e , f o r i n s t a n c e a s rec i p i e n t o f w a s t e , and b o t h t h e l i v i n g and n o n - l i v i n g
resources, including recrea-
t i o n a l u s e s , a r e o f g r e a t i m p o r t a n c e t o t h e c o u n t r i e s around t h e B a l t i c . E x p e r i m e n t a l r e s u l t s h a v e been o b t a i n e d on mixing r a t e s by means of n a t u r a l and a r t i f i c i a l tracers i n t h e open sea, and i n t h e c o a s t a l zone c u r r e n t meter r e c o r d s combined w i t h r e p e a t e d s e c t i o n s have been u s e d t o d e t e r m i n e v a r i o u s exchange r a t e s .
The wind, h e a t i n p u t and s t r a t i f i c a t i o n have a d e c i s i v e i n f l u e n c e
on the v e r t i c a l mixing.
I t i s shown t h a t b o t h t h e v e r t i c a l exchange i n t h e open
sea and t h e c o a s t a l zone a r e i m p o r t a n t f o r t h e f l u x e s . The mixing i n t h e d e e p and b o t t o m waters i s i n v e s t i g a t e d u s i n g s h o r t and l o n g
t e r m o b s e r v a t i o n s , and some c o n s i d e r a t i o n is g i v e n t o l o n g term f l u c t u a t i o n s . I m p l i c a t i o n s o f t h e r e s u l t s f o r t h e environmental c o n d i t i o n s i n t h e B a l t i c a r e presented.
INTRODUCTION
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 water body i n t h e w o r l d .
A population
o f a b o u t 1 9 m i l l i o n p e o p l e i n s e v e n states around it c o n t r i b u t e s a c o n s i d e r a b l e amount o f waste i n p u t , i n c l u d i n g n a t u r a l o r g a n i c m a t e r i a l , metals, o r g a n o c h l o r i n e s and p e t r o l e u m h y d r o c a r b o n s .
I n a d d i t i o n , t h e atmospheric i n p u t of anthropogenic
substances is considerable.
Harmful e f f e c t s on t h e B a l t i c mammals and s e a b i r d s
have been d e m o n s t r a t e d .
An i n c r e a s e i n t h e p r i m a r y p r o d u c t i o n h a s been i n d i c a t e d
a l o n g w i t h l o c a l c h a n g e s o f d o m i n a t i n g primary p r o d u c e r s , and d e c r e a s i n g product i o n a t d e p t h s below a b o u t 70 m , as w e l l a s a change i n t h e s t r u c t u r e of t h e bent h i c and t h e p e l a g i c ecosystem. The c o n c e n t r a t i o n l e v e l s o f p o l l u t a n t s i n B a l t i c b i o t a a r e , however, g e n e r a l l y
n o t e l e v a t e d compared t o t h e l e v e l s found i n North Sea c o a s t a l areas. The r i v e r s e n t e r i n g t h e B a l t i c have a p r o f o u n d i n f l u e n c e on t h e system.
They
have been s u b j e c t t o r e g u l a t i o n s i n r e l a t i o n t o h y d r o - e l e c t r i c power c o n s t r u c t i o n s , b u t no f l o w h a s a s y e t been r e v e r s e d . The l i v i n g r e s o u r c e s of t h e B a l t i c a r e i m p o r t a n t , t h e y i e l d d u r i n g t h e l a s t
.I
d e c a d e b e i n g a p p r o x i m a t e l y c o n s t a n t around 800.000 t o n n e s p e r y e a r , w i t h no d e creasing trends.
The B a l t i c Sea i s a v e r y i m p o r t a n t t r a n s p o r t a t i o n medium f o r
t h e s t a t e s around i t , and t h e r e c r e a t i o n a l i m p o r t a n c e i s a l s o g r e a t . The o v e r a l l problem i s t o what e x t e n t t h e n a t u r a l B a l t i c ecosystem can a d j u s t t o t h e human u s e o f t h e a r e a w i t h o u t b e i n g c o m p l e t e l y d e s t r o y e d .
This c l e a r l y
depends on a c o m b i n a t i o n o f many f a c t o r s , i n v o l v i n g p h y s i c s , chemistry.;
biology.
Here i n p a r t i c u l a r t h e m i x i n g c o n d i t i o n s and t h e i r i m p l i c a t i o n s w i l l b e c o n s i d e red.
I t seems c l e a r t h a t t h e v e r t i c a l t r a n s f e r ,
and i t s s p a c e and t i m e v a r i a t i o n ,
i s a very i m p o r t a n t f a c t o r f o r t h e environmental c o n d i t i o n s .
A t h o r o u g h assess-
ment o f t h e s t a t e o f t h e B a l t i c marine e n v i r o n m e n t b a s e d on r e c e n t d a t a h a s been c a r r i e d o u t d u r i n g t h e l a s t 2 - 3 y e a r s under t h e a u s p i c e s o f t h e H e l s i n k i Convent i o n ( M e l v a s a l o e t a l . 1 9 8 1 ) , and a t r e a t m e n t o f B a l t i c Sea oceanography i s g i v e n by V o i p i o (Ed. 19811.
AREA DEFINITION AND TOPOGRAPHY The B a l t i c S e a , a n i n t r a - c o n t i n e n t a l
m e d i t e r r a n e a n sea w i t h a n area o f a b o u t
370.000 km2 and volume of a b o u t 21.000 k m 3 , c o n s i s t s o f t h e Gulf o f B o t h n i a , i n c l u d i n g t h e Aland S e a , t h e Gulf o f F i n l a n d , and t h e B a l t i c p r o p e r w i t h t h e C e n t r a l , Bornholm and Arkona b a s i n s .
The C e n t r a l b a s i n i n c l u d e s t h e E a s t e r n and Western
Gotland b a s i n s and t h e N o r t h e r n C e n t r a l b a s i n s
( F i g . 1 ) . The Danish Sounds and
t h e K a t t e g a t , c o n s t i t u t i n g t h e T r a n s i t i o n A r e a , are sometimes i n c l u d e d i n t h e B a l t i c Sea a l t h o u g h it i s a d i f f e r e n t o c e a n o g r a p h i c regime.
The s i l l d e p t h i n
t h e Sound between Sweden and Denmark ( t h e Oresund), is 7-8 m and i n t h e B e l t Sea t h e s i l l d e p t h i s 17-18 m a t Darsser.
One o f t h e o u t s t a n d i n g f e a t u r e s o f t h e
B a l t i c topography i s t h e d i v i s i o n i n t o a s e r i e s o f b a s i n s s e p a r a t e d from e a c h o t h e r by s h a l l o w areas and s i l l s ( T a b l e 1).
The mean d e p t h i s 56 m b u t r o u g h l y
1 7 % o f t h e a r e a i s shallower than 1 0 m. The n o r t h e r n boundary of t h e T r a n s i t i o n Area i s d e f i n e d by t h e l i n e Skaw M a r s t r a n d , and t h e o c e a n o g r a p h i c b o u n d a r i e s between t h e B a l t i c p r o p e r and t h e T r a n s i t i o n Area a r e t h e l i n e s Gedser Rev (Wattenberg 1 9 4 9 ) .
-
Darsser O r t and DragcBr
- Limhamn
The area i s g e n e r a l l y s h a l l o w , t h e mean d e p t h o f t h e K a t t e g a t
b e i n g 2 3 m , w i t h t h e l a r g e s t d e p t h s i n t h e Oresund a b o u t 50 m , SE of t h e i s l a n d Ven, and i n t h e Great B e l t up t o 80 m i n narrow t r e n c h e s .
A
very important
c h a r a c t e r i s t i c i s t h a t t h e c o n n e c t i o n s between t h e B a l t i c Sea and t h e open o c e a n a r e b o t h s h a l l o w and narrow.
The s e c t i o n a r e a o v e r t h e s i l l i n t h e 0 r e s u n d i s
0.1 km2 and i n t h e B e l t Sea 0.16 km2.
401 TABLE 1 Major B a l t i c d i v i s i o n s w i t h maximum d e p t h s , s i l l d e p t h s a t o u t e r boundary, volumes and mean d e p t h s .
Max d e p t h
Name
m B a l t i c Sea ( t o t a l )
Arkona Sea Bornholm Sea E a s t e r n G o t l a n d Sea
S i l l depth m
Vo?ume
Mean d e p t h
km
m
4 59
17
20900
56
55
17
430
23
106
45
1780
46
-
-
-
Gdansk/or Danzig Bay
116
88
1460
57
Gotland Deep
249
60
3570
81
F & r 8 Deep
205
140
1270
-
N o r t h e r n C e n t r a l Sea
459
115
2090
L a n d s o r t Deep
4 59
138
780
Western Gotland Sea
205
100
1640
61
410
23
G u l f o f Riga
-
G u l f of F i n l a n d Aland Sea Archipelago Sea
300
70
72
-
1100
31
410
75
40
40
170
19
B o t h n i a n Sea
293
90
4300
67
B o t h n i a n Bay
126
25
1490
41
F i g . 1.
B a l t i c Sea s u b d i v i s i o n s w i t h s e c t i o n showinq d e p t h o f v a r i o u s b a s i n s (from J a n s o n 1 9 7 8 ) . D o t t e d l i n e i n l e f t hand f i g u r e shows p o s i t i o n o f t o p d g r a p h i c s e c t i o n shown o n r i g h t hand s i d e .
THE WATER BALANCE
The dominating f a c t o r i s t h e r i v e r inflow which according t o i n v e s t i g a t i o n s covering s l i g h t l y d i f f e r e n t p e r i o d s f a l l s i n t h e range 473-440 km3 p e r y e a r , o r about 2 % of t h e t o t a l volume of t h e B a l t i c Sea (Witting 1918, Brogmus 1952, Soskin 1963, Mikulski 1970).
Long-term records of t h e r i v e r inflow show a v a r i a b i l i t y
.
of about 20% between maximum and minimum. Remaining s i g n i f i c a n t terms i n t h e f r e s h water budget a r e t h e p r e c i p i t a t i o n and evaporation which on a y e a r l y b a s i s f o r t h e whole a r e a very c l o s e l y balance. However, they both show marked r e g i o n a l and s e a s o n a l v a r i a t i o n s . Considerable amounts of various substances a r e brought t o t h e B a l t i c Sea through t h e r i v e r r u n o f f , i n c l u d i n g humic substances, p a r t i c u l a t e m a t t e r , n u t r i e n t s and metals. The water exchange between t h e B a l t i c Sea and t h e open ocean i s d r i v e n both by t h e r i v e r runoff and by t h e meteorological c o n d i t i o n s over t h e North Sea
-
B a l t i c Sea a r e a . The average c i r c u l a t i o n i n t h e T r a n s i t i o n Area i s a two-layered flow.
However,
due t o t h e i n f l u e n c e of meteorological c o n d i t i o n s , t h e flow i s o f t e n a one-layer flow with t h e whole water column moving e i t h e r from o r towards t h e B a l t i c . south-westerly
t o north-westerly winds above about 1 0 m s-’
For
and with a minimum
d u r a t i o n of s e v e r a l days over t h e North Sea - Skagerrak a r e a , t h e c u r r e n t i n t h e T r a n s i t i o n Area i s towards t h e B a l t i c i n t h e whole water column. d i r e c t i o n s with wind f o r c e s of 1 0 m s-’
For o t h e r wind
o r more over t h e B a l t i c - North Sea a r e a
t h e c u r r e n t i s o u t of t h e B a l t i c ( D i e t r i c h 1951). The most favorable c o n d i t i o n s f o r inflows of s a l i n e water i n t o t h e B a l t i c occur with a high p r e s s u r e over J u t l a n d and a low p r e s s u r e over Sweden, whereas outflow s i t u a t i o n s occur with high p r e s s u r e over Scandinavia.
P a r t i c u l a r l y s t r o n g inflows
can occur when an outflow s i t u a t i o n i s followed by a s e r i e s of i n t e n s e west wind situations.
This was t h e c a s e i n November-December 1951 when about 200 km3 o f
highly s a l i n e water of about 2 2
O
b
p e n e t r a t e d i n t o t h e B a l t i c over a t h r e e week
period (Wyrtki 1954) Using t h e c l a s s i c a l Knudsen hydrographical theorem t o c a l c u l a t e t h e long-term average water exchange, i t i s found t h a t t h e inflows of f r e s h water and s a l t water a r e almost equal, o r about 470 km3 p e r y e a r , and t h e outflow about twice a s l a r g e . An important c h a r a c t e r i s t i c of t h e water t r a n s p o r t i s i t s l a r g e v a r i a b i l i t y . Recent s t u d i e s using long-term c u r r e n t measurements i n s e v e r a l s e c t i o n s i n t h e
Belt Sea show t h a t t h e t o t a l t r a n s p o r t i s i n t h e range 3-4000 km3 per year (Jacobsen 1980) For t h e c o n d i t i o n s i n t h e B a l t i c bottom waters t h e major inflows of s a l i n e water a r e p a r t i c u l a r l y important. years.
They occur a p e r i o d i c a l l y a t i n t e r v a l s of 2-5
There has been a tendency f o r t h e
during t h e l a s t decades.
frequency of t h e s e inflows t o i n c r e a s e
Dickson (1971, 1973) found a r a t h e r good c o r r e l a t i o n
between p o s i t i v e s a l i n i t y a n o m a l i e s i n t h e European s h e l f seas and t h e o c c u r r e n c e o f major i n f l o w s i n t o t h e B a l t i c .
I t s h o u l d b e n o t e d t h a t on a n a v e r a g e t h e r e i s
a c o n t i n u o u s i n f l o w of d e e p w a t e r i n t o t h e B a l t i c .
T h i s water does n o t p e n e t r a t e
down t o t h e b o t t o m i n t h a B a l t i c b a s i n s e x c e p t d u r i n g major i n f l o w s . The r e s i d e n c e t i m e f o r t h e w a t e r i n t h e B a l t i c i s .about 35 y e a r s , c a l c u l a t e d u s i n g t h e y e a r l y a v e r a g e w a t e r exchange and t a k i n g i n t o a c c o u n t t h a t a b o u t 1 / 3 o f t h e w a t e r i n t h e o u t f l o w from t h e B a l t i c i s mixed down i n t o t h e r e t u r n f l o w .
SALINITY AND TEMPERATURE DISTRIBUTIONS s u r p l u s , c o n s t i t u t i n g a p o s i t i v e w a t e r b a l a n c e , t h e narrow and
The f r e s h - w a t e r
s h a l l o w c o n n e c t i o n s w i t h t h e o c e a n , and t h e t o p o g r a p h i c d i v i s i o n i n t o s e v e r a l b a s i n s have a major i n f l u e n c e o n t h e o c e a n o g r a p h i c c o n d i t i o n s o f t h e B a l t i c S e a . An i m p o r t a n t c h a r a c t e r i s t i c o f t h e B a l t i c i s t h e marked permanent s a l i n i t y stratification
(Fig. 2 ) .
The f r e s h - w a t e r
s u p p l y i s mixed downwards by a c o m b -
n a t i o n o f w i n d - g e n e r a t e d mixing and t h e r m o h a l i n e c o n v e c t i o n d u r i n g f a l l and e a r l y winter.
T h i s p r o c e s s g e n e r a t e s an a l m o s t homohaline l a y e r s e p a r a t e d from t h e
d e e p and bottom waters by a permanent h a l o c l i n e l a y e r of a b o u t 20 m t h i c k n e s s . The t h i c k n e s s o f t h e s u r f a c e l a y e r v a r i e s from a b o u t 40 m i n t h e south-west b a s i n s t o a b o u t 60 m i n t h e C e n t r a l b a s i n
(Fonselius 1969).
According t o Matthdus (1979)
t h e mean d e p t h o f t h e h a l o c l i n e l a y e r h a s n o t v a r i e d more t h a n 1 0 % d u r i n g t h i s c e n t u r y , and t h e mean d e p t h o f t h e t o p of t h e h a l o c l i n e l a y e r h a s d e c r e a s e d by a b o u t 6 m. The w a t e r exchange between t h e C e n t r a l b a s i n and t h e Gulf o f B o t h n i a g o e s e s s e n t i a l l y t h r o u g h t h e Aland S e a .
The incoming w a t e r o r i g i n a t e s from t h e t o p 70
l a y e r o f t h e C e n t r a l b a s i n , which h a s s m a l l s a l i n i t y and d e n s i t y v a r i a t i o n s .
The
mixing d u r i n g t h e i n f l o w f u r t h e r r e d u c e s t h e d e n s i t y v a r i a t i o n s , i m p l y i n g t h a t t h e s t r a t i f i c a t i o n i n t h e Gulf of B o t h n i a i s c o n s i d e r a b l y weaker t h a n i n t h e B a l t i c proper.
The s t r a t i f i c a t i o n i s s t a b l e t h r o u g h o u t t h e y e a r b u t t h e d e p t h
o f t h e weakly d e v e l o p e d h a l o c l i n e v a r i e s s t r o n g l y and t h e h a l o c l i n e c a n be a b s e n t d u r i n g p a r t of t h e y e a r . The d e e p water s a l i n i t i e s i n t h e Gulf o f B o t h n i a a r e 3-7 F i n l a n d 5-9
oband
i n t h e B a l t i c p r o p e r 10-13
O h .
"b,i n t h e Gulf of
I n connection with p a r t i c u -
l a r l y s t r o n g i n f l o w s from t h e K a t t e g a t t h e bottom w a t e r s a l i n i t y i n t h e Bornholm b a s i n c a n r e a c h 23
Obo
11 %o, r e s p e c t i v e l y .
and i n t h e e a s t e r n and w e s t e r n Gotland b a s i n s 14 oband I n connection with such i n f l o w s a secondary h a l o c l i n e
l a y e r d e v e l o p s a t a d e p t h of 110-130 m ( V o i p i o and MBlkki 1 9 7 2 ) . The r e s i d e n c e t i m e o f t h e bottom waters depends p r i m a r i l y on t h e d e n s i t y d i f f e r e n c e t o t h e o v e r l y i n g w a t e r s , which is e s s e n t i a l l y d e t e r m i n e d by t h e s a l i n i t y . A f t e r s t r o n g i n f l o w s o f h i g h l y s a l i n e waters, r e p l a c i n g t h e o l d bottom waters, t h e d e n s i t y o f t h e new bottom w a t e r n o r m a l l y must d e c r e a s e s i g n i f i c a n t l y by v e r -
t i c a l mixing b e f o r e a new i n f l o w c a n r e p l a c e it.
During t h e s e p e r i o d s , which can
404
7' '1 50.
( \ \\\
100.
I
\
\
"'
\
I
I
I
2
I
Fig. 2.
P r o f i l e s of s a l i n i t y and t e m p e r a t u r e from t h e G o t l a n d b a s i n showing h a l o c l i n e and development o f s e a s o n a l t h e r m o c l i n e .
I
9)
13
-
-
0
3 II 10
Fig. 3 .
e
0
-
- xx
0
00 ooo
0 0
0
v)
OO
0
8
312c ..-C
0
0
0
0
"0
a
V
O
JLX X
X S I
15
=a
xn
Long-term v a r i a t i o n s of s a l i n i t y (x) and t e m p e r a t u r e in t h e L a n d s o r t Deep.
(0)
a t 300 m d e p t h
l a s t up t o a b o u t 5 y e a r s , t h e motion i n t h e bottom w a t e r i s v e r y weak and t h e y
are t h e r e f o r e o f t e n c a l l e d p e r i o d s of s t a g n a t i o n .
I n t h e Arkona b a s i n and normally
i n t h e Gulf o f B o t h n i a t h e bottom w a t e r i s renewed e v e r y y e a r due t o a combination o f water exchange and t h e r m o h a l i n e c o n v e c t i o n . The v e r t i c a l t e m p e r a t u r e d i s t r i b u t i o n shows marked s e a s o n a l v a r i a t i o n s ( F i g . 2). During f a l l and e a r l y w i n t e r t h e c o n v e c t i o n r e a c h e s t h e t o p o f t h e p r i m a r y h a l o c l i n e , where it i s s t o p p e d by t h e s t r o n g s t r a t i f i c a t i o n .
During t h e s p r i n g a
s t r o n g t h e r m o c l i n e i s d e v e l o p e d o v e r t h e whole B a l t i c Sea a t d e p t h s between 1 5 The t e m p e r a t u r e maximum o c c u r s i n August w i t h up t o 18OC a t 20 m.
and 20 m.
During f a l l t h e t e m p e r a t u r e d e c r e a s e s , and t h e d e p t h of t h e t h e r m o c l i n e may t h e n i n c r e a s e t o 50 'a 60 m. On t o p o f t h e h a l o c l i n e t h e s o - c a l l e d w i n t e r water remains which was formed during t h e preceding fall-winter
period.
The summer t h e r m o c l i n e e f f e c t i v e l y
s u p p r e s s e s v e r t i c a l mixing and n u t r i e n t t r a n s f e r from d e e p e r l a y e r s t o t h e e u p h o t i c zone, which i s a b o u t 20 m d e e p . The d e e p w a t e r t e m p e r a t u r e i n t h e Bornholm b a s i n v a r i e s between a b o u t 2 and 14OC whereas i n t h e C e n t r a l b a s i n t h e deep water t e m p e r a t u r e normally l i e s between 3 and 6OC.
LONG-TERM VARIATIONS AND THEIR CAUSES AND EFFECTS
Both t e m p e r a t u r e and s a l i n i t y show i m p o r t a n t long-term f l u c t u a t i o n s ( S o s k i n 1963, Hela 1966a. F o n s e l i u s 1969, Matthaus 1 9 7 9 ) , w i t h a c l e a r t r e n d t o w a r d s an increase 0.8
-
(Fig. 3 ) .
1.7
Obo
The s a l i n i t y i n t h e d e e p and bottom w a t e r s h a s i n c r e a s e d by
and t h e t e m p e r a t u r e by 0.6 - 2.7OC d u r i n g t h e p r e s e n t c e n t u r y .
s a l i n i t y i n c r e a s e i n t h e s u r f a c e l a y e r is s l i g h t l y l e s s , by a b o u t 0.2 - 0.5 t h a n i n t h e d e e p water.
The
"b,
These v a r i a t i o n s c a n be c a u s e d b o t h by t h e v a r i a t i o n s
o f t h e r i v e r r u n o f f and o f t h e water exchange w i t h t h e K a t t e g a t - N o r t h Sea.
There
seems t o b e a c o u p l i n g between p e r i o d s of l o w s a l i n i t y and p e r i o d s o f h i g h r u n o f f and v i c e v e r s a ( e . g . F o n s e l i u s 1969, K a l e i s 1 9 7 6 ) .
The changes of t h e r i v e r run-
o f f a r e i n t u r n p r o b a b l y r e l a t e d t o changes i n t h e a t m o s p h e r i c c i r c u l a t i o n ( e . g . S o s k i n 1963) a l t h o u g h t h e r e h a s n o t been found any c l e a r c o r r e l a t i o n between c e r t a i n t y p e s o f c l i m a t i c f l u c t u a t i o n s (Hela 1966a) and t h e r i v e r r u n o f f f l u c t u a t i o n s . There d o e s n o t seem t o b e any s i g n i f i c a n t long-term d e c r e a s i n g t r e n d i n t h e r i v e r r u n o f f d u r i n g t h e l a s t 100 y e a r s , a l t h o u g h t h e r e a r e s h o r t e r p e r i o d s w i t h marked trends,
( L a u n i a i n e n and K o l j o n e n , 1 9 8 1 ) .
The s a l i n i t y i n c r e a s e may b e r e l a t e d
t o v a r i a t i o n s i n t h e r i v e r r u n o f f as w e l l as t o c h a n g e s i n t h e f r e q u e n c y o f major i n f l o w s o f h i g h s a l i n i t y water from t h e K a t t e g a t , e s p e c i a l l y when t h e s e a r e coupled
t o a p o s i t i v e s a l i n i t y anomaly o v e r t h e European s h e l f seas as shown by Dickson (1972). The t e m p e r a t u r e and s a l i n i t y f l u c t u a t i o n s have i m p o r t a n t i m p l i c a t i o n s f o r t h e c o n d i t i o n s i n t h e B a l t i c Sea.
The d e n s i t y s t r a t i f i c a t i o n across t h e h a l o c l i n e
406 l a y e r and i n t h e d e e p e r waters i s m a i n l y d e t e r m i n e d by the s a l i n i t y .
The f l u c t u a -
t i o n s g e n e r a t e v a r y i n g d e g r e e s o f s t r a t i f i c a t i o n i n t h e deep and bottom w a t e r i m p l y i n g d i f f e r e n t c o n d i t i o n s of v e r t i c a l mixing.
S t u d i e s of t h e long-term v a r i a -
t i o n s o f t h e s a l i n i t y g r a d i e n t a c r o s s t h e h a l o c l i n e i n t h e Gotland b a s i n do n o t show any s i g n i f i c a n t t r e n d o f change d u r i n g t h e c e n t u r y (Matthaus 1 9 7 9 ) , which would s u g g e s t t h a t t h e s t a b i l i t y h a s n o t changed s i g n i f i c a n t l y . T h i s i s i m p o r t a n t i n r e l a t i o n t o v e r t i c a l mixing s i n c e t h e s t a b i l i t y h a s a major i n f l u e n c e on t h e mixing ( e . g . K u l l e n b e r q 1 9 7 4 ) . The t e m p e r a t u r e i n c r e a s e i n t h e d e e p w a t e r s may be due t o a s h i f t o f i n f l o w s t o w a r d s t h e warmer s e a s o n . I t i m p l i e s an i n c r e a s e d r a t e o f oxygen consumption and a l s o t h a t less oxygen e n t e r s w i t h t h e i n f l o w i n g water. T h i s may w e l l have i n f l u e n c e d t h e development of t h e oxygen c o n d i t i o n s ( e . 9 . Kullenberg 1970). ~
1 . Features of t h e circulation T h e r e i s a weak c y c l o n a l mean c i r c u l a t i o n i n t h e B a l t i c P r o p e r 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 , w i t h v e l o c i t i e s o f t h e o r d e r o f c e n t i m e t e r s p e r s e c o n d . T h i s c i r c u l a t i o n i s e s s e n t i a l l y t h e r m o h a l i n e , t h e mean winds o v e r t h e B a l t i c b e i n g v e r y weak. The f l u c t u a t i n g p a r t of t h e m o t i o n , which c a n r e a c h v e l o c i t i e s o f 50 c m s - ’ ,
i s g e n e r a t e d by t h e m e t e o r o l o g i c a l c o n d i t i o n s . wind and p r e s s u r e g r a d i e n t s . s t o r m s o f t e n o c c u r o v e r t h e B a l t i c Sea.
Strong
I n t h e t o p l a y e r t h e f l u c t u a t i n g motion
i s d i r e c t l y p r o p o r t i o n a l t o t h e wind stress, and i n t h e d e e p e r l a y e r s t h e motion i s r e l a t e d t o t h e d i v e r g e n c e and c u r l o f t h e wind s t r e s s .
I m p o r t a n t f e a t u r e s of
t h e motion a r e t h e i n e r t i a l o s c i l l a t i o n s and v a r i o u s t y p e s of s e i c h e s g e n e r a t e d by f l u c t u a t i n g winds and a i r p r e s s u r e .
The t i d a l motion i s weak, o f t h e o r d e r o f
c e n t i m e t e r s p e r second.
M I X I N G I N THE BALTIC
General The mixing i n t h e B a l t i c Sea i s weaker t h a n i n t h e open o c e a n and t h a n i n a r e a s o f s t r o n g t i d a l c u r r e n t s l i k e t h e North S e a .
The mixing c a n b e g e n e r a t e d by pro-
c e s s e s a t t h e b o u n d a r i e s , by b r e a k i n g of i n t e r n a l waves which have been g e n e r a t e d i n t h e i n t e r i o r o r have r a d i a t e d i n t o t h e i n t e r i o r from t h e b o u n d a r i e s , by i n e r t i a l motion, by f a l l and w i n t e r t i m e c o n v e c t i o n i n t h e s u r f a c e l a y e r down t o t h e p r i mary h a l o c l i n e . The main e n e r g y s o u r c e f o r t h e mixing i s t h e wind, and d u r i n g f a l l and e a r l y w i n t e r t h e loss of h e a t t h r o u g h c o o l i n g .
The l a y e r down t o the p r i m a r y h a l o c l i n e
w i l l a l w a y s become t h o r o u g h l y mixed d u r i n g some p e r i o d s i n f a l l and w i n t e r .
The
p r i m a r y i n t e r e s t i n r e l a t i o n t o mixing i s t h e exchange a c r o s s t h e h a l o c l i n e l a y e r and t h e mixing i n t h e d e e p and b o t t o m w a t e r s .
The l a t t e r mixing h a s a g r e a t i n -
f l u e n c e on t h e exchange r a t e o f t h e bottom w a t e r s , and i s t h u s o f g r e a t s i g n i f i cance i n r e l a t i o n t o t h e oxygen c o n d i t i o n s i n t h e s e waters.
407 The d e e p w a t e r i n f l o w from t h e Danish S t r a i t s , a c r o s s t h e Bornholm s i l l and t h e S t o l p e Channel i n t o t h e B a l t i c P r o p e r i s a l s o a main s o u r c e of energy f o r t h e i n t e r i o r mixing.
E n t r a i n m e n t o f w a t e r i n t o t h e i n f l o w i n g w a t e r from below and t o
some e x t e n t from above w i l l g e n e r a t e c o n s i d e r a b l e v e r t i c a l mixing.
T h i s i s an
i m p o r t a n t p r o c e s s s i n c e i t o c c u r s more or less c o n t i n u o u s l y . S e v e r a l i n v e s t i g a t i o n s have shown t h a t i n t e r n a l s m a l l s c a l e motion o c c u r i n t h e B a l t i c d e e p w a t e r s ( e . g . H o l l a n 1969, K r a u s s e t a 1 1 9 7 3 ) .
The d o m i n a t i n g
t y p e o f f l u c t u a t i n g motion i s t h e i n e r t i a l motion, which i s found i n t h e whole
water column i n c o n n e c t i o n w i t h s u i t a b l e wind e v e n t s and which g e n e r a t e s s h e a r s w i t h a s s o c i a t e d mixing. Above t h e h a l o c l i n e The e f f i c i e n c y o f w i n d - g e n e r a t e d mixing i n e r o d i n g and d e e p e n i n g t h e s e a s o n a l t h e r m o c l i n e h a s been d e m o n s t r a t e d
( e . g . Krauss 1978, K u l l e n b e r g 1978) on t h e b a s i s
o f o b s e r v a t i o n s i n r e l a t i o n t o the p a s s i n g o f a sequence o f s t o r m s o v e r t h e s o u t h e r n B a l t i c Proper
(Fig. 4 ) .
C o n s i d e r i n g t h a t t h e f r e q u e n c y of s t o r m s o v e r t h e B a l t i c
i s l a r g e , t h i s c o n s t i t u t e s a v e r y i m p o r t a n t e n e r g y s o u r c e f o r t h e mixing, i n t h e i n t e r i o r as w e l l a s i n t h e c o a s t a l zone.
R e s u l t s on t h e v e r t i c a l mixing r a t e s i n
t h e t o p l a y e r o b t a i n e d by means o f d i f f e r e n t methods are a l s o p r e s e n t e d i n T a b l e 2 . I t s h o u l d be n o t e d t h a t d u r i n g calm o r weak wind c o n d i t i o n s o f some l e n g t h t h e
mixing i n t h e t o p l a y e r c a n b e v e r y weak, e s p e c i a l l y d u r i n g t h e warm s e a s o n . These p e r i o d s o f v e r y low mixing c a n e x t e n d f o r many d a y s , and q u i t e c l e a r l y t h e y have biological significance i n relation t o the productivity.
An example o f dye pro-
f i l e s o b t a i n e d d u r i n g s u c h a p e r i o d i n t h e c e n t r a l B a l t i c i s shown i n F i g . 5.
1t
i s n o t e d t h a t l a y e r s can b e formed a l s o d u r i n g weak s t r a t i f i c a t i o n .
-
v e r t i c a l m i x i n g below t h e h a l o c l i n e Mixing r a t e s f o r t h e d e e p and bottom waters may b e e s t i m a t e d from o b s e r v e d d e c r e a s e s o f t h e s a l i n i t y of t h e d e e p and bottom w a t e r f o l l o w i n g a bottom w a t e r r e n e w a l ( F i g . 6 ) , and assuming t h a t t h e d e c r e a s e of s a l i n i t y i s due t o a v e r t i c a l f l u x of s a l t .
The t i m e - i n t e r v a l between r e n e w a l s c a n b e r a t h e r w e l l d e t e r m i n e d
together with t h e s a l i n i t y decrease.
The t o t a l s a l t f l u x h a s been c a l c u l a t e d
u s i n g h y d r o g r a p h i c d a t a from a few s t a t i o n s i n t h e B a l t i c P r o p e r r e p r e s e n t i n g d i f f e r e n t p a r t s o f t h e area.
The volumes were o b t a i n e d from E h l i n e t a1 ( 1 9 7 4 ) .
The v e r t i c a l mixing c o e f f i c i e n t , K
z'
was c a l c u l a t e d u s i n g t h e e x p r e s s i o n
where A i s t h e area a t t h e l e v e l i n q u e s t i o n ( o b t a i n e d from E h l i n e t a1 1 9 7 4 ) and t is the time-interval.
The s a l i n i t y g r a d i e n t , d S / d z ,
a p p r o p r i a t e l e v e l from t h e h y d r o g r a p h i c d a t a .
w a s determined f o r t h e
R e s u l t s a r e given i n Table 2.
The
40 8
Fig. 4 .
Thermocline e r o s i o n d u r i n g September s t o r m i n the s o u t h e r n c e n t r a l Baltic.
UD
I
-35m
time 1842
T
Fig. 5.
Rhodamine dye l a y e r s a f t e r 20 h o u r s of i n s i t u t r a c i n g d u r i n g a p e r i o d of s e v e r a l d a y s of calm in t h e E a s t e r n G o t l a n d b a s i n .
409 TABLE 2
Vertical mixing c o e f f i c i e n t s , K Z ,
f o r various layers i n the Baltic.
Method and
Depth
Range of
remarks
range
K -lo6
m Dye d i f f u s i o n , calm w e a t h e r Seasonal h e a t
Reference
_
m’s-l
45- 55
0.8-3.9
22- 3 5
5
50- 70
10
- 15
-
100
Kullenberg (197433. 1977) MatthZus (1977)
penetration Seasonal h e a t
0- 20
penetration
20- 30
30 - 3 0 1 0 ~
MatthZus (1977)
40- 50
10 - 3-103
Matthaus
Seasonal h e a t
20- 30
60
penetration
50- 60
5-10’ - 5 * 1 0 3
60- 70
Open B a l t i c 10
Conservation c a l c u l a t i o n s
104
10’-
(1977)
- 200
c o a s t a l zone 80
of s a l t flux
MatthBus (1977)
Hela (1966b)
S h a f f e r (1979a)
Thermocline deepening d u r i n g storm
700
30- 40
J e n s e n and K u l l e n b e r g (1981)
Dye d i f f u s i o n , calm
30- 40
15
-
60
K u l l e n b e r g (1981)
weather 200-240
Salinity decrease
> -
a f t e r inflow
100
> 150 -
1965 Fig. 6.
J e n s e n and
1970
-
35
4 -
5
10
present
5 - 10
1975
1980
V a r i a t i o n s o f s a l i n i t y a t 240 m d e p t h i n t h e Gotland Deep f o l l o w i n g i n f l o w s ( d a t a from S . F o n s e l i u s , p e r s . c o m . ) .
410 v a l u e s a p p e a r r e a s o n a b l e , and are comparable t o r e s u l t s from t h e h a l o c l i n e l a y e r . The e n e r g y s u p p l y f o r t h e mixing i s d e r i v e d from t h e d e e p w a t e r i n f l o w t h r o u g h t h e Danish S t r a i t s and from t h e wind.
The l a t t e r t r a n s f e r s a s u b s t a n t i a l amount
of e n e r g y t o t h e t o p l a y e r ( K u l l e n b e r g 1977) and p a r t o f t h i s e n e r g y w i l l p e n e t r a t e t o t h e d e e p and bottom w a t e r s , i n e r t i a l o s c i l l a t i o n s b e i n g one t r a n s f e r mechanism. The r e s u l t s summarized i n T a b l e 2 q u i t e c l e a r l y show t h a t t h e v e r t i c a l mixing
i s v e r y v a r i a b l e , w i t h area, d e p t h and depending upon t h e c o n d i t i o n s .
This i s
q u i t e what s h o u l d be e x p e c t e d , and t h e r e s u l t s a r e c o n s i s t e n t w i t h e a c h o t h e r a l t h o u g h v e r y d i f f e r e n t methods have been used.
The v a l u e s f o r t h e d e e p and
bottom waters o b t a i n e d by means of o b s e r v a t i o n s from d i f f e r e n t t i m e s d u r i n g t h i s c e n t u r y do n o t s u g g e s t any s i g n i f i c a n t change i n t h e mixing r a t e s d u r i n g t h e present century.
Vertical fluxes I t i s i m p o r t a n t t o d e t e r m i n e t h e r a t e o f exchange between t h e v a r i o u s l a y e r s
i n t h e B a l t i c as w e l l as t o c l a r i f y t h e d i s t r i b u t i o n i n s p a c e of t h e t r a n s f e r . I n t h e c o a s t a l zone v e r y e f f i c i e n t v e r t i c a l t r a n s f e r a c r o s s t h e h a l o c l i n e l a y e r may b e g e n e r a t e d by s u i t a b l e winds g i v i n g r i s e t o a d i v e r g e n c e a t t h e c o a s t , w i t h a s s o c i a t e d compensating flow and u p w e l l i n g o r downwelling i n t h e c o a s t a l zone The w i d t h , Lc,
( e . g . Walin 1972a, S h a f f e r 1975, 1979a, b ) .
o f t h e c o a s t a l dyna-
mics zone may b e e s t i m a t e d by t h e e x p r e s s i o n Lc
^.
Ho N/€
where H
0
i s t h e d e p t h o f t h e h a l o c l i n e a t t h e boundary between t h e c o a s t a l zone
and t h e open sea.
Using t y p i c a l v a l u e s from t h e B a l t i c one f i n d s a w i d t h Lc i n
t h e r a n g e 5-10 km ( e . g . Walin 197213).
T h i s i s i n r e a s o n a b l e a g r e e m e n t w i t h ob-
s e r v a t i o n s a l t h o u g h t y p i c a l c o a s t a l zone dynamics a l s o have been o b s e r v e d o v e r greater widths (Shaffer 1975).
The v e r t i c a l f l u x a s s o c i a t e d w i t h wind e v e n t s
of t h i s k i n d has b e e n computed by S h a f f e r (1975, 1979b) on t h e b a s i s of o b s e r v a t i o n s , o v e r a p e r i o d o f some months i n t h e f a l l , i n r e p e a t e d s e c t i o n s ' o f s a l i n i t y and t e m p e r a t u r e , n u t r i e n t s and c u r r e n t s . fusive flux of 1 2 -
kg s a l t m-'
s-',
H e found a n a v e r a g e v e r t i c a l d i f -
w i t h a n a d v e c t i v e f l u x d u r i n g t h e same
p e r i o d a b o u t a n o r d e r o f magnitude l a r g e r .
I n a l a t e r s t u d y i n t h e same a r e a
S h a f f e r L1979a) c a l c u l a t e d t h e f l u x e s a c r o s s t h e 8 . 5 Obo i s o h a l i n e u s i n g o b s e r v a t i o n s from a s i x weeks p e r i o d i n t h e s p r i n g t i m e . s i v e and a d v e c t i v e f l u x e s o f 5.10-6 kg s a l t m-' respectively.
s-l
H e found v a l u e s f o r t h e d i f f u -
and 7 0 - 1 0 6 kg s a l t m-'
F o r comparison, S h a f f e r c a l c u l a t e d t h e f l u x a c r o s s t h e 8.5
s-',
Obo
i s o h a l i n e f o r t h e e n t i r e B a l t i c , f i n d i n g t h e f l u x e s t o b e 1.1-10-6 and 3.4-106 kg
s a l t m-'
s-',
respectively.
F o r t h e s e c a l c u l a t i o n s h e used i n f l o w o b s e r v a t i o n s
t h r o u g h t h e Bornholm S t r a i t and t h e S t o l p e Furrow p r e s e n t e d by Rydberg ( 1 9 7 8 ) .
411 S h a f f e r ‘ s r e s u l t s d e m o n s t r a t e t h a t l a r g e f l u x e s c a n o c c u r i n t h e c o a s t a l zone. However, how o f t e n and o v e r how l a r g e a p a r t o f t h e t o t a l c o a s t l i n e o f t h e B a l t i c Sea?
These q u e s t i o n s have n o t y e t been answered.
Here t h e r e s u l t s o f S h a f f e r
w i l l b e u s e d t o e s t i m a t e t h e p o s s i b l e v e r t i c a l f l u x i n t h e c o a s t a l zone f o r t h e whole B a l t i c . With a l e n g t h o f t h e c o a s t l i n e a t t h e 60 m l e v e l o f a b o u t 1200 km, and a w i d t h of t h e zone of c o a s t a l dynamics on a n a v e r a g e o f 1 0 km, w e f i n d an i n t e g r a t e d d i f f u s i v e f l u x o f s a l t a c r o s s t h e h a l o c l i n e l a y e r i n t h e c o a s t a l zone o f up t o
1 4 4 t o n s a l t s-’,
and a b o u t an o r d e r o f magnitude more as a d v e c t i v e f l u x .
The d i f f u s i v e f l u x may b e compared w i t h t h e c o r r e s p o n d i n g f l u x i n t h e open Baltic,
c a l c u l a t e d b y means o f o b s e r v e d v k r t i c a l mixing c o e f f i c i e n t s , K Z , and
s a l i n i t y gradients across the halocline layer. r a n g e 1-3
Obo
p e r 10 m.
Values o f K
These a r e on an a v e r a g e i n t h e
d e t e r m i n e d by v a r i o u s t e c h n i q u e s f o r t h e
h a l o c l i n e l a y e r are p r e s e n t e d i n T a b l e 2 .
The r a h g e i s f a i r l y l a r g e so maximum
and minimum estimates o f t h e i n t e g r a t e d s a l t f l u x c a n o n l y b e g i v e n , assuming t h a t t h e v a l u e s a r e r e p r e s e n t a t i v e f o r t h e whole a r e a . mined by K u l l e n b e r g
The v a l u e s o f K
deter-
(1971, 1977) from dye e x p e r i m e n t s o f one o r two d a y s ’ d u r a -
t i o n d u r i n g calm c o n d i t i o n s a r e p r o b a b l y minimum v a l u e s .
The a r e a o f t h e B a l t i c
P r o p e r i s 105km2 a t 60 m d e p t h ( E h l i n e t a1 1 9 7 4 ) , assuming t h i s t o b e a n a v e r a g e depth o f t h e h a l o c l i n e l ay er.
The minimum d i f f u s i v e s a l t f l u x i s 60 t o n s-’,
u s i n g t h e maximum v a l u e o f t h e s a l i n i t y g r a d i e n t . value of K
f o r t h e whole open B a l t i c a t t h e h a l o c l i n e t o b e 100.10-6m2
f i n d t h a , d i f f u s i v e s a l t f l u x t o be gradient.
Taking t h e maximum a v e r a g e
lo3
t o n s-’,
s-I
we
u s i n g t h e minimum v a l u e o f t h e
These v a l u e s a r e c e r t a i n l y comparable w i t h t h e d i f f u s i v e f l u x f o r t h e
c o a s t a l zone.
The maximum v a l u e i s comparable w i t h t h e a d v e c t i v e f l u x i n t h e
c o a s t a l zone,
I t a p p e a r s t h a t t h e v e r t i c a l exchange i n t h e B a l t i c o c c u r s a t com-
p a r a b l e m a g n i t u d e s o v e r t h e whole s e a area. I t i s o f i n t e r e s t t o compare t h e y e a r l y i n f l o w o f s a l t t o t h e B a l t i c w i t h t h e
vertical salt flux.
C o n s i d e r i n g a n a n n u a l i n f l o w o f 500 km3 t h r o u g h t h e Danish
S t r a i t s w i t h a s a l i n i t y o f 17 Obo w e f i n d a n i n f l o w o f 270 t o n s a l t s-I.
This
number compares w e l l w i t h t h e t o t a l d i f f u s i v e f l u x a c r o s s t h e h a l o c l i n e l a y e r . An a d v e c t i v e f l u x o f a b o u t
lo3
t o n s-’
i n t h e c o a s t a l zone a s an a n n u a l a v e r a g e
a p p e a r s , however, t o be q u i t e u n r e a l i s t i c .
I t can b e concluded t h a t t h e e s t i m a t e s
f o r t h e i n t e r i o r v e r t i c a l m i x i n g a r e r e a l i s t i c , and t h a t t h e v a l u e s may b e used t o d i s c u s s i m p l i c a t i o n s f o r t h e B a l t i c ecosystem.
H o r i z o n t a l mixing Only a l i m i t e d number o f d i r e c t e x p e r i m e n t a l s t u d i e s of h o r i z o n t a l mixing e x i s t . For t h e s o u t h e r n B a l t i c , K u l l e n b e r g i n t h e r a n g e 3.5 m h-’to
(1977) found h o r i z o n t a l d i f f u s i o n v e l o c i t i e s
7 . 2 m h-’ i n t h e thermo-
and h a l o c l i n e l a y e r s .
s u r f a c e l a y e r S c h o t t e t a1 (1978) found v a l u e s i n t h e r a n g e 9 . 7 m h-’
In the t o 2 1 m h-’.
412 These r e s u l t s a r e based on dye mixing o b s e r v a t i o n s , c a r r i e d o u t d u r i n g weak winds. I n t h e L a n d s o r t area K u l l e n b e r g (1964) found v a l u e s i n t h e r a n g e 4-18 m h-’
for
t h e s u r f a c e l a y e r t o 2 5 m , b a s e d on t h e o b s e r v a t i o n of d i s p e r s i o n o f i n t e r n a l l a y e r s o f suspended m a t t e r r e s u l t i n g from a sewage s l u d g e dumping e x p e r i m e n t . The
,.
h o r i z o n t a l mixing i n t h e B a l t i c i s weaker t h a n it is f o r i n s t a n c e i n t h e North S e a , by a b o u t a f a c t o r of 5 on s i m i l a r s c a l e s .
T h i s i s o f some i n t e r e s t i n re-
l a t i o n t o t h e t r a n s f e r of m a t e r i a l from t h e c o a s t a l zone o u t w a r d s , i n p a r t i c u l a r a l o n g t h e i s o p y c n a l s i n thermo-
and h a l o c l i n e l a y e r s .
Considerable p e r i o d s o f
t i m e , o f t h e o r d e r o f s e v e r a l months, w i l l be r e q u i r e d f o r m a t e r i a l t o become t r a n s f e r r e d across t h e c o a s t a l zone i n t o t h e i n t e r i o r .
The most e f f i c i e n t t r a n s -
f e r w i l l o c c u r d u r i n g s t r o n g wind c o n d i t i o n s i n t h e f a l l a n d l a t e w i n t e r t o e a r l y spring.
FACTORS INFLUENCING THE M I X I N G The c o n d i t i o n s i n t h e B a l t i c h a v e d i s p l a y e d a c o n s i d e r a b l e v a r i a b i l i t y d u r i n g the present century.
I n p a r t i c u l a r t h e oxygen c o n d i t i o n s i n t h e d e e p and bottom
waters h a v e d e t e r i o r a t e d .
T h i s can conceivably b e r e l a t e d t o s e v e r a l f a c t o r s
and p r o c e s s e s , one b e i n g t h a t t h e r a t e o f v e r t i c a l mixing h a s changed. The r a t e o f v e r t i c a l exchange i s e s s e n t i a l l y d e p e n d i n g upon t h e d e n s i t y s t r a t i f i c a t i o n ( s t a t i c s t a b i l i t y ) and t h e energy a v a i l a b l e for t u r b u l e n t mixing a g a i n s t t h e buoyancy f o r c e s .
The s t a b i l i t y a c r o s s t h e h a l o c l i n e l a y e r h a s shown f l u c t u a -
t i o n s b u t t h e r e h a s been no l o n g - t e r m i n c r e a s e ( K u l l e n b e r g 1 9 7 7 , 1981; Matthaus
1980). I t a p p e a r s t h a t no l o n g - t e r m d e c r e a s i n g t r e n d o f v e r t i c a l exchange r a t e c a n b e e x p e c t e d on t h e b a s i s of s t a b i l i t y c h a n g e s .
Considerable short-term fluc-
t u a t i o n s o v e r s e v e r a l y e a r s o f t h e v e r t i c a l exchange r a t e s c a n , however, b e exp e c t e d on t h e b a s i s o f s t a b i l i t y f l u c t u a t i o n s r e l a t e d t o i n f l o w s .
I t should a l s o
b e n o t e d t h a t t h e r e i s no s i n g l e r e l a t i o n s h i p between s t a b i l i t y and v e r t i c a l mixing. The s t a b i l i t y i s d e t e r m i n e d by t h e s a l i n i t y d i f f e r e n c e a c r o s s t h e h a l o c l i n e layer
(Fig. 7 )
( K u l l e n b e r g 1981/82) and i s t h e r e f o r e also r e l a t e d t o f l u c t u a t i o n s
i n the r i v e r runoff.
T h i s c o u l d be i m p o r t a n t f o r s h o r t - t e r m v a r i a t i o n s b u t c o u l d
n o t have g e n e r a t e d a l o n g - t e r m s i g n i f i c a n t change i n t h e mixing r a t e s , s i n c e t h e long-term r u n o f f changes a r e v e r y s m a l l . The s a l i n i t y d i f f e r e n c e a c r o s s t h e h a l o c l i n e l a y e r s i n t h e Bornholm, Gotland and L a n d s o r t Deeps a r e shown i n F i g . 8 .
T h e r e a r e no marked o v e r a l l t r e n d s .
Ten
y e a r s moving a v e r a g e s o f t h e s t a b i l i t y a c r o s s t h e h a l o c l i n e l a y e r c a l c u l a t e d from l i g h t v e s s e l o b s e r v a t i o n s i n t h e K a t t e g a t a r e a a r e shown i n F i g . 9, t o g e t h e r w i t h t h e s e r i e s from t h e Bornholm B a s i n .
A
d e c r e a s e o f s t a b i l i t y i s shown for t h e
l a t t e r area s i n c e a b o u t 1 9 2 0 , w i t h a c o r r e s p o n d i n g i n c r e a s e i n t h e K a t t e g a t a r e a . A r i s e o f t h e h a l o c l i n e l a y e r c o u l d imply a n i n c r e a s e d exchange between t h e
s u r f a c e and t h e deep w a t e r s i n c e t h e s u r f a c e a r e a o f t h e l a y e r would b e l a r g e r ,
413
1201
/it /O
Kattegat
/A
Bornholm basin
6
S t a b i l i t y , g i v e n by Emax = ApipAz m - I , a c r o s s h a l o c l i n e l a y e r s a l i n i t y d i f f e r e n c e s i n t h e K a t t e g a t and t h e Bornholm b a s i n s .
F i g . 7.
1880
1890 1900 1910
1950 Bp
1920 1930 1940
1970
-ro-=--=
E
X X
X
.,
0 0
.
0 0
4 1
3 AS%.
F i g . 8.
Variations of s a l i n i t y differences across the halocline layer i n the Bornholm ( x ) , L a n d s o r t (01, and G o t l a n d ( A ) Deeps d u r i n g t h e p r e s e n t century.
and t h e wind e n e r g y d r i v i n g t h e mixing would p e n e t r a t e t o t h e h a l o c l i n e i n a shorter t i m e .
However, t h e h a l o c l i n e h a s o n l y become a b o u t 5 m s h a l l o w e r d u r i n g
t h e c e n t u r y (Matthaus 1980) which c a n h a r d l y g i v e r i s e t o a l a r g e t r a n s f e r change. The major d r i v i n g f o r c e f o r t h e f l u c t u a t i n g c i r c u l a t i o n and mixing i n t h e B a l -
t i c , t h e wind, h a s shown c o n s i d e r a b l e f l u c t u a t i o n s ( K u l l e n b e r g 1 9 7 7 ) .
These a r e . .
r e l a t e d t o t h e c l i m a t i c v a r i a b i l i t y w i t h a l t e r n a t i n g predominance of c y c l o n i c and a n t i c y c l o n i c atmospheric c i r c u l a t i o n over t h e north-eastern
European c o n t i n e n t
( e . g . Hela 1 9 6 6 a ) . I t i s d i f f i c u l t t o a s c e r t a i n any l o n g - t e r m t r e n d i n t h e wind s t r e n g t h , mainly b e c a u s e o f d i f f e r e n t o b s e r v a t i o n t e c h n i q u e s .
The r e c o r d used
by K u l l e n b e r g (1977) from Gedser Rev l i g h t v e s s e l o v e r t h e p e r i o d 1900 t o 1960 d i d n o t d i s p l a y any marked t r e n d .
However, a l o n g e r r e c o r d a p p e a r s to' show a
l o n g - t e r m t r e n d ( s e e P e d e r s e n , t h i s volume). On t h e b a s i s o f t h e p r e s e n t c a l c u l a t i o n s o f v e r t i c a l exchange r a t e s i n t h e deep waters o f t h e B a l t i c P r o p e r , t h e r e d o e s n o t a p p e a r t o b e any s i g n i f i c a n t t r e n d o f c h a n g i n g mixing r a t e s .
I t i s c o n c l u d e d t h a t long-term
changes i n t h e
v e r t i c a l exchange r a t e s c a n n o t b e the main c a u s e f o r long-term d e t e r i o r a t i n g oxygen c o n d i t i o n s i n t h e d e e p and bottom w a t e r s o f t h e B a l t i c S e a .
IMPORTANCE OF THE M I X I N G FOR THE CONDITIONS I N THE BALTIC I t i s o f i n t e r e s t t o c o n s i d e r b r i e f l y t h e i m p o r t a n c e o f t h e v e r t i c a l exchange
r a t e s f o r t h e exosystem of a s e m i - e n c l o s e d s e a l i k e t h e B a l t i c .
The n u t r i e n t
c o n t e n t and i t s v a r i a b i l i t y i n t h e s u r f a c e l a y e r i s o f c e n t r a l i m p o r t a n c e .
Limit-
i n g n u t r i e n t s f o r d i f f e r e n t p a r t s o f t h e B a l t i c d u r i n g d i f f e r e n t s e a s o n s are phosp h a t e and n i t r a t e .
The i m p o r t a n c e o f t h e n i t r o g e n a s a p o s s i b l y d o m i n a t i n g l i m i t -
i n g f a c t o r h a s , however, been emphasized i n r e c e n t y e a r s . I t i s p e r t i n e n t t o s e p a r a t e between t h e c o n d i t i o n s i n t h e B a l t i c P r o p e r and
t h e Gulf of B o t h n i a .
I n t h e l a t t e r a r e a t h e v e r t i c a l s t a b i l i t y is comparatively
weak, t h e oxygen c o n d i t i o n s have n o t d e t e r i o r a t e d as i n t h e B a l t i c P r o p e r , and t h e n u t r i e n t s have n o t i n c r e a s e d as much i n t h e s u r f a c e l a y e r .
T h i s shows t h e
i m p o r t a n c e of t h e v e r t i c a l exchange f o r t h e oxygen c o n d i t i o n s .
I t a l s o suggests
t h a t t h e n u t r i e n t i n c r e a s e i n t h e B a l t i c P r o p e r c a n n o t a l o n e b e due t o an i n c r e a s e d i n p u t from l a n d t h r o u g h r i v e r s and w a s t e water i n p u t . I n t h e B a l t i c Proper t h e phosphate c o n c e n t r a t i o n s have i n c r e a s e d s i n c e about t h e mid-1950's
( F o n s e l i u s 1 9 6 9 ) , b o t h i n the d e e p and s u r f a c e w a t e r s .
Around
1969 t h e r a t e of i n c r e a s e of p h o s p h a t e c o n c e n t r a t i o n s i n t h e mixed s u r f a c e l a y e r w i n t e r w a t e r showed a marked i n c r e a s e
(Nehring 1 9 7 9 ) , and s i n c e t h a t y e a r an
i n c r e a s e o f t h e n i t r a t e c o n c e n t r a t i o n s i n t h e same w a t e r h a s a l s o b e e n e s t a b l i s h e d (Nehring 1 9 7 9 ) .
N e h r i n g ' s d a t a show t h a t maxima and minima o f b o t h n i t r a t e and
phosphate c o n c e n t r a t i o n s a r e a l t e r n a t e l y o c c u r r i n g d u r i n g c o i n c i d i n g p e r i o d s . The p e r i o d s of c o n c e n t r a t i o n maxima seem t o c o i n c i d e w i t h t h e p e r i o d s of good oxygen c o n d i t i o n s i n t h e bottom w a t e r
( T a b l e 3 ) and t h e m i n i m a w i t h t h e p e r i o d s
415 TABLE 3 C o r r e l a t i o n between n u t r i e n t e x t r e e m e s i n t h e w i n t e r s u r f a c e w a t e r and oxygen e x t r e e m e s i n t h e b o t t o m water i n t h e Gotland b a s i n ( d a t a from F o n s e l i u s 1 9 7 8 and Nehring 1 9 7 9 ) .
Year
PO+-P
NO3-N
pg a t R-' 1954/55
0.3
a t 240 m
1963/64
pg a t R-'
R-'
m l R-'
1 - 2
0
ml
- 0.4 0.1
1961/62 1962/63
0.7
H2S
02
In winter surface layer
- 0.9
- 0.1
0
1
2
0
0.8
0
1964/65
0.2 - 0.4
1 - 2
0
1966/67
0.1
- 0.2
0
1
0.3
- 0.5
1 - 2
0
1967/68
50.1
1968/69 1970/71
-
1.3
-
2.5
0.4
1972/73
0.2
1.0
1973/74
0.5
3 - 4
-p
F i g . 9.
1905
15
25
35
0
- 3
45
0.5
- 1.5 0
1 - 2
55
65
2
- 2.5 0 1.5 0
kdf
S t a b i l i t y , g i v e n by Emax = Ap/pAz m - I , a c r o s s t h e h a l o c l i n e l a y e r i n t h e Bornholm b a s i n ( 0 ) and i n t h e K a t t e g a t a t t h e Anholt N ( A ) and t h e K a t t e g a t S W ( 0 ) l i g h t v e s s e l during t h e p r e s e n t century.
416 of hydrogen s u l p h i d e t h e r e (Table 3 ) . delay a f t e r bottom water renewals.
The peaks occur with only a s l i g h t time
This s u g g e s t s t h a t t h e deep and bottom waters
a r e s i g n i f i c a n t sources of n u t r i e n t s .
The s t o r a g e t h e r e i s gradually t r a n s f e r r e d
towards t h e s u r f a c e l a y e r i n connection with bottom water renewal and deep water inflow.
Nehring (1979) demonstrated a c o r r e l a t i o n between t h e s a l i n i t y i n c r e a s e ,
and t h e n u t r i e n t i n c r e a s e , and concluded t h a t probably an i n c r e a s i n g amount of Kattegat water i n t r u d e d i n t o t h e B a l t i c , l e a d i n g t o an i n c r e a s i n g upward t r a n s f e r of n u t r i e n t s and s a l t t o t h e s u r f a c e l a y e r .
An i n c r e a s e of t h e inflow cannot be
s u b s t a n t i a t e d a t p r e s e n t , b u t t h e r e s u l t s show t h a t n u t r i e n t s a r e supplied from t h e deep and bottom waters through v e r t i c a l t r a n s f e r t o t h e s u r f a c e l a y e r .
The
v e r t i c a l t r a n s f e r occurs over t h e whole B a l t i c Proper. I t should be noted t h a t t h e i n c r e a s e i n t h e r a t e of i n c r e a s e o f n u t r i e n t con-
c e n t r a t i o n s around 1969 coincided with a temporary breaking of t h e t r e n d of an i n c r e a s i n g volume of hydrogen s u l p h i d e c o n t a i n i n g deep and bottom waters, a s given by Jansson (1978).
This supports t h e conclusion above.
The phosphate and n i t r a t e c o n c e n t r a t i o n s i n t h e Gotland b a s i n s u r f a c e l a y e r winter water have increased by f a c t o r s of 3 and 2 . 5 , from about 0.2 ug a t
II-'
and 1 . 5 ug a t !?.-I,
r e s p e c t i v e l y (Nehring 1979). The phosphate
r e s p e c t i v e l y , i n 1968.
c o n c e n t r a t i o n i n t h e deep and bottom waters is a f a c t o r o f 3 t o 1 0 l a r g e r than i n t h e s u r f a c e w i n t e r water (Fonselius 1969).
The t o t a l volume beneath t h e 100 m
l e v e l of t h e B a l t i c Proper i s about 1700 km3 (Ehlin e t a 1 1 9 7 4 ) , mostly found i n t h e Gotland b a s i n , whereas t h e 0-50 m volume i n t h e Gotland b a s i n i s about 3000 km3. A couple o f inflows o f about 200 km3 water from t h e K a t t e g a t ,
l e a d i n g t o inflows
of about 400 km3 i n t o t h e Gotland b a s i n , would be a b l e t o generate t h e t r a n s f e r of t h e r e q u i r e d amount of n u t r i e n t s t o t h e s u r f a c e w i n t e r w a t e r ,
Since 1968 a t
l e a s t t h r e e inflows of t h a t category have occurred (Fonselius 1978). B i o l o g i c a l l y t h e changes have implied an i n c r e a s e i n n u t r i e n t s and a s l i g h t decrease i n t h e r a t i o N:P i n t h e water.
I t remains t o be seen whether t h i s t r e n d
of changing N : P r a t i o continues, and i f it can imply t h a t n i t r o g e n becomes increas i n g l y important a s a most l i m i t i n g f a c t o r f o r t h e primary production.
Thwsupply
of n u t r i e n t s may a l s o have become more p u l s a t i n g , o c c u r r i n g over d i f f e r e n t p e r i o d s of t h e y e a r .
This may imply t h a t an unbalance between t h e primary and secondary
productions i s e s t a b l i s h e d , so t h a t t h e zooplankton grazing cannot cope with puls e s of phytoplankton production which occur o u t s i d e t h e 'normal' production c y c l e s , provided'no o t h e r f a c t o r such a s l i g h t l i m i t s t h e primary production.
The r e s u l t
w i l l then be an increased t r a n s f e r of organic matter t o t h e h a l o c l i n e l a y e r and t h e deep water through dead phytoplankton. oxygen consumption r a t e i n t h e s e waters.
This, i n t u r n , l e a d s t o an i n c r e a s i n g S h a f f e r (1979b) c a l c u l a t e d t h a t t h e r a t e
of oxygen consumption had increased s i n c e t h e 1 9 3 0 ' s i n t h e i n t e r m e d i a t e waters. Most o f t h e i m p l i c a t i o n s above p o i n t a t t h e g r e a t importance o f v e r t i c a l mixing f o r t h e c o n d i t i o n s i n a semi-enclosed s e a l i k e t h e B a l t i c .
A c l o s e cooperation
417 between h y d r o d y n a m i c i s t s and s c i e n t i s t s from o t h e r marine s c i e n c e s i s c l e a r l y r e q u i r e d t o s o l v e e c o s y s t e m problems o f s u c h r e g i o n s and make f o r e c a s t s of t h e development which c a n b e r e l i a b l y used f o r e n v i r o n m e n t a l management.
REFERENCES Brogmus, W . , 1952. Eine R e v i s i o n d e s W a s s e r h a u s h a l t e s d e r O s t s e e . K i e l . Meeresf o r s c h . , 9: 15-42. Dickson, R . R . , 1971. A c u r r e n t and p e r s i s t e n t pressure-anomaly p a t t e r n a s t h e p r i n c i p a l c a u s e o f i n t e r - m e d i a t e h y d r o g r a p h i c v a r i a t i o n i n t h e European s h e l f sea. Dtsch. Hydrogr. Z . , 24: 97-119. Dickson, R. R . , 1973. The p r e d i c t i o n of major B a l t i c i n f l o w s . Dtsch. Hydrogr. Z . , 26: 97-105. D i e t r i c h , G . , 1951. Oberflachenstrbmmqngen i m K a t t e g a t t , i m Sund und i n d e r B e l t s e e . Dtsch. Hydrogr. Z . , 4: 129-140. E h l i n , U . , M a t t i s s o n , I . and Z a c h r i s s o n , G . , 1974. Computer b a s e d c a l c u l a t i o n s of volumes o f t h e B a l t i c area. P r o c . 9 t h Conf. B a l t i c Oceanogr. K i e l , 17-20 A p r i l 1974, pp. 115-128 F o n s e l i u s , S . , 1969. Hydrography o f t h e B a l t i c Deep b a s i n s 111. F i s h . Board Swed., S e r . Hydrogr., 23: 97 pp. F o n s e l i u s , S. H., 1978. On n u t r i e n t s and t h e i r r o l e as p r o d u c t i o n l i m i t i n g f a c t o r s i n t h e B a l t i c . A c t a Hydrochim. H y d r o b i o l . , 6: 329-339. H e l a , I . , 1966a. S e c u l a r c h a n g e s i n t h e s a l i n i t y of t h e u p p e r w a t e r s of t h e n o r t h e r n B a l t i c S e a . Comm. Phys.-Math. SOC. S c i . Fenn., 31, 1 4 : 2 1 pp. Hela, I . , 1966b. V e r t i c a l eddy d i f f u s i v i t y i n t h e B a l t i c S e a . Geophysica 9 : 219-234. H o l l a n , E . , 1969. D i e V e r h d e r l i c h k e i t d e r S t r d m m u n g s v e r t e i l u n g i m Gotlandbecken am B e i s p i e l von Strbmmungsmessungen i m Gotland T i e f . K i e l e r M e e r e s f o r s c h . , 25: 19-70. J a c o b s e n , T . , 1980. Sea water exchange o f t h e B a l t i c : Measurements and methods. The N a t i o n a l Agency o f Environmental P r o t e c t i o n , Copenhagen. The B e l t P r o j e c t . 1978. The B a l t i c - A s y s t e m s a n a l y s i s o f a semi-enclosed s e a . J a n s s o n , B.-O., I n : H . Charnock and G. Deacon ( E d i t o r s ) , Advances i n Oceanography. Plenum P r e s s , Oxford, p p . 131-184. J e n s e n , T . G. and K u l l e n b e r g , G . , 1981. On t h e e f f i c i e n c y o f t h e wind t o g e n e r a t e v e r t i c a l mixing. Geophysica 1 7 : 47-61. K a l e i s , M. V . , 1976. P r e s e n t h y d r o g r a p h i c c o n d i t i o n s i n t h e B a l t i c . Ambio, Spec. R e p . , 4: 37-44. K r a u s s , W . , 1978. I n e r t i a l waves and mixing i n t h e t h e r m o c l i n e (BOSEX-results). P r o c . XI c o n f . B a l t i c o c e a n o g r . p a p e r 56: 709-728, Rostock, DDR, 1979. K r a u s s , W . , Koske, P. and Kielmann, J . , 1973. O b s e r v a t i o n s on s c a t t e r i n g l a y e r s and t h e r m o c l i n e s i n t h e B a l t i c S e a . K i e l e r M e e r e s f o r s c h . , 29: 85-89. K u l l e n b e r g , B . , 1964. F d r s B k s t i p p n i n g a v r b t s l a m i 6 s t e r s j b n 8-12 j u l i 1963. R e p o r t t o Stockholm m u n i c i p a l i t y , i n Swedish, 75 pp. K u l l e n b e r g , G., 1970. On t h e oxygen d e f i c i t i n t h e B a l t i c d e e p w a t e r . T e l l u s , 2 2 : 357. K u l l e n b e r g , G., 1971. Vertical d i f f u s i o n i n s h a l l o w waters. T e l l u s , 23: 129-135. K u l l e n b e r g , G . , 1974a. An E x p e r i m e n t a l and T h e o r e t i c a l I n v e s t i g a t i o n of t h e T u r b u l e n t D i f f u s i o n i n t h e Upper Layer o f t h e S e a . Rep. N o . 25, I n s t . Phys. Oceanogr., U n i v e r s i t y of Copenhagen, 272 pp. K u l l e n b e r g , G . , 1974b. Some o b s e r v a t i o n s o f t h e v e r t i c a l mixing i n t h e B a l t i c . P r o c . 9 t h Conf. B a l t i c Oceanogr, K i e l , 17-20 A p r i l 1974, pp. 129-137 (mimeogr.) K u l l e n b e r g , G., 1977. O b s e r v a t i o n s of t h e mixing i n t h e B a l t i c thermo- and h a l o c l i n e l a y e r s . T e l l u s , 29: 572-587. K u l l e n b e r g , G . , 1981. P h y s i c a l Oceanography. I n : A. V o i p i o ( E d i t o r ) , The B a l t i c Sea, Ch. 3 . E l s e v i e r Oceanography S e r i e s 30, E l s e v i e r , Amsterdam, pp. 135-181. K u l l e n b e r g , G., 1982. The B a l t i c S e a . I n : B. H . Ketchum ( E d i t o r ) , Ecosystems o f t h e World, v o l . E s t u a r i e s and Enclosed S e a s , c h . 1 3 , E l s e v i e r , Amsterdam, i n press.
418
J.
Launiainen, and K o l j o n e n , J . , 1981. S e a s o n a l and l o n g - p e r i o d v a r i a t i o n o f I n Proceedings of 3rd temperature a t Finnish fi x ed observation s t a t i o n s . Seminar o n t h e Gulf o f B o t h n i a , S N V , i n p r e s s . M a t t h l u s , W . , 1977. M i t t l e r e v e r t i k a l e Wzrmeaustauschkoeffizienten i n d e r O s t s e e . Acta Hydrophys. B e r l i n , 2 2 , 2 : 73-92. M a t t h a u s , W . , 1979. Long-term v a r i a t i o n s i n t h e p r i m a r y h a l o c l i n e i n t h e Gotland B a s i n . ICES, C.M. 1919/C:22, mimeo. Matthaus, w., 1980. Z u r V a r i a b i l i t a t d e r primaren h a l i n e n Sprungschicht i n d e r G o t l a n d s e e . B e i t r Z g e z u r Meereskunde, 44/45, p p . 27-42. Melvasalo, T . , Pawlak, J . , G r a s s h o f f , K . , T h o r e l l , L. and T s i b a n , A. ( E d i t o r s ) , 1981. Assessment o f t h e e f f e c t s o f p o l l u t i o n on t h e n a t u r a l r e s o u r c e s o f t h e B a l t i c Sea. B a l t i c Sea Environment P r o c e e d i n g s No. 5A and 5B, H e l s i n k i Comm i s s i o n 1981. M i k u l s k i , Z . , 1970. I n f l o w o f r i v e r water t o t h e B a l t i c Sea i n t h e p e r i o d 19511960. Nord. H y d r o l . , 4 : 216-227. Nehring, D., 1979. R e l a t i o n s h i p s between s a l i n i t y and i n c r e a s i n g n u t r i e n t conc e n t r a t i o n s i n t h e mixed w i n t e r s u r f a c e l a y e r o f t h e B a l t i c from 1969 t o 1 9 7 8 . ICES C.M. 1979/C:24, and Ann. B i o l . , ICES 1980. Rydberg, L., 1978. Deep w a t e r f l o w and oxygen consumption w i t h i n the B a l t i c . Rep. No. 27, Oceanographic I n s t i t u t e , U n i v e r s i t y o f Gothenburg, 1 2 pp. S h a f f e r , G . , 1975. B a l t i c c o a s t a l dynamics p r o j e c t - t h e f a l l downwelling r e g i m e o f f Askti. C o n t r i b . Ask6 L a b . No. 7 , U n i v e r s i t y o f Stockholm, 69 pp. S h a f f e r , G . , 1979a. C o n s e r v a t i o n c a l c u l a t i o n s i n n a t u r a l c o o r d i n a t e s ( w i t h a n example from t h e B a l t i c ) . J o u r n a l P h y s i c a l Oceanography 9 , 4 : 847-855. S h a f f e r , G . , 1979b. On t h e phosphorous and oxygen dynamics o f t h e B a l t i c Sea. C o n t r i b . Ask6 Lab. N o . 26, U n i v e r s i t y o f Stockholm, 90 p p . S o s k i n , I . M . , 1963. Long-term Changes i n t h e H y d r o l o g i c a l 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 . Hydromet. P r e s s , L e n i n g r a d , i n R u s s i a n , 159 pp. V o i p i o , A . , and MLlkki, P . , 1912. V a r i a t i o n s o f t h e v e r t i c a l s t a b i l i t y i n t h e northern B a l t i c . H a v s f o r s k n i n g s i n s t . S k r . 23: 3-12. E l s e v i e r Oceanogr. S e r . 30, A m s t e r V o i p i o , A. ( E d i t o r ) , 1981. The B a l t i c Sea. dam 1981, 418 pp. Walin, G . , 1972a. On t h e h y d r o g r a p h i c r e s p o n s e t o t r a n s i e n t m e t e o r o l o g i c a l d i s t u r b a n c e s . T e l l u s , 24: 169-186. Walin, G., 1972b. Some o b s e r v a t i o n s o f t e m p e r a t u r e f l u c t u a t i o n s i n t h e c o a s t a l region of the B a l t i c . T e l l u s , 24: 187-198. Wattenberg, H . , 1949. Entwurf e i n e r n a t u r l i s h e n E i n t e i l i n g d e r Ostsee. Kieler M e e r e s f o r s c h . , 6 : pp 1 0 . W i t t i n g , R . , 1918. H a f s y t a n , G e o i d y t a n o c h Landhdjningen utmed B a l t i s k a H a f v e t och v i d Nordsjon. F e n n i a , 39, 5: 1-346. Wyrtki, K., 1954. D e r g r o s s e S a l z e i n b r u c h i n d e r O s t s e e i n November und Dezember 1951. K i e l e r M e e r e s f o r s c h . , 10, 1: pp. 19.
419
FINESTRUCTURE OF THE OPEN PART OF
THE BALTIC SEA A. Aitsam, J. Laanemets, M-J. L3lover I n s t i t u t e o f Thermophysics and E l e c t r o p h y s i c s Academy o f Sciences o f t h e Estonian S. S. R. INTRODUCTION Data from p r o f i l i n g instruments are w i d e l y used t o study t h e processes r e s p o n s i b l e f o r t h e v e r t i c a l s t r u c t u r d o f oceanic v a r i a b l e s . goals o f t h e f i n e -
One o f t h e
and m i c r o s t r u c t u r e s t u d i e s i s t h e p a r a m e t r i z a t i o n o f
unresolved processes i n c i r c u l a t i o n models.
The model o f Osborn and Cox
(Osborn and Cox, 1973) may serve as an example.
According t o t h i s model,
t h e mean c o e f f i c i e n t s o f v e r t i c a l mixing i n a given l a y e r can be obtained from t h e balance between t h e t u r b u l e n t p r o d u c t i o n and t h e d i s s i p a t i o n o f temperature inhomogeneities. conditions.
However, t h i s model works o n l y under c e r t a i n
A t t h e p r e s e n t time,
t h e r e i s no general theory about t h e
g e n e r a t i o n o f f i n e s t r u c t u r e i n t h e oceans and seas.
R e l y i n g on t h e a v a i l -
a b l e data, t h e f o l l o w i n g processes have been proposed:
1) random deforma-
t i o n o f t h e d e n s i t y f i e l d by i n t e r n a l waves; 2) i n t r u s i o n s caused by f r o n t s ; 3) processes o f double d i f f u s i o n (Woods, 1980).
The study o f f i n e s t r u c t u r e
i n a s y n o p t i c eddy i s o f i n t e r e s t because, as suggested by Woods (1980), t h e energy o f eddies may be t r a n s f e r r e d t o small-scale processes through i n t e r n a l waves and f r o n t a l processes. I n t h i s paper, we analyze t h e f i n e s t r u c t u r e o f t h e deep waters o f t h e open p a r t o f t h e B a l t i c Sea under calm weather c o n d i t i o n s on t h e one hand and w i t h i n a s y n o p t i c eddy on t h e o t h e r hand.
MEASUREMENTS AND METHODS OF ANALYSIS I n o r d e r t o study t h e f o r m a t i o n o f t h e v e r t i c a l s t r u c t u r e i n t h e deep l a y e r o f t h e B a l t i c Sea, several s e r i e s o f v e r t i c a l p r o f i l e s were obtained w i t h a N e i l Brown Mark I11 probe a t t h e c e n t r a l s t a t i o n o f t h e BOSEX area i n 1979.
All
vessel
a t depths r a n g i n g from 65 m t o 95 m.
these p r o f i l e s were measured i n calm weather from a d r i f t i n g
p r o f i l e s was 3 minutes.
The time i n t e r v a l between
The probe was lowered a t a r a t e o f 30 cm/s, and t h e
r e c o r d i n g frequency was 3 1 times p e r second f o r each parameter.
The r e -
s u l t i n g v e r t i c a l r e s o l u t i o n i s about 1 cm. I n 1979 and 1980, s e r i e s o f surveys w i t h t h e N e i l Brown Mark I11 probe were performed i n t h e BOSEX area i n an attempt t o d e t e c t eddies o f synoptic s c a l e (Aitsam and Elken, 1980).
The dimensions o f t h e survey area were 20 x
420
25 miles and the grid spacing was 5 miles. The duration of each survey was one day. All these profiles were analyzed with the aim of detecting the influence of the synoptic scale phenomena on the vertical finestructure of the deep layer of the Baltic Sea. The preliminary processing of the CTD data i s described in detail by Laanemets and Lilover (1981). Let us simply mention that the rolling of the vessel and the time lag of the temperature sensor are taken into account to reduce the errors in the salinity and density calculations. The temperature and salinity data are interpolated at constant depth intervals of Az = 2 cm. For this study, we use only data collected during the lowering of the probe. As the fluctuations at finestructure scales of the temperature, aalinity, and density fields are essentially random, statistical methods are widely used in their study. In this paper, the variances and spectra of the fluctuations are calculated. The measured series are divided into mean and fluctuating components using a 5 m cosine filter. Spectra are calculated by the FFT method after preliminary smoothing with a 4-sample Kaiser-Bessel filter (Harris, 1978). The wavenumber bandwidth of the calculated spectra is 0.2 5 k 5 24 .'-m
RESULTS AND DISCUSSION In the BOSEX area the effect of the coasts and of the Danish Sounds can be considered unimportant. The vertical profiles of temperature, salinity and density vary monotonously with depth in the deep layer (60 to 95 m.). We analyzed the data with the presumption that three processes can be responsible for the formation of vertical structure within the scales of finestructure and microstructure: i) small-scale turbulence; ii) double-diffusive convection (both temperature and salinity increase with depth in the deep layer of the Baltic Sea); i i i ) kinematic effects of internal waves. To determine the importance of double-diffusive convection, we calculated the function Rp(iAz) = -p(iAz) ASi/a(iAz)ATi with Az = 10 cm, and using a density formula appropriate for the Baltic Sea (Millerb and Kremling, 1976) in the calculation of a = -(3p/3T)p,S=const and
B = (aP/aS)p,J=const. The analysis of the function Rp(iAz) shows that its numerical value is smaller than 15 only at a few separate points of the vertical profiles; in general Rp(iAz) > 15, which indicates that only molecular diffusion is taking place. Certainly, the final assessment of the
421 importance o f d o u b l e - d i f f u s i o n convection i n t h e generation o f t h e v e r t i c a l s t r u c t u r e and m i x i n g i n t h e deep l a y e r o f t h e open p a r t o f t h e B a l t i c r e q u i r e s a more d e t a i l e d a n a l y s i s . The s p e c t r a l a n a l y s i s o f t h e v e r t i c a l p r o f i l e s observed i n t h e deep l a y e r o f t h e BOSEX area shows t h a t t h e averaged s p e c t r a o f temperature ST(k),
s a l i n i t y Ss(k)
and r e l a t i v e d e n s i t y So (k) t
can g e n e r a l l y be w e l l
approximated by t h e power law
1 (Fig. 1).
f o r wavenumbers i n t h e range 0.7 < k < 25 m I n i n d i v i d u a l s p e c t r a l curves, interval 3 < k < 6 m-l.
a l o c a l maximum can be n o t i c e d i n t h e
No s u b i n t e r v a l o f small-scale t u r b u l e n c e was ob-
served on any s i n g l e spectrum.
F i g u r e 2 shows a s e c t i o n o f isotherms,
i s o h a l i n e s and isopycnals based on one s e r i e s o f p r o f i l e s .
The absence o f
mixed l a y e r s and t h e smallness o f t h e amplitudes o f t h e i n t e r n a l waves can be n o t i c e d i n F i g u r e 2.
The mean amplitude o f t h e v e r t i c a l displacements i n
t h i s l a y e r , as determined from t h e v a r i o u s spectra, i s about 0.2 m. The agreement between t h e mean amplitudes determined from t h e temperat u r e , s a l i n i t y and d e n s i t y s p e c t r a i n d i c a t e s t h a t a l l i s o l i n e s are s i m i l a r l y deformed.
T h i s supports t h e assumption t h a t t h e observed f l u c t u a t i o n s o f
t h e p h y s i c a l v a r i a b l e s a t f i n e s t r u c t u r e scales a r e t h e r e s u l t o f t h e i n f l u ence o f i n t e r n a l waves. We now t u r n our a t t e n t i o n t o t h e study o f f i n e s t r u c t u r e and m i x i n g i n s y n o p t i c eddies. Fjodorov e t a l .
I n e a r l i e r papers on t h i s t o p i c , Dykman e t a l . (1980) and (1981)
have analyzed t h e r e s u l t s o f v e r t i c a l p r o f i l e s ob-
t a i n e d d u r i n g t h e POLYMODE program. (Dykman e t a l . ,
The r e s u l t s o f t h e s p e c t r a l a n a l y s i s
1980) showed t h a t t h e normalized variance o f t h e displace-
ments o f i n t e r n a l waves i s s m a l l e r i n t h e eddy c e n t e r t h a t a t t h e p e r i p h e r y .
I t has a l s o been shown t h a t t h e r a t e o f energy d i s s i p a t i o n , t h e eddy center.
E,
increases i n
On t h e b a s i s o f t h e i r a n a l y s i s o f t h e 8, S c h a r a c t e r i s -
t i c s , and o f anomalies i n t h e d i s t r i b u t i o n o f hydrogen and pH, Fjodorov e t al.
(1981) have suggested a hypothesis about water t r a n s f o r m a t i o n i n eddies
as a r e s u l t o f mixing, which i n t u r n i s connected t o v e r t i c a l motions i n t h e eddy c e n t e r . We now discuss t h e r e s u l t s o f t h r e e o f our own surveys i n t h e B a l t i c Sea:
t h e 6 t h and t h e 7 t h surveys o f t h e R/V "Ayu-Dag"
1979, and t h e second survey o f c r u i s e No. X V I I I i n 1980. maps o f t h e r e l a t i v e dynamic topography (RDT), synoptic
scale were d e t e c t e d f o r surveys No.
c r u i s e No. X I V i n On t h e basis o f
eddylike perturbations o f
7 and 2 (Aitsam and Elken,
422
1
0
2
7
Fig. 1. Ensemble averaged spectra of temperature (-), salinity (- - - ) and relative density ( - - - ) for the first series of measurements. The spectral power law. curves are well approximated by the
1980). tions.
On the ROT maps of the 6th survey there were no similar perturba-
We chose to use the variances of the temperature, salinity, and relarespectively, as tive density fluctuations, denoted by uT, 2 us, 2 and u2 % ’ measures of the horizontal variability of the vertical finestructure in the synoptic scale eddy. From the results discussed earlier, it is obvious that the main mechanism of the finestructure generation is the random deformation of the density field by internal waves. By normalizing the variances with
423
70
--_--_
80
H [ml,
F i g . 2.
Isotherms ( - - ) , i s o h a l i n e s ( - ) and isopycnals
(---I
s e r i e s o f measurements i n t h e depth i n t e r v a l 70 t o 90 m.
o f the f i r s t
The h o r i z o n t a l
l e n g t h scale i s about 1 km and t h e i n t e r v a l between p r o f i l e s i s about 40 in. t h e squares o f t h e g r a d i e n t s o f t h e corresponding p h y s i c a l parameters, we o b t a i n estimates o f t h e mean square displacements o f t h e i n t e r n a l waves. Therefore, v a r i a t i o n s o f t h e normalized variances i n t h e synoptic scale eddy can be i n t e r p r e t e d as v a r i a t i o n s i n t h e energy f l o w from t h e eddy t o t h e i n t e r n a l wave f i e l d .
The variances and s p e c t r a o f t h e temperature, s a l i n i t y
and r e l a t i v e d e n s i t y f l u c t u a t i o n s were c a l c u l a t e d f o r t h e p r o f i l e s o f the 6 t h and 7 t h surveys.
Only d a t a from depths between 65 and 90 m were i n c l u -
ded i n t h e c a l c u l a t i o n s .
F o r t h e 7 t h survey, t h e variances are one o r two
424
o r d e r o f magnitude l a r g e r a t t h e p e r i p h e r y o f t h e eddy t h a n i n t h e center. The d i s t r i b u t i o n s o f t h e variances c a l c u l a t e d from t h e p r o f i l e s o f t h e 6 t h survey ( i n t h e same depth range) show no r e g u l a r p a t t e r n . The same c o n c l u s i o n can be drawn from a comparison o f t h e spectra:
the
s p e c t r a l l e v e l s o f t h e 7 t h survey are h i g h e r on t h e edges o f t h e eddy than i n t h e c e n t e r , and those o f t h e 6 t h survey a r e i r r e g u l a r .
I n general, t h e
shapes o f t h e s p e c t r a a r e w e l l approximated by power laws, a f a c t which i n d i c a t e s t h e dominating e f f e c t o f t h e i n t e r n a l wave f i e l d .
A d i f f e r e n t method was used t o analyze t h e data o f t h e second survey o f t h e R/V
"Ayu-Dag"
parameters (T,
18th cruise.
The variances and s p e c t r a o f t h e p h y s i c a l
S, at) were a l s o c a l c u l a t e d over a 25 m depth i n t e r v a } , b u t
t h e depth o f t h e isopycnal s u r f a c e ut = 6.75 ( t h e beginning o f t h e halocine) was chosen as t h e reference l e v e l o f t h e i n t e r v a l . Such a choice o f r e f e r e n c e l e v e l e l i m i n a t e s t h e d i s t o r t i n g e f f e c t o f t h e s y n o p t i c s c a l e v a r i a b i l i t y f o r the f o l l o w i n g reason. open p a r t ,
may be d i v i d e d i n t o f o u r l a y e r s :
thermocline, (Fig.
3).
The B a l t i c , i n i t s
t h e upper mixed l a y e r ,
the
t h e i n t e r m e d i a t e l a y e r o f w i n t e r convection and t h e h a l o c l i n e The amplitude o f t h e isopycnal displacement i n t h e h a l o c l i n e can
be about 20 m on t h e p e r i p h e r y o f a s y n o p t i c eddy. a r e c a l c u l a t e d over a f i x e d depth i n t e r v a l ,
Hence, when s t a t i s t i c s
the contribution o f
having d i f f e r e n t c h a r a c t e r i s t i c s may vary w i t h i n a s y n o p t i c eddy.
layers
T h i s may
be t h e reason f o r t h e h i g h v a r i a b i l i t y i n t h e variances c a l c u l a t e d from t h e 7 t h survey.
The 2nd survey o f t h e 1 8 t h c r u i s e t o o k p l a c e a t t h e end o f May.
A t t h a t time,
t h e seasonal thermocline was missing, and an e d d y l i k e p e r t u r -
b a t i o n was p r e s e n t i n t h e h a l o c l i n e (Fig. 4).
F i g u r e 5 shows t h e d i s t r i b u -
t i o n of t h e n a t u r a l l o g a r i t h m o f t h e temperature f l u c t u a t i o n s variance ( I n
2
aT) i n t h e lower l a y e r (extending 25 m below t h e reference l e v e l ) . I t can be seen t h a t
t h e temperature variance
(for
vertical
scales
s m a l l e r than 5 in) i s minimum i n t h e c e n t e r o f t h e eddy and increases towards the periphery.
The d i s t r i b u t i o n o f t h e normalized temperature variance i s
shown i n F i g u r e 6. t h a t o f t h e variance.
The p a t t e r n o f t h e normalized v a r i a n c e i s s i m i l a r t o The normalized variances a t t h e p e r i p h e r y a r e t w i c e
as l a r g e as t h e c e n t e r values.
The v a r i a b i l i t y f a c t o r o f t h e normalized
v a r i a n c e over t h e whole experiment area i s 8. I n summary, t h e data o f t h e seventh and second surveys e x h i b i t a c e r t a i n r e g u l a r i t y i n t h e d i s t r i b u t i o n o f variance i n s y n o p t i c s c a l e eddies, although t h e v a r i a b i l i t y
(1980).
i s s m a l l e r than t h a t r e p o r t e d by Dykman e t a l .
I n t h e upper l a y e r (extending 25 m above t h e r e f e r e n c e l e v e l ) , t h e
v a r i a b i l i t y o f t h e normalized variance i s l a r g e r than 10 and no r e g u l a r i t y i s observed.
I n t h i s l a y e r t h e mean g r a d i e n t o f temperature a l s o v a r i e s by
more than one order.
425
0
B I i
110
0.0
Temp; Sigma Ti
max 20.OjlOl I
Fig. 3. Characteristic vertical profiles of temperature ( T ) , salinity (S) and relative density (D) in the BOSEX area.
Fig. 4. Map of the relative dynamic topography (RDT) for survey No. 2. Crosses indicate the position o f the stations. The smaller frame delimits the area of the finestructure study.
426
Fig. 5. D i s t r i b u t i o n of t h e natural logarithm of t h e temperature variance 2 i n t h e lower layer. ( l n uT) Survey No. 2. The s p e c t r a of temperature, s a l i n i t y and r e l a t i v e d e n s i t y were calcul a t e d f o r a l l p r o f i l e s i n both t h e upper and lower l a y e r . The s p e c t r a l slopes vary over a wide range (from -2.8 t o -3.6) i n t h e lower l a y e r (Fig. 7). However, most s p e c t r a have a slope c l o s e t o - 3 , so t h a t one can i n t e r p r e t t h e f l u c t u a t i o n s a s t h e r e s u l t of t h e i n t e r v a l wave influence. Neither
t h e s p e c t r a (Fig. 7b) nor t h e v e r t i c a l p r o f i l e s of t h e temperature, s a l i n i t y and r e l a t i v e d e n s i t y gradients (Fig. 8) show any evidence of small-scale turbulence i n t h e c e n t e r of t h e eddy in the lower layer. Some upper l a y e r s p e c t r a a t s t a t i o n s located above t h e eddy ( t h e method used t o d e t e c t an eddy does not reveal anything i n t h i s l a y e r , due t o weak s t r a t i f i c a t i o n ) have slopes c l o s e t o - 3 up t o wavenumbers of about 25 in-' (Fig.
9a).
In some s p e c t r a t h e r e i s a break i n slope a t wavenumber k* i n
427
Fig. 6. Distribution of the normalized temperature variance [oT/(dT/dz) 2 23 in the lower layer. Survey No. 2. the range 1 < k, < Ern-’, and for k > k, the spectra have slopes typical o f small-scale turbulence (Fig. 9b,c). When this is the case, the vertical profile of the relative density gradient above the center of the eddy exhibits patches of small-scale inversions accompanied by turbulence (Fig. 1 0 ) . The vertical scale of these layers is about 0.5 to 1.0 m. Existing data do not permit to relate these turbulent events to the eddy. It should be emphasized that the lack of evidence in our data o f smallscale turbulence in the center o f an eddy in the halocline (where the manifestations of the synoptic eddy are strongest) could be fortuitous. Because of the strong stratification in the halocline o f the Baltic Sea, the smallscale turbulence is characterized by great intermittency in space and occurs as a rare event in time. Therefore, we believe that single profiles may not be representative, and that long series o f profilings at a fixed location are needed. In conclusion, we may say that the internal waves are the main factor affecting the vertical finestructure in the halocline. The processes of
P N m
a)
-101 10
I
'
I I 11111
I
0 10
, , ,,,,,
,
I
1
10 k$l
1
I
I I11111
n
10"
I
I
I
I IIIIII
1
10' k[n
~..
Spectra of temperature (-1, salinity (- - - ) and relative density ( - - - > in the lower layer, calculated from the profiles at station.No. 1 (a), No. 9 (b) and No. 14 (c). Fig.
7.
c
0
.r
In
4
c 4)
c, 4
W
L
3
7
4
.c W
v)
.-c
c
W
c,
L 4
.r
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U
In
c, A .-
> W
c aJ u
c, 4
-7
2
No. 9.
V e r t i c a l p r o f i l e s o f temperature, s a l i n i t y and r e l a t i v e density gradients i n the lower layer a t s t a t i o n F
F i g . 8.
No a c t i v e regions are apparent on the p r o f i l e s . 429
430
I
1
--
c , v )
Q
o m
-0
3 U
7
m
U
7
c
.I-
I
n
v)
t
3
Q
.r
U
O
0 ) .
L
O
c
'-
=lz
Q
c, m L
n o
5:
Fig. 9. Spectra o f temperature (-), salinity (- - - ) and relative density (-.-) in ‘ihe upper layer, calculated from the profiles at station No. l(a), No. 9(b) and No. ll(c).
I
z Ln
U
Fig. 10. No. 9.
Vertical p r o f i l e s o f temperature, s a l i n i t y and r e l a t i v e density gradients in the upper layer a t s t a t i o n Patches o f small-scale density inversions can be noticed. 431
432
double d i f f u s i o n and s m a l l - s c a l e t u r b u l e n c e are o f minor importance, a l though t h e y c e r t a i n l y r e q u i r e f u r t h e r study.
F i n a l l y , the d i s t r i b u t i o n of
t h e variances o f temperature, s a l i n i t y and r e l a t i v e d e n s i t y e x h i b i t s a c e r t a i n r e g u l a r i t y i n s y n o p t i c eddies.
REFERENCES Aitsam, A. and Elken J., 1980. Results o f CTD surveys i n t h e BOSEX area o f t h e B a l t i c Sea ( i n Russian). I n : Tonkaya s t r u k t u r a i s i n o p t i c h e s k a j a izmenchivost morei, T a l l i n n , pp. 19-23. Dykman, V.Z., Efremov, O . I . , Kiseleva, O.A. and Panteleev, N . A . , 1980. I n t e r n a l waves and t u r b u l e n c e i n t h e s y n o p t i c s c a l e ( i n Russian). I n : Tonkaya s t r u k t u r a i s i n o t i c h e s k a j a izmenchivost morei, Tallinn,, pp. 64-68. Fedorov, K.N., Ginzburg, A . I . and Zatsepin, A.G., 1981. Thermohaline s t r u c t u r e and t r a c e s o f m i x i n g i n s y n o p t i c eddies and G u l f stream r i n g s ( i n Russian). Okeanologiya, 3: 25-29. H a r r i s , F r . J . , 1918. On t h e use o f windows f o r harmonic a n a l y s i s w i t h t h e d i s c r e t e F o u r i e r transform. Proc. o f t h e I E E E , 66: 51-83. Laanemets, J. and L i l o v e r , M.-J., 1981. The d a t a processing scheme o f measurements w i t h t h e N e i l Brown Mark 111 CTD. I n : The I n v e s t i g a t i o n and M o d e l l i n g o f Processes o f t h e B a l t i c Sea. T a l l i n n , pp. 10-19. M i l l e r o , F r . J. and Kremling, K., 1916. The d e n s i t i e s o f B a l t i c Sea waters, Deep-sea Res., 3:1129-1138. Osborn, T. and Cox, C . , 1972. Oceanic f i n e - s t r u c t u r e . Geophysical F l u i d Dynamics 3: 321-345. Woods, J.D., 1980. Do waves l i m i t t u r b u l e n t d i f f u s i o n i n t h e ocean? Nature 288: 219-224.
433
SYNOPTIC SCALE VARIABILITY OF HYDROPHYSICAL
FIELDS I N THE BALTIC PROPER ON THE B A S I S OF CTD MEASUREMENTS A. Aitsam, J. Elken I n s t i t u t e o f Thermophysics and Electrophysics Academy o f Sciences o f t h e Estonian S.S.R. ABSTRACT The r e s u l t s o f CTD surveys i n t h e ' B a l t i c Proper on r e c t a n g u l a r g r i d s w i t h spacing o f 5 n a u t i c a l m i l e s a r e analyzed.
Eddylike p e r t u r b a t i o n s o f
t h e r e l a t i v e dynamic topography (ROT), w i t h diameters equal t o 2 t o 5 t i m e s t h e i n t e r n a l Rossby r a d i u s o f deformation Rd (E 10 km), are described.
The
t y p i c a l m i g r a t i o n speed o f these p e r t u r b a t i o n s i s a few cm/sec and i t 5 s d i r e c t e d along t h e averaged isobaths w i t h shallower water on t h e r i g h t .
It
i s shown t h a t t h e speed and d i r e c t i o n of m i g r a t i o n o f t h e eddies can be e x p l a i n e d i n terms of topographic waves.
The hypothesis t h a t some o f t h e
observed eddies might be generated by b a r o c l i n i c i n s t a b i l i t y o f sheared mean f l o w s i s discussed on t h e b a s i s o f a simple model. estimate absolute v e l o c i t i e s method.
An attempt i s made t o
using a generalization o f the beta-spiral
Synoptic s c a l e processes i n t h e B a l t i c a r e compared t o t h e i r ocea-
n i c counterparts.
INTRODUCTION Synoptic eddies (Koshlyakov and Monin, 1978; Woods and Minnett, 1979) o r "mesoscale" eddies ( t h e l a t t e r term i s w i d e l y used by t h e MODE Group, 1978) a r e a common phenomenon i n t h e open ocean as w e l l as near f r o n t a l currents.
The B a l t i c Sea i s one o f t h e most thoroughly i n v e s t i g a t e d semi-
enclosed seas (Jansson, 1978); y e t , s y n o p t i c scale v a r i a b i l i t y has n o t been s t u d i e d here as much as i n t h e ocean.
Previous observations worth mention-
i n g i n c l u d e t h e s e c t i o n o f thermocline anomaly observed by Keunecke and Magaard (1974)
u s i n g a towed t h e r m i s t o r s t r i n g ; i n t e r e s t i n g data from the
s i x t i e s i n t h e Arcona Basin (Kielmann e t a l . , (Sustavov
e t al.,
1978);
1973) and i n t h e Gotland Basin
and r e s u l t s o f t h e B a l t i c - 7 5 experiment i n t h e
Bornholm Basin (Kielmann e t a l . ,
1976).
As f o r numerical model s t u d i e s ,
e d d y l i k e motions can be s i m u l a t e d i f t h e r e s o l u t i o n o f t h e model i s s u f f i c i e n t (Simons, 1978; Kielmann, 1978). The aim o f our s t u d i e s i s t o broaden our knowledge o f t h e three-dimens i o n a l s t r u c t u r e o f s y n o p t i c s c a l e p e r t u r b a t i o n s and o f t h e i r e v o l u t i o n . The f i e l d experiments described i n t h e n e x t s e c t i o n t o o k p l a c e mainly i n t h e
BOSEX area.
434
I n t h i s paper, we consider t h e r e s u l t s o f v e r t i c a l CTD c a s t s obtained d u r i n g several surveys.
A t t h e present time, t h i s i s t h e o n l y p o s s i b l e way
t o achieve s u f f i c i e n t s p a t i a l coverage and r e s o l u t i o n t o document l o w f r e quency motions f r o m t h e surface down t o t h e bottom l a y e r s .
The complete
l i s t o f measurements a l s o i n c l u d e s d i r e c t c u r r e n t measurements a t various mooring s t a t i o n s ,
and CTO p r o f i l e s obtained w i t h an u n d u l a t i n g underwater
u n i t towed i n t h e upper l a y e r .
U n f o r t u n a t e l y , t h e most i n t e n s i v e d e n s i t y
anomalies were n o t covered by d i r e c t c u r r e n t measurements.
Some o f t h e
r e s u l t s o f t h i s complex p r o j e c t a r e described i n another paper
earlier
(Aitsam e t a l . , 1981). METHODS
A l a r g e number o f hydrographic measurements has been made i n t h e ocean as w e l l as i n t h e B a l t i c Sea d u r i n g t h e l a s t century.
However, h i s t o r i c a l
data are t o o sparse i n space and t i m e t o r e s o l v e t h e s y n o p t i c s c a l e motions.
A q u a l i t a t i v e l y new approach was implemented i n t h e course o f s p e c i a l l y designed p r o j e c t s , such as POLYGON-67 (Koshlyakov e t a l . , (Koshlyakov
and Grachev,
1973),
MODE (McWilliams,
1970), POLYGON-70
1976) and POLYMODE; i n
these experiments, hydrographic casts were o b t a i n e d a t s t a t i o n s c o v e r i n g a r e g u l a r g r i d w i t h proper g r i d spacing.
We have no i n f o r m a t i o n about s i m i l a r
measurements i n t h e B a l t i c Sea and our t a s k was t o apply "oceanic" methods and h i s t o r i c a l experiences t o t h e B a l t i c . simply a reduced model o f t h e ocean,
However, t h e B a l t i c Sea i s n o t
so t h a t t h e a p p l i c a t i o n o f oceanic
r e s u l t s t o t h e B a l t i c case r e q u i r e s caution. For t h e design o f an oceanographic experiment, t h e optimal sampling r a t e and t h e optimal c o n f i g u r a t i o n and spacing o f s t a t i o n s can be found i f t h e c o r r e l a t i o n and s p e c t r a l c h a r a c t e r i s t i c s are known ( B r e t h e r t o n e t a l . , The s p a t i a l c o r r e l a t i o n f u n c t i o n s were n o t known a t t h e s t a r t o f our
1976).
i n v e s t i g a t i o n s , so we e l e c t e d t o make measurements on a r e c t a n g u l a r g r i d w i t h a spacing o f 5 n a u t i c a l m i l e s between g r i d p o i n t s .
The l a t t e r choice
was based on t h e hypothesis t h a t the scales o f t h e eddies and o f t h e i n t e r n a l Rossby r a d i u s o f deformation, Rd,
a r e s i m i l a r i n t h e ocean and i n t h e
I n t h e B a l t i c , Rd i s about 10 km.
Baltic.
We s e l e c t e d experimental areas
w i t h r e l a t i v e l y smooth bottom slopes, and w i t h depths g r e a t e r than 80 m i n order
to
include the halocline.
The o r i e n t a t i o n o f t h e g r i d was chosen
according t o t h e p e c u l a r i t i e s o f t h e bottom topography.
The number o f
s t a t i o n s was l i m i t e d t o ensure t h a t surveys c o u l d be completed i n two days o r less. The v a r i o u s surveys w e r e performed d u r i n g c r u i s e s o f t h e R/V "Ayu-Dag". Most surveys were conducted i n t h e BOSEX area (Aitsam and Elken, 1980), and some t o o k p l a c e i n t h e Bornholm Basin and i n t h e Gotland Basin t o t h e n o r t h
435 1).
o f t h e BOSEX a r e ( F i g .
The surveys are l i s t e d i n Table 1.
I n this
t a b l e , t h e f i r s t i t e m o f t h e survey number denotes t h e c r u i s e number o f t h e
R/V "Ayu-Dag".
The l e n g t h s ( i n n a u t i c a l m i l e s ) o f t h e sides o f t h e g r i d s i n
t h e x- and y - d i r e c t i o n s are t a b u l a t e d under t h e heading "Survey area". x-
and y-axes
a r e d i r e c t e d eastward and northward:
1981 surveys; t h e axes a r e r o t a t e d 30' 1980.
respectively,
The
f o r the
clockwise f o r t h e surveys o f 1979 and
The lower l e f t and upper r i g h t coordinates d e f i n e the geographical
coordinates
o f t h e working area;
they correspond t o t h e corners o f t h e
"boxes" shown i n F i g u r e 1. I n t h e BOSEX area t h e bottom topography i s s l o p i n g mainly i n t h e x - d i r e c t i o n (see t h e maps i n Aitsam e t a l . ,.,' 1981, and i n Aitsam and Talpsepp. On t h e l e f t s i d e o f t h e area t h e slope exceeds 5-10-3, i n t h e cen-
1980).
t r a l p a r t t h e slope i s more moderate, r a n g i n g from 5-10-4 t o t h e r i g h t s i d e t h e depth decreases.
and on
A t y p i c a l depth i s 100 m.
The i n s t r u m e n t used i s t h e N e i l Brown Mark I11 CTD-profiler, c h a r a c t e r i s t i c s a r e described elsewhere (Laanemets and L i l o v e r , 1981).
whose The
d a t a were c o l l e c t e d on a REVOX audio tape recorder, and subsequently t r a n s f e r r e d t o a HP-9825A microcomputer f o r p r e l i m i n a r y data processing and s t o r age on HP-9885 f l e x i b l e d i s k s . I n t h e p r e l i m i n a r y data processing phase, temperature and c o n d u c t i v i t y data a r e i n t e r p o l a t e d a t pressure i n t e r v a l s o f 0.1 dbar; s a l i n i t y and density
values
(1981).
are
then
c a l c u l a t e d as described i n Laanemets and L i l o v e r
To f a c i l i t a t e f u r t h e r analyses, temperature,
s a l i n i t y and d e n s i t y
values a t s e l e c t e d pressure l e v e l s as w e l l as temperature,
s a l i n i t y and
pressure values a t s e l e c t e d d e n s i t y l e v e l s are compiled i n e a s i l y r e t r i e v a b l e format.
Also some i n t e g r a t e d p r o p e r t i e s , such as t h e r e l a t i v e dynamic
e. t h e d i f f e r e n c e o f dynamic h e i g h t s ) , henceforth denoted RTD, topography (i. a r e c a l c u l a t e d between s e l e c t e d pressure l e v e l s .
The RDT i s c a l c u l a t e d
according t o t h e formula:
where p1 and p2 denote pressure values ( i n dbars i n t h e argument o f RDT, w i t h p1 < p2); g, water;
and D(p2,
t h e a c c e l e r a t i o n due t o g r a v i t y ; p , t h e d e n s i t y o f t h e
p,),
t h e RDT i n cm, o r w i t h t h e accuracy o f
g in
dynamic cm. The d a t a i n pressure coordinates and t h e RDT have minor instrumental e r r o r s f o r s y n o p t i c scale s t u d i e s , except f o r t h e s a l i n i t y i n t h e thermoc l i n e l a y e r where n e g a t i v e spikes can occur. v e r t i c a l coordinate,
When d e n s i t y i s used as t h e
s p e c i a l care must be taken.
For long-term processes
436
I
Figure 1.
i
Basic areas f o r CTD surveys i n 1979, 1980 and 1981 (boxes), w i t h
depth contours (dashed l i n e s ) labeled i n meters. t h e water ii assumed t o be s t a b l y s t r a t i f i e d .
However, d e n s i t y inversions
are present i n some o f the observed p r o f i l e s .
These i n v e r s i o n s are removed
t o guarantee one-to-one correspondence o f pressure and density.
The e s t i -
TABLE 1.
L i s t o f the CTD surveys
Survey Number
day
Time month year
13/1 13/2 13/3 13/4 13/5 15/1 15/2 16/1 17/1 18/1 18/2 18/3 19/1 20/1 20/2 22/1 22/2 23/1 23/2 23/3 23/4 23/5
27 28 29-30 2-3 10-11 5-6 15-16 25-26 8-9 30-31 8-9 10-11 1-3 10-11 2-3 25-26 29-30 3-5 15-16 21-22 26-27 4-5
05 05 05 06 06 08 08 09 05 05 06 06 07 08 09 04 04 06 06 06 06 07
79 79 79 79 79 79 79 79 80 80 80 80 80 80 80 81 81 81 81 81 81 81
Duration (hrs)
Survey area
Number o f casts
18 21 34 20 20 24 20 23 24 32 33 27 39 37 30 34 32 44 26 26 25 25
20x20 20x20 30x20 20x20 20x20 20x20 20x20 20x20 20x25 20x25 20x25 25x20 20x25 25x25 20x25 25x25 25x25 25x30 20x20 20x20 20x20 20x20
21 21 38 21 21 21 21 21 30 30 30 27 30 36 30 36 36 42 25 25 25 25
Geographical Coordinates Lower l e f t Upper r i g h t Latitude Longitude Latitude Longitude 50'14.5'N 50'14.5'N 50'14.5'N 50'14.5'N 50'14.5'N 50'14.5'N 50'14.5'N 50'14. 5'N 56'03.4' N 56'03.4'N 56'03.4" 56'05.4' N 56'03.4" 56'03.4'N 56'03.4' N 55'00. O ' N 55'00.O'N 56'31.0'N 56'31. O'N 56'31.0'N 56'31.0'N 56'31. O ' N
18'21.3'E 18'21.3' E 18'21.3' E 18'21.3' E 18'21.3' E 18'21.3'E 18'21.3' E 18'21.3' E. 18'18.8'E 18'18.8'E 18'18.8'E 18'31.1' E 18'18.8' E 18'18.8 ' E 18'18.8' E 15'30.O'E 15'30. O ' E 18'55.4 ' E 18'55.4' E 18'55.4' E 18'55.4' E 18'55.4' E
56'21.1'N 56'21.1' N 56'15.7" 56'21.1" 56'21.1'N 56'21.1" 56'21.1'N 56'21.1' N 56'14.8" 56'14.8' N 56'14.8 ' N 56'09.3'N 56'14.8' N 56'12.1" 56'14.8" 55'25. O'N 55'25.0' N 57'01.0 ' N 56'51.0'N 56'51. O ' N 56'51.0' N 56'51. O'N
19'11.1' E 19'11.1'E 19'25.0' E 19'11. 1'E 19'11.1' E 19'11.1' E 19'11.1' E 19'11.1' E 19'12.4' E 19'12.4' E 19'12.4'E 19'27.8'E 19'12.4'E 19'20.1' E 19'12.4' E 16'13.4' E 16'13.4' E 19'40.7 ' E 19'32.1' E 19'32.1' E 19'32.1'E 19'32.1'E
438 mates o f t h e measurement e r r o r based on " t o t a l d i f f e r e n c e " type expressions are n o t good because t h e p r o f i l e s can be t o o jagged w i t h i n t h e d e n s i t y e r r o r intervals.
The e r r o r on t h e q u a n t i t y $ (temperature, s a l i n i t y o r pressure)
a t t h e d e n s i t y value
at
i s determined as f o l l o w s .
i n s t r u m e n t a l e r r o r s on $ and at, and l e t 41(a,) t h e measured p r o f i l e s o f
$(p)
Then t h e t r u e value o f $ a t
at
- Aat,
at
be t h e
Consider a l l t h e values o f $
and ot(p).
(at
w i t h i n the density i n t e r v a l
L e t A$ and Aut
be t h e r e l a t i o n obtained from
+ Aut),
and f i n d
i s between t h e l i m i t s
(qmin
-
and. , , ,$
+ A$),
A$,
and i t should be determined i n d i v i d u a l l y every t i m e . The t y p i c a l v e r t i c a l s t r a t i f i c a t i o n o f t h e B a l t i c waters i s w e l l known. The upper boundary o f t h e h a l o c l i n e i s l o c a t e d between 60 and 80 m,.,'and separates t h e upper c o l d / f r e s h
it
waters from t h e l o w e r warm/salty waters.
D u r i n g summer, a very steep thermocline a t a depth o f 1 5 t o 30 m separates t h e warm upper "quasi-homogeneous''
l a y e r and t h e c o l d i n t e r m e d i a t e l a y e r .
When i n t e r p o l a t i n g nonsimultaneous and nonaveraged measurements on a horizontal grid,
i t i s n o t easy t o e x t r a c t t h e synoptic s c a l e component o f
the v a r i a b i l i t y .
Among the several p o s s i b l e i n t e r p o l a t i o n and f i l t r a t i o n
techniques, t h e optimal i n t e r p o l a t i o n (Gandin, "mesoscal e" oceanographers
1965) has t h e f a v o r o f most
(McWi 11iams , 1976).
For s p e c i a l
purposes,
if
s t a t i s t i c s are n o t w e l l known, t h e l e a s t squares polynomial f i t t i n g ( N i k i t i n and Vinogradova, 1980) c o u l d be u s e f u l . Whatever t h e technique,
t h e s i g n a l t o n o i s e r a t i o i s a v e r y important
parameter which i n d i c a t e s how j u s t i f i e d t h e i n t e r p o l a t i o n procedure can be. I n t h e a l g o r i t h m o f optimal i n t e r p o l a t i o n , t h e e r r o r norm ( r a t i o o f t h e d i s p e r s i o n s o f n o i s e and s i g n a l ) i s e x p l i c i t l y c a l c u l a t e d , and i f t h e value o f t h i s norm i s c l o s e t o one, t h e maps c o n s t r u c t e d by t h e i n t e r p o l a t i o n method are o n l y s l i g h t l y i n f l u e n c e d by t h e measurements. I n order t o estimate t h e e r r o r norms, we c o l l e c t e d s e r i e s o f p r o f i l e s a t given stations
i n d i f f e r e n t seasons.
measure t h e e r r o r d i s p e r s i o n s was one day, casts one hour.
The d u r a t i o n o f each s e r i e s t o and t h e t i m e i n t e r v a l between
During h o r i z o n t a l surveys, t h e d u r a t i o n and t h e t i m e i n t e r -
v a l were about t h e same, b u t t h e measurements were made a t d i f f e r e n t s t a tions.
The e r r o r d i s p e r s i o n ,
E',
i n c l u d e s t h e random measurement e r r o r s and
t h e h i g h frequency n o i s e ( i n t e r n a l waves), a l l y .stationary, contamination trends
of
i n the
which can be assumed s t a t i s t i c -
homogeneous and u n c o r r e l a t e d i n space; "instantaneous"
synoptic
it also includes
p a t t e r n s due t o d i u r n a l
scale p e r t u r b a t i o n s .
The
variations
l a t t e r factor
and
imposes
c e r t a i n l i m i t a t i o n s on t h e survey d u r a t i o n and on t h e number o f s t a t i o n s . Our experience i n d i c a t e s t h a t maps obtained from surveys t a k i n g more t h a n two
days
cannot
be considered
instantaneous,
and some dynamical
and/or
439
statistical
The s i g n a l d i s p e r s i o n , u
time c o r r e c t i o n s are required.
determined from t h e d e v i a t i o n s from the mean of
2
,
is
t h e data obtained i n t h e
h o r i z o n t a l surveys; u2 i n c l u d e s b o t h t h e d i s p e r s i o n o f t h e "cooled" synoptic s c a l e p e r t u r b a t i o n s , and i t s t i m e contamination and h i g h frequency noise. 2 2 Some t y p i c a l d i s t r i b u t i o n s o f t h e e r r o r norm3, q = E /u , f o r t h e summer s t r a t i f i c a t i o n
i n t h e BOSEX area are presented i n F i g u r e 2, w i t h
e i t h e r pressure o r d e n s i t y as t h e " v e r t i c a l " coordinate.
Note t h a t q can be
l a r g e r than one due t o s t a t i s t i c a l u n c e r t a i n t i e s and because t h e i m p l i c i t hypothesis o f s t a t i s t i c a l homogeneity and s t a t i o n a r i t y i s n o t always v a l i d . F i g u r e 2 shows t h a t , when t h e pressure i s used as t h e v e r t i c a l c o o r d i nate, t h e d e n s i t y , temperature and s a l i n i s y p r o f i l e s above t h e 70 dbar l e v e l above t h e h a l o c l i n e ) a r e d i s t u r b e d by " e r r o r s " ; hence i t i s n o t poss-
(i.e.
i b l e t o t r y t o "separate"
o r i d e n t i f y "cooled" p a t t e r n s i n such data.
This
c o n c l u s i o n does n o t apply t o t h e s a l i n i t y i n t h e l a y e r above t h e thermoc l ine
which i s n o t d i s t u r b e d by v e r t i c a l displacements o f i n t e r n a l waves
and d u r n a l heat exchange v a r i a t i o n s .
1eve1 a r e 0 . 1 t o 0.2,
T y p i c a l values o f q below t h e 70 dbar
i n d i c a t i n g t h a t h o r i z o n t a l low frequency inhomogene-
i t i e s dominate over s h o r t - t e r m temporal v a r i a t i o n s i n t h e h a l o c l i n e . he e r r o r norms f o r t h e p r o f i l e s o f pressure, temperature and s a l i n i t y as f u n c t i o n s o f d e n s i t y a r e s m a l l e r than those c a l c u l a t e d i n p-coordinate.
F o r t h e pressure, t y p i c a l values o f q are 0.3-0.5 5.5-6.5), layer,
and 0.1-0.2
i n t h e thermocline (ut =
i n t h e h a l o c l i n e (ut = 7.5-8.5).
I n t h e intermediate
t h e h i g h e r v a l u e o f q can be explained by measurement e r r o r s :
v e r t i c a l d e n s i t y g r a d i e n t i s small i n t h a t l a y e r .
the
As t o t h e temperature and
s a l i n i t y p r o f i l e s i n at-coordinate,
they should t h e o r e t i c a l l y be f r e e o f t h e
kinematic e f f e c t o f i n t e r n a l waves.
The r e l a t i v e l y higher values o f q above
t h e ut = 7.5 l e v e l can be e x p l a i n e d by measurement e r r o r s r a t h e r than by p h y s i c a l processes.
I n these l a y e r s the temperature and s a l i n i t y v a r i a t i o n s
(due t o t h e f i n e s t r u c t u r e ) w i t h i n each d e n s i t y e r r o r i n t e r v a l can be compara b l e t o t h e t h e r m o c l i n i c i t y e f f e c t s described by Woods (1979). cline
(below at
= 7.5),
thermoclinicity
I n t h e halo-
c l e a r l y dominates and q i s very
small. The values o f q f o r t h e r e l a t i v e dynamic topography (RDT) sented i n t h e f i g u r e .
are n o t pre-
I f t h e thermocline and/or t h e h a l o c l i n e l i e between
t h e l i m i t s o f i n t e g r a t i o n , t h e RDT anomalies are caused mainly by t h e t o t a l v e r t i c a l displacement o f these t r a n s i t i o n l a y e r s , and t h e m a n i f e s t a t i o n s o f fine-scale/short-term procedure.
phenomena a r e e l i m i n a t e d v i a t h e v e r t i c a l i n t e g r a t i o n
T y p i c a l values o f q a r e 0.2-0.5
than 0 . 1 f o r t h e h a l o c l i n e .
f o r t h e thermocline, and l e s s
Note t h a t f o r t h e MODE r e g i o n t h e e r r o r norms
a r e w i t h i n t h e range o f 0.1-0.3
(McWilliams, 1976).
I
__ .--0-
/
100: dbar
dbar'
"t\
9.0 F i g u r e 2.
"A
9.0
9.0
V e r t i c a l d i s t r i b u t i o n o f t h e e r r o r norms, q =
as function o f pressure (above); (below).
2
......
-z
'2,
E
2/u 2 , o f d e n s i t y (ut), temperature (T) and s a l i n i t y ( S )
e r r o r norms o f pressure ( p ) ,
The s o l i d l i n e s represent d a t a from survey 20/1,
IA
temperature and s a l i n i t y as f u n c t i o n o f d e n s i t y
t h e dashed l i n e s d a t a from survey 20/2.
441 From t h i s study o f t h e e r r o r norms, we conclude t h a t , i n t h e h a l o c l i n e , t h e amp1 i t u d e o f t h e "cooled"
p a t t e r n s o f synoptic scale p e r t u r b a t i o n s i s
l a r g e r t h a n t h a t o f t h e s h o r t - t e r m v a r i a t i o n s ( w i t h p e r i o d s i n f e r i o r t o one day);
i t i s t h e r e f o r e meaningful t o map t h e observed f i e l d s .
A t t h e same
t i m e we doubt t h a t i t would be j u s t i f i e d t o p l o t , h o r i z o n t a l maps ( o r sections)
o f t h e temperature,
s a l i n i t y o r d e n s i t y f i e l d s a t any given depth
(pressure) l e v e l above 70 m (dbar) when more than a f e w hours elapse between neighbor s t a t i o n s . The knowledge o f t h e s p a t i a l c o r r e l a t i o n f u n c t i o n s i s r e q u i r e d t o draw maps u s i n g t h e optimal i n t e r p o l a t i o n techniques (Gandin,
1965).
Unfortun-
a t e l y , no d a t a o t h e r than those c o l l e c t e d d u r i n g t h e v a r i o u s surveys are a v a i l a b l e f o r determining these c o r r e l a t i o n f u n c t i o n s .
When o n l y a f e w data
p o i n t s from one survey a r e used, t h e s t a , t i s t i c a l u n c e r t a i n t i e s a r e l a r g e , b u t v a r i a t i o n s from survey t o survey are g r e a t e r than t h e estimated c o n f i dence i n t e r v a l . F i g u r e 3 shows an example o f t h e c o r r e l a t i o n f u n c t i o n of D (70,30),the RDT between 30 and 70 db ( i . e . t h e h a l o c l i n e anomalies), s i n g l e survey
(lower
I n t h e a n a l y t i c a l f i t t i n g t h e a n i s o t r o p y was taken i n t o account
by t h e c o r r e l a t i o n e l l i p s e s . i n t h i s example,
The c o r r e l a t i o n r a d i i a r e more than 10 miles
so t h e g r i d spacing chosen f o r t h e measurements (5 m i l e s )
i s almost o p t i m a l exceed 20%.
and t h e average c o r r e l a t i o n s over 6 surveys
The c o r r e l a t i o n s were c a l c u l a t e d i n f o u r d i r e c t i o n s w i t h 45'
(upper panel). increment.
panel)
f o r t h e data o f a
i n terms o f i n t e r p o l a t i o n e r r o r s :
t h e l a t t e r do n o t
However, some o f t h e o t h e r RDT d a t a gave t o o s h o r t c o r r e l a t i o n
l e n g t h s i n comparison w i t h t h e g r i d spacing.
As a r u l e , t h e parameters
which have l a r g e e r r o r norms a r e u n c o r r e l a t e d a t t h e d i s t a n c e o f t h e g r i d spacing. Various experiments show t h a t t h e i n t e r p o l a t e d maps are v i s u a l l y n o t very sensitive t o the variations o f the c o r r e l a t i o n functions.
However,
t h i s c o n c l u s i o n does n o t apply t o t h e study o f t h e s p a t i a l d e r i v a t i v e s and t h e dynamical equations.
Generally, f o r repeated surveys (close i n t i m e t o
each o t h e r ) t h e averaged c o r r e l a t i o n f u n c t i o n s were used.
For some cases
t h e c o r r e l a t i o n l e n g t h s were increased t o o b t a i n more e f f e c t i v e p o i n t s f o r the interpolation.
SYNOPTIC SCALE DISTRUBANCES The r e l a t i v e dynamic topography (RDT),
c a l c u l a t e d by formula (l), i s
t h e main o b j e c t o f our i n t e r e s t f o r two reasons. small
error
norms
and s u f f i c i e n t l y l a r g e c o r r e l a t i o n l e n g t h s t o ensure
correct interpolation. property:
it i s
F i r s t , t h e RDT has f a i r l y
Second, and more i m p o r t a n t l y , t h e RDT i s a dynamical
t h e geostrophic
stream f u n c t i o n o f r e l a t i v e c u r r e n t s .
442
a)
1
1
0
0
-1
-1
1
30 -1 -
Figure 3. Spatial correlation functions of the r e l a t i v e dynamic topography (RDT) between 30 and 70 d b , D (70,30), in four directions (indicated by subscripts). Circles represent data points, vertical bars indicate the 90% confidence l i m i t s , and solid l i n e s are the r e s u l t s of two-dimensional analyt i c a l f i t s . Upper panel shows the average correlation functions over s i x 1980 surveys; lower panel shows r e s u l t s of the single survey 18/2.
443
Indeed, f o r t h e nondimensional parameter values c h a r a c t e r i s t i c o f the B a l t i c Proper,
t h e c o n d i t i o n s f o r t h e quasi-geostrophic approximation t o be v a l i d
a r e s a t i s f i e d i n t h e low frequency range.
However, i t should be emphasized
t h a t t h e r e f e r e n c e l e v e l f o r geostrophic c a l c u l a t i o n s o f t h e absolute veloc i t y by t h e dynamical method i s n o t w e l l known. proposed (Fomin, currents.
Several methods have been
1964), b u t i n t h i s s e c t i o n we s h a l l o n l y discuss r e l a t i v e
I f t h e RDT i s c a l c u l a t e d by (l), i t represents t h e v e l o c i t y o f
t h e upper l a y e r r e l a t i v e t o t h a t o f t h e l o w e r l a y e r i n t h e t r a d i t i o n a l sense o f a stream f u n c t i o n .
An RDT change o f 1 dyn.cm over 5 m i l e s corresponds t o
a r e l a t i v e c u r r e n t speed o f 8.65 cm/sec.
I f t h e isopycnals are displaced
upward, t h e RDT anomaly i s negative, and'vice versa. Three examples o f t h e e v o l u t i o n o f e d d y l i k e phenomena can be described on t h e b a s i s o f r a p i d l y succeeding surveys i n t h e BOSEX area. The d a t a o f August 1979 show an e d d y l i k e p e r t u r b a t i o n o f t h e RDT w i t h a The l e f t - h a n d s i d e o f Figure 4 shows t h r e e RDT
diameter o f 20 km (9 2Rd). i n t e g r a l s between d i f f e r e n t
levels
for
survey
15/1; t h e r i g h t - h a n d side
shows t h e same i n t e g r a l s f o r survey 15/2 t e n days l a t e r . o f t h e thermocline [D(30,10)]
The deformations
and o f t h e h a l o c l i n e [D(90,30)]
have the same
s i g n , and b o t h r e f l e c t an upward displacement from t h e mean p o s i t i o n i n t h e center o f the perturbation.
The d i f f e r e n c e i n geostrophic c u r r e n t s above
and below t h e h a l o c l i n e i s 5 t o 7 cm/sec.
The comparison o f t h e two s e r i e s
o f maps shows t h a t t h e eddy migrates 10 m i l e s along t h e average isobaths i n
10 days ( m i g r a t i o n speed the r i g h t .
3
2 cm/sec),
w i t h t h e shallower water remaining on
I t can a l s o be seen t h a t t h e a x i s o f t h e eddy i s n o t v e r t i c a l
( t h e c e n t e r s do n o t c o i n c i d e i n t h e h a l o c l i n e and thermocline maps) and i t appears t h a t t h e thermocline p e r t u r b a t i o n migrates f a s t e r than t h a t o f the halocline. dent:
The i n t e n s i f i c a t i o n o f the h a l o c l i n e p e r t u r b a t i o n i s a l s o e v i -
t h e r e l a t i v e r o t a t i o n a l speed doubles i n 10 days. The maps o f surveys 1 3 / 1 t o 13/4 (Figure 5) show a p o s i t i v e e d d y l i k e
RDT p e r t u r b a t i o n o f weak i n t e n s i t y i n t h e upper c e n t r a l p a r t o f t h e area. The p e r t u r b a t i o n appears in t h e ha1o c l ine o n l y , because no thermocl ine has developed y e t .
On t h e b a s i s o f a s i n g l e survey,
i t c o u l d be hypothesized
t h a t t h e p e r t u r b a t i o n i s caused by i n t e r n a l waves.
However, t h e presence o f
t h e p e r t u r b a t i o n on t h r e e successive d a i l y maps (13/1-3) i s convincing e v i dence t h a t t h e p e r t u r b a t i o n ( l o w e r i n g o f isopycnals, w i t h axes
Rx z 1 5 km,
R E 20 km) i s a s y n o p t i c f e a t u r e . The speed o f t h e p e r t u r b a t i o n d r i f t i s Y o f t h e o r d e r o f 1.5 cm/sec w i t h t h e shallower water on t h e r i g h t . Although t h e c u r r e n t speeds a r e t o o weak f o r a c o r r e c t comparison,
the r e l a t i v e
c u r r e n t s a t t h e c e n t r a l s t a t i o n , determined on t h e b a s i s o f mooring s t a t i o n data and averaged over 5 days, correspond s a t i s f a c t o r i l y t o t h e geostrophic
444
1 ( 90,lO)
1511 5.-6.08.79
I(90,301
1511: 5.-6.08.79
D (90101
1512:15.-16.08.:
D (90,30)
1512 : 15-16.08:
03
N30,lO)
1512:15.-16.08.7!
1511: 5.-6.08.79.
0
F i g u r e 4.
5
10
6 miles
Maps o f RDT anomalies ( i n dynamic cm) f o r surveys 15/1 (on t h e
l e f t ) and 15/2 (on t h e r i g h t ) .
The contour i n t e r v a l i s 0 . 1 dyn.cm.
445
D(90,30)
F i g u r e 5.
1313 : 29.0579
Maps o f RDT anomalies ( i n dynamic cm) f o r surveys 13/1-4.
contour i n t e r v a l i s 0 . 1 dyn.cm.
The
446
v e l o c i t y determined f r o m RDT.
On t h e r i g h t s i d e o f t h e area, t h e edge o f a
l a r g e negative RDT anomaly can be observed.
An e x t e n s i o n
of survey 13/3
a l l o w s us t o document t h e scales .and shape o f t h i s p e r t u r b a t i o n .
The halo-
c l i n e i n t e r s e c t s t h e bottom slope a t t h e r i g h t edge o f t h e survey extension (decreasing depth).
The anomaly i s t o n g u e l i k e i n shape, and i t extends 40 The streamlines o f D(90,30) remain unclosed along
km i n t h e y - d i r e c t i o n .
t h e l i n e where t h e h a l o c l i n e disappears because o f decreasing depths. The data o f surveys 18/1 t o 18/3 ( e a r l y summer 1980) show an i n t e n s i v e and l a r g e e d d y l i k e p e r t u r b a t i o n .
The isopycnals a r e d i s p l a c e d upward by
more than 20 m i n t h e c e n t e r o f t h e eddy.
The t o t a l depth i s about 100 in.
The diameter o f t h i s eddy i s more than t w i c e as l a r g e as t h a t o f the,.eddies p r e v i o u s l y observed; i t exceeds 40 km.
The d i f f e r e n c e i n geostrophic c u r -
r e n t between t h e 60 m and 90 m l a y e r s i s about 20 c d s e c . o f D(70,30) f o r t h r e e d i f f e r e n t surveys ( F i g . perturbation.
I n 9 days ( i . e .
The contour maps
6) show t h e e v o l u t i o n o f t h e
between survey 18/1 and 18/2), t h e c e n t e r o f
t h e p e r t u r b a t i o n moves 5 t o 10 m i l e s eastward across t h e isobaths, and i t "escapes"
t h e survey area.
A t t h e p e r i p h e r y o f t h e eddy, t h e l i n e s o f con-
s t a n t RDT become more d i s t o r t e d than i n p r e v i o u s surveys; t h e contour l i n e s on t h e l e f t - h a n d s i d e o f t h e area tend t o become p a r a l l e l t o t h e isobaths, Survey 18/3 (which covers a d i f f e r e n t
w i t h shallower water on t h e r i g h t .
area s e l e c t e d on t h e b a s i s o f t h e observed m i g r a t i o n o f t h e eddy c e n t e r , and which was completed immediately a f t e r survey 18/2) r e v e a l s a " s p l i t t i n g " o f t h e l a r g e eddy i n t o two s m a l l e r ones w i t h diameters o f about 20 km. t i m e o f t h e l a s t survey,
A t the
t h e s p l i t t i n g i s n o t f u l l y completed and t h e p e r -
t u r b a t i o n s have a common area.
I t must a l s o be p o i n t e d o u t t h a t t h e t i m e
e v o l u t i o n o f such an i n t e n s i v e p e r t u r b a t i o n i s uneven.
Between surveys 18/1
and 18/2, t h e time e v o l u t i o n was moderately slow, b u t survey 18/3 shows a "collapse-like
behavior",
i . e changes i n t h e isopycnal depths occur much
f a s t e r than d u r i n g p r e v i o u s days.
This r a p i d s p l i t t i n g o f t h e p e r t u r b a t i o n
leads t o a rearrangement o f 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 d e n s i t y anomalies. The
isopycnals
gether" f o r 7.5
observed d u r i n g surveys
5
ut
5
18/1 and 18/2 a r e d i s p l a c e d " t o -
8.5, and t h e c r o s s - c o r r e l a t i o n between pressure a t ut
= 7.0 and RDT D(70,30)
i s l a r g e r than 0.95.
For t h e d a t a o f survey 18/3,
t h e l a t t e r c o r r e l a t i o n i s reduced t o 0.8 and l e s s . .We f i n d i t a l s o i n t e r e s t i n g t o analyze t h e temperature f i e l d on given isopycnal surfaces. (above t e h a l o c l i n e )
F i g u r e 7 shows temperature maps on t h e s u r f a c e at = 6.5 f o r surveys 18/1 and 18/2.
Because t h e c o r r e l a t i o n
r a d i i a r e f a i r l y small, these maps were n o t c o n s t r u c t e d by optimal i n t e r p o lation,
b u t by s p l i n e
c e n t e r o f t h e eddy;
interpolation.
t h e l o c a l minimum,
The temperature i s maximum a t t h e l o c a t e d a t a d i s t a n c e o f about 10
447
D(70.301 18/1: 30.-31.05.80
0
Fig.
6.
5
10
15 miles
Maps o f ROT anomalies ( i n dynamic cm) f o r surveys 18/1 to 18/3.
The contour i n t e r v a l surveys 18/2 and 18/3.
i s 0.2 dyn.cm f o r survey 18/2, and 0 . 1 dyn.cm f o r
448
Fig. 7.
10
5
0
15 miles
Maps o f temperature on t h e isopycnal s u r f a c e ut = 6.5 f o r surveys
18/1 and 18/2. The contour i n t e r v a l i s 0 . 5 O C . miles, i s not r e f l e c t e d i n the density f i e l d .
This l o c a l minimum seems t o
have a s t a b l e o r i e n t a t i o n w i t h respect t o t h e c e n t e r o f t h e eddy. v a r i a t i o n s i n temperature a r e l a r g e ( Z 4°C
w i t h e r r o r z 1°C)
The
compared t o
oceanic d a t a (see Woods and M i n n e t t , 1979, who r e p o r t v a r i a t i o n s o f about 0.1"C.)
The temperature d i s t r i b u t i o n on at-surfaces
can be considered a
t r a c e r under t h e assumption t h a t t h e process r e s p o n s i b l e f o r t h e f o r m a t i o n o f t h e anomalies i s slow.
I n such a case, t h e water i n t h e c e n t e r o f t h e
eddy should m i g r a t e w i t h t h e eddy, and t h e e d d y l i k e p e r t u r b a t i o n c o u l d n o t be o f wavelike o r i g i n s i n c e mass i s a c t u a l l y t r a n s p o r t e d i n t h e d i r e c t i o n which would be t h a t o f t h e phase speed.
The o t h e r p o s s i b i l i t y i s t h a t t h e
eddy permanently generates t h a t k i n d o f anomalies.
Another f e a t u r e o f
survey 18/1 i s t h a t t h e s a l i n i t y above t h e h a l o c l i n e i s markedly h i g h e r a t t h e c e n t e r o f t h e eddy than elsewhere (,in pressure coordinate); vides
evidence t h a t
pumping o r m i x i n g processes
upwell
t h i s pro-
salty halocline
waters. F i g u r e 8 shows maps o f RDT D(70,30) o f t h e s i n g l e surveys,
number 19/1.
and temperature a t ut = 6.5 f o r one
A n e g a t i v e RDT p e r t u r b a t i o n i s l o c a t e d
i n t h e upper r i g h t corner o f t h e area, b u t t h e contour l i n e s a r e n o t closed.
449
~~
F i g . 8. at
= 6.5
‘15 miles
10
5
0
Maps o f RDT ( l e f t panel) and temperature on t h e isopycnal surface ( r i g h t panel)
for
The contour i n t e r v a l s a r e 0.1
survey 19/1.
dyn.cm f o r RDT and 0.5OC f o r temperature. Assuming t h a t t h e p e r t u r b a t i o n i s e d d y l i k e , r o u g h l y equal t o 30 t o 40 kin.
t h e diameter appears t o be
The displacements o f t h e thermocline and
h a l o c l i n e appear t o have t h e same sign.
The p a t t e r n o f t h e temperature
f i e l d ( r i g h t panel) i s s i m i l a r t o t h a t o f surveys 18/1 and 18/2:
t h e tem-
p e r a t u r e i s maximum a t t h e c e n t e r o f t h e p e r t u r b a t i o n and a l o c a l minimum i s observed nearby. Some o t h e r p e r t u r b a t i o n s have been observed d u r i n g some o f t h e s i n g l e surveys conducted i n t h e BOSEX area.
The RDT D(70,30) o f survey 17/1 i n d i -
cates a j e t l i k e anomaly (contour l i n e s almost p a r a l l e l t o t h e isobaths) i n t h e western p a r t o f t h e area.
As observed i n t h e surveys o f s p r i n g and
e a r l y summer o f 1980, t h e isopycnals are deeper a t t h e western edge o f the area where t h e water i s shallower. l i k e p e r t u r b a t i o n s with’diameters
The data o f survey 20/1 show t w o eddyo f about 20 km (2Rd).
depressed a t t h e c e n t e r o f b o t h p e r t u r b a t i o n s ,
The thermocline i s
b u t t h e h a l o c l i n e i s de-
pressed i n one case and u p l i f t e d i n t h e other. The processing o f t h e 1981 d a t a i s n o t completed y e t . d e s c r i b e some o f t h e p e r t u r b a t i o n s w i t h o u t f i g u r e s .
Hence, we s h a l l
450
Two surveys
- 22/1
and 22/2
-
were c a r r i e d o u t i n t h e Bornholm Basin a t
t h e end o f A p r i l 1981.
The h a l o c l i n e i n t h e Bornholm Basin i s sharper than
i n t h e B a l t i c Proper.
The Bornholm Basin and t h e S t o l p e Furrow ( i n t h e
e a s t e r n p a r t o f t h a t basin) are t h e regions through which t h e s a l t y N o r t h Sea waters e n t e r t h e B a l t i c Proper i n t h e bottom l a y e r s .
Several d e n s i t y
and ROT anomalies were observed i n the Bornholm Basin, b u t t h e i r s t r u c t u r e i s more complicated than i n t h e BOSEX area.
A c h a r a c t e r i s t i c feature i s the
r a i s i n g o f the isopycnals i n t h e shallower p a r t s o f t h e working area; t h e converse was observed i n t h e BOSEX area.
I n t h e c e n t r a l p a r t of t h e working
area, t h e c r o s s - c o r r e l a t i o n s between t h e displacements o f d i f f e r e n t isopycn a l s are poor:
some displacements even change s i g n over small
v e r t i c a l i n t e r v a l s w i t h i n a given p e r t u r b a t i o n .
(5-;10
m)
Hence, i t i s hard t o be-
l i e v e t h a t t h e observed p e r t u r b a t i o n s are synoptic scale eddies.
Unfortu-
n a t e l y , no e r r o r norm estimates are a v a i l a b l e . I n June o f 1981, f i v e surveys were performed i n t h e Gotland area ( n o r t h
o f t h e BOSEX area) d u r i n g t h e j o i n t Soviet-German Physical/Chemical ment.
maps o f surveys 23/3 t o 23/5. b a t i o n i n RDT D(80,50)
I n survey 23/3 a p o s i t i v e , t o n g u e l i k e p e r t u r -
appears i n t h e upper l e f t p a r t o f t h e area;
p e r t u r b a t i o n extends 20 km i n t h e x - d i r e c t i o n . 23/4),
Experi-
Two d i s t i n c t p e r t u r b a t i o n s and t h e i r e v o l u t i o n can be f o l l o w e d on t h e the
Over t h e n e x t 5 days (survey
t h e p e r t u r b a t i o n seems t o expand along t h e isobaths:
the t i p o f the
tongue migrates 20 km i n t h e y - d i r e c t i o n and t h e tongue widens t o 30 km i n the x-direction.
I n t h e upper p a r t o f t h e p e r t u r b a t i o n , a s l i g h t e d d y l i k e
c e n t e r begins t o t a k e shape.
On the map o f survey 23/5 (8 days l a t e r ) , t h e
w i d t h o f t h e p e r t u r b a t i o n has decreased t o 20 km i n t h e x - d i r e c t i o n , and t h e eddylike center i s stretched out i n the y-direction.
The o t h e r disturbance
i s a n e g a t i v e e d d y l i k e p e r t u r b a t i o n , 15 t o 20 km i n diameter, l o c a t e d i n t h e right-central 23/4,
p a r t o f t h e map o f survey 23/3.
Between surveys 23/3
and
we c o l l e c t e d data along a s e c t i o n o f t h e eddy w i t h a p r o f i l i n g i n t e r -
val o f 1 mile.
The r e s u l t s show t h a t t h e RDT v a r i e s smoothly between t h e
g r i d s t a t i o n s o f t h e survey and t h a t i n t e r p o l a t i o n gives n e a r l y t h e same p i c t u r e as do measurements on a f i n e h o r i z o n t a l scale. 23/4,
On t h e map o f survey
t h e eddy i s a t t h e same place, b u t i n t h e upper l e f t p a r t o f t h e eddy
t h e s t r e a m l i n e s o f t h e r e l a t i v e v e l o c i t y have become denser because t h e positlve
RDT p e r t u r b a t i o n described above i s impinging on t h e negative
eddylike perturbation.
A f t e r 8 days (survey 23/5),
t h e eddy has migrated
about 11-14 km along t h e isobaths towards t h e n o r t h e a s t e r n corner o f t h e area, i . e . w i t h shallow water on t h e r i g h t .
M i g r a t i o n along t h e isobaths i s
c h a r a c t e r i s t i c o f b o t h p e r t u r b a t i o n s i n s p i t e o f t h e f a c t t h a t t h e average bottom slopes have completely d i f f e r e n t o r i e n t a t i o n s below t h e d i f f e r e n t perturbations.
451
THEORETICAL INTERPRETATION G e n e r a l l y speaking, t h e t h e o r y o f s y n o p t i c scale motions i s complicated and needs f u r t h e r study.
The f i r s t eddies observed i n t h e ocean were i n t e r -
p r e t e d as t h e s u p e r p o s i t i o n o f l i n e a r b a r o t r o p i c and b a r o c l i n i c Rossby waves (Koshlyakov and Grachev, 1973; McWilliams and F l i e r l , 1976).
I n t h i s sec-
t i o n , we do n o t t r y t o develop general t h e o r i e s , b u t we l o o k f o r t h e simpl e s t p o s s i b l e quasi-geostrophic
motions c o n s i s t e n t w i t h parameter values
c h a r a c t e r i s t i c o f t h e B a l t i c Sea, and we p o i n t o u t some d i f f e r e n c e s between t h e l i n e a r regimes o f t h e oceans and o f deep seas.
I n p a r t i c u l a r , some
p e c u l a r i t i e s o f topographic waves and b a r o c l i n i c i n s t a b i l i t y o f sheared mean c u r r e n t s a r e discussed i n connection wifih observational r e s u l t s . L e t x,y,z and n o r t h ,
be C a r t e s i a n coordinates w i t h x and y d i r e c t e d t o t h e e a s t
and z p o i n t i n g down w i t h z = 0 a t t h e undisturbed surface.
sketch o f t h e model i s presented i n Figure 9. sloping i n the x-direction,
i.e.
A
Consider a b a s i n w i t h bottom
w i t h depth H = Ho + a x , and assume t h a t a
<< 1, so t h a t as a f i r s t approximation t h e d i f f e r e n c e between H and Ho can be neglected f o r moderate h o r i z o n t a l scales except i n terms i n v o l v i n g t h e depth g r a d i e n t s .
L e t us assume t h a t t h e water column c o n s i s t s o f two l a y e r s
o f thicknesses hl
and h2 r e s p e c t i v e l y , and constant ( b u t d i f f e r e n t ) V a i s a l a
frequencies N1 and N2. a t the interface.
A t t h e same time t h e d e n s i t y i s assumed continuous
Consider a l s o a mean f l o w
i s c o n s t a n t i n t h e upper l a y e r (Vs) (Vs
-
Vb)/hp,in
t h e lower l a y e r .
v(z) i n t h e y - d i r e c t i o n , which
and has a constant v e r t i c a l g r a d i e n t ,
The E a r t h ' s r o t a t i o n i s taken i n t o account
by t h e usual 8-plane approximation, f = f o + By, where t h e d i f f e r e n c e between t h e C o r i o l i s parameter f and t h e constant f o can be neglected except i n t h e y - d e r i v a t i v e o f f.
The l i n e a r i z e d quasi-geostrophic
equation ex-
p r e s s i n g t h e c o n s e r v a t i o n o f p o t e n t i a l v o r t i c i t y can be w r i t t e n as f o l l o w s
:ig.
9.
Sketch o f t h e t w o - l a y e r model.
452
where JI i s t h e stream f u n c t i o n , t denotes t h e t i m e v a r i a b l e and A Laplace's The s u b s c r i p t k = 1,2 i d e n t i f i e s t h e upper and lower l a y e r r e -
operator. spectively.
The v e r t i c a l boundary c o n d i t i o n s w i l l be g i v e n l a t e r .
Their
form depends on t h e s o l u t i o n one i s l o o k i n g f o r , and t h e i r p h y s i c a l meaning i s t h e requirement o f zero normal v e l o c i t y a t t h e surface and a t t h e bottom and o f c o n t i n u i t y a t t h e i n t e r f a c e . A
Topographic
Waves
L e t us f i r s t consider t h e case o f topographic waves (Rhines, w i t h o u t mean f l o w
= 0).
model (hl waves.
(i = 0).
1970)
and, f o r s i m p l i c i t y , l e t us analyze a one-layer
The s u b s c r i p t s can then be o m i t t e d f o r these topographic
We l o o k f o r wave s o l u t i o n s o f t h e form
JI = O(z) exp [ i ( k x where $(z)
+
ly
-
wtll
(3)
i s t h e v e r t i c a l s t r u c t u r e f u n c t i o n , k and 1 a r e t h e wavenumbers The s u b s t i t u t i o n o f (3) i n t o equation (2) g i v e s t h e
and w i s t h e frequency.
f o l l o w i n g e q u a t i o n f o r $(z): d
2
5
- (q2 (?9) dz f
where q2 = k2 + 1'.
*dz= o
+
E) $ w
= 0,
The boundary c o n d i t i o n s are
a t z = ~ ,
2 !!t=-T@ atz=H. dz The 'system (4).
(5), (6)
has two classes o f s o l u t i o n s depending on
whether q2 + pk/w i s p o s i t i v e o r negative. 2 I f 0 + pk/w > 0, t h e s o l u t i o n i s
453
and t h e transcendental equation d e f i n i n g w i s
Parameter values c h a r a c t e r i s t i c o f t h e BOSEX area are: sec-l,
N =
lo-'
sec-l,
I Axl = I AY I
H = 100 m,
01
f = 1.25~10-~
= 5 ~ 1 0 - ~p , = 1.3~10-'~ cm-l sec-l, and
= 40 km, where Ax = 2n/k, and A = 2n/l. For these y- 2 values, t h e second term under t h e r a d i c a l i s o f order 10 . A s long as t h e parameters vary w i t h i n reasonable l i m i t s , t h e r o l e o f p does n o t increase
wavelengths
considerably.
Therefore,
i n t h e Ba1tj.c Sea, t h e p - e f f e c t can be neglected
f o r t h e " f a s t b a r o c l i n i c " waves (Rhines,
1977), and equation (8) takes t h e
form o f t h e well-known d i s p e r s i o n r e l a t i o n f o r topographic waves
I n t h e l i m i t NrlH/f
>> 1, (9) reduces t o t h e d i s p e r s i o n equation f o r
bottom-trapped topographic waves, w = -N a s i n e , where 0 i s t h e angle between t h e wave v e c t o r and t h e bottom slope. For NqH/f << 1, equation (9) 2 becomes w = - a l f / r l H , a p p r o p r i a t e f o r b a r o t r o p i c waves. Since f3 has no e f f e c t on t h e s o l u t i o n ,
t h e o r i e n t a t i o n o f t h e bottom slope and o f t h e
c o o r d i n a t e axes can be a r b i t r a r y . I f q2 + pk/w < 0, t h e s o l u t i o n describes slow b a r o c l i n i c waves.
p-effect
dominates t h a t o f t h e bottom slope;
The
t h e presence o f a slope i s
i m p o r t a n t , b u t t h e v a r i a t i o n o f i t s magnitude has o n l y minor i n f l u e n c e .
For
t h e parameter values corresponding t o t h e B a l t i c Sea, t h e p e r i o d s o f these waves are l o n g e r than years.
Therefore, such waves a r e n o t r e l e v a n t t o t h e
study o f s y n o p t i c v a r i a b i l i t y . Consequently, i n t h e absence o f a mean shear f l o w and w i t h a l i n e a r l y s l o p i n g bottom,
only bottom-intensified o r nearly barotropic ( f o r
wavelengths) topographic waves can e x i s t .
large
These waves have no modal s t r u c -
t u r e and a s i n g l e frequency w corresponds t o each p a i r o f wavenumbers k and 1.
As l o n g as d+(z)/dz
does n o t change i t s ( p o s i t i v e ) s i g n i n t h e v e r t i c a l
d i r e c t i o n , t h e displacements o f t h e f r e e surface and o f t h e isopycnal surfaces have t h e same sign.
This i s t h e reason why no attempt was made t o
d i s t i n g u i s h cyclones and a n t i c y c l o n e s i n t h e d e s c r i p t i o n o f t h e experimental data. then,
I f t h e eddies a r e formed by a s u p e r p o s i t i o n o f topographic waves, u n l i k e t h e oceanic case,
an a n t i c y c l o n e has a c o l d c e n t e r i n the
t h e r m o c l i n e and a s a l t y c e n t e r i n t h e h a l o c l i n e ; a cyclone has warm and
454
f r e s h c e n t e r s r e s p e c t i v e l y i n t h e thermo- and h a l o c l i n e . Since
N # constant f o r t h e observed s t r a t i f i c a t i o n , t h e problem consis-
t i n g o f equations ( 4 ) , d i f f e r e n c e method.
(5),
i s homogeneous, so t h a t ,
quency
ui
( 6 ) was a l s o solved n u m e r i c a l l y u s i n g a f i n i t e
The system o f l i n e a r equations f o r d i s c r e t e @(z) values i n order t o obtain n o n t r i v i a l solutions, the f r e -
has t o be such t h a t t h e determinant o f t h e system i s equal t o zero.
F i g u r e 10 shows v a r i o u s p r o f i l e s o f $(z) summer s t r a t i f i c a t i o n . of A
Y
calculated f o r a typical
The v a r i o u s p r o f i l e s correspond t o d i f f e r e n t values
(we assume k = 0), and t h e y are normalized by t h e c o n d i t i o n
F i g . 10.
V e r t i c a l s t r u c t u r e f u n c t i o n o f topographic waves, $(z),
August s t r a t i f i c a t i o n .
f o r the
The v a r i o u s curves correspond t o d i f f e r e n t values o f
The wavenumber i n t h e x - d i r e c t i o n , A,,. cases.
k,
i s s e t equal t o zero i n a l l
455
S i n c e g(z) r e p r e s e n t s t h e a m p l i t u d e o f t h e stream f u n c t i o n , i t i s p r o F o r A = 1 0 km, we f i n d t h a t t h e Y There a r e no v e r t i c a l shear i n
portional t o the horizontal velocity.
motion i s concentrated i n t h e bottom layers. the
horizontal
velocity
and
no
displacements o f
the
isopycnals
i n the
thermocline. F o r A = 200 km, t h e f u n c t i o n g(z) corresponds t o t h e baroY t r o p i c regime, and t h e whole w a t e r column moves w i t h t h e same v e l o c i t y . For i n t e r m e d i a t e wavelengths,
t h e r e a r e v e r t i c a l shears o f v e l o c i t y i n b o t h t h e
t h e r m o c l i n e and t h e h a l o c l i n e .
The i s o p y c n a l displacements i n t h e thermo-
5
A < 80 km. y .The o b s e r v a t i o n s p r e s e n t e d i n F i g u r e 4 can be modeled by t h e superposi-
c l i n e a r e l a r g e s t f o r 20 km t i o n o f two p l a n e waves, km. are:
F o r such a model,
+
c = (0;
( k , 1) and (-,k,l),w i t h Ax = 40 km, and A = -40 Y t h e n u m e r i c a l l y d e t e r m i n e d phase speed and p e r i o d
3 ) c d s e c ; T = 15.6 days.
The e s t i m a t e d m i g r a t i o n speed o f
t h e RDT p e r t u r b a t i o n between surveys 1 5 / 1 and 15/2 i s 2 cm/sec. a c c o u n t t h e u n c e r t a i n t i e s a f f e c t i n g t h e parameter v a l u e s , between t h e model and t h e o b s e r v a t i o n i s n o t s i g n i f i c a n t . t h e speed o f m i g r a t i o n o f t h e RDT p e r t u r b a t i o n ,
Taking i n t o
the difference
The d i r e c t i o n and
as w e l l as t h e presence o f
g e o s t r o p h i c v e l o c i t y shears i n t h e t h e r m o c l i n e and i n t h e h a l o c l i n e , c o r respond s a t i s f a c t o r i l y t o t h e t o p o g r a p h i c wave model. The o b s e r v a t i o n s shown i n F i g u r e 5 can be i n t e r p r e t e d i n a s i m i l a r way.
t
U s i n g e s t i m a t e d wavelengths Ax = 25 km and A = -40 km, t h e t h e o r y y i e l d s Y = (0; 1.9) cm/sec and T = 23.8 days. On t h e b a s i s o f t h e e x p e r i m e n t a l d a t a , t h e m i g r a t i o n speed o f t h e RDT p e r t u r b a t i o n i s 1 . 5 cm/sec.
Hence, we be-
l i e v e t h a t t h e c o n c l u s i o n o f t h e p r e v i o u s paragraph i s a l s o v a l i d i n t h i s case. B.
Baroclinic i n s t a b i l i t y L e t us now c o n s i d e r e q u a t i o n (2)
with
p =
0, a p p l i e d t o a t w o - l a y e r
f l u i d w i t h o u t d e n s i t y jump, i n t h e presence o f a sheared mean f l o w , i ( z ) , described a t t h e beginning o f t h i s section.
as
We assume t h e s o l u t i o n t o b e o f
t h e form
$k = Re ($,(z) where b o t h gk(z)
exp[il(y
-
ct)]]
s i n kx
and t h e phase speed,
s a t i s f i e s t h e equation
c,
, a r e complex.
(10) The f u n c t i o n g k
4 56
s u b j e c t t o t h e f o l l o w i n g boundary c o n d i t i o n s : a t z = 0,
dz
The general s o l u t i o n o f equation (11) i s a sum o f h y p e r b o l i c s i n e and cosine, where t h e c o e f f i c i e n t s must be determined so as t o s a t i s f y t h e boundary c o n d i t i o n s (12)-(15).
The system o f l i n e a r equations f o r t h e determin-
a t i o n o f t h e c o e f f i c i e n t s i n t h e general s o l u t i o n i s homogenous; i n o r d e r t o o b t a i n a n o n t r i v i a l s o l u t i o n , t h e phase speed c must be such t h a t t h e d e t e r minant i s equal t o zero.
Therefore, c must s a t i s f y a q u a d r a t i c equation.
I n some parameter range, t h e phase speed has a nonzero imaginary p a r t ; t h e corresponding s o l u t i o n s describe unstable waves.
The c a l c u l a t i o n s r e p o r t e d
here were made by M. Pajuste. I n t h i s paper, we p r e s e n t o n l y t h e r e s u l t s f o r t h e one-layer case (hl
0).
(The s o l u t i o n s f o r t h e two-layer
cated.)
=
b u t more compli-
The phase speed i s given by
vs c =
case a r e s i m i l a r ,
+ Vb + c 0 2
--vs Y
vb [ ( V s
vs
-
Vb 2
t
{(
-
Vb)(coth y
+
co 2
1 1 - -1
-
co ( t a n h y
-
y ) I l +i
1(
,
where co i s the phase speed o f topographic waves w i t h o u t mean f l o w (co < 0 if
c1
> 0) and y = NrlH/f.
In general, t h e phase speed i s complex, c = c r
+ ic
i' The s o l u t i o n f o r
t h e stream f u n c t i o n , JI. i s
JI = Re((@, + iQi) e x p [ i l ( y - c r t ) ] ] s i n kx exp(1 cit) = I $I cos (Icy - c r t + e(z)]) s i n kx exp(1 tit),
457 where (Iand , Oi f u n c t i o n $(z),
a r e t h e r e a l and imaginary p a r t s o f t h e v e r t i c a l s t r u c t u r e
I $1
2 4 , and t h e z-dependent phase, e ( z ) , = ($, 2 + (I~)
i s given
by
I f t h e phase speed has a nonzero imaginary p a r t , ci
# 0, we a l s o have
Q i # 0; t h e waves a r e then unstable, and t h e i r amplitude increases w i t h t i m e as exp(1
tit).
The phase i s n o t constant v e r t i c a l l y , and t h e axes o f eddy-
l i k e p e r t u r b a t i o n s are i n c l i n e d w i t h re?pect t o t h e v e r t i c a l . The t w o - l a y e r model w i t h p = 0 contains, as p a r t i c u l a r cases, t h e model o f Tang (1975) (corresponding t o a = 0, Vb = O), and t h e b a r o c l i n i c i n s t a b i l i t y model o f Eady (1949) ( a = 0, Vb = 0, hl = 0). For t h e c a l c u l a t i o n s described h e r e a f t e r , we used t h e f o l 1owing param e t e r values:
2.5-10-2 s e c - l ;
H = 100 in,
hl
= 60 m, h2 = 40 m, N1 = lo-* sec-’,
f o r t h e one-layer case, we chose N = 1.25.10
2
sec-l.
N2
=
Since
t h e observed RDT anomalies were almost c i r c u l a r , o n l y waves f o r which Ax = A
Y
( o r k = 1) were s t u d i e d . The i n s t a b i l i t y r e g i o n f o r a = 0, h
1
= 0 i s independent o f t h e mean
d e r i v e d by Eady (1949).
(A > 2.6 f l Rd) a l l t h e waves are unstable, as Y The same r e s u l t holds f o r 01 = 0, hl # 0, b u t t h e
critical
equal
and f o r y < 2.399
flow,
values.
wavelength
is
to
44.5
km f o r t h e above-given
parameter
I f a > 0, t h e i n s t a b i l i t y r e g i o n depends on b o t h t h e wavelength and
t h e mean flow,
b u t waves a r e more unstable i f Vs
-
Vb > 0.
I n other words,
t h e s t a b i l i t y domain i s s m a l l e r when t h e d i r e c t i o n o f t h e upper l a y e r mean f l o w r e l a t i v e t o t h e bottom c u r r e n t i s opposed t o t h a t o f t h e phase speed o f t h e topographic waves. Two-folding times f o r t h e amplitudes o f t h e unstable waves are presented i n F i g u r e 11 as f u n c t i o n o f t h e wavelength A o f t h e mean c u r r e n t Vs and t w o - l a y e r
-
Vb.
f o r d i f f e r e n t shears Y’ For a = 0, t h e r e s u l t s obtained from t h e one-
models a r e close,
r e q u i r e s much g r e a t e r values of Vs model.
b u t f o r a = 5.10-4
-
t h e one-layer model
Vb f o r i n s t a b i l i t y than t h e two-layer
According t o t h e two-layer model, f o r a mean c u r r e n t d i f f e r e n c e o f
2.5 cm/sec between t h e s u r f a c e and bottom l a y e r s , t h e amplitude o f t h e most u n s t a b l e waves doubles i n 10 days. B a l t i c Sea. t o 5 Rd).
Both values are q u i t e r e a l i s t i c f o r t h e
These most u n s t a b l e waves correspond t o A ?? 50 t o 60 km (E 4 Y The dominating wavelength o f t h e RDT p e r t u r b a t i o n observed d u r i n g
surveys 1 8 / 1 and 18/2, estimated by t h e c o r r e l a t i o n f u n c t i o n , i s 80 t o 90 km; t h i s i s somewhat l a r g e r t h a n t h e scale o f t h e most unstable waves calcul a t e d from t h e b a r o c l i n i c i n s t a b i l i t y theory.
This d i f f e r e n c e , however, i s
4 58
I
a)
C)
(days) T2
241
I
16
i
8-
\. -.-.-.-.-.10.0
d)
Two-folding times (T2)
f o r the amplitudes o f t h e u n s t a b l e waves as
‘unctions o f t h e wavelength A Y’
The v a r i o u s curves correspond t o d i f f e r e n t
i g . 11.
,slues o f t h e mean v e l o c i t y shear
Vs
-
Vb.
Panels a and b show t h e r e s u l t s
t h e one-layer model, panels c and d those o f t h e t w o - l a y e r model. 4 lottom slope ci = 0 f o r panels a and c, and CY = 5.10 f o r b and d.
If
The
459
reasonably small, and we suggest t h a t t h i s RDT p e r t u r b a t i o n was generated by When t h e amplitude o f t h e wave reaches some c r i t i -
baroclinic instability. cal
value,
describe
t h e l i n e a r i z e d t h e o r y presented above ceases
the
further
development o f t h e waves:
growth p r e d i c t e d by (17)
t o be v a l i d t o
t h e i n f i n i t e amplitude
i s l i m i t e d by nonlinear,processes.
The data o f
survey 18/3 show t h e s p l i t t i n g o f a l a r g e and i n t e n s i v e eddy i n t o two s m a l l e r ones,
and t h a t i s one p l a u s i b l e mechanism which would l i m i t the
amp1 itude growth.
I t must be p o i n t e d o u t t h a t such quasi-geostrophic waves i n t h e presence o f shear mean f l o w a r e v e r y s e n s i t i v e t o parameter v a r i a t i o n s . i n c l i n a t i o n o f the v e r t i c a l
oceanic (Koshlyakov and Grachev, the theoretical
Some
a x i s o f p e eddy i s c h a r a c t e r i s t i c o f both 1973) and B a l t i c f i e l d observations, b u t
phase d i s t r i b u t i o n e(z)
v e r t i c a l g r a d i e n t s o f b o t h signs.
o f t h e unstable waves can have
I n the one-layer model, t h e amplitude
o f t h e unstable waves above a s l o p i n g bottom has maxima a t t h e surface and a t t h e bottom.
I n t h e two-layer
model,
( 0I
i s maximum a t t h e i n t e r f a c e
(upper boundary of t h e h a l o c l i n e ) , and t h e amplitude decreases more r a p i d l y towards t h e bottom than towards t h e surface. solutions
for
the
above-mentioned models.
For s t a b l e waves t h e r e are t w o I n the one-layer
model,
one
v e r t i c a l s t r u c t u r e f u n c t i o n $ ( z ) decreases monotonously w i t h depth, whereas t h e o t h e r increases.
For t h e two-layer model, b o t h $(z)
are very s i m i l a r ;
t h e y a r e maximum a t t h e i n t e r f a c e and decrease f a s t e r towards t h e bottom t h a n towards t h e s u r f a c e (as f o r t h e unstable waves o f t h i s model). The l i n e a r quasi-geostrophic f e r e n t f r o m t h a t o f t h e ocean.
regime o f t h e B a l t i c Sea i s somewhat d i f I n t h e B a l t i c , t h e e f f e c t o f t h e bottom
slope overwhelms t h e p l a n e t a r y p - e f f e c t i n t h e constant slope model, b u t the r o l e o f t h e Rossby deformation r a d i u s as determinator o f t y p i c a l h o r i z o n t a l scales i s common t o b o t h t h e B a l t i c and t h e oceanic cases.
The mean c u r r e n t
shear i n t r o d u c e s new types o f waves, b u t they a r e s t i l l i n f l u e n c e d by the s l o p i n g bottom.
It should be emphasized t h a t t h e assumption o f a constant
bottom slope i s a s i m p l i f i c a t i o n , l i s parameter,
and t h a t t h e r e a l bottom topography i s
t h i s i s i n c o n t r a s t t o t h e r e g u l a r v a r i a t i o n o f t h e Corio-
very i r r e g u l a r :
which dominates ocean dynamics.
The p e r t u r b a t i o n s o f t h e
bottom topography and o f t h e atmospheric f o r c i n g , which can be important c o n t r i b u t o r s t o t h e dynamics o f synoptic scale motions, a r e n o t considered here. ON THE ESTIMATION
OF ABSOLUTE VELOCITIES
The c l a s s i c a l dynamic method (Fomin,
1964) allows t h e c a l c u l a t i o n o f
r e l a t i v e geostrophic c u r r e n t s from d e n s i t y data.
For t h e determination o f
a b s o l u t e v e l o c i t i e s , i t i s necessary t o know t h e c u r r e n t a t some reference
460
l e v e l e i t h e r from d i r e c t measurements (McWilliams,
1976) o r as a r e s u l t o f
The o l d i d e a t h a t deep water v e l o c i t i e s are small does n o t f i t
speculation.
i n t o d a y ' s conceptions.
S c h o t t and Stommel (1978) proposed t h e b e t a - s p i r a l
method t o overcome t h e problem o f the r e f e r e n c e l e v e l v e l o c i t y f o r l a r g e scale currents.
T h i s method uses t h e geostrophic r e l a t i o n s t o g e t h e r w i t h
t h e l i n e a r equation o f v o r t i c i t y conservation on a p-plane and i t assumes the immiscibility o f the density s t r a t i f i c a t i o n . The s y n o p t i c eddies cannot be t r e a t e d by t h e p - s p i r a l method, b u t t h e g e n e r a l i z a t i o n proposed by Korotayev and Shapiro (1978) a l l o w s t h e c a l c u l a t i o n o f t h e a b s o l u t e v e l o c i t y o f n o n s t a t i o n a r y quasi-geostrophic c u r r e n t s and eddies.
I n t h i s s e c t i o n , we use t h e method o f Korotayev and s a p i r o
w i t h a s l i g h t l y d i f f e r e n t formulation.
We choose t o use d e n s i t y as t h e
v e r t i c a l coordinate, w i t h t h e hope t h a t these "Lagrangian" coordinates m i g h t l e a d t o b e t t e r v e r t i c a l r e s o l u t i o n than " E u l e r i a n " pressure coordinates f o r t h e case o f t h e v e r y sharp d e n s i t y l a y e r i n g observed i n t h e B a l t i c . For t h e v e r t i c a l d i s c r e t i z a t i o n , consider a m u l t i - l a y e r e d water column consisting o f N layers o f constant densities.
The p o t e n t i a l v o r t i c i t y con-
s e r v a t i o n equation, which holds f o r each l a y e r , has t h e form
where u k and vk are t h e v e l o c i t i e s , o f the k-th layer.
Decompose t h e
6,
t h e v o r t i c i t y , and hk t h e t h i c k n e s s
By d e f i n i t i o n ,
i n t o a reference
leve
value, denoted by an overbar, p l u s a value r e l a t i v e t o t h a t r e f e r e n c e
velocities
and t h e v o r t i c i t y
eve1
denoted by a prime, as f o l l o w s : Uk=
-u +
Vk=
i
u;(
+ v;(
, ,
t,=E+t;,. Note t h a t t h e reference l e v e l values a r e independent o f depth ( o r l a y er).
ti
I f t h e d a t a o f two r a p i d l y succeeding surveys a r e a v a i l a b l e , uk, v '
k'
and hk as w e l l as t h e i r t i m e and space d e r i v a t i v e s can be c a l c u l a t e d
u s i n g t h e geostrophic r e l a t i o n s f o r t h e v e l o c i t i e s and t h e d e f i n i t i o n o f relative vorticity. S u b s t i t u t i n g (19) can be o b t a i n e d
i n t o (18),
the f o l l o w i n g system o f l i n e a r equations
461
5
Xi + Fk = 0,
2 Aki i=l
where t h e Xi's
k = l,N
a r e f u n c t i o n s o f t h e unknown reference l e v e l values
and where t h e Aki's
and F k ' s depend o n l y on t h e r e l a t i v e values o f t h e
v a r i a b l e s (which a r e known from t h e observations):
I n order t o solve
(ZO), one must t a k e N 2 5.
c l u d e t h e s u r f a c e and/or
There i s no need t o i n -
bottom l a y e r s among t h e l a y e r s s e l e c t e d f o r t h e
s o l u t i o n o f t h e system. I f t h e o b s e r v a t i o n a l d a t a are w i t h o u t e r r o r s and (18) holds e x a c t l y ,
and i f N > 5, o n l y 5 equations a r e l i n e a r l y independent and t h e remaining (N
-
5)
equations a r e l i n e a r combinations o f t h e former.
because o f e r r o r s and s m a l l - s c a l e noise, (20)
I n practice,
i s overdetermined f o r N > 5,
and t h e s o l u t i o n can be found by a l e a s t squares method, i . e . by m i n i m i z i n g t h e sum N R =
2
5
t ( 2 Aki Xi k=l
+ Fk)
i=l
.
(23)
T h i s procedure i s f o l l o w e d a t every p o i n t x, y o f t h e d a t a g r i d . values o f
i,
and ag/ax,
&ay
The
are calculated separately despite the f a c t
Z9P
Fig.
12.
Estimated a b s o l u t e v e l o c i t i e s f o r t h e near-surface l a y e r ( l e f t )
and on t h e ut = 8.5 surface ( r i g h t ) f o r survey 18/1.
An arrow whose l e n g t h
equals t h e i n t e r p o l a t i o n s t e p corresponds t o a v e l o c i t y o f 10 cm/sec. t h a t t h e y a r e r e l a t e d through s p a t i a l d e r i v a t i v e s . enormously complicated
if
the horizontal
But t h e problem becomes
f i e l d s are g i v e n as numerical
t a b l e s and t h e equations solved f o r a l l p o i n t s simultaneously. For a t e s t o f t h e method, we chose t h e data o f surveys 1 8 / 1 and 18/2 f o r which t h e t i m e i n t e r v a l i s 9 days.
The pressure values as f u n c t i o n s o f
d e n s i t y were i n t e r p o l a t e d by optimal i n t e r p o l a t i o n t o a denser g r i d (spacing o f 0.25 at u n i t s ) and t h e values o f Aki
and Fk were c a l c u l a t e d .
The t i m e
d e r i v a t i v e s were c a l c u l a t e d by one-sided d i f f e r e n c e s and t h e space d e r i v a t i v e s by c e n t r a l d i f f e r e n c e s , t h e l a t t e r from t h e d a t a o f survey 18/1. The r e f e r e n c e l e v e l was chosen a t t h e surface, involved only intermediate layers w i t h
b u t t h e m i n i m i z a t i o n o f (23)
N = 8 t o 11.
The estimated a b s o l u t e v e l o c i t i e s a r e presented i n F i g u r e 12 f o r t h e s u r f a c e l a y e r and on t h e ut = 8.5 surface, which i s i n t h e middle o f t h e halocline.
The d i r e c t i o n s o f t h e v e l o c i t y v e c t o r s r e p l i c a t e t h e p a t t e r n o f
463 t h e RDT p e r t u r b a t i o n shown i n F i g u r e 6, c i e n t l y smooth.
However,
and the v e l o c i t y f i e l d i s s u f f i -
we t h i n k t h a t t h e magnitudes o f t h e reference
l e v e l (surface)
c u r r e n t s are underestimated,
should be weaker
or even reverse.
and t h a t t h e bottom c u r r e n t s
I n m i n i m i z i n g (23), t h e dominant t e r m s o f t h e system (20) were Ak4X4 and Ak5X5,
which represent t h e advection o f reference l e v e l v o r t i c i t y by t h e
r e l a t i v e velocity. a r e one order
The o t h e r terms o f (20),
o f magnitude s m a l l e r .
a f t e r l e a s t squares f i t t i n g ,
The same q u a l i t a t i v e
r e s u l t s were
o b t a i n e d by Korotayev and Shapiro (1978), b u t they estimated t h e absolute v e l o c i t y a t one l o c a t i o n only.
Our l a r g e r h o r i z o n t a l data s e t allows us t o
compare "independently" estimated values,. o f
The c o r r e l a t i o n between these values i s bad, v o r t i c i t y g r a d i e n t s being s y s t e m a t i c a l l y higher.
Hence,
we
are unable t o estimate t h e balance o f
terms i n t h e v o r t i c i t y c o n s e r v a t i o n equation and t o determine which t e r m s are t h e most i m p o r t a n t c o n t r i b u t o r s t o t h e dynamics o f synoptic s c a l e processes. Nevertheless, we t h i n k t h a t our attempt t o estimate absolute v e l o c i t i e s f o r s y n o p t i c s c a l e processes was p a r t i a l l y successful and t h a t t h e s h o r t comings a r e due t o t h e q u a l i t y o f t h e d a t a r a t h e r than t o t h e method.
The
data were n o t c o l l e c t e d w i t h t h e d i r e c t purpose o f e s t i m a t i n g t h e absolute v e l o c i t y , and t h e temporal and s p a t i a l r e s o l u t i o n s were probably n o t optimal f o r t h e c a l c u l a t i o n o f t h e high-order d e r i v a t i v e s which are necessary f o r t h e method. DISCUSSION AND CONCLUSIONS
First,
l e t us summarize t h e p u r e l y experimental r e s u l t s obtained from
t h e CTD surveys:
1)
t h a t t h e s t r a t i f i c a t i o n o f t h e B a l t i c Proper i s
It i s evident
d i s t u r b e d by low-frequency motions.
Such motions can be d i s t i n c t l y sepa-
r a t e d from s h o r t - t e r m v a r i a t i o n s ( w i t h p e r i o d s s h o r t e r than one day),
es-
p e c i a l l y i n the halocline.
2)
The most common s p a t i a l s t r u c t u r e o f t h e s y n o p t i c scale perturba-
t i o n s c o n s i s t s o f "mountains" and " v a l l e y s " o f isopycnal surfaces.
For many
p e r t u r b a t i o n s t h e geostrophic streamlines o f r e l a t i v e v e l o c i t y are closed, being nearly c i r c u l a r .
For t h a t reason we can consider them t o be eddies.
I n t h e most d i s t i n c t i v e eddies, perturbation.
t h e isopycnals r i s e i n t h e center o f t h e
464
3)
The t y p i c a l h o r i z o n t a l dimensions o f t h e eddies a r e o f t h e o r d e r
o f 2 t o 6 Rd (Rd E 1 0 km). the vertical.
4)
The eddy a x i s can be i n c l i n e d w i t h r e s p e c t t o
,
The usual d i r e c t i o n o f m i g r a t i o n o f t h e eddies i s along t h e aver-
aged isobaths w i t h shallower water on t h e r i g h t .
The t y p i c a l m i g r a t i o n
speed i s a few cm/sec. 5)
The v e r t i c a l s y n o p t i c s c a l e displacements o f t h e isopycnals can be
more than 20 m.
The r e l a t i v e c u r r e n t s i n t h e eddies can exceed 10 t o 1 5
cm/sec.
6)
The t y p i c a l l i f e t i m e o f t h e eddies i s more t h a n 10 days.
The
i n t e n s i f i c a t i o n o f an eddy was documented, as was t h e s p l i t t i n g o f a l a r g e and i n t e n s i v e eddy i n t o two s m a l l e r ones.
7)
In
The l a r g e and i n t e n s i v e eddies r e v e a l s i g n i f i c a n t t h e r m o c l i n i c i t y .
t h e i n t e r m e d i a t e l a y e r between the thermocl ine and t h e h a l o c l ine,
the
temperature d i s t r i b u t i o n on a f i x e d d e n s i t y s u r f a c e can have v a r i a t i o n s o f up t o 4 O C .
8)
The eddies and o t h e r s y n o p t i c s c a l e p e r t u r b a t i o n s t e n d t o have
l a r g e r dimensions along t h e averaged isobaths than along t h e bottom slope. The s t r e a m l i n e s o f r e l a t i v e c u r r e n t s can i n t e r s e c t t h e bottom contours where t h e depth decreases.
From the section e n t i t l e d "theoretical interpretation",
the following
p o i n t s can be made:
1)
The speed and t h e d i r e c t i o n o f m i g r a t i o n o f t h e eddies can be
e x p l a i n e d i n terms o f topographic waves.
Also,
t h e v e r t i c a l shears o f t h e
h o r i z o n t a l c u r r e n t s i n t h e thermocline and i n t h e h a l o c l i n e may correspond to
those
o f topographic waves.
The magnitude o f
the current
shear
is
g r e a t e r i n t h e h a l o c l i n e t h a n i n t h e thermocline, f o r topographic waves, and t h e shear has t h e same s i g n i n b o t h l a y e r s .
2)
I n t h e simple model o f b a r o c l i n i c i n s t a b i l i t y , t h e wavelengths o f
t h e most u n s t a b l e waves agree w e l l w i t h t h e dimensions o f t h e l a r g e r eddies.
A v e r t i c a l shear o f t h e mean f l o w o f t h e order o f a few cm/sec can produce reasonable growth r a t e s f o r unstable waves. t h a t t h e observed eddies can be generated
T h i s leads us t o t h e hypothesis by b a r o c l i n i c
instability o f
sheared mean flows. Comparing our r e s u l t s t o those o b t a i n d f o r t h e ocean, we note t h a t t h e nondimensional diameters o f t h e eddies ( w i t h Rd as t h e s c a l e u n i t ) a r e t h e same i n t h e B a l t i c and i n t h e ocean. a reduced model o f t h e ocean.
The B a l t i c Sea, however, i s n o t simply
The m i g r a t i o n and t h e e v o l u t i o n o f t h e eddies
a r e c o n t r o l l e d by t h e bottom topography r a t h e r t h a n by t h e p l a n e t a r y effect.
From a t h e o r e t i c a l p o i n t o f view,
p-
i t i s only f o r the barotropic
465
case t h a t t h e p - e f f e c t ( i n t h e ocean) can be simply replaced by the i n f l u ence o f t h e bottom slope ( i n t h e B a l t i c ) .
I n t h e s t r a t i f i e d water o f t h e
B a l t i c , t h e e f f e c t o f bottom topography completely dominates t h a t o f beta, and many o f t h e oceanic t h e o r e t i c a l r e s u l t s cannot be d i r e c t l y a p p l i e d t o t h e B a l t i c case.
The o t h e r c o m p l i c a t i o n i s t h a t , in,,contrast t o t h e r e g u l a r
v a r i a t i o n o f t h e C o r i o l i s parameter, t h e bottom topography i s very i r r e g u lar,
and t h e assumption o f a constant slope i s o n l y v a l i d i n a few cases.
Disturbances o f t h e bottom topography on a scale comparable t o t h a t o f t h e eddies can a l s o be important. The
limitations
of
the
experiments
d i d not allow t o
"oceanic" q u e s t i o n o f whether t h e eddies ,,are "closed-packed" Monin, 1978) o r s i n g u l a r (Nelepo and Korotayev, 1979).
answer
the
(Koshlyakov and
I n t h e l a t t e r paper,
t h e authors a s s e r t t h a t eddies are s i n g u l a r n o n l i n e a r phenomena, between which e x i s t s a background o f Rossby waves.
They show t h e o r e t i c a l l y t h a t t h e
n o n l i n e a r eddies m i g r a t e westwards l i k e Rossby waves. Woods (1980) d i s t i n g u i s h e s between wavelike motions t h a t r a d i a t e energy and momentum, and a d v e c t i v e - l i k e motions (eddies and f r o n t s ) t h a t t r a n s p o r t momentum and energy by advection o f water p a r t i c l e s .
A t t h e present time,
we a r e n o t a b l e t o c l a s s i f y t h e observed eddies ( d e f i n e d otherwise l i k e Woods) i n those terms. The c u r r e n t s i n t h e B a l t i c Sea are considered t o be m o s t l y wind-induced (Jansson, 1978).
With t h e h e l p o f a l i n e a r numerical model, Kielmann (1978)
shows t h a t f l u c t u a t i n g winds can generate topographic eddies.
The computa-
t i o n s o f Simons (1978), based on a n o n l i n e a r model, i n d i c a t e t h a t t h e eddies a r e n o t r e l a t e d i n a s t r a i g h t f o r w a r d manner t o t h e wind f o r c i n g .
Our obser-
v a t i o n s i n d i c a t e t h a t t h e storm which occurred between surveys 18/1 and 18/2 had no obvious i n f l u e n c e on t h e RDT p a t t e r n s . Numerous i n t e r e s t i n g phenomena were observed, not e n t i r e l y clear.
t h e nature o f which i s
From our p o i n t o f view, cooperative experiments such as
BOSEX i n 1977 should be u s e f u l t o complement t h e knowledge o f t h e dynamics
o f t h e B a l t i c Sea.
REFERENCES Aitsam, A. and Elken, J., 1980.
Results o f CTD surveys i n t h e BOSEX area o f
t h e B a l t i c Sea ( i n Russian).
In:
T o n k a y a ' s t r u k t u r a i sinopticheskaya
izmenchivost morei, T a l l i n n , pp. 19-23. Aitsam,
A.,
Elken.
J., Pavelson, J. and Talpsepp, L., 1981.
Preliminary
r e s u l t s o f the investigation o f spatial-temporal characteristics o f the B a l t i c Sea s y n o p t i c v a r i a b i l i t y .
In:
The I n v e s t i g a t i o n and M o d e l l i n g
o f Processes i n t h e B a l t i c Sea, P a r t I,pp. 70-98.
466
Aitsam,
A.,
and Talpsepp,
synoptic
scale
Russian).
In:
L.,
1980.
currents
in
Investigation o f the v a r i a b i l i t y o f
the
Central
Baltic
in
1977-1980
(in
Tonkaya s t r u k t u r a i sinopticheskaya izmenchivost morei,
T a l l i n n , pp. 14-18. B r e t h e r t o n , F.P.,
Davis, R.E.
and Fandry, C.B.,
A technique f o r ob-
1976.
j e c t i v e a n a l y s i s and design o f oceanographic experiments a p p l i e d t o
MODE-73. Eady, E . T . , Fomin, L.M.,
23:
Deep-sea Research,
1949.
559-582.
Long waves and cyclone waves.
1964.
Tellus,
The dynamic method i n oceanography.
3:
33-52.
Elsevier Scientific
P u b l i s h i n g Company, 212 pp. Gandin,
1965.
L.S.,
Objective analysis o f meteorological f i e l d s .
'Israel
Program f o r S c i e n t i f i c T r a n s l a t i o n s , Jerusalem. Jansson, 6.-O., sea.
1978.
In:
-
The B a l t i c
a system a n a l y s i s o f a semi-enclosed
Advances i n Oceanography, Plenum P u b l i s h i n g Corporation, pp.
131-183. Keunecke,
and Magaard,
K.-H.,
L.,
1974.
Measurements by means o f towed
t h e r m i s t o r cables and problems o f t h e i r i n t e r p r e t a t i o n w i t h r e s p e c t t o mesoscale processes.
6:
Liege,
Memoires de l a Societe Royale des Sciences de
147-160.
Kielmann, J., 1978.
Mesoscale eddies i n t h e B a l t i c .
Proc. o f t h e X I
In:
Conference o f B a l t i c Oceanographers, Rostock, pp. 729-755. H o l t r o f f , J. and Reimer, U.,
Kielmann, J.,
B e r . I n s t . Meeresk. K i e l , Kielmann, J., Krauss, W.
26:
1976.
Data r e p o r t B a l t i c '75.
23.
and Keunecke, K.-H.,
1973.
Currents and s t r a t i f i -
c a t i o n i n t h e B e l t Sea and Arcona Basin d u r i n g 1962-1968. Meeresforschungen, Korotayev,
G.K.
Kieler
2: 90-111.
and Shapiro,
N.B.,
1978.
On t h e c a l c u l a t i o n o f absolute
v e l o c i t y o f geostrophic c u r r e n t s from t h e data o f s y n o p t i c surveys ( i n Russian).
In:
Eksperimentalnye
gramme "POLYMODE", Sevastopol Koshlayakov, M.N.,
Galerkin, L.I.
issledovaniya
PO
mezhdunarodnoi p r o -
, pp. 83-95. and Truong D i n Hien, 1970.
s t r u c t u r e o f t h e open ocean geostrophic c u r r e n t s .
On t h e meso-
Okeanologiya, & I :
805-814. Koshlayakov, M.N. physical
and Grachev, Y.M.,
1973.
polygon i n t h e T r o p i c a l
Mesoscale c u r r e n t s a t a hydro-
Atlantic.
Deep-sea
Research,
0:
507-526. Koshlayakov,
M.N.
and Monin,
A.S.,
Ann. Rev. E a r t h Planet. S c i . ,
6:
1978. 495-523.
Synoptic eddies i n t h e ocean.
467
Laanemets,
J.
and L i l o v e r ,
M.-J.,
1981.
The data processing scheme o f
measurements w i t h t h e N e i l Brown Mark 111 CTD. and M o d e l l i n g o f
Processes i n t h e B a l t i c Sea,
In:
The I n v e s t i g a t i o n
P a r t I, T a l l i n n ,
pp.
10-19. McWill iams, J. C. , 1976.
Maps f r o m t h e Mid-Ocean Dynamics Experiment: P a r t
I, Geostrophic Streamfunction. and F l i e r l , G.R.,
McWilliams, J.C.
1976.
analyses o f MODE a r r a y data. The MODE Group,
1978.
3.
Phys.
Oceanogr.
5(6):
810-827.
Optimal, quasi-geostrophic waves
Deep-sea Research,
23:
285-300.
The Mid-Ocean Dynamics Experiment.
Deep Sea Re-
2: 859-910.
search, Nelepo, B . A .
and Korotayev, G . K . ,
1979. ,,,The s t r u c t u r e o f s y n o p t i c a l v a r i -
a b i l i t y from t h e d a t a on h y d r o l o g i c a l surveys i n t h e POLYMODE observational
area ( i n Russian).
Morskie g i d r o f i z i c h e s k i e issledovanya,
3:
3-20. Nikitin,
O.P.
K.G.,
and Vinogradova,
1980.
Separation o f t h e synoptic
component o f temperature f i e l d from XBT-survey data and some appl i c a tions.
Ocean M o d e l l i n g (unpublished manuscript).
Rhines, P.,
1970.
fied fluid. Rhines, P . ,
Edge-, bottom-,
1977.
Interscience, Schott,
6:
T. J . ,
1978.
3:
Sustavov, J.V.,
In:
The Sea, Wiley-
189-318.
F. and Stommel, H., 1978.
Tellus,
1: 273-302.
The dynamics o f unsteady c u r r e n t s .
d i f f e r e n t oceans. Simons,
and Rossby waves i n a r o t a t i n g , s t r a t i -
Geophysical F l u i d Dynamics,
Beta s p i r a l s and absolute v e l o c i t i e s i n
Deep-sea Research, Wind-driven
2: 961-1010.
c i r c u l a t i o n s i n t h e southwest B a l t i c .
272-283.
E.S.
Chernyshova,
and Michaylov, A . E . ,
t i c eddy genesis i n t h e B a l t i c Sea.
In:
1978.
On t h e synop-
Proc. o f t h e X I Conference o f
B a l t i c Oceanographers, Rostock, pp. 795-805. Tang, C.M.,
1975.
B a r o c l i n i c i n s t a b i l i t y o f s t r a t i f i e d shear flows i n t h e
ocean and atmosphere. Woods, J.D.,
1979.
J. Geophys. Res.,
80: 1168-1175.
M o d e l l i n g oceanic t r a n s p o r t i n s t u d i e s o f c l i m a t e r e -
sponse t o p o l l u t i o n .
In:
Man's Impact on Climate, E l s e v i e r S c i e n t i f i c
P u b l i s h i n g Company, pp. 99-107. Woods, J.D., ture, Woods, J.D.
1980.
288:
Do waves l i m i t t u r b u l e n t d i f f u s i o n i n t h e ocean?
and M i n n e t t , P.J.,
1979.
Analysis o f mesoscale t h e r m o c l i n i c i t y
w i t h an example from t h e t r o p i c a l thermocline d u r i n g GATE. Research,
Na-
219-224.
3: 85-96.
Deep-sea
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469
SYNOPTIC VARIABILITY OF CURRENTS I N THE BALTIC PROPER
A. Aitsam, L . Talpsepp I n s t i t u t e o f Thermophysics and Electrophysics Academy o f Sciences o f t h e Estonian S . S . R . INTRODUCTION The discovery o f s y n o p t i c scale v a r i a b i l i t y i s one o f t h e r e s u l t s o f several experiments conducted i n d i f f e r e n t p a r t s o f t h e World Ocean d u r i n g t h e l a s t two decades. Rossby waves,
Phenomena o f synoptic scale i n c l u d e open sea eddies,
topographic waves and topographic Rossby waves, b a r o c l i n i c
i n s t a b i l i t i e s o f l a r g e s c a l e motion o f t h e ocean, e t c . gations
show t h a t
topography,
the latitude,
Theoretical i n v e s t i -
t h e atmospheric c o n d i t i o n s ,
t h e s t r a t i f i c a t i o n o f the water,
t h e bottom
and t h e character o f l a r g e
s c a l e motion are o f c r u c i a l importance i n determining t h e forms and scales o f s y n o p t i c v a r i a b i l i t y , and must be i n v o l v e d i n t h e o r e t i c a l models. I n view o f t h e importance o f synoptic v a r i a b i l i t y i n t h e energetics o f t h e ocean, several e x p e d i t i o n s f o r t h e study o f t h e v a r i a b l i t y a t t h e corresponding scale were c a r r i e d o u t i n t h e B a l t i c Sea.
Given t h e c h a r a c t e r i s t i c
scale, t h e study o f t h e B a l t i c i s r e l a t i v e l y l e s s expansive than t h a t o f the ocean.
As f a r as t h e B a l t i c Sea can be regarded as a model o f t h e ocean, i t
i s reasonable t o study t h e aforementioned processes i n t h a t model.
However,
t h e i d e n t i f i c a t i o n o f d i f f e r e n t phenomena i s n o t simple because t h e bottom topography, t h e b a s i n geometry, and t h e s t r a t i f i c a t i o n o f t h e B a l t i c Sea are complicated.
A t t h e I n s t i t u t e o f Thermophysics and E l e c t r o p h y s i c s , Academy
o f Sciences o f t h e Estonian S.S.R.,
experimental s t u d i e s o f synoptic v a r i -
a b i l i t y have been made s i n c e 1977, and experiments u s i n g autonomous mooring s t a t i o n s w i t h r e c o r d i n g c u r r e n t meters were c a r r i e d o u t i n 1977, 1979 and 1980.
I n t h i s paper, we describe t h e r e s u l t s o f these experiments.
During
t h e same experiments, some temperature and s a l i n i t y mappings were a l s o made i n c e r t a i n regions o f t h e B a l t i c Sea:
t h e r e s u l t s o f these d e n s i t y mappings
a r e discussed i n a p r e v i o u s paper (Aitsam e t a l . , 1980).
We a l s o note t h a t
t h e r e s u l t s o f t h e experiments w i t h r e c o r d i n g c u r r e n t meters were d i f f e r e n t i n d i f f e r e n t years and i n t h e f o l l o w i n g these r e s u l t s w i l l have d i f f e r e n t interpretations. MEASUREMENTS The d i r e c t measurement o f c u r r e n t s u s i n g autonomous mooring s t a t i o n s i s one o f t h e most r e l i a b l e methods f o r s t u d y i n g synoptic scale processes.
470
Measurements o f c u r r e n t v e l o c i t i e s and temperature u s i n g autonomous mooring s t a t i o n s w i t h r e c o r d i n g c u r r e n t meters were c a r r i e d o u t i n t h e open p a r t o f t h e B a l t i c Sea i n 1977, 1979 and 1980.
The most i m p o r t a n t character-
i s t i c s o f t h e experiments a r e g i v e n i n Table 1. TABLE 1 The open sea experiments w i t h autonomous mooring s t a t i o n s (AMS) i n 1977-1980 1977
1979
1980
4
2- 6
2- 3
20 September 20 m i l e s
35 May-June 10 m i l e s
Number o f AMS Number o f l e v e l s i n AMS d u r a t i o n (days) t i m e o f year separation distance
102 May-August 10 km
I n 1977 t w o mooring s t a t i o n s l o c a t e d 20 m i l e s a p a r t w e r e i n s t a l l e d as p a r t o f t h e i n t e r n a t i o n a l BOSEX experiment. made a t f o u r depths d u r i n g 20 days.
A t b o t h s t a t i o n s measurements were
Aanderaa instruments were used.
In
1979, 5 autonomous mooring s t a t i o n s w i t h one measuring i n s t r u m e n t i n t h e surface
l a y e r and one i n t h e bottom l a y e r were i n s t a l l e d .
Six current
meters were i n s t a l l e d a t t h e c e n t r a l s t a t i o n o f t h e area i n order t o study t h e v e r t i c a l d i s t r i b u t i o n o f k i n e t i c energy. ments were used. days.
Both VACM and Aanderaa i n s t r u -
The experiment t o o k p l a c e i n May-June and l a s t e d f o r 36
I n 1980, s i x mooring s t a t i o n s w i t h instruments a t depths o f 45 and 80
meters were i n s t a l l e d f o r 102 days.
One s t a t i o n w i t h two measuring i n s t r u -
ments was l o s t and one c u r r e n t meter d i d n o t work. F i g u r e 1 shows t h e bottom topography o f t h e s i t e o f t h e 1980 e x p e r i ment.
The mooring s t a t i o n s a r e deployed i n a c r o s s l i k e p a t t e r n .
The loca-
t i o n o f t h e mooring s t a t i o n s o f t h e 1979 experiment i s s l i g h t l y northward o f this site.
The s t a t i o n N o f 1977 i s l o c a t e d a t t h e same slope.
Three
c h a r a c t e r i s t i c s e c t i o n s o f t h e bottom topography are presented i n F i g u r e 2; t h e d i s t a n c e between these s e c t i o n s i s 10 km. RESULTS OF THE 1977 EXPERIMENT I n t h i s s e c t i o n , we p r e s e n t and discuss t h e r e s u l t s o f t h e c u r r e n t measurements made i n 1977.
The k i n e t i c energies measured a t s t a t i o n N and E
a r e presented i n Table 2.
The mean v e l o c i t i e s over t h e measuring p e r i o d ,
denoted
and
i,
and t h e t o t a l k i n e t i c energy o f t h e f l u c t u a t i o n s , K , a r e
471
F i g u r e 1. Bottom topography a t t h e s i t e o f t h e 1980 experiment.
10
F i g u r e 2.
20
C h a r a c t e r i s t i c s e c t i o n s o f t h e bottom topography.
km
472
TABLE 2 The v e r t i c a l d i s t r i b u t i o n o f k i n e t i c energy a t s t a t i o n s N and E o f t h e "BOSEX 77" area. Station
depth (m)
u
(cm/sec)
(cm/sec)
K (cm2/sec2)
KE (cm2/sec 2 )
N
20 30 105 118
-0.34 -0.52 -0.09 0.61
-0.71 0.47 -0.15 1.44
248 231 63 80
35 29 10 23
E
80 40 108 121
0.50 1.71 2.45 2.29
1.71 2.69 6.12 4.82
138 64 52 50
35 12 .39 22
given.
The q u a n t i t y KE w i l l be described l a t e r .
i c energy K increases w i t h depth a t s t a t i o n N.
We can see t h a t t h e k i n e t -
A t s t a t i o n E, where t h e
bottom i s f l a t , t h e k i n e t i c energy does n o t increase w i t h depth.
The l a t t e r
o b s e r v a t i o n suggests t h a t t h e k i n e t i c energy increase i s r e l a t e d t o t h e bottom topography.
We b e l i e v e t h a t t h e increase o f k i n e t i c energy agrees
w e l l w i t h t h e t h e o r y o f bottom-trapped topographic waves developed by Rhines (1970)
f o r an i n f i n i t e basin.
The governing equations f o r t h e h o r i z o n t a l
stream f u n c t i o n P a r e as f o l l o w s :
-dP_ - o dz
a t z = 0,
where a l i n e a r wave o f t h e f o r m e x p ( i ( k x + ky - w t ) i s assumed, ct denotes 2 t h e bottom slope, f t h e C o r i o l i s parameter, N t h e V a i s a l a frequency, and z t h e v e r t i c a l coordinate,
d i r e c t e d upwards w i t h i t s o r i g i n a t t h e sea sur-
f ace, For t h e case N = constant, t h i s equation y i e l d s t h e f o l l o w i n g s o l u t i o n :
P = Po cosh ( 0 N z / f ) ; where s i n 0 = k/q;
the dispersion r e l a t i o n i s w =
-ctN
s i n e c o t h (q NH/f),
f o r r e l a t i v e l y s h o r t waves and s t r o n g s t r a t i f i c a t i o n .
t h i s r e l a t i o n becomes w = ct N sine.
The assumption o f c o n s t a n t N i s based
on t h e s t r a t i f i c a t i o n c h a r a c t e r i s t i c o f t h i s r e g i o n d u r i n g September 1977 (Fig.
3).
The h o r i z o n t a l stream f u n c t i o n P i n d i c a t e s an increase i n t h e
v e l o c i t y components w i t h depth.
Thus, on t h e b a s i s o f Table 2, t h e t h e o r e t -
473
F i g u r e 3.
C h a r a c t e r i s t i c v e r t i c a l p r o f i l e s o f temperature ( T ) , s a l i n i t y
(S).
and r e l a t i v e d e n s i t y (0) d u r i n g BOSEX a t s t a t i o n N o f t h e 1977 experiment.
15 cml s
0
-15 5.70 OC
5101
F i g u r e 4.
400h r s
1
Time s e r i e s o f t h e e a s t e r n v e l o c i t y component and o f t h e tempera-
t u r e a t a depth o f 118 m a t s t a t i o n N.
414
i c a l r e s u l t s are supported by t h e observed k i n e t i c energy d i s t r i b u t i o n , as i n t h e study o f Thompson and Luyten (1977).
We t h i n k t h a t , although t h e v e r t i c a l d i s t r i b u t i o n o f t h e t o t a l k i n e t i c energy demonstrates t h e presence o f bottom-trapped waves, s t r o n g e r evidence i s p r o v i d e d by t h e d i s t r i b u t i o n o f t h e q u a n t i t y KE which c h a r a c t e r i z e s t h e energy o f o s c i l l a t i o n s w i t h p e r i o d s from one t o s i x days. t h e k i n e t i c energy increases w i t h depth due t o KE.
We can see t h a t
The preceding t h e o r e t i -
c a l c a l c u l a t i o n s show t h a t t h e p e r i o d s o f t h e topographic waves f a l l w i t h i n this interval.
As mentioned above, s t a t i o n E i s s i t u a t e d a t a d i s t a n c e o f
about 35 km from t h e r e g i o n o f rough bottom slope.
Since t h e k i n e t i c energy
K does n o t increase w i t h depth a t s t a t i o n E and t h e r e i s no o t h e r evi,dence f o r l o w frequency o s c i l l a t i o n s , i t seems l i k e l y t h a t o s c i l l a t i o n s observed a t s t a t i o n N do n o t propagate t h a t f a r .
The absence o f low frequency o s c i l -
l a t i o n s a t s t a t i o n E seems t o support t h e i d e a o f bottom-induced waves. Only r e s u l t s o f s t a t i o n N w i l l be discussed h e r e a f t e r . F i g u r e 4 shows t h e v a r i a t i o n o f t h e eastern component o f t h e v e l o c i t y and t h a t o f t h e temperature d u r i n g t h e f i r s t 400 hours.
The same data a f t e r
removal o f t h e h i g h frequency o s c i l l a t i o n s are shown i n F i g u r e 5, where t h e dominant p e r i o d s are much more v i s i b l e .
These p e r i o d s a r e a l s o apparent i n
t h e temperature s e r i e s as t h e c u r r e n t d i r e c t e d upslope upwells warmer water. The h i g h e s t temperature occurs a t the t i m e when t h e upslope c u r r e n t changes i t s sign.
The same s e r i e s a t t h e 105 m l e v e l a r e shown i n F i g u r e 6.
It
should a l s o be noted t h a t t h e coherence between temperature and upslope current
i s s t r o n g e s t a t frequencies corresponding t o topographic waves.
Using a l e a s t squares method, t h e dominant p e r i o d s a r e found t o be equal t o
68 and 44 hours. Using t h e k i n e t i c energy d i s t r i b u t i o n o b t a i n e d from s p e c t r a l c a l c u l a t i o n s and t h e Rhines model o f topographic waves, t h e o r e t i c a l wavelengths are found equal t o 12-14 km a t those frequencies. t o check t h i s t h e o r e t i c a l r e s u l t .
We have no experimental data
I n o r d e r t o determine t h e wave o r i e n t a -
t i o n , we have t o f i n d t h e angle $ o f c o o r d i n a t e system r o t a t i o n such t h a t t h e coherence between components i n t h e new system i s minimal.
Minimizing
t h e coherence we o b t a i n t h e formula
t a n 2Jll = \ s"u
puv
-
svv
where Suu and Svv a r e t h e s p e c t r a l d e n s i t i e s o f t h e v e l o c i t y components, and
Puv i s t h e cospectrum.
The o r i e n t a t i o n and energy o f waves a r e character-
i z e d by energy e l l i p s e s , where t h e angle $ i s obtained from (l), and t h e axes o f t h e e l l i p s e s are t h e eigenvalues o f t h e m a t r i x
475
0
-5
5.65
'c
5.35 350
F i g u r e 5.
hrs
Same as F i g . 4 a f t e r removal o f t h e high frequency o s c i l l a t i o n s .
10
cm/s
0 -5
F i g u r e 6.
Same as F i g . 5 as t h e 105 m l e v e l o f s t a t i o n
N.
416
The l e n g t h o f t h e axes o f t h e e l l i p s e s gauges t h e s p e c t r a l d e n s i t y o f t h e v e l o c i t y components i n t h e new coordinate system.
I n F i g u r e 7 we see t h a t
t h e waves propagate along t h e slope, and t h a t t h e r e i s more energy a t t h e aforementioned dominant periods.
DESCRIPTION OF THE DATA OBTAINED DURING THE 1979 AND 1980 EXPERIMENTS I n t h e May-June 1979 data,
f i n d no evidence o f t h e presence o f
we
bottom-trapped topographic waves i n t h e same r e g i o n .
For instance, t h e r e i s
no increase o f t h e k i n e t i c energy o f t h e f l u c t u a t i o n s i n t h e bottom l a y e r . The s p e c t r a l a n a l y s i s shows t h a t t h e r e i s considerably l e s s energy i n t h e synoptic i n t e r v a l as compared t o t h e data o f t h e 1977 o r 1980 experiments. F i g u r e 8 shows a s e r i e s o f maps o f d a i l y mean c u r r e n t s a t a depth o f 15 meters above t h e bottom. cm/s.
D a i l y mean v e l o c i t i e s a r e o f t h e order o f 2-5
On t h e whole t h e p i c t u r e i s n o t simple, although eddy l i k e c u r r e n t s
can be observed a t t h e end o f t h e experiment p e r i o d . (Fig.
The v e c t o r diagrams
9) f o r t h e surface l a y e r a t s t a t i o n s SW, NW are s i m i l a r t o t h e d i a -
grams o b t a i n e d a f t e r a 30 km eddy has extended t o t h e n o r t h a t t h e r a t e o f 2-3 cm/s.
I t should be mentioned t h a t i n e r t i a l o s c i l l a t i o n s w i t h p e r i o d s o f
about 13.8 hours dominate t h e water motion, having amplitudes o f up t o 15 cm/sec which vary i n space and i n time.
PERIOD Bdays
N
\
L 2 2.7 2
1.6
1.14
I 0.88 F i g u r e 7.
c-=
# #
Energy e l l i p s e s a t t h e 118 m l e v e l o f s t a t i o n N.
411
1’
-
/’
I/ I
3
,
\
f/ 3
-
t 15
16
/
f f ’
C f 19
\
N /
22 J
21
ti 27
a
F i g u r e 8.
-
f
rt %
28
/
47
31
f
\ ----c
d
c-
33
34
Maps of d a i l y mean c u r r e n t s i n t h e bottom l a y e r i n 1979.
478
Scale unit 3 km
l
i
r
Station NW
Scale unit 2 km
Figure 9. Vector diagrams of daily mean currents a t the s i t e o f the 1979 experiment.
419 A t t h a t t i m e (May-June 1979), s t i l l weather was p r e v a i l i n g over t h e B a l t i c Sea.
I t has been more than once hypothesized t h a t t h e atmosphere may
be t h e source o f energy f o r topographic waves.
the l o w level o f
Thus,
energy o f t h e s y n o p t i c s c a l e v a r i a b i l i t y f o r t h a t year can be explained by t h e absence o f t h e energy t r a n s f e r from t h e atmosphere.
A l s o , t h e bottom
topography o f t h e experimental s i t e i s q u i t e complicated, thus demanding a complicated model. The r e s u l t s o f t h e 1980 experiment show a s l i g h t l y d i f f e r e n t s i t u a t i o n i n t h e area.
There a r e l a r g e f l u c t u a t i o n s w i t h p e r i o d s o f s i x t o n i n e days
i n t h e v e l o c i t y components.
Figures 10 and 11 show the v a r i a t i o n o f d a i l y
mean v e l o c i t i e s a t s t a t i o n s
B and C, r e S p e c t i v e l y , d u r i n g 102 days.
frequency o s c i l l a t i o n s can be n o t i c e d i n those time series. t h a t such p e r i o d s a l s o e x i s t i n temperature records.
Low
Figure 1 2 shows
Note t h a t t h e tempera-
t u r e f l u c t u a t i o n s are s l i g h l y damped a t t h e end o f t h e experiment. The s p e c t r a o f t h e v e l o c i t y components have peaks approximately w i t h i n t h e range o f 6-8 days. S(u)
Figures 13 and 14 show t h e s p e c t r a l f u n c t i o n u
o f t h e v e l o c i t y components a t s t a t i o n s E and C.
i n e r t i a l frequency and a t 6-7 days.
-
There are peaks a t t h e
I n these p l o t s , t h e t o t a l energy i s
p r o p o r t i o n a l t o t h e area under t h e curve.
Peaks a t 6-8 days are apparent i n
a l l t h e measurements. Figure
15 shows t h e v e c t o r s
Aanderaa RCM-4 c u r r e n t meters. can be observed.
o f d a i l y mean c u r r e n t s obtained w i t h
Low frequency v a r i a b i l i t y o f t h e c u r r e n t s
F i g u r e 1 6 d i s p l a y s t h e t i m e sequence o f d a i l y mean cur-
r e n t s i n t h e bottom l a y e r o f t h e experiment area.
Eddylike c u r r e n t s can be
seen a t v a r i o u s times. D u r i n g t h e 1980 experiment, t h e mean v e l o c i t y a t s t a t i o n s B and C (Figu r e 17) i s d i r e c t e d along t h e channel. south-south-east
The v e l o c i t y i s d i r e c t e d t o t h e
d u r i n g t h e f i r s t 70 days and i n t h e opposite d i r e c t i o n
d u r i n g t h e l a s t month.
The s t r a t i f i c a t i o n shown i n F i g u r e 18 i s representa-
t i v e o f t h e whole d a t a s e t .
MODEL OF BAROCLINIC INSTABILITY I n t h i s s e c t i o n , we consider t h e q u e s t i o n o f whether b a r o c l i n i c i n s t a b i l i t y can be t h e reason f o r t h e observed v a r i a b i l i t y .
I n view o f t h e ob-
s t a b i l i t y w i l l be i n v e s t i g a t e d using a two-layer
served
stratification,
model.
L e t us consider a channel extending i n t h e y - d i r e c t i o n w i t h bottom
s l o p i n g i n t h e x - d i r e c t i o n , and l e t us assume t h a t mean c u r r e n t s are present
i n both layers.
Using t h e s u b s c r i p t i = 1,2 t o i d e n t i f y t h e upper and lower
l a y e r r e s p e c t i v e l y , and denoting by
480
15 m/s .
-15
( 102 days
1
i
15
cm/s
x -component
'.
y - component (102 days
1
-15 Figure 10.
Time series of the v e l o c i t y components a t s t a t i o n B o f the 1980
experi rnent.
-151 Figure 11.
Time series o f the v e l o c i t y components a t s t a t i o n C.
481
B
F i g u r e 12.
D a i l y mean temperatures a t various s t a t i o n s o f t h e 1980 experi-
ment.
5 .O6 l
w . s(4
x -component
cm2 sec-day
cm2 sec.day
10days
F i g u r e 13.
The s p e c t r a l f u n c t i o n w
c i t y components a t s t a t i o n
-
E i n 1980.
S(w) o f t h e e a s t e r n and northern velo-
1 13.8hrs
482
1.43~107
1odays
F i g u r e 14.
The s p e c t r a l f u n c t i o n w
6
1
S(u) o f t h e e a s t e r n and n o r t h e r n velo-
c i t y components a t s t a t i o n C i n 1980.
F i g u r e 15.
V e l o c i t y v e c t o r s a t v a r i o u s s t a t i o n s o f t h e 1980 experiment.
483
t h e mean nondimensional v e l o c i t i e s along t h e channel,
Vi Hi
t h e mean l a y e r thicknesses,
pi
the densities,
qi
t h e wavelike p e r t u r b a t i o n s propagating i n t h e y - d i r e c t i o n ($,
include
1, t h e m u l t i p l i c a t o r ei('y-Lut) a c h a r a c t e r i s t i c v e l o c i t y i n t h e upper l a y e r ,
U g
t h e a c c e l e r a t i o n due t o g r a v i t y ,
CI
t h e bottom slope,
f
t h e C o r i o l i s parameter, and
L
a length scale c h a r a c t e r i s t i c o f the perturbation,
t h e equations o f t h e model are:
where 2 2 F1 = f L /g'H1,
2 2 F2 = f L /g'H2,
T = afL/H2u, A = axx + g ' = g(P2
-
a
YY'
fpP2.
T h i s model i s d e r i v e d from an o r d i n a r y quasi-geostrophic system, where t h e stream f u n c t i o n s JI1,
J12
are assumed o f t h e form
L e t us now consider t h e d i s p e r s i o n curves obtained from t h e model.
Two
s o l u t i o n s f o r t h e f i r s t mode a r e presented i n F i g u r e 19 ( f o r seven groups o f parameters).
I n t h i s f i g u r e , t h e wavelength ( i n km) i s measured along t h e
abscissa, and t h e p e r i o d ( i n days) along t h e o r d i n a t e . two s o l u t i o n s c o i n c i d e , t h e waves become unstable.
A t wavelengths where
The doubling time D o f
t h e amplitudes o f t h e u n s t a b l e waves i s shown i n t h e same f i g u r e .
Thus, i n
F i g u r e 19a ( t h e parameter values a r e given i n 'the f i g u r e caption, where Ap = p2
-
p1 denotes t h e d e n s i t y jump) unstable waves appear a t wavelengths o f
about 30-35 km and they have p e r i o d s o f 7-8 days. dependence of i n s t a b i l i t y on parameter changes. jump has been changed.
We can a l s o study t h e
I n F i g u r e 19b t h e d e n s i t y
I t appears t h a t when t h e d e n s i t y jump i s increased,
waves become u n s t a b l e a t s h o r t e r wavelengths and t h e doubling time o f t h e i r amplitude i s increased.
484
Figure 16.
10 cm/s
Maps of daily mean currents i n the bottom layer i n 1980.
485
C station
B station
i
Figure 17. 1980.
7 H = 82m
Vector diagrams of daily mean currents at stations B and C in
Salinity
0
15.1
Press
100
0;0,o
Temperature, SigmaT; N
15.0,15.0,0.1
Figure 18. Characteristic vertical profiles of temperature (T), salinity (S), relative density ( D ) , and Vaisala frequency (N) during the 1980 experiment.
486
25
F i g u r e 19.
45km
‘ 0’5
45 km
25
D i s p e r s i o n curves and d o u b l i n g t i m e
(D) o f t h e amplitudes o f
u n s t a b l e waves i n t h e two-layer model f o r t h e f o l l o w i n g values o f t h e parameters: 0.003, cm/sec-’;
(a) V1 = - 5 cm/sec-’, a = 0.001;
V2 = 2.5 cm/sec-’,
(b) Ap = 0.002;
(d) continuous l i n e :
CI
H1
=
70 in, H2 = 30 m , Ap =
(c) a = 0.0015, V1 = -10 cm/sec-’,
V2 = 5 = 0.0015, H1 = 60 m, H2 = 40 m; dashed l i n e
: a = 0.0015, H1 = 40 m, H2 = 60 rn; (e) CI = 0.0005, V1 = -3.5 cm/sec-’, V = 0, H1 = 60 rn, H2 = 40 rn; (f) a = 0.0015, V1 = 5 cm/sec-l, V2 = -3.5 cm/sec2 - 1 .
Note:
parameters n o t e x p l i c i t e l y given f o r cases ( b ) - ( f )
a r e as i n case (a).
487
15 cm/s
(102 days)
x-component
15 cm/s
-1 5
F i g u r e 20.
Time s e r i e s o f t h e n o r t h e r n v e l o c i t y component a t s t a t i o n E i n
1980.
If t h e bottom slope i s decreased, t h e amplitude o f unstable waves doub l e s more longer.
rapidly,
their
wavelengths
become s h o r t e r
and t h e i r periods
On t h e c o n t r a r y , an i n c r e a s e i n t h e mean v e l o c i t i e s shortens b o t h
t h e l e n g t h s and t h e p e r i o d s o f unstable waves,
and t h e amplitudes o f un-
s t a b l e waves double much more r a p i d l y (Fig. 19c). F i g u r e 19d shows how a change i n t h e thickness o f t h e upper and lower l a y e r s a l t e r s t h e parameters o f unstable waves.
Figure 19e demonstrates
t h a t b a r o c l i n i c i n s t a b i l i t y may occur when t h e r e i s no mean c u r r e n t i n t h e bottom l a y e r .
I n a l l t h e cases discussed so f a r , t h e mean c u r r e n t i s d i -
r e c t e d so t h a t t h e shallower water i s t o t h e r i g h t o f t h e downstream d i r e c tion.
We f i n d t h a t b a r o c l i n i c i n s t a b i l i t y i s very s e n s i t i v e t o t h e d i r e c -
t i o n o f t h e c u r r e n t i n t h e upper l a y e r .
Indeed, i f t h e mean c u r r e n t i s
d i r e c t e d so t h a t t h e shallower water i s t o t h e l e f t o f t h e downstream d i r e c t i o n , no b a r o c l i n i c i n s t a b i l i t y occurs. D i s p e r s i o n curves f o r t h a t case are shown i n F i g u r e 1 9 f .
As p o i n t e d o u t e a r l i e r , t h e temperature f l u c t u a t i o n s
4aa d i s p l a y e d i n F i g u r e 12 dampen d u r i n g t h e l a s t t h i r d o f t h e experiment.
The
same can be s a i d o f t h e v a r i a t i o n o f t h e v e l o c i t y components a t s t a t i o n E shown i n F i g . first,
20.
Here t h e amplitude o f t h e f l u c t u a t i o n s
increases a t
b u t d u r i n g t h e l a s t month o f the experiment, a change i n s i g n o f t h e
mean v e l o c i t y
i s f o l l o w e d by an abrupt t e r m i n a t i o n o f a f a i r l y u n i f o r m
increase (as i n t h e temperature s e r i e s ) .
The l a t t e r circumstance can be
e x p l a i n e d u s i n g t h e model o f b a r o c l i n i c i n s t a b i l i t y . CONCLUSIONS The r e s u l t s presented here demonstrate t h e existence o f s y n o p t i c v a r i a b i l i t y i n t h e B a l t i c Sea.
We have shown t h a t s t r a t i f i c a t i o n , bottom Xopo-
graphy, and t h e c h a r a c t e r o f t h e mean f l o w a f f e c t t h e temporal and s p a t i a l scales o f s y n o p t i c v a r i a b i l i t y .
Although i t i s n o t t h e o r e t i c a l l y shown
here, i t seems p o s s i b l e t h a t atmospheric c o n d i t i o n s are a l s o very important. T h i s p o s s i b i l i t y , and t h e mechanism by which such a c o u p l i n g might operate, deserve f u r t h e r i n v e s t i g a t i o n .
REFERENCES Aitsam, A., Elken, J., Pavelson and L. Talpsepp, 1981. P r e l i m i n a r y r e s u l t s o f t h e study o f s p a t i a l and temporal c h a r a c t e r i s t i c s 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 n the Baltic. I n : The I n v e s t i g a t i o n and M o d e l l i n g o f Processes i n t h e B a l t i c Sea, P a r t I,pp. 70-98. Rhines, P., 1970. Edge-, bottom-, and Rossby waves i n a r o t a t i n g s t r a t i f i e d f l u i d , Geophysical F l u i d Dynamics, 1: 273-302. Thompson, R.O. R.Y. and J. Luyten, 1976. Evidence f o r bottom-trapped topographic Rossby waves from s i n g l e c u r r e n t moorings, Deep-sea Research, 23: 625-635.
489
THE VARIABILITY OF THE TEMPERATURE, S A L I N I T Y AND DENSITY FIELDS I N THE UPPER LAYERS OF THE BALTIC SEA A. Aitsam,
J. Pavelson
.'
I n s t i t u t e o f Thermophysics and E l e c t r o p h y s i c s , Academy o f Sciences o f t h e Estonian S.S.R. INTRODUCTION I n r e c e n t years, t h e use o f a towed CTD has proved successful i n d e t e r mining t h e s t r u c t u r e o f t h e temperature;' s a l i n i t y and d e n s i t y f i e l d s .
The
s p a t i a l d i s t r i b u t i o n s o f f i e l d s obtained by t h i s method i n a comparatively s h o r t t i m e have an e s s e n t i a l l y h i g h e r r e s o l u t i o n than those obtained from observations a t d i s c r e t e p o i n t s .
Depending on t h e aims o f t h e i n v e s t i g a -
t i o n , t h r e e towing regimes a r e p o s s i b l e : 1. 2.
t h e CTD moves a t a f i x e d depth (Gargett, 1978), t h e CTO performs wavelike motion between two l e v e l s ( A l l e n e t a l . 1980),
3.
t h e CTD moves a l o n g a f i x e d isotherm o r isopycnal (Katz,
1973,
1975). I n most o f t h e s t u d i e s j u s t mentioned,
t h e s p a t i a l s t r u c t u r e o f the
temperature and s a l i n i t y f i e l d s was obtained w i t h o u t s e p a r a t i n g t h e "background" o f i n t e r n a l waves.
However, when s t u d y i n g t h e v a r i a b i l i t y o f these
v a r i a b l e s , t h e r e l a t i v e p a r t due t o i n t e r n a l waves should be determined. This i s i m p o r t a n t f o r a c o r r e c t e v a l u a t i o n o f t h e c h a r a c t e r i s t i c s o f t h e non-wave
perturbations.
As a f i r s t approximation,
an isopycnal a n a l y s i s
m i g h t be used as i n r e c e n t s t u d i e s by Woods and M i n n e t t (1979), and Cairns (1980).
Despite i t s shortcomings,
t h i s method i s t h e b e s t one a t present.
The aim of t h e p r e s e n t study i s t o determine t h e main c h a r a c t e r i s t i c s o f t h e temperature, s a l i n i t y and d e n s i t y f i e l d s on h o r i z o n t a l scales l a r g e r than 1 km i n t h e upper l a y e r s o f t h e open p a r t o f t h e B a l t i c Sea.
F i r s t , we
s h a l l describe t h e experiments and t h e processing o f t h e data.
Then, the
most t y p i c a l r e s u l t s w i l l be presented and discussed.
F i n a l l y , some hypothe-
ses about t h e o r i g i n o f t h e observed s t r u c t u r e w i l l be formulated.
EXPERIMENTS AND DATA PROCESSING
All
the
experimental
data were obtained u s i n g t h e towed measuring
device c o n s t r u c t e d a t t h e I n s t i t u t e o f Thermophysics and E l e c t r o p h y s i c s o f t h e Academy o f Sciences o f t h e Estonian S.S.R. 1981).
(Pavelson and Portsmuth,
The i n s t r u m e n t c o n s i s t s o f an underwater u n i t , t h e "FISH",
onboard system ( F i g u r e 1).
The " F I S H "
and an
i s equipped w i t h a CTD MARK I11
490
2
MINI -
INTERFACE
z
PL 0 T TER .''
. COMPUTER H P 9825A
HP 9862A
i
r - - ---
-- 1
I
I
CABLE
%
CT D
b
DECK UNIT
TAPE RECORDER KENNEDY 9832
1
U N D E R WATER UNIT
'FISH'
F i g u r e 1.
Block diagram o f t h e towed measuring device.
( N B I S ) and guided by means o f small wings a c t i v a t e d by a m i n i a t u r e e l e c t r i c motor.
The data are t r a n s m i t t e d t o t h e onboard t e r m i n a l and s t o r e d on a
tape r e c o r d e r KENNEDY-9832 w i t h t h e h e l p o f s p e c i a l i n t e r f a c e s . o f t h e "FISH"
The c o n t r o l
motion and t h e p r e l i m i n a r y p l o t t i n g o f temperature s e c t i o n s
a r e performed by an HP-9825-A computer. For t h e experiments r e p o r t e d i n t h i s paper, t h e computer was programmed t o give the "FISH"
a wavelike motion.
The t o w i n g speed was between 5 and 7
knots, t h e CTD was lowered t o a depth o f 40 m, and t h e l e n g t h o f t h e h o r i z o n t a l c y c l e v a r i e d from 370 t o 500 m. hertz,
the v e r t i c a l
Using a measuring frequency o f 30
r e s o l u t i o n was b e t t e r than 5 cm,
since the v e r t i c a l
v e l o c i t y d i d n o t exceed 1.5 m s-I. Experiments u s i n g t h e towed CTD were performed d u r i n g t h e 9 t h and 1 5 t h c r u i s e s o f t h e R/V "Ayu-Dag" Sea.
i n t h e c e n t r a l and southern p a r t s o f t h e B a l t i c
The l o c a t i o n s o f t h e CTD s e c t i o n s a r e shown i n F i g u r e 2.
9 t h c r u i s e (1978),
t i o n s 1, 2 and 3; t h e l e n g t h s o f these s e c t i o n s were 90, respectively.
During t h e
we worked i n t h e extended BOSEX area and o b t a i n e d sec-
D u r i n g t h e 1 5 t h c r u i s e (1979),
85 and 120 km
measurements were made along
s e c t i o n 4 (200 km), extending from t h e BOSEX area t o t h e I s l a n d o f Bornholm. Hydrometeorological c o n d i t i o n s d u r i n g these two c r u i s e s were various.
The
measurements o f t h e 9 t h c r u i s e t o o k p l a c e a t t h e beginning o f August, i . e . ,
491 a t a t i m e o f weak winds and s t r o n g thermal s t r a t i f i c a t i o n .
During t h e 1 5 t h
c r u i s e ( a t t h e end o f September), s t r o n g v a r i a b l e winds and a negative heat f l u x p r e v a i l e d and combined t o d e s t r o y t h e s t r a t i f i c a t i o n o f t h e upper l a y ers.
F i g u r e 2.
Locations o f t h e "FISH" tow sections.
A c h a r a c t e r i s t i c f e a t u r e o f measurements made w i t h a towed h i g h f r e quency device, when s t u d y i n g s y n o p t i c scale phenomena, i s t h e accumulation For example, some o f o u r s e r i e s have up
o f a g r e a t amount o f i n f o r m a t i o n .
6 t o 16 x 10 data p o i n t s . i n essential
losses
method i s n o t used here. processing
It i s e v i d e n t t h a t subsampling t h e s e r i e s r e s u l t s
i n the determination o f isolines.
Therefore,
this
The d a t a processing c y c l e includes a p r e l i m i n a r y
and t h e d e t e r m i n a t i o n o f c h a r a c t e r i s t i c p e r t u r b a t i o n s o f t h e
temperature and s a l i n i t y f i e l d s .
First,
syncroerrors a r e e l i m i n a t e d from
t h e CTD data; t h e r e a r e about 300 syncroerrors p e r hour. i n c o r r e c t values o f pressure P,
A t t h e same stage,
temperature T and c o n d u c t i v i t y C a r e r e Those Pi,
moved, u s i n g t h e f o l l o w i n g c r i t e r i a :
Ti and Ci which do n o t meet
the conditions
-
Pi-l < 1 dbar, a r e considered i n c o r r e c t . Pi
Ti
-
Ti-l
< l0C,
Ci
-
Ci-l
-1 < 1 mmho cm
I n t h e second step, a l l t h e s e r i e s a r e smoothed, t o lessen t h e i n f l u ence o f t h e v e r t i c a l m i c r o s t r u c t u r e and t h e noise l e v e l .
Taking a running
average o f t h e d a t a w i t h a 1 m f i l t e r appears t o be t h e b e s t way t o e l i m i nate t h e m i c r o s t r u c t u r e , a l t h o u g h i t r e s u l t s i n a c e r t a i n deformztion o f t h e s y n o p t i c s c a l e thermohaline s t r u c t u r e .
From t h e smoothed s e r i e s , s a l i n i t y
492
and s p e c i f i c d e n s i t y ,
at,
are c a l c u l a t e d based on known formulae f o r t h e
B a l t i c Sea ( P e r k i n and Walker, 1971; M i l l e r o and Kremling, 1976). I n t h e f i n a l step, a l l p o s s i b l e s p a t i a l i s o l i n e s a r e determined.
Time
i s o l i n e s are transformed i n t o s p a t i a l i s o l i n e s w i t h t h e h e l p o f t h e c o r r e s ponding n a v i g a t i o n data.
This i s f o l l o w e d by t h e p l o t t i n g o f s e c t i o n s o f
t h e T, S , and ut f i e l d s i n space P ; f i n a l l y , s e c t i o n s o f t h e T and S f i e l d s a r e p l o t t e d i n space at, i n t e r n a l waves.
i n o r d e r t o e l i m i n a t e t h e kinematic e f f e c t o f
The comparison o f the s e c t i o n s o f b o t h types a l l o w s us t o
d i v i d e t h e f i e l d s i n t o components, t o separate t h e v a r i o u s p e r t u r b a t i o n s and t o evaluate t h e i r c h a r a c t e r i s t i c s .
ERRORS The e s t i m a t i o n o f e r r o r s interpretation. 1.
i s a l s o i m p o r t a n t i n d a t a processing and
The main sources o f e r r o r s are:
t h e thermal i n e r t i a o f t h e pressure sensor, p a r t i c u l a r l y i n case
o f h i g h temperature g r a d i e n t s ;
2. lated;
3.
t h e accuracy w i t h which P,T,C
a r e measured, and S and ut calcu-
t h e use o f T and ut i n s t e a d o f t h e p o t e n t i a l temperature, 8 , and
t h e p o t e n t i a l d e n s i t y ue. The a n a l y s i s o f our c a l c u l a t i o n s leads t o t h e f o l l o w i n g conclusion. When t h e s t r a t i f i c a t i o n i s s t r o n g (e.g.
summer o f 1978), t h e r e c o r d i n g o f a
change i n t h e v e r t i c a l d i r e c t i o n o f t h e CTD motion i s s i g n i f i c a n t l y delayed due t o t h e thermal i n e r t i a o f t h e pressure sensor.
T h i s causes apparent
s h i f t s i n t h e depths o f t h e v a r i o u s i s o l i n e s w i t h i n t h e f o l l o w i n g ranges: up t o 1, 5 and 2 m f o r isotherms, i s o h a l i n e s and isopycnals, r e s p e c t i v e l y . Therefore, we chose t o use o n l y CTD d a t a c o l l e c t e d d u r i n g t h e upward motion o f t h e FISH.
I n doing so,
t h e h o r i z o n t a l r e s o l u t i o n i s decreased by a
f a c t o r two b u t t h i s i s n o t c r i t i c a l i n view o f t h e scales o f t h e phenomena under study. The second source o f e r r o r s i s t h e absolute accuracy o f t h e i n s t r u ments.
I n view o f t h e l o n g term s t a b i l i t y o f t h e p r o b e ' s o p e r a t i o n and
p a r t i a l c a l i b r a t i o n , AT = k 0.005°C,
AC =
*
0.005 mmho cm-'
and AP = k 3 m
may be taken as e r r o r bounds.
The l a t t e r r e f l e c t s mainly t h e thermal i n e r -
t i a o f t h e pressure sensor.
Since we a r e mainly i n t e r e s t e d i n r e l a t i v e
i s o l i n e changes and d a t a a r e c o l l e c t e d . i n one v e r t i c a l d i r e c t i o n o n l y , t h e pressure e r r o r may be considered systematic.
Based on t h e formulae used i n
t h e c a l c u l a t i o n s , i t can be determined t h a t AS = t 0.010 O/oo and Ao,
= t
0.0085 ut u n i t s . Finally,
l e t us consider t h e problem o f t h e deformation o f t h e i s o -
l i n e s , which i s r e l a t e d t o t h e nonconservative nature o f t h e temperature and
493
density.
under t h e i n f l u e n c e o f
Indeed,
p a r c e l moves up and down. same water
parcel
Cairns (1980),
i n t e r n a l waves,
a given water
A t c e r t a i n depths, because o f compression, t h e
has d i f f e r e n t temperature and d e n s i t y .
According t o
t h e use o f d e n s i t y i n s t e a d o f p o t e n t i a l d e n s i t y leads t o the
f o l l o w i n g e r r o r s i n temperature and s a l i n i t y : AT = AS =
where
ds(K/g)t dz
= c o e f f i c i e n t o f a d i a b a t i c compredsion,
K
5=
displacement o f water p a r c e l due t o i n t e r n a l waves.
I t can be seen t h a t t h e s m a l l e r t h e v e r t i c a l d e n s i t y g r a d i e n t and t h e l a r g e r
t h e amplitude o f t h e i n t e r n a l waves, the g r e a t e r are t h e e r r o r s i n t h e i s o pycnal a n a l y s i s .
Taking values t y p i c a l o f t h e upper l a y e r o f t h e B a l t i c Sea
= 10-1 O C m-', dS/dz = 5 x O/oo m-', and u n i t s m - l ) and f o r t h e amplitude o f t h e i n t e r n a l waves,
f o r t h e g r a d i e n t s (dT/dz dut/dz
u 2 x lo-'
= 2 x lo-'
we g e t AT
-1
and AS -1
OC
O/oo.
We s h a l l add t h e e r r o r s made i n
t h e d e t e r m i n a t i o n o f isotherms and isopycnals i n space P w i t h o u t c o n s i d e r i n g c o m p r e s s i b i l i t y AT
=
2 x
OC
and Aut E 5 x
ut u n i t s .
a r e s m a l l e r than t h e corresponding absolute accuracies.
The l a t t e r
Consequently, i t i s
necessary t o use t h e p o t e n t i a l temperature and d e n s i t y i n isopycnal a n a l y s i s o n l y i n t h e presence o f extremely small d e n s i t y gradients. RESULTS I n t h i s s e c t i o n , we p r e s e n t and discuss t h e r e s u l t s o b t a i n e d along t h e s e c t i o n s described e a r l i e r . experiments i s s t r i k i n g .
The d i f f e r e n c e between t h e 1978 and t h e 1979
During t h e summer experiment (1978), t h e s t r u c t u r e
o f t h e i s o l i n e s o f t h e temperature and s a l i n i t y f i e l d s i s r a t h e r smooth.
In
t h e thermocline r e g i o n , l o n g w a v e l i k e p e r t u r b a t i o n s w i t h l e n g t h s o f 30-40 km and amplitudes o f up t o 3 m can be d i s t i n g u i s h e d .
The r e s u l t s o f t h e sec-
t i o n made along t h e a x i s o f t h e B a l t i c Sea i n autumn (1979) are q u i t e d i f f e r e n t i n character.
We f i n d l a r g e f l u c t u a t i o n s (up t o 10 m) o f t h e i s o -
l i n e s a t a l l depths where measurements were made. p e r t u r b a t i o n s i s 20-25 km, i . e .
The l e n g t h scale o f these
s m a l l e r than i n summer.
Wavelike perturba-
t i o n s o f small scales were n o t studied, s i n c e they are d i s t o r t e d because o f t h e Doppler e f f e c t d u r i n g f i e l d measurements.
T y p i c a l examples o f s e c t i o n s
o b t a i n e d d u r i n g these experiments a r e presented i n Figures 3 and 4.
494
Distance ( km 1
F i g u r e 3.
Temperature,
(summer 1978). density:
from tow s e c t i o n 1
temperature: l0C; s a l i n i t y : 0.05 O/oo;
0.2 at u n i t s .
F i g u r e 4 ( f a c i n g page). s e c t i o n 4 (autumn 1979).
0.05 O/oo;
s a l i n i t y and d e n s i t y f i e l d s
Contour i n t e r v a l s :
density:
Temperature, s a l i n i t y and d e n s i t y f i e l d s f r o m tow Contour i n t e r v a l s :
0 . 1 at u n i t s .
temperature:
l0C; s a l i n i t y :
495
I
10
I
Distance I k m ) 20 30 40 50 Isotherms
I
I
I
1
Isdhalines
I
I s 0pycnals
496
On t h e b a s i s o f temperature s e c t i o n s , i t i s p r a c t i c a l l y impossible t o i d e n t i f y p e r t u r b a t i o n s o f non-wave salinity field, only.
Therefore,
method,
origin.
However,
on s e c t i o n s o f t h e
such p e r t u r b a t i o n s can be d i s t i n g u i s h e d , b u t q u a l i t a t i v e l y
however,
we
shall
use t h e isopycnal
has a grave shortcoming.
analysis
hereafter.
This
I f non-wave p e r t u r b a t i o n s o f
temperature and s a l i n i t y do n o t f u l l y compensate each o t h e r , d e n s i t y sect i o n s w i l l n o t r e f l e c t a " p u r e l y " wavelike p i c t u r e .
When t h i s i s t h e case,
t h e study o f t h e temperature and s a l i n i t y f i e l d s i n at-space
may n o t y i e l d
r e l i a b l e estimates o f t h e dimensions and amplitudes o f t h e p e r t u r b a t i o n s . As a f i r s t approximation,
l e t us assume t h a t t h e observed p e r t u r b a t i o n s
o f temperature and s a l i n i t y a r e d e n s i t y compensated.
Then, we may i d e n t i f y
p e r t u r b a t i o n s w i t h t h e f o l l o w i n g s t a t i s t i c s f o r t h e 1978 summer experiment (Table 1). Table 1 C h a r a c t e r i s t i c s o f t h e temperature f i e l d p e r t u r b a t i o n s , summer 1978
Maximum length (h)
Mean distance (km)
8
10
19
28
0.6
13
4
8
21
0.8
No.
Upper l a y e r (16°C) Intermediate l a y e r (4°C)
Mean temperature change ("C)
Mean length (h)
The f o l l o w i n g conclusions can be drawn from these r e s u l t s . and l o n g p e r t u r b a t i o n s dominate i n t h e upper l a y e r .
Relatively rare
I n the intermediate
l a y e r , below t h e thermocline, t h e r e are more p e r t u r b a t i o n s , b u t t h e i r dimensions a r e c o n s i d e r a b l y smaller.
Note t h a t t h e mean temperature change i s
l a r g e r i n t h e i n t e r m e d i a t e l a y e r t h a n i n t h e upper l a y e r . We were unable t o c a l c u l a t e analogous s t a t i s t i c s f o r t h e 1979 autumn experiment because t h e isotherms v a r i e d g r e a t l y ( t h e thermocline i s a t t h e bottom o f t h e l a y e r under study over p a r t o f t h e s e c t i o n ) .
I n spite o f
t h a t , temperature p e r t u r b a t i o n s w i t h l e n g t h scales o f 4 t o 12 km and average amplitudes o f
l0C
may be i d e n t i f i e d a g a i n s t a background o f s m a l l - s c a l e
"noise" ( p e r t u r b a t i o n s s h o r t e r t h a n 4 km w i t h amplitudes o f 0.3"C).
A considerable non-wave v a r i a b i l i t y o f s a l i n i t y i s observed m a i n l y i n t h e upper l a y e r . temperature.
I n most cases, t h e p e r t u r b a t i o n s a r e s i m i l a r t o those o f
For example i n F i g u r e 3, we see a s a l i n i t y p e r t u r b a t i o n which
i s about 18 km long.
There i s a sharp s a l i n i t y g r a d i e n t on b o t h s i d e s o f
491
t h e p e r t u r b a t i o n . A s i m i l a r perturbation can a l s o be seen in t h e temperat u r e f i e l d i n ot-space (Fig. 5), i . e . a f t e r removal of t h e v a r i a b i l i t y due t o i n t e r n a l waves.
Distance [ k m )
0
4.0
1
5
10
15
120-
+
20
25
Figure 5. Temperature and s a l i n i t y f i e l d s in at-space ( f i r s t half o f the s e c t i o n presented i n Fig. 3 ) .
498
Thus,
i n t h e p r e s e n t case, t h e temperature and t h e s a l i n i t y o f t h e
water mass a r e d i f f e r e n t
f r o m those o f t h e neighboring environment.
To
study t h e d e n s i t y c h a r a c t e r i s t i c s o f these water masses, we s h a l l use t h e T-S p r e s e n t a t i o n (Gargett, 1978).
The essence o f t h e method i s as f o l l o w s .
Moving a t a f i x e d depth w i t h i n t h e core of a g i v e n water mass corresponds t o moving up and down on a T-S curve on account o f i n t e r n a l waves.
Crossing
t h e border1 i n e between t w o d i f f e r e n t water masses corresponds t o s w i t c h i n g I f t h e t r a n s l a t i o n from one T-S
t o another T-S curve.
takes p l a c e along an isopycnal,
curve t o another
we may consider t h a t t h e temperature and
s a l i n i t y p e r t u r b a t i o n s a r e d e n s i t y compensated. p l a c e a t an angle t o t h e isopycnals,
I f t h e t r a n s l a t i o n takes
we may draw t h e c o n c l u s i o n t h a t t h e F i g u r e 7 shows t h e T-S p l o t
p e r t u r b a t i o n s are n o t compensated by d e n s i t y .
a t a depth o f 10 m f o r t h e example j u s t discussed.
Despite a considerable
sparseness o f t h e data p o i n t s i n t h e f i r s t h a l f o f t h e p e r t u r b a t i o n , t w o types o f t r a n s l a t i o n s o r "crossings" may be d i s t i n g u i s h e d .
I n the left-hand
p a r t o f t h e p e r t u r b a t i o n , t h e passage over t h e 4 km s u b p e r t u r b a t i o n i s n o t isopycnal ( d o t t e d l i n e s 1 and 2 ) .
However, on t h e r i g h t - h a n d edge o f t h e
p e r t u r b a t i o n ( d o t t e d l i n e 3) t h e c r o s s i n g o f t h e water mass boundary i s isopycnal,
i . e . w i t h o u t any d e n s i t y jump.
Thermohaline p e r t u r b a t i o n s along
t h e r e l a t i v e l y more v a r i a b l e s e c t i o n of t h e 1979 experiment are even harder t o detect.
The f i l t e r i n g o f t h e i n t e r n a l waves g i v e s a p i c t u r e w i t h i r r e g u -
l a r v a r i a b i l i t y (Fig.
6).
Nevertheless,
an 11 km l o n g p e r t u r b a t i o n ( t h e
amplitude o f t h e temperature change i s 1.3OC, change 0 . 1 O/oo)
and t h a t o f t h e s a l i n i t y
can be d i s t i n g u i s h e d ; 10 km f u r t h e r , a c o n s i d e r a b l y l a r g e r
p e r t u r b a t i o n begins.
Two problems i n s t u d y i n g t h i s t y p e o f v a r i a b i l i t y are
t h e f a c t s t h a t p o i n t s on t h e T-S plane a r e g r e a t l y s c a t t e r e d , and t h a t t h e density r e l a t i o n s o f the perturbations are d i f f i c u l t t o elucidate. CONCLUSION F i n a l l y , we would l i k e t o say a few words a b o u t . t h e o r i g i n o f t h e t h e r mohal i n e p e r t u r b a t i o n s . "cold-fresh"
We have observed o n l y two types o f p e r t u r b a t i o n s :
and "warm-salty".
Those types i n d i c a t e w i t h h i g h p r o b a b i l i t y
t h a t d e n s i t y compensation i s achieved.
Since t h e observed patches o f water
masses w i t h d i f f e r e n t T and S c h a r a c t e r i s t i c s a r e d e n s i t y compensated, we may c a l l
7
these patches "macro-intrusions".
"cold-fresh"
B a l t i c , and t h a t t h e "warm-salty" origin.
We b e l i e v e t h a t t h e observed
i n t r u s i o n was advected from neighboring areas o f t h e n o r t h e r n i n t r u s i o n was probably o f southern B a l t i c
We note t h a t t h e f i r s t type o f p e r t u r b a t i o n s p r e v a i l e d i n t h e
summer o f 1978 and t h e second type i n t h e autumn o f 1979.
499
I
F i g u r e 6. F i g . 4).
Temperature and s a l i n i t y f i e l d s i n ot-space
(same s e c t i o n as i n
500
Salinity (%-)
F i g u r e 7.
T-S p l o t o f s e c t i o n 1 a t a depth o f 10 m.
U n f o r t u n a t e l y , our data a r e s t i l l i n s u f f i c i e n t t o answer some key quest i o n s about t h e thermohaline v a r i a b l i t y i n t h e upper l a y e r s o f t h e B a l t i c . Nevertheless,
t h e d a t a presented i n t h i s paper demonstrate t h a t t h e CTD
towing method i s useful f o r t h e study o f t h e s p a t i a l s t r u c t u r e o f t h e tempera t u r e and s a l i n i t y f i e l d s on meso- and s y n o p t i c scales.
REFERENCES A l l e n , C.H., Simpson, J.H., Carson, R.M., 1980. The s t r u c t u r e and v a r i a b i l i t y o f s h e l f sea f r o n t s as observed by an u n d u l a t i n g CTD system. Oceanologica Acta, 3(1): 59-68. I n t e r n a l waves and Cairns, J.L., 1980. V a F i a b i l i t y i n t h e G u l f o f Cadiz: globs. J. Phys. Oceanogr., g ( 4 ) : 579-595.
501 G a r g e t t , A.E., 1978. M i c r o s t r u c t u r e and f i n e s t r u c t u r e i n an upper ocean f r o n t a l regime. J. Geophys. Res. , g ( C 1 0 ) : 5123-5134. Katz, E.J., 1973. P r o f i l e o f an isopycnal surface i n t h e main thermocline o f t h e Sargasso Sea. J. Pys. Oceanogr., 3: 448-457. Katz, E.J., 1975. Tow s p e c t r a from MODE. J. Geophys. Res., 8019): 11631167. M i l l e r o , F.J., Kremling, K . , 1976. The d e n s i t i e s o f B a l t i c Sea waters. Deep-sea Res., 23: 1129-1138. Pavelson, J., Portsmuth, R . , 1981. A towed system f o r thermohaline f i e l d s measurements. The I n v e s t i g a t i o n and M o d e l l i n g o f t h e Processes i n t h e B a l t i c Sea., T a l l i n n , pp. 16-25. Walker, E.R., 1972. S a l i n i t y c a l c u l a t i o n s from " i n s i t u " Perkin, R.G., measurements. J. Geophys. Res. , 77(33). Woods, J.D., M i n n e t t , P.J., 1979. Analysis o f mesoscale t h e r m o c l i n i c i t y Deep-sea w i t h an example from t h e t r o p i c a l thermocline d u r i n g GATE. 85-96. Res.,
z:
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503 MODELING OF THE CLIMATIC SCALE VARIABILITY OF THE HYDRODYNAMICS OF THE BALTIC SEA
T. K u l l a s , V. Kraav I n s t i t u t e o f Thermophysics and E l e c t r o p h y s i c s Academy o f Sciences o f t h e Estonian S.S.R. ABSTRACT
A numerical model i s used t o describe t h e c h a r a c t e r i s t i c s o f t h e hydrodynamical regime and t h e d i s t r i b u t i o n s o f temperature, s a l i n i t y and d e n s i t y i n t h e B a l t i c Sea.
The model equations gre t h e l i n e a r i z e d equations o f
motion ( w i t h o u t h o r i z o n t a l d i f f u s i o n ) ,
t h e c o n t i n u i t y equation, t h e equa-
t i o n s o f c o n s e r v a t i o n o f heat and s a l t , and a n o n l i n e a r equation o f s t a t e . The system o f equations i s i n t e g r a t e d n u m e r i c a l l y using a f i n i t e d i f f e r e n c e method.
Some r e s u l t s o f numerical experiments on t h e seasonal changes o f
t h e h y d r o l o g i c a l c h a r a c t e r i s t i c s o f the B a l t i c Sea are presented.
Although
t h e modeling o f such seasonal changes g i v e s s a t i s f a c t o r y r e s u l t s , several d i f f i c u l t i e s are obvious.
One o f t h e p o s s i b l e ways o f saving computer t i m e
i s t h e p a r a m e t r i z a t i o n o f t h e v e r t i c a l p r o f i l e s o f v e l o c i t y , temperature and s a l in i ty. INTRODUCTION Oceanic processes can be described by a s e t o f dynamic and thermodynamic equations t o g e t h e r w i t h an equation o f s t a t e and t h e law o f conservat i o n o f mass.
There are, o b v i o u s l y , very many processes t o be described:
t r a n s p o r t o f heat,
s a l t and momentum by advection,
convection and turbu-
lence, evaporation and p r e c i p i t a t i o n , r a d i a t i o n , etc. I n o r d e r t o model hydrodynamic processes o f c l i m a t o l o g i c a l scale, we must make p h y s i c a l and numerical approximations because our p o s s i b i l i t i e s o f observing t h e system o r c a l c u l a t i n g i t s behavior are l i m i t e d . t h e c l i m a t o l o g i c a l v a r i a b i l i t y o f hydrophysical f i e l d s ,
I n models o f
several p h y s i c a l
processes must be parameterized because t h e y are impossible t o describe explicitly.
Such processes i n c l u d e t h e t r a n s p o r t o f heat by r a d i a t i o n , t h e
t u r b u l e n t f l u x e s o f heat, s a l t and momentum, convection, mesoscale eddies, bottom s t r e s s and so on. BAROCLINIC MODEL
OF THE BALTIC SEA
For several years,
we have used a time-dependent, b a r o c l i n i c , three-
dimensional numerical model t o c a l c u l a t e t h e seasonal v a r i a b i l i t y o f t h e h y d r o l o g i c a l 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 ( K u l l a s and Tamsalu, 1979). The b a s i c equations o f t h e model are:
504
where t h e v a r i o u s symbols a r e d e f i n e d as f o l l o w s : x,y,z:
C a r t e s i a n coordinates
u,v,w:
components o f t h e v e l o c i t y v e c t o r
f
:
C o r i o l i s parameter
t
:
time
5
:
deviation
o f t h e f r e e s u r f a c e e l e v a t i o n from i t s average
value c
P
.
s p e c i f i c heat f o r constant pressure
.
:
d e n s i t y o f sea water
po
:
mean d e n s i t y
g
:
acceleration o f gravity
p
K,KT,KS:
c o e f f i c i e n t s o f v e r t i c a l t u r b u l e n t exchange o f momentum and vertical
t u r b u l e n t d i f f u s i o n o f heat and s a l t ,
p
:
c o e f f i c i e n t o f horizontal turbulent d i f f u s i o n
T
:
temperature
S
:
salinity.
The system o f equations (1)-(6)
-
respectivey
r e q u i r e s t h e f o l l o w i n g boundary c o n d i t i o n s :
a t t h e surface, t h e shear s t r e s s (due t o wind) and t h e f l u x e s o f heat and s a l t a r e s p e c i f i e d ;
-
a t t h e bottom, we use t h e n o - s l i p c o n d i t i o n and we assume t h a t t h e r e i s no f l u s o f heat and s a l t ;
-
along closed boundaries, t h e normal v e l o c i t y component and t h e normal g r a d i e n t s o f temperature and s a l i n i t y a r e s e t equal t o zero;
-
along open boundaries, t h e mass t r a n s p o r t , temperature and s a l i n i t y are specified.
505 As i n i t i a l c o n d i t i o n s , we use observed d i s t r i b u t i o n s o f temperature and s a l i n i t y and we assume t h a t t h e water i s a t r e s t .
The c o e f f i c i e n t s o f
v e r t i c a l t u r b u l e n t exchange are f u n c t i o n s o f t h e Richardson number, and the coefficient o f horizontal turbulent diffusion i s a function o f the velocity g r a d i e n t and o f t h e c h a r a c t e r o f t h e h o r i z o n t a l scale o f turbulence ( g r i d size).
I n o r d e r t o improve t h e approximation o f the topography, we use t h e
method o f "bottom s t r a i g h t e n i n g " . c o o r d i n a t e 0 = z/H(x,y),
i . e . we t r a n s f o r m z i n t o t h e c u r v i l i n e a r
where H(x,y)
The system o f equations (1)-(6)
i s t h e l o c a l depth o f t h e water.
i s solved by an i m p l i c i t f i n i t e d i f -
ference method t h a t i s s t a b l e f o r a r b i t r a r y t i m e step. We now p r e s e n t some r e s u l t s o f numerjcal experiments aimed a t modeling seasonal changes o f h y d r o l o g i c a l c h a r a c t e r i s t i c s i n t h e open p a r t o f t h e B a l t i c Sea.
These changes a r e caused by v a r i a t i o n s i n t h e a i r temperature
and t h e wind s t r e s s a t t h e sea surface.
The c e n t r a l p a r t o f t h e B a l t i c
b a s i n was covered w i t h a u n i f o r m g r i d , w i t h Ax = Ay = 25 miles. c a l g r i d s i z e was taken equal t o 0.125
The t i m e step was taken equal t o 5 days.
9 levels.
The v e r t i -
H, i . e . t h e c a l c u l a t i o n s were made a t The shear s t r e s s due t o
wind and t h e heat f l u x were obtained from t h e e m p i r i c a l r e l a t i o n s 2
t X Z=
Q
Pa Y (U
= p
c cD O P
+
v2>+
*
(To
-
u
*
Ta)
(U2
+
V')'
,
where we denote by
tXZ'
Q
t
yz
Pa
Y U,V
t h e components o f wind s t r e s s , t h e heat f l u x , the a i r density, a constant, t h e h o r i z o n t a l components o f t h e wind v e l o c i t y a t t h e l e v e l o f an anemometer,
cD Ta
t h e Stenton number, and by t h e a i r temperature a t t h e meas'uring l e v e l .
The temperature f i e l d of t h e B a l t i c Sea i s extremely v a r i a b l e .
Figure
1 shows t h e v e r t i c a l d i s t r i b u t i o n o f temperature i n t h e Gotland Deep a t d i f f e r e n t times o f t h e year, and Figure 2 shows t h e v e r t i c a l d i s t r i b u t i o n o f temperature along a l o n g i t u d i n a l s e c t i o n i n t h e B a l t i c a f t e r 225 days o f calculation.
The comparison o f o b s e r v a t i o n a l data and t h e o r e t i c a l r e s u l t s
506 shows good agreement i n t h e f o r m a t i o n and deepening o f t h e thermocline. However, t h e comparison a l s o i n d i c a t e s t h a t heat from t h e s u r f a c e l a y e r s i s t r a n s f e r r e d t o o q u i c k l y t o t h e deeper l a y e r s o f t h e b a s i n i n t h e model results.
The reason f o r t h e r a p i d t r a n s f e r o f heat i n t h e v e r t i c a l d i r e c -
t i o n i s t h a t t h e c o e f f i c i e n t o f v e r t i c a l t u r b u l e n t d i f f u s i o n and t h e v e r t i c a l g r i d spacing a r e t o o l a r g e .
The c a l c u l a t i o n s show t h a t zones of up-
w e l l i n g and downwelling e x i s t i n t h e B a l t i c Sea.
The area where t h e most
i n t e n s i v e u p w e l l i n g occurs i s t h e n o r t h e r n p a r t o f t h e Gotland Deep, as i n d i c a t e d by a n o t i c e a b l e r i s i n g o f t h e isotherms. Although t h e modeling o f seasonal changes u s i n g a three-dimensional b a r o c l i n i c model g i v e s s a t i s f a c t o r y r e s u l t s , several d i f f i c u l t i e s art+ e v i dent.
1.
When u s i n g mean meteorological d a t a (wind,
cloudiness, a i r temp-
e r a t u r e ) as boundary c o n d i t i o n s , i t i s questionable whether t h e conventional p a r a m e t r i z a t i o n o f momentum, heat and s a l t f l u x e s a t t h e sea s u r f a c e i s appropriate.
Indeed, t h e e x i s t i n g equations f o r c a l c u l a t i o n g these f l u x e s
describe o n l y small-scale
2.
exchanges between t h e ocean and t h e atmosphere.
When u s i n g l a r g e t i m e steps (many days),
i t i s d i f f i c u l t t o para-
m e t r i z e t h e t u r b u l e n t exchanges i n the upper boundary l a y e r , since t h e heat f l u x may change i t s s i g n d u r i n g t h e averaging i n t e r v a l , and t h e r e e x i s t two d i f f e r e n t regimes o f t u r b u l e n c e (advective and convective).
3.
The methods
of
p a r a m e t r i z i n g bottom f r i c t i o n when c a l c u l a t i n g
i n t e g r a l c i r c u l a t i o n are incorrect.
1 1 I
Bottom f r i c t i o n does n o t depend on t h e
TPCI 22 33 44 55 6 6 7 7 8 89 91 10 T “TI7 I
-
20
!
I
I
!
I
’
IQ IQ
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id
i
,-’
I 60
0.
l
i
I I
100
/i i
i!
! i
1 1
I !
140
!!
zIm1 Fig.
1.
Vertical
distribution
of
temperature i n t h e Gotland Oeep (a:
beginning o f t h e c a l c u l a t i o n , b : s p r i n g , c:summer, d:autumn).
507
F i g . 2.
V e r t i c a l d i s t r i b u t i o n o f temperature along a l o n g i t u d i n a l s e c t i o n
i n t h e B a l t i c a f t e r 225 days o f c a l c u l a t i o n . v e l o c i t y p r o f i l e , nor on t h e bottom topography. 4.
The c a l c u l a t e d v e r t i c a l p r o f i l e s o f temperature and s a l i n i t y do
n o t agree w e l l w i t h t h e observations because i t i s impossible t o describe more p r e c i s e l y t h e zones o f l a r g e shears i n t h e model. 5.
There i s no r e l i a b l e method f o r smoothing t h e bottom topography.
The roughness o f t h e bottom o f t h e B a l t i c Sea causes mistakes i n t h e averagi n g process. PARAMETRIZATION OF THE VERTICAL PROFILES The numerical modeling approach described i n t h e p r e v i o u s s e c t i o n enables us t o model r e a l processes o n l y i n a l i m i t e d range o f s p a t i a l and temporal scales.
An a l t e r n a t i v e approach, which can l e a d t o a s u b s t a n t i a l
saving o f computer time,
i s t o parametrize t h e v e r t i c a l p r o f i l e s o f velo-
c i t y , temperature and s a l i n i t y .
I n doing so, we must take i n t o account t h e
f a c t t h a t 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 B a l t i c Sea can be d i v i d e d i n t o 3 layers:
1)
t h e s u r f a c e boundary l a y e r , o f thickness h;
2)
t h e i n t e r m e d i a t e l a y e r , o f thickness hM = H
-
h
-
hg, where H is t h e
t o t a l depth o f t h e water;
3)
t h e bottom l a y e r , o f t h i c k n e s s hB. I n t h e d e t e r m i n a t i o n o f 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 upper l a y e r , we
use t h e hypothesis of s e l f - s i m i l a r i t y of t h e boundary l a y e r ( Z i l i t i n k e v i c h
508
and Monin, 1974).
According t o t h a t hypothesis, n o n s t a t i o n a r i t y and h o r i -
z o n t a l inhomogeneity depend o n l y on t h e t h i c k n e s s o f t h e boundary l a y e r h, t h e t i m e t, and t h e h o r i z o n t a l coordinates x and y. i s scaled by h,
p r o f i l e s i s "universal," t h e instantaneous U*
= (T./P)
4.,
Hence, i f t h e h e i g h t z
t h e s t r u c t u r e o f t h e v e l o c i t y , temperature and s a l i n i t y i . e . i t i s determined a t every t i m e and p o s i t i o n by
and l o c a l values o f t h e f o l l o w i n g i n t e r n a l parameters:
Q = R(cpp) -l; S ' ;
g/p;
f; h
(10)
where we denote by u*
t h e shear v e l o c i t y ,
T.
the f r i c t i o n a l stress,
P
t h e d e n s i t y o f t h e water,
Q
t h e normalized heat f l u x a t t h e surface,
R S'
t h e heat f l u x a t t h e surface, t h e normalized s a l i n i t y f l u x i n t h e surface l a y e r .
Combining these parameters, we can form t h e f o l l o w i n g q u a n t i t i e s w i t h dimensions
of
velocity,
temperature,
salinity
and
length respectively:
where
aT ci
S
denotes t h e c o e f f i c i e n t o f thermal expansion, an analogous c o e f f i c i e n t f o r s a l i n i t y ,
K
t h e von Karman's constant, and
M
t h e mass f l u x .
Using these parameters we can form one more combination, dimension i s l e n g t h , and t w o dimensionless parameters, ~1,
A,
whose
and p , g i v e n by:
The values o f v e l o c i t y , temperature and s a l i n i t y , scaled by u*, T*,
and S,,
r e s p e c t i v e l y , depend on t h e nondimensional h e i g h t z/h and on t h e parameters po and 1.1.
The p r o f i l e s o f v e l o c i t y , temperature and s a l i n i t y a r e g i v e n by:
where
Q = i u , v, T, S l , 0 = {u*/K; u*/K; T, f
Q
and where
S*],
= i f u , f v , fT, f S ) , t h e u n i v e r s a l f u n c t i o n s determined f r o m observa-
t i o n a l data o r from numerical experiments using models o f boundary layers. Thus, t h e d e t e r m i n a t i o n o f 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 surface l a y e r i s reduced t o a two-dimensional. equation f o r t h e thickness o f t h e boundary layer. On t h e b a s i s o f h i s a n a l y s i s o f temperature d i s t r i b u t i o n s i n t h e i n t e r mediate l a y e r o f t h e B a l t i c Sea, Tamsalu (1979) dimensional combination (Ts
-
-
T)/(Ts
f u n c t i o n o f t h e nondimensional depth
5
TH)
= (H
e r a t u r e o f t h e upper quasi-homogeneous
discovered t h a t t h e non-
i s approximately a u n i v e r s a l
-
z)/(H - h) (Ts
lower boundary o f t h e i n t e r m e d i a t e l a y e r ,
i.e.
a t z E H).
expression f o r t h e s a l i n i t y , i n terms o f Sh = S J Z Z h and SH = t o be a l s o u n i v e r s a l .
i s t h e temp-
l a y e r , TH t h e temperature a t t h e An analogous
SIZ=H,
proved
Thus, i n t h e i n t e r m e d i a t e l a y e r t h e f o l l o w i n g approx-
imations are j u s t i f i e d :
where
kT(C),
ks(5)
a r e t h e nondimensional f u n c t i o n s f o r temperature and
s a l i n i t y , respectively. The v e l o c i t i e s i n t h e i n t e r m e d i a t e l a y e r can be assumed t o s a t i s f y the geostrophic equations, i . e .
I n t h e p a r a m e t r i z a t i o n o f 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 bottom boundary l a y e r , t h e mass f l u x i s excluded from t h e parameters determining t h e s t r u c t u r e ( a t z = H, aM/az = aT/az = aS/az 0). determined by t h e parameters uA,f and hs.
Hence t h e v e r t i c a l s t r u c t u r e i s
510 The t h i c k n e s s o f t h e bottom boundary l a y e r i s determined by t h e f o l lowing formula (Weatherly and
A h
=
*
M a r t i n , 1978):
U:
2 2 1/4 f (1 + No/f )
’
where A i s a c o n s t a n t (A = 1.3), and
No i s t h e V a i s a l a frequency o u t s i d e t h e boundary l a y e r . The shear v e l o c i t y a t t h e bottom i s determined from t h e law o f drag f r i c t i o n as a f u n c t i o n o f t h e geostrophic v e l o c i t y i n t h e upper p a r t 6f t h e boundary l a y e r and o f t h e bottom roughness. CONCLUSION I n c o n c l u s i o n we can say t h a t t h e modeling o f t h e c l i m a t i c v a r i a b i l i t y o f t h e thermohaline f i e l d s i n t h e B a l t i c Sea leads t o t h e s o l u t i o n o f twodimensional equations f o r t h e thicknesses o f t h e boundary l a y e r s and f o r t h e f r e e surface elevation. REFERENCES K u l l a s , T.E.
and Tamsalu, R.E.,
1979.
A p r e d i c t i v e model o f t h e B a l t i c Sea
and i t s numerical r e a l i z a t i o n ( i n Russian).
In:
Water Resources,
2:
144- 154. Tamsalu, R.E.,
1979.
Modeling o f the dynamics and s t r u c t u r e o f t h e B a l t i c
Sea Waters ( i n Russian). Wheatherly, G.L.
and
In:
M a r t i n , P.J.,
Zvaigzne, Riga, 152 pp. 1978.
t h e oceanic bottom boundary l a y e r .
On t h e s t r u c t u r e and dynamics o f
J. o f Physical Oceanography,
8:
557-570. Z i l i t i n k e v i c h , S.S. and Monin, A . S . ,
1974.
S i m i l a r i t y t h e o r y f o r t h e atmos-
p h e r i c p l a n e t a r y boundary l a y e r ( i n Russian). S.S.S.R.
Fiz.atmos.okeana,
lO(6): 587-599
.
In:
I z v . Akad:
Nauk
511
MODELING OF SOME HYDRODYNAMICAL PROCESSES
BY A MODEL OF ROTATIONALLY ANISOTROPIC TURBULENT FLOW
J. Heinloo I n s t i t u t e o f Thermophysics and E l e c t r o p h y s i c s Academy o f Sciences o f t h e Estonian S.S.R. ABSTRACT An o r i g i n a l method f o r d e s c r i b i n g geop,hysical turbulence i s presented. The method takes i n t o account r o t a t i o n a l 1 y " a n i s o t r o p i c eddy1 i k e p a t t e r n s o f the turbulent flow f i e l d .
The general equations are i l l u s t r a t e d by various
s p e c i a l cases which may be o f relevance. t o some oceanographic phenomena. INTRODUCTION A growing i n t e r e s t i n e d d y l i k e p a t t e r n s i s one o f t h e c h a r a c t e r i s t i c f e a t u r e s o f t h e r e c e n t e v o l u t i o n o f turbulence theory.
The concept o f eddy
i s discussed more and more o f t e n i n t h e s c i e n t i f i c l i t e r a t u r e about turbulence,
i n c l u d i n g t h e oceanographic l i t e r a t u r e .
The concept o f eddies as
s p e c i f i c c a r r i e r s o f t h e t u r b u l e n t nature o f a f l o w i s being pieced t o g e t h e r s t e p by step b u t more and more d e f i n i t e l y .
T h i s development i n f l u e n c e s t h e
makeup o f t h e problem o f t u r b u l e n t flows i n general, as w e l l as t h e premises o f s p e c i f i c models o f t u r b u l e n t flows.
The d i f f i c u l t y o f d e f i n i n g more o r
l e s s s t r i c t l y a " t u r b u l e n t eddy" i s one o f t h e main r e s t r i c t i o n s t o t h e f u r t h e r evolution o f the theory i n t h a t direction. Nemirovsky and Heinloo (1980) takes
have proposed an o r i g i n a l method t h a t
i n t o account e d d y l i k e p a t t e r n s o f t h e t u r b u l e n t f l o w f i e l d and a t
l e a s t p a r t i a l l y avoids t h i s u n c e r t a i n t y .
The essence o f t h e method l i e s i n
t a k i n g i n t o account t h e e d d y l i k e p a t t e r n o f t h e f l o w f i e l d by i n t r o d u c i n g a c o r r e l a t i o n between a kinematic and some geometric c h a r a c t e r i s t i c s o f t h e flow field.
T h i s a l l o w s t h e i n c l u s i o n o f many important c h a r a c t e r i s t i c s o f
t u r b u l e n c e i n t h e averaged d e s c r i p t i o n o f "eddying" t u r b u l e n t flows.
For
example we can t a k e i n t o account t h e o r i e n t a t i o n and t h e r o t a t i o n a l v e l o c i t y o f eddies i n t h e environment, etc.,
without
determining
some aspects o f t h e i r cascadelike s c a t t e r i n g ,
e x a c t l y t h e meaning o f "the"
t u r b u l e n t eddy.
GENERAL EQUATIONS As t h e main c h a r a c t e r i s t i c o f t h e t u r b u l e n t f l o w p a t t e r n , we i n t r o d u c e the quantity
8,
d e f i n e d by
512
GI
where
i s t h e p u l s a t i o n o f t h e v e l o c i t y f i e l d and s i s t h e l e n g t h o f t h e
a r c o f t h e v e l o c i t y p u l s a t i o n s t r e a m l i n e ; t h e overbar over t h e expression denotes averaging. The c o n d i t i o n
6
# 0 determines t h e c l a s s o f t u r b u l e n t environments
c a l l e d " r o t a t i o n a l l y a n i s o t r o p i c " by Nemirovsky and Heinloo (1980). The equations o f motion f o r t u r b u l e n t f l o w s w i t h r o t a t i o n a l l y a,nisot r o p i c eddy p a t t e r n s have t h e form
,
(3)
and where t h e v a r i o u s symbols a r e d e f i n e d as f o l l o w s : P
:
some c h a r a c t e r i s t i c d e n s i t y o f t h e r e g i o n
P*
:
t h e r e a l d e n s i t y o f t h e environment
P + 9
:
t h e pressure
:
the gravitational acceleration
3
:
t h e angular v e l o c i t y o f t h e E a r t h ' s r o t a t i o n
p,y,~,8
:
c o e f f i c i e n t s o f environmental v i s c o s i t y
J k(1),k(2)
:
t h e e f f e c t i v e moment o f eddy i n e r t i a
:
constants
.
Equations (2) are t o be i n t e g r a t e d t o g e t h e r w i t h t h e equation o f cons e r v a t i o n o f mass
513 Equation (4) can be w r i t t e n i n t h e f o r m k p * = V - [ K . V p * ] , with
-
K = k
I
+
k(”
E
- if
+
(a2 I -
k(*)
if 6)
where
I i s t h e u n i t tensor, and E i s the Levy-Chiwitt tensor I f we decompose K i n t o i t s symmetric and antisymmetric p a r t s
= k I + k(2) (Q2 I
K(’)
-
6 if)
(7)
we can w r i t e as f o l l o w s t h e term on the r i g h t - h a n d s i d e o f equation (5) which c o n t a i n s t h e antisymmetric p a r t o f K:
where
Now we can r e w r i t e equation (5) i n t h e form
T h i s shows t h a t t h e antisymmetric p a r t o f K i n f l u e n c e s t h e d e n s i t y f i e l d as some a d d i t i o n a l mean v e l o c i t y . SPECIAL CASES I n t h i s s e c t i o n , we discuss t h r e e s p e c i a l cases t h a t are described by equations (2) and (4).
1.
+
Let
v = 0,
it
=
it(t.1,
vp* = (0, 0,
= const)
.
514 I n t h i s case, equations (2) and (4) reduce t o
-= - 2 at
pJ
[(4(y +
K)
+ k")
5
- Vp*)I
-
k")
Vp*
Equation (13) can describe two i n t e r e s t i n g e f f e c t s : vector
6
around t h e v e c t o r
:",
51
*
6 + 6 x Go
(13)
t h e precession o f t h e
and t h e d i f f e r e n t r a t e s o f a t t e n u a t i o n (de-
cay) o f d i f f e r e n t components o f
6
caused by t h e s t r a t i f i c a t i o n o f t h e en-
v i ronment. I n t h e s p e c i a l case where t h e l a s t t e r m o f (13) can be neglected ( t h i s t e r m represents t h e moment o f p u l s a t i o n s o f t h e C o r i o l i s f o r c e ) ,
ferences
i n t h e a t t e n u a t i o n r a t e o f t h e components o f
turning o f the vector
6
6
the d i f -
r e s u l t s i'n t h e
i n t h e d i r e c t i o n o f t h e v e c t o r Vp*.
When such a
s i t u a t i o n i s achieved, t h e environmental s t r a t i f i c a t i o n ceases t o i n f l u e n c e the attenuation o f
6.
Another s i t u a t i o n occurs when we do n o t n e g l e c t t h e moment o f pulsat i o n s o f the C o r i o l i s force.
Then
6,
which a t some t i m e i s d i r e c t e d along
Vp*, w i l l be r o t a t e d w i t h r e s p e c t t o Vp* by t h e moment o f p u l s a t i o n s o f t h e C o r i o l i s f o r c e a t t h e n e x t i n s t a n t ; i n o t h e r words,
6
acquires a component
p e r p e n d i c u l a r t o Vp* and becomes a f f e c t e d again by t h e damping i n f l u e n c e o f t h e environmental s t r a t i f i c a t i o n .
This d i s c u s s i o n shows t h e importance o f
t h e C o r i o l i s f o r c e and o f t h e s t r a t i f i c a t i o n i n t h e process o f eddy decay i n t h e environment. 2.
Let
We can then d e r i v e t h e f o l l o w i n g equation f o r
eJ(&
+
V V-6)
-
4(y +
~ ) +6 pJ6
x
2
6
= 0.
Equation (15) describes t h e d i f f u s i o n o f
6 as
6,
(15)
w i t h simultaneous decay o f
a r e s u l t o f f r i c t i o n and eddy s c a t t e r i n g , and w i t h r o t a t i o n o f
6 around
Go.
3.
+
Let
+ v = 0, g = (O,O,g),
6
= fi(z,t),
R, = 0, p* = p * ( z , t )
,
(16)
and assume t h a t t h e moment o f p u l s a t i o n s o f t h e C o r i o l i s f o r c e can be neg l ected.
515
Equations ( 2 ) and (4) become
Let
6
be caused by t h e b r e a k i n g o f surface waves.
As long as
d
de-
creases w i t h depth, t h e c h a r a c t e r i s t i c d i f f u s i o n t i m e o f p* a l s o decreases w i t h depth.
Consequently,
t h e surface l a y e r w i l l be mixed over a s h o r t e r
p e r i o d o f t i m e than t h e l a y e r below i t , and b o t h l a y e r s become separated by a "jump" l a y e r , i . e . a r e g i o n w i t h r e l a t i v e l y r a p i d change o f p*.
REFERENCE Nemirovsky, Y.V. l e n t flows.
and Heinloo, J.L., 1980. Novosibirsk.
The l o c a l v o r t e x theory o f turbu-
( I n Russian).
This Page Intentionally Left Blank
517
A CASCADE MODEL OF TURBULENT DIFFUSION
J. Heinloo, A. Toompuu I n s t i t u t e o f Thermophysics and E l e c t r o p b y s i c s Academy o f Sciences o f t h e Estonian S.S.R. ABSTRACT Some formal aspects o f t h e c o n s t r u c t i o n o f models d e s c r i b i n g phenomena i n v o l v i n g a v a r i e t y o f p h y s i c a l processes are developed.
By i n t r o d u c i n g a
c e r t a i n h i e r a r c h y o f f i l t r a t i o n operators, .we d e r i v e a system o f equations t h a t represent t h e t u r b u l e n t d i f f u s i o n o f a s c a l a r substance a t t h e l e v e l o f t h e second-order moment ( v a r i a n c e o f concentration).
The r e s u l t i s i l l u s -
t r a t e d by a t h e o r y o f t u r b u l e n t d i f f u s i o n i n a t u r b u l e n t f l o w w i t h r o t a t i o n a l l y a n i s o t r o p i c eddy p a t t e r n . INTRODUCTION The simultaneous presence o f a \ v a r i e t y o f p h y s i c a l processes which have d i f f e r e n t space and t i m e scales, d i f f e r e n t sources o f energy, and d i f f e r e n t p r o p e r t i e s o f space-time dynamics.
s t r u c t u r e i s a t y p i c a l f e a t u r e o f oceanic hydro-
It i s u s e f u l t o t a k e t h i s s t a t e o f a f f a i r s i n t o account when
c o n s t r u c t i n g s p e c i a l models o f hydrodynamic processes i n t h e sea.
In this
paper we examine some formal aspects o f one o f t h e p o s s i b l e ways o f conI n order t o describe t h e process o f t u r b u l e n t d i f -
s t r u c t i n g such models.
f u s i o n , we i n t r o d u c e a c e r t a i n h i e r a r c h y o f f i l t r a t i o n (averaging) operators each o f which i s assumed t o f i l t e r one o f t h e p h y s i c a l processes present. GENERAL TREATMENT Consider a sequence o f N operators o f f i l t r a t i o n , f o r instance, i n some special
case,
averaging operators
( i n t h e sense proposed i n Heinloo and
Toompuu, 1981, and Toompuu and Heinloo, 1981). be f i l t r a t e d ,
L e t q denote t h e q u a n t i t y t o
qk t h e r e s u l t o f t h e f i l t r a t i o n o f q by t h e f i l t r a t i o n opera-
t o r o f index k(k = 1,. . . ,N),
and q the r e s u l t o f the successive f i l t r a (k) t i o n of q by t h e operators o f i n d i c e s 1 t o k. . F o r an a r b i t r a r y q u a n t i t y q , s e t t i n g g i n ) = q(n-l)
-
q(,.),
t h e expansion
the pulsation o f the quantity
518 Now l e t q denote t h e c o n c e n t r a t i o n o f a passive substance t h a t s a t i s f i e s t h e equation o f mass conservation
where t h e v e c t o r ;(O)
i s the f l u x o f q a t the zero-th l e v e l o f description.
S u b s t i t u t e expansion (1) f o r q and an analogous expansion f o r
$ i n t o (2),
and apply t h e f i l t r a t i o n operators f r o m t h e f i r s t t o t h e k - t h t o t h e r e s u l t i n g equation.
I n doing s o , t a k e i n t o account t h e f o l l o w i n g r u l e
which f o l l o w s from t h e d e f i n i t i o n o f a f i l t r a t i o n o p e r a t o r (Toompuu and Heinloo, 1980).
The r e s u l t o f these operations i s t h e equation
-
= (;: q{n))n (n = 1,... ,k) i s t h e f l u x o f q (n) t h a t i s determined by t h e v e l o c i t y p u l s a t i o n s a t t h e n - t h l e v e l o f descrip-
where t h e v e c t o r S(n) tion.
L e t c(k) = (q';k))k
be t h e variance o f t h e substance c o n c e n t r a t i o n a t t h e
k - t h l e v e l o f d e s c r i p t i o n and C(k) = c(k)k+l, have
. . . ,N'
According t o (l), we
and C(k) f o l l o w from equation ( 3 ) .
The equations f o r q2
(N)
A f t e r some
simple b u t l a b o r i o u s t r a n s f o r m a t i o n s , these equations can be w r i t t e n
(& + :(N)
a + N; (z
where
N
- V) q:N) - V) C(k)=
=V
'
6(N+1)
- t
(N+l,n)
n=O
V
-
6(k)
-
k-1 N+1 1 (k,n) + t (n,k) n=O
n=k+l
(4)
519
(N+l,n)
=
j(,)(n) .
(k,n) = 2 ( j i k ) ( n )
'
'
q(N) q{k))(N)
2 a re t h e terms t h a t descr ibe t h e i n t e r a c t i o n o f t h e v a r i a b l e s 9") and C(k) and C(n), r e s p e c t i v e l y , and where N h(N+l) = Z. n=O
+
and C(k),
t
q(N) JN(n)
a re t h e f l u x vecto rs o f q2
0)
and C(k), r e s p e c t i v e l y .
I f t h e problem i s s e t i n general,
f o r instance before the p r e c i s e
meaning o f t h e f i l t r a t i o n oper at ions i s est ablished, t h e q u a n t i t i e s ( N +l , n) and (k,n) can ta ke p o s i t i v e as w e l l as negative values. However, i f the preceding mathematics i s used t o describe t h e t r a n s f e r o f some substance i n a t u r b u l e n t flow, and i f t h e f i l t r a t i o n operators are chosen i n such a way t h a t t h e scales o f t h e motion t o be described increase w i t h k, i t can be shown t h a t
The i n e q u a l i t i e s (5)
a p p l i e d t o equations (4)
are the mathematical
expression o f th e cascade process o f r e d i s t r i b u t i o n o f inhomogeneities i n a t u r b u l e n t f l o w (Fi g. 1). SPECIAL CASE I n ord e r t o descr ibe t h e process o f t u r b u l e n t d i f f u s i o n , tageous
to
i ntroduce
several
i t i s advan-
f i l t r a t i o n operators simultaneously.
This
a1 lows us t o apply d i f f e r e n t c l o s u r e assumptions t o processes o f d i f f e r e n t scales t h a t may have var ious physical o r i g i n o r d i f f e r i n some important characteristics. L e t i s i l l u s t r a t e t h e proposed formalism by a model o f d i f f u s i o n i n a t u r b u l e n t f l o w w i t h r o t a t i o n a l l y a n i s o t r o p i c eddy pattern.
The concept o f
r o t a t i o n a l l y a n i s o t r o p i c t u r b u l e n t f l o w was introduced by Nemirovsky and Heinloo, 1977, t o descr ibe a t u r b u l e n t f i e l d which can be characterized by t h e r e l a t i v e o r i e n t a t i o n o f eddy motion i n t h e environment. I n a d e t a i l e d d is c ussi on o f t h e theory,
Nemirovsky and Heinloo (1980)
pointed o u t t h a t
520
N+ I N
:I-I
k
I 0
Fig. 1. Schematic representation o f the cascade process o f redistribution of inhomogenities between different levels of description in a turbulent flow (transitions t o o r from all intermediate levels, 2 t o N-2, are denoted by dashed arrows). the existence of oriented eddy motion in the environment leads t o certain correlation between kinematic and geometric characteristics of the field o f motion. Based on the existence of such a correlation, a new kinematic characteristic o f environment, denoted 6 , is introduced (a definition of 6 can be found in another paper by Heinloo appearing in this volume). It must be obvious that the case 6 # 0 corresponds t o some specific features o f the process o f turbulent diffusion. Since the contributions t o the quantity 3 originate only in large-scale eddies (i.e. t h e eddies responsible for the orientation of the eddy motion in the environment), the quantity 6 influences only that part o f the diffusion that is affected by large-scale eddies. Let us choose the "black-and-white" diffusion of the molecules o f a substance as the zero-th level o f description (note that j ( 0 ) = 0 in this case). As the first filtration operator we choose the averaging operation over the so-called "elementary volume", i.e. a volume large enough for the molecular pulsations to be filtered out, o r smoothed, and small enough for
521
the f i e l d s o f time.
G1
and q1 t o be considered continuous f u n c t i o n s o f space and
The second operator o f f i l t r a t i o n (averaging) i s chosen i n order t o and q,l
f i l t e r the pulsations o f
which are caused by motion o f small-
scale eddies. The t h i r d operator o f f i l t r a t i o n (averaging) f i l t e r s the inhomogeneities o f G(2) and q(2), which are caused by the motion o f largescale eddies.
As f o r the d i f f u s i o n terms i n (3) and ( 4 ) , i t i s assumed t h a t
where Q denotes an a r b i t r a r y s c a l a r q u a n t i t y , kM and kT t h e c o e f f i c i e n t s o f molecular and t u r b u l e n t d i f f u s i o n ( t h e l a s t one being determined by the motion o f t h e small-scale
eddies),
and where K-, = KT(R)
i s t h e tensor o f
d i f f u s i o n c o e f f i c i e n t s determined by t h e motion o f large-scale eddies. Expanding KT i n t o a s e r i e s i n
6
(keeping i n mind t h a t
KT(b)
= 0), and
l i m i t i n g t h e expansion t o terms o f f i r s t and second order, we have
KT = -k(') T
E
*
fi
+ ki2)
(6 I - d)
,
(7)
where E i s t h e Levy-Chiwitt tensor, I i s the u n i t tensor, and k i l l and kT (2) are constant.
Taking i n t o account the assumptions (5)
and (6), we can
d e r i v e from equations (3) and (4) t h e f o l l o w i n g system, henceforth r e f e r r e d t o as equations (8):
622
93)
if
4
V
k Following the physical ideas of the cascade character o f turbulent diffusion, we can retain on the right-hand side o f equations (8) the terms that correspond to interactions between neighboring levels and neglect the terms that describe "dissipation" o f the fields q2 and C(3) into sybse(3) quent levels. Also, some assumptions are needed concerning the terms 2kT(V qi3)I3 2 and 2$(V q{2))2,32 in order to close the system of equations (8). These assumptions could be
where
tT
and tM are characteristic time scales of decay of C(3)
and C(2).
REFERENCES Heinloo, J. and Toompuu, A. , 1981. Applications of averaging (filtration) operators to hydrodynamical problems and to experimental data. The Investigation and Modelling of the Processes of the Baltic Sea, Part 11, Tallinn, pp. 78-81. Nemirovsky, Y.V. and Heinloo, J.L., 1977. A new approach to the description o f turbulent flows (in Russian). Nemirovsky, Y.V. and Heinloo, J.L., 1980. The local vortex theory o f turbulent flows. Novosibirsk (in Russian). Toompuu, A. and Heinloo, J., 1980. The generalized representation of a state o f a physical situation and its application to problems of hydrodynamics (in Russian).
523
WATER QUALITY STUDY OF THE BALTIC SEA BY OPTICAL REMOTE SENSING METHODS
J. Lokk, A. Purga I n s t i t u t e o f Thermophysics and E l e c t r o p h y s i c s Academy o f Sciences o f t h e Estonian S.S.R. INTRODUCTION O p t i c a l remote sensing methods enable us t o save t i m e i n studying t h e spatial
and temporal
v a r i a b i l i t y o f oceanic p r o p e r t i e s ,
and t o c o l l e c t
simultaneous data f o r l a r g e area. I n t h i s paper, we discuss t h e p o s s i b i l i t y o f u s i n g measurements o f t h e upward s p e c t r a l radiance t o study the d i s t r i b u t i o n o f suspended and d i s solved m a t t e r i n t h e sea. t h e research vessel R/V
The experiments were performed d u r i n g c r u i s e s o f "Ayu-Dag"
i n t h e B a l t i c Proper, and from aboard a
h e l i c o p t e r i n c o a s t a l areas. DISCUSSION
The study o f t h e s p a t i a l d i s t r i b u t i o n s o f v a r i o u s c o n s t i t u e n t s i n t h e sea by remote sensing methods i s somewhat l i m i t e d by t h e f a c t t h a t we can o n l y measure d i r e c t l y t h e o p t i c a l l y a c t i v e m a t t e r i n t h e water, phytoplankton pigments,
suspended matter, and y e l l o w substance.
such as The quan-
t i t y o f o t h e r substances can o n l y be estimated i n an i n d i r e c t way, u s i n g
known r e l a t i o n s h i p s between these substances and t h e o p t i c a l l y a c t i v e matter.
Many authors simply use t h e c o r r e l a t i o n s between t h e c o n c e n t r a t i o n o f
a given substance and sea b r i g h t n e s s i n one o r two s p e c t r a l bands.
This
method can o n l y be used under c e r t a i n c o n d i t i o n s , f o r we know t h a t b r i g h t ness i s n o t o n l y a f u n c t i o n o f water q u a l i t y b u t i t i s a l s o s t r o n g l y corr e l a t e d w i t h t h e downward s p e c t r a l i r r a d i a n c e . radiance v a r i e s g r e a t l y i n t h e B a l t i c area.
The downward s p e c t r a l i r For a d i r e c t study o f t h e
c h a r a c t e r i s t i c s o f water masses, we use t h e s p e c t r a l radiance index, p ( A ) , d e f i n e d by t h e expression:
Br(A) = Bo(A)
where B r ( A )
i s t h e sea radiance toward t h e n a d i r p o i n t and BO(A)
i s the
d i f f u s e radiance. When measurements a r e made t o study suspended and d i s s o l v e d matter i n t h e sea, r e f l e c t i o n s from t h e sea surface contaminate t h e data.
However, i n
s t u d i e s o f t h e c o n d i t i o n s o f t h e sea surface ( o i l s l i c k s , waves, e t c . ) ,
the
524
sun g l i t t e r s c o n s t i t u t e t h e main s i g n a l .
Experiments show t h a t , on a cloud-
l e s s day and w i t h a h i g h sun, about 40% o f t h e sea s u r f a c e i s covered w i t h sun g l i t t e r s i n t h e B a l t i c Sea.
I n order t o o b t a i n r e l i a b l e i n f o r m a t i o n on
subsurface l a y e r s i n t h e presence o f sun g l i t t e r s , we have t o make measurements when t h e h e i g h t o f t h e sun i s l e s s t h a n 50" o r t o i n c l i n e t h e r a d i o meter a t some angle from t h e n a d i r p o i n t i n t h e d i r e c t i o n f a c i n g t h e sun. Assuming t h a t a l l r a d i a t i o n r e g i s t e r e d i n near i n f r a r e d i s r e f l e c t e d o n l y from t h e water surface, we can then estimate c o r r e c t i o n s f o r r e f l e c t e d l i g h t i n t h e o t h e r s p e c t r a l bands. An a l t e r n a t i v e method i s t o use, lowing
expression
(Lokk
and
as a f i r s t approximation, t h e f o l -
Pelevin,
1978;
Pelevin,
Pelevina:'
and
Kel b a l ikhanov, 1979):
where R(A)
denotes t h e d i f f u s e s p e c t r a l radiance index, B&(A)
the zenith
p o i n t s p e c t r a l radiance and 0.02 i s t h e value o f t h e Fresnel c o e f f i c i e n t f o r o r t h o g o n a l l y f a l l i n g l i g h t beam radiance.
The u n d e r l y i n g assumption i s t h a t
t h e z e n i t h p o i n t and a 20° area around i t have equal b r i g h t n e s s .
We w i l l
have t h e b e s t r e s u l t s i f t h e s u r f a c e i s smooth. The two beam approximation discussed by Morel and' P r i e u r (1977) desc r i b e s t h e d i f f u s e s p e c t r a l radiance index by t h e expression:
where k i s a nondimensional c o e f f i c i e n t , p(A) t h e backward s c a t t e r i n g coe f f i c i e n t and K(A) t h e l i g h t a b s o r p t i o n c o e f f i c i e n t (absorbance). The absorbance can be c a l c u l a t e d i n t h e f o l l o w i n g way
where K ~ ( A ) denotes t h e absorbance by pure water,
K
a),
K
by phytoplankton pigments (mainly c h l o r o p h y l l
P
(A) t h e absorbance caused
(A) t h e absorbance caused Y by d i s s o l v e d o r g a n i c m a t t e r ( y e l l o w substance) and K~ t h e absorbance caused by n o n s e l e c t i v e p a r t i c l e s o r "grey" suspended m a t t e r .
Using ( 4 ) ,
equation
( 3 ) can be w r i t t e n as R(A) = k
p(A)
p(A)
+ KW(A)
+ K
P
(A) + K (A) + Y
'
KM
(5)
525 For water, t h e f u n c t i o n p ( A ) v a r i e s slowly.
Q u a l i t a t i v e spectral distribu-
t i o n curves o f o t h e r q u a n t i t i e s are known.
The i n f l u e n c e o f t h e d i f f e r e n t
components on t h e s p e c t r a l curve R(A)
v a r i e s w i t h t h e wavelength.
The
dominant f a c t o r s i n v a r i o u s s p e c t r a l bands can be categorized as f o l l o w s :
550-600 nm
KM' M'
(p,
denotes
the
backward
scattering
from suspended m a t t e r )
500-550 and 600-680 nm 400-500 nm 350-400 nm
K,, KM,
KM,
p,, B,, B,,
K~(A)
K~(A), K~(A)
~ ~ 0 ~1 ~, 0 B(A) 1 , .
I n t h e case o f c l e a r oceanic water, d e r e t h e i n f l u e n c e o f some components i s small, results.
t h e system o f equations based on (5) gives s a t i s f a c t o r y
However, when t h e water c o n s i s t s o f a complicated m i x t u r e o f
o p t i c a l l y a c t i v e m a t t e r ( l i k e t h e B a l t i c Sea and t h e e s t u a r i e s o f l a r g e rivers),
t h e r e s u l t s are found wanting.
Accuracy i n such c o n d i t i o n s i s
determined by t h e s i m p l i f i c a t i o n s t h a t have been made on a case by case basis.
Choosing these s i m p l i f i c a t i o n s g i v e s us t h e p o s s i b i l i t y o f f i n d i n g
more s e n s i t i v e s p e c t r a l ranges and r e l a t i o n s f o r c a l c u l a t i n g t h e q u a n t i t a t i v e d i s t r i b u t i o n o f some substances.
As an example, F i g u r e 1 shows a map
based on measurements f r o m t h e h e l i c o p t e r a f t e r a s t r o n g storm i n t h e G u l f o f Riga (Pelevin, Gruzevich and Lokk, 1980).
The map shows t h e d i s t r i b u t i o n
( i n r e l a t i v e u n i t s ) o f y e l l o w substance i n t h e sea.
The r a t i o p369/p560
used t o d e s c r i b e t h e y e l l o w substance c o n t e n t o f t h e water.
is
The measure-
ments were confirmed by a n a l y z i n g water samples c o l l e c t e d a t various s i t e s from t h e h e l i c o p t e r f o r c a l i b r a t i o n and,determination o f t h e o p t i c a l charact e r i s t i c s o f t h e main o p t i c a l l y a c t i v e substances i n l a b o r a t o r y . A more p r e c i s e method i s one which u t i l i z e s t h e whole spectrum o f l i g h t backscattered from t h e sea.
Knowing t h e o p t i c a l c h a r a c t e r i s t i c s o f t h e most
i m p o r t a n t substances o b t a i n e d i n l a b o r a t o r y experiments f o r the study area, we can e s t i m a t e t h e u n i v e r s a l s p e c t r a l curves f o r d i f f e r e n t concentrations, g i v e n by
where
PA) = p'(A)
+ K
and where we denote by
P'
526
r
Fig. 1.
O i s t r i b u t i o n o f t h e r a t i o p369/p560 f o r t h e Riga G u l f area on t h e
b a s i s o f t h e d a t a o f 18 and 19 September 1977. d e f i n e d as follows
The numerical s c a l e i s
521 K
t h e n o n s e l e c t i v e absorbance by p a r t i c l e s ,
P
p'(A)
t h e backward s c a t t e r i n g c o e f f i c i e n t f o r w a t e r w i t h suspended matter,
K
t h e p u r e w a t e r absorbance,
W
t h e r e l a t i v e absorbances b y c h l o r o p h y l l and y e l l o w substance,
KP' KY
r e s p e c t i v e l y , and by c,
s
the
concentrations
of
chlorophyll
and
yellow
substance.
The c o n c e n t r a t i o n s o f o p t i c a l l y a c t i v e substances can t h e n be o b t a i n e d by comparing t h e measured s p e c t r a l d i s t r i b u t i o n curves w i t h t h e c a l c u l a t e d curves.
The "measured"
concentrations a r e , t h e s e t o f values f o r which t h e
c a l c u l a t e d spectrum i s most s i m i l a r t o the' observed s p e c t r a l c u r v e .
Figure
2 shows a c t u a l measured s p e c t r a l c u r v e s and F i g u r e s 3, 4 and 5 show v a r i o u s e s t i m a t e d model curves. Finally, the
i t may be t h a t measurements o f c h l o r o p h y l l c o n c e n t r a t i o n by
UNESCO method and b y t h e remote method a r e i n h e r e n t l y d i f f e r e n t .
I n one
case t h e a n a l y s i s a p p l i e s t o samples from d i s c r e t e depths which may a l l be outside
t h e maximum c o n c e n t r a t i o n
layers,
whereas i n t h e o t h e r case t h e
v a r i a b l e we measure accounts f o r a l l t h e c h l o r o p h y l l i n t h e a c t i v e l a y e r (really
up t o Secchy d i s c
v i s i b i l i t y depth) w i t h d i f f e r e n t i n f l u e n c e a t
d i f f e r e n t depths. CONCLUSIONS
We have shown t h a t i n f o r m a t i o n a b o u t t h e f u l l
spectrum o f u p w e l l i n g
l i g h t i s needed f o r w a t e r q u a l i t y s t u d i e s b y o p t i c a l remote s e n s i n g methods.
In w a t e r s w i t h a c o m p l i c a t e d c o m p o s i t i o n of o p t i c a l l y a c t i v e m a t t e r (e.g. estuaries,
c l o s e d seas) i n f o r m a t i o n i s needed a b o u t t h e o p t i c a l p r o p e r t i e s
o f t h e main components p r e s e n t i n t h e a r e a ( c h l o r o p h y l l , y e l l o w substance, etc.).
528
15-
10-
05 -
I
F i g . 2.
I
I
400
500
600
nm
Measured spectral radiance.
I
1.0
I L 400 I.
Orno
500
600
nm
3. Computed spectral radiance w i t h a ) c=O.1, y=O.O, 8=0.0020; b) c=O.Ol, ~ 1 . 0 , B=O.O018; C ) ~ ~ 2 . 0~ , 0 . 0 , B=O.O020; d) ~ ~ 2 . 0yzl.0, , B=O. 0020. Fig.
529
I
c= 20 p=(01+ 1.0 1
1.0- 10
- a
051
'0.1 500
400 Fig. 4.
600
700 nm
Dependence o f t h e s p e c t r a l radiance, p(A),
f i x e d c h l o r o p h y l l c o n c e n t r a t i o n (c=Zmg.m
-3
on t h e parameter p f o r
).
-
p = 0.1 m- 1
C =(Q5+ 5.0) .
0.5
1.0 -
.
0.5 .
5.0
400 Fig.
5.
500
600
Dependence o f t h e s p e c t r a l
concentration f o r
p =
0 . 1 rn
-1.
700 nm
radiance,
p(A),
on t h e c h l o r o p h y l l
530 REFERENCES Eerme, K. and J . Lokk, 1980. On t h e B a l t i c Sea water b r i g h t n e s s and c o l o u r measurements by t h e research vessel "Ayu-Dag" i n August 1977. Proc. o f t h e 1 1 t h Conf. o f B a l t i c Oceanographers, V o l . 2, Rostock. Lokk, J. and V. P e l e v i n , 1977. The i n t e r p r e t a t i o n o f t h e spectrum o f t h e u p w e l l i n g r a d i a t i o n based on the B a l t i c Sea. Proc. o f t h e 1 1 t h Conf. o f B a l t i c Oceanographers, Vol. 2, Rostock. Morel, A. and P r i e u r , L., 1977. Analysis o f v a r i a t i o n s i n ocean c o l o r . Limnol. Oceanogr. , 22: 709-722. Pelevin, V.N., M.A. Pelevina and B.F. Kelbalikhanov, 1979. Upwelling spectrum s t u d i e s from aboard a h e l i c o p t e r ( i n Russian) Opticheskie metody i z u c h e n i j a okeanov i v n u t r e n n i h vodojemov, Novosibirsk. Pelevin, V . , A. Gruzevich and J. Lokk, 1980. On t h e p o s s i b i l i t y o f e v a l u a t i n g t h e d i s t r i b u t i o n o f y e l l o w substance i n t h e sea water by t h e outcoming r a d i a t i o n spectra ( i n Russian), Svetovye p o l j a v okeane., Mos kva. Schmidt, D. and K.A. U l b r i c h t , 1978. Mass occurrence o f blue-green algae i n t h e Western B a l t i c e v a l u a t i o n o f s a t e l l i t e imagery and i m p l i c a t i o n s on marine chemistry and p o l l u t i o n . Proc. o f t h e 1 1 t h Conf. o f B a l t i c Oceanographers, Vol. 1, Rostock.
531
THE INFLUENCE OF HYDRODYNAMICS ON THE CHLOROPHYLL FIELD I N THE OPEN BALTIC MAT1 KAHRU Department o f t h e B a l t i c Sea, I n s t i t u t e o f Thermophysics and E l e c t r o p h y s i c s , P a l d i s k i S t . 1, T a l l i n n 200031, USSR INTRODUCTION The c o n c e n t r a t i o n o f c h l o r o p h y l l
-
rescence
2 - more c o r r e c t l y , i t s i n v i v o f l u o -
i s u n i q u e among t h e many b i o l o g i c a l parameters c h a r a c t e r i z i n g a because i t i s amenable t o measurement by i n s i t u and
p e l a g i c ecosystem, remote sensors.
The c h l o r o p h y l l
t h e p h y t o p l a n k t o n abundance.
5
c o n c e n t r a t i o n i s i m p o r t a n t as an index o f
Moreover,
i t may be a u s e f u l i n d i c a t o r o f
hydrodynamic processes, as d i s c u s s e d i n t h i s paper. The s p a t i o - t e m p o r a l
dynamics o f c h l o r o p h y l l i s much more c o m p l i c a t e d
t h a n t h a t o f t h e common h y d r o g r a p h i c v a r i a b l e s , e.g.
s a l i n i t y , due t o i t s
i n t e n s e v e r t i c a l f i n e s t r u c t u r e and i t s e s s e n t i a l l y n o n c o n s e r v a t i v e n a t u r e . The t i m e s c a l e s o f t h e s p a t i a l l y heterogeneous n o n c o n s e r v a t i v e processes, t h e p h y t o p l a n k t o n r e p r o d u c t i o n and t h e g r a z i n g by z o o p l a n k t o n , a r e o f t h e Hydrodynamics c o n t r o l s t h e c h l o r o p h y l l f i e l d by 1) advec-
o r d e r o f 1 day.
t i o n and d i f f u s i o n , and 2) b y changing t h e l o c a l r a t e s , e . g . ,
o f reproduc-
A d e l i c a t e b a l a n c e between t h e s e processes determines
t i o n and g r a z i n g .
w h i c h one o f them dominates on some p a r t i c u l a r space and t i m e s c a l e s . S k e l l a m (1951), followers
(Okubo,
reproduction.
K i e r s t e a d and S l o b o d k i n (1953),
1978)
and a number o f t h e i r
have examined t h e b a l a n c e between d i f f u s i o n and
T h e i r a n a l y s i s l e a d s t o a c r i t i c a l p a t c h s i z e , below which a However, t h e c o n c e p t i s o n l y o f
p h y t o p l a n k t o n p a t c h i s e r a s e d by d i f f u s i o n .
l i m i t e d c o g n i t i v e v a l u e t o a f i e l d e c o l o g i s t because a l l t h e r e l e v a n t p r o cesses a r e s p a t i a l l y heterogeneous. The
relative
assessed
by
the
Wroblewski (1973).
s = -u (
importance
of
nondimensional
advection number,
S,
versus
reproduction
introduced
by
may
O'Brien
be and
For a geostrophic flow;
f )%
r %
where U i s t h e c h a r a c t e r i s t i c speed of t h e o r g a n i z e d f l o w , r i s t h e maximum g r o w t h r a t e o f t h e p l a n k t o n , f i s t h e C o r i o l i s parameter, and AH i s t h e eddy d i f f u s i v i t y f o r momentum.
When S exceeds u n i t y , a d v e c t i o n becomes dominant
532
over b i o l o g i c a l turnover i n determining the h o r i z o n t a l c h l o r o p h y l l d i s t r i b u t i o n ., For parameter values t y p i c a l o f the B a l t i c (r = Z X ~ O - s~- I ; f = AH = 106 cm2 s- 1) i.t appears t h a t advection dominates i f U > 2 cm s-’. Despite t h e u n c e r t a i n t y i n t h e estimate o f AH, the gross v a l i d i t y o f t h i s r e s u l t w i l l be demonstrated l a t e r . S-1;
METHODS The c h l o r o p h y l l f i e l d and i t s i n t e r a c t i o n w i t h the hydrodynamic processes i n the south-eastern Gotland Basin were studied by means o f r e c u r r e n t quasi -synopti c surveys a t s t a t i o n s coveri ng various rectangular g r i d s , w i t h a spacing o f 5 n a u t i c a l m i l e s (9.3 km) between g r i d p o i n t s . A t y p i c a l g r i d area was 20x25 n a u t i c a l miles. A t each g r i d p o i n t , v e r t i c a l p r o f i l e s were fluorometer, measuring c h l o r o p h y l l 5 obtained using a Variosens fluorescence, and a N e i l Brown Mark 111 CTD probe. The fluorometer c a l i b r a & t i o n and other d e t a i l s may be found i n Kahru (1981a) and Kahru
fi situ
(1981). The d u r a t i o n o f a survey was about 1 day. As the c h l o r o p h y l l concentrations a t f i x e d depths are r e a d i l y contaminated by i n t e r n a l waves and t h e v a r i a b l e v e r t i c a l f i n e s t r u c t u r e (Kahru e t a l . , 1981), o n l y v e r t i c a l l y i n t e g r a t e d concentrations are considered i n t h i s paper. The CTD data o f t h e same surveys are i n t e r p r e t e d i n d e t a i l by Aitsam and Elken ( t h i s v o l -
ume). OBSERVATIONS AND DISCUSSION
The ecology o f t h e B a l t i c Sea has been r e c e n t l y reviewed by Jansson A c h a r a c t e r i s t i c f e a t u r e o f t h e B a l t i c Sea hydrography i s t h e d i s (1978). t i n c t l a y e r i n g o f t h e water column i n t o 3 l a y e r s i n summer:
t h e upper
l a y e r , which coincides approximately w i t h the p h o t i c l a y e r ; t h e intermediate layer, o r t h e w i n t e r convection layer; and t h e deep, s a l i n e l a y e r (Fig. 1). The 2 peaks i n t h e Brunt-Vaisala frequency, separating t h e layers, a r e associated w i t h t h e seasonal thermocline (depth o f 15 t o 30 m) and t h e A f t e r the s p r i n g phytoplankton bloom, l a s t permanent h a l o c l i n e (50-70 m). i n g f o r a few weeks, the upper 2 layers are almost depleted o f inorganic nitrogen, and t h e phytoplankton growth i s l i m i t e d by b i o l o g i c a l d e s t r u c t i o n and by the r a t e o f upward m i x i n g o f n i t r a t e s from t h e deep l a y e r (where the n i t r a t e concentration remains about 100 times higher than i n t h e higher layers). Consequently, the i n f l u e n c e o f t h e hydrodynamics on the phytoplankt o n growth i s manifested mainly through t h e t r a n s f e r o f n u t r i e n t s i n t o the upper layer. surveys.
A number o f mixing p a t t e r n s i s revealed by t h e c h l o r o p h y l l
533
I '
--; '---.-.-.-. *---= ./
2 0--;
I
I --I
0
Y
5QIQ
1
80-
I
; I I
IL
i
._' ii I! 6 0.- '\ .\'' (.
/' .'
i
i:
j
..
UL ..........
!
i
\ 40-j
Tf'
i
AF.-.~-.--J
1
f
i ....
.........
\
-!
DL
\
ii
Fig. 1. Typical thermohaline layering of the Baltic Proper into 3 layers: upper (UL), intermediate (IL), and deep layer (DL), with plots of temperature (T, "C), salinity (S, 0/oo), density (D, sigma-t), and the BruntVaisala frequency (N, rad s-') ( f r o m Kahru et al., 1981).
*) 5
10
.............. ................. .....
...
'
-2
mg CHL m
15 nm.
Fig. 2. Chlorophyll distribution (mg m-2, integrated between 2.5 and 32.5 in) in relation to the bottom topography (m). July 15-16, 1979. The upper left patch was observed repeatedly and i s ascribed to bottom mixing on the shallow bank. The upper right patch remains unexplained.
534
The bathymetry o f t he B a l t i c i s ver y i r r e g u l a r so t h a t t h e currents
1973) and, hence, t h e i n t e n s i t y o f v e r t i c a l mixing are When a s t r a t i f i e d f l u i d flows over a shallow submarine bank, and i f t h e f l o w i s s u b c r i t i c a l w i t h respect t o th e i n t e r n a l Froude number, t he isopycnals are compressed (Turner, 1973), (Kielman e t a l . ,
s u b ject t o a strong topographical inf luence.
and th e bottom turbulence may cause an upward t r a n s p o r t o f n u t r i e n t s .
This
can be recognized on some o f t h e c h l o r o p h y l l maps (Fig. 2). Although l i t t l e i s known about bottom m ixing i n t h e B a l t i c , t h i s k i n d o f boundary mixing can
be important f o r t h e o v e r a l l ecology due t o the frequent occurrence o f shallow banks. Geostrophic cur r ent s, s i g n i f i c a n t l y guided by t h e topography, are ,assoc i a t e d w i t h th e s l o p i n g o f isopycnals.
The r e s u l t i n g v e r t i c a l displacement
o f t h e thermocline and/or o f t h e h a l o c l i n e m odifies t h e thicknesses o f the
b a s ic l a ye rs. water
We have est ablished s i g n i f i c a n t r e l a t i o n s h i p s between t h e
stratification
and t he c h l o r o p h y l l
m i x i n g under c e r t a i n condit ions.
level,
suggesting i n t e n s i f i e d
I n p a r t i c u l a r , both t h e r i s i n g o f t h e t o p
o f th e deep l a y e r (Fig. 3) and t h e narrowing o f t h e intermediate l a y e r (Fig. 4) a re c l e a r l y associated w i t h an increase i n c h l o r o p h y l l concentration i n
I suggest t h a t the r i s i n g o f the h a l o c l i n e and the com-
several surveys. p re s si on of
nl I
E
I
loo B O S E X area,
May
8-9 , 1980
X
r
0.68
E 0 r I
0
60
80
70 Deep
layer
m
depth
Fig. 3. Dependence o f c h l o r o p h y l l 2 i n t h e upper 10-m l a y e r (mg m-’) h a l o c l i n e depth.
on t h e
535
mgm-2t
BOSEX
area, J u l y
1 - 3 , 1980
90
H
\+
+
E B H Eddy
u 0
+
-t
+
'*
40 4
40
F i g . 4.
45
50
m I n te rme d i a t e layer t hickness
Dependence o f t h e t o t a l c h l o r o p h y l l
t h e intermediate l a y e r thickness. c y c l o n i c eddy c e n t e r ,
55
60
2 i n t h e upper 60 m l a y e r on
The c i r c l e d p o i n t s , o r i g i n a t i n g from a
suggest suppressed m i x i n g i n t h e eddy c e n t e r .
They
have been e x c l u d e d when f i t t i n g t h e c u r v e b y l e a s t squares ( f r o m Kahru e t al.,
1981).
the
intermediate
layer,
both favorable
to
shears, can g i v e r i s e t o i n s t a b i l i t i e s , e.g.
the
development
of vertical
i n t e r n a l wave b r e a k i n g , c a u s i n g
i n t e n s e m i x i n g and, hence, i n c r e a s e d c h l o r o p h y l l biomass.
Figure 5 presents
a t y p i c a l s e c t i o n a c r o s s a t o p o g r a p h i c a l l y g u i d e d b a r o c l i n i c j e t , showing t h e b o t t o m c o n t o u r and t h e c o r r e s p o n d i n g i n t e g r a t e d c h l o r o p h y l l concentrations.
Here, c o n t r a r y t o t h e case o f b o t t o m m i x i n g , t h e c h l o r o p h y l l concen-
t r a t 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 t h e depth:
t h e shallowest area w i t h
t h e t h i c k e s t i n t e r m e d i a t e l a y e r s u p p o r t s t h e l o w e s t c h l o r o p h y l l l e v e l and v i c e versa. The c h l o r o p h y l l f i e l d shows s t r i k i n g mesoscale
(Z
10 km) p a t t e r n s even
i f t h e c o n c e n t r a t i o n i s i n t e g r a t e d v e r t i c a l l y o v e r t h e upper 60 m l a y e r .
The c o r r e l a t i o n s w i t h t h e s t r a t i f i c a t i o n suggest t h a t most o f t h e v a r i a b i l -
i t y i s caused by uneven n u t r i e n t f l u x e s f r o m t h e deep l a y e r r a t h e r t h a n by l a t e r a l m i x i n g o f d i f f e r e n t w a t e r masses.
I t i s tempting t o t r y t o estimate
t h e v e r t i c a l d i f f u s i v i t i e s t h a t m i g h t be r e s p o n s i b l e f o r t h e g e n e r a t i o n of such h e t e r o g e n e i t i e s .
U s i n g a r a t i o o f n i t r o g e n / c h l o r o p h y l l = 16, a p p r o p r i -
536
1
I
5
10
15
nautical miles
5. S e c t i o n across a b a r o c l i n i c j e t along t h e isobaths showing t h e bathymetry, t h e isopycnals i n t h e i n t e r m e d i a t e l a y e r , and t h e corresponding t o t a l c h l o r o p h y l l l e v e l s . BOSEX area, J u l y 1 - 3 , 1980. Fig.
a t e f o r n i t r o g e n - d e f i c i e n t phytoplankton ( S t r i c k l a n d , 1965), t h e c h l o r o p h y l l concentrations
may be c r u d e l y expressed i n terms o f n i t r o g e n .
For t h e
surveys shown i n Figures 3 and 4, t h e d i f f e r e n c e s between maximum and m i n i mum concentrations i n t h e upper 60 m l a y e r are 2220 and 875 mg N m-*, spectively.
re-
These amounts correspond t o about 18% and 8%, r e s p e c t i v e l y , o f
t h e mean t o t a l n i t r o g e n above t h e h a l o c l i n e .
As a f i r s t approximation, t h e
n i t r a t e f l u x across t h e h a l o c l i n e may be estimated as
Q=-K,
aNO3
az
537
aNO3 where K,
i s t h e v e r t i c a l d i f f u s i v i t y and
az
i s the v e r t i c a l gradient o f n i -
trate.
The l a t t e r i s a p p r o x i m a t e l y equal t o 3 mg N ~ n - ~ / mf o r t h e 50-70 m
layer.
By means o f dye d i f f u s i o n experiments, K u l l e n b e r g (1977) o b t a i n e d a
~ s-' v a l u e o f KZ = 2 . 2 ~ 1 0 - m2
f o r t h e mean v e r t i c a l d i f f u s i v i t y i n t h e h a l o -
c l i n e o f t h e Bornholm Basin.
S u b s t i t u t i n g t h e s e numer,jcal v a l u e s i n t o equa-
we o b t a i n a n upward n i t r o g e n f l u x o f 0.57 mg N m-'/day.
t i o n (2),
i s e x t r e m e l y s m a l l i n v i e w o f t h e observed v a r i a b i l i t y .
This f l u x
Indeed, a t t h i s
r a t e , more t h a n 1000 days would be needed t o accumulate an amount o f n i t r a t e s i m i l a r t o t h e t y p i c a l observed v a r i a t i o n s (more t h a n 500 mg N m-').
As t h e
t i m e s c a l e o f t h e p h y t o p l a n k t o n patches i s p r o b a b l y o f t h e o r d e r o f 1 0 days, t h e observed c h l o r o p h y l l v a r i a b i 1 it y can,not be e x p l a i n e d w i t h t h e above value o f t h e v e r t i c a l d i f f u s i v i t y .
Consequently, processes w i t h d i f f u s i v i -
t i e s h i g h e r by a t l e a s t 2 o r d e r s o f magnitude ( > at
least
locally
and t e m p o r a r i l y .
m2 s - l ) s h o u l d e x i s t
I n t h e B a l t i c thermocline,
vigorous
s h o r t - t e r m m i x i n g caused b y i n t e r n a l wave b r e a k i n g i n t h e i n t e n s e shear zones, c r e a t e d by i n e r t i a l waves, was shown by Krauss (1978). i t y o f n u t r i e n t t r a n s f e r across t h e thermocline,
e.g.
The p o s s i b i l -
d u r i n g storms,
is
f u r t h e r s u b s t a n t i a t e d by t h e v e r y l o w n i t r a t e v a l u e s below t h e thermo- and above t h e h a l o c l i n e . vertical Hence,
The i n t e r m i t t e n c y and d r a m a t i c v a r i a b i l i t y o f t h e
m i x i n g i n s t r a t i f i e d w a t e r s has been s t r e s s e d b y Woods (1977). the vertical diffusivities >
observations,
are not necessarily
m2 s-',
r e q u i r e d t o e x p l a i n my
i n c o n t r a d i c t i o n with t h e 2 orders o f
magnitude l o w e r v a l u e s measured by K u l l e n b e r g (1977) i n q u i e t e r c o n d i t i o n s . However,
t h e e v i d e n c e p r e s e n t e d h e r e f a r t h e e x i s t e n c e of i n t e n s e m i x i n g
e v e n t s i n t h e h a l o c l i n e o f t h e open B a l t i c i s i n d i r e c t and no well-document e d observations a r e a v a i l a b l e . S a t e l l i t e images ( U l b r i c h t and Horstmann,
1979) as w e l l as o u r CTD
s u r v e y s ( A i t s a m and E l k e n , t h i s volume) show a f r e q u e n t occurrence o f mesoscale eddies:
on e v e r y s u r v e y e d d y l i k e d i s t u r b a n c e s o f t h e r e l a t i v e dynamic
t o p o g r a p h y can be d i s c e r n e d .
The a n a l y s i s o f t h e i n t e r a c t i o n between ener-
g e t i c mesoscale e d d i e s and t h e c h l o r o p h y l l f i e l d i s c o m p l i c a t e d by t h e a d v e c t i o n and s t i r r i n g a c t i o n d u r i n g t h e p h y t o p l a n k t o n g r o w t h phase (1-3 days):
t a k i n g i n t o a c c o u n t t h e e f f e c t o f a d v e c t i o n , we have t o r e l a t e t h e
chlorophyll
biomass t o m i x i n g c o n d i t i o n s s e v e r a l days e a r l i e r .
T h i s has
h a r d l y been f e a s i b l e i n p r a c t i c e , and t h e a p p a r e n t e f f e c t o f a d v e c t i o n i s a r e d u c t i o n i n t h e c o r r e l a t i o n between t h e s t r a t i f i c a t i o n ( i . e .
mixing condi-
t i o n s ) and t h e c h l o r o p h y l l l e v e l . Two surveys made 10 days a p a r t d u r i n g c o m p a r a t i v e l y even p h y t o p l a n k t o n g r o w t h showed t h a t t h e c h l o r o p h y l l f i e l d was d i s t o r t e d b y a p a s s i n g eddy as a p a s s i v e s c a l a r f i e l d (Kahru, 1981b).
638 Another s u r v e y ( F i g . 4) seems t o i n d i c a t e t h a t t h e m i x i n g a c t i v i t y i n a
It seems t h a t t h e h y p o t h e s i s o f a
c y c l o n i c eddy i s r e m a r k a b l y suppressed.
r e d u c t i o n o f m i x i n g energy i n t h e eddy c e n t e r i s s u p p o r t e d by o b s e r v a t i o n s suggesting
a
decrease
i n wave
energy
i n t h e c e n t e r o f oceanic
eddies
( F r a n k i g n o u l , 1974; Dykman e t a l . , 1981). Three surveys made d u r i n g t h e decaying phase o f a p a r t i c u l a r l y e n e r g e t i c mesoscale eddy show u n u s u a l l y weak c o r r e l a t i o n s between t h e s t r a t i f i c a t i o n and t h e c h l o r o p h y l l l e v e l . advection,
stirring,
observational
This i s probably t h e r e s u l t o f t h e vigorous
and c u r r e n t shears,
a s s o c i a t e d w i t h t h e eddy.
e v i d e n c e f o r t h i s c o n c l u s i o n i s as f o l l o w s .
t r a n s l a t i o n a l v e l o c i t y o f a b o u t 2 cm s-'
The
The eddy has a
and t h e r o t a t i o n a l v e l o c i t i ? s a r e
The i s o p y c n a l e l e v a t i o n s i n t h e c e n t e r a r e 22 m a t
e s t i m a t e d a t 20 cm s-I.
t h e t o p o f t h e deep l a y e r .
A l t h o u g h t h e n u t r i e n t c o n c e n t r a t i o n s were n o t
measured, a s i g n i f i c a n t i n c r e a s e i n t h e n e a r - s u r f a c e s a l i n i t y p r o v i d e s e v i dence o f i n t e n s e v e r t i c a l m i x i n g and n u t r i e n t i n p u t .
T h i s e v i d e n c e i s based
on a c l o s e r e l a t i o n s h i p between t h e n u t r i e n t s and s a l i n i t y ( N e h r i n g , 1979) as b o t h a r e m i x e d upwards f r o m t h e deep,
saline layer.
between t h e upper and deep l a y e r s a l i n i t i e s
The c o r r e l a t i o n
i s maximal d u r i n g t h e most
a c t i v e phase o f t h e eddy ( F i g . 6A), a l s o s u g g e s t i n g v e r t i c a l m i x i n g , and i t decreases l a t e r t o z e r o as a r e s u l t o f s t r o n g v e r t i c a l shears. time
the
near-surface
salinity
reaches
i t s maximum.
A t t h e same
The o c c u r r e n c e o f
v i g o r o u s s t i r r i n g i s a l s o s u b s t a n t i a t e d by a decrease i n t h e s p a t i a l s c a l e s of variability
5m x-.
\
' -..\ "'60 \
m
..
ChiTOT/Sal 60m x
'.
1.o
I3
A
.- 0.5
x
* : : : . : : : . : . : : ;
Fig.
6.
%\.
\
'5OT
X
,. x
5m
..
0.0
\
\
\
X
\
-r \
..
. . .
/x
x--x
-.
Trends i n s e v e r a l parameters on 3 c o n s e c u t i v e s u r v e y s d u r i n g t h e
breakdown o f an e n e r g e t i c mesoscal e eddy:
c o r r e l a t i o n s between t h e t o t a l
c h l o r o p h y l l and t h e s a l i n i t y a t 60 m, and between t h e s a l i n i t i e s a t 5 m and
60
m (A);
s p a t i a l a u t o c o r r e l a t i o n s over 5 n a u t i c a l m i l e s o f t h e t o t a l chlo-
r o p h y l l and t h e s a l i n i t y a t 5 m (B).
539
of
t h e near-surface s a l i n i t y , i . e .
f i n e - g r a i n e d p a t t e r n (Fig.
6B).
by a s h i f t f r o m a coarse-grained t o a
The c h l o r o p h y l l f i e l d a l s o shows an unA1 though s u b s t a n t i a l amounts o f n u t r i e n t s
usually fine-grained pattern.
were probably mixed i n t o t h e upper l a y e r by t h e c y c l o n i c eddy, t h i s i s n o t apparent i n t h e c h l o r o p h y l l / s a l i n i t y c o r r e l a t i o n due,to t h e vigorous advect i o n , s t i r r i n g , and shears.
The O'Brien-Wroblewski parameter, equation (l),
c a l c u l a t e d f o r t h e r o t a t i o n a l v e l o c i t y o f t h e eddy, s u r e l y exceeds u n i t y , which confirms t h e dominance o f advection over t h e phytoplankton reproduction.
I n accordance w i t h t h i s concept, t h e weakening o f t h e eddy coincides
w i t h a s l i g h t increase i n b o t h t h e c h l o r o p h y l l / s a l i n i t y c o r r e l a t i o n and t h e s p a t i a l scales o f t h e c h l o r o p h y l l f i e l d ([,ig.
6).
I t should be s t r e s s e d t h a t our a b i l i t y t o i n t e r p r e t t h e b i o l o g i c a l dynamics and i t s ccinpl i c a t e d i n t e r a c t i o n w i t h vigorous hydrodynamic processes i s by no means unambiguous.
More d e t a i l e d synoptic surveys o f sev-
e r a l r e p r e s e n t a t i v e b i o l o g i c a l and hydrographic parameters are needed. routine
use
of
biological
sensors mounted on a v e r t i c a l l y
A
undulating
' B a t f i s h ' (Denman and Herman, 1978) would represent a s u b s t a n t i a l progress. CONCLUSIONS The c h l o r o p h y l l
f i e l d i n t h e open B a l t i c Sea i s c l o s e l y r e l a t e d t o
v a r i o u s hydrodynamic processes.
The s p a t i a l and temporal scales considered
i n t h i s paper a r e t h e s o - c a l l e d mesoscales (10-100 km and 1-10 days), where t h e b i o l o g i c a l t u r n o v e r r a t e o f t h e phytoplankton becomes comparable t o t h e processes o f advection and d i f f u s i o n .
An increase i n c h l o r o p h y l l biomass
may be a s c r i b e d t o t h e phytoplankton growth i n response t o a n u t r i e n t i n p u t from t h e deep l a y e r as a r e s u l t o f v e r t i c a l mixing. a r e discerned
from t h e c h l o r o p h y l l p a t t e r n s :
Several m i x i n g regimes
bottom m i x i n g on shallow
banks, shear induced m i x i n g i n a t h i n i n t e r m e d i a t e l a y e r , and a suppression o f m i x i n g i n t h e c e n t e r o f a c y c l o n i c eddy. the halocline ( >
High v e r t i c a l d i f f u s i v i t i e s i n
m2 s - l ) , a t l e a s t l o c a l l y and t e m p o r a r i l y , a r e needed
t o e x p l a i n t h e observed c h l o r o p h y l l v a r i a b i l i t y by uneven n u t r i e n t f l u x e s . T h i s eddy d i f f u s i v i t y i s 2 orders o f magnitude higher than t h a t measured by dye experiments with
the
i n "quiet"
O'Brien-Wroblewski
c o n d i t i o n s (Kul lenberg, 1977). criterion,
vigorous
I n accordance
advection and s t i r r i n g
dominate over t h e b i o l o g i c a l t u r n o v e r f o r some periods.
For these periods
t h e apparent c o r r e l a t i o n s between t h e c h l o r o p h y l l l e v e l s and t h e hydrography a r e decreased.
540
ACKNOWLEDGEMENTS
I am indebted t o Prof. A. Aitsam f o r h i s support and guidance.
Without
t h e h e l p o f many members o f t h e Department o f t h e B a l t i c Sea t h i s work would have been impossible; t h e t e c h n i c a l assistance o f R. sions w i t h J.
Elken were most h e l p f u l .
Portsmuth and discus-
I thank P r o f .
J.C.J.
s u p p o r t i n g my p a r t i c i p a t i o n i n the Colloquium and D r . B.M.
Nihoul f o r
Jamart f o r h e l p
i n processing t h e manuscript.
REFERENCES Denman, K.L. and Herman, A.W., 1978. Space-time s t r u c t u r e o f a contine'ntal ecosystem measured by a towed p o r p o i s i n g v e h i c l e . J. Mar. Res., 36: 693-714. Dykman, V.Z., K i s e l e v , O.A. and Efremov, O . I . , 1981. Studies o f i n t e r n a l wave energy i n synoptic eddies based on t h e temperature f i e l d s t r u c 441-446. t u r e . Oceanology, Frankignoul , C . J., 1974. P r e l i m i n a r y observations o f i n t e r n a l wave energy f l u x i n frequency, depth-space. Deep-sea Res., 21: 895-909. Jansson, B.-0, 1978. The B a l t i c - A system a n a l y s i s o f a semi-enclosed sea. In: H. Charnock and G. Deacon ( e d i t o r s ) , Advances i n Oceanography, Plenum Press, New York, pp. 131-183. Kahru, M., 1981a. V a r i a b i l i t y i n the c h l o r o p h y l l f i e l d i n t h e B a l t i c Sea. A. Atisam ( e d i t o r ) , The i n v e s t i g a t i o n and m o d e l l i n g o f processes In: i n t h e B a l t i c , Academy o f Sciences o f t h e USSR, T a l l i n n , pp. 165-171. V a r i a b i l i t y i n t h e three-dimensional s t r u c t u r e o f t h e Kahru, M., 1981b. c h l o r o p h y l l f i e l d i n t h e open B a l t i c Sea. Oceanology, 21: 685-690. Kahru, M., Aitsam, A. and Elken, J., 1981. Coarse-scale s p a t i 3 s t r u c t u r e o f phytoplankton standing crop i n r e l a t i o n t o hydrography i n t h e open B a l t i c Sea. Mar. Ecol. Prog. S e r . , i n press. 1973. Currents and s t r a t i f i c a Kielman, J., Krauss, W. and Keunecke, K.-H., t i o n i n t h e B e l t Sea and Arkona Basin d u r i n g 1962-1968. Kieler Meeresforsch., 29: 90-111. Kierstead, H. and r o b o d k i n , L.B., 1953. The s i z e o f water masses cont a i n i n g p l a n k t o n blooms. J. Mar. Res., 12: 141-147. Krauss, W., 1978. I n e r t i a l waves and m i x i n g i n t h e thermocline (BOSEX-Results). Proc. 11 Conf. B a l t i c Oceanogr., Rostock, pp. 709-728. Kullenberg, G.E.B., 1977. Observations o f t h e m i x i n g i n t h e B a l t i c thermoand h a l o c l i n e l a y e r s . T e l l u s , 29: 572-587. Nehring, D., 1979. R e l a t i o n s h i p s between s a l i n i t y and i n c r e a s i n g n u t r i e n t concentrations i n t h e mixed w i n t e r surface l a y e r o f t h e B a l t i c from 1969 t o 1978. I C E S C.M. C: 24, 8 pp. O ' B r i e n , J.J. and Wroblewski, J X . , 1973. On advection i n phytoplankton models. J. Theor. B i o l . , 38: 197-202. Okubo, A., 1978. H o r i z o n t a l d E p e r s i o n and c r i t i c a l scales f o r phytoplankt o n patches. I n : J.H. S t e e l e ( e d i t o r ) , S p a t i a l p a t t e r n s i n p l a n k t o n communities, Plenum Press, New York, pp. 21-42. Random d i s p e r s a l i n t h e o r e t i c a l populations. BioSkellam, J.G., 1951. m e t r i k a , 38: 196-218. S t r i c k l a n d , L.D.H., 1965. Production o f organic m a t t e r i n t h e p r i m a r y stages o f t h e marine food chain. In: J.P. R i l e y and G. Skirrow ( e d i t o r s ) , Chemical Oceanography, Academic Press, London, Vol. 1, pp. 447-610. 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, New York, 367 pp.
11:
541
Ulbricht, K.A. and Horstmann, U., 1979. Blue green algae in western Baltic; detection from satellite. Int. Symp. Sensing, July 2-8, 1978, Freiberg, FRG, 9 pp. Woods, J.D., 1977. Parameterization of unresolved motions. In: (editor), Modelling and prediction o f the upper layers o f Pergamon Press, Oxford, pp. 118-140.
the southon Remote E . B . Kraus the ocean,
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543 CHARACTERISTIC PROPERTIES OF TURBULENT TRANSPORT
I N THE BLACK SEA V.I. P.P.
Zats and R.V.
Ozmidov
Shirshov I n s t i t u t e o f Oceanology Academy o f Sciences, USSR
The p r o p e r t i e s o f t u r b u l e n t t r a n s p o r t i n t h e Black Sea are p e c u l i a r because t h e Black Sea i s a c l o s e d basin w i t h no s i g n i f i c a n t t i d a l c u r r e n t s and a somewhat unusual hydrometeorological regime.
F o r example, t h e w e l l -
known contamination o f t h e main body o f t h e Black Sea by hydrogen sulphide
i s i n d i c a t i v e o f r a t h e r weak v e r t i c a l m i x i n g i n t h e deep l a y e r s o f t h e basin.
I n t h i s study o f t h e c h a r a c t e r i s t i c p r o p e r t i e s o f t u r b u l e n t exchange
i n t h e B l a c k Sea, we use t h e d a t a o f long-term c u r r e n t observations obtained w i t h buoy s t a t i o n s as w e l l as t h e r e s u l t s o f experiments on t h e d i f f u s i o n of dye a r t i f i c i a l l y i n t r o d u c e d i n t h e water. We have c a l c u l a t e d t h e h o r i z o n t a l t u r b u l e n t t r a n s f e r c o e f f i c i e n t s , K1, u s i n g measurements o f t h e f l u c t u a t i o n s o f t h e h o r i z o n t a l v e l o c i t y components obtained w i t h p r o p e l l e r - t y p e c u r r e n t meters. on buoy s t a t i o n s Caucasus.
The instruments were mounted
l o c a t e d i n deep c o a s t a l waters o f f t h e Crimea and t h e
The s t a t i o n s were l o c a t e d a t d i f f e r e n t distances from t h e shore
and t h e depth o f t h e lowest instrument ranged from 100 t o 200 meters. sampling r a t e o f t h e v e l o c i t y observations was 5 t o 30 minutes.
The
The s e r i e s
so obtained were f i l t e r e d w i t h a cosine f i l t e r w i t h t h e parameter ranging from 20 minutes t o a few tens o f hours,
The c a l c u l a t i o n o f K1 was performed
The r e s u l t s show t h a t t h e values o f K1 a r e c r i t i c a l l y
by E r t e l ' s method.
dependent on t h e averaging t i m e scale, To.
2
a r e lo2 t o lo3 cm / s
f o r c o a s t a l regions;
For small To, t h e values o f K1 f o r t h e core o f near-coastal
c u r r e n t s (about 5 m i l e s f r o m t h e c o a s t l i n e ) , t h e values o f K1 are l a r g e r , up
4 cm2/s.
t o 10
magnitude,
The values o f K1 increase w i t h To by about one order o f
and they reach some " s a t u r a t i o n " value f o r To
20 hours.
The
dependence o f K1 on To can be approximated by a power law w i t h an exponent n t h a t depends on t h e sampling r a t e o f t h e observations and on t h e hydrometeor o l o g i c a l conditions.
The value o f n i s i n t h e range 0 t o 2, b u t i n most
cases we f i n d t h a t 0 < n < 1. The values o f K1 u s u a l l y decrease w i t h depth.
However, we have some-
times noted an increase o f K1 i n t h e i n t e r m e d i a t e l a y e r s ( i n t h e depth range
27-75 m o r 50-100 m,
f o r example).
I n t h e bottom l a y e r s t h e h o r i z o n t a l
t r a n s p o r t c o e f f i c i e n t s a r e u s u a l l y smaller than i n t h e main water body by 1 to
3
orders o f magnitude.
During p e r i o d s o f calm weather o r unsteady
breeze, K1 i s u s u a l l y almost c o n s t a n t i n t h e upper l a y e r ;
i t i s maximum i n
544
t h e i n t e r m e d i a t e l a y e r below which i t decreases down t o t h e bottom.
A t high
t u r b u l e n t m i x i n g i s most i n t e n s e i n t h e upper l a y e r .
wind v e l o c i t i e s ,
In
t h i s case, K1 e i t h e r decreases monotonically w i t h depth o r i t decreases down t o the
i n t e r m e d i a t e l a y e r and remains almost constant thereunder.
As a
rule, the horizontal turbulent transport i n coastal regions i s anisotropic. The e l o n g a t i o n o f t h e e l l i p s e s o f t r a n s p o r t i s v a r i a b l e and depends on t h e d i s t a n c e from t h e s h o r e l i n e .
A number o f s t a t i s t i c a l c h a r a c t e r i s t i c s o f t h e c u r r e n t v e l o c i t y v a r i a b i l i t y was c a l c u l a t e d u s i n g t h e long-term c u r r e n t observations.
As ex-
pected, t h e variance o f t h e c u r r e n t v e l o c i t y f l u c t u a t i o n s increases w i t h t h e averaging scale T
0'
The variance o f t h e c u r r e n t f l u c t u a t i o n s u s u a l l y de-
creases w i t h depth, b u t now and again maxima o f variance a r e observed i n t h e intermediate
layers.
The c o n t r i b u t i o n o f t h e f l u c t u a t i o n s
w i t h periods
r a n g i n g f r o m 40 min t o 3 hours t o the t o t a l energy i s u s u a l l y 45 t o 60% f o r t h e surface l a y e r (10-20 m), 30% f o r t h e
about 10% f o r t h e t h i n bottom l a y e r and 10 t o
intermediate layers.
But these estimates may v a r y from one
season t o another and they depend on t h e weather c o n d i t i o n s and t h e hydrological situation. The shape o f t h e a u t o c o r r e l a t i o n f u n c t i o n s o f t h e v e l o c i t y components f o r deep s h e l f regions o f t h e Black Sea t u r n e d o u t t o be r a t h e r diverse. The observed f u n c t i o n s can be approximated e i t h e r by exponential f u n c t i o n s o r by a combination o f exponential and harmonic f u n c t i o n s w i t h d i f f e r e n t values o f t h e parameters.
The p e r i o d i c components i n t h e c o r r e l a t i o n func-
t i o n s a r e u s u a l l y more obvious f o r l a r g e smoothing p e r i o d s (exceeding t h e i n e r t i a l period).
The decrease o f t h e a u t o c o r r e l a t i o n f u n c t i o n values f o r a
one p o i n t s h i f t o f t h e argument (10 min) reaches 60 t o 90% f o r t h e upper l a y e r , 30 t o 90% f o r t h e i n t e r m e d i a t e l a y e r (depending on t h e c h a r a c t e r o f and 10 t o 30% f o r t h e bottom l a y e r .
the current).
The p e r i o d i c component
e x t r a c t e d u s i n g t h e c o r r e l a t i o n f u n c t i o n does n o t always correspond e x a c t l y t o t h e t h e o r e t i c a l value o f t h e i n e r t i a l o s c i l l a t i o n s a t t h e p o i n t o f observation.
T h i s phenomenon may be explained by t h e nonhomogeneity
o f the
c u r r e n t v e l o c i t y f i e l d and o f t h e o v e r l y i n g wind f i e l d as w e l l as by t h e i n f l u e n c e o f t h e bottom topography and t h e s h o r e l i n e geometry. I n most cases, nents, S(w),
t h e s p e c t r a l f u n c t i o n s o f t h e c u r r e n t v e l o c i t y compo-
a r e maximum over a whole frequency band i n t h e upper l a y e r and
minimum near t h e bottom. decrease w i t h depth.
I n general,
Sometimes,
t h e i n e r t i a l frequency peaks a l s o
however,
u s u s a l l y f o r weak unstable cur-
r e n t s , t h e maximum value o f S(w) can be observed i n t h e i n t e r m e d i a t e l a y e r s . For storm winds, the shoreline.
t h e f u n c t i o n s S(w) Approximations o f S(w)
g e n e r a l l y increase w i t h d i s t a n c e from by power expressions f o r frequencies
h i g h e r t h a n t h e i n e r t i a l frequency g i v e values o f t h e exponent i n t h e range
545
1 t o 4.
The n o n u n i v e r s a l i t y o f t h e s p e c t r a i l l u s t r a t e s t h e g r e a t v a r i e t y o f
f a c t o r s i n f l u e n c i n g c o a s t a l hydrodynamics. Estimates o f t h e r a t e o f t u r b u l e n t energy d i s s i p a t i o n , t o 1.8 x
cm2
i n t h e upper l a y e r . values o f
-
s - ~ , and t h e maximum values o f
E
E,
range f r o m
are u s u a l l y found
The l i f e t i m e s o f t u r b u l e n t eddies, estimated using t h e
and t h e v e l o c i t y variances, range from 20 t o 102 hours; d u r i n g
E
t h a t time, t h e eddies can be advected over distances from 5 t o 3 1 km. Some unusual p r o p e r t i e s o f t h e h o r i z o n t a l turbulence were revealed by c u r r e n t observations i n a shallow s h e l f r e g i o n near t h e western coast o f t h e
A t these s t a t i o n s , t h e maximum o f t h e f u n c t i o n S(u) s h i f t s f r o m
B l a c k Sea.
t h e i n e r t i a l frequency t o t h e h i g h frequency r e g i o n as t h e depth o f t h e observations
increases.
The s p e c t r a l makimum i s l e s s pronounced a t t h e
shallow water s t a t i o n s than a t s t a t i o n s where t h e depth i s 70 t o 90 m.
The
s p e c t r a a l s o show maxima corresponding t o p e r i o d s o f s y n o p t i c v a r i a b i l i t y ( 2 t o 4 days).
The r a t e o f energy d i s s i p a t i o n a t s t a t i o n s l o c a t e d on shallow
water shelves reaches values o f 1 . 5 x average,
t o 1.4 x
cm2
-
s - ~ . On t h e
these values a r e about one order o f magnitude higher than those
o b t a i n e d a t s t a t i o n s l o c a t e d on t h e deep water shelves.
The v e r t i c a l s t r u c -
t u r e o f t h e h o r i z o n t a l t u r b u l e n c e i s e s s e n t i a l l y dependent on season and weather c o n d i t i o n s a t s t a t i o n s l o c a t e d on b o t h t h e deep and shallow water s he1ves. The c a l c u l a t i o n o f t h e v e r t i c a l t u r b u l e n t t r a n s f e r c o e f f i c i e n t ,
K,
was
performed u s i n g wind waves parameters and t h e data o f dye d i f f u s i o n e x p e r i 2 ments. The values o f K, range from 45 t o 79 cm /s f o r waves due t o wind o f 2 f o r c e I11 I V on t h e B e a u f o r t scale, and from 150 t o 350 cm /s f o r waves
-
due t o wind o f f o r c e V
-
VI.
The wind waves produce t u r b u l e n c e p e n e t r a t i n g
t o depths o f 10 t o 30 m d u r i n g storms.
The values o f K,
determined u s i n g
t h e d a t a from t h e dye d i f f u s i o n experiments i n t h e surface' l a y e r are about 2 20 t o 30 cm /s f o r waves o f I11 - I V Beaufort numbers. From experiments on submerged j e t s o f dye a t depths o f 30 t o 50 m d u r i n g t h e p e r i o d o f w i n t e r 2 For h i g h convection, we c a l c u l a t e d values o f K, equal t o 100 t o 200 cm /s. 2 v e r t i c a l d e n s i t y g r a d i e n t s , t h e values o f K, decrease t o 0 . 1 t o 2.0 cm / s . Because KZ depends on t h e d e n s i t y s t r a t i f i c a t i o n and weather c o n d i t i o n s as w e l l as on t h e dynamical regime o f each p a r t i c u l a r r e g i o n , one can observe two-,
three-,
c o e f f i c i e n t K.,
and f o u r - l a y e r s t r u c t u r e s i n ' t h e v e r t i c a l d i s t r i b u t i o n o f t h e
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547
SUBJECT I N D E X
A d r i a t i c S e a , 3,
7,
10, 11, 18,
A f r i c a n c u r r e n t , 98,
114-116,
A f r o - S i c i l i a n B a s i n , 99,
179,
183.
403.
Alboran S e a , 13, 17, 33, 114, 119, 122, 303.
70,
60,
75,
76, 80-82,
87,
88,
Algero-ProvenGal B a s i n , 10, 129. AlDeX
(AlDine E x p e r i m e n t ) , 3,
6 , 7,
10.
Andaman ( S e a o f ) , 1. Antiamphidrome, 351. Aral
,
Lake
389.
Arkona B a s i n , 387, 405, Arno R i v e r ,
433.
11.
Atmospheric, see a l s o . p r e s s u r e - C i r c u l a t i o n , 3, 405, 414. - C o n d i t i o n s , 469, 488. - F a c t o r s , 13. - F o r c i n g , 1, 3, 7, 11, 459. - InDUt, 399. - Motions, 187, 189, 200. 202. Auckland c u r r e n t , 350. Azores a n t i c y c l o n e , 18. Baroclinic - L a y e r , 155. - Flow, 160. - Waves, 163. - Mode, 323, 324. B a r o c l i n i c model, 503,
506.
BarOtrODiC
-
Waves, 163.
B a r o t r o n i c model, 245, 246,
248,
265,
267,
274,
B e r n o u l l i e q u a t i o n , 155, 160. B e n t h i c e c o s y s t e m , 399. B-effect, B-plane,
453, 303,
459, 451,
Black S e a , 18, 23,
181.
101, 117.
Air-sea - Air-sea boundary l a y e r , 10. A i r - s e a i n t e r f a c e , 11, 177;182, - A i r - s e a i n t e r a c t i o n , 3, 10, 11. Aland Sea, 400, 401,
124, 177,
106, 111, 114, 116, 117, 119, 122.
464,
465.
460. 69,
115,
117, 122, 543-545.
B o n i f a c i o S t r a i t , 108, 111, 124, 125.
2?9,
303
94,
99,
101, 106,
111,
548 Bora wind, 7, 1 8 , 1 1 5 . Bornholm Basin, 3 8 7 , 3 9 1 , 3 9 2 , 3 9 6 , 397, 4 0 3 , 4 0 5 , 4 1 2 , 4 1 3 , 4 1 5 , 4 3 3 , 4 3 4 , 4 5 0 , 537.
BOSEX area, 4 1 9 - 4 2 1 ,
425,
433-435,
Bothnia (Gulf of), 400, 401,
403,
439, 405,
443, 406,
449,
450,
Boundary conditions, 156, 1 6 0 - 1 6 3 , 335,
337,
339,
342,
346,
367,
453,
472,
490,
534-536.
414.
189, 2 2 2 , 2 2 5 , 2 4 6 , 4 5 2 , 456, 504, 506.
304-306,
308,
331,
332,
Boussinesq - Approximation, 246, 3 2 7 . - Fluid, 79. Brunt-VaisalS frequency, 3 4 6 , 4 5 1 , 4 7 2 , 4 8 5 , 5 1 0 , 5 3 2 , 533. Buoyancy, 1 6 6 , 2 1 7 , 4 1 2 . Butterworth filter, 2 1 2 . Cadix - Bay of Cadix, 7 0 . - Gulf of Cadix, 1 7 , 3 3 . Caribbean - Caribbean Basin, 3 0 5 . - Caribbean Current, 3 0 0 , 3 0 1 , 3 2 2 , 324. - Caribbean Sea, 2 9 9 - 3 0 1 , 303, 3 0 4 , 325. Caspian Sea, 3 8 9 . Catalan Sea, 129. Cattegat Basin, 387. Celtic Sea, 2 0 6 , 2 0 8 . Chery friction coefficient, 382. China Sea, 1. Circulation, see also atmospheric circulation, 1, 10, 75, 76, 81-83, 98, 1 0 6 , 1 0 8 , 117, 1 2 4 , 1 2 7 , 1 2 9 , 131, 1 4 7 , 189, 1 9 0 , 192, 196, 2 0 5 , 209, 210, 233-239, 3 3 1 - 3 3 4 , 3 4 1 , 3 4 3 - 3 4 6 , 3 9 9 , 402, 406, 4 1 9 .
8 7 , 88, 97, 149, 150, 157-159, 179, 181, 187, 2 4 3 , 261, 2 8 8 , 3 1 7 , 3 2 0 , 3 2 5 , 3 2 9 ,
Coherence analysis, 214. Colville cape, 381. Concentration basin, 1 3 , 1 4 , 1 8 . Cook Strait, 3 7 0 . Coriolis - Coriolis effect, 1 1 7 . - Coriolis force, 33, 70, 143, 2 2 7 - 2 2 9 , 231, 3 4 6 , 514. - Coriolis parameter, 8 0 , 1 6 6 , 1 8 2 , 222, 289, 3 2 5 , 3 2 6 , 334, 3 8 2 , 451, 4 5 9 , 465,
472,
483,
504,
531.
Correlation, 1 4 , 70, 139, 1 8 6 , 1 9 2 , 210, 2 1 3 , 215, 2 2 3 , 2 2 4 , 226-228, 261, 450,
324, 377, 457, 463,
378, 511,
385, 520,
388, 523,
Cospectrum, 474. Current, see also residual - Inertial currents, 212. - Storm currents, 233, 237. - Wind induced currents, 4 6 5 .
391, 535,
3 9 3 , 402, 4 0 5 , 537-539, 544.
415,
434,
441,
231, 260, 442, 446,
549
-
T i d a l c u r r e n t , 33, 37, 69, 205, 208, 210, 218-220, 222, 233, 360, 362, 364, 366, 368, 376, 381, 382, 406, 543. T o t a l ( g l o b a l ) c u r r e n t , 37, 38, 41, 42, 48-50, 53, 55.
237,
356-358,
Danube River, 18. Density anomalies, 178, Density i n v e r s i o n , 431, D i f f u s i v i t i e s , 535,
182, 434,
446, 450.
436.
537,
539.
Diffusion, - Molecular d i f f u s i o n , 521. - Turbulent d i f f u s i o n , s e e turbulence. - Tensor of d i f f u s i o n c o e f f i c i e n t s , 521. - C h a r a c t e r i s t i c d i f f u s i o n time, 515. Dispersion, - Curves, 483. 486, 487. - R e l a t i o n , 453, 472. m p p l e r e f f e c t , 493. Downwelling, 143,
147-149,
Drag, 219, 329. - C o e f f i c i e n t , 81, 215,
151, 304,
410,
308,
506.
510.
Dynamic mean v e l o c i t y , 386. E a s t e r l y winds,
18.
Eddy, 2, 3, 10. 41, 47, 76, 91, 98, 99, 114, 145, 150, 152, 243, 244, 250-?54, 256, 258-262, 269, 270, 274, 277, 279, 282, 283, 285, 287-289, 299, 300, 302, 303, 307-315, 317, 318, 320, 322-324, 367, 419, 421-424, 426, 427, 432, 434, 443, 446, 448, 450, 451, 459, 460, 463, 464, 465, 469, 476, 479, 511, 512, 517, 519, 520, 521, 535, 537-539, 545. - Eddy c o e f f i c i e n t , 329, 331, 332, 334, 347. - Eddy energy, 270, 271, 274, 279, 318, 322, 324, 419. - Eddy generation ( f o r m a t i o n ) , 283, 287, 299, 303, 318, 324. - Eddy-mean e n e r g e t i c s , 244, 252, 270-272, 274, 275, 277, 283, 285, 287, 289, 291, 325. - Eddy r a d i u s ( d i a m e t e r ) , 243, 244, 249, 251, 252, 258-261, 288, 289, 464. - Eddy shedding, 243, 244, 248, 249, 251, 252, 254, 256, 258, 260-273, 265-267, 270, 275, 279, 285, 287, 288, 290, 303, 310, 315, 316, 318-320. - Eddy v i s c o s i t y , 80, 81, 179, 222, 248, 262, 274, 275, 285, 287, 289, 307, 308, 310, 326, 531. Ekman - D r i f t , 156. - Flow, 331, 341. - Layer, 179, 331-344, 346-348. - ::umber, 762, 265, 2;9, 326, 334. - Regime, 160. - Transport, 329, 331, 337, 341, 343,
344,
346.
Energy, s e e a l s o t u r b u l e n c e , eddy - Energy d i s s i p a t i o n r a t e s , 349, 352, 374, 377, 378, 381, 421. - K i n e t i c energy, 30, 267, 268, 270. 271, 274-276, 290, 292, 293, 302, 322, 324, 386, 470, 472, 474, 476. - P o t e n t i a l energy, 30, 270, 274, 290, 292, 293, 386. Enstrophy, 307. E t e s i a n winds, see Meltemi. Finland (Gulf o f ) , 400, F l o r i d a S h e l f , 264,
265,
401, 269,
403, 288.
406.
306,
318,
550 Florida Straits, 244,
246,
247,
271,
305.
Fourier analysis, 196, 352. Friction, 136, 222-224, 346,
352,
354,
370,
Frictional - Effects, 88, 331, - Force, 69. - Stress, 508.
226-228,
231,
371, 506,
514.
346,
248,
258,
270,
292,
321,
334,
342,
344,
354.
Froude number, 534. Fundy (Bay of), 378. GARP
(Global Atmospheric Research Programme), 3, 7.
Geostrophic - Geostrophic - Geostrophic - Geostrophic - Geostrophic - Geostrophic
current, 131, 443, 446, 459, 460, 534. equilibrium, 165. flow, 133, 136, 300, 331, 341, 343, 531. velocity, 269, 443, 455, 510. wind, 215, 239.
Genova ( G u l f of), 18, 136, 187, 189, Gibraltar (Straits o f ) , 13-17,
190.
19, 21,
23,
27,
Gravity (acceleration of), 80, 213, 245, 289,
33, 326,
71, 382,
75,
76,
435,
81,
483,
87, 504,
98,
101.
512.
Greenwich meridian, 33. Grenada Basin, 315,
317,
318,
320,
325.
Group velocity, 323. Gulf Stream, 244, 258. Gyres, 2, 60, 70,
75.
76, 82,
83,
87,
Halocline, 388, 441,
443,
390, 391, 396, 399, 446, 448-450, 453-455,
106. 180. 236,
279,
301,
302,
325.
403-407, 410-416, 424, 427, 434, 438, 439, 459, 462-464, 532, 534, 536, 537, 539.
Harmonic analysis, 214, 220, 236. Hauraki Gulf, 349, 350, 351,
352,
354,
371,
381.
Hydrometeorological conditions, 490, 543. Hydrostatic approximation, 246,
303.
Ice, 1. Inertial effects, 88, Inertial flow, 155,
357.
156.
Inertial motion, 406, 407. Instabilities, 17, 60, 61, 243,
-
244, 251, 252, 322-324, 352, 457. 483, Basoclinic instability, 3, 10, 79, 243-246, 283, 285, 287-289, 318, 322, 433, 451, 455, Barotropic instability, 10, 243, 244, 252, 288, 318, 322. Mixed instability, 270, 274, 275, 285, 287. 299,
302,
303,
318,
254, 256, 258, 259, 262, 288, 289, 535. 251, 252, 270. 271, 274, 275, 279, 457, 459-464, 469, 479, 487, 488. 270, 271, 274, 275, 217, 283, 285,
IOC (International Oceanographic Commission), 3. Ionian Sea, 94, 99,
101, 103,
Irish Sea, 205, 206, 208-210,
117,
121,
177.
221,
224,
226,
233,
235-238.
551 I s o b a t h , 189,
190,
433,
41,
60,
I s o h a l i n e , 28,
443, 410,
446,
449,
421,
450,
423,
Isopycnals, 412, 421, 423, 424, 443, 492-496, 498, 534, 536, 538.
464.
492,
494,
446,
495,
448-450,
499.
453,
455,
463,
464,
489,
JOC ( J o i n t Organizing Committee), 3. Kelvin waves, 168. Knudsen hydrographical theorem, 402. Labrador Sea, 7. Laplace - Equation, 155, 156. - Transformation, 162. Lee e f f e c t s , 301. Length s c a l e , 11, 179, 227, 228, 310, 323, ‘324, 496. - I n e r t i a l l e n g t h s c a l e , 258, 267, 290. - F r i c t i o n a l l e n g t h s c a l e , 258, 267, 290. Levantin Basin, 98, 99, L i f e t i m e , 464,
101, 117,
332,
333,
343,
382, 423,
187-190,
192,
196, 202.
483,
493,
124.
545.
Ligurian - Ligurian c u r r e n t , 131. - Ligurian Sea, 10, 93, 101, 129-131, Liguro-ProvenGal Basin, 3, Lions (Gulf o f ) , 7,
10, 11, 96,
101, 106,
109,
111, 120,
124.
138,
143,
151,
152,
163,
251, 252, 254, 287-289, 303.
256,
258-260,
11, 18, 116, 117,
Loop c u r r e n t , 243, 244, 247-249, 269, 270, 277, 279, 283, 285, Malin Shelf Sea, 206, 226,
141,
233,
236,
97, 129,
238,
155, 262,
165.
263,
265,
267,
181, 389, 402,
406,
419,
239.
Manning c o e f f i c i e n t , 382. Medalpex, 1, 3, Meltemi, 108,
7,
Messina S t r a i t , 99, Meteorological 544, 545.
11.
111, 114. 101.
(weather) c o n d i t i o n s , 7,
Mexico (Gulf o f ) , 79, 243,
244,
246-248,
10, 17, 266,
19,
274,
150, 277,
287,
288,
289,
303.
Miocene Age, 349. M i s t r a l , 3,
7,
10, 18.
Mixed l a y e r ( w a t e r ) , 3,
7.
11, 33, 379, 383, 403,
421, 424,
515.
Mixing, see a l s o t u r b u l e n c e , wind, 10, 17, 19, 28, 30, 60, 61, 71, 99, 106, 116, 147, 177, 179, 181, 205, 208, 329, 331, 348, 349, 352, 381, 386-3868 399, 400, 403, 405-407, 410-412, 414, 416, 421, 448, 532-535, 537-539, 543, 544. - Mixing c o e f f i c i e n t s , 407, 409, 411, 419. Modon, 277, 279, 285, 289. - Generation, 277, 283. NATO - NATO Conference on Modelling o f Marine Systems, 1. - NATO Mediterranean Outflow P r o j e c t , 17, 34. - NATO Subcommittee on Oceanic Research, 14.
562
-
NATO Technical Reports, 14, 73.
Neva River, 385, 386, 389, 392, 395. Nile River, 18. North Sea, 1, 400, 402, 406, 412, 450. Nutrients, 1, 402, 405, 410, 414, 415, 416, 532, 534, 535, 538, 539. O'Brien - Wroblewski parameter, 531, 539. Ob River, 389. Oscillations, see also waves - Baroclinic oscillations, 168, 170, 173-175. - Barotropic oscillations, 168, 170. - Inertial oscillations, 160, 406, 410, 476. Pelagic ecosystem, 399, 531. Phytoplankton, 381, 416, 523, 524, 531, 532, 536, 537, 539. Po River, 11, 18, 179, 183. Poincar6-Kelvin amphidromy, 168, 175. Pressure - Air pressure, 387, 391, 392, 397, 406. - Atmospheric pressure, 10, 69, 70, 129, 133, 136, 138-140,
-
190,
212,
213,
215
238.
Barometric pressure, 385, 388, 392, 393. Pressure anomaly, 317, 322. - Pressure field, 13, 227, 244, 269, 289, 317. - Pressure gradient, 205, 223, 226, 221, 229, 231, 233, 238, 239, 246, 332, 335,
-
406.
Pycnoline, 179, 181, 209, 245. - Pycnoline anomaly (PA), 82, 249, 315-321. Radiance, 523, 524, 528, 529. Reduced-gravity, 75, 79, 80, 82, 87, 155, 163, 243, 245, 248, 251-253, 270-272,
274,
275,
279, 287-289,
299,
304,
310,
318-324,
Relative dynamic topography ( R D T ) , 421, 425, 435, 439, 441-450, 463,
465,
256-267,
326. 455,
457, 459,
537.
Reservoir effect, 389, 390. Residence time, 205, 387, 399, 403. Residual current, 366, 367, 370, 372, 381. Reynolds number, 243, 261, 262, 265-267,
290.
Rhone River, 11, 18, 116. Richardson number, 505. Riga ( G u l f of), 525, 526. River runoff, 116, 117, 119, 385, 386, 387, 388, 389, 392, 393, 395, 399, 402, 405, 412.
Rossby - Rossby deformation radius, 11, 163, 172, 241, 254, 317, 323, 433, 434, 459. Rossby number, 243, 254, 258, 262, 265, 266, 290. - Rossby waves, 87, 249, 252, 254. 256, 258, 261, 262, 267, 279, 283, 285, 287-
-
289,
317,
320,
450, 465,
469.
Salinity anomalies, 403, 405. Sand bank formation, 357, 381.
563
-
-
Q u a r t e r d i u r n a l t i d e , 382. Semi-diurnal t i d e , 34, 37, 41, 208, 212, 234, 351, 352, 382. T i d a l c y c l e (frequency, p e r i o d ) , 19, 25, 33, 37, 41, 55, 56, 349, 366, 367, 371, 374,
-
-
382.
T i d a l e f f e c t s , 19, 30, 41, 53, 69, T i d a l f o r c i n g , 34, 41, 53.
Time s e r i e s , 7, 480,
183,
189,
196, 200,
136.
223,
225,
230,
232,
386-394,
397,
473, 479,
487.
Trade winds, 303,
325.
Tramontane wind, 3, 7, 18,
143.
T r e s Forcas (Cape), 76, 82,
106.
T u r b i d i t y , 381. Turbulence, s e e a l s o energy - Turbulence production, 386. - Turbulent d i f f u s i o n , 504-506, 517, 519, 520, 521, 522. - Turbulent d i s s i p a t i o n , 10. - Turbulent e f f e c t s , 106. - Turbulent exchanges, 504, 505, 506, 543. - Turbulent flow, 511, 512, 517, 519, 520. - Turbulent f l u x e s , 11, 503. - Turbulent t r a n s f e r c o e f f i c i e n t s , 543, 545. Tuscan Archipelago, 187, 202. Tyrrhenian Sea, 99,
101, 129,
131,
136,
187,
190,
192, 202.
Upwelling, 1, 11, 91, 97, 165,
192, 329,
331,
10,3,' 108, 111, 114-116, 127, 143, 332, 341, 342, 347, 381, 410, 506.
V a r i a b i l i t y , 47,
75, 87, 91, 122, 149-152, 402, 412, 414, 422, 424, 433, 438, 453, 510, 523, 535, 537, 538, 544, 545.
Venezuelan Basin, 304,
305,
205, 237, 469, 479,
145,
147-152n 155,
299-302, 308, 310, 322, 488, 489, 496-498, 500,
163,
393, 503,
325.
Volga River, 389. Von Karman's c o n s t a n t , 508. V o r t i c i t y , 75, 87, 349, 357,
187, 192, 243, 252, 258, 259, 367, 370, 374, 381, 451, 460, 463.
262, 265, 269,
287,
317,
323,
325,
Vuoksi River, 395. Waikou River, 350, 377,
381.
Waves - Acoustic waves, 91. - Gravity waves, 247, 248. - I n e r t i a l - g r a v i t y waves, 165, 166, 168, 170, 172, 174, 175. - I n t e r n a l waves, s e e a l s o t i d a l waves, 1, 7, 13, 27, 33, 34, 39-41, 44-47, 51-53, 57, 58, 60, 61, 63-69, 71, 406, 419-424, 426, 427, 438, 439, 443, 489, 492, 493,
-
-
497, 498,
532,
535.
Standing waves, 234, 349, 353, 371. Surface waves, 1, 10, 515. T i d a l waves, see a l s o i n t e r n a l waves, 33, 34, 351, 353, 354, 371. Topographic waves, 433, 451-457, 464, 469, 472, 474, 476, 479. Wave number, 256, 290, 354, 382, 420, 421, 426, 452, 453, 454. Wind waves, 166, 545.
Wind s t r e s s , 10, 80, 81, 189,
190,
199, 200,
136, 149, 152, 155, 156, 160-162, 177, 179, 182, 183, 187, 213, 215, 222-224, 226-229, 231, 233, 235, 238, 239, 367,
554
Sediment s t r u c t u r e , 377. S e i c h e , 7,
189, 406.
S h e a r , see a l s o i n s t a b i l i t i e s , 19, 30, 86, 331, 332, 337, 342, 344, 346, 347, 407, 507, 508, 510, 535, 538, 539. S i r o c c o , 114, S l i c k s , 53,
201, 433,
202, 451,
243, 453,
283, 455,
303, 306, 322, 457, 458, 459,
323, 464,
181.
523.
S p a r t e l (Cape o f ) , 30, 34, 53. S p e c t r a l a n a l y s i s , 172, 421,
476.
( G u l f o f ) , 329,
330,
S t . Lawrence
347.
S t a b i l i t y , 322-324, 387, 390, 406, 412-414, - N e u t r a l s t a b i l i t y , 215. - Numerical s t a b i l i t y , 307. - S t a b i l i t y a n a l y s i s , 251, 322, 325. - S t a b i l i t y d i a g r a m , 265-267. S t a t i s t i c a l a n a l y s i s , 147,
187,
457,
479,
492.
456,
407,
408,
189.
S t e n t o n number, 505. S t e w a r t s o n l a y e r , 329,
334-347.
S t o k e s d r i f t , 234. Storm, 7 , 10, 148,
165,
181, 209,
226,
239,
409,
465, 525, 544, 545.
S t r a t i f i c a t i o n , 3, 106, 147. 151, 152, 177, 179, 181, 303, 329, 343, 346, 347, 378, 379, 381, 382, 403, 405-407, 412, 426, 427, 438, 439, 454, 460, 463, 469, 472, 479, 488, 491, 492, 514, 534, 535, 537, 538, 545. - S t r a t i f i e d f l o w , 323, 386. - S t r a t i f i e d w a t e r , 7, 235, 387. 436, 465, 537. Streamfunction, 483.
155,
S t r e a m l i n e s , 157-159,
156,
160,
252,
258,
199, 332,
200, 344,
343, 346,
344, 446,
441, 450,
443, 463,
452, 464,
455,
456,
472,
512.
S t r o u h a l number, 261. Tamaki S t r a i t s , 349, Tasman S e a , 350,
351,
367.
352.
Temperature i n v e r s i o n , 379. Temperature-salinity - Curve, 498. - Diagram, 29-32, 34, 6 1 , 62. - S t r u c t u r e , 329. T h e r m o c l i n e , 3, 11, 106, 117, 165, 379, 381, 390, 396, 399, 404, 405, 407-409, 433, 435, 438, 439, 449, 453, 454, 455, 464, 493, 496, 506, 532, 534, 537.
424,
Thermohaline - C o n v e c t i o n , 403, 405. - L a y e r i n g , 533. - P e r t u r b a t i o n s , 498. - S t r u c t u r e , 491. T i d e s , 7, 10, 13, 14, 17, 19, 20, 25, 28, 214, 221, 227-229, 352, 353, 366, 371, - C o o s c i l l a t i n g t i d e , 354, 370. - C o t i d a l l i n e s , 353. - D i u r n a l t i d e , 20, 37, 60, 212.
30, 33, 34, 37, 41, 60, 61, 375, 376, 378, 386, 391.
63-69,
205,
555 386, 388,
390-392,
Yucatan S t r a i t s , 243, Zooplankton, 416,
406,
465,
505.
244,
246,
249,
251,
254,
267, 269,
271,
288,
289. 300,
305.
531.
Acknowledgments The e d i t o r , i s endebted t o h i s research s t u d e n t Ph. Ngendakumana f o r h i s h e l p i n p r e p a r i n g the index.
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