Hydrodynamics of the Equatorial Ocean: Proceedings of the 14th International Liege Colloquium on Ocean Hydrodynamics (Elsevier Oceanography Series)

HYDRODYNAMICS OF THE EQUATORIAL OCEAN

FURTHER TITLES IN THISSERIES 1 J.L.MER0 THE MINERAL RESOURCES OF THE SEA 2 L.M. FOMIN 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 I N MARINE GEOLOGY 7 W.J. WALLACE THE DEVELOPMENTS OF THE CHLORINITY/SALINITY CONCEPT I N OCEANOGRAPHY 8 ETLISLTZIN SEA-LEVEL CHANGES 9 R.H.PARKER THE STUDY OF BENTHIC COMMUNITIES 10 J.C.J. NIHOUL (Editor) MODELLING OF MARINE SYSTEMS 1 1 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 MARINE PHOTOSYNTHESIS 14 N.G. JERLOV ~MARINE OPTICS 15 G.P. GLASBY MARINE MANGANESE DEPOSITS 16 V.M. KAMENKOVICH FUNDAMENTALS OF OCEAN DYNAMICS 17 R.A.GEYER SUBMERSIBLES AND THEIR USE I N OCEANOGRAPHY AND OCEAN ENGINEERING 18 J.W. CARUTHERS FUNDAMENTALS OF MARINE ACOUSTICS 19 J.C.J. 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 INDIAN 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) MAR I N E FOR ECASTING 26 H.G. RAMMING and 2. KOWALIK NUMERICAL MODELLING MARINE HYDRODYNAMICS 27 R.A. GEYER (Editor) MAR IN E ENVIRONMENTAL POL LUTl ON 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 32 J.C.J. NIHOUL (Editor) ECOHYDRODYNAMICS 33 R. HEKlNlAN PETROLOGY OF THE OCEAN FLOOR 34 J.C.J. NIHOUL (Editor) HYDRODYNAMICS OF SEMI-ENCLOSED SEAS 35 B. JOHNS (Editor) PHYSICAL OCEANOGRAPHY OF COASTAL AND SHELF SEAS ~

Elsevier Oceanography Series, 36

HYDRODYNAMICS OF THE EQUATORIAL OCEAN PROCEEDINGS OF THE 14th INTERNATIONAL LIEGE COLLOQUIUM ON OCEAN HYDRODYNAMICS

Edited by JACQUES C.J. NIHOUL Professor of Ocean Hydrodynamics, University of Lizge, LiGge, Belgium

ELSEVl E R Amsterdam - Oxford - New York

1983

ELSEVIER SCIENCE PUBLISHERS B.V., Molenwerf 1, P.O. Box 21 1,1000 AE Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY INC. 52, Vanderbilt Avenue New York, N.Y. 10017

ISBN 0-444-42196-3 (VOl. 36) ISBN 0-444-41623-4 (Series) 0 Elsevier Science Publishers B.V., 1983

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 publishers, Elsevier Science Publishers, B.V., P.O. Box 330,1000 AH Amsterdam, The Netherlands. Printed in The Netherlands

V

The International Liege Colloquia on Ocean Hydrodynamics are organized annually.

Their topics differ from one year

to another and try t o address, as much as possible, recent problems and incentive new subjects in physical oceanography. Assembling a group of active and eminent scientists from different countries and o f t e n d i f f e r e n t d i s c i p l i n e s , 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. The Scientific Organizing Committee and all the participants wish to express their gratitude to the Belgian Minister of Education, the National Science Foundationof Belgium, the University of Liege, the Intergovernmental Oceanographic Commission and the Division of Marine Sciences (UNESCO) and the Office of Naval Research for their most valuable support.

This Page Intentionally Left Blank

VII LIST OF PARTICIPANTS ARY, S., Mr., University of Niamey, Niger. BAH, A., Dr., Ecole Polytechnique de Conakry, Guinea. BOUKARY, S., Mr., University of Niamey, Niger. BOYD, J.P. Dr., Space Research Bldg., Ann Arbor, Mi., U.S.A. BUSALACCHI, A.J., Dr., ~loridaState university, Tallahassee, Fl., U.S.A. CASAS-VAZQUEZ, J., Prof., Dr., universidad Autonoma de Barcelona, Bellaterra, Barcelona, Spain. DELAFOSSE, G., Dr., EPSHOM, Brest, France. DELECLUSE, P., Dr., Museum d'Histoire Naturelle, Laboratoire d'Oc6anographie Physique, Paris, France. DISTECHE, A., Prof., Dr., Universite de LiGge, Belgium. DJENIDI, S., Mr., 2, rue BP

Cite Plaisance, Annaba, Algeria.

ERIKSEN, Ch., Prof., Dr., Massachusetts Institute of Technology, Cambridge, Mass., U.S.A. FAHRBACH, E., Dr., Institut fur Meereskunde an der Universitat Kiel, Kiel, Germany. FINE, R.A., Dr., National Science Foundation, Washington, D.C., U.S.A. FOUMAKOYE, G., Mr., University of Niamey, Niger. FRANKIGNOUL, C., Prof., Dr., Universit6 Paris VI, Laboratoire de Physique et Chimie Marines, Paris, France. GASPAR, Ph., Mr., Universit6 de Louvain, Louvain-La-Neuve, Belgium. GIBSON, C.H., Prof., Dr., University of California San Diego, La Jolla, Ca., U.S.A. GONELLA, J.A., Dr., Museum d'Histoire Naturelle, Laboratoire d'oceanographie Physique, Paris, France. HALPERN, D., Prof., Dr., Pacific Marine Environmental Laboratory, Seattle, Wa., U.S.A. HENROTAY, P., Mr., Universite de LiGge, Belgium. HISARD, Ph., Dr., Antenne ORSTOM, Centre Oceanologique de Bretagne, Brest, France. KINDLE, J.C., Dr., NORDA, Naval Ocean Research NSTL Station, Ms., U.S.A.

&

Development Activity,

KRAUS, E.B., Prof., Dr., Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder, Boulder, Co., U.S.A. LASS, H.-U., Dr., Institut fiir Meereskunde, Rostock-Warnemunde, Germany.

LEBON, G., Prof., Dr., Universite de Lisge, Belgium. LEVY, Cl., Melle, Museum d'Histoire Naturelle, Laboratoire d'oceanographie Physique, Paris, France. Mc PHADEN, M.J., Dr., JISAO, University of Washington, Seattle, Wa., U.S.A. MERLE, J., Dr., Museum d'Histoire Naturelle, Laboratoire d'Oc6anographie Physique, Paris, France. MONREAL, M.A., Mme, CICESE, Ensenada, B.C., Mexico.

VIII MOLINARI, R.L., Dr., NOAA/AOML/PhOL, Miami, Fla., U.S.A. MOORE, D.W., Prof., Dr., JIMAR, University of Hawaii at Manoa, Honolulu, Hawaii, U.S.A. NGENDAKUMANA, Ph., Mr., Bujumbura, Republic of Burundi. NIHOUL, J.C.J., Prof., Dr., Universitf5 de Liege, Belgium. OLBERS, D.J., Dr., Max-Planck-Institut fur Meteorologie, Hamburg, Germany. PANITZ, H.-J., Dr., Institut fur Geophysik und Meteorologie, Universitat Koln, Germany. DU PENHOAT, Y., Dr., Antenne ORSTOM, Centre Ocf5anologique de Bretagne, Brest, France. PICAUT, J., Dr., Laboratoire d'Ocf5anographie Physique, Facult6 des Sciences, Brest, France. REVERDIN, G., Dr., Museum d'Histoire Naturelle, Laboratoire d'Ocf5anographie Physique, Paris, France. RIPA, P., Dr., CICESE, Ensenada, B.C., Mexico. RONDAY, F.C., Dr., Universit6 de LiPge, Belgium. R O W , M.A., Mr.,

Department of Oceanography, University of Southampton,U.K.

RUAL, P., Dr., Antenne ORSTOM, Centre Oc6anologique de Bretagne, Brest, France. SALAS DE LEON, D.A., Mr., CICESE, Ensenada, B.C., Mexico. SARACHIK, E.S., Dr., Center for Earth and Planetary Physics, Harvard University, Cambridge, Mass., U.S.A. SERVAIN, J., Dr., Laboratoire d'ocganographie Physique, Facult6 des Sciences, Brest, France. SMITZ, J., Mr., Universit6 de LiPge, Belgium. TRANNOY, P., Mr., Ecole Polytechnique, Palaiseau, France. TREGUIER, A.-M., Melle, Ecole Polytechnique, Palaiseau, France.

IX

CONTENTS

M.J. MC PHADEN

:

Equatorial sea surface temperature variations on

seasonal time scales M. FIEUX and C. LEVY

Ocean J. MERLE

:

.................................................. Seasonal observations in the Western Indian

................................................................. :

17

Seasonal variability of subsurface thermal structure in

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

the tropical Atlantic Ocean P.

1

SPETH and H.J. PANITZ

:

31

The variability of local winds at 22' W

and their influence on the oceanic system at the equator in the Atlantic during FGGE

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

R.L. MOLINARI, E. KATZ, E. FAHRBACH, H.U. LASS and B. VOITURIEZ

51

:

Near surface temperature observations obtained in the equatorial Atlantic Ocean during FGGE E. FAHRBACH

:

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

65

On the variation of the heat content in various verti-

cal layers in the central equatorial Atlantic G. REVERDIN, M. FIEUX, J. GONELLA and J. LUYTEN

......................... :

Free drifting buoy

measurements in the Indian Ocean equatorial jet

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

N.N. KORCHASHKIN and I.D. LOZOVATSKY

:

83

99

Investigation of small scale

structure of hydrophysical fields in the equatorial region of the Indian Ocean

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

R.V. OZMIDOV and M.L. PYZHEVICH

:

Velocity field fine structure and

..... equatorial undercurrent ....

shear instability of currents in equatorial regions of the oceans C.H. GIBSON

:

Turbulence in the core of the

A.J. BUSALACCHI, K. TAKEUCHI and J.J. O'BRIEN

:

:

125

131

On the interannual

wind-driven response of the tropical Pacific Ocean E.B. KRAUS and H.P. HANSON

121

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

155

On westward propagation of sea surface

temperature anomalies in the equatorial Pacific

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

197

P. DELECLUSE and S.G.H. PHILANDER

:

Variability of coastal zones in

low latitudes (with application to the Somali Current, the Gulf of Guinea and the El Niiio Current)

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

Y. du PENHOAT, M.A. CANE and R.J. PATTON

:

219

Reflections Of lOW fre-

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

quency equatorial waves on partial boundaries P. DELECLUSE

Coastal effects on upwelling

:

J.C.J. NIHOUL and A. BAH

RIPA and S.G. MARINONE

:

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

281

The effect of zonal currents on equato-

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

rial waves

W. FENNEL and H.U. LASS trapped waves

:

:

291

Theory of frequency spectra of equatorially

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

J.P. BOYD and Z.D. CHRISTIDIS J.C. KINDLE

259

Model of the Gulf of Guinea upwelling.

:

Influence of the coast's irregularities P.

237

:

.

339

.....

353

Instability on the equatorial f3-plane

On the generation of Rossby solitons during El Niiio

319

1

EQUATORIAL SEA SURFACE TEMPERATURE VARIATIONS ON SEASONAL TIME SCALES M. J. MC PHADEN The Joint Institute for the Study of the Atmosphere and Ocean University of Washington Seattle, Washington, 98195

1.1

INTRODUCTION

The study of sea surface temperature (SST) variability in the equatorial oceans is of great value to physical oceanographers and atmospheric scientists alike.

Aside from an interest in simply documenting and describing equator-

ial SST, oceanographers often use SST as a tracer for subsurface dynamical phenomena that are either too difficult or too expensive to observe directly. For example, the accumulation of warm water off the coast of Peru has often been interpreted as evidence for the existence of equatorial Kelvin waves (e.g. McCreary, 1976).

Likewise, Moore &

cold SST in the Gulf of Guinea

e.(1978) have hypothesized that

during coastal upwelling season is the result

of a coastal Kelvin wave, which through a complex series of events involving equatorial waves, is excited by changing winds in the western equatorial Atlantic.

The physical basis for this dynamical influence on SST is that when

cold thermocline water is brought closer to (further from) the surface, it is easier (harder) to mix across the base of the mixed layer. leads to colder (warmer) SST.

This in turn

These are only qualitative arguments however,

and ignore other important physical processes such as horizontal advection by surface currents. To quantify the connection between SST and subsurface dynamics, it is therefore necessary to determine the relative significance of various terms in the upper ocean heat budget. Variations in SST may also induce important dynamical effects in the equatorial oceans.

McPhaden (1981) has shown in a steady state model that the

response to zonally varying SST patterns is two orders of magnitude larger in the equatorial oceans than at mid latitudes and is comparable in magnitude and spatial structure to the wind-driven equatorial circulation.

This strong

dynamical effect is due to the sensitivity of geostrophic currents to small changes in horizontal thermal gradients at low latitudes.

Our understanding of

equatorial dynamics will therefore be limited to the extent that quanitative information on the processes which generate and maintain SST gradients is lacking. SST is an important lower boundary condition for atmospheric general cir-

2

culation models.

Results from a number of recent numerical experiments based

on these models have shown that equatorial SST anomalies have a larger effect on the overlying atmosphere than comparable mid-latitude anomalies (e.9. Shukla, 1975; Rowntree, 1976).

Moreover, these effects can be global in nature as

Bjerknes (1966, 1969) suggested in his early work on meridional teleconnections. It is clear therefore that effective climate modeling will require a better understanding of the factors that control equatorial SST than we have at present. This study has two purposes.

The first, which is discussed in Section 2, is

to provide a brief description of seasonal SST variations in the equatorial oceans and the processes which affect them.

The second, which is discussed in

Section 3, is to present in detail the results of a case study of SST variability in the central equatorial Indian Ocean.

It will be shown that in the vi-

cinity of Gan Island (OO041'S, 73OlO'E), surface heat flux accounts for most of the observed SST variations on seasonal time scales.

This paper concludes in

Section 4 with a summary and comments on the relevance of the Gan results to other equatorial regimes.

1.2

OBSERVED SEASONAL SST VARIATIONS

The patterns of SST variability on seasonal time scales in the equatorial oceans are well documented from historical data analyses.

The most striking

feature of the seasonal cycle is the development during the northern summer in the Pacific (east of the dateline) and Atlantic of a cold tongue extending from the eastern boundary (Fig. 1 and Fig. is generally found between l0S

-

is more symmetric about the equator. ishes from

5OC

2).

The axis of this temperature minimum

3 O S except at its westernmost limit where it

In both oceans, the seasonal range dimin-

in the east to < l 0 C in the west.

In the Pacific, Horel (1982)

has shown that the minimum temperature occurs later in the year as one progresses to the west; it is not clear whether a similar progression occurs in the Atlantic. The Pacific, unlike the Atlantic, is subject to large interannual fluctuations in SST which are characterized by basin scale warm anomalies of Q2'C (Wyrtki, 1975).

Such "El Niiio" episodes are a manifestation of the Southern

Oscillation, a coupled ocean-atmosphere phenomenon of global scale.

Theoreti-

cal arguments involving ocean basin width and the dynamic response of the equatorial ocean to wind forcing explain why the Pacific and not the Atlantic should experience such events (Philander and Pacanowski, 1981).

However, we do not

now have a complete detailed understanding of the generation, evolution, and decay of El Niiio in terms of ocean dynamics, thermodynamics, and air-sea interaction.

A better quantitative knowledge of the processes affecting the season-

al march of SST in non-El Niiio years will no doubt improve our understanding of

El Niiio as well.

3 Seasonal SST variations in the equatorial Indian Ocean are dramatically different from those in the Pacific and Atlantic.

To the east of 55'E,

i.e.

outside the influence of the east African coast, SST shows little significant spatial variation, and the annual range is typically only "2'C

(Fig. 3 ) .

Furthermore, one does not observe an equatorial SST minimum. These differences can be rationalized in terms of the prevailing wind systems. The Indian Ocean is characterized by a monsoon circulation in which northeasterlies predominate in northern winter and southwesterlies predominate in northern summer. Westerly jets appear twice a year along the equator between the northeast and southwest monsoons.

These "transition jets" of April/May and October/

November are of sufficient intensity that on a yearly average winds at the equator are westerly.

On the other hand, the Pacific and Atlantic,

excluding limited areas in the eastern and western Pacific and eastern Atlantic that are influenced by monsoon regimes, are dominated by the easterly Trade Winds.

While these wind systems may exhibit seasonal variations, they

rarely reverse direction for extended periods of time.

The relevance of these

differences will become more apparent below. Equatorial SST variations are difficult to interpret because there is a multiplicity of physical processes that can affect them over a wide range of space and time scales.

The most important of these processes are 1) insola-

tion, 2 ) evaporative (or latent1 heat loss, 3 ) upwelling, which is the combined

140"

1609E

180"

160"W

140'

1209

100-

80"

20"

100

00 140'

160'E

180'

160OW

140'

1200

140' 20e

160'E

1800

160"W

140"

1200

80'

1000

80" 20

10'

10

0'

0'

140'

1800

160'E

Fig. 1. SST in (1976).

OC

160'W

140'

1200

1000

80'

for February and August in the Pacific Ocean from Robinson

4

Fig. 2 SST in “C for Jan-Feb-Mar. and July-Aug-Sept. in the Atlantic Ocean g . (1980) from D X n g

5

Fig. 3. SST in O C for February and August in the Indian Ocean from Hastenrath and Lamb (1979).

6

effect of an upward mass flux of cold thermocline water and upper ocean turbulent mixing process, and 4) horizontal advection by strong surface flows such as the South Equatorial Current (SEC).

Of secondary importance in gen-

eral are sensible heat exchange and long wave radiation from the sea surface, and lateral turbulent mixing.

There may be, however, restricted areas where

these latter phenomena assume a more significant role, e.g. turbulent lateral mixing in frontal zones of the eastern Pacific and Atlantic.

Nonetheless

they will be ignored in the following discussion. One can clearly see the effects of insolation in Figure 2.

In March there

is a large area of water warmer than 27OC straddling the equator in the Atlantic.

By September, 27'C

water has migrated northward with the sun and is

centered near 10°N in the vicinity of the Intertropical Convergence Zone (ITCZ). To the south, temperature gradually decreases into the southern hemisphere where it is winter.

Solar heating however cannot explain the equatorial SST

minimum or the zonal variations associated with that minimum in the Pacific and Atlantic.

Nor can evaporative heat loss, because this tends to be nega-

tively correlated with SST (e.g. Weare,

eta.,1981).

When the surface is

cold, decreased evaporation anomalously warms it, and vice versa, so that evaporative heat fluxes operate to diminish SST extrema rather than to create them.

By contrast, equatorial minima can be attributed to equatorial upwelling.

Equatorial upwelling is a coupled dynamic/thermodynamic phenomena driven by the easterly Trade Winds.

Easterlies produce an Ekman divergence at the equa-

tor which is balanced by an upward mass flux from the thermocline.

This brings

cold water to the surface where it is mixed by turbulence generated in the high vertical shear zone between the Equatorial Undercurrent (EUC) and SEC. The east-west variation in upwelling intensity is due to continual easterly wind forcing which piles water up in the west and removes it from the east via the SEC. east (Colin

This results in a deeper thermocline in the west than in the

a., 1971; Halpern, 19801, where because of the closer proximity

of cold water to the surface, a given level of turbulent energy generation will produce more rapid cooling. The lack of an equatorial SST minimum in the Indian Ocean can be understood within this framework, since there winds are typically westerly along the equator.

This favors an Ekman convergence and downward mass flux which depresses

the thermocline.

Moreover, an EUC may develop during the latter part of the

northeast monsoon, but it is a short-lived, transient phenomena.

More often

flow at all depths to 200 m is from the west with relatively little vertical shear across the base of the mixed layer (McPhaden, 1982a).

Thus, the equator-

ial upwelling is supressed in the Indian Ocean. One can argue that the position of the SST minimum south of the equator in the Pacific and Atlantic is the result of an upwind displacement of the

Ekman surface divergence (Cromwell, 1953) and EUC (e.g. Charney and Spiegel (1971) by the southerly wind component of the Southeast Trades.

However, the

axis of minimum temperature does not always coincide with the EUC axis (and therefore the axis of maximum shear induced mixing).

This observational fact

is consistent with recent theoretical work by McPhaden (1980, 19811, who showed that in a stratified equatorial ocean steady meridional winds drive shallow, frictional surface flows that are not capable of displacing the EUC off the equator.

Together with the fact that the SEC has speeds of O(50 cm sec-') and

and the SST gradients are generally very pronounced, this indicates that horizontal advection must be important as well. While the above interpretation is qualitatively correct, there is a great deal of uncertainty concerning how, in a quantitative sense, the above processes interact in space and time to produce the observed SST patterns.

In

part this uncertainty is a consequence of the degree to which various processes can be correlated.

Consider, for example, the hypothetical scenario in which

a seasonal intensification of the Trades leads to a stronger SEC and hence stronger zonal advection of cold water from the east.

Simultaneously, local

surface divergence and shear between the SEC and EUC may intensify, resulting in more pronounced upwelling.

Isolating the effects of these two processes on

SST will be very difficult unless carefully selected measurements are made and

rigorous analyses carried out.

An example of one such analysis is Wyrtki's

(1981) box model calculation of the combined heat, salt, and mass budgets of the equatorial Pacific.

He concludes that on average upwelling is more impor-

tant than zonal advection by a factor of 2 or more in maintaining the Pacific cold tongue.

This is an illuminating result, but unfortunately one that is

sensitive to a number of model assumptions, such as meridional extent of the equatorial box and depth of the Ekman layer.

It clearly indicates, however,

that progress can be made in the quantitative assessment of SST variability. In the following section we examine in depth the results of diagnostic study from the Indian Ocean, where it is shown that surface heat fluxes account for most of the observed temperature fluctuations.

1.3 1.3.1

SST VARIATIONS IN THE CENTRAL EQUATORIAL INDIAN OCEAN:

A CASE STUDY

Observed variability

Knox (1976) and McPhaden (1982a, b) have extensively discussed month to month fluctuations in oceanic and atmospheric data from the island of Gan (OO041'S, 73'10'E)

in the central equatorial Indian Ocean.

This section sum.

marizes the important results of McPhaden's (1982b) heat and turbulent kinetic energy budget study for the period January 1973 to May 1975.

Figure 4 shows

time series of temperature and mixed layer depth (MLD), defined as the first depth below the surface at which the vertical temperature gradient exceeds

8 5OC/lOO m.

The mixed layer is extremely well mixed at this location and is

on average 1.55 m deep (Fig. 5) so that the 0 - 20 m average in Fig. 4 is equivalent to SST and the 60-80 m average corresponds to upper thermocline temperature.

One sees an interesting change in the spectral content of tem-

perature between the surface and the thermocline.

The former is dominated

by a 1 cycle per year (cpy) variation with a maximum in May and minimum in November, wheras the latter is dominated by a 2 cpy variation.

The thermo-

cline variations are a manifestation of the zonal, geostrophically balanced currents driven by westerly transition winds (McPhaden, 1982a).

It is not

E

Y

I

0

c

a w 40 n U

w 80

> a

-I

I20

n w

xI 30 26

w CK

3 l-

22

w

16

5I-

12

~

a CK a

197311974

197411975

Fig. 4. Weekly estimates of mixed layer depth (MLD) and temperature averaged 180 m for the period January 1973 - May between 0 - 20 m, 60 - 80 m and 160 1975. Smooth lines are low passed versions consisting of monthly means.

-

9 im,ediately clear, however, what controls SST.

If zonal advection were im-

portant, one might expect 2 cpy variations in SST; if SST were chansing in response to fluctuations in the intensity of vertical mixing as the thermocline moves up and down, one might expect the time series in SST to mirror that of MLD.

In fact, it will be shown below that surface heat flux is the primary

controlling mechanism on SST at this location. Components of the surface heat flux calculated from standard bulk formulae are shown in Fig. 6. Total flux, Qo, is defined as

Qo

=

QR +

Qs

+

(1)

QL

, is ( = Qsw - QLW ) is the net radiative flux at the sea surface, Q R insolation or incoming shortwave radiation, QLw is outgoing longwave radiation,

where Q

Qs is sensible heat flux, and QL is latent heat flux.

Net shortwave minus

longwave radiation (Q ) is plotted, since Q is fairly constant ( - 6 0 W m- 2 ) R LW over the record length. Variations in Q are therefore mostly due to variaR

tions in Qsw.

Net radiation shows a strong 1 cpy variation even though at

these latitudes a 2 cpy variation dominates clear sky radiation due to the fact that cloud cover is higher during the southwest monsoon than during the

TEMPERATURE ("C) 10 20 30

160

200

Fig. 5 . Temperature as a function of depth averaged over the period January 1973 - May 1975. Arrow indicates mean mixed layer depth.

10 n o r t h e a s t ii1onsoon.

L a t e n t h e a t f l u x e x h i b i t s a s t r o n g 2 cpy f l u c t u a t i o n t h a t

i s c l e a r l y r e l a t e d t o t h e z o n a l t r a n s i t i o n winds.

S e n s i b l e h e a t f l u x shows a

s i m i l a r v a r i a t i o n , though t h i s component i s i n g e n e r a l a t l e a s t an o r d e r of magnitude weaker t h a n o t h e r f l u x t e r m s . t h e ocean.

Total surface flux i s typically into

I t i s h i g h e s t i n b o r e a l w i n t e r when t h e winds are l i g h t and t h e

s k i e s a r e r e l a t i v e l y c l e a r ; it i s l o w e s t d u r i n g t h e t r a n s i t i o n months of April/May and October/November,

when t h e winds a r e i n t e n s e and t h e sky i s

overcast.

I00

-

Y

E

O

3

Y

x 200 3 _I

LL

I-

a

100

w

I

0

-100

F i g . 6. Weekly estimates of l a t e n t ( Q ) , s e n s i b l e ( Q , ) , n e t r a d i a t i v e (Q,), and t o t a l surface h e a t f l u x (Qo) f o r p e r i o d J a n u a r y 1973 - May 1975. Smooth l i n e s a r e l o w p a s s e d v e r s i o n s c o n s i s t i n g of monthly means. Positive v a l u e s i n d i c a t e t h a t t h e ocean i s being heated.

tke

11 1.3.2

Mixed layer temperature balance

Following Niiler and Kraus (1977), one can integrate the temperature conservation equation from the surface to the base of the mixed layer to get

Temperature (T) in this expression is equivalent to SST because of the homogeneity of the mixed layer temperature (q.v. Fig. 5). is located at z

=

The base of the mixed layer

-h, whereQ-his vertical turbulent heat diffusion and AT is a

temperature jump due to entrainment mixing.

Entrainment velocity, we, is

defined a s w

e

= -ah -

at

w

-h

> o

(3)

~ in which ah/at is the time rate of change of mixed layer thickness and w - is a vertical upwelling velocity in the thermocline just below the base of the mixed layer.

The inequality means that entrainment occurs only when the layer

deepens relative to changes in thermocline depth.

Horizontal vector velocity

is designated 5. The variable 10 represents penetrative radiation which is -45% of incident solar flux (Ivanov, 1977); y determines its attenuation with

depth.

Lateral turbulent diffusion has been neglected.

To examine the temperature balance on monthly time scales, subtract the mean

from equation (2) to get

where primes denote fluctuations about the mean (denoted by an overbar), e.g. (QO/h)' = Qo/h

-

(QO/h), etc., and

T =

tl

-

to is record length.

The term pre-

ceeded by l / ~corrects for trends introduced by the fact that the end points of the time series are at different temperatures.

Time series of observed T, h, u,

and Qo can now be used to estimate the relative importance of various terms in

(4). For the turbulent diffusive flux term, this requires a model in which Q-, = pC K aT/az where K is a vertical eddy diffusivity and aT/az is the temper-

P

ature gradient below the base of the mixed layer. ment term requires estimates of both w

Calculation of the entrain-

and AT.

The simplest balance to test with the present data set is one in which horizontal advection, penetrative radiation, entrainment, and turbulent diffusive fluxes are neglected.

Then integration of (4) yields

12

where T

Q

an estimated mixed layer temperature is derived from a single heat

source, viz. the surface flux Qo.

The integration constant T(t2). where

to < t2 < tl, is arbitrary and chosen such that the average T

Q

over the record

length is equal to the average of the observed mixed layer temperature.

Thus

( 5 ) predicts fluctuations and not absolute values of mixed layer temperature,

Figure 7 shows a calculation of T

Q

of observed (QO/h)'.

based on a trapezoidal rule integration

Superimposed on this is the observed mixed layer tempera-

Though there are some O(l0C) discrepancies between these two TOBS. curves, most notably in April 1973, the rms temperature difference ture,

-___

1

u aT =- [ (Toss - T )I] ',

Q

is only 0.32OC.

Moreover, the coherence squared be-

tween these curves is 0.81, i.e. 81% of the variance in mixed layer temperature can be accounted for by considering only surface fluxes. One might have expected zonal advection to dominate the surface temperature balance at Gan since the zonal currents in this region can attain speeds of %lo0 cm sec-' on monthly averages.

Fowever, as is evident in Fig. 3 , zonal

gradients in SST in the central ocean are extremely weak.

A simple scale anal-

ysis indicates that no more than 20% of the observed variance in SST could be

31 I

I

Fig. 7. A comparison of observed monthly mean mixed layer temperature (TOBS ) with computed temperature (T ) from ( 5 ) .

Q

13 due to this process. Estimates of upwelling velocity, w

from vertical motion of isotherms in -h' the thermocline and ah/at from Fig. 4 indicate significant entrainment velocities of 0(10-4 cm sec-l) only during the transitionmonths of 1973.

These are

due to wind stirring by the transition jets, and are such that a 50 m mixed layer would cool by 0.1OC over 1 month.

This would tend to reduce but not

eliminate the discrepancies in Fig. 7 between T

and T in the spring and OBS For the record as a whole, however, entrainment is generally not

Q

fall of 1973.

active due to the lack of significant shear generated turbulence like that found in the Pacific and Atlantic in association with the EUC (e.9. Crawford and Osborn, 1979a, b). One can show from a scale analysis that other physical processes neglected in (5) are small as well.

An error analysis for the surface flux term indicates

however an uncertainty in T

Q

erization schemes.

of ?20% due to inherently inaccurate bulk paramet-

This is comparable in magnitude to the supposed advection

term and could plausibly account for the discrepancy between the two curves in Fig. 7 by itself. It is important to note that in the calculation of T

Q

level was taken to be the time varying MLD.

from (5) the reference

Had this reference level been em-

bedded in the thermocline, say at a fixed depth of 200 m, changes in depth averaged temperature (or equivalently heat content) would be an order of magnitude larger than could be accounted for by surface fluxes.

This is a consequence of

the fact that vertical motion of the thermocline due to fluctuating geostrophic currents dominates the heat balance of the upper tropical ocean below the mixed layer (e.g. Merle, 1980).

These fluctuations must be filtered out by a proper

choice of reference level for investigations of SST variability.

1.4

CONCLUSION

Simultaneous oceanic and atmospheric measurements from January 1973 to May 1975 were used to examine the surface temperature balance near Gan.

Results

indicate that surface heat flux accounts for about 80% of the observed mixed layer temperature, or equivalently SST, on monthly time scales.

Zonal advec-

tion is of secondary importance, and entrainment mixing is negligible most of the time, though on occasion sufficient turbulence is generated by wind stirring during the transition months to penetrate the thermocline.

A major source of

uncertainty in these calculations is the parameterization of surface heat flux from bulk formulae which introduces errors equivalent to 1 2 0 % of the observed SST signal. These results may be relevant to other regions of the equatorial oceans.

For

instance, oceanic conditions in the Pacific west of the dateline in many respects resemble those in the central Indian Ocean.

Both regions are character-

14 ized by monsoon winds, weak horizontal SST gradients, deep mixea layers, and the absence of an equatorial SST minimum.

Hence it may be that in the western

Pacific, SST variations on seasonal time scales are also determined primarily by surface fluxes.

In regions of the equatorial ocean influenced by Trade

Winds, it is expected that though surface fluxes may not dominate the seasonal cycle, they should have a noticeable effect.

Indeed, Stevenson and Niiler

(1982) found from data collected during the Hawaii-Tahiti Shuttle Experiment (Wyrtki

&.,

1981) that SST in the central Pacific was significantly corela-

ted with the surface heat fluxes.

In areas such as this, it would clearly be

desirable to have accurate estimates of upwelling and horizontal advection to close the temperature balance.

ACKNOWLEDGMENTS The author gratefully acknowledges the support provided by the Joint Institute for the Study of the Atmosphere and Ocean and by the School of Oceanography, University of Washington, Seattle, Washington.

REFERENCES Bjerknes, J., 1966. A possible response of the atmospheric Hadley circulation to equatorial anomalies of ocean temperature. Tellus, 18:820-829. Bjerknes, J., 1969. Atmospheric teleconnections from the equatorial Pacific. Mon. Wea. Rev., 97: 163-172. Colin, C., Henin, C., Hisard, P., and Oudot, C. Le Courant de Cromwell dans le Pacifique central en fevrier. Cah. ORSTOM Ser. Oceanogr., 9: 167-186. Charney, J. G . , and Spiegel, S. L., 1971. The structure of wind-driven equatorial currents in homogeneous oceans. J. Phys. Oceanogr., 1:149-160. Crawford, W. R., and Osborn, T. R., 1979a. Microstructure measuremtents in the Atlantic Equatorial Undercurrent during GATE. Deep-sea Res., 26, GATE supplement 2: 285-308. Crawford, W. R . , and Osborn, T. R., 1979b. Energetics of the Atlantic Equatorial Undercurrent. Dee -Sea Res., GATE Supplement 2: 309-323. Cromwell, T., 1953. Circflation in a meridional plane in the equatorial Pacific. J. Mar. Res., 12: 196-213. Duing, W., Ostopoff, F., and Merle, J. (editors), 1980. Physical Oceanography of the Tropical Atlantic During GATE. University of Miami, 117 pp. Hastenrath, S., and Lamb, P. J., 1979. Climatic Atlas of the Indian Ocean, Part I: Surface Circulation and Climate. University of Wisconsin Press, 109 pp. Halpern, D., 1980. A Pacific equatorial temperature section from 172'E to 931-940. llOoW during winter and spring 1979. Deep-sea Res., Horel, J. D., 1982. The annual cycle of the tropical Pacific atmosphere and ocean. Mon. Wea. Rev., 110: in press. Ivanov, A., 1977. Oceanic absorption of solar radiation. Modelling and PreDiction of the Upper Layers of the Ocean, E. B. Kraus (Editor). Pergamon Press, Oxford: 47-71. Knox, R. A., 1976. On a long series of measurements of Indian Ocean equatorial currents near Addu Atoll. Deep-sea Res., 23: 211-221. McCreary, J. P., 1976. Eastern tropical response to changing wind systems: with application to El Nino. J. Phys. Oceanogr., 6: 632-645. McPhaden, M. J., 1980. Models of the Equatorial Ocean Circulation. Ph. D. dissertation, Scripps Institution of Oceanography, 105 pp.

s,

z:

15 McPhaden, M. J., 1981. Continuously stratified models of the steady state equatorial ocean. J. Phys. Oceanogr., 11: 337-354. McPhaden, M. J., 1982a. Variability in the central equatorial Indian Ocean, Part I: Ocean dynamics. J. Mar. Res., 40: 157-176. McPhaden, M. J., 198213. Variability in the central equatorial Indian Ocean, Part 11: Oceanic heat and turbulent energy balances. J. Mar. Res., 40: 403-419. Merle, J., 1980. Seasonal heat budget in the equatorial Atlantic Ocean. J . Phys. Oceanogr., g: 464-469. Moore, D. W., Hisard, P., McCreary, J. P., Merle, J., O'Brien, J. J., Picaut, J., Verstraete, J., and Wunsch, C . , 1978. Equatorial adjustment in the eastern Atlantic. Geophys. Res. Lett., 2: 637-640. Niiler, P. P., and Kraus, E. B., 1977. One-dimensional models of the upper __ ocean. Modelling and Prediction of the Upper Layers of the Ocean, E. B. Kraus (editor), Perqamon Press, Oxford, 143-172. Philander, S. G . H., and Pacanowski, R. C., 1981. Response of cquatorial 86: 1903-1916. oceans to periodic forcing. J. Geophys. Res., Rowntree, P. R., 1976. Tropical forcinq of atmospheric motions in a numerical model. Quart J. Roy. Meteor. SOC., 102: 583-605. Robinson, M. K., 1976. Atlas of the North Pacific Ocean Monthly Mean Temperatures and Mean Salinities of the Surface Layer. Naval Oceanogr. Office, Ref. Pub. 2, 173 figures. Shukla, J., 1975. Effect of Arabian sea-surface temperature anomaly on Indian summer monsoon: A numerical experiment with the GFDL model. J. Atmos. Sci., 32: 503-511 Stevenson, J., and Niiler, P. P., 1982. Tropical heat flux and storage during the FGGE Shuttle experiment. (Unpublished manuscript). Weare, B. C., Struh, p. and Samuel, M. ~ . , 1 9 8 1 . Annual mean surface heat fluxes in the tropical Pacific Ocean. J. Phys. Oceanogr., 11: 705-717. Wyrtki, K., 1975. El Niiio--the dynamic response of the equatorial Pacific Ocean to atmospheric forcing. J. Phys. Oceanogr., 5: 572-584. Wyrtki, K., 1981. An estimate of equatorial upwelling in the Pacific. J . Phys. Oceanogr., 11: 1205-1214. Wyrtki, K., Firing, E., Halpern, D., Knox, R., McNally, G . J., Patzert, W. C. Stroup, E. D., Taft, B. A., and Williams, R., 1981. The Hawaii to Tahiti Shuttle Experiment. _ Science, 211: __ _22-28.

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17

SEASONAL OBSERVATIONS IN THE WESTERN INDIAN OCEAN

Michele FIEUX and CLAIRE LEVY L.O.P. Museum Paris

-

LA 175 CNRS

Abstract XBT and surface salinity observations which are part of the SINODE (Surface INdian Ocean Dynamics Experiment) program are presented to describe the variations in the surface layers of the western Indian ocean between Cape Guardafui and Reunion island. In the Somali area, the temperature structure presents a high variability related to a strong eddy structure; the surface salinities are a good indicator of the circulation. At the equator, during the two transition periods, after the two monsoons, when the eastward jet is present, the temperature structures are different :the thermocline is broader after the SW monsoon. South of the equator, the South Equatorial Current northern limit wanders between 6 ' s and 9 ' s .

1.

INTRODUCTION The "MARION DUFRESNE" who supplies the "Terres Australes

et Antarctiques FranGaises" in the southern Indian Ocean crosses the tropical and equatorial western region of the Indian ocean four times a year.To reach the seasonal variations, since the SINODE cruises of 1979 and 1980, this opportunity is used to make XBT sections, surface temperature and salinity measurements, ship drift estimations along the route between Qpe

Guardafui and la Reunion,

and to launch satellite tracked drifting buoys at the equator. Here are presented the preliminary results from the first eight SINODE cruises except the drifting buoys ones which are presented in this volume by REVERDIN et al.. The routes are somehow different from one cruise to another (Fig.1 and 2 ) . During SINODE 1 , SINODE 2 and SINODE 6 zig-zag sections were done in the Somali basin. I t is only during SINODE 4 , SINODE 7 and SINODE 8 that the direct meridional route had to be followed because no ship time was available. Surface temperature and salinity were recorded continuously except during SINODE 7. The ship drifts, estimated from the difference between dead reckoning

18 and satellite positioning, were obtained only for SINODE 4 , 5 , 7 , 8. The X B T probes

(T 7 type) gave the temperature down to at least

850 meters. Due to the ship program constraints, the cruises are not evenly spread over the seasons

;

the months sampled are May,

June, July, October, November and December i.e. at the beginning and during the S w monsoon, during the transition period of October and during the beginning of the NE monsoon.

Fig. 1. Routes and ship drift of cruises : SINODE 1, SINODE 2, SINODE 4 and SINODE 7.

19

,, ,.,

,,

,2;i 10.E

Fig. 2. Routes and ship drift of cruises :SINODE 3, SINODE 5, SINODE 6 and SINODE 8 .

2.

2.1

PRELIMINARY RESULTS Somali basin The temperature structure in that area is similar to the

density structure because the density variations are more dependent o n the temperature than on the salinity. The slope of the isopycnes along a section gives the component of the geostrophic current perpendicular to the section. Thus the geostrophic current perpendicular to the section can be guessed from the slope of the isotherms.

20 I n t h e Somali b a s i n t h e lominant f e a t u r e of m o s t of temperature

( e x c e p t i n J u n e 1 9 7 9 a n d May 1 9 8 0 ) i s a t r o u g h

sections

i n t h e t h e r m o c l i n e w i t h a s t e e p e r f r o n t on t h e n o r t h e r n on t h e s o u t h e r n one of

the

side than

t h e 2OoC isotherm l i e s i n t h e middle

(fig.3,

t h e thermocline t h u s can be taken as t h e thermocline index

(QUADFASEL,

1982)).

10' N l

5' N 4

,

,

,

00 i

,

,

~

......

. ___

-

SINODE 3 SINODE 4

Oct 80 D e c 80

SINODE 5

May 81 J u l y 81 O c t 81 Nov 81

- SINODE 6

__

SINODE 7 SINODE 8

_._ F i g . 3.

20' C i s o t h e r m d e p t h .

T h i s t r o u g h c o r r e s p o n d s t o a n a n t i c y c l o n i c eddy p r i n t , northern

al.

Somali eddy

1966,

(Bruce,

1982) which

stress c u r l

1968,

the

1 9 7 8 , SWALLOW e t

1979, DOING,

s e e m s t o b e d r i v e n b y t h e SW m o n s o o n w i n d

(SCHOTT e t a l .

t o a p p e a r , ANDERSON 1 9 8 0 ) . I n J u n e 7 9

a n d May 8 0 , t h e s e c t i o n s w e r e m a d e j u s t o n e o r t w o d a y s a f t e r t h e t h e SW m o n s o o n s o t h e e d d y w a s n o t f o r m e d y e t .

onset of vations

show t h e b e g i n n i n g o f

a cooling

(AT

1

2°C)

The o b s e r -

i n the surface

l a y e r close t o t h e c o a s t which i s a r a p i d r e s p o n s e t o t h e o n s e t (SCHOTT e t a 1 sation of 7'

,

1980). I n October of

t h e s a m e y e a r a f t e r t h e ces-

t h e SW m o n s o o n t h e t r o u g h w a s b r o a d w i t h a n a x i s a r o u n d

N and a n o r t h e r n

f r o n t a r o u n d 9'30

N

I n December 8 0 ,

(fig.4).

a t t h e b e g i n n i n g o f t h e N E m o n s o o n t h e t r o u g h w a s much r e d u c e d a n d the northern

f r o n t h a s m i g r a t e d t o a r o u n d 11'30

N.

The s u r f a c e

d r i f t s are i n agreement with t h e subsurface temperature s t r u c t u r e w i t h a s t r o n g n o r t h e a s t w a r d d r i f t i n t h e f r o n t area and a southwest w a r d d r i f t f r o m 1 0 ° N t o a r o u n d 4"N w h i c h b r i n g s h i g h s a l i n i t y w a -

t e r s from t h e Arabian Sea of

(S%.,,

3 6 % , ) . I n May 8 1 ,

after the onset

t h e S W m o n s o o n w i t h n o o b s e r v a t i o n b e t w e e n D e c e m b e r a n d May,

a n o r t h e r n eddy w i t h a n o r t h e r n f r o n t around

there

i s t h e p r i n t of

ll"N,

l e s s s t e e p t h a n i n t h e p r e v i o u s December

drifts directions

(Fig.2)

( F i g . 3 ) . The s h i p

are coherent with t h e subsurface struc-

21 400 E

60°

E

00' E

60. E

I

I

I

I

SEC

i I

I 00.E

60' E

60.E

F i g . 4. P o s i t i o n s of t h e n o r t h e r n f r o n t s , of t h e buoy d r i f t s a t t h e e q u a t o r and o f t h e t h e r m o c l i n e r i d g e n o r t h o f t h e S o u t h E q u a t o r i a l C u r r e n t , f o r e a c h c r u i s e when a v a i l a b l e .

ture

: t h e s u r f a c e s a l i n i t y i s h i g h i n t h e eddy

o f 5"N t h e s u r f a c e s a l i n i t y d e c r e a s e s southern origin

(LEETMAA

et al.

( s > 35.6%,)

( S < 35.3%,) which

and a n o r t h e r n

of

f r o n t a r o u n d 8'45N.

10'N

and

12'N.

south

1972). A t t h e beginning of J u l y 81,

t h e t r o u g h i s m u c h more s o u t h w i t h t h e a x i s a r o u n d 7'30N

eddy between

;

shows i t s

T h e r e i s t h e s i g n of

The s a l i n i t y i s h i g h e r

(Flg.3)

a smaller

t h a n 36%, n o r t h

10°N ( w a t e r f r o m A r a b i a n S e a ) a n d h i g h e r t h a n 3 5 . 6 % " b e t w e e n

22 3'N

and

10'N. 8 1 , t h e t r a c e o f a n a n t i c y c l o n i c eddy i s p r e -

I n October s e n t b e t w e e n 3'30

a n d 7'30

N

which i s q u i t e s o u t h

N with t h e northern f r o n t around l o N

( f i g . 3 ) . North of

shows t h e s o u t h e r n p a r t o f

it, the temperature section

a n o t h e r a n t i c y c l o n i c eddy.

The s h i p

d r i f t d i r e c t i o n s a r e i n agreement w i t h a d o u b l e eddy s t r u c t u r e ( F i g . 1). Between

i n May 81, 1'30

and 2 ' N

1'N

N a n d 2'30

N in July

8 1 and 1"N and 3 " 3 0 N i n O c t o b e r 8 1 , t h e r e a r e c o o l e r a n d f r e s h e r waters a t the surface ward d r i f t d i r e c t i o n s . s i o n of

o r 2"

(1'

C c o o l e r ) which correspond

This can be r e l a t e d t o t h e eastward extenand

t h e s o u t h e r n l o o p which l e a v e s t h e c o a s t around 3'N

b r i n g s w a t e r s from t h e S o u t h E q u a t o r i a l

C u r r e n t and E a s t A f r i c a

c o a s t a l c u r r e n t w i t h low s a l i n i t y c h a r a c t e r i s t i c s (LEETMAA

t o east-

SWALLOW e t a l .

e t al.,

(SC

t o appear i n J . P . O . ) .

81, 6 w e e k s l a t e r t h e r e was o n l y o n e t r o u g h b e t w e e n 6'N with a n o r t h e r n f r o n t around

10'30

N

35.3%0). I n November and

llON

( F i g . 3 ) . Again t h e s u r f a c e

d r i f t d i r e c t i o n s a r e i n agreement with t h e subsurface s t r u c t u r e ( F i g . 5 ) a n d w i t h t h e s u r f a c e s a l i n i t y w h i c h i s maximum b e t w e e n a n d 10'N of

c o r r e s p o n d i n g t o t h e w e s t w a r d d r i f t of

the northern

ward d r i f t ,

eddy.

I n c o n t r a s t north of

t h e s u r f a c e s a l i n i t y i s lower

t o t h e v a l u e s b e t w e e n 3'N pear

south of

0'30

and

?ON.

1O"N i n t h e n o r t h e a s t (35.6 < S < 3 6 % 0 ) s i m i l a r

The v a l u e s l e s s t h a n 3 5 . 3 % 0 a p -

N i n the eastward equatorial j e t .

To s u m m a r i z e t h e s e o b s e r v a t i o n s seems t h a t t h e p r i n t o f a f t e r t h e o n s e t of

1°N

the southern p a r t

the northern

i n t h e Somali b a s i n ,

it

Somali eddy i s always t h e r e

t h e SW monsoon w i t h a t r o u g h a s d e e p a s 1 5 0 me-

t e r s and w i t h a s t e e p e r f r o n t i n t h e n o r t h which c o u l d be due t o t h e p r e s e n c e of

the coast.

The s u r f a c e s a l i n i t y i s a g o o d i n d e x o f

t h e c i r c u l a t i o n : westward d r i f t i n t h e s o u t h e r n b r a n c h of b r i n g s h i g h Arabian Sea s a l i n i t y w a t e r s low s a l i n i t y w a t e r s Somali c u r r e n t l o o p .

(S

ri

35.380)

Drift,

(S>

a r e brought

f r o m t h e SEC by t h e

s u r f a c e s a l i n i t y and s u b s u r f a c e

t u r e a r e u s u a l l y i n good agreement

S t r U C -

( F i g . 5 ) . The o b s e r v a t i o n s made

o n d i f f e r e n t y e a r s a t t h e same s e a s o n a r e n o t s i m i l a r , i n October

t h e eddy

36%,),on the contrary,

f o r example

81, a s h a r p t e m p e r a t u r e r i d g e i s p r e s e n t around 8"N,

much f u r t h e r s o u t h t h a n i n O c t o b e r 8 0 when t h e s t r u c t u r e was a s i n gle-eddy

one w i t h n o r t h e r n

f r o n t a r o u n d 9 O 3 0 N.

t h e s e o b s e r v a t i o n s , t h a t a t t h e end of

But i t seems,

from

t h e eddy supposed l i f e t h e

23 northern subsurface front gets steeper

(cf. Nov.

81 a n d Dec.80)

w h i c h c o u l d b e d u e t o t h e c o n c e n t r a t i o n of t h e e d d y e n e r g y i n a much restricted coastal zone.

Fig. 5. Surface salinity, surface drift and depth of SINODE 8 , November 1981.

2 O o C isotherm during

24

F i g . 6. E q u a t o r i a l t e m p e r a t u r e s e c t i o n from ( i n May 1 9 8 0 ) .

2.2

to

62' 3 0 ' E

Equatorial region t h e e q u a t o r t h e e a s t w a r d j e t which a p p e a r s e a s t of

A t

r o u n d 49'

et al.

April-May

1981,

LUYTEN,

and October-November

e t al.

(with speed around l m / s ) a n d i n November section

a-

- 50° E , between t h e monsoons, d u r i n g t h e t r a n s i t i o n

E

periods of

(WYRTKI,

1 9 7 3 , CRESSWELL,

1980) w a s p r e s e n t d u r i n g e a c h c r o s s i n g

e x c e p t i n J u l y 8 1 d u r i n g t h e SW m o n s o o n

8 1 when t h e j e t w a s p r e s e n t f u r t h e r e a s t o f

the

(Fig.4). The t h e r m o c l i n e s t r u c t u r e

with

46' 3 0 ' E

longitude along the equator

d o e s n o t s h o w much v a r i a t i o n s

(Fig.6,8)

May 8 0 w h e r e t h e t h e r m o c l i n e i s t h i n n e r .

except w e s t of

49'E

in

This western equatorial

a r e a , where t h e j e t d o e s n o t e x i s t , p r e s e n t s low s a l i n i t y c h a r a c teristics (fig.7).

(S < 35.20%,)i.e.waters The

a r o u n d 49'E.

of

southern hemisphere o r i g i n

s a l i n i t y f r o n t e x t e n d s from 0 t o 9 0 meters and s t a n d s As

in

1980,

t h e 49'E

July 81 temperature section pre-

s e n t s a t h i n n e r t h e r m o c l i n e t h a n a t 53O ponds t o t h e r e t u r n o f

-

54OE

: i t s s l o p e corres-

Somali c u r r e n t f r e s h e r flow from t h e coast.

25 62'30E

46'30E

Om

m m

Fig. 7. E q u a t o r i a l s a l i n i t y s e c t i o n from (May 1 9 8 0 ) .

46' 30' E

to

62'

30'E

C o m p a r i n g now t h e t w o t r a n s i t i o n p e r i o d s c r o s s - e q u a t o r i a l

sections

it appears t h a t the

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

period

Dec.)

DIN

(0ct.-

e t al.)

ses o f

Nov.-

when t h e

j e t speeds are higher

(cf.REVER-

( F i g . 9 ) . This difference must r e f l e c t d i f f e r e n t proces-

formation of

the

j e t and/or

d i f f e r e n t water masses involved.

The two d i f f e r e n t c i r c u l a t i o n s y s t e m s a t t h e e n d o f

t h e two monso-

o n s seem t o a f f e c t d i f f e r e n t l y t h e e q u a t o r i a l s t l r u c t u r e d u r i n g t h e two e a s t w a r d j e t t r a n s i t i o n p e r i o d s . The c r o s s - e q u a t o r i a l

temperature

e a s t w a r d j e t p e r i o d d o n o t show a

s e c t i o n s made d u r i n g t h e

s t r o n g convergence.

The j e t m u s t

be f e d p a r t l y by w a t e r s f r o m t h e w e s t a n d p a r t l y t h r o u g h h o r i z o n t a l convergence.

26

E5'

18.

10.

10.

1szoo 62. E

debs* 30 May 79 4 Junr 79 62OE O P E

03*30 E

Fig. 8. Cross e q u a t o r i a l temperature s e c t i o n s a t d i f f e r e n t times and l o n g i t u d e s during t h r e e c r u i s e s .

Fig. 9. year.

Cross e q u a t o r i a l temperature s e c t i o n s a t d i f f e r e n t p e r i o d s o f t h e

21

2.3

South equatorial current and counter-current region T h e XBT sections have been expanded down to Reunion island.

The p r o m i n e n t feature i s the slope of the isotherms between Reunion and a thermocline ridge which varies with the cruises from 9 ' s 6's

to

(Fig.4 and 10). This slope is the mark of the south equatorial

current ( S E C ) which i s steadier and stronger during the SW monsoon period w h e n the SE trade winds are also stronger and when the currents are weak and variable in the region between the thermocline ridge ( l i m i t o f the SEC) and the equator. During the NE monsoon the SE trade winds decrease and the SEC retreats towards the South like

in December 8 0 . increases

Simultaneously the South Equatorial Counter current

( b etween 2 ' 5

and 8 ' 3 0

S in December 80 - Fig.1). Until

now, due to ship program constraints, the sections have not been carried o u t during characteristic period soon). D u r i n g the transition periods mocline r i d g e lies around 6 " -

7 O

(i.e. full SW or NE mon-

(May and Oct - Nov) the ther-

S exc ept in May 81 (Fig.4). In

December 80 a t the beginning of the NE monsoon the ridge had retracted down t o 8 " 3 0

S.

A t depth, in the central water, the ridge o f

the d e e p isotherms i s somewhat displaced towards the south and could be a s far asll's

- 12"s. I n the SECC region the depth varia-

tions o f the thermocline is very small.

0

100

100

100

.oo

¶OO

600

I00

-00

Fig. 10.

South Equatorial Current sections (SINODE 5).

28 3.

CONCLUSION The p r e l i m i n a r y

r e s u l t s of

the

f i r s t e i g h t S I N O D E XBT

s e c t i o n s i n t h e w e s t e r n I n d i a n o c e a n show t h e h i g h v a r i a b i l i t y o f t h e t e m p e r a t u r e s t r u c t u r e i n t h e Somali b a s i n which c a n be r e l a t e d t o the circulation variations. t i e s a r e a good i n d i c a t o r o f perature sections.

In t h a t region,

the

surface salini-

t h e c i r c u l a t i o n t o g e t h e r w i t h t h e tem-

The n o r t h e r n

f r o n t of

t h e Somali eddy i s always

s t e e p e r than t h e southern one. A t

t h e e q u a t o r , during t h e e x i s t e n c e of

the eastward j e t ,

t h e two t r a n s i t i o n p e r i o d s p r e s e n t d i f f e r e n t t e m p e r a t u r e s t r u c t u r e s with a broader thermocline during the Nov.Dec.)

with the northern

(Oct.

jet is faster.

when t h e South of

second t r a n s i t i o n p e r i o d

the equator,

the thermocline ridge associated

l i m i t of

South E q u a t o r i a l Current,

the

varies

between 6 O S and 9OS. Sections during the characteristic periods soons) w i l l permit a b e t t e r d e s c r i p t i o n of

( N E a n d SW mon-

the annual cycle.

The g e o s t r o p h i c c a l c u l a t i o n s u n d e r t a k e n ,

u s i n g mean T - S

w i l l allow t o quantify the circulation.

relationships, A s the

o b s e r v a t i o n s made o n d i f f e r e n t y e a r s a t t h e same

season a r e not similar,

a c a r e f u l study of

the correlation with the

wind s t r e s s v a r i a t i o n s h a s t o be done t o f u r t h e r u n d e r s t a n d t h e s e different features.

Acknowledgments T h i s s t u d y i s i n c l u d e d i n t h e SINODE p r o g r a m s u p p o r t e d by t h e "Terres A u s t r a l e s e t Antarctiques FranGaises" r i e d o u t on b o a r d t h e i r t o i r e d'Ocdanographie relle,

the

"MARION

DUFRESNE", by t h e L a b o r a -

P l i y s i q u e du Museum N a t i o n a l

Laboratoire Associd

seph GONELLA. probes,

ship,

The F r e n c h

(TAAF) a n d c a r -

d ' H i s t o i r e Natu-

1 7 5 d u CNRS, u n d e r t h e d i r e c t i o n o f J o -

"Marine N a t i o n a l e " p r o v i d e d t h e

t h e o t h e r o n e s w e r e p r o v i d e d by t h e T A A F .

1 9 7 9 XBT

29 REFERENCES

.

Anderson,D.L.T.,1980 The Somali Current. Ocean Modelling, No.34 (unpublished manuscript) . Bruce, J.G. 1968 . Comparison o f near surface dynamic topography during the two monsoons i n the western Indian Ocean. Deep-sea Res., 1 5 , 665-677. Bruce, J.G., 1979 . Eddies o f f the Somali coast during the southwest monsoon. J. Geophys. Res., 8 4 , 7742-7748. Cresswell, G., M.Fieux and J.Gonella . The Wyrtki equatorial jet, MayIJune 1980. Tropical ocean-Atmosphere Newsletter - January 1981. Unpublished manuscript. Duing, W.,1978 . The Somali Current. P a s t and recent observations. I n : Review Papers o f Equatorial Oceanography, Fine Workshop Proceedings. Nova/Nyit Univ. Press (unpublished manuscript). Fieux,M., J.F. Murail, G.Soares, 1980 . Navigation et sections bathythermiques (XBT). Recueil des donnees collectees, campagne SINODE - MD 18 - P E M G . Vol.1. Rapp. Int. d u Laboratoire d'OcBanographie Physique d u Museum Paris. (Unpublished manuscript). F i e u x , ~ . ,~ . ~ r e m o n tA,. ~ a r t a v t s e f f ,J.F. ~ u r a i l ,1982. Navigations sections bathythermiques (XBT) et bouees derivantes. Recueil des donnees collectees, campagne SINODE 11-MD 22 - Vol.1. Rapp. Int. d u Laboratoire d'oceanographie Physique d u Museum Paris. (Unpublished manuscript) . Leetmaa,A.and.V. Truesdale, 1972. Changes in the currents i n 1970 o f f the E a st African coast with the onset o f the southeast mo1.s o o n . J. Geophys.Res., 7 7 , 3281-3283. Leetmaa, A., D.R. Quadfasel, and D.Wilson, 1982 : Development o f the f l o w field during the onset o f the Somali Current, 1979 in J . Phys. Oceanogr. Luyten, J.R., M.Fieux, and J.Gonella, 1980 . Equatorial currents i n the w e s tern Indian Ocean. Scienc e, 209, 600-603. Quadfasel, D.R. 1982. L o w frequency variability o f the 20'C isotherm topography i n the western Indian Ocean. J.Geophys. Res., 8 7 , C 3 , pp. 1990-1996. Schott,F. a n d D.R. Quadfasel, 1980 . Development o f the Northern S o m a l i current gyre i n 1979. Science. Vol, 209. Aug.1980. pp.593-595. Schott,F., a n d D.R. Quadfasel, 1982. Variability o f t h e Somali CUrr e n t system during the monsoon o n s e t , 1979 (to appear in J . P h y s Oceanogr 1 Swallow,J.C. and J.G. Bruce, 1966 . Cu rrent measurements off the S o m a l i coast during the Southwest Monsoon o f 1964. Deep Sea Res. 13-5, 861-888. Swa l l o w , J.C. and M.Fieux, 1982 . Historical evidence for two gyres i n the S o m ali Current. J. Mar. Res. V01.40, Suppl.pp.747-755. Swallow, J.C., R.Molinari, J.G.Bruce, O.B. Brown. Development o f near-surface flow pattern and water mass distribution i n the Somali b a s in, i n response t o the southwest monsoon o f 1979. T o appear in J. Phys. Oceanogr. Wyrtki, K. 1973. An equatorial jet i n the Indian Ocean. Science,l81 262-264.

.

This Page Intentionally Left Blank

31

SEASONAL VARIABILITY OF SUBSURFACE THERMAL STRUCTURE I N THE TROPICAL ATLANTIC OCEAN

J . MERLE 'ORSTOM/LOP/MUSEUM

43 r u e C u v i e r 75005 P A R I S ABSTRACT

A merged d a t a s e t i n c l u d i n g MBT, XBT, and NANSEN

the 20' S

-

-

CTD o b s e r v a t i o n s , made i n

30" N t r o p i c a l A t l a n t i c r e g i o n u n t i l 1978, i s used t o s t u d y t h e sea-

sonal changes i n t h e upper ocean thermal s t r u c t u r e . Maximum changes i n depth o f t h e t h e r m o c l i n e and i n t h e 0-300 meters l a y e r h e a t c o n t e n t a r e found i n two r e gions : ( i ) N o r t h o f t h e e q u a t o r ( u n t i l 10" N) and West o f 25" W ( i i ) C e n t r a l and E a s t e r n e q u a t o r . Annual s i g n a l s o f t h e r m o c l i n e depth (and h e a t c o n t e n t ) var i a t i o n s a r e n o t i n phase i n t h e two r e g i o n s . The maximum depth o f t h e thermoc l i n e i s observed i n f a l l i n t h e North-West e q u a t o r i a l r e g i o n and i n S p r i n g i n t h e E a s t e r n C e n t r a l e q u a t o r i a l r e g i o n . A double seasonal t i l t o f t h e t h e r m o c l i n e i s r e s u l t i n g o f t h e s e changes i n t h e two r e g i o n s : one

along the equatorial

plan, t h e o t h e r one a l o n g a zonal p i v o t l i n e s i t u a t e d under t h e mean p o s i t i o n o f t h e ITCZ. T h i s double a x i s o f r o t a t i o n o f t h e t h e r m o c l i n e on a seasonal t i m e s c a l e seems t o be t h e r e s u l t o f two k i n d s o f response o f t h e ocean t o t h e wind f o r c i n g : ( i ) a remote e q u a t o r i a l response which m a i n l y a f f e c t s t h e E a s t e r n equat o r i a l r e g i o n . ( i i ) A l o c a l N o r t h e q u a t o r i a l response a s s o c i a t e d t o t h e seasonal m i g r a t i o n o f t h e ITCZ which induces a change i n t h e s i g n o f t h e c u r l o f t h e wind s t r e s s and an up and down movement o f t h e t h e r m o c l i n e . 1 ) INTRODUCTION The l a r g e seasonal and i n t e r a n n u a l changes o f Sea S u r f a c e Temperature (SST) i n t h e t r o p i c s a r e w e l l known. T h e i r e f f e c t s on t h e atmosphere have been i n v e s t i g a t e d r e c e n t l y by b o t h o b s e r v a t i o n s and models (HOREL and WALLACE, 1981

-

ROWNTRY 1976). The c l i m a t o l o g i c a l e f f e c t o f these SST v a r i a t i o n s o v e r t h e c o n t i nents seems a l s o t o be s i g n i f i c a n t (SHUKLA 1975, MOURA and SHUKLA 1981). The P a c i f i c ocean draws f i r s t t h e a t t e n t i o n because o f t h e l a r g e i n t e r a n n u a l SST s i g n a l which a f f e c t s i t s e a s t e r n b a s i n (EL NINO) and because o f t h e economi-

c a l consequences o f t h i s phenomenon. More r e c e n t l y t h e t r o p i c a l A t l a n t i c ocean focussed a l s o t h e a t t e n t i o n because o f t h e p a r t i c u l a r i t y o f t h e SST v a r i a b i l i t y

32

which i s m o s t l y c o n f i n e d i n t h e annual s i S n a l (MERLE, FIEUX, HISARD 1979). Some k i n d o f "EL NINO" responses have been i n f e r r e d , d i f f e r e n t o f those o f t h e P a c i f i c b u t s i m i l a r by t h e i r p h y s i c a l mechanisms (HISARD and MERLE 1979 ; HISHKU 1980 ; MERLE 1980-a). The SST changes c o u l d be due i n a f i r s t p a r t , t o t h e subs u r f a c e thermal s t r u c t u r e changes. B u t l i t t l e i s known about t h i s subs u r f a c e v a r i a b i l i t y . We know t h a t i n b o t h P a c i f i c and A t l a n t i c oceans t h e r e i s an East-West e q u a t o r i a l s l o p e o f t h e t h e r m o c l i n e . The mean depth o f t h e 20°C i s o t h e r m i s about 150 meters i n t h e West and about 50 meters i n t h e East. S a l i n i t y and d e n s i t y d i s t r i b u t i o n p r e s e n t a l s o an East-West s l o p e ( F i g . 1 a - b - c ) . We know t h a t t h e l a r g e range o f SST v a r i a b i l i t y i n t h e E a s t o f t h e e q u a t o r i a l bas i n i s m o s t l y due t o t h e s h a l l o w i n g o f t h e t h e r m o c l i n e and i t s seasonnal surfac i n g . We know t h a t i n t h e West, even i f t h e SST v a r i a b i l i t y i s s m a l l , t h e t h e r m o c l i n e has t h e l a r g e s t d e p t h v a r i a t i o n (MERLE 1980-b). A phase change o f t h e annual s i g n a l o f d e p t h v a r i a t i o n o f t h e t h e r m o c l i n e i s observed between t h e West and t h e East o f t h e e q u a t o r i a l b a s i n s u g g e s t i n g a seasonal t i l t o f t h e thermoc l i n e i n an e q u a t o r i a l p l a n around a p i v o t p o i n t s i t u a t e d i n t h e m i d d l e o f t h e b a s i n (MERLE 1980-b).

50W

40

30

20

IOE

0

10

sow

40

x)

20

10

0

IOE

u0

50

100

150

200

250

F i g . 1. E q u a t o r i a l s e c t i o n o f ( a ) temperature averaged f r o m 0' t o 2" S, ( b ) s a l i n i t y averaged from 2" N t o 2' S, ( c ) d e n s i t y ( 6 t ) averaged from 2" N t o 2' S.

33

I n o r d e r t o understand t h e response o f t h e upper t r o p i c a l ocean t o t h e atmosp h e r i c f o r c i n g , s e v e r a l s e t s o f q u e s t i o n s need t o be i n v e s t i g a t e d : ( i ) how does the t h e r m o c l i n e v a r y seasonnally and i n t e r a n n u a l l y i n t h e t r o p i c a l ocean as a whole ? ( i i ) How does t h i s t h e r m o c l i n e v a r i a b i l i t y a f f e c t t h e SST o r does n o t a f f e c t i t ? ( i i i ) What i s t h e r e l a t i v e importance o f t h e d i f f e r e n t f o r c i n g mechanisms on SST and d e p t h o f t h e t h e r m o c l i n e ? namely a ) t h e l o c a l wind f o r c i n g ; b) t h e remote wind f o r c i n g ; c ) t h e l o c a l thermodynamic f o r c i n g ? The purpose o f t h i s s t u d y i s t o b r i n g some new f a c t s t o t h e q u e s t i o n : how does t h e t h e r m o c l i n e v a r y s e a s o n n a l l y i n t h e t r o p i c a l A t l a n t i c ocean ? We use a data f i l e i n c l u d i n g a l l t h e MBT, XBT, and NANSEN o b s e r v a t i o n s a v a i l a b l e u n t i l 1978. These d a t a and t h e i r p r o c e s s i n g s a r e examined i n s e c t i o n 2. S e c t i o n 3 desc r i b e s t h e mean thermal s t r u c t u r e . S e c t i o n 4 d e s c r i h w t h e of t h e d e p t h of t h e t h e r m o c l i n e

(ZOO

q Paq n n a1

variahilitv

C i s o t h e r m ) . ' S e c t i o n 5 Dreserrts snmp c n n w -

quences o f t h i s t h e r m o c l i n e v a r i a b i l i t v upon h e a t c o n t e n t and h e a t b i i d w t . I n S e c t i o n 6, some p r e l i m i n a r y c o n c l u s i o n s of these f a c t s a r e presented. 2) DATA PROCESSING The d a t a base used i n t h i s s t u d y i s a merged f i l e o f FIBT, XBT, and NANSEN temperature d a t a . About 140,000 temperature p r o f i l e s a r e c o n s i d e r e d between 20" S, 20" N, A f r i c a n c o a s t and 80" W. Most o f t h e p r o f i l e s come f r o m t h e NODC b u t

a d d i t i o n n a l XBT f r o m t h e French Navy and

NANSEN

-

CTD c a s t f r o m t h e oceanogra-

p h i c v e s s e l CAPRICORNE a r e a l s o i n c l u d e d , The f i l e i n c l u d e s t h e o l d e s t c r u i s e s l i k e t h e METEOR i n 1924, t h e ATLANTIS i n 1931, t h e DISCOVERY i n 1935, t h e CROWFORD i n 1957 and t h e EQUALANT e x p e d i t i o n i n 1962-1963. Most o f t h e GATE d a t a a r e i n t h e f i l e b u t t h e f i l e ends i n 1978 and does n o t i n c l u d e t h e FGGE data. The d a t a d i s t r i b u t i o n i s i r r e g u l a r i n t i m e and space. N e v e r t h e l e s s f o r t h e purpose of t h e l a r g e s c a l e s t u d y p r e s e n t e d h e r e , a m o n t h l y mean w i t h a l a r g e g r i d spac i n g (4" i n l o n g i t u d e and 2" i n l a t i t u d e ) b r i n g s a s u f f i c i e n t number o f observ a t i o n s i n each r e c t a n g l e ( u s u a l l y o v e r 3 0 ) . The c o n f i d e n c e i n t e r v a l i s t h u s r e duced t o about.Z°C,

A w e i g h t e d i n t e r p o l l a t i o n from a d j a c e n t squares and months

has been a p p l i e d i n o r d e r t o reduce t h e n o i s e l e y e l i n some square w i t h s c a n t y d a t a o r no d a t a a t a l l , P r i o r t o t h i s smoothing procedure, v a r i o u s s c r e e n i n g r o u t i n e s have been a p p l i e d t o e l i m i n a t e

conspicuous d a t a ,

The m o n t h l y mean temperature i s c a l c u l a t e d i n each box a t each s t a n d a r d l e v e l . Each t y p e o f d a t a (MBT, XBT, NANSEN) a r e weighted by t h e i r awn s t a n d a r d d e v i a t i o n and frequency. The depth o f a g i v e n i s o t h e r m i s i n t e r p o l l a t e d l i n e a r l y . Heat c o n t e n t and r a t e o f h e a t s t o r a g e a r e c a l c u l a t e d as f o l l o w i n g : t h e r e l a t i v e

34

h e a t c o n t e n t a t a d e p t h Zn and w i t h r e f e r e n c e t o 0 ' C, i s c a c u l a t e d by :

w i t h T i , t h e temperature a t each s t a n d a r d l e v e l i n degrees c e n t i g r a d e s ; Z i , t h e d e p t h o f s t a n d a r d l e v e l s i n meters ;

-Cp,

t h e h e a t c a p a c i t y o f sea-water ;

D, t h e mean d e n s i t y o f t h e w a t e r column.

JTCp has been taken equal t o 0.4096. Then HS(Z,,,) i s g i v e n i n J o u l e p e r square meter. I n t h i s s t u d y Zm = 300 m o r 50 m. The r a t e o f h e a t s t o r a g e HS f o r a g i v e n month, i s o b t a i n e d through t h e d i f f e r e n c e o f h e a t c o n t e n t between two a d j a c e n t months. F o r example, HS J u l y = (HS August

-

HS June) / 2 ; HS i s converted i n t o

w a t t p e r square m e t e r .

3 ) MEAN THERMAL STRUCTURES

Dynamic topography o f t h e s u r f a c e ( F i g . 2 a ) , h e a t c o n t e n t i n t o t h e 0-300

me-

t e r s l a y e r ( F i g . 2b), and depth o f t h e t h e r m o c l i n e o f t h e 20' C i s o t h e r m ( F i g . 2c) p r e s e n t s i m i l a r f e a t u r e i n t h e e q u a t o r i a l A t l a n t i c ocean. I n t h e r e g i o n s where dynamic topography i s low, as i t i s a l o n g t h e N o r t h e q u a t o r i a l t r o u g h near 10"

N o r a l o n g t h e e q u a t o r , t h e h e a t c o n t e n t i s low and t h e t h e r m o c l i n e i s sha-

l l o w , Between t h e s e two lows a N o r t h e q u a t o r i a l dynamic r i d g e a l o n g 3-4'

N is

c h a r a c t e r i z e d b y a maximum o f h e a t c o n t e n t and by a t r o u g h i n t h e t h e r m o c l i n e . Furthermore t h e r m a l s t r u c t u r e s p r e s e n t a zonal s l o p e . Dynamic h e i g h t and h e a t c o n t e n t a r e h i g h e r i n t h e West where t h e t h e r m o c l i n e i s deeper t h a n i n t h e E a s t . These f e a t u r e s i n d i c a t e c l e a r l y t h a t t h e h e a t c o n t e n t i s d i r e c t l y f u n c t i o n o f t h e d e p t h o f t h e t h e r m o c l i n e . The same remark i s v a l i d f o r oceanic topography (and c o n s e q u e n t l y t h e g e o s t r o p h i c c i r c u l a t i o n ) o f t h e upper l a y e r s . T h i s i s obv i o u s l y a r e s u l t o f t h e s h a r p and t h i n t h e r m o c l i n e l a y e r t h a t i s almost perman e n t i n t h e t r o p i c s . T h i s t h e r m o c l i n e i s s e p a r a t i n g a w e l l mixed and warm superf i c i a l l a y e r f r o m t h e deep c o l d w a t e r s l a y e r . The r e s u l t i s an almost p e r f e c t t w o - l a y e r s ocean ( F i g . 3 ) , T h i s p e c u l i a r a s p e c t o f t h e near s u r f a c e thermal s t r u c t u r e s o f t h e t r o p i c a l oceans s i m p l i f i e s c o n s i d e r a b l y t h e s t u d y o f t h e response o f t h e s u p e r f i c i a l ocean t o t h e a t m o s p h e r i c f o r c i n g . C h a r a c t e r i s t i c s o f t h i s response can be d i v i ded i n two parameters : (i) t h e depth o f t h e t h e r m o c l i n e , ( i i ) t h e temperature

o f t h e mixed l a y e r ( o r o f t h e Sea Surface).These t w o paramaters a r e p r o b a b l y n o t

35

i

F i g . 2 : a Surface dynamic topography r e l a t i v e t o 500 DB. 8 b Mean annual h e a t c o n t e n t from 0 t o 300 m e t e r s depth ( i n 10 J/m2). c ) Plean annual d e p t h o f t h e 20" C i s o t h e r m .

36

t o t a l y independent e s p e c i a l l y i n t h e u p w e l l i n g r e g i o n s . I n a f i r s t approximation

t h e depth o f t h e t h e r m o c l i n e i s a d i r e c t response o f t h e ocean t o t h e wind

f o r c ng ( e i t h e r l o c a l , remote o r g l o b a l ) . The temperature o f t h e mixed l a v e r i s t h e r e s u l t o f t h e response o f t h e s u p e r f i c i a l ocean t o t h e l o c a l thermodynamic f o r c i n g o f t h e atmosphere. These s i m p l i f i e d views a p p l y e s p e c i a l l y i n t h e west e r n r e g i o n s where t h e t h e r m o c l i n e i s deep. I n t h e East and d u r i n g t h e u p w e l l i n g seasons t h e t h e r m o c l i n e reaches t h e s u r f a c e . T h i s i s c r e a t i n g p a r t i c u l a r s u r f a c e conditions ( c o l d water) t h a t i n t u r n modify

t h e c o n d i t i o n s o f t h e l o c a l thermo-

dynamic f o r c i n g ( t h e ocean absorbs h e a t f r o m t h e atmosphere). Here t h e two f o r c i n g s and t h e two c o r r e s p o n d i n g responses o f t h e ocean ( d e p t h o f t h e t h e r m o c l i n e and temperature o f t h e mixed l a y e r ) a r e c l e a r l y n o t independent.

F i g . 3 : M e r i d i o n a l t e m p e r a t u r e s e c t i o n a l o n g 23.5" W d u r i n g GATE (June-Septemb e r 1974). I n t h i s s t u d y we w i l l c o n s i d e r o n l y t h e v a r i a b i l i t y o f t h e d e p t h o f t h e t h e r m o c l i n e on a seasonal t i m e s c a l e . We a s s i m i l a t e t h i s depth t o t h e d e p t h o f t h e

20" C i s o t h e r m which i s a p p r o x i m a t i v e l y i n t h e m i d d l e o f t h e t h e r m o c l i n e (see F i g . 1 a and F i g . 3 ) . We assume t h a t 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 o f t h e subsurf a c e thermal s t r u c t u r e s i s weak c o m p a r a t i v e l y t o t h e seasonal v a r i a b i l i t y . I f t h i s i n t e r a n n u a l v a r i a b i l i t y i s l a r g e we a r e i n s e r i o u s danger o f i m p o r t a n t b i a -

ses due t o t h e unequal y e a r l y d i s t r i b u t i o n o f t h e data. B u t we know t h a t t h e SST i n t e r a n n u a l v a r i a b i l i t y i s about 1 t o 5 t i m e s t h e seasonal v a r i a b i l i t y (MERLE e t a l . 1979). The c o n s i s t e n c y of t h e r e s u l t s presented i n t h e f o l l o w i n g s e c t i o n s gives confiaence i n c n e i r s i g n i i i L d n c e .

4) SEASONAL VARIABILITY OF THE 20" C ISOTHERM TOPOGRAPHY F i g . 4 a and 4 b show t h e topography o f t h e 20" C i s o t h e r m d u r i n g March and August. D u r i n g March t h e s t r u c t u r e i s s i m p l e r t h a n d u r i n g August. The 20" C i s o -

37

therm i s deep in the North West, reaching 200 meters in a trough around 20" N . The sloping isotherm moves upward slowly u n t i l 40" W a n d more rapidly f u r t h e r east t o reach the surface near the African c o a s t . Further S o u t h , from 10" N t o 1 5 " S , the topography does not show any p a r t i c u l a r p a t t e r n . There i s a general East-West slope a n d a s l i g h t doming extending t o the south of the equator from the South-East t o the West and underlining the Benguela Current a n d the SouthEquatorial Current.

Fig. 4 b : Depth of the 20" C isotherm in A u g u s t (meters).

38 I n August t h e p a t t e r n i s t o t a l y d i f f e r e n t . Three axes o f d e f o r m a t i o n appear.

A c e n t r a l t r o u g h i s e x t e n d i n g a t about 3-4 degrees N o r t h . T h i s t r o u g h i s border e d by two r i d g e s . The N o r t h r i d g e , c e n t e r e d a t about 10" N, i s t o t h e South o f t h e N o r t h E q u a t o r i a l C u r r e n t (NEC). The South r i d g e i s l y i n g a l o n g t h e e q u a t o r . Between t h e N o r t h r i d g e and t h e 3-4" N t r o u g h f l o w s t h e N o r t h E q u a t o r i a l CounterC u r r e n t (NECC). And between t h e 3-4" N t r o u g h and t h e e q u a t o r i a l r i d g e f l o w s t h e n o r t h e r n branch o f t h e South E q u a t o r i a l C u r r e n t (SEC). March and August a r e t h e two extreme months o f t h e seasonal v a r i a b i l i t y b u t p r o g r e s s i v e changes a r e observed between these two p e r i o d s o f t h e y e a r . The N o r t h e q u a t o r i a l t r o u g h which i s t h e dominant f e a t u r e o f t h e N o r t h e r n Summer i n t h e

20" C i s o t h e r m topography, b e g i n s t o appear i n June and ends i n November (maps a r e n o t shown h e r e ) .

A F o u r i e r a n a l y s i s has been performed t o d e r i v e maps o f t h e maximum change o f depth and phase o f t h e Annual Component ( F i g . 5 a e t b ) . The depth change o f t h e

20" C i s o t h e r m shows a l a r g e maximum a t t h e North-West o f t h e e q u a t o r b e t ween 3'

-

8" N o r t h and 25"

-

45" West. The d i f f e r e n c e o f d e p t h i s o v e r 60 m e t e r s .

A t t h e o t h e r end o f t h e ocean, South o f t h e e q u a t o r and c l o s e t o t h e A f r i c a n c o a s t , a n o t h e r maximum appears ( o v e r 50 meters d e p t h change). These two maxima a r e a s s o c i a t e d a l o n g t h e e q u a t o r w i t h a band o f r e l a t i v e l y l a r g e d e p t h v a r i a t i o n ( o v e r 40 m e t e r s ) . N o r t h o f 20" N and South o f 10" S t h e change o f d e p t h i s a l s o i n c r e a s i n g r a p i d l y . B u t i t i s a d i f f e r e n t phenomenon i n r e g i o n s where t h e t h e r m o c l i n e i s l e s s marked and where t h e 20" C i s o t h e r m c o u l d even r e a c h t h e s u r f a c e . The 15" N

-

10" S band i s marked by i m p o r t a n t phase changes. A f i r s t phase

change i s observed a l o n g t h e e q u a t o r f r o m t h e G u l f o f Guinea i n t h e East t o t h e N o r t h B r a s i l i n t h e West. I n t h e G u l f o f Guinea t h e maximum d e p t h of t h e 20" C i s o t h e r m i s observed d u r i n g t h e f i r s t months o f t h e y e a r ( f r o m t h e end of Feb r u a r y near t h e A f r i c a n c o a s t t o A p r i l - M a y a t 10" w). Between 1 5 " W and 20" W t h e phase change i s v e r y r a p i d ( a b o u t 180 days change o v e r 5" o f l o n g i t u d e ) , F u r t h e r West u n t i l t h e B r e s i l i a n c o a s t , t h e maximum depth o f t h e 20" C i s o t h e r m i s found i n October-November. around 25"

Thus a t i l t o f t h e t h e r m o c l i n e w i t h a p i v o t p o i n t

W c o n f i r m s a p r e v i o u s r e s u l t o b t a i n e d w i t h a d i f f e r e n t and s m a l l e r

d a t a s e t (MERLE 1980 b ) . The second phase change i s observed a l o n g a l i n e s t a n d i n g r o u g h l y f r o m 3

-

4" N i n t h e West t o about 10" N i n t h e E a s t . T h i s phase change i s a l s o v e r y r a p i d and l a r g e ( a b o u t 180 d a y s ) , T h i s suggests a m e r i d i o n a l t i l t o f t h e thermoc l i n e a l o n g a p i v o t l i n e a p p r o x i m a t i v e l y under t h e mean p o s i t i o n o f t h e ITCZ. We w i l l d i s c u s s t h i s p o i n t l a t e r on,

39

Fig. 5 a : Depth change i n meters o f t h e 20" C i s o t h e r m ( a p p r o x i m a t i v e l y t w i c e the amplitude o f t h e annual component o f a F o u r i e r a n a l y s i s ) .

F i g . 5 b : Phase ( i n days) o f t h e annual component o f t h e i n a Fourier analysis .

20' C i s o t h e r m depth

5 ) SEASONAL CHANGES OF HEAT CONTENT A p r e v i o u s s t u d y o f h e a t budget i n t h e e q u a t o r i a l A t l a n t i c ocean (MERLE 1980

b ) showedthat seasonal v a r i a t i o n s o f h e a t c o n t e n t i n t h e West and i n t h e East o f the e q u a t o r i a l b a s i n a r e d i f f e r e n t ( F i g . 6 a and b ) . I n t h e West t h e 0-300 meters heat c o n t e n t s i g n a l i s l a r g e r t h a n t h e one o f t h e East. More over t h e two s i g n a l s are n o t i n phase. Conversely, t h e 0-50 meters h e a t c o n t e n t s i g n a l i s s m a l l e r i n

40

t h e West t h a n i n t h e East b u t t h e y a r e i n phase. These r e s u l t s i n d i c a t e t h a t i n t h e West, and a t l e a s t a t t h e e q u a t o r , t h e s u b s u r f a c e thermal s t r u c t u r e s v a r y seasonally, independently o f the o v e r a l l surface conditions.

50

L

55

r

>

\

\

I I

I

_ 0'-2'N ---0'-205

$w' 1

' < J , F , M , A # H ,J , J

, A , S , O , N , D , J

, J , F , U , A , M , J , J , A , S , O , N , D , J , f ,

, F ,

(a) (b 1 F i g . 6 a) : Seasonal v a r i a t i o n of h e a t c o n t e n t i n t h e West e q u a t o r i a l A t l a n t i c 0-2" N and 0-2" S f r o m 0 t o 300 meters and 0 t o 50 meters ( f r o m MERLE 1980). b ) : Seasorial v a r i a t i o n of h e a t c o n t e n t i n t h e East e q u a t o r i a l A t l a n t i c (0-2" it and 0-2" S) from 0 t o 300 m e t e r s and 0 t o 50 m e t e r s ( f r o m MERLE 1980). Amplitudes and phases o f t h e annual component o f h e a t c o n t e n t f o r b o t h t h e 0-50 n e t e r s and 0-300 meters l a y e r s i n d i c a t e t h a t i n t h e Western p a r t o f t h e

whole i n t e r t r o p i c a l r e g i o n (20' N

- 15'

S ) t h e subsurface (0-300 m e t e r s ) thermal

c o n d i t i o n s a r e independent o f t h e n e a r s u r f a c e (0-50 m e t e r s ) thermal c o n d i t i o n s ( F i g . 7 a-b and F i g . 8 a-b). The annual v a r i a t i o n o f t h e 0-300 meters h e a t c o n t e n t l a y e r and o f t h e depth o f t h e 20" C i s o t h e r m a r e v e r y s i m i l a r when a m p l i t u d e and phase a r e concerned, The 0-300 meters h e a t c o n t e n t shows a l a r g e maximum o f a m p l i t u d e i n t h e West and a t t h e N o r t h o f t h e e q u a t o r w i t h v a l u e s c l o s e t o 6.108 J/m;.

An e a s t e r n equato-

r i a l maximum i s a l s o observed w i t h v a l u e s o v e r 10.108 ,j/m2 a t t h e A f r i c a n c o a s t and s o u t h o f t h e e q u a t o r . The phase map shows a l s o a phase d i f f e r e n c e between t h e E a s t e r n and t h e Western p a r t o f t h e e q u a t o r i a l band w i t h a t r a n s i t i o n p o i n t a t about 15' W, Another change phase i s observed a l o n g an a l m o s t zonal l i n e near 6-8'

N which i s v e r y s i m i l a r t o t h e one d e s c r i b e d f o r t h e 20" C i s o t h e r m depth.

The annual v a r i a t i o n o f t h e 0-50 m e t e r s h e a t c o n t e n t ( F i g . 8 a

-

b) i s simi-

l a r t o t h e SST annual v a r i a t i o n i n b o t h a m p l i t u d e and phase ( F i g . 9 a

-

b ) . The

maximum o f a m p l i t u d e i s found j u s t South o f t h e e q u a t o r i n t h e Gulf of Guinea 8 w i t h a maximum o v e r 5 10 J/m2 near t h e A f r i c a n c o a s t . A zone o f minimum ( l e s s 8 t h a n 2 10 J/m2) i s l y i n g under t h e mean p o s i t i o n of t h e ITCZ. The phase map shows a s l i g h t i n c r e a s e i n t h e d a t e of t h e maximum o f h e a t c o n t e n t f r o m t h e G u l f

of

41

F i g . 7 a : Amplitude of the annual component o f heat content from 0 t o 300 me-

ters ( i n lo8 J/m2).

Fi g. 7 b : Phase of t h e annual component o f heat content from 0 t o 300 meters \ in Says).

42

F i g . 8 a : Amplitude o f t h e annual component o f h e a t c o n t e n t from 0 t o 50 meters ( i n 108 J/m2).

F i g . 8 b : Phase o f t h e annual component o f h e a t c o n t e n t f r o m 0 t o 50 ( i n days).

meters

43

Guinea toward the West, a t the equator. The phase change i s observed under the mean position o f the ITCZ as f o r the SST phase change (Fig. 9 b ) .

Fig. 9 a : Amplitude of the a n n u a l component of Sea Surface Temperature ( i n degrees C )

Fig. 9 b : Phase of the annual component o f Sea Surface Temperature ( i n days)

I n order t o d i f f e r e n t i a t e the surface and subsurface oceanic energy exchanges, we computed the r a t e of heat content change f o r two 1ayers:rhe layer mcludinq the thermocline (0-300 meters) and the surface layer (0-50m e t e r s ) . We selected two nonths :
44

10 a presents the r a t e of heat storage (change of heat content) in the 0-300 met e r s layers during June. Positive values extend North of the equator where the thermocline i s depressed, negative values a r e covering the whole Gulf of Guinea where the thermocline i s upwelling. The extrema a r e over 300 W/m2. Comparing these numbers with the net heat exchange a t the surface during the same month obtained by HASTENRATH and LAMB (1978), we see t h a t the r a t e of heat storage of t h e 0-300 meters layer i s about ten times t h e heat exchange a t the surface. (The maximum value of heat gain obtained by HASTENRATH and LAMB (1978) i s confined along a zonal band south of the equator with a value close t o 50 W/m2). I n September (Fig. 10 b) t h e s i t u a t i o n i s reversed. Positive values (over 300 W/m2) extend along the equator i n the Gulf o f Guinea where the thermocline i s downwe1 1 ing. In the 0-50 meters layer (Fig. 11 a - b ) t h e f e a t u r e s a r e d i f f e r e n t : the changes in heat content a r e confined in t h e East (Gulf of Guinea and Dakar reg i o n ) . In June, the r a t e of heat storage i s negative with extrema over 180 W/m2 in the Gulf of Guinea. The Dakar region, in reverse shows positive values (over 160 W/m2). I t i s i n t e r e s t i n g t o note t h a t , i n t h e Dakar region, the r a t e o f heat storage i s l a r g e r in the 0-50 meters layer than i n the 0-300 meters layer and of opposite s i g n . When the sun i s heating the mixed l a y e r , the deep cold waters a r e upwelling. In September the r a t e o f heat storage i n the 0-50 meters layer i s pos i t i v e in the Gulf of Guinea (over 160 W/m2 a t the African coast and S o u t h of the e q u a t o r ) , and negative i n the Dakar region ( l e s s than 60 W / m Z ) . 6 ) CONCLUSION

The seasonal signal of the subsurface thermal v a r i a b i l i t y of the tropical A t l a n t i c ocean presents a maximum amplitude in the region North of the equator ( 3 - 8" N ) and West of 30" W . This maximum v a r i a b i l i t y appears in the depth of the 20" C isotherm and i n t h e heat content of the 0-300 meters l a y e r . A secondary zone of maximum seasonal v a r i a b i l i t y extends a l l along the equator i n the central and East p a r t o f t h e basin with a net increase i n the East near the African coast. The seasonnal s i g n a l s i n these two regions (North-West of equator and South East of equator) a r e n o t i n phase. The maximum depth o f the thermocline (and maximum of heat c o n t e n t l i s observed during Spring time (February-April) i n the Eastern equatorial region, and in Fall (October-December) i n the North-West equatorial region. T h u s a phase difference of about 6-8 months separates the two events. The r e s u l t i n g seasonal movement of the thermocline induces a double t i l t of the thermocline : one i n an equatorial plan w i t h a pivot p o i n t around 25" W ; another one, along a pivot l i n e approximatively p a r a l l e l t o the equator s i t u a t e d

45

F i g . 10 a : Rate of change of heat content from 0 t o 300 meters in June ( i n W /

.n2).

F i g . 10 b : Rate of change of heat content from 0 t o 300 meters in September ( i n W/m2).

46

F i g . 11 a : R a t e o f change o f h e a t c o n t e n t from 0 t o 50 m e t e r s i n June ( i n W/m2)

F i g . 11 b : R a t e o f change of h e a t c o n t e n t from 0 t o 50 m e t e r s i n September ( i n 'l/m2).

47

Fig. 12 a and b : Seasonal m i g r a t i o n o f t h e I T C Z o b t a i n e d from t h e a t l a s o f

HASTENRATH and

LAMB ( 1 9 7 7 ) .

48

between 3 and 8'

N. The zonal t i l t o f t h e t h e r m o c l i n e a t t h e e q u a t o r was a l r e a d y

known (MERLE 1980b ) and c o n f i r m e d by e q u a t o r i a l models (CANE and SARACHIK 1980 PHILANDER and PACANOWSKY 1981). The m e r i d i o n a l N o r t h e q u a t o r i a l t i l t o f t h e t h e r m o c l i n e i s a new f a c t b r o u g h t up by t h i s s t u d y . T h i s m e r i d i o n a l seasonal o s c i l l a t i o n o f t h e t h e r m o c l i n e i s s i t u a t e d approximat i v e l y under t h e mean p o s i t i o n o f t h e I n t e r t r o p i c a l Convergence Zone (ITCZ). The ITCZ p o s i t i o n v a r i e s s e a s o n a l l y o v e r a l a r g e l a t i t u d i n a l band which extends r o u g h l y f r o m t h e e q u a t o r t o 10-15'

N o r t h ( F i g . 12 a

-

b ) and covers t h e oceanic r e -

g i o n s where maximum a m p l i t u d e and phase changes i n t h e depth o f t h e t h e r m o c l i n e a r e observed. The c u r l o f t h e w i n d s t r e s s changes s i g n N o r t h and South o f t h e ITCZ. Thus, we can e a s e l y s p e c u l a t e t h a t t h i s seasonal up and down movement of t h e t h e r m o c l i n e a s s o c i a t e d t o t h e l a t i t u d i n a l m i g r a t i o n o f t h e ITCZ r e s u l t s d i r e c t l y from t h e change i n t h e s i g n o f t h e c u r l o f t h e wind s t r e s s . Recent c a l c u l a t i o n s u s i n g a m o n t h l y mean wind d a t a s e t c o n f i r m t h i s h y p o t h e s i s (DELCROIX, personnal communication). A l i n e a r two l a y e r model u s i n g t h e same w i n d d a t a s e t p r o v i d e s a l s o an amazing s i m i l a r i t y w i t h o u r r e s u l t s i n b o t h phase and a m p l i t u d e changes o f t h e annual component o f t h e t h e r m o c l i n e depth v a r i a t i o n (PICAUT and BUSALLACHI 1982). Thus i t appears t h a t t h e seasonal v a r i a t i o n o f t h e upper thermal s t r u c t u r e s i n t h e t r o p i c a l A t l a n t i c ocean a r e m o s t l y due t o t h e c o m b i n a t i o n o f two events : ( i ) an e q u a t o r i a l p e r t u r b a t i o n which a f f e c t s t h e E a s t e r n e q u a t o r i a l r e g i o n ;( i i ) a N o r t h e q u a t o r i a l p e r t u r b a t i o n due t o t h e l o c a l response o f t h e subsurface ocean t o t h e niqration of t h e ITCZ. ACKNOWLEDGEMENTS T h i s s t u d y belongs t o t h e FOCAL program and has been p a r t l y supported by CNRS /PNEDC r e s e a r c h c o n t r a c t . We thank t h e BNDO (CNEXO) f o r p a r t o f t r e a t m e n t . Yves TOURRE and T h i e r r y DELCROIX have p r o v i d e d h e l p f u l comments and c o r r e c t i o n s .

49

REFERENCES Cane M.A., and E.S. S a r a c h i k , 1981 : The response o f a l i n e a r b a r o c l i n i c equat o r i a l ocean t o p e r i o d i c f o r c i n g . J. Mar. Res., 39, 651-693. Hastenrath S. and Lamb P.J., 1977 : C l i m a t i c a t l a s o f t h e t r o p i c a l A t l a n t i c and Eastern P a c i f i c oceans. The U n i v e r s i t y Wisconsin Press, 112 p. Hastenrath S. and Lamb P.J., 1978. Heat budget A t l a s o f t h e T r o p i c a l A t l a n t i c and E a s t e r n P a c i f i c Ocean. The U n i v e r s i t y Wisconsin Press, 140 p. Hisard P. and MERLE J . , 1979. Onset o f summer s u r f a c e c o o l i n g i n t h e G u l f o f Guinea d u r i n g GATE, Deep Sea Res., GATE, Suppl . I 1 t o V , 26, 325-342. Hisard P., 1980 : O b s e r v a t i o n de reponses de t y p e "El Nino" dans 1 ' A t l a n t i q u e t r o p i c a l o r i e n t a l - G o l f e de Guinee. Ocean. ALta, 3, 69-78. Horel J.D., and J.M. Wallace, 1981 : P l a n e t a r y - s c a l e atmospheric phenomena assoc i a t e d w i t h t h e Southern O s c i l l a t i o n . Mon. Idea. Rev., 109, 813-829. Merle J . , M. F i e u x and P. H i s a r d , 1979 : Annual s i g n a l a n m t e r a n n u a l anomalies o f sea-surface temperatures i n t h e e a s t e r n e q u a t o r i a l A t l a n t i c ocean. DeepSea Res., GATE Suppl.11 t o V, 26,77-102. Merle J., 1980a : V a r i a b i l i t e thermique a n n u e l l e e t i n t e r a n n u e l l e de l ' o c e a n . A t l a n t i q u e e q u a t o r i a l E s t . L'hypothese d ' u n " E l Nino" A t l a n t i q u e . Ocean. Acta, 3, 209-220. Merle J., 1980b : Seasonal heat-budget i n t h e e q u a t o r i a l A t l a n t i c Ocean, J. Phys. Oceanogr. 10, 3, 464-469. Moura A.D., and J. Shukla, 1981 : On t h e dynamics o f d r o u g h t s i n n o r t h e a s t Braz i l : Observations. t h e o r v and numerical exoeriments w i t h a General C i r c u l a t i o n Model. J. Atmos. Sci:, 38, ( t o appear): P i c a u t J. and A.J. B u s a l a c c h i . 3383 : Seasonal v a r i a b i l i t v f r o m a model o f t h e t r o p i c a l A t l a n t i c . (To appear i n J. Phys. Oceanogr.). P h i l a n d e r S.G and R.C Pacanowski, Ips1 : Response o f e q u a t o r i a l oceans t o p e r i o d i c f o r c i n g . J. Geophys. Res,, 86, 1903-1916. Rowntree P.R., 1976 : Response o f t h e atmosphere t o a t r o p i c a l A t l a n t i c Ocean temperature anomaly. Q.J.R. M e t e o r o l o . SOC., 102, 607-625. Shukla J., 1975 : E f f e c t o f A r a b i a n sea-surface temperature anomaly on I n d i a n summer monsoon : A numerical e x p e r i m e n t w i t h t h e GFDL model. J. Atmos. S c i . , 32, 503-511. -

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51

THE VARIABILITY OF LOCAL WINDS AT 22OW AND THEIR INFLUENCE ON THE OCEANIC SYSTEM AT THE EQUATOR IN THE ATLANTIC DURING FGGE

P. SPEW and H.-J. PANITZ Institut fur Geophysik und Meteorologie der Universitat zu Koln Kerpenerstr. 13 D-5000 Koln 41 Federal Republic of Germany

ABSTRACT Local wind forcing is a possible mechanism which drives fluctuations of the oceanic system in the equatorial region. Local winds in the equatorial belt between s'1

and 3ON along 22OW are analysed by spectral

methods for two periods in 1979. For the first period from February to March the wind was strongly influenced by the ITCZ. For the second period from May to June we found fluctuations of the zonal wind component in the 7 day

range. These oscillations were meridionally coherent.

The meridional wind showed fluctuations in the 3-4 day range which could be identified as easterly waves. We found a coherent relationship between the zonal wind and the zonal currents at the 7 day period at the Equator. A

similar relationship could not be found between the atmospheric

easterly waves and oceanic oscillations of the same period. The upwelling events, one in the February/March period and one at the end of May, are not connected with the local wind.

52

1

INTRODUCTION

The upper e q u a t o r i a l A t l a n t i c r e a c t s r e l a t i v e l y quick t o changes i n atmospheric f o r c i n g . I n t h e p a s t l o c a l wind f o r c i n g w a s made r e s p o n s i b l e f o r some observed oceanic o s c i l l a t i o n s by various a u t h o r s . We have used measurements along 22OW between l0S and 3ON during t h e

First

5MP (global

Atmospheric Research Program) g l o b a l Weather Experiment (FGGE) i n 1979 t o i n v e s t i g a t e such a r e l a t i o n s h i p . I n t h e following s e c t i o n we summarize what i s known about t h e e q u a t o r i a l c u r r e n t system i n t h e A t l a n t i c i n so f a r a s a wind f o r c i n g i s concerned. The d a t a a r e described i n Section 3 and i n Section 4 r e s u l t s of s p e c t r a l a n a l y s i s follow. A conclusion i s given i n Section 5.

2

THE EQUATORIAL CURRENT SYSTEM I N THE ATLANTIC OCEAN

Since Neumann (1960) and Voigt (1961) t h e E q u a t o r i a l _Undercurrent (EUC) i s a well-known f e a t u r e of t h e A t l a n t i c Ocean. A s described by Katz e t

al.

(1981) t h e EUC i s an ever p r e s e n t eastward zonal flow, about 200 km

wide and centered w i t h i n 100 km of t h e Equator, which flows counter t o t h e u s u a l l y p r e v a i l i n g t r a d e winds. Though not always a subsurface flow, t h e core of t h e EUC i s g e n e r a l l y t o be found between 50 m and 125 m depth i n t h e upper p a r t of t h e thermocline. The EUC c a r r i e s high s a l i n i t y water with a maximum above t h e v e l o c i t y c o r e (e.g. Cornus and Meincke, 1979). The mean depths of t h e v e l o c i t y and s a l i n i t y maxima decrease monot o n i c a l l y from t h e western p a r t of t h e A t l a n t i c t o t h e east. Only on t h e average t h e EUC i s o v e r l a i d by t h e westward flowing s o u t h E q u a t o r i a l

-Current

(SEC)

.

From r e c e n t i n v e s t i g a t i o n s , which a r e mainly r e s u l t s of t h e FGGE, it seems reasonable t o u s t o conclude t h a t t h e western e q u a t o r i a l A t l a n t i c

i s i n c l o s e equilibrium with t h e s e a s o n a l l y varying winds (Katz e t a l . , 1981; Lass e t a l . ,

19821, which i s i n c o n t r a s t t o t h e P a c i f i c . To demon-

s t r a t e t h i s Katz and Garzoli (1982) compared observations from FGGE d i r e c t l y t o p r e d i c t i o n s derived from a zonally wind-forced nonlinear model of Philander and Pacanowski (1980). Katz and Garzoli (1982) conclude t h a t t h e oceanic c y c l e of t h e region can be reasonably described by two s e q u e n t i a l events: t h e response t o a westward zonal wind which begins i n mid-May and t h e response t o t h e c e s s a t i o n of t h a t wind a f t e r January. With t h e o n s e t of t h e wind t h e thermocline deepens by about

40 m. Connected with t h i s i s an i n i t i a l l y westward, b u t soon near-zero,

53 surface c u r r e n t and an EUC which r a p i d l y l e v e l s o f f . With t h e r e l a x a t i o n of the wind t h e thermocline r i s e s and t h e s u r f a c e flow becomes eastward, and the undercurrent t r a n s p o r t f i r s t i n c r e a s e s t o i t s annual maximum i n March and then decreases t o i t s minimum j u s t a f t e r t h e wind resumes again. The minimum undercurrent t r a n s p o r t l a g s t h e minimum zonal wind s t r e s s by about two months (Katz e t a l . , 1981). For t h e e a s t e r n A t l a n t i c (Gulf of Guinea) s e v e r a l mechanisms have been proposed t o e x p l a i n t h e e q u a t o r i a l and c o a s t a l upwelling. Servain e t a l . (1982) analysed h i s t o r i c a l s e a s u r f a c e temperatures (SST) and surface winds. Their r e s u l t s support t h e remote f o r c i n g mechanism proposed by Moore e t a l .

(1978). According t o t h i s hypothesis i n c r e a s i n g e a s t e r l y

winds i n t h e western e q u a t o r i a l A t l a n t i c e x c i t e an i n t e r n a l e q u a t o r i a l Kelvin wave t h a t propagates i n t o t h e Gulf of Guinea. Servain e t a l . (1982) p o i n t o u t , t h a t an anomaly of t h e zonal wind s t r e s s near t h e north Brazilian c o a s t i s followed by a SST anomaly i n t h e Gulf of Guinea about one month l a t e r , which implies a wave propagation speed of 1.1 ms-'. In t h e e q u a t o r i a l b e l t low frequency e n e r g e t i c f l u c t u a t i o n s with time scales from a few days t o a few weeks a r e superimposed on t h e processes as mentioned above (e.g.

Moore and Philander, 1977; Weisberg e t a l . ,

1979).

The most prominent of t h e s e wave-like d i s t u r b a n c e s are i n e r t i a - g r a v i t y waves and a north-south meandering of t h e EUC. For t h e former Garzoli and Katz (1981) f i n d f o r t h e western t r o p i c a l A t l a n t i c v a r i a b l e s p e c t r a l density l e v e l s i n t h e band of 2-5 days centered a t 3.75 days. The most l i k e l y i n t e r p r e t a t i o n of t h i s s p e c t r a l peak i s an atmospherically forced, v e r t i c a l l y propagating i n e r t i a - g r a v i t y wave with a v e r t i c a l wavelength of 1.730 m. The westward propagating meander of t h e EUC with a p e r i o d of %I6 days, a phase speed of 1.1.7 ms-'

(Diiing e t a l . , 1975) and a wavelength

around 2 , 0 0 0 km (Diiing e t a l . , 1975: 2,600 km; Diiing and Hallock, 1979: 1,800 km) could a l s o b e observed during FGGE ( L a s s e t a l . ,

1980). Addi-

t i o n a l l y Diiing and Hallock (1979) observed, t h a t t h e s e long o s c i l l a t i o n s

of the EUC have a l a g of 1.4 days r e l a t i v e t o t h e s u r f a c e c u r r e n t s . This meander i s b e l i e v e d t o be caused by i n s t a b i l i t i e s of t h e e q u a t o r i a l c u r r e n t system (Philander, 1976; Philander, 1978) or by wind-generated e q u a t o r i a l l y trapped waves (Hallock, 1979). The s e a s o n a l l y varying b e l t of r e l a t i v e l y low SST along t h e Equator (Merle, 1978; Hastenrath and Lamb, 1977) a r e o f t e n a t t r i b u t e d t o upwelling caused by t h e e q u a t o r i a l f-divergence, which we consider t o be a more local e f f e c t . On t h e o t h e r hand t h e s e l o w SST could be caused by a second mechanism: t h e meridionally increased v e r t i c a l mixing due t o t h e high current shear between EUC and SEC. But Fahrbach and Bauerfeind (1982)

54 demonstrated that this mechanism is not responsible for local temperature decrease - at least at 2 2 O W at the Equator. DATA

3

In the preceeding section we mentioned the possible relationship between the atmospheric flow and the current system in the equatorial Atlantic. We intended to find out which of these results can be verified by in situ measurements of combined oceanic and meteorological measurements. For that purpose it was planned to deploy 5 surface moorings by R.V. METEOR over an entire 6 month period along 2 2 O W between l0S and 3ON. However, because of technical problems, we got measurements only of two separate time periods. The times of surface wind recordings are given in Table 1. For that reason we have to restrict ourselves to an examination of relatively short period fluctuations and we will begin with a discussion of the data (compare also Garzoli et al., 1982). TABLE 1 Times of surface wind recording during 1979 at 2 2 O W .

3ON 2ON

I

ION

I

Eq.

I

10s

I

I

01.02.

- 29.03.

01.02.

-

31.01.

- 30.03.

09.03.

18.02. - 07.03.

30.01.

-

I I

I

05.05.

-

07.05.

- 16.06.

17.06.

28.03.

I

The oceanographic equipment consisted of Vector Averaging Current Meters (VACM: sampling interval 7.5 min.) at 15 m depth at l0S, Equator, 1°N and 3N '

for the first period and at the Equator for the second period.

Below the depth of 15 m Aanderaa current meters were used down to 600 m (sampling interval 30 min.). For

2ON

there were no current measure-

ments in the near surface layer for both periods. Additionally some moorings were equipped with thermistor chains. Wind speed and wind direction were registrated by Aanderaa datalogger, with sampling intervals of 10 minutes or 2 0 minutes, which depends on the equipment. From these data hourly averages for the zonal and meridional wind component were calculated. The zonal (u: positive to the east) and the meridional (v: positive to the north) wind component along 2 2 O W at l0S, Equator, l'N, in Figure 1.

2ON and 3ON for the February/March period are shown

55 Figure 3 gives a similar representation for the Equator and 2ON for

the May/June period. Eiourly averages are displayed. Figures 2 and 4 show the daily variation of the magnitude of the mean

- -

wind vector, (u2+v2)' I 2 , to the mean magnitude, (u2+v2)

An overbar

represents a daily average. The steadiness is expressed as a percentage; it equals zero for winds which shift randomly, and one hundred for winds that always blow in the same direction.

TIME

[Me]

nw

[OAYS!

Fig. 1. Time series of zonal (left) and meridional (right) wind components (ms-l) along 22OW between l0S and 3ON for February/March 1979.

Fig. 2. Wind steadiness ( % ) for February/March 1979. For further explanation see text.

m5 205 30.5 x)6 TIME [DAVS]

TIME [OAS]

TIME [DAY$

Fig. 3 . Time series of zonal (left) and meridional (right) wind components (ms-l) at the Equator and at ZON for May/ June 1979.

Fig. 4. Wind steadiness

(%)

for May/June 1979.

56 We have related our wind measurements to the daily position of the Intertropical Convergence Zone (ITCZ),which was subjectively determined from METEOSAT cloud images (Kohne and Speth, 1982). The band of maximum cloudiness was defined as the position of the ITCZ using Nicholson's (1975) criteria to distinguish the intensity. The mean monthly position of the ITCZ over the Atlantic from January to November 1979 is shown in Figure 5.

30W

low

20w I

0

10 E 15 N

1

EQ

EQ

FGGE

5s-

5s

1979 I

40W

3OW

I

I

20w

I

I

low

I

1

0

I

I

10 E

Fig. 5. Mean monthly position of the ITCZ over the Atlantic from January to November 1979.

From January through May the ITCZ was found around 4 O N with its southernmost position in March. Beginning in June the ITCZ migrated to the north with a mean position around 7O- 8ON. However, the band of maximum cloudiness was not necessarily identical with the surface flow discontinuity. Sadler (1975) and Ramage (1974) suggested that the cloudiness maximum was separated from the zone of trade wind confluence. The climatological mean position of the maxima of cloudiness, precipitation frequency and convergence lie %350 km south of the surface confluence in the eastern Atlantic (Hastenrath and Lamb, 1977). We found the same for our FGGE data. To determine the synoptic-scale surface flow we have used the objective analysis of the European Centre for Medium Range Weather Forecasts in Reading, UK. For the western Atlantic the maximum cloud zone was north of the con-

fluence zone, which is in good agreement with the results of Sadler (1975). At 22OW for February/March and May/June 1979 the band of maximum cloudiness was close to the surface flow discontinuity, generally not more than one degree north of it.

57 W e s e e from F i g u r e s 1 and 2 t h a t f o r February/March t h e wind w a s i n

g e n e r a l from s o u t h - e a s t ,

as e x p e c t e d f o r a t r a d e wind r e g i o n . The s t e a d i -

ness w a s r e l a t i v e l y l o w i n t h e n o r t h and i n c r e a s e d southward. W e c a n see from F i g u r e 5 and e s p e c i a l l y from t h e d a i l y p o s i t i o n o f t h e ITCZ ( n o t shown h e r e ) t h a t a low s t e a d i n e s s w a s always c o n n e c t e d w i t h a southward movement o f t h e ITCZ. Between F e b r u a r y 26 and March 6 t h e ITCZ w a s f a r t o t h e s o u t h . S o w e c a n i d e n t i f y from F i g u r e 1 a s t r o n g c o n f l u e n c e between 1°N and t h e E q u a t o r . T h i s w a s c o n f i r m e d by s y n o p t i c s u r f a c e o b s e r v a t i o n s which were performed f r e q u e n t l y a b o a r d R.V.

METEOR. I n C o n t r a s t

t o t h e s e f e a t u r e s t h e t r a d e - w i n d s a r e v e r y s t a b l e and s t r o n g e r from May t o June ( F i g u r e s 3 and 4 ) . These r e s u l t s are i n q u a l i t a t i v e agreement with h i s t o r i c a l d a t a ( e . g . H e l l e r m a n , 1 9 8 0 ) . Our p r i n c i p a l a i m w a s t o i n v e s t i g a t e t h e i n f l u e n c e of t h e a t m o s p h e r i c motion on t h e o c e a n i c c i r c u l a t i o n . So f a r w e d e s c r i b e d t h e a v a i l a b l e m e t e o r o l o g i c a l d a t a s e t s . The f i g u r e s 6 and 7 r e p r e s e n t a s e l e c t i o n of

the ocea'nographic measurements, which w e need f o r d i s c u s s i o n i n s e c t i o n 4 Those are t e m p e r a t u r e s i n 15 m d e p t h ( F i g u r e 6 ) . Our i n t e r p r e t a t i o n of Figure 6 i s , t h a t w e f i n d i n e a c h o f t h e c o n s i d e r e d p e r i o d s a n u p w e l l i n g event a t t h e E q u a t o r . I t s t a r t s w i t h J a n u a r y 1 7 and May 29 r e s p e c t i v e l y .

W5

205

30.5

10.6

W5

TIME [DAVS]

Fig. 6 . T i m e - s e r i e s of SST ('(2) a t t h e Equat o r and a t I O N f o r February/March 1979 ( t o p ) and a t t h e E q u a t o r f o r May/June 1979 ( b o t t o m ) .

M5 3 0 5

a6

105 2 0 5 30 5 106 TIME [ D A V ~

Fig. 7 T i m e - s e r i e s o f t h e z o n a l and m e r i d i o (top) a t n a l c u r r e n t component (ms-') t h e E q u a t o r a t 70 m d e p t h and t i m e series of w a t e r - t e m p e r a t u r e s ( O C ) b o t t o m ) a t 70 m and 9 0 m a t t h e Equator f o r May/June 1979.

58

For the first period the upwelling event can also be identified in ION. Additionally, we need currents and temperatures of the second period (Figure 7). At the Equator we find the EUC in 7 0 m, which is the mean depth of its core for that period. In the meridional current component we find a low frequency variability, which we attribute to the 16-days meander, as described by Duing et al. (1975). A similar meander was inferred by Lass et al. (1980) from current profile measurements across the Equator along 28'40'W

between May and June 1979. They found that the meander was

week at the beginning of the observations and amplified simultaneously with the amplification of the SEC after May 20. The temperatures in 70 m depth and also in 90 m depth (Figure 7, bottom) show similar fluctuations.

4

SPECTRAL ANALYSIS

To come close to our goal we have applied spectral methods to our data. Wind spectra for the February/March observations barely showed any significant features and are not reproduced here. Spectra for the May/June period are shown in Figure 8 in which the following representation was chosen.

Ea122W: SPP :

P,

/

/ I

10-3

;

<\

----

-

ZONAL COMPONENT

2N122W ZONAL COMPONENT 76

\

10 2 FREOUENCY

w-3

10 1 [H

'1

lo"

10-1

FREOUENCY 2

100

[H']

2N122W MERlO COMPONENT -46

io3

a-2 FREQUENCY

10-1 [H-I

Fig. 8. Power spectral estimates (m2s-2) of the zonal and meridional wind components at the Equator (left) and at 2 O N (right), indicated by solid lines. Additionally, power spectral estimates of the wind components at St. Peter and St. Paul Rocks (SSP) are presented by dashed lines. All spectra are computed for May/June 1979. The abscissa gives the period in a logarithmic scale, while the ordinate is the power density multiplied by the frequency. This kind of representa-

59 t i o n h a s t h e a d v a n t a g e t h a t t h e area under t h e c u r v e s i s p r o p o r t i o n a l t o t h e t o t a l v a r i a n c e . S i g n i f i c a n t peaks i n t h e s p e c t r a are marked by arrows. The s o l i d c u r v e s r e p r e s e n t s p e c t r a a t t h e E q u a t o r ( l e f t ) and a t 2 O N ( r i g h t ) f o r t h e z o n a l and m e r i d i o n a l wind components. The s p e c t r a l e s t i m a t e s o f each t i m e series w i t h z e r o mean v a l u e and z e r o l e a s t square l i n e a r t r e n d w e r e o b t a i n e d by d i v i d i n g t h e t i m e series i n t o s e g ments w i t h a l e n g t h o f 512 h o u r s . We a l l o w e d a 50 % o v e r l a p p i n g and a p p l i e d a s i n u s - s h a p e d Hanning window. A f t e r a d i r e c t F a s t F o u r i e r T r a n s formation t h e f r e q u e n c y s p e c t r a w e r e a v e r a g e d o v e r a l l segments. I t i s s e e n from F i g u r e 8 t h a t maxima do e x i s t f o r p e r i o d s of -1 day

i n each spectrum. The m e r i d i o n a l wind component e x h i b i t s a d d i t i o n a l maxima f o r -3 t o 4 d a y s i n b o t h l a t i t u d e s and 10 d a y s on t h e E q u a t o r . T h i s

i s i n good agreement w i t h K r i s h n a m u r t i and K r i s h n a m u r t i (1979) who found s p e c t r a l p e a k s i n t h e ".4

t o 6 d a y s r a n g e and around 11 d a y s p e r i o d i n

the s o u t h e a s t t r a d e s d u r i n g GATE ( g a r p A t l a n t i c T r o p i c a l E x p e r i m e n t ) . The z o n a l wind component, however, h a s maxima f o r -7 d a y s , which i s most expressed i n Z O N . C o - s p e c t r a ,

n o t r e p r e s e n t e d h e r e , show t h a t t h e z o n a l

wind components between t h e E q u a t o r and 2 O N a r e c o h e r e n t f o r t h i s p e r i o d ; the z o n a l wind component a t 2'N

l a g s t h a t on t h e E q u a t o r by -7 h o u r s .

The m e r i d i o n a l wind components e x h i b i t a h i g h c o h e r e n c e i n t h e 3 t o 4 range. The m e r i d i o n a l wind component a t t h e E q u a t o r l e a d s w i t h ".5 h o u r s . The l a t t e r r e s u l t i s c o n s i s t e n t w i t h a westward t r a v e l l i n g d i s t u r b a n c e with an a x i s d i r e c t e d from s o u t h w e s t t o n o r t h e a s t . T h i s i s i n agreement with Burpee (1974) who found t h e same f e a t u r e s f o r e a s t e r l y waves (wave length % 3 , 0 0 0 km) of a p e r i o d o f

'W.5 d a y s o v e r West-Africa a t t h e 700 m b

l e v e l . H e found a n i n c l i n a t i o n o f t h e a x i s o f ".480 km p e r 5 d e g r e e s l a t i tude which c o r r e s p o n d s t o a l a g o f -5.5

hours p e r 2 degrees l a t i t u d e .

This i s comparable t o o u r r e s u l t , b u t w i t h a tendency t h a t t h e t r o u g h a x i s i s a l i t t l e more i n c l i n e d (see Reed e t a l . , 1 9 7 7 ) . For t h e p e r i o d F e b r u a r y 2 , 1979 t o J a n u a r y 23, 1980 wind r e c o r d s a t S t . P e t e r and S t . P a u l Rocks

Garzoli e t a l .

(0°55.13'N,

29°20.60'W)

a r e a v a i l a b l e from

( 1 9 8 2 ) . W e have computed s p e c t r a from t h e s e d a t a f o r t h e

same p e r i o d s as f o r t h e measurements from 22OW and i n c l u d e d i n F i g u r e 8. These s p e c t r a show e s s e n t i a l l y t h e s a m e s t r u c t u r e as t h o s e f o r 2 Z o W , however, t h e v a r i a n c e of r e l a t i v e l o w f r e q u e n c i e s i s much l a r g e r . T h i s e f f e c t i s l a r g e r t h a n it c o u l d b e e x p e c t e d from t h e d i f f e r e n t h e i g h t of the wind r e c o r d e r s ( S t . P e t e r and St. P a u l Rocks: 21.3 m ; 2 2 O W :

1.5 m ) .

Coherence s p e c t r a f o r t h e wind components a t 2 2 O W and 29OW w e r e computed by G a r z o l i e t a l .

( 1 9 8 2 ) . From t h e s e it i s i n f e r r e d t h a t t h e wind com-

ponents are c o h e r e n t f o r t h e p e r i o d s of -3-4

d a y s and 7 d a y s . The phase

between t h e wind components a t 2 2 O W and 29OW ( n o t shown) s u g g e s t s a w e s t -

60 ward wave propagation with a wavelength of $5,000 km. We argue that also this result is consistent with Burpee (1974). We are aware of the fact that the two positions are 800 km apart and the data intervals are short, but the absence of any previous simultaneous in situ wind records from the Central Atlantic moves us to comment on what we have.

To investigate how far the oceanic oscillations at 2 Z 0 N are forced by the local wind we have computed co-spectra and empirical orthogonal functions of the wind and oceanic parameters. For periods of $7 days for the May/June campaign, we could find a coherence between the zonal wind and the zonal current component in depths of 15 m, 70 m and 90 m at the Equator').

The connection is most pronounced at 70 m and is shown in

Figure 9. The signal is first to be

seen at 15 m and has at 70 m a lag

of 3.5 days (not shown) against the wind. The temperature is in phase with the zonal current component (not shown, but compare the time series in Figure 7). We did not find a similar relationship for 2ON.

CO-SPECTRUM ZON.WIND - ZON.CURRENT 70M

1 ,713

,

, ,

, ,,

.,

, , , , ,, , , I0 2 ,Ol FREQUENCY [H']

,

,

, , , ,,

Fig. 9. Auto-spectral estimates (10-2m2s-2) of the zonal current component at 70 m at the Equator (left) and its co-spectrum (10-'m2s-2) with the zonal wind component (right). Both spectral presentation are calculated for May/June 1979

Garzoli and Katz (1981) studied observations from inverted echo sounders near the Equator in the western Atlantic. They found an increase in the variance centered at 3.5 days, which they interpreted as an atmospherically forced and equatorially confined, vertically propagating inertiagravity wave. Because our spectra for the meridional wind component exhibit peaks for periods of $3-4 days we expected to find coherent oscilla1)

Current meters were developed in the following depths: 15 m, 70 m, 90 ml 110 m, 255 m, 590 m (Equator) and 45 m, 65 m, 85 m, 105 m, 255 m~ 590 ( ZON) .

61 tions of the currents. However from our data we could not confirm the existence of such coherent relationships with the local wind at 22OW. Moreover, we could

not

find any other coherent oscillations with the

local wind, with the exception we discussed in the penultimate paragraph.

5

CONCLUSION It was our aim to investigate the atmospheric forcing of currents

in the equatorial Atlantic at 22OW. We had data available for two periods: February/March and May/June of 1979. For that reason we had to restrict ourselves to an examination of relatively short period fluctuations. During the first period the steadiness of south-east trades was relatively low in the north and increased southward; the wind spectra barely showed any significant characteristics. We attribute both features to the fact that during the February/March period the measurements were made pretty close to the ITCZ. Towards May/June the ITCZ migrates to the north, the wind steadiness is high, and in the zonal wind spectra we find increased variance for periods of Q7 days. The zonal wind component at 2ON lags that on the Equator by Q? hours. The meridional wind components exhibit increased variance for periods of Q10 days on the Equator and Q3 to 4 days on the Equator and 2ON. We attribute the latter periods to easterly waves with an axis inclined from southwest to northeast. From these characteristics of the wind field it was not surprising to us that for February/March we could not find any coherent oscillations between the local wind and the ocean. For May/June we could detect a significant coherence for periods of %7 days between the zonal wind and the zonal current only for the Equator. This relationship is most pronounced in the mean depth of the core of the EUC, where the current has a lag of Q3.5

days. We expected that the increased variance in the meridi-

onal wind components for periods of Q3-4 days would be favourable to excite inertia-gravity waves in the ocean. However, we could not confirm such a relationship from our data. A l s o the two upwelling events, starting February 17 and May 2 9 , whlch

were observed in the time series of temperature in 15 m depth are not coherent with the local wind. Because Fahrbach and Bauerfeind (1982) demonstrated that these low SST are not a result of increased vertical mixing due to a strong current shear ,between EUC and SEC, we conclude that these upwelling events could be caused by the remote forcing mechanism proposed by Moore et al. (1978). The necessary assumption for this, namely increasing easterly winds in the western equatorial Atlantic, did exist for the February/March as well as for the May/June period (com-

62

pare Figures 4 and 9 of Garzoli et al., 1982). However, we cannot exclude the possibility of an upwelling e w ? +

caused by the f-divergence under

permanent easterly trade winds as Wyrtki and Eldin (1982) found for the Central Pacific. They conclude that the upwelling becomes evident at the sea surface 10-20 days after the onset of a strong zonal wind. We could not infer such a relationship because of the shortness of our time-series. For the meridional current component at the Equator for the May/June period we found a low frequency variability, which we attribute for the

16 - days meander. We could deduce this only from the time series, because of their relatively short length. This was also the reason that we made no attempt to look for their possible generation by the wind.

63

REFERENCES Burpee, R.W., 1974. Characteristics of North African easterly waves during the Summer of 1968 and 1969. J.Atmos.Sci., 2, 1556-1570. Cornus, H.P. and J. Meincke, 1979. Observation of near-surface layer changes related to the Atlantic equatorial undercurrent. Deep-sea Res., g , 1291-1299. Diiing, W., P. Hisard, E. Katz, J. Meincke, L. Miller, K.V. Moroshkin, G. Philander, A.A. Rybnikov, K. Voigt and R. Weisberg, 1975. Meanders and long waves in the equatorial Atlantic. Nature, 257, 280-284. Diiing, W. and 2 . Hallock, 1979. Equatorial waves in the upper central Atlantic. Deep-sea Res., GATE Suppl. I1 to Vol. 26, 161-178. Fahrbach, E. and E. Bauerfeind, 1982. The variability of equatorial thermocline spreading as an indication of equatorial upwelling. Submitted to: Ocganographie Tropicale. Garzoli, s.T-. and E.J. Katz, 1981. Observations of inertia-gravity waves in the Atlantic from inverted echo sounders during FGGE. J.Phys.Ocean., 11, 1463-1473. Garzoli, S.L., E.J. Katz, H.-J. Panitz, P. Speth, 1982. In situ wind measure281-288. ments in the equatorial Atlantic during 1979. Ocean-Acta, Hallock, Z . , 1979. On wind-excited, equatorially trapped waves in the 261-284. presence of mean currents. Deep-sea Res., Suppl. I1 to Vol. 2, Hastenrath, S . and P.J. Lamb, 1977. Some aspects of circulation and climate over the eastern tropical Atlantic. Mon.Wea.Rev., 105, 1019-1023. Hastenrath, S . and P.J. Lamb, 1978. Climatic Atlas of the tropical Atlantic and eastern Pacific oceans. The University of Wisconsin Press, Madison, Wisc. 53701. Hellerman , S., 1979. Charts of the variability of the wind stress over the 63-75. tropical Atlantic. Deep-sea Res., Suppl. I1 to VoL. 2, Katz, E.J., R.L. Molinari, D.E. Cartwright, P. Hisard, H.U. Lass, A. de Mesquita, 1981. The seasonal transport of the equatorial undercurrent in the western Atlantic (during the Global Weather Experiment), Ocean.Acta, 4, 445-450. Katz, E.J. and S . L . Garzoli, 1982. Response of the western equatorial Atlantic ocean to an annual wind cycle. Manuscript. Kohne, A. and P. Speth, 1982. Variation of the ITCZ in the Atlantic during FGGE. Tropical Ocean Atmosphere Newsletter, 2, 7. Krishnamurti, T.N., R. Krishnamurti, 1979. Surface meteorology over the GATE A-scale. Deep-sea Res., GATE Suppl. I1 to Vol. 2, 29-61. Lass, H.U., W. Fennel, R. Helm, F. Mockel, M. Sturm, K.-H. Till, H. Wiechert and H. Will, 1980. Vorlaufige Ergebnisse der Expedition des Forschungsschiffes "A.v. Humboldt" in dem aquatorialen Atlantik wahrend des Globalen Wetterexperimentes (FGGE) SOP I1 1979. Beitr.Meeresk., 44/45, 89-107. Lass, H.U., V. Bubnov, J . M . Huthnance, E.J. Katz, J. Meincke, A. de Mesquita, F. Ostapoff, B. Voituriez, 1982. Seasonal changes in the zonal pressure gradient in the equatorial Atlantic west of lOoW during the FGGE year. Submitted to 0cean.Acta. Merle, J., 1978. Atlas hydrologique saisonnier de l'oc6an atlantique intertropical. Travaux et documents de l'O.R.S.T.O.M., No. 82. Moore, D.W. and S.G.H. Philander, 1977. Modelling of the tropical oceanic circulation, in: The Sea: Ideas and observations on progress in study of the seas, Vol. 5,J. Wiley and Sons Inc. Moore, D.W., P. Hisard, J. McCreary, J. Merle, J.J. O'Brien, J. Picaut, J . M . Verstraete and C. Wunsch, 1978. Equatorial adjustment in the eastern Atlantic, Geophys.Res.Lett., 2, 637-640.

s,

64 Neumann, G., 1960. Evidence for an equatorial undercurrent in the Atlantic Ocean. Deep-sea Res., 6, 328-334. Nicholson, S.E., 1975. Variation of the Intertropical Convergence Zone during phases 1, 2 and 3 of GATE experiment. GATE-Report No. 14., Vol. 1,169-175. Philander, S.G.H., 1976. Instabilities of zonal equatorial Currents. Journ.Geophys.Res., 81,3725-3735. Philander, S.G.H., 1978. Instabilities of zonal equatorial current, 11. Journ. Geophys .Res., 83 (C7), 3679-3682. Philander, S.G.H. and R.C. Pacanowski, 1980. The generatibn OfequaCOrla~ currents. Journ.Geophys.Res., 85, 1123-1136. Ramage, C.S., 1974. Structure of an oceanic near-equatorial trough deduced from research aircraft traverses. Mon.Wea.Rev., 102, 754-759. Reed, J.R., D.C. Norquist, E.R. Recker, 1977. The structure and properties of African wave disturbances as observed during Phase I 1 of GATE. Mon.Wea.Rev., 105,317-333. Sadler, J.C., 1975. The monsoon circulation and cloudiness over the GATE area. Mon.Wea.Rev., 103,369-387. Servain, J., J. Picaut and J. Merle, 1982. Evidence of remote wind forcing in the equatorial Atlantic ocean. J.Phys.Ocean., 12, 457-463. Voigt, K., 1961. Aquatoriale Unterstrdmung auch im Atlantik. (Ergebnisse von Stromungsmessungen auf einer atlantischen Ankerstation der "Michail LOmOnOSSov" am tiquator im Mai 1959). Beitr-Meeresk., 1,56-60. Weisberg, R.H., L. Miller, A. Horigan and J.A. Knauss, 1979. Velocity observations in the equatorial thermocline during GATE. Deep-sea Res., GATE SUPPl. II to Vole 26, 217-248. Wyrtki, K. and G. Eldin, 1982. Equatorial upwelling in the Central Pacific. J.Phys.Ocean., 12, 984-938.

65

NEAR SURFACE TEMPERATURE OBSEFWATIONS OBTAINED I N 'ME EQUATORIAL ATLANTIC OCEAN DURING FGGE (1979)

Robert L. Molinari*, National Oceanic and Atmospheric Administration, Atlantic Oceanographic and Meteorological Laboratories, M i a m i , Florida, U.S.A.

E l i K a t z , Lmnt-Doherty Palisades, New York, U.S.A.

Geological

Observatory,

Eberhard Fahrbach, I n s t i t u t e of lrlarine &search, Federal Republic of Germany

Columbia

University,

University of K i e l ,

Kiel,

Hans Ulrich Lass, Academy of Sciences of GDR, I n s t i t u t e of Marine Research, Rostock-Warnemunde, G e m n W c r a t i c Republic Bruno Voituriez, Antenne ORSTail-Oceanographic Center of B r e s t , Brest, France ABSTRACT

Temperature and surface wind d a t a collected across the equatorial Atlantic Ocean during t h e F i r s t

G4Rp

Global E x p e r h n t (FUZE), 1979, have been conpiled

t o study the seasonal evolution of the mar-surface temperature f i e l d . developnt

of

the

large-scale,

sea-surface

temperature

(SST) f i e l d

The

is

characterized by the appearance during boreal summer of a tongue of cold water which extends frcm the e a s t e r n to vestern basin, on and south of the equator. During 1979, the cold water f i r s t appears a t 4OW and 28OW during early May and a t 22OW saw four weeks later.

East of abcut 2OoW, the t h e m l i n e rises and

the mixed layer b e m s shallower simultaneously with the lowering of SST's.

West of about 30°W, the t h e m l i n e and mixed layer deepen a t t h i s time. Below average temperatures a r e observed through October, as the thermocline

redeepens i n the east and continues to deepen i n the west. t h e m c l i n e d i s t r i b u t i o n s along the equator have been -red g i c a l d i s t r i b u t i o n s derived frcm h i s t o r i c a l data. qualitatively

similar to the climatological

me

fields.

me

1979 SST and to climatolo-

FGGE year f i e l d s a r e

Surface wind data

collected during FGGE i n d i c a t e t h a t t h e surface cooling occurs within several days of an increase i n b t h components of wind a t 4OW and 28OW and within several weeks of t h e wind increase a t 22Ow.

*Prepared while v i s i t i n g s c i e n t i s t at:

Museum National d ' H i s t o r i e Naturelle Oceancqraphie Physique, L.A. 175, CNRS P a r i s , France

66

Changes i n h e a t c o n t e n t over v a r i o u s t i m e i n t e r v a l s here computed from t h e

FGGE d a t a f o r a layer 50 m t h i c k .

These changes have been compared to changes

which w u l d be induced by energy f l u x e s through t h e sea s u r f a c e , determined Tne comparison shows t h a t s u r f a c e energy f l u x e s can n o t

chatolog&cally.

account f o r t h e i n i t i a t i o n of t h e c o l d water tongue.

A

box model centered on

t h e e q u a t o r and extending from l O o W t o 3O0W was c o n s t r u c t e d to determine what p r o c e s s e s m y be a c t i v e during t h e e a r l y s t a g e s of the d e v e l o p e n t of t h e Cooling w i t h i n t h e box is e s t h t e d a t a rate o f -3.0°C/60

tongue.

t h e f i r s t of May through t h e f i r s t of J u l y .

days from

?his is approximately balanced by

warming due to s u r f a c e energy f l u x e s (+1.5OC/60 advection

by South Q u a t o r i a l O-lrrent (-1.6OC/60

(-1.2'C/60

days) and upwelling (-1.2"C/60

days).

days) and cooling due t o days) , v e r t i c a l mixing 'Ihe o b s e r v a t i o n s f u r t h e r

s u g g e s t t h a t mixing and upwelling are important d u r i n g t h e e a r l y s t a g e s of t h e d e v e l o p w n t of the tongue, while advection p l a y s a mre i m p r t a n t role a t

later times

.

INTRODUCTION

1.

I n b t h the A t l a n t i c and P a c i f i c Oceans, a tongue of cold water extends on

the e q u a t o r frcm t h e eastern to t h e c e n t r a l b a s i n s during

and south of

n o r t h e r n hemisphere s w r b u t n o t northern hemisphere w i n t e r (Hastenrath and L&,

I n the A t l a n t i c , t h e tongue extends f a r t h e s t to t h e west along

1977).

t h e equator d u r i n g August and September.

According to Hastenrath (19801, the

tongues play a n h p r t a n t role i n t h e g l o b a l h e a t balance, as t h e y s e r v e as s i n k s f o r the e x c e s s r a d i a t i o n received by t h e tropics r e l a t i v e t o higher latitudes. P h y s i c a l oceanographic data *re d u r i n g the F i r s t Experiment.

GFlRp

collected

i n a l l the tropical Oceans

Global Experirrent (EGGE), also c a l l e d t h e Global W a t h e r

A p r t i o n of

those data c o l l e c t e d i n the e q u a t o r i a l A t l a n t i c

Ocean by v a r i o u s i n v e s t i g a t o r s and i n s t i t u t i o n s have been canbined and w i l l be reviewed, w i t h p a r t i c u l a r emphasis on t h e cold water tongue, f o r the following purposes:

(1) to d e s c r i b e the t m p r a l and spatial e v o l u t i o n of the nears u r f a c e temperature during

f i e l d of

t h e e q u a t o r i a l A t l a n t i c Ocean

an extended p e r i o d encanpassing FGGE,

through March 1980;

January

1979

67

to determine i f t h e FGGE-year temperature d i s t r i b u t i o n s were,

(2)

i n terms of long-term averages, "normal" or anomalous; and

to determine what atmospheric and oceanic f a c t o r s contribute to

(3)

the evolution of t h e temperature f i e l d . Scane guidance f o r planning future e f f o r t s i n the Atlantic should

result as a

consequence of the analyses performed to meet these objectives. The analyses and results presented herein a r e q u a l i t a t i v e and preliminary

i n nature, a s not a l l the FGGE data a r e available a t t h i s time and those data available are not

in a form s u i t a b l e for detailed q u a n t i t a t i v e analyses.

Efforts are noll underway to obtain the e n t i r e FGc;E Atlantic data-set,

in

particular, expendable bathythemgraph (XBT) data and surface temperature and wind observations. data-set.

More q u a n t i t a t i v e analyses a r e planned f o r the expanded

Haever, the present discussion w i l l provide the framework f o r the

future e f f o r t . 2.

DATA

AND PROCESSING

The ships

Table 1.

involved and t h e i r cperating areas and times a r e l i s t e d i n

Tne majority of

the data were collected by Conductivity Depth

Temperature (CTD) units, k u t some XBT data are also used. intercalibrations of

N o ship-to-ship

In general ,

the temperature sensors were performed.

calibrated CTD temperature data are accurate to b e t t e r than .05OC.

TABLE 1

Participating s h i p s i n the Equatorial A t l a n t i c Ocean during FGGE*

Operating Area Ship

Latitude

BESNARD CAF'RICOFWE

2OS 4"s

-

2ON

aXmAJ3 HUMEOLDT KURCHATOV METEOR

2OS 2'5 2OS 2'5 2OS 10's

-

2ON

OCEANUS RESEARCHER

4ON

- 5'N

- N'2 - 3'N - 2ON - 1°N

Longitude 28"W

-

4O0w

4OW

28OW - 4OoW 28.7"N 18.5OW - 22.5OW 22ow 28OW - 4OoW l l o W - 27.5OW

+proximate

rates

Jan/Feb/Mar/Jul 1979 J u l 1978 Jan/Apr/Jun Oct 1979 F'eb 1980 S e p / e t 1979 May/Jun 1979 Mar/Apr 1979 FebJun 1979 Feb/Mar 1980 Jul/Aug 1978 Jan/Feb/Jul 1979 Feb/Mar 1980

*Includes only those s h i p s whose observations are considered i n the t e x t .

68

Several f o m of d a t a presentations are used to describe the evolution of

the near-surface

temperature f i e l d .

In these presentations,

when several

s t a t i o n s per day a r e a v a i l a b l e a t one location, the data were averaged over tw-day

periods

to

reduce

some of

the

higher

frequency

variability.

S p a t i a l l y , averaging was t y p i c a l l y performed through subjective contouring of the

fields.

is planned

Objective mapping

when

is

the l a r g e r data-set

available. I n the following discussion, the f i r s t depth a t which the temperature is 0.5OC less than the sea-surface temperature (SST) is used t o define the mixed l a y e r depth.

Using a mre s t r i n g e n t d e f i n i t i o n , e.g.,

0.2OC less, typically,

did not a l t e r the mixed layer depth d i s t r i b u t i o n s because of the intense thermocline located j u s t below t h e mixed layer i n the region.

me

depth of the 23'C

thermocline.

isotherm is taken t o represent the depth of the

This d e f i n i t i o n permits canparison with previous studies.

The

23OC isotherm is generally located within the region of maximun v e r t i c a l temperature gradient a s sham

a comparison between the average depth of

t h i s isotherm and the average depth of maximm gradient f o r several c r u i s e s (Table 2 ) .

The only s i g n i f i c a n t difference occurs during s m r in the

isotherm sometimes breaks the surface.

e a s t e r n Atlantic, when t h e 23'C

The

average mximm gradient depth during these c r u i s e s is about 30 m, while the average 23OC

isotherm depth is about 15 m.

Although

these depths a r e

d i f f e r e n t , both representations indicate that the thermocline is s h a l l m r a t t h i s tire than during other c r u i s e s .

TABLE 2 Comparison of average thermocline depths (m) by cruise as given by the depth of the 23OC isotherm and by the depth of the maximun v e r t i c a l temperature gradient. Also given i n parenthesis a r e standard deviations (m).

mnth/Year Jul Jan Apr Jun Oct Jan Jan

May Jun Oct Feb

Mar

1978 1979 1979 1979 1979 1980 1979 1979 1979 1979 1980 1979

Operating Area Latitude Longitude 4.5's 5's 6OS 5's 5's

5's 4's 2's 2's 2's 0' 4's

-

2'N 5'N 5'N 3N ' 5"N

-

4"N 2'N 2'N 2'N

- 5ON - 3N' - 1°N

1'E 4OW

4'W 4OW 4W ' 4OW 27.5OW 28.7OW 28OW 38.5OW 28OW - 40% 40°W 28OW 27 .SOW 1°E

-

-

N-r of Data Points

53 33 17 43 18 16

41 30 39 27 6

Average Depth 23OC isotherm Gradient 33 37(11) 40 ( 1 0 ) 30(10) 46(10) 49(14) 86(7) 78(12) 90(20) 112(17) 91(11) 88(13)

69 3.

BASIWWIDE TEXPERn”KJRE DISTRIBUTIONS

Sea-surface temperature d i s t r i b u t i o n s have been c o n s t r u c t e d f o r f i v e quasisynoptic time i n t e r v a l s , each approximately one-mnth the mean-monthly

long.

Isotherms from

SST c h a r t s of Hastenrath and Lamb (1977) are also shown on

the synoptic SST d i s t r i b u t i o n s (Figs. 1, 2, and 3 ) .

The p r e d m i n a n t f e a t u r e

i n t h e January-February 1979 d i s t r i b u t i o n is a n enclosed p a t c h o f c o l d e r water centered somewhat south of t h e e q u a t o r a t a b u t 16OW (Fig. 1). SST‘s along the equator d u r i n g this period range from less than 26.2OC w i t h i n t h e p a t c h ,

to g r e a t e r than 28.5OC to t h e east o f t h e p a t c h and g r e a t e r t h a n 27.2OC to the west.

-13 JANUARY - 13 FEBRUARY

1979

AVERAGE JANUARY FROM ---- HASTENRATH AND LAMB (19771

SEA-SURFACE TEMPERATURE (‘C)

-

APRIL- 8 MAy 1979

___-AVERAGE APRIL FROM HASTENRATH AND LAMB (1977)

Fig. 1. Sea-surface temperature, SST (“C), d i s t r i b u t i o n s f o r t h e times indicated ( s o l i d l i n e s ) . Dashed l i n e s r e p r e s e n t isothem f r a n the appropriate m a n m n t h l y SST c h a r t of Hastenrath and Lamb (1977). Dots represent s t a t i o n p s i t i o n s . Net

h e a t i n g a t 4OW and between 18.5OW and 28.7OW has occurred between

January-February

and April-May

1979 (Fig. 1).

Maximun temperatures i n the

east are greater than 29.OoC and i n t h e vest, 28.2OC. Somewhat c o l d e r waters a r e s t i l l observed i n t h e c e n t r a l A t l a n t i c . By June-July, a tongue of c o l d water, w i t h c o l d e s t waters i n the east, appears on the equator (Fig. 2 ) .

me

synoptic pattern appears v e r y similar to t h e c l i m a t o l o g i c a l pattern given by

70 t h e Hastenrath

and Lamb

(1977) isotherms.

The few d a t a a v a i l a b l e during

O c t o b e r s h m t h a t temperatures r a i n e d r e l a t i v e l y l m i n t h e e x t r a western

A t l a n t i c through the e a r l y f a l l (Fig. 2 ) . increased (Fig. 3 ) .

E3y February-March 1980, SST's had

Although not w d l defined, t h e r e is saTe suggestion

Of

a

cold water patch centered a t a b u t t h e same l o c a t i o n as during boreal winter 1979. SEA-SURFACE TEMPERATURE

-22 JUNE -

JULY 1979

____

(TI

I V E R I O E WLY FROM HASTENRITH AND LIMB l1977l

SEA-SURFACE TEMPERATURE ('C) 5-N 4.N 3.N 2.N 1N . 0. I*S

2 5

3 . S C S

50s

-I ocT,- 18OCT, Fig. 2.

Same a s Figure 1.

Fig. 3.

Same a s Figure 1.

197g

____AVERAGE OCTOBER FROM HASTENRATH AN0 LAMB (1977)

71 Time-longitude p l o t s of SST, 23OC isotherm depth and mixed layer depth have teen constructed fran data collected along the equator. been oonstructed fran the man-monthly

Similar p l o t s have

SST charts of Hastenrath and Lamb

(1977) and the seasonal 23OC isotherm depths of Merle (1980). The 1979-1980

equatorial SST distributions and the climatological SST

distributions are q u a l i t a t i v e l y q u i t e similar (Fig. 4).

In both representa-

tions, temperatures range from a minimum of less than 23OC, cccuring i n JulyAugust, to a maxhun of greater than 2 8 T , occuring sometime in April-May. Although these data are not adequate to describe precisely the evolution of the synoptic SST f i e l d , maximun cooling in the east occurs between late April and l a t e June, a s it does in the climatological data-set.

It is d i f f i c u l t to

resolve the timing of the cooling west of 30°W, but coldest t-ratures

are

observed somewhat l a t e r during September-October in both representations. "

40.:

3s

10.

5.w 0.

~

"

'

'

.

-

. ..

SE4-SURF4CE TEMPER4TURE IT1 4T 0. 1978-1980

5eEid ' J A ~ 1978 1979

'MAR

'~4;

'JW 'sEPI

'No;

'JANI

'MAR

1980

Fig. 4 . T i m longitude p l o t s along the equatorial plane of sea-surface temperature, SST ("C), d i s t r i b u t i o n s observed during 1979 ( l e f t panel) and taken fran the mean m n t h l y SST charts of Hastenrath and Lamb (1977) ( r i g h t panel). Eats represent s t a t i o n locations.

Fs was the case for the SST d i s t r i b u t i o n , the 1979-1980 23'C isotherm depth distribution and the climatological distribution appear quite similar (Fig. 5).

Minimm isotherm depths, in both cases, occur between SOW and l O o W during

July and August.

A l s o s h a m on Fig.

5, are m n t h l y averaged t h e m c l i n e

depths inferred fran an inverted echo sounder deployed a t 40OW.

A l l three

representations indicate t h a t deepest t h e m l i n e depths in the west occur sometime during e a r l y f a l l and a r e greater than 120 m. Although the synoptic data are inconclusive, there is some suggestion t h a t t e m p r a l changes during 1979-1980, p a r t i c u l a r l y during the spring i n the east, a r e similar to changes during the climatological year.

72

Fig. 5. Time l o n g i t u d e p l o t s along t h e e q u a t o r i a l plane of the depth d i s t r i b u t i o n (m) of t h e 23OC isotherm observed during 1979 ( l e f t p a n e l ) and Dots from the m a n seasonal d i s t r i b u t i o n of Merle (1980) ( r i g h t p a n e l ) . represent s t a t i o n p s i t i o n s . The e v o l u t i o n of t h e e q u a t o r i a l mixed l a y e r f i e l d is s h a m i n Fig. 6.

Tne

d a t a suggest t h a t t h e c o o l i n g o f SST i n t h e east is a s s o c i a t e d i n i t i a l l y with

a shallower mixed l a y e r .

Cooling i n t h e wst, p a r t i c u l a r l y during Cctober,

appears to be associated with a deeper mixed l a y e r .

,

40'-

,

,

,

,

,

,

,

,

,

35" -

30'

-

25'-

20' 15" -

40

____-_------

10" -

30

5'WO'-

MIXED LAYER DEPTH (m)

Fig. 6. Time l o n g i t u d e plot along t h e e q u a t o r i a l p l a n e of mixed l a y e r depth (m) d i s t r i b u t i o n observed d u r i n g 1979. Dots r e p r e s e n t s t a t i o n p s i t i o n s .

EVOLUTION OF EQUA!JDRIAL SURFACE WIND AM) TFMPERATURE DISTRIBUTIONS ALCNG

4.

SEVERAL MERIDIANS

S u r f a c e wind and o c e a n i c temperature d a t a c o l l e c t e d simultaneously a t or near

the sam e q u a t o r i a l p s i t i o n

(4OW, 22Ow,

and 28OW) are compared to

c o n s i d e r p s s i b l e phase r e l a t i o n s between atmospheric and oceanic phenamena. Wind d a t a collected a t Oo,

4OW have been kindly supplied by P. Rual, ORSTCr4,

73

Brest, France

and those a t O o , 22OW by H. 3. Panitz, University of Cologne,

Cologne, Federal Republic of G e m n y .

Zonal wind c m p n e n t s obtained a t

18.5OW f r m wind stress data given by Bubnov (1981) are used to f i l l - i n some gaps in the 22OW t h series.

Finally, Katz e t al. (1981) present a the

series of wind data collected a t 0.g0N, 29.35OW which is used to represent equatorial conditions a t 28OW. in contrast to 2 2 O W and 28OW, the m r i d i o n a l component of the wind

A t 4'W,

is larger than the zonal compnent

(Figs.

7,

8 , and 9 ) .

Observed wind

components a t a l l three longitudes increase by a t least a factor of two during May.

i%<

: : j

Simultaneously, SST's decrease a t the three p s i t i o n s . oq4" w

4

2.5 2

v-

----

__ FEE

--

-" __-___

--_

--- ---APR

JUN

AUG

OCT

__

__ DEC

Fig. 7. Temporal evolution along 4 O W of the follcwing variables (data collected during 1979, except where indicated): panel A; average wind speed ccnpnents, panel B; sea surface temperature, panel C; mixed layer depth and panel D; t h e m l i n e depth. me m a n f o r each temperature variable is given as a s t r a i g h t line. ?he winds increase a t 4 O W sane t i m e between 3 May and 5 June (Fig. 7 ) .

SST

decreases over 5OC between 24 April and 1 6 May, rises some 2OC and then f a l l s again during June.

The data available between 24 April and 16 May =re

obtained fran a surface current meter mooring and subsurface temperature data

were not given ( J a r r i g e and mal, 1981).

Both the synoptic and climatological

depth d i s t r i b u t i o n s indicate t h a t the t h e m l i n e rises concurrently with the cooling (Fig. 51,

although as in the case of surface winds,

gaps in the

74

subsurface temperature

records preclude

the d e f i n i t i o n of

precise phase

Similarly, the mixed layer depth becaws shallower a t t h i s t i m e .

relations.

w5 201 dx 401 gk? 601 60

27

5'I

26

I-

24

;--. 'f..- I.,..

I

60 loo 1

JAN

1

1

MAR

1

Dl I

1 1 MAY

*

I

1

'

JUL

1

Same a s Figure 7, except f o r 22OW.

Fig. 8.

._-29

- Oa.

27 -

28

60c

B

27.5°W/28.70W X

*.-:

Dl

Fig. 9. San-e as Figure 7, except f o r 27.5OW/2a0W. The t h e m l i n e depth curve f r m 40°W is taken f r a n m a n monthly inverted echo sounder data. Temperatures belcw the record average, as ell as another 2OC ccoling event,

a r e also observed a t 4 O W during October

(Fig. 7 ) .

thermocline and mixed layer a r e deeper than during June.

However, the

Deepest mixed layers

are associated with the lcwest temperatures during October (Fig. 1 0 ) . mere are no obvious systematic changes i n thermxline depth a t this time. Warming

75

begins concurrently w i t h a charqe i n zonal wind component f r m e a s t e r l y to westerly and a d e c r e a s e i n total wind speed (Fig. 1 0 ) . I

OCTOBER / 1979

Fig. 10. Time series of sea-surface temperature, mixed thermocline depth (upper p a n e l ) and wind speed ccnnpnents derived f r m twice d a i l y o b s e r v a t i o n s a t 0", 4"W.

layer

depth,

(lover p a n e l )

A t 22"W, a t least t h e zonal wind compnent of wind accelerates a f t e r t h e

f i r s t of May (Fig. 8 ) .

S u r f a c e layers begin to cool some f o u r w e k s later,

and a s a t 4"W, c o o l i n g does n o t o c c u r monotonically.

A t least tr\o p r i o d s of

cooling are observed; one o c c u r s between 28 May and 6 June and t h e o t h e r , which is n o t as w l l resolved, b e t w e n 10 J u n e and 13 J u l y .

S h a l l m r mixed

the lcwer tenrperatures observed d u r i n g June (Fig. 8 ) . However, i t is n o t clear whether t h e shallower t h e m c l i n e depths are r e l a t e d to s e a s o n a l or h i g h e r frequency v a r i a b i l i t y . l a y e r and

t h e m c l i n e d e p t h s are associated

with

Temperature d a t a collected simultaneously on t h e e q u a t o r a t 70 m s h a i l a r g e

amplitude, periodic changes i n t h e temperature (Fig. 11). Assuming an average t h e m l i n e gradient

of

about 8"C/50

m,

these temperature changes imply

changes i n t h e m c l i n e depth of some 30 to 40 m. A t 28"W, both i n c r e a s e s i n wind and d e c r e a s e s i n SST begin

the f i r s t week of May (Fig. 9 ) . July.

During June,

3SoW, where between 8 June and Further

shultaneo&y

early

t h e r e is a 20 m deepening of the mixed layer, kut no

systematic changes i n thermocline depth. sham).

some t h e during

Temperatures have f a l l e n some 3°C J!Y

wst

at

Only a few d a t a are a v a i l a b l e a t

5 J u l y t e m p r a t u r e s f a l l saw 1°C

4O0w,

increases

in

thermocline

depth

(not

occur

w i t h i n c r e a s e s i n wind i n t e n s i t y a t 29"W (Fig. 9 ) , as d e s c r i b e d

by Katz and G a r z o l i (1982). the d a t a , wekest winds are observed during March-April a t t h e t h r e e l o c a t i o n s . Highest SST's o c c u r a t this time. Within the temporal r e s o l u t i o n of

76

28.00 27.00 26.00

25.00 24.00

5.PIRY 1979

25.

15.

4.JUN

14.

0 tl I G I l T l

EQUATOR 3

70M

23.50 z'z.50 Y

21 .50

Ls

20.50

Y

0

19-50

18.50

17.50 16.50

Fig. 11. T h e series of temperature a t 15 m (upper panel) and 70 m (1-r panel) obtained fran current mter moorings a t Oo, 22Ow. 5.

HEAT E!UDGET CCFPUTATIONS

Some order-of-magnitude

estimates of what terms Can be important in the

local heat budget have been made. through the sea-surface the summer.

First,

it is shown t h a t energy fluxes

a r e not r e s p n s i b l e f o r the Cooling observed during

Changes i n heat content of the mixed layer a t the three m r i d i a n s

have been estimated from the temperature data for time periods which are functions of data a v a i l a b i l i t y .

N e t heat gain through the sea-surface

has

been estimated f r m the m a n m n t h l y heat gain charts of Hastenrath and Lamb (1978).

These charts are contoured a t a 40 W/m2

contour interval and thus,

only an approximate range of heat gain can be obtained.

Changes i n heat

content are expressed i n t e r n of changes i n temprature over an average mixed Surface heat gain values are converted to changes

layer (Figs. 7 , 8, and 9 ) .

in mixed layer temperatures for comparison purposes in Table 3 . A t a l l three locations, the Ocean receives throughout the year a net input

Thus, as found by Merle (1980) fran c l b a t o l o g i c a l data, the s m r cooling is driven by processes internal to the ocean, rather than by external atmospheric processes. F u r t h e m r e , a t 22% and 28OW, the warming

of energy.

observed a t other times of the year is less than muld be caused by surface energy exchanges.

fius,

even a t times of warming, e i t h e r some internal

oceanic processes serve to retard heating of surface layers or significant interannual v a r i a b i l i t y fluxes.

(of

the order 50 W/m2)

occurs

i n surface heat

The rapid warming observed during June a t 2 2 O W m y be related to

southward advection of wamr water a f t e r the i n i t i a l cooling.

77

TABLE 3 Observed temperature changes and average mixed l a y e r f o r t h e t h e periods given and t h e range of temperature changes e s t h t e d f o r t h e same periods using m a n m n t h l y n e t h e a t g a i n s through t h e sea-surface from t h e a t l a s of Hastenrath and Lamb (1978).

Latitude

J u l i a n Days Average Mixed (from 1 J a n 1979) Layer Depth

(m)

Observed Temperature Change ("C)

Range o f E s t b t e d Temperature Change ("C)

4OW

21-121 121-174 174-299 299-382

25

0.7 -3 .O -0.7 2.6

0 0.9 4.2 2.0

22ow

42- 64 64- 93 93-130 130-156 156-163 163-194

30

-0.1 0.8 0.1 -2.0 2.1 -2.6

1.2 1.2 1.0 0.7 0.2 0.9

31-133 133-152 152-191 191-276 276-431

45

1.2 -0.8 -1.9 0.4 1.6

3.7 0.3 0.7 2.6 2.9

28OW

-

-

-

2.8 1.8 6.3 2.8 1.4 1.8 2.0 1.4 0.4 1.8 4.2 0.5 1.0 3.9 5.8

Processes which can cool t h e s u r f a c e l a y e r s include advection o f c o l d water f r m t h e east by t h e South E q u a t o r i a l C u r r e n t (SEC), u p e l l i n g f r a n belm and v e r t i c a l mixing.

Wyrtki (1981) c o n s i d e r s these processes i n a &el

We adopt h i s &el

P a c i f i c Ocean.

of t h e

f o r a p p l i c a t i o n to t h e A t l a n t i c Ocean, b u t

consider t h e i n i t i a t i o n of t h e c o l d water tongue r a t h e r t h a n its maintenance,

as d i d Wyrtki (1981). For t h e s e camputations, a combination of c l i m a t o l o g i c a l However, when a l l the FGGE-year d a t a are a v a i l a b l e , t h e computation w i l l be repeated using o n l y those d a t a .

and s y n o p t i c d a t a are used.

A box &el w i l l be used which extends f r a n 5OS to 5'N (so t h a t reasonable estimates of E!anan t r a n s p o r t are pssible), f r a n l O o W to 3 3 O W ( t o avoid p s s i b l e lateral boundary e f f e c t s ) and f r a n t h e sea-surface to 50 m ( a n average mixed l a y e r depth for early b o r e a l summer, Fig. 5 ) . ?he h e a t budget of t h e box can be w r i t t e n

-aT =

at

0

s

+Qm +

QUP

+

QMIX

78

where aT/at = average temperature change w i t h i n t h e box,

Qs Qmv

= temperature change caused by heat-flux

through t h e sea-surface,

= temperature change caused by h o r i z o n t a l advection, = temperature change caused by upwelling, and

QMIX A

= temperature change caused by v e r t i c a l mixing.

least squares f i t to the f i v e s m r cooling rates given i n Table 3

i n d i c a t e s an average cooling rate of about -3OC/60 July.

Temperature

days between May and

i n c r e a s e due to h e a t g a i n through t h e sea-surface

is

estimated f r m t h e boreal s m r n e t oceanic h e a t g a i n c h a r t s of Hastenrath and Lamb (1978) a t + 1.5OC/60

days.

Temperature change caused by advection o f c o l d e r waters through t h e eastern boundary by the SEC can be expressed a s

where U is the volume t r a n s p r t of t h e SEC, Tloow is t h e temperature of SEC waters a t 1OoW, T33oWI a t 33OW and V, t h e v o l m o f t h e box.

Bubnov and

Egorhikin (1979) observed a n average t r a n s p r t of t h e SEC during boreal summer 1974 of 15 x lo6 m3/s.

Both t h e s y n o p t i c and c l i m a t o l o g i c a l r e p r e s e n t a t i o n s

of SST f o r boreal s m r (Fig. 2), about 27OC.

i n d i c a t e Tloow is about 24OC and T33.W

The r e s u l t a n t cooling due to advection is -1.6OC/60

is

days.

The change i n temperature w i t h i n t h e box due to u p e l l i n g w i l l be estimated following the approach of Wyrtki (1981).

I n t h i s approach,

where W is t h e u p e l l i n g rate and is c q u t e d as a d i f f e r e n c e between m

n

divergence and geostrophic convergence a t t h e equator, T1 is t h e temperture o f t h e hater leaving t h e box through the tlleridional b u n d a r y and To is t h e temperature o f t h e upwelled water a t 50 m.

Eman t r a n s p r t o u t of t h e box is

estimated by assuming t h e t r a n s p r t through 5'

where

T~

is p r a p o r t i o n a l to

is the zonal wind stress ccanponent,

Coriolis parameter.

p

is d e n s i t y and f is the

Climatological wind stress d a t a given i n l h i n g e t al.

(1980) are used to determine

T ~ .

For t h e s m r m n t h s of J u l y , August, and

September t h e southward E h n t r a n s p r t through 5OS is 16 x northward transport through 5ON is 9 x 106 m3/s.

lo6

m3/s.

The

79 H a e v e r , as noted by Wyrtki (19811, the divergence of Elanan f l u x is not equal to t h e rate of upwelling because o f g e o s t r o p h i c t r a n s p o r t t c m r d s t h e equator which o c c u r s on a d i f f e r e n t v e r t i c a l l e n g t h scale t h a n d o e s t h e former

me

flux.

c l h t o l q i c a l s e a s o n a l dynamic t o p g r a p h y c h a r t f o r boreal smmr

of Merle (1978) s h m s t h a t g e o s t r o p h i c f l w a t both 5's and 5'N equator.

Geostrophic c u r r e n t s are approximately c o n s t a n t i n the upper 50 m

and decrease to about 0 a t 100 m.

lo6

c h a r t are 8 x

m3/s

Geostrophic t r a n s p o r t s camputed frcm this

i n the upper 50 m and 4 x

lo6

m3/s between 50 m and

100 m across both the n o r t h e r n and southern boundaries. i n t o the box is about 8 x

t r a n s p r t , W, about 22'C

is towards t h e

l o 6 m3/s.

Thus, t h e upnlelling

Temperatures a t 50 m are

and a t the m r i d i o n a l boundaries about 26'C

(Fig. 2).

With t h e s e

e s t h t e s t h e change i n temperature w i t h i n t h e box due to equatorial upwelling is -1.2OC/60 days. Temperature changes due to v e r t i c a l mixing can be expressed as

where A is h o r i z o n t a l area, K is 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 c o e f f i c i e n t and

aT/az is v e r t i c a l temperature g r a d i e n t . value of 0.1 x

loT4 m2/s

Wyrtki (1981) assumes a c o n s t a n t

f o r t h e d i f f u s i o n c o e f f i c i e n t , although he n o t e s t h a t We assume a value of

it is probably h i g h e r i n t h e r e g i o n o f t h e Undercurrent. 2 x

m2/s

the

findings

elsewhere.

f o r a region

3O

of

Fahrbach

and

The

vertical

tmperature

wide enamipassing t h e Undercurrent ( f o l l m i n g Bauerfeind,

1982)

gradient

0.1

x

the

area of

Undercurrent is taken as 8OC/50 m and elsewhere as 12'C/50 change due to v e r t i c a l mixing is t h u s e s t i m a t e d as -1.2'C/60

me

m2/s

and

within

m.

the

Temperature

days.

balance given i n (1) can n m be w r i t t e n

-3.O0C/60

days = 1.5'C/60

-3.O0c/60 days = -2.5'C/60

days

-

1.6'C/60

days

-

1.2'C/60

days

-

1.2'C/60

days

days

These e s t i m a t e s are obviously q u a l i t a t i v e and s u f f e r from being based on canbinations of suggest t h a t ,

s y n a p t i c and clin-atological d a t a sets.

However,

they do

i n c o n t r a s t to t h e P a c i f i c where t h e e f f e c t s of

vertical

d i f f u s i o n are small (Wyrtki, 19811, a l l t h r e e processes, h o r i m n t a l advection,

u p l l i n q - a n d d i f f u s i o n can c o n t r i b u t e e q u a l l y i n i t i a t i o n of t h e c o l d water tongue.

in

the A t l a n t i c to t h e

80 6.

SLIMMAW AND DISCUSSION

The q u a l i t a t i v e similarities

between

the climatological and FGGE-year

representations of the equatorial SST and t h e m l i n e depth f i e l d s (Figs. 4 and 5) suggest t h a t t h e upper layer thermal structure observed during FGGE can be considered typical of an average year.

Tnis representativeness implies

t h a t phase relationships between atmospheric and oceanic phenanena derived frcm the FGGE data describe average rather than anomlous conditions. In summary, the follcwing phase relationships between surface wind and oceanic temperature structure were observed during FGGE.

Cooling of surface

layers s t a r t s coincidentally with the early-May acceleration of the surface wind a t 28% and probably a t 4 O W (Figs. 9 and 7, respectively) and sane four weeks later a t 22OW (Fig. 8 ) .

Although obvious, it is wrth noting t h a t

cooling starts later a t 2 2 O W than to the rest or to the east.

Tne t h e m l i n e

deepens rest of about 35OW (Fig. 5) coincidentally with the wind increase a t 29OW (Fig. 9 ) .

A t 4OW,

the t h e m l i n e rises and both c q n e n t s of wind

increase scine time during the sane six-week period in boreal spring (Fig. 7 ) . Although fram the s h i p observations it appears t h a t the t h e m l i n e rises a t 22OW when the wind increases (Fig. 8 ) , temperature data f r m current meter observations indicate part or a l l of t h i s rise m y be related to higher frequency perturbations of the t h e m c l i n e (Fig. 11). ?he meridional compnent of the wind remains high a t least through October

a t 4 O W , while both components remain high a t 28OW (Figs. 7 and 9 ) .

SST's are

belcw the record mean a t these t h s and the t h e m c l i n e has deepened since June a t both locations.

Winds decrease during March and April when highest

temperatures are observed. The heat budget computations suggest t h a t the i n i t i a t i o n of the cold water tongue

between

May

and

July

is

related

to

upwelling,

diffusion

and

Previous numerical modelling and observational studies suggest how

advection.

these processes can be related to the increase i n wind observed during May. Tne magnitude of cooling caused by u p e l l i n g is p a r t i a l l y a function of the depth of the thermocline (i.e., the closer the thermocline is to the surface, the

colder

transprts)

.

the

upelled

water

for

the

same

Previms observational (Katz e t al.,

numerical &elling

Ekman

and

geostrophic

1977, for instance) and

e f f o r t s (Philander and Pacancwski,

1980, for instance)

s h m t h a t the t h e m l i n e of the equatorial Atlantic should r e s p n d i n phase

to basin-wide

increases

i n the

zonal wind component (i.e.,

the oceanic

r e s p n s e is i n equilibriun with the atmspheric forcing). Although the spatial and temporal resolution of the data are limited, there is a strong suggestion of such an equilibriun r e s p n s e i n the ohservations (Fig.

5).

81

E l i r t h e m r e , westward winds are also conducive to e q u a t o r i a l u p e l l i n g .

Thus,

as the westward c m p n e n t of t h e wind i n c r e a s e s a t a l l t h r e e p i t i o n s during May (Figs. 7 , 8 and 9 ) upnlelling is l i k e l y to p l a y a l a r g e r role i n cooling the s u r f a c e waters t h a n previously. Philander and P a c a n w s k i (1981) s h m that increased m r i d i o n a l winds can produce,

through advection, a c o l d water tongue with spatial c h a r a c t e r i s t i c s similar to t h o s e observed (i.e., asymmetric with respect to t h e equator, Fig. 2 ) . The meridional c q n e n t o f wind also i n c r e a s e s during FGGE. Katz

and Garzoli (1982) f i n d that s u r f a c e speeds of t h e SEC between 2'5

and 2'N

have a s i g n i f i c a n t westward c q n e n t (.25 to .50 m/s) o n l y during J u l y .

Tnus, advection is l i k e l y to p l a y a s i g n i f i c a n t role only a t later s t a g e s of the d e v e l o p w n t of the cold water tongue. The f a c t t h a t cooling o c c u r s e a r l i e r a t 28OW than 22OW also s u g g e s t s t h a t advection m y not p l a y a c r u c i a l role i n cooling e a r l y i n t h e s m r . The t h e m l i n e c o n t i n u e s deepening a t 28OW and redeepens a t 4OW through October.

However, SST's r e n n i n less t h a n average, while a t 4OW t h e m r i d i o n a l

ccmponent and a t 28Ow both components of wind remain high (Figs. 7 and 9 ) . the east, V o i t u r i e z

In

(1981) s u g g e s t s t h a t h o r i z o n t a l divergence a t t h e sea

surface s o u t h of t h e e q u a t o r , induced by t h e meridional component of t h e wind, can serve to maintain t h e tongue.

I n t h e west,

Plolinari

(19821, using

d r i f t i n g b o y d a t a , s u g g e s t s t h a t advection by the SEC p l a y s a large role i n m i n t a i n i n g the tongue later i n t h e s m r .

As t h e winds decrease along t h e e q u a t o r during boreal w i n t e r and s p r i n g , SST's i n c r e a s e , b u t a t a s l m r rate t h a n would be p r e d i c t e d fram h e a t g a i n s through the sea s u r f a c e (Table 3 ) . Fahrbach and Bauerfeind (1982) shcw t h a t , a t 2 2 O W , d u r i n g February-March

1979 v e r t i c a l mixing acts continuously to cause

spreading of t h e isotherms and t h u s , cooling of the s u r f a c e l a y e r s .

They also

shew that d u r i n g c e r t a i n upwelling e v e n t s v e r t i c a l advection w i l l enhance t h e

cooling of t h e s u r f a c e l a y e r s .

One such event occurred during 17-20 February

1979 on the western edge of the patch of cold water c e n t e r e d a t 16OW during January-February

1979 ( F i g . 1).

Thus,

u p e l l i n g and mixing can serve to

retard warming of t h e s u r f a c e layers and can c o n t r i b u t e to t h e maintenance o f the cold water p a t c h observed d u r i n g boreal winter. ACKNOWLEDGMENTS

The a u t h o r s m u l d l i k e to thank the dedicated o f f i c e r s and crew of t h e research v e s s e l s involved i n FGGE.

The f i r s t a u t h o r was p a r t i a l l y s u p p r t e d

by the Centre National d e l a Recherche S c i e n t i f i q u e o f France, t h e Department of Energy and t h e NOAA S p e c i a l Research Programs O f f i c e .

82 REFERENCES Bubnov, V. A. (1981). Some f e a t u r e s of s y n o p t i c and seasonal v a r i a b i l i t y of t h e Loronosov Current. In: Recent Progress i n Equatorial Oceanography: A R e p r t of t h e F i n a l Weeting of SCOR W r k i n g Group 47 i n Venice, I t a l y , A p r i l 27-30, 1981. Edited by J. P. ETcCreary, D. W. Emre and J. M. W i t t e . Nova Universityh.Y.1.T. P r e s s , 87-96. Bubnov, V. A. and V. D. Egorihkin (1979). Study of water c i r c u l a t i o n i n t h e tropical Atlantic. D e e p - S e a g . , E , Suppl. 2, 125-136. Duing, W., F. O s t a p f f , and J. Merle (1980). Physical Oceancqraphy of t h e T r o p i c a l A t l a n t i c d u r i n g GATE. I.O.C., UNESCO, P a r i s , 117 pp. The v a r i a b i l i t y of e q u a t o r i a l Fahrbach, E. and E. Bauerfeind (1982). thermocline spreading as a n i n d i c a t i o n of e q u a t o r i a l upwelling. To appear i n Oceanographia Tropicale. Heat budget of t r o p i c a l Ocean and atmosphere. 2. Hastenrath, S. (1980). phys. Oceanogr. , lo,159-170. Hastenrath, S. and P. Lamb (1977). C l i m a t i c A t l a s of t h e T r o p i c a l A t l a n t i c and Eastern P a c i f i c Oceans. U n i v e r s i t y o f Wisconsin P r e s s , 105 pp. Hastenrath, S. and P. Lamb (1978). Heat Budget A t l a s of t h e T r o p i c a l A t l a n t i c and Eastern P a c i f i c Oceans. U n i v e r s i t y of Wisconsin Press, 104 pp. J a r r i g e , F. and P. Rual (1981). Measurements i n t h e E q u a t o r i a l Current of the A t l a n t i c and P a c i f i c Oceans. In: Recent Progress i n Equatorial A report of t h e F i n i Meeting of SCOR W r k i n g Group 47 i n Oceanography: Venice, I t a l y , A p r i l 27-30, 1981. Edited by J. P. McCreary, D. W. Moore, and J. M. W i t t e . Nova U n i v e r s i t y , N.Y.I.T. Press, 111-120. Katz, E. J., R. W l e v i c h , J. Bruce, V. Bubnov, J. Cochrane, W. Duing, P. Hisard, H. U. Lass, J. Meincke, A. deMesquita, L. Miller, and A. Rybnikov. (1977). Zonal p r e s s u r e g r a d i e n t along t h e e q u a t o r i a l A t l a n t i c . J . Mar. Res. , 35, 293-307. Katz, E. J., R. L. M l i n a r i , D. E. C a r t w i g h t , P. Hisard, H. U. Lass, and A. deMesquita (1981). The s e a s o n a l t r a n s p o r t of t h e Equatorial Undercurrent i n t h e western A t l a n t i c ( d u r i n g t h e Global W a t h e r Experiment). J 445-450. , Oceanologica A c t a , I Katz, E. J. and S. G a r z o l i (1982). Response of t h e v e s t e r n e q u a t o r i a l A t l a n t i c Ocean to an annual wind cycle. To appear i n Deep-Sea E. Merle, J. (1978). A t l a s hydrolcqique s a i s o n n i e r d e 1'Ocean A t l a n t i q u e i n t e r t r o p i c a l . Trav. Doc. ORSTCM, No. 82, 184 pp. Kerle, J. (1980). Seasonal h e a t budget i n t h e e q u a t o r i a l A t l a n t i c Ocean. J . Phys. Oceanogr., 10,464-469. M l i n a r i , R. L. (1982). Sea-surface temperature and dynamic h e i g h t d i s t r i b u t i o n s i n t h e c e n t r a l tropical South A t l a n t i c Ocean. To appear i n Oceanologica Acta. P h i l a n d e r , S. G. H. and R. C. Pacancwski (1980). The a e n e r a t i o n of e a u a t o r i a l c u r r e n t s . J. Geophys. E., 85, i i 2 3 - i i 3 6 . Philander, S . G . H. and R. C. Pacancwski (1981). The oceanic response to c r o s s - e q u a t o r i a l winds ( w i t h amlications to coastal u m e l l i n a ~i n low l a t i t u d e s ) . w 1 l u s , 33, 201-210:~ The e q u a t o r i a l u p e l l i n g i n the e a s t e r n A t l a n t i c V o i t u r i e z , B. (1981). Ocean. In: Recent Progress i n Equatorial Oceanography: A R e p r t of t h e F i n a l ! @ z i n g of SCOR W r k i n g Group 47 i n Venice, I t a l y , P p r i l 27-30, 1981. Edited by J. P. McCreary, D. W. Moore, and J. M. W i t t e . Nova University/N.Y.I.T. P r e s s , 229-248. Wyrtki, K. (1981). An estimate of e q u a t o r i a l u p e l l i n g i n t h e P a c i f i c . 2. phys. Oceanogr., 1205-1214.

11,

83

ON THE VARIATION OF THE HEAT CONTENT I N VARIOUS VERTICAL LAYERS I N THE CENTRAL EQUATORIAL ATLANTIC EBERHARD FAH RBACH

ABSTRACT From January t o June 1979 R.V. "Meteor" working i n t h e FGGE programme surveyed t h e c e n t r a l e q u a t o r i a l A t l a n t i c on a s e c t i o n a l o n g 2 2 " W from 3 " N t o 2 " s. Ten h y d r o g r a p h i c s e c t i o n s and moored c u r r e n t m e t e r d a t a a r e used t o s t u d y t h e v a r i a t i o n s i n t h e h e a t c o n t e n t o f t h e upper 600 m o f t h e ocean. The changes w i t h i n f o u r v e r t i c a l l a y e r s d e f i n e d by f i x e d i s o t h e r m s a r e i n v e s t i g a t e d . The observed changes a r e a t t r i b u t e d t o t h e v a r i a t i o n s o f t h e e q u a t o r i a l c u r r e n t system. I t i s concluded t h a t a d v e c t i o n by t h e South E q u a t o r i a l C u r r e n t i n t h e s u r f a c e mixed l a y e r and by t h e N o r t h and South E q u a t o r i a l U n d e r c u r r e n t s i n t h e thermostad and main t h e r m o c l i n e d e t e r m i n e t h e observed v a r i a t i o n s o f t h e h e a t c o n t e n t which a r e an o r d e r o f magnitude h i g h e r t h a n t h e h e a t f l u x t h r o u g h t h e surface.

1.

INTRODUCTION One o f t h e aims o f t h e " F i r s t GARP Global Experiment" (FGGE) was t h e i n v e s t i -

gation o f t h e r o l e o f t h e ocean i n t h e g l o b a l h e a t budget. The m e r i d i o n a l heat f l u x i n t h e N o r t h A t l a n t i c Ocean c o n t r i b u t e s 40 % o f t h e t o t a l h e a t t r a n s p o r t .

This t r a n s p o r t balances t h e n e t h e a t l o s s n o r t h o f 30' N ( O o r t and Vonder Haar, 1976). The t r o p i c a l A t l a n t i c p r o v i d e s an annual mean n e t heat g a i n between 6' N and 6 ' S o f about 50

W

m-2

( H a s t e n r a t h and Lamb, 1978). I f one c a l c u l a t e s a

seasonal t i m e r a t e - o f change o f t h e h e a t c o n t e n t w i t h i n t h e upper 300 m, one f i n d s t h a t t h e r a t e s a r e an o r d e r o f magnitude h i g h e r t h a n t h e net h e a t g a i n (Merle, 1980). I t must be concluded t h a t an i m p o r t a n t r e d i s t r i b u t i o n o f h e a t occurs w i t h i n t h e i n t e r i o r o f t h e ocean. T h i s s t u d y discusses t h e r e d i s t r i b u t i o n o f heat w i t h i n a watercolumn i n t h e e q u a t o r i a l A t l a n t i c . The heat c o n t e n t i s r e l a t e d t o p h y s i c a l l y d e f i n e d v e r t i c a l layers. The i n t e r a c t i o n o f t h e l a y e r s s h a l l g i v e i n s i g h t t o t h e r e d i s t r i b u t i o n processes. The r e l a t i o n between t h e l a y e r s and t h e atmospheric d r i v i n g f o r c e s shall e x p l a i n t h e dynamical processes. The t h e r m o c l i n e separates t h e s u r f a c e mixed l a y e r , which i s exposed t o d i r e c t contact w i t h t h e h e a t sources, from t h e i n t e r i o r o f t h e ocean. I n t h e e q u a t o r i a l A t l a n t i c a j e t - l i k e u n d e r c u r r e n t i s c o n f i n e d t o t h e t h e r m o c l i n e . The h i g h v e r t i -

c a l c u r r e n t shear induces s i g n i f i c a n t v e r t i c a l m i x i n g , and m e r i d i o n a l c i r c u l a t i o n c e l l s a r e a s s o c i a t e d w i t h e q u a t o r i a l u p e l l i n g . B o t h processes a r e r e s p o n s i b l e

84 f o r v e r t i c a l t r a n s p o r t s and a r e v i s i b l e as e q u a t o r i a l t h e r m o c l i n e spreading Fahrbach and Bauerfeind, 1982). The i n c l i n a t i o n o f i s o p y c n a l s c r e a t e h o r i -

(e.g.

z o n t a l p r e s s u r e g r a d i e n t s which i n d u c e m e r i d i o n a l a c c e l e r a t i o n s . 2.

THE DATA From 27 January 1979 t o 23 June 1979, R.V.

"Meteor", w o r k i n g i n t h e FGGE pro-

gram, surveyed t h e c e n t r a l e q u a t o r i a l A t l a n t i c on a s e c t i o n a l o n g 22' W f r o m 3'

N

t o 2' S ( F i g . 1). D u r i n g t h i s t i m e f i v e moorings were deployed on t h e meridian.

5OoW

40'

100

00

F i g . 1. The a r e a o f o b s e r v a t i o n by R.V. "Meteor" d u r i n g t h e " F i r s t GARP Global Experiment". The d o t s r e p r e s e n t l o c a t i o n s o f t h e moorings, t h e l i n e r e p r e s e n t s a ten-times repeated hydrographic section. T a u t w i r e t e c h n i q u e s w i t h s u r f a c e buoys were used i n o r d e r t o measure w i n d and n e a r s u r f a c e c u r r e n t s . The e q u a t o r i a l mooring r e l e a s e d i t s e l f a f t e r f o u r days and was r e i n s t a l l e d on 10 February 1979. Because o f w i r e c o r r o s i o n a l l moorings had t o be removed a t t h e end o f March. A t 1' S o n l y one i n s t r u m e n t c o u l d be r e covered. Two moorings c o u l d b e r e i n s t a l l e d from May t o June a t 0' and 2' N. Duri n g t h e o b s e r v a t i o n p e r i o d , a h y d r o g r a p h i c s e c t i o n down t o 600 m was r e p e a t e d t e n t i m e s w i t h a c o n t i n u o u s Howaldt-Bathysonde CTD and a r o s e t t e sampler. The sal i n i t y d a t a were r e c a l i b r a t e d t o f i t t h e s a l i n i t y samples w h i c h were determined w i t h a G u i l d l i n e salinometer.

The s t a t i o n s l a i d between 10 and 1 5 nm a p a r t . Com-

p a r i s o n s between t h e c o n v e n t i o n a l CTD d a t a w i t h t h o s e o b t a i n e d by a towed undul a t i n g CTD-system, w i t h a p r o f i l i n g d i s t a n c e o f one t o two n a u t i c a l m i l e s , shows t h a t t h e c o n v e n t i o n a l d a t a i s s t r o n g l y a l i a s e d (Sy and Meincke, 1981). It i s f o u n d t h a t a v e r a g i n g o v e r 30 nms remedies t h i s problem. T h e r e f o r e t h e d a t a used h e r e i n has been averaged o v e r t h i s d i stance. I n o r d e r t o i l l u s t r a t e t h e d i s t r i b u t i o n o f t h e s e c t i o n s i n t i m e and t o show

85

t h e temporal a l i a s i n g i n t h e CTD d a t a , t h e t e m p e r a t u r e r e c o r d o f t h e e q u a t o r i a l c u r r e n t m e t e r a t 15 m i s s h a m a l o n g w i t h c o r r e s p o n d i n g CTD temperatures (Fig.

2).

28.0

1. Oh 15. 1. 15. I FEB. MAR.

1.

I

I

1.

15.

I

APR.

15. MAY

1.

I

15. JUN.1979

F i g . 2. The t i m e d i s t r i b u t i o n o f t h e t e n h y d r o g r a p h i c s e c t i o n s c a r r i e d o u t during FGGE i n a c o n t i n u o u s t e m p e r a t u r e r e c o r d a t 15 m on t h e equator. The d o t s represent t e m p e r a t u r e s measured w i t h t h e CTO, t h e b a r s show t h e t i m e i n t e r v a l o f the s e c t i o n s . It becomes e v i d e n t t h a t a l i n e a r i n t e r p o l a t i o n between two c o n s e c u t i v e s e c t i o n s

i s n o t adequate. Another p r o b l e m w i t h t h e i n t e r p r e t a t i o n o f t h e d a t a i s t h e h i g h advection r a t e s . The South E q u a t o r i a l C u r r e n t (SEC) i s p r e s e n t a t 15 m w i t h an average o f 25 cm s-'

t o t h e west, and t h e E q u a t o r i a l U n d e r c u r r e n t (EUC) f l o w s i n

75 m w i t h 100 cm s-l i n t h e o p p o s i t e d i r e c t i o n . It f o l l o w s t h a t v a r i a t i o n s w h i c h are observed between two c o n s e c u t i v e s e c t i o n s w i t h a t i m e i n t e r v a l o f 10 days might be t h e consequences o f l o c a l processes s e p a r a t e d by as much as 900 km. 3.

THE LAYERS I n o r d e r t o study t h e r e d i s t r i b u t i o n o f h e a t w i t h i n t h e w a t e r column I

defined v e r t i c a l l a y e r s and c a l c u l a t e d t h e h e a t c o n t e n t w i t h i n each l a y e r a t each s t a t i o n .

I d e f i n e d t h e l i m i t s o f each o f f o u r l a y e r s by an upper and l o w e r

isotherm (Fig.

3).:

- Surface mixed l a y e r (M) - Thermocl i n e ( T ) - Themostad (TD) - Main t h e r m o c l i n e (MT)

t

2

25 'C

25 'C > t > 16 'C 16 'C > t 11 'C > t

2

11 ' C

9 'C

I n c o n t r a s t t o t h e d e f i n i t i o n o f t h e t r a n s i t i o n f r a n t h e s u r f a c e mixed l a y e r t o the t h e r m o c l i n e by a f i x e d temperature, a g i v e n t e m p e r a t u r e d i f f e r e n c e t o t h e surface (e.g. can be used.

A T = 0.5 K, M o l i n a r i e t a l .

, 1983)

o r a local v e r t i c a l gradient

I n f i g u r e 4 t h e m e r i d i o n a l d i s t r i b u t i o n o f t h e mixed l a y e r d e p t h i s

shown w i t h v a r i o u s d e f i n i t i o n s f o r t h e average o v e r t h e t e n s e c t i o n s . W i t h a d e f i n i t i o n o f AT = 0.2 appears a t 0'30'

K o r 0.5 K a c l e a r minimum i n t h e m i x e d l a y e r d e p t h

N, which i s n o t found w i t h t h e 25 'C d e f i n i t i o n .

would be b e t t e r w i t h a 26 'C d e f i n i t i o n ,

The agreement

b u t a t t i m e s when t h e r e i s a c o l d mixed

layer, t h e 26 'C i s o t h e r m l i e s w e l l i n a zone o f v e r y s m a l l v e r t i c a l g r a d i e n t s which cannot be a s s i g n e d t o t h e t h e r m o c l i n e . Even i f an upward s p r e a d i n g o f t h e

86

c TEMP I 0 E G . C

-

250.00 -

1

,

Fig. 3. Mean t e m p e r a t u r e s e c t i o n a l o n g 22' W c a l c u l a t e d f r o m t e n s e c t i o n s between January and June 1979.

6 0 0 .OO 650

.OO

1

t h e r m o c l i n e i s b e t t e r reproduced w i t h t h e AT = 0.5

K definition,

I r e j e c t e d it,

because t h e d i u r n a l t e m p e r a t u r e v a r i a t i o n s w h i c h a r e known f r o m t h e moored c u r r e n t m e t e r s f a l l w e l l i n t o t h i s range. W i t h an average f r o m o n l y two o r t h r e e s t a t i o n s t h i s can l e a d t o s e r i o u s d e f o r m a t i o n s o f t h e mixed l a y e r depth. As t h e aim o f t h i s work i s t h e v a r i a b i l i t y o f t h e l a y e r s , I compared t h e t i m e change o f v a r i o u s l y d e f i n e d l a y e r s a t t h e e q u a t o r (Fig. 5). As t h e t i m e changes agree r a t h e r w e l l , I accepted t h e 25 'C d e f i n i t i o n . The d e f i n i t i o n o f t h e t r a n s i t i o n f r o m t h e mixed l a y e r t o t h e t h e r m o c l i n e by t h e v e r t i c a l g r a d i e n t was r e j e c t e d because s t r o n g v e r t i c a l smoothing was necessary t o a v o i d s p u r i o u s r e s u l t s .

I n consequence t h e e f f e c t o f t h e t i m e

changes was h i g h l y reduced. T h i s i s t r u e f o r t h e deeper l a y e r s as w e l l . The t h e r m o c l i n e d e p t h i s d e f i n e d by o t h e r a u t h o r s (e.g.

Merle, 1980) by t h e

d e p t h o f t h e 23 'C isotherms. T h i s corresponds w e l l w i t h o u r upper l i m i t o f t h e t h e r m o c l i n e , d e f i n e d by 2 5 'C (Figs. 4 and 5). F o r each i n d i v i d u a l s t a t i o n I c a l c u l a t e d t h e h e a t c o n t e n t o f each l a y e r as t h e v e r t i c a l i n t e g r a l o v e r t h e t e m p e r a t u r e m u l t i p l i e d w i t h t h e mean d e n s i t y and t h e s p e c i f i c heat.

2lOrn r-

I

Fig. 4. The d e p t h o f t h e average s u r f a c e mixed l a y e r and thermoc l i n e d e f i n e d i n d i f f e r e n t ways. The c u r v e s denoted by 0.2, 0.5 and 25 s t a n d f o r mixed l a y e r s d e f i n e d by a d i f f e r e n c e o f 0.2 K or 0.5 K t o t h e t e m p e r a t u r e i n 5 m depth. The d e p t h o f t h e 23 'C and 25 'C isotherms a r e denoted by 23 and 25.

loot

8ot

.-" m

0"

100-

80 -

60 40 -

20 -

Fig. 5. Time v a r i a t i o n o f t h e mixed l a y e r d e p t h a t t h e e q u a t o r d e f i n e d and denoted as i n Fig.4.

4. THE MEAN CONDITIONS The mean c o n d i t i o n s , d e f i n e d o v e r o u r o b s e r v a t i o n p e r i o d , a r e somewhat a r t i f i c i a l , because t h e y i n c l u d e a warm p e r i o d f r o m January t o mid-February,

this i s

f o l l o w e d by a c o o l e r p e r i o d l a s t i n g u n t i l t h e b e g i n n i n g o f March, t h e n i t s t a y s warm u n t i l t h e o n s e t o f t h e summer c o o l i n g a t t h e end o f May (Fig. 2). Even i f t h i s d a t a cannot produce a c l e a r seasonal o r annual mean, t h e e f f e c t o f averaging i s t o reduce t h e e f f e c t o f s h o r t p e r i o d noise.

88

I n f i g u r e 6a t h e e x t e n t o f t h e d i f f e r e n t l a y e r s i s shown. The s u r f a c e mixed l a y e r (M) decreases s l i g h t l y from n o r t h t o south. The t h e r m o c l i n e ( T ) i s c l e a r l y s p r e a d by about 30 m n e a r t h e equator.

The t h e r m o s t a d decreases by about 50 m

S . The squeezing o f t h e t h e r m o s t a d i s n o t o n l y due t o

w i t h a minimum a t 0'30'

t h e s p r e a d i n g o f t h e t h e r m o c l i n e , b u t a l s o t o a c l e a r doming f r o m below (Fig. 3). The same e f f e c t i s observed f o r t h e main t h e r m o c l i n e (MT). I f one l o o k s a t t h e h e a t c o n t e n t w i t h i n t h e i n d i v i d u a l l a y e r s , we f i n d a

r a t h e r s i m i l a r f e a t u r e (Fig.6b).

The s u r f a c e mixed l a y e r i s c h a r a c t e r i z e d by a

d e c r e a s i n g h e a t c o n t e n t f r o m t h e n o r t h t o t h e south. The maximum i n t h e thermoc l i n e i s a p p r o x i m a t e l y b a l a n c e d by t h e minimum i n t h e thermostad.

The o b s e r v a t i o n

o f t h e good c o r r e l a t i o n between t h e h e a t c o n t e n t and t h e l a y e r t h i c k n e s s i s conf i r m e d by t h e c a l c u l a t i o n o f r e g r e s s i o n s . I t shows c o r r e l a t i o n c o e f f i c i e n t s h i g h e r t h a n 0.98 f o r a l l l a y e r s . I t f o l l o w s t h a t t h e change i n t h e l a y e r t h i c k ness i s t h e dominant process p r o d u c i n g t h e change o f t h e h e a t c o n t e n t w i t h i n a 1 ayer. 9

280

109~k-2

b

116

7

-

-

8t

m 260

240

-24

t 220

1

109 Jm-

-30

t

t

-a m m

n

-

I-

N

-22

-28

-

-

-20

-26

-

-

200

, 180

3"

2 O

1" N 0" S 1"

2"

160

F i g . 6. ( a ) The v e r t i c a l e x t e n t (H) and ( b ) t h e h e a t c o n t e n t (Q) o f t h e v a r i o u s v e r t i c a l l a y e r s c a l c u l a t e d f r o m an average o v e r f i v e months. The symbols denote t h e f o l 1owi ng 1ayers: M TD S1

-

-

S2 300

-

-

-

Surface mixed l a y e r T Thermocline Thermostad MT Main t h e r m o c l i n e Sum o v e r t h e upper 4 l a y e r s Sum o v e r t h e complete w a t e r column o f 600 m Sum o v e r t h e upper 300 m

When one c a l c u l a t e s t h e sum o v e r t h e f o u r l a y e r s ( Q s l ) , minimum between 1'30'

one f i n d s a c l e a r

N and 1' S. T h i s sun corresponds t o t h e h e a t c o n t e n t o f

89

t h e "Warmwassersphare" (Defant, 1928) which i s supposed t o be t h e d i r e c t h e a t r e s e r v o i r o f c l i m a t e (e.g. Krauss, 1980). As t h e h e a t c o n t e n t i s m a i n l y determined by t h e i n d i v i d u a l l a y e r t h i c k n e s s , t h e heat c o n t e n t between f i x e d depths, e.g. Q s between ~ 0 m and 600 m, and Q300 between 0 m and 300 m, show much s m a l l e r v a r i a b i l i t y . QS2 f o l l o w s t h e n o r t h - s o u t h decrease of t h e mixed l a y e r , b u t shows a s l i g h t maximum a t t h e equator. T h i s i s due t o t h e d o m i n a t i n g downward spreading o f t h e t h e r m o c l i n e . Q300 shows t h e same e f f e c t s b u t w i t h l e s s i n t e n s i t y . I t i s c a l c u l a t e d t o compare t h e p r e s e n t r e s u l t s w i t h t h o s e o f Merle (1980), who has extended h i s c a l c u l a t i o n s down t o t h i s l e v e l . 5. THE T I M E VARIATION OF THE LAYERS

One can d e f i n e t h e h e a t c o n t e n t ( Q ) o f a g i v e n l a y e r as t h e p r o d u c t o f t h e v e r t i c a l mean t e m p e r a t u r e ( t ) w i t h i n t h e l a y e r and l a y e r t h i c k n e s s

(H). I n con-

sequence t h e t i m e v a r i a t i o n o f t h e h e a t c o n t e n t can be due t o a change o f mean temperature and/or a change i n l a y e r t h i c k n e s s . F r m t h e m e r i d i o n a l d i s t r i b u t i o n (Figs. 6a and b ) one sees t h a t l a y e r t h i c k n e s s i s t h e d o m i n a t i n g e f f e c t . T h i s i s not s u r p r i s i n g i f one c o n s i d e r s t h e e q u a t i o n : (Hdt + t d H ) P From t y p i c a l values i n t h e v a r i o u s l a y e r I c a l c u l a t e d t h e i n c r e a s e o f t h e mean dQ = p c

temperature (dT) which i s e q u i v a l e n t t o a 1 m change i n t h e l a y e r t h i c k n e s s (Table 1 ) .

Surface mixed l a y e r Thermocli ne Thermost ad

t

H

27 'C 19.5 'C 12.5 'C

60 m 50 m 225 m

dT 0.45 K 0.39 K 0.06 K

Table 1. T y p i c a l numbers f o r t h e v a r i o u s l a y e r s ; see t e x t . I f one c o n s i d e r s t h a t t h e l a y e r t h i c k n e s s e s a r e v a r y i n g by t e n s of meters, a c o r -

responding v a r i a t i o n o f t h e mean t e m p e r a t u r e would be i n c o m p a t i b l e w i t h a d e f i n i t i o n o f l a y e r s by f i x e d temperatures. Because t h e l a y e r s a r e chosen as r e g i o n s where t h e v e r t i c a l g r a d i e n t i s v a r y i n g o n l y s l i g h t l y t h e mean t e m p e r a t u r e o f t h e l a y e r s h o u l d s t a y c o n s t a n t . I f n o t , a d e v i a t i o n f r o m l i n e a r i t y has t o be assumed. I f t h e mean t e m p e r a t u r e decreases, t h e g r a d i e n t i n t h e upper p a r t o f the l a y e r must become h i g h e r t h a n t h e one i n t h e l o w e r p o r t i o n . The e x t e n t and t h e mean t e m p e r a t u r e o f t h e t h r e e upper l a y e r s a t 3 'N and a t t h e equator f o r t h e t e n s e c t i o n s i s shown i n f i g u r e 7. The comparison o f t h e temperature and d e p t h ranges shows t h a t t h e normal c o n t r i b u t i o n o f t h e temperat u r e change i s about t e n p e r cent. I n t h e s u r f a c e mixed l a y e r and t h e t h e n n o s t a d

90

exceeding r a t e s a r e found. T h i s i s due t o t h e f a c t , t h a t t h e s u r f a c e mixed l a y e r has no upper temperature l i m i t and t h e thermostad shows t h e h i g h e s t v a r i a n c e i n v e r t i c a l gradients.

0"

12: n-

1oc

28

"C

75

27

5c 25

Mixed Layer

26

Thermocline

20

100 rn

75

"C

5c 19 25

250 rn

13

"C

225

T hermostad

20c

12

VERTICAL EXTENT X MEAN TEMPERATUR 111 I I I I I I I I I I I I I I1 I1111 I I l l I l l I 1

1.

I

1.

1.

F.

I

M.

I

1.

1.

A.

I

M.

1 J.

F i g . 7. V e r t i c a l e x t e n t and v e r t i c a l mean t e m p e r a t u r e of t h r e e l a y e r s a t 3 ' N and a t t h e equator. I n t h e mixed l a y e r , i n c r e a s i n g l a y e r depth c o r r e l a t e s w i t h i n c r e a s i n g temp e r a t u r e a t 3' N and a t t h e equator. T h i s can be understood by t h e f a c t , t h a t d u r i n g c o l d p e r i o d s t h e uppermost p a r t o f t h e t h e r m o c l i n e i s i n c l u d e d i n t h e mixed l a y e r d e f i n e d by a f i x e d temperature. I n t h e t h e r m o c l i n e a t 3' N one f i n d s i n most cases an i n c r e a s i n g l a y e r t h i c k ness combined w i t h d e c r e a s i n g temperature. Due t o t h e e q u a t o r i a l t h e r m o c l i n e

91 spreading t h e v a r i a b i l i t y i n c r e a s e s towards t h e equator. D u r i n g s e c t i o n s t h r e e and n i n e t h e upward s p r e a d i n g produces an i n c r e a s e o f temperature. I n t h e l o n g p e r i o d v a r i a t i o n l o w temperatures c o r r e l a t e w i t h a t h i n t h e r m o c l i n e l a y e r . I n t h e thermostad n o general c o r r e l a t i o n i s found. I n February and May i t s t h i c k n e s s i n c r e a s e s w i t h d e c r e a s i n g temperature. P o s i t i v e c o r r e l a t i o n i s due t o

a decrease o f t h e upper g r a d i e n t i n t h e thermostad, t o g e t h e r w i t h a decrease o f t h e l a y e r t h i c k n e s s . The o b s e r v a t i o n , t h a t t h i s g r a d i e n t decreases t o g e t h e r w i t h t h e thermostad t h i c k n e s s can be e x p l a i n e d when one t a k e s i n t o account, t h a t t h e thermostad i s s u p p o r t e d by m i x i n g f r o m above (e.g.

Halpern, 1980). D e c r e a s i n g

mixing would i n c r e a s e t h e upper g r a d i e n t and decrease t h e supply o f w e l l mixed water. I n consequence t h e t h i c k n e s s of t h e thermostad would decrease. I t i s e v i dent t h a t t h i s o b s e r v a t i o n does not exclude o t h e r processes which can account f o r n e g a t i v e c o r r e l a t i o n and w i l l be d i s c u s s e d l a t e r . THE TIME VARIATION OF THE HEAT CONTENT

6.

The m e r i d i o n a l d i s t r i b u t i o n o f t h e t i m e averaged h e a t c o n t e n t ( F i g . 6b) o f t h e upper 600 m corresponds t o t h a t o f t h e mixed l a y e r . Therefore one e x p e c t s a c o r r e l a t i o n o f t h e h e a t c o n t e n t w i t h t h e mixed l a y e r t e m p e r a t u r e (Fig. 2 ) . Surp r i s i n g l y t h e c o r r e l a t i o n i s n e g a t i v e . The warmest temperatures from March t o May correspond t o t h e s m a l l e s t h e a t c o n t e n t ( F i g . 8). T h i s i s v i s i b l e i n t h e upper 300 m; more e v i d e n t i n t h e upper 600 m; and s t r o n g e s t i n t h e "Warmwassersphare".

26 in9

32

im-z

1. Oh 15. 1 FEB

/

1.

I

15.

MAR.

1.

I

15. APR.

1.

1

15.

MAY

1.

I

15. JUN.1979

Fig. 8. The t i m e v a r i a t i o n of t h e m e r i d i o n a l average f r o m 3 ' N t o 2' S o f t h e heat c o n t e n t i n t h e upper 300 m, 600 m and i n t h e "Warmwassersphare" c a l c u l a t e d from t h e FGGE d a t a (denoted by 300, 600 and WWS). The h e a t c o n t e n t i n t h e upper 300 m, c a l c u l a t e d by M e r l e from h i s t o r i c a l d a t a i s denoted w i t h Me.

92

The t r e n d w i t h i n t h e upper 300 m can be compared w i t h t h e r e s u l t s from Merle

(1980). The s t r o n g l y reduced a m p l i t u d e seen i n M e r l e ' s h e a t c o n t e n t compared t o t h a t found i n t h i s s t u d y i s due t o t h e space and time averaging i n t h e f o r m e r N e v e r t h e l e s s , t h e gross f e a t u r e s correspond. There i s a d e l a y o f several months between M e r l e ' s and t h e p r e s e n t data.

In M e r l e ' s data, t h e s p r i n g t i m e maximum

o c c u r s i n A p r i l and t h e minimum i s observed i n J u l y . 116 1

91 109 J A - 2 87-

t

1

-

-26

-32

-14

-

-

t '

- n -24 -30

6-

-12

t t -; -$

4-

-

-22

-28

3-

-10

-

-

2-

-

-20

-26

I-

2 5 I--

1. O h 15. I FEB.

1.

1

15. MAR.

1.

1

15. APR.

1.

1

15. MAY

1.

I

15. JUN.1979

i

F i g . 9 . The t i m e v a r i a t i o n o f t h e m e r i d i o n a l average from 3' N t o 2' S i n t h e l a y e r s shown i n Fig. 6. The c o n t r i b u t i o n o f t h e i n d i v i d u a l l a y e r s t o t h e sum o f t h e h e a t c o n t e n t i s shown f o r t h e m e r i d i o n a l average i n f i g u r e 9. Whereas t h e r m o c l i n e and main t h e r m o c l i n e a r e v a r y i n g very smoothly as do

Qsl

and Q S 2 , t h e mixed l a y e r and

thermostad i n t e r a c t i n t e n s i v e l y i n a s h o r t e r t i m e scale. T h i s i m p r e s s i o n i s b i a s e d because t h e r e a r e more e x t r a e q u a t o r i a l s t a t i o n s t h a n e q u a t o r i a l ones, a v e r a g i n g out e q u a t o r i a l t h e r m o c l i n e spreading.

I n f i g u r e s 10 and 11 f o r each

l a y e r , f i v e l a t i t u d e s between 3' N and 2' S a r e presented. The h e a t c o n t e n t o f t h e upper 600 m ( Q S 2 , Fig.lOa)

shows a s m a l l e r m e r i d i o n a l

v a r i a b i l i t y as t h e i n d i v i d u a l l a y e r s . It s h o u l d be n o t i c e d t h a t t h e maximum i n March i s due t o an i n c r e a s e a t t h e s o u t h e r n s t a t i o n s whereas t h e maximum i n June r e s u l t s f r o m an i n c r e a s e i n t h e north. The s u r f a c e mixed l a y e r ( F i g . l o b , QM) shows a s i m i l a r m e r i d i o n a l dependence. The s p r i n g t i m e maximum i s preceded by even h i g h e r values i n t h e north. The i n c r e a s e towards t h e maximum i s n e a r l y a month l a t e r t h a n t h a t o f QS2. A s t r i k i n g f e a t u r e occurs d u r i n g t h e summer c o o l i n g , where t h e h e a t c o n t e n t c o n t i n u o u s l y i n c r e a s e s i n t h e n o r t h but decreases dramati c a l l y south o f 1' N w i t h a minimum a t t h e equator. The t h e r m o c l i n e ( F i g . l l a ,

QT)

93

shows h i g h e s t v a r i a b i l i t y a t t h e e q u a t o r r e f l e c t i n g e q u a t o r i a l t h e r m o c l i n e spreadi,ng. The maxima occur i n February and June, s i m u l t a n e o u s l y w i t h a n i n c r e a s e o f

QS2. The m o s t l y n e g a t i v e c o r r e l a t i o n between 1' N and 1' S can be e x p l a i n e d by a meridional f l u c t u a t i o n o f t h e t h e n n o c l i n e maximum across t h e equator.

I n the ther-

mostad ( F i g . l l b , QTD) one f i n d s t h e s t r o n g e s t v a r i a t i o n s f u r t h e s t f r o m t h e equat o r . A 180'-phase r e l a t i o n between t h e n o r t h e r n and t h e s o u t h e r n s t a t i o n s i n d i c a t e a t i l t i n g of t h e l o w e r boundary a c r o s s t h e equator. The s t r o n g e s t i n c r e a s e o f t h e meridional average o f QTD i n February and June c o i n c i d e w i t h maxima o f QTD a t t h e

32

t

109~m-2

t N

a"

1. Oh 15.

I

FEB.

1.

I

15.

MAR.

1.

I

15.

APR.

1.

I

15.

MAY

1.

I

*.

1. Oh 15.

I

FEB.

1.

I

15.

MAR.

1.

I

15.

APR.

1.

1

15.

MAY

15. JUN. 1979

..".*...

1.

I

15. JUN. 1979

Fig. 10. The t i m e v a r i a t i o n of t h e m e r i d i o n a l average from 3 ' N t o 2' S o f t h e heat c o n t e n t ( a ) i n t h e l a y e r from t h e surface t o 600 m, ( b ) i n t h e s u r f a c e mixed l a y e r .

94

8 109 J

-

a

-2

6

t

+

0 4

2

-

109

4

b

n

'.+
I-

0 10

I

I

1

FEB.

1

MAR.

I

APR.

I

MAY

I

JUN.1979

Fig. 11. The t i m e v a r i a t i o n o f t h e m e r i d i o n a l average f r o m 3' N t o 2' S o f t h e h e a t c o n t e n t ( a ) i n t h e t h e r m o c l i n e , ( b ) i n t h e thermostad. equator. The i n c r e a s e of QTD proceeds f r o m t h e s o u t h t o t h e n o r t h , i t p l a y s t h e s i g n i f i c a n t r o l e i n t h e i n c r e a s e o f Qs2 because QM and Q T cancel each o t h e r .

7.

DISCUSSION AND CONCLUSIONS

The i n c r e a s e o f t h e v a r i a t i o n s o f t h e h e a t c o n t e n t w i t h t h e l a y e r d e p t h (Fig.

8) and t h e c o r r e l a t i o n o f p e r i o d s o f s t r o n g i n c r e a s e w i t h i n t h e thermostad and t h e u p p e r 600 m, i n d i c a t e t h a t t h e thermostad p l a y s a s i g n i f i c a n t r o l e i n t h e h e a t budget o f t h e e q u a t o r i a l A t l a n t i c .

As t h e t h e r m o s t a d i s n o t i n d i r e c t con-

t a c t w i t h t h e h e a t sources, v a r i a b l e a d v e c t i o n has t o be t a k e n i n t o account t o understand t h i s observation.

95 The mean c u r r e n t s y s t m f r o m January t o March w i t h i n t h e a r e a o f o b s e r v a t i o n i s shown by t h e d a t a o f t h e moored c u r r e n t meters ( F i g . 12). The westward South E q u a t o r i a l C u r r e n t (SEC) i s observed i n t h e mixed l a y e r .

It s u p p l i e s warm w a t e r

from t h e b o r d e r o f t h e G u l f o f Guinea. The eastward E q u a t o r i a l U n d e r c u r r e n t s u p p l i e s h i g h s a l i n e w a t e r f r o m t h e South A t l a n t i c s u b t r o p i c a l s a l i n i t y maximum. It reaches down t o t h e thermostad, where w e s t e r l y f l o w i s f o u n d i n t h e E q u a t o r i a l

I n t e r m e d i a t e C u r r e n t ( E I C ) , e x t e n d i n g down t o t h e main t h e r m o c l i n e . T h i s c u r r e n t

i s r e l a t e d t o a w e s t - e a s t s l o p e o f t h e isotherms (e.g.

Merle, 1980). The r e s u l t -

i n g p r e s s u r e g r a d i e n t c r e a t e s a m e r i d i o n a l convergence when t h e C o r i o l i s f o r c e increases o f f t h e equator.

T h i s convergence i s v i s i b l e i n t h e c u r r e n t measure-

ments (Fig. 12) and as a doming i n t h e t e m p e r a t u r e (Fig. 3). To t h e n o r t h and 3N

LN

1N

0

W----'

-6

I 50

1w -

150-

2w

m350

-

\

\

4w-

Fig. 12. The mean c u r r e n t s f r o m moored c u r r e n t measurements between 3 1 January and 30 March 1979, u zonal component, p o s i t i v e t o t h e e a s t , v - m e r i d i o n a l component, p o s i t i v e t o t h e n o r t h .

-

south o f o u r o b s e r v a t i o n a r e a t h e main t h e r m o c l i n e s l o p e s upward g i v i n g r i s e t o t h e N o r t h and South E q u a t o r i a l U n d e r c u r r e n t s (NEUC, SEUC, e.g.

V o i t u r i e z , 1981).

Both c u r r e n t s t r a n s p o r t South A t l a n t i c C e n t r a l Water (SACW). The o r i g i n o f t h e

SACW i s assumed t o be t h e s u b t r o p i c a l f r o n t i n t h e South A t l a n t i c ( D e f a n t , 1936). An i n c r e a s e o f t h e t r a n s p o r t by t h e u n d e r c u r r e n t s would widen t h e t h e r -

96 mostad away f r o m t h e equator, and t h e r e f o r e i n c r e a s e t h e h e a t c o n t e n t o f t h e w a t e r column. Consequently, t h e doming w i l l be enhanced. A f u r t h e r mechanism t o produce thermostad w a t e r c h a r a c t e r i s t i c s i s t h e v e r t i c a l m i x i n g between h i g h s a l i n e w a t e r o f t h e EUC and t h e deep w a t e r below as p o i n t e d o u t by H a l p e r n (1980). T h i s process i n c r e a s e s t h e thermostad a t t h e e q u a t o r t o g e t h e r w i t h t h e t h e r m o c l i n e spreading. I f t h i s process i s a c t i v e , a decrease o f t h e upper l a y e r c o n t e n t s h o u l d be observed. The i d e n t i f i c a t i o n o f t h e s e two processes i s p o s s i b l e by l o o k i n g f o r t h e most i n t e n s e t h e r m o c l i n e s p r e a d i n g which i s f o u n d i n s e c t i o n s t h r e e and nine. D u r i n g b o t h cases t h e heat c o n t e n t has i n c r e a s e d i n t h e thermostad and decreased i n t h e mixed l a y e r . Because t h e mixed l a y e r shows t h e h i g h e s t heat c o n t e n t i n t h e n o r t h c o r r e l a t e d w i t h c u r r e n t s t o t h e west, one can conclude t h a t t h e i n c r e a s e i n t h e t h e r m o s t a d i s due t o a d v e c t i o n o f h e a t by t h e SEC, and c o n s e c u t i v e downward transport. S l i g h t t h e r m o c l i n e s p r e a d i n g a s s o c i a t e d w i t h i n t e n s e doming o f t h e l o w e r boundary of t h e thermostad appears d u r i n g s e c t i o n s f o u r and s i x . T h i s has t o be i n t e r p r e t e d as i n f l u e n c e o f t h e u n d e r c u r r e n t s . The v a r i a t i o n o f t h e m e t e o r o l o g i c a l s i t u a t i o n d u r i n g t h e o b s e r v a t i o n p e r i o d i s p r e s e n t e d i n f i g u r e 13. The p e r i o d s o f s t r o n g s o u t h e a s t e r l y winds d u r i n g

Wind

la

Geopotential Anomaly 3"N-0"

m2s-2

1

-

0____Y

/*-• /.--

-

- --

-

b

Zonal current -

1.

I

1.

F.

I

1.

1.

M.

I

A.

I

1.

M.

I

-

J.1979

F i g . 13. ( a ) D a i l y means o f t h e wind v e c t o r v e l o c i t y measured on buoys a t 2 ' N and 3' N. ( b ) The d i f f e r e n c e between t h e g e o p o t e n t i a l anomaly a t 5 d b a r r e l a t i v e t o 500 d b a r a t 3' N and t h e equator. ( c ) The 4-day means o f t h e zonal c u r r e n t a t 7 5 m ( p o s i t i v e t o t h e e a s t ) f r o m moored c u r r e n t m e t e r measurements.

97

February and June a r e i n t e r r u p t e d by a p e r i o d o f l i g h t winds when t h e I n t e r t r o p i c a l Convergence Zone (ITCZ) has moved southward (Kohne and Speth, 1982). The geop o t e n t i a l anomaly and t h e zonal c u r r e n t s v a r y c o n c u r r e n t l y w i t h t h e wind. The p e r i o d s o f h e a t supply f r o m above a r e c o r r e l a t e d t o t h e presence o f t h e SEC. When t h e SEC weakens, t h e n o s t a d h e a t c o n t e n t n e v e r t h e l e s s i n c r e a s e s by supply o f SACW t h r o u g h t h e u n d e r c u r r e n t s .

It must be n o t i c e d t h a t b o t h processes can a c t s i m u l t a n e o u s l y . T h i s i s t h e case i n February, when t h e h e a t g a i n i n t h e thermostad i s h i g h e r t h a n t h e h e a t l o s s from t h e l a y e r s above.

I n t h i s case t h e u n d e r c u r r e n t s overcompensate t h e

heat l o s s due t o r e l a x i n g o f t h e SEC and p r o v i d e a n e t i n c r e a s e o f t h e whole water column, ACKNOWLEDGEMENTS T h i s d a t a s e t c o u l d o n l y b e o b t a i n e d t h r o u g h t h e d i r e c t p a r t i c i p a t i o n o f C. Brockmann and J. Meincke. A. Sy processed t h e complete STD-data set.

I am v e r y

g r a t e f u l t o Mrs. P e t e r s e n f o r p r e p a r i n g t h e drawings and Mrs. S c h u s t e r f o r t y p i n g t h e manuscript.

REFERENCES Cochrane, J.D., K e l l y , F.J., Jr. and O l l i n g , C.R. 1979. Subthermocline Counterc u r r e n t s i n t h e Western E q u a t o r i a l A t l a n t i c Ocean. J. Phys. Oceanogr., 9: 724-738. Defant, A. 1928. D i e s y s t e m a t i s c h e E r f o r s c h u n g des Weltmeeres. Z e i t s c h r . Ges. Erdkunde: 459-505. Defant, A. 1936. D i e Troposphare. Oeutsche A t l a n t i s c h e Exped. "Meteor" 1925-1927, Wiss. Erg., Bd. V I , T e i l 1 ( 3 ) : 289-411. Fahrbach, E. and B a u e r f e i n d , E. 1982. The v a r i a b i l i t y o f t h e e q u a t o r i a l thermoc l i n e s p r e a d i n g as a n i n d i c a t i o n o f e q u a t o r i a l u p w e l l i n g i n t h e A t l a n t i c Ocean. Oceanogr. trop., 17: 119-130. Halpern, D. 1980. A P a c i f i c e q u a t o r i a l t e m p e r a t u r e s e c t i o n f r o m 172' E t o 110' W d u r i n g w i n t e r and s p r i n g 1979. Deep Sea Res., 27A: 931-940. Hastenrath, S. and Lamb, P. 1978. Heat Budget A t l a s o f t h e T r o D i c a l A t l a n t i c and E a s t e r n P a c i f i c Oceans. U n i v e r s i t y o f Wisconsin Press, Madison: 112 p. Kohne, A. and Speth, P. 1982. V a r i a t i o n o f t h e ITCZ i n t h e A t a n t i c d u r i n g FGGE. Trop. Ocean-Atmosphere N e w s l e t t e r 9, p. 7. Krauss, W. 1980. G o l f s t r o m und N o r d o s t a t l a n t i s c h e Warmeanomal e. Umschau 80, H e f t 6: 167-174. Merle, J. 1980. Seasonal Heat Budget i n t h e E q u a t o r i a l A t l a n t c Ocean. J. Phys. Oceanogr., 10 ( 3 ) : 464-469. and V o i t u r i e z , B. 1983. M o l i n a r i , R.L., Katz, E., Fahrbach, E., Lass, H.-U. Near s u r f a c e t e m p e r a t u r e o b s e r v a t i o n s o b t a i n e d i n t h e e q u a t o r i a l A t l a n t i c Ocean d u r i n g FGGE (1979). Subm. t o Proceedings o f t h e May 1982 L i e g e Colloquium on Ocean Hydrodynamics. D o r t , A. and Vonder Haar, T.H. 1976. On t h e observed annual c y c l e i n t h e oceanatmosphere h e a t b a l a n c e o v e r t h e N o r t h e r n Hemisphere. J. Phys. Oceanogr., 6: 781-800.

98 SY , A. and Meincke, J . 1981. A comparison o f hydrographic f e a t u r e s observed i n t h e E q u a t o r i a l A t l a n t i c d u r i n g FGGE u s i n g a conventional CTD and a towed system. FGGE-Equatori a1 Oceanography, SCOR WG 47, Venice Conference Proceedings, 55-60.

V o i t u r i e z , B. 1981. Les sous-courants equatoriaux nord e t sud e t l a f o r m a t i o n des d h e s thermiques tropicaux. Oceanologica Acta, 4 ( 4 ) : 497-506.

99

FREE DRIFTING BUOY MEASUREMENTS IN THE INDIAN OCEAN EQUATORIAL JET Gilles R E V E R D I N '

, Michele FIEUX' , Joseph G O N E L L A ' and Jim L U Y T E N 2

Abstract Twenty one buoy t r a j e c t o r i e s obtained i n the Indian Ocean from May 1979 t o June 1982, a r e used t o i n f e r the c u r r e n t system within 10" of the EQuator. The currents were mainly zonal and manifested a dominant semi-annual cycle. They were confined within four degrees of the Equator. This cycle i s predominantly related t o the Monsoon wind regime; i t i s associated with zonal r e d i s t r i b u t i o n of mass, induced by the zonal wind component or by basin s c a l e pressure gradients. Interannual v a r i a t i o n s a r e important, b u t they did not mask t h e occurence of the j e t . Part of the v a r i a b i l i t y was r e l a t e d t o zonally propagating events, as the one responsible of the reversal of the autumn j e t . They were a l s o waves i n the meridional component of t h e currents a t the equator in the period range extending from 5 t o 20 days. Meanders in the western Arabian Sea North of the Equator during the south-west Monsoon a r e probably connected t o the intense eddy a c t i v i t y near the coast in t h i s area.

1.

INTRODUCTION

During 1979-1981, 21 d r i f t i n g buoys were deployed in the equatorial Indian Ocean f o r the study of the seasonal v a r i a b i l i t y of the equatorial currents. The investigation was made possible by the p a r t i c i p a t i o n of France (Laboratoire d'oceanographie Physique, with the l o g i s t i c support of the Terres Australes e t Antartiques Franqaises), England (10s) Australia (CSIRO) and the United S t a t e s ~

(WHOI). Due t o the disappearance of the Coriolis force a t the equator as well as i t s variation with l a t i t u d e , equatorial areas a r e d i s t i n c t i v e i n two ways. F i r s t , zonal momentum t r a n s f e r r e d from the atmosphere t o t h e ocean concentrates on the equator to form a narrow a c c e l e r a t i n g j e t . Second, the equator a c t s as a wave

1. LOP Museum / CNRS LA 175 / 43, r u e C u v i e r - F-75231 P a r i s Cedex, F r a n c e . Woods Hole Mass. 02543 U.S.A.

2. WHOI

100

guide. Flow changes induced by the presence of c o a s t l i n e s , v a r i a b i l i t y in wind p a t t e r n s and i n s t a b i l i t i e s of the current system tend t o propagate a l o n g the equator (Moore e t a l . , 1977). Various observations reveal t h a t equatorial waves occur over a very l a r g e domain, from 2 - 3 days t o a year ( s e e , f o r example : Eriksen, 1980 ; Luyten e t a l . , 1982 ; Weisberg e t a l . , 1979).

I n the Indian Ocean, low frequency waves and semi-annual equatorial j e t a r e prominent f e a t u r e s . These phenomena are n a l l y varying monsoon c i r c u l a t i o n . Measurements made from v i c i n i t y of Gan Island show t h a t the j e t i s approximately cal east-west component of the wind s t r e s s (Knox, 1976).

formation of an r e l a t e d t o the seaso973 t o 1975 i n the n phase with the 10-

The buoys were deployed near the equator, mostly in the western Indian Ocean, between May 1979 and November 1981, during the SINODE c r u i s e s (Surface Indian Ocean Dynamics Experiment). Current v a r i a b i l i t y was evaluated f o r d i f f e r e n t time s c a l e s : the e n t i r e t h r e e year data s e t provides a p i c t u r e of seasonal and i n t e r annual v a r i a b i l i t y , while individual t r a j e c t o r i e s i n d i c a t e the d i s t r i b u t i o n of k i n e t i c energy of a Lagcangian t r a c e r in the 1 - 30 day range. I n t h i s paper, we will evaluate, i n a f i r s t p a r t , the accuracy of a d r i f t i n g buoy t o serve as a t r a c e r of near surface motions.We will then i n v e s t i g a t e the seasonal cycle of the c u r r e n t s , within the data s t r i p within 10" of the equator. The width of the equatorial j e t i s evaluated, as well as the mass transport associated with i t . I n a t h i r d p a r t , Lagrangian s t a t i s t i c s a r e e s t a b l i s h e d , t o find how the currents c o r r e l a t e in space and time. I n a fourth part,wave l i k e events in the buoy s h i f t v e l o c i t i e s a r e described. Wave packets Dropagating t o the west, and associated t o the disappearance of the Eastward equatorial j e t , a r e analysed i n view of t h e theory of the spin u p of an ocean from r e s t . Meanders on two t r a j e c t o r i e s North of the Equator i n A u g u s t , September a r e then compared t o i n v e s t i g a t e the propagation of the s i g n a l . F i n a l l y , the temporal v a r i a b i l i t y f o r periods l e s s than a month i s studied t o determine i f trapped e q u a t o r i a l waves a r e observable as those being observed on moored current data i n the equatorial regions (Luyten and Roemnick, 1982 ; Weisberg e t a l . , 1979).

101

2.

ACCURACY OF CURRENT MEASUREMENTS

The SINODE d r i f t i n g buoys were drogued a t 15 meters i n order t o couple the surface portion of the buoy t o the surface mixed layer motion. However, the buoy motion i s complicated by the surface wave action and the drag of the wind on the buoy. For these buoys, b o t h e f f e c t s could t h e o r e t i c a l l y produce a 5 cm/s e r r o r in the measurements of the c u r r e n t , f o r wind i n t e n s i t i e s of 10m/s a t 10 meters above the sea surface (Bervas,1978). The spectrum of the velocity of the buoy caused by the wind d r a g s h o u l d be d i r e c t l y proportional t o the spectrum of the wind (Kirwan & a l . , 1978). I n May and June 1979, current p r o f i l e r measurements from the Marion Dufresne, located within 100 km of some of the buoys were taken. The difference between the Eulerian and the Lagrangian eastward component of the velocity was l e s s than 5 cm/s. A t t h i s time, the wind was t o the e a s t a t

5 m/s. This gives an upperbound of the

wind

e f f e c t on drogued buoys f o r ty-

pical conditions in the equatorial Indian Ocean. Most of the buoys were tracked by the Argos system. An analysis of the t r a c king accuracy was done f o r a buoy anchored a t the equator in the eastern Atlant i c Ocean. Standard deviation about the mean buoy position was 300 meters d i s tributed i n f i r s t approximation l i k e white noise. During the SINODE experiment buoy positions were collected 6-8 times/day. This implies an e r r o r i n one day mean current l e s s than 1 cm per second ; i t decreases f o r longer time scales and becomes negligible a f t e r two days ( f i g . 1 ) . There can a l s o be an a l i a s i n g of the t i d a l currents a t the semidiurnal period due t o the s p a r s i t y of the positions. To t e s t t h i s e f f e c t , we simulated sampling by Argos on current meter data

a t 150 meter depth moored during F . G . G . E .

i n the equatorial Indian Ocean. No s i g n i f i c a n t r e j e c t i o n of energy a t lower frequencies was found. I t appears therefore, t h a t e r r o r s in sampling and positioning a r e n o t masking oceanographic current v a r i a b i l i t y f o r time s c a l e s longer than a day. In order t o f i l t e r out these e r r o r s the t r a j e c t o r i e s were smoothed with a one day f i l t e r i n g process. 3.

SEASONAL CYCLE

The main objective of the program was t o study the seasonal cycle of the equatorial currents because the data a r e scarce and because the c i r c u l a t i o n i s primarily zonal on the basin s c a l e , the data a r e averaged temporally and zonally. We chose a temporal resolution of one month. Due t o the meridional displacements of the buoys during t h a t time, the s p a t i a l resolution was chosen as 2'30' i n latitude.

102 (CM/SIz /CPH

lo5

104

lo3

102

1\00

5yO

I

4

270,

7

'YO

10-2

5;

, , 2;

4

7

SPECTRAL ENERGY DENSITY F i g . 1 : spectrum of the zonal and meridional component of buoy 2105 d r i f t veloc i t y . The 90 % confidence i n t e r v a l i s indicated. I n t h i c k dashed l i n e , noise spectrum due t o the positioning by Argos (evaluated i n the Gulf of Guinea).

Monthly means were constructed from the zonal l y averaged buoy v e l o c i t i e s , combining the data from a l l three years. I t i s d i f f i c u l t t o d i s t i n g u i s h here between zonal inhomogeneities and interannual v a r i a t i o n s . However, f o r the basic features of the seasonal cycle, monthly mean buoy v e l o c i t i e s are i n agreement with h i s t o r i c a l d a t a , including c u r r e n t meter and hydrographic observations (Table I , f i g . 2 ) . The estimated variance due tozonal inhomogeneities i s of t h e order of (30 cm/s)2. This variance i s o f t h e same order of magnitude as the variance obtained from the h i s t o r i c a l d a t a , including p a r t of interannual and zonal v a r i a t i o n s (Table I ) . This leads us t o estimate, t h a t interannual v a r i a t i o n s a r e probably n o t l a r g e r than (30 cm/s)', o r approximately 25 % of the seasonal cycle.

103

50.E

80'

5'N

JUNE

DECEMBER

Fig. 2. Map of monthly buoy t r a j e c t o r i e s . The three years of data are indicated by d i f f e r e n t l i n e s . Thin f u l l l i n e f o r May 1979 -April 1980; thick f u l l l i n e f o r May 1980-April 1981; dashed l i n e f o r May 1981-June 1982. The dots correspond t o the o r i g i n s of the monthly d r i f t s of the buoys.

104 TABLE 1 E q u a t o r i a l c u r r e n t measurements, e s t i m a t e d f r o m v a r i o u s papers (cm/s) X

I

1964 1973 1973 1574 1975 1975 1976 1976 1977 Average Variance

J

F

M -60*

-20 20 -50 10

-80 -40 -25 -5 -60 -50 -40 0 -70 -40 -30

-10 -22 25 -10 -50 -25 28 24 29

A

M

80* 100 10 40 -10 0 10 60 36 40

J

J

A

S

O

N

0

1

40" 80 50 80 50 10 40 50 30 60 55 53 24

Authors

(1) (2) 30 -20 30 80 120 120 40 0 10 60 80 80

(3)

(4) (5) (6)

The main f e a t u r e s o f t h e m o n t h l y mean c i r c u l a t i o n ( f i g . 3) a r e :

-

the reversal o f the currents twice a year ; a v e r y s t r o n g e q u a t o r i a l eastward j e t i n A p r i l - M a y and October-November ; a weak eastward f l o w i n J u l y - A u g u s t ; and an a n t i s y m m e t r i c c i r c u l a t i o n i n January-February w i t h eastward f l o w o f t h e e q u a t o r and westward f l o w n o r t h o f i t .

On t h e average, t h e c u r r e n t a t t h e e q u a t o r i s d i r e c t e d toward t h e e a s t . The j e t i s c o n c e n t r a t e d i n t h e v i c i n i t y o f t h e e q u a t o r ( a t 5" N and 5" S, t h e c u r r e n t s a r e s i g n i f i c a n t l y weaker) and maximum m o n t h l y d r i f t v e l o c i t i e s a r e o v e r h / s . The maximum d a i l y c u r r e n t s observed on buoy t r a j e c t o r i e s a r e l a r g e r (1.4m/s). The c u r r e n t system i s m a i n l y z o n a l . The r n e r i d i o n a l v e l o c i t i e s on t h e e q u a t o r are p o s s i b l y r e l a t e d t o a Sverdrup b a l a n c e (Mc Phaden, 1582). F a r t h e r from t h e equat o r , t h e wind f i e l d s t e n d t o show t h a t t h e m e r i d i o n a l v e l o c i t i e s a r e p r o b a b l y r e l a t e d t o an Ekman t r a n s p o r t . To s t u d y f u r t h e r t h e seasonal c y c l e , we f i t t e d by l e a s t squares, t h e m e r i d i o n a l p r o f i l e s o f t h e zonal v e l o c i t y

I n t h i s expression,

y

f o r each month, by a Gaussian

i s t h e l a t i t u d e i n degrees and

V

was

105

chosen by l e a s t squares f i t of t h e observations. The half-width i s between and 250 k m .

200

There e x i s t d i f f e r e n t ways of estimating t h e o r e t i c a l l y t h e half-width of the j e t . The scaling of the l i n e a r wind driven c i r c u l a t i o n , corresponds t o a radius of deformation Noh A = (--)

‘1’

B

where h i s the thermocl i ne depth, No a c h a r a c t e r i s t i c Brunt-Vai s a l a frequency of the upper ocean and B the equatorial value of the Rossby parameter (Philander e t a l . , 1980). With typical values f o r the Indian Ocean of h = 200 m No i n t h e range lo-’ s - ’ t o 2 lo-‘ s - ’ , we obtain f o r A between 200

and

260 k m . In terms of the equatorial wave theory, the equatorial radius of deformation depends on the v e r t i c a l mode n , as and

The wind forcing i s probably projected mainly on t h e f i r s t and second modes. With values of t h e wave speeds cn computed from p r o f i l e s a t 62” E from the Marion Dufresne in May and June 1979, we determine : n = l

c1 = 2.50 m/s

Al

=

310 km

n = 2

c2 = 1.60 m/s

a2 =

250 km

Observations made i n the Indian Ocean in 1979 and 1980 i n d i c a t e , using the vertical propagation of t h e semi annual cycle of the deep currents t h a t t h e equatorial radius of deformation should have a value 280 km (Luyten e t a l . , 1982). Our value i s s l i g h t l y smaller. The difference i s probably related t o

-

the f a c t t h a t non l i n e a r i t i e s tend t o narrow eastward j e t s s i g n i f i c a n t l y (Philander, 1979; Cane, 1979). More than seventy per cent of the energy i n the meridional p r o f i l e s i s contained i n the f i t t e d Gaussian. The amplitude of the Gaussian ( f i g . 4 ) gives an indication of t h e zonal t r a n s p o r t of mass i n the surface layer. The bars in f i g . 4 give an indication of the variance of the estimates. The variance i s due t o the interannual v a r i a b i l i t y , the zonal inhomogeneity o r the small time s c a l e variab i l i t y i P the currents measured by t h e buoys, b u t a l s o t o the f a c t t h a t the Gaussian does not f i t exactly the real p r o f i l e s . When the currents a r e symmetrical about the equator, the Gaussian should c o r r e c t l y represent the j e t . This i s evidently not the case i n January and February,neither i n July and August.As the winds a r e predominantly cross-equatorial a t t h i s time,the currents should be anb tisymmetri cal (Phi 1 ander & a1 , 1981 ) . Therefore, the apparent e r r o r s i n January

.

106

ioooo

7O30

r

c

I

4

m/r

t'

DRIFTING BUOYS VELOCITIES INDIAN OCEAN - 1979-1982 F i g . 3 : m o n t h l y mean c u r r e n t s o b t a i n e d f o r each 2'30' l a t i t u d i n a l s t r i p . The crosses i n d i c a t e t h e v a r i a n c e o f t h e d a i l y c u r r e n t d i s t r i b u t i o n about t h e a v e r age r e p r e s e n t e d by t h e arrows, which s t a r t a t t h e g r i d p o i n t s .

and February r e p r e s e n t t h e c u r r e n t system observed d u r i n g these months. Nevert h e l e s s , t h e a m p l i t u d e o f t h e Gaussian s h o u l d s t i l l p r o v i d e a good i n d i c a t i o n o f t h e zonal t r a n s p o r t o f mass i n e q u a t o r i a l areas.

107 It i s i n t e r e s t i n g t o compare t h e c u r r e n t s w i t h t h e c l i m a t o l o g i c a l v a r i a t i o n s

o f the 20°C i s o t h e r m i n t h e I n d i a n Ocean west of 65"E w i t h i n 5" o f t h e e q u a t o r (Ouadfasel, 1 9 8 2 ) , as o b t a i n e d f r o m h i s t o r i c a l data. Assuming no e n t r a i n m e n t through t h e t h e r m o c l i n e , t h e e q u a t i o n r e l a t i n g t h e depth h o f t h e 20°C i s o t h e r m t o the t r a n s p o r t o f t h e j e t i s :

where S i s t h e s u r f a c e o f t h e domain, T j i s t h e t r a n s p o r t by t h e j e t and Tb i s the mass t r a n s p o r t t h r o u g h t h e n o r t h e r n and s o u t h e r n boundaries. I f Tb i s n e g l i g i b l e , T j and h s h o u l d be i n q u a d r a t u r e . Such a phase l a g between h and t h e j e t magnitude i s o b s e r v a b l e ( f i g . 4 ) .

I n o r d e r t o e v a l u a t e q u a n t i t a t i v e l y such a ba-

lance,the t r a n s p o r t by t h e j e t i s computed by assuming a homogeneous depth o f 80 meters a f f e c t e d by t h e eastward t r a n s p o r t . We a l s o s u b s t r a c t t h e mean e a s t -

ward t r a n s p o r t which corresponds t o a mean j e t magnitude o f 25 cm/s.

d y n e / cm

*

- + 0 4

-+02

0

F i g . 4 : t h e e q u a t o r i a l seasonal c y c l e . t h e a m p l i t u d e o f t h e j e t deduced f r o m buoy d r i f t d a t a . The v e r t i c a l b a r s g i v e an e s t i m a t e o f t h e v a r i a n c e f o r each m o n t h l y e s t i m a t e . The c u r v e was f i t t e d v i sual l y . b t h e d e p t h o f 20°C i s o t h e r m averaged o v e r a domain west o f 65"E and between 5" North and 5" South, a c c o r d i n g t o Quadfasel ( 1 9 8 2 ) . c and d r e p r e s e n t t h e zonal w i n d s t r e s s f o r t h e p e r i o d s : f i r s t January 1979 T1 t h November 1 9 7 9 , f i r s t March 1 9 8 1 - 7 t h March 1982. The wind s t r e s s was averaged o v e r a f i v e degrees wide e q u a t o r i a l band ( c ) , and a l o n g t h e buoy t r a c k s i n t h e same band (d). -cx i s computed f r o m b u l k aerodynamic f o r m u l a : a

-

108 The e v a l u a t e d

Tj

-

and

do dt

p r e s e n t some s t r i k i n g d i f f e r e n c e s ( t a b l e 2 ) ,

b u t t h e o r d e r s o f magnitude a r e comparable. Table 2 E s t i m a t e d seasonal t r a n s p o r t s o f mass i n boundary 1a y e r Month

I J -10.5 -10

F

M

A

M

J

-20 -12

-3

6

11 2

0

10

8 0

J

A

S

-6.5

-9

2

-4

4

-13

O

N

D

15 22

-4

11

0

8

1) J e t eastward t r a n s p o r t a f t e r s u b s t r a c t i n g t h e mean y e a r l y average. 2 ) T r a n s p o r t a s s o c i a t e d w i t h t h e v a r i a t i o n o f mass i n t h e western I n d i a n Ocean. The t r a n s p o r t by t h e j e t i s 50% l a r g e r t h a n v a l u e s t h a t can be e x p l a i n e d e x c l u s i v e l y by t h e changes i n t h e mass c o n t e n t i n t h e w e s t e r n I n d i a n Ocean, b e t ween 5' N and 5" S ( T a b l e 1 1 ) . There a r e numerous reasons f o r t h i 5 . Tn t h e f i r s t p l a c e t h e r e c o u l d be a westward t r a n s p o r t i n t h e t h e r m o c l i n e above t h e 20" C i s o t h e r m , which i s n o t accounted f o r w i t h buoy d r i f t s . T h i s i s p r o b a b l y t h e

case f r o m May t o January, where t h e p r e s s u r e g r a d i e n t m i g h t be d i r e c t e d toward t h e west ( E r i k s e n , 1979). I n t h e second p l a c e , t h e v a r i a t i o n s o f t h e 20" C i s o therm i n t h e west a r e n o t r e s t r i c t e d w i t h i n 5" o f t h e e q u a t o r ( Q u a d f a s e l , 1982). There i s i n p a r t i c u l a r a v e r y l a r g e d e p r e s s i o n o f t h e t h e r m o c l i n e i n t h e N o r t h western A r a b i a n Sea, o f f s h o r e o f Somali, i n t h e g r e a t g y r e west Monsoon (Swallow e t a l . ,

d u r i n g t h e South-

1983). I n t h e t h i r d p l a c e , t h e r e m i g h t be some

m i x i n g , due t o u p w e l l i n g a l o n g t h e Somali c o a s t , o r e n t r a i n m e n t t h r o u g h t h e t h e r m o c l i n e d u r i n g t h e summer months, when t h e winds blow s t r o n g l y f r o m t h e southwest o v e r t h e w e s t e r n A r a b i a n Sea. The eastward w i n d s t r e s s , w i t h i n 2" o f t h e e q u a t o r , i s a l s o g i v e n on f i g . 4. We used t h e winds p r o v i d e d by t h e European Center o f Medium-range Weather Forec a s t s (ECMWF) f o r 1979 (F.G.G.E.

analyzed f i e l d s ) and f r o m March 1981 t o March 1982. These two p e r i o d s cover most o f t h e buoy t r a j e c t o r i e s . We observe an i n -

phase r e l a t i o n s h i p between t h e c u r r e n t s and t h e winds. T h i s was discussed i n det a i l s elsewhere (Knox, 1976 ; Cane, 1980 ; Mc Phaden, 1982) as b e i n g a p r o o f t h a t t h e c u r r e n t s i n t h e m i d d l e of t h e I n d i a n Ocean i n t h e v i c i n i t y o f Gan I s l a n d (Oo 30'S, 73"E) respond l o c a l l y t o t h e winds. The l o c a t i o n o f Gan i s w e l l s u i t e d f o r t h i s k i n d o f argument, as t h e eastward w i n d s t r e s s i s q u i t e l a r g e t h e r e . F u r t h e r t o t h e west, t h e eastward component o f t h e w i n d s t r e s s i s n o t

so w e l l d e f i n e d . I n 1979, as i n 1981, no w e l l d e f i n e d eastward wind s t r e s s occur e d d u r i n g t h e autumn t r a n s i t i o n p e r i o d . I n 1979, t h e eastward w i n d s t r e s s was more t h a n two t i m e s s m a l l e r t h a n what was observed i n 1981 and d i d n o t exceed

109

5.10-2dyne/cm2, when averaged from 50" E t o 95" E . With such an i n t e n s i t y almost half a year would be needed t o a c c e l e r a t e the j e t t o the observed values. However, there i s no s t r i k i n g difference between maximum v e l o c i t i e s of autumn j e t during the two years ( f i g . 8 ) . I t i s possible t h a t the j e t i s caused by the accumulation of mass above the thermocline i n the western Indian Ocean, during the Southwest Monsoon. When the meridional wind relaxes alonq the East African coast, there i s probably a mass r e d i s t r i b u t i o n of the water accumulated mainly North o f t h e equator (probably r e l a t e d t o the curl o f the wind s t r e s s in t h i s area, as suggested by C o x , 1 9 7 9 ) . This might c r e a t e an eastward surface j e t a t the equator, caused by the conservation of absolute v o r t i c i t y .

4.

SPATIAL AND TEMPORAL VARIABILITY

The s t a t i s t i c a l properties of the lagrangian velocity time s e r i e s provided by the buoys will be established i n t h i s chapter. The advantage of lagrangian s t a t i s t i c s i s twofold . I n the f i r s t place i t gives indication of how propert i e s conserve themselves along the flow. In the second place, i t affords the opportunity of investigating the s p a t i a l s c a l e s , when numerous buoys a r e present a t the same time. Eulerian measurements are complementary f o r the study of the correlation i n time. An array of c u r r e n t meters can a l s o give some indication of the c o r r e l a t i o n i n space.They a r e , however, very expensive f o r t h a t purpose. We will r e s t r i c t the aim of t h i s chapter t o the s t a t i s t i c a l study of quantit i e s : the monthly mean d r i f t v e l o c i t i e s , and the f l u c t u a t i o n s from t h i s mean. Due t o o u r ignorance of a precise zonal mean,spatial v a r i a b i l i t y was assessed by studying t h e s t r u c t u r e functions

where the overbars i n d i c a t e an average of t h e buoy velocity over monthly track segments, the brackets r e f e r t o an ensemble average over the buoys contained in the same 2'30' l a t i t u d i n a l band during one given month and Ax i s the zonal separation. The zonal component o f t n e s p a t i a l inhomogeneity i s assumed t o he proportional t o the mean c u r r e n t (We eliminated the months with weak eastward or westward flows). The s p a t i a l variances can thus be estimated, by considering the l i m i t of t h e function S& and S:, f o r large separations, They a r e found ( f i g . 5) t o be roughly within the range of 10- 1 2 cm/s f o r the meridional veloc i t y component and within the range of 30 - 40 % of f o r the zonal velocity component. These i n t e r v a l s a r e v a l i d a t the 90 % confidence interval r e f e r r i n g

t o a student T t e s t . The s p a t i e l inhomogeneities a r e not correlated f o r separa-

110

tions l a r g e r than

10"

-

14"

14" - 18"

f o r Ti and

for V

(fig. 5).

/p \

-/I/ /

/ / / / 2

I

I

I

I

I

I

I

I

I

I

I

4

6

8

10

12

14

16

18

20

22

24

*

fix degree

Fig. 5 : s p a t i a i s t r u c t u r e functions f o r the monthly buoy d r i f t s within 5 degrees of the equator. a zonal component, normalized by the mean monthly v e l o c i t y . b meridional component.

I t i s a l s o i n t e r e s t i n g t o see how smaller time s c a l e f l u c t u a t i o n s a r e correl a t e d in space; f o r t h i s purpose we evaluated t h e c o r r e l a t i o n function C,,,t(O,Ax)

= <[u'(t,X)

u'(t,x+Ax)]/o:>

c v ~ v l ( o , A x )= < [ v ' ( t , x ) v'(t,x+Ax)]/o:> where the f l u c t u a t i o n s

ul(t,x)

=

u'(t,x)

u ( t , x ) - G(t,x)

and

and

v'(t,x) v'(t,x)

a r e defined as =

v ( t , x ) - V(t,x)

There i s a large decrease of the c o r r e l a t i o n f o r large A x , when we eliminate the long time scales in u ' , by taking f o r u a moving average along t h e buoy ( f i g . 6). The small time s c a l e s d e c o r r e l a t e i n space over s h o r t e r separations A x than the average u. Typically there i s no c o r r e l a t i o n a t Ax of t h e order of 6 t o 8 degrees. The e f f e c t s of c o r r e l a t i o n i n the meridional d i r e c t i o n should a l s o be evaluated. Unfortunately, they cannot be s e r i o u s l y handled with lagrangian measurements. I t i s probable t h a t the c o r r e l a t i o n s c a l e s should'be smaller l a t i t u d i n a l l y than l o n g i t u d i n a l l y , a s i t i s f o u n d f o r d e e p c u r r e n t m e a s u r e ments ( E r i ksen, 1981).

111

I n order t o i n v e s t i g a t e t h e time scales c h a r a c t e r i s t i c of these f l u c t u a t i o n s ,

a lagrangian c o r r e l a t i o n function was evaluated by computing along each monthly buoy track segment i n i t i a t e d a t time t , t h e quantity u;(t) u l ( t + A t ) and by averaging i t over a l l buoys assuming t h a t these small time scales are s t a t i s -

t i c a l l y s t a t i o n a r y and t h a t they a r e homogeneous in space in a tered along t h e equator. We estimate the functions

5"

s t r i p cen-

0.5

0

-0.5

F i g . 6 : s p a t i a l c o r r e l a t i o n functions f o r the f l u c t u a t i o n s a zonal component (eliminating the l a r g e time s c a l e s , with a l i n e a r moving f i l -

ter). -_ b meridional

component.

c zonal component (without elimination of long time s c a l e s ) .

The variances uu, and uvu a r e nearly equal t o 2 5 cm/s ( t h e larger periods were eliminated by taking f o r u a moving average). We observe (Fig. 7 ) avery and Cv,v, f o r small A t , with a sign reversal a f t e r 3 steep decrease of Cuvu,

112

t o 4 days. This i s followed by some o s c i l l a t i o n s , s l i g h t l y d i f f e r e n t from zero a t the 90% confidence l e v e l , b u t not d i f f e r e n t from zero a t the 95% confidence. This i s typical of some l a r g e band width spectra (band-widthwl/14 day-'). We consider t h a t i t corresponds approximately t o 4 independent degrees of freedom in a one month period.

I

01

0

-0 5

F. J . 7 : temporal c o r r e l a t i o n functions. a zonal component (eliminating the large time s c a l e s , with a l i n e a r moving f i l ter) .

-b meri di onal

component.

c zonal component (without eliminating l a r g e time s c a l e s ) .

5.

EQUATORIAL WAVES P a r t of the observed zonal v a r i a b i l i t y can be explained by the occurence of

propagating events with periods l e s s than a month. The intense eastward j e t i n the previous s e c t i o n , was present i n November and disappeared a t the end of November o r December i n the e a s t e r n s e c t o r of the Indian Ocean. The j e t disappeared abruptly, as deduced by buoy t r a j e c t o r i e s ( f i g . 8 ) in 1979 and i n 1981. I n 1980, nothing can be s a i d , as the data were scarce. During both y e a r s , during which there was s u f f i c i e n t d a t a , t h e disappearance of the j e t propagated from the e a s t t o the west. I t s speed was about 55 cm/s i n 1979 and 40 cmls i n 1981.

113

I

60° E

I

70°

I

800

I

900

I

1000

F i g . 8 : buoy t r a j e c t o r i e s between October and February, w i t h i n 3" o f t h e equat o r . The v e r t i c a l s c a l e corresponds t o t i m e (days i n european numerals, months i n roman numerals). The h o r i z o n t a l s c a l e corresponds t o l o n g i t u d e . F u l l l i n e s f o r 1979, dashed l i n e s f o r 1981.

The r e v e r s a l o f t h e zonal v e l o c i t y , can be r e l a t e d t o Rossby wave f r o n t s (Gonella e t a l . ,

1981; L u y t e n and Roemnich, 1982). According t o t h e l i n e a r theo-

ry o f t h e s p i n up o f t h e ocean ( P h i l a n d e r a l . ,

1980 ; Cane, 1979), t h e e v o l u t i o n

o f the f l o w f r o m r e s t can be s c h e m a t i c a l l y d e s c r i b e d as f o l l o w s . A t f i r s t , an a c c e l e r a t i n g e q u a t o r i a l j e t forms, a s s o c i a t e d w i t h a deepening o f t h e e q u a t o r i a l mixed l a y e r on a t i m e s c a l e o f t h e o r d e r o f 10 days. We w i l l assume, f o r s i m p l i c i t y , t h a t t h e r e i s o n l y one e x c i t e d v e r t i c a l mode. A K e l v i n wave f r o n t generated a t t h e western boundary and a Rossby wave f r o n t

generated a t t h e e a s t e r n

boundary suppress t h e a c c e l e r a t i o n i n t h e s u r f a c e l a y e r . The K e l v i n f r o n t

tra-

vels t h r e e times f a s t e r t h a n t h e f a s t e s t Rossby f r o n t . When t h e K e l v i n wave has

114

crossed three q u a r t e r s of the basin, the two f r o n t s will a d d t h e i r e f f e c t s , r e s u l t i n g in a deceleratioq of Lhc torrents. This deceleration will stop a f t e r passage of additional Rossby f r o n t s generated a t the eastern boundary, as a res u l t of the r e f l e c t i o n of the Kelvin f r o n t . The second Rossby f r o n t follows the f i r s t one, with a delay of 20 t o 40 days f o r the s i z e of the Indian Ocean ( f o r the f i r s t o r second v e r t i c a l mode r e s p e c t i v e l y ) , a n d leaves very small currents behind. The observed disappearance of the j e t i s probably r e l a t e d t o t h i s Rossby wave f r o n t s ger,erated a t the e a s t e r n boundary and superposed on an unaccelerating flow. The propagation of the observed f r o n t has the same velocity as typical long Rossby Haves corresponding t o the second v e r t i c a l mode. This description has t o be s e r i o u s l y revised, when taking i n t o account the n o n - l i n e a r i t i e s , as Rossby waves a r e p a r t i c u l a r l y s e n s i t i v e t o these e f f e c t s , due t o t h e i r small group velociLy ( t h e surface j e t speed i s 90 cm/s) (Philander, 1979' ; Mc Phaden e t a l . , 1979). The changes of the propagation velocity of the f r o n t from one year t o the o t h e r , can be p a r t i a l l y a t t r i b u t e d t o d i f f e r e n t v e r t i c a l s t r u c t u r e of the curr e n t s (presence or absence o f a n undercurrent). Other e f f e c t s could a f f e c t the phenomena. Changes i n the wind s t r e s s f o r example, or i n s t a b i l i t i e s of the curr e n t s , producing a meandering of the j e t . As already s t a t e d f o r 1979, the wind s t r e s s magnitude could not explain the amplitude of the c u r r e n t s . After abrupt disappearance of the j e t , there i s some flow r e v e r s a l , which could be due p a r t i a l l y t o the non-linear character of the flow o r overshooting. The November f r o n t i n 1979 west of the Maldive Islands (73" East) was n o t clearl y i d e n t i f i e d . Two explanations a r e suggested : the surface wind may have been out of phase with the Rossby f r o n t i n those areas o r p,art of the energy was d i s s i p a t e d o r blocked by the Maldive Island chain ( D u Penhoat, 1982 ; Yoon, 1981). I n August and September, several buoys meandered i n the western Indian Ocean north of the equator i n a n eastward mean c u r r e n t . I n t e r e s t i n g properties can be deduced from two buoy t r a j e c t o r i e s separated roughly by 70 k m . The meanders propagated westward with a phase speed of 23 cm/s ( f i g . 9 ) . As t h i s phase speed was of the same order o f magnitude as the mean currents ( 1 9 cm/s), a change of reference frame was necessary t o determine the c h a r a c t e r i s t i c period o f the phenomena in a fixed reference frame. The period of the meander was i n the range 15 - 30 days with a wave length of 700 km.

115

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

m.........

......

188 I

Fig. 9 : August t o November 1981 buoy tracks i n the western Indian Ocean.

They could be r e l a t e d t o waves excited a t the western boundary by i n s t a b i l i t i e s of the current system north o f the equator. They could a l s o be excited by local changes of the northward component of the Monsoon winds (Delecluse, personal communication). The ECMWF analyzed data show t h a t i n 1981 the relaxation of the monsoon winds a t the equator occured suddenly near the 15th of September, long a f t e r the appearance o f the meandering. Further s t u d i e s a r e required

on t h i s subject i n order t o i n f e r the e f f e c t o f wind changes i n i n t e r a c t i o n

116

with a western boundary. An analysis of the buoy t r a j e c t o r i e s i n terms of the l i n e a r theory of equatorial waves i s probably not adequate due t o the importance of non-linearity i n t h i s a r e a , located north of the equator. F i n a l l y , evidence of 7

-

20 day waves was found a t the equator i n the rneri-

dional component of buoy v e l o c i t i e s ( f i g . 10, f i g . 11). Considering the i n t h i s period range (Table 1 1 1 ) , i t appears t h a t the waves a r e present i n November and i n December, as well as in April and in May. Their peak tude i s l a r g e r than 20 cm/s. The energy decays rapidly with l a t i t u d e as

spectra mainly amplishown

by the r a t i o o f neridional k i n e t i c energy over zonal k i n e t i c energy (Table 111). The signal seems t o be correlated over large distances along the equator ( 1000 k m ) . There i s some evidence on the data of westward phase propagation a t high speed (about 1,50 m/s). The central period of t h i s energy band, i s approximately 1 2 days i n the lagrangian frame of reference. There should not be very large nonlinear i n t e r a c t i o n between such waves and the j e t because of the l a r g e phase speed (1,50 m / s ) , compared t o t h e j e t speed (0,90 m / s ) . 2105- NOVEMBER 1980-JANUARY

1981

MERIDIONAL V E L O C I T Y COMPONENT

-\

W

-100

A1

LATITUDE 1

I

1

58

80

0

I 87

0 I

0

78

83

I

1

1

I

1

90

91

I

1

so

1

1

I

I

89

88

LONGITUDE

Fig. 10. November 1980 t o January 1981 meridional v e l o c i t y (dashed l i n e ) and horizontal v e l o c i t y ( f u l l l i n e ) of buoy 2105. Longitude and l a t i t u d e a r e i n d i cated every 10 days.

117

FREQUENCY X SPECTRAL ENERGY DENSITY

F i g . 11 : s p e c t r a o f zonal and n e r i d i o n a l v e l o c i t y components o f buoys w i t h i n 2 degrees o f t h e e q u a t o r f o r t h e months November t o January ( 2 0 e q u i v a l e n t degrees o f freedom) .

Two e x p l a n a t i o n s a r e a v a i l a b l e f o r t h e s e waves : e i t h e r i t i s a f l u c t u a t i n g equatorial c u r r e n t induced by t h e wind which i s p o s s i b l e , because t h e i n e r t i a l f r i c t i o n a l time scale o f

s p i n - u p o f t h e upper ocean i s a p p r o x i m a t e l y 10 days.

Or they a r e o c e a n i c e q u a t o r i a l waves. To t e s t t h e f i r s t h y p o t h e s i s , we looked a t t h e w i n d d a t a (ECMWF analysed f i e l d s ) . There i s more energy a t t h e s e periods i n t h e zonal component t h a n i n t h e m e r i d i o n a l component o f t h e wind stress. Furthermore t h e energy i s n o t l a r g e r d u r i n g t h e t r a n s i t i o n months. As there a r e

few d a t a a s s i m i l a t e d f o r t h e a n a l y s i s i n t h e e q u a t o r i a l I n d i a n

118 ocean, t h e s p e c t r a a r e p r o b a b l y n o t v e r y r e l i a b l e ; however, i t seems u n l i k e l y t h a t t h e l o c a l i n f l u e n c e of t h e winds c o u l d e x p l a i n c o m p l e t e l y t h e upper ocean variability. TABLE 3 Energy o f t h e c u r r e n t s f o r p e r i o d s between 7 and 20 days i n

(cm/s)

a ) Seasonal c y c l e f o r buoys w i t h i n 2 degrees o f t h e e q u a t o r . b ) M e r i d i o n a l dependence, when comparison i s p o s s i b l e . F o r b o t h t a b l e s : 1) m e r i d i o n a l k i n e t i c energy; 2 ) zonal k i n e t i c energy; 3 ) r a t i o o f m e r i d i o n a l o v e r zonal k i n e t i c energy; 4 ) number o f buoys. a)

1 2 3 4

J

F

M

150 190

270 210

280 270

4

2

3

Latitude y ldearees) \

d

A

M

750 310 320 170 1.28 3 2

o < y < 2

J

J

A

S

O

N

D

960 150 1.50 4

680 420

210 150

440 520

650 1180

3

3

3

2 < y < 4

4 < y < 8

430 390 1.12 20

240 220 1.10 16

7

I

590 460 1.27 14

1 2 3 4

These waves a f f e c t p r i m a r i l y t h e m e r i d i o n a l v e l o c i t y component. They c o u l d correspond t o mixed Rossby g r a v i t y waves (Moore e t a l . ,

1 9 7 7 ) . T h e i r energy

would propagate eastward and c o u l d be generated by i m p u l s i v e m e r i d i o n a l winds ( D e l e c l u s e , p e r s o n a l communication). They c o u l d a l s o be due t o i n s t a b i l i t i e s of t h e e q u a t o r i a l j e t , as i t c o i n c i d e s i n t i m e w i t h i t . T h i s l a s t p o i n t i s r e i n f o r c e d by t h e f a c t , t h a t d e s p i t e v e r y d i f f e r e n t wind c o n d i t i o n s i n t h e autumn o f 1979 and 1 9 8 1 , t h e j e t had t h e same i n t e n s i t y ( f i g . 8 ) and t h e waves a r e more e n e r g e t i c i n 1981 t h a n i n 1979. I t c o u l d a l s o e x p l a i n , why i t i s n o t SO f r e q u e n t i n April-May,as

t h e j e t i s n o t s o i n t e n s e . However,analytical

two-

l a y e r s s t a b i l i t y a n a l y s i s tended t o prove t h a t eastward e q u a t o r i a l j e t a r e s t i l l stable f o r l a r g e r v e l o c i t i e s (Philander, 1976).

6.

CONCLUSION D r i f t i n g buoys t r a c k e d by t h e Argos system have been an a c c u r a t e t o o l f o r

s t u d y i n g t h e c u r r e n t dynamics o f t h e upper ocean f o r p e r i o d s l o n g e r t h a n one day. I n t h e I n d i a n Ocean, w i t h 21 buoys launched o v e r a t h r e e y e a r s p e r i o d , we e v a l u a t e d t h e seasonal c y c l e o f t h e z o n a l l y averaged c u r r e n t s . Two maxima of t h e eastward e q u a t o r i a l j e t were observed i n A p r i l - M a y and October-November,

119

separated by weaker c u r r e n t s . Despite the dispersion of the data over three years and d i f f e r e n t longitudes, the seasonal cycle of the j e t could be estimated t o have a variance of 20 cm/s, and the v a r i a t i o n s of the current with longitude corresponded t o a variance of 30% of the mean c u r r e n t . The j e t was confined within 4' of the equator. The half-width was smaller than what could be predicted from l i n e a r theory. Events on smaller time s c a l e s , l e s s than a month, are correlated o n a space s c a l e l e s s than 10 degrees of longitude. Some of the current v a r i a b i l i t y could be r e l a t e d t o propagating events. The reversal of the autumn equatorial j e t was found t o be propagating t o the west

a t a speed of 40 cm/s i n 1981 an d 55 cm/s i n 1979. There i s some question on the i n t e r p r e t a t i o n of t h i s a s a n occurence of a Rossby wave f r o n t , as the j e t should influence the propagation of the wave. Energy f o r periods between 5 and 20 days was concentrated in the meridional velocity component. This appears typical f o r mixed Rossby g r a v i t y waves. A plausible i n t e r p r e t a t i o n i s , t h a t the waves could be generated by i n s t a b i l i t i e s of the equatorial surface j e t . Meanders in A u g u s t and September were followed by two buoys. They were probably p a r t of the large eddy a c t i v i t y concentrated n o r t h of the equator during the summer Monsoon in the western Indian Ocean. They were propagating westward. The occurence of wave-like e v e n t s , which a r e not d i r e c t l y correlated with the wind, r e s t r i c t the domain of frequencies where the d i r e c t local influence of the wind on the currents ( r e l a t e d t o the boundary layer s t r u c t u r e ) can be seen . I t i s probably s t i l l possible t o derive from the wind data some r e l a t i o n ships between the formation of the equatorial j e t and events i n the zonal wind stress l a s t i n g from 5 days t o one month. For longer periods, the buoys are probably n o t well s u i t e d i n equatorial regions, as they do not stay in the same latitudinal s t r i p f o r a very lon? time. Furthermore, waves excited a t the boundaries would have enough time t o propagate some remote e f f e c t s , which could perturb the buoy t r a j e c t o r i e s .

Acknowledgements The twenty one buoy t r a j e c t o r i e s would not have been obtained without a wide cooperation between a l l the members o f the INDEX group 10s ( J Swallow) ; CSIRO ( G Creswell) ; WHO1 ( 3 Luyten, G Needell) ; LOP Museum Paris and the support of NOAA (USA) and TAAF (France). J . F . Murail a s s i s t e d i n the data a n a l y s i s . The drawings were done by Mrs Christoforides. The typewriting was made by J Maheux. We a r e g r e a t l y indebted t o R . Molinari f o r h i s useful comments on the manuscript.

120

REFERENCES

BERVAS J.Y., 1978 - Influence des forces de t r a i n e e s u r l a derive d'une bouee equipee d'une ancre f l o t t a n t e . - Rapport i n t e r n e TDI, COB CNEXO CANE M., 1979 - The response of an equatorial ocean t o simple wind s t r e s s patt e r n s - I1 : Numerical r e s u l t s . - Journal of Marine Research, Vol. 37, pp. 253-299. CANE P I . , 1980 - On the dynamics of equatorial c u r r e n t s , with application t o the Indian Ocean. - Deep Sea Res., Vol. 2 7 , p p . 525-544. COX M . , 1979 - A numerical study of Somali current eddies - J . Phys. Oc., Vol. 9, pp. 311-326. DU P E N H O A T Y . , M.A. CANE and R.J. PATTON, 1982 Reflections o f low-frequency e a u a t o r i a l waves on p a r t i a l boundaries - i n the present volume. ERIKSEN C . , 1981 - Deep currents and t h e i r i n t e r p r e t a t i o n as equatorial waves i n t h e western P a c i f i c Ocean - J . Phys. Oc., vol. 11, p p . 48-70. GONELLA J . , M. FIEUX and G . PHILANDER, 1981 - Mise en evidence d'ondes de Rossby equatoriales dans l'Ocean Indien & p a r t i r de bouees derivantes - C . R . Acad. Sc. P a r i s , T . 292, p p . 1397-1399. KIRWAN A . D . , G. Nc NALLY and PAZAN S . , 1978 - Wind drag and r e l a t i v e separations of undrogued d r i f t e r s - J . Phys. Oc., Vol. 8, pp. 1146-1150. KNOX R . , 1976 - On a long s e r i e of measurements of Indian Ocean equatorial curr e n t s near Addu Attol - Deep Sea Res., Vol. 23, p p . 211-221. KORT V . G . , 1977 - Equatorial current i n the Indian Ocean during the Northeast monsoon- Oceanology, Vol. 1 7 , n o 2 , p p . 115-120. LEETMAA A. and H . STOMMEL, 1980 - Equatorial current observations in the West e r n Indian Ocean i n 1975 and 1976 - J . Phys. Oc,, Vol. 10, p p . 258-269. LUYTEN J . and ROEMNICH D . , 1982 - Equatorial currents a t semi-annual period in the Indian Ocean - J Phys. Oc., Vol. 1 2 , pp. MC PHADEN M., 1982 - V a r i a b i l i t y i n the central equatorial Indian Ocean - Part I : Ocean Dynamics - Journal o f Marine Research, Vol. 40, p p . 157-176. MC PHADEN M, and R . KNOX, 1979 - Equatorial Kelvin and i n e r t i o - g r a v i t y waves in zonal shear flow J . Phys. Oc., Vol. 9, p p . 263-277. MOORE D. and G. PHILANDER, 1977 - Modeling of the t r o p i c a l oceanic circulation - The Sea, Vol. V I ; , Wiley Interscience, Ny, PP. 319-361. NEYMAN V . G . , V . A . BUBNOY and V . D . YEGORIKHIN, 1978, -Investigation of equator i a l currents i n the western p a r t of the Indian Ocean. PHILANDER G . , 1979 Nonlinear coastal and equatorial j e t s - J . Phys. Oc., Y O ] . 9, pp. 739-747.b PHILANDER G . , 1979 - Equatorial waves -in the presence of the equatorial under3 , Phys. Oc., Vol, 9 , p p . 254-262. current PHILANDER G. and P . DELECLUSE,1982 - Coastal currents i n low l a t i t u d e - submitted t o Deep Sea Research. PHILANDER G. and R. PACANOWSKI, 1980 - The generation of equatorial currents J . Geoph. Res., Vol. 85, n o C2, p p . 1123-1136. PHILANDER G. and R . PACANOWSKI, 1981 - Response o f equatorial ocean t o periodic forcing - J . Geoph. Res., Vol. 868 n o C3, pp. 1903-1916. PHILANDER G. and R . PACANOWSKI, 1981 - The oceanic response t o cross-equatorial winds with a p p l i c a t i o n t o coastal upwelling i n low l a t i t u d e s -Tellus, Vol. 33, pp. 201-210. QUADFASEL D . R . , 1982 - Low frequency v a r i a b i l i t y o f the 20°C isotherm topography i n the western Indian Ocean J . Geoph. Res., Vol. 87, n"C3, p p . 19901996. SWALLOW J.C., 1967 - Equatorial undercurrent in the western Indian Ocean in 1964 - Studies i n t r o p i c a l Oceanography, Miami, n o 5 , pp. 15-36. SWALLOW J . C . , R . L . MOLINARI, 3.6. BRUCE and 0. BROWN - Development of near surface flow p a t t e r n and water mass d i s t r i b u t i o n i n the Somali basin in response t o the Southwest Monsoon of 1979 - submitted t o J . Phys. Oc. WEISBERG R . H . , A. HORIGAN and C.COLIN, 1979 Equatorially trapped Rossby-qrav i t y wave propagation i n the gulf of Guinea. 3. Mar. Res.. vol 37. m.67-86. YOON J . H . , 1981 - Effects of Islands on equatorial waves - J.Geoph. Res., Vol. 86, n o C 11, pp. 10913-10920.

-

-

-

-

-

-

121

INVESTIGATION OF SMALL-SCALE STRUCTURE OF HYDROPHYSICAL FIELDS I N THE EQUATORIAL REGION OF THE I N D I A N OCEAN.

KORCHASHKIN,

N.N.

I.D.

LOZOVATSKY

The r e s u l t s of t h e i n v e s t i g a t i o n of t h e small-scale s t r u c t u r e of v e l o c i t y , electroconductivity and temperature f i e l d s i n t h e ocean a r e considered using the data from measurements i n t h e region of t h e e q u a t o r i a l c u r r e n t s and i n t h e area of t h e Mascaren r i d g e i n t h e Indian ocean. Thus, according t o t h e d a t a from vertical soundings a t t h e equator i n t h e depth range

0-1000 m ,

l a y e r s of

intensive 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 , with t h i c k n e s s e s a few t e n s of meters, were revealed, l o c a t e d i n t h e lower p a r t of t h e upper quasiuniform l a y e r ( 5 0 - 8 0 m) and under t h e sharp thermocline, a t a depth o f

160 - 2 3 0 m ,

which

i s the upper boundary of t h e e q u a t o r i a l subsurface Tareev c u r r e n t . In t h e upper part of t h e thermocline ( 8 0 - 160 m) where 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 i s sharply increased, t h e l e v e l of small-scale v e l o c i t y f l u c t u a t i o n s i s much smaller. S p e c t r a l a n a l y s i s of v e l o c i t y and temperature f l u c t u a t i o n s shows t h a t

i n the lower p a r t of t h e upper quasiuniform l a y e r and i n t h e weakly s t r a t i f i e d layers of t h e thermocline, t h e v e l o c i t y s p e c t r a

and t h e temperature s p e c t r a

Su

St

d i s p l a y t h e i n e r t i a l - c o n v e c t i v e range of s c a l e s where t h e Kolmogorov-Obuchov

"-

5/3 law" holds. Immediately a f t e r t h e i n e r t i a l range, t h e r e i s a viscous range

i n the s p e c t r a

Su

range of power law

with sharp decrease of t h e s p e c t r a l d e n s i t y l e v e l and t h e 'I-

1" i n t h e s p e c t r a

St

p r e d i c t e d by B a t c h e l o r s ' s theory -

which then goes over i n t o t h e viscous-conductive range. Thus, according t o the d a t a from t h e f i e l d measurements, a good agreement between sea turbulence spectra both of v e l o c i t y and temperature and t h e r e s u l t s of l a b o r a t o r y measurements and known r e l a t i o n s was obtained. The c h a r a c t e r i s t i c e s t i m a t e s of d i s s i pation of v e l o c i t y

E

and temperature

E t

i r r e g u l a r i t i e s , obtained using t h e

results of t h e s e measurements, a r e of t h e o r d e r and

-

OC2/s

for

10

-3

- 10

R i = N2/V:

velocity f l u c t u a t i o n s ,

V,

for

E

E/bVg

on a

i s i l l u s t r a t e d ( f i g . 1) i n o r d e r t o explore

an i n t e r r e l a t i o n of turbulence c h a r a c t e r i s t i c s . Here

Vaisala-Brunt

cm2/s3

E t .

The law of dependence of t h e dimensionless r e l a t i o n s h i p Richardson number

-1

b

i s t h e variance of

a mean v e r t i c a l g r a d i e n t of t h e mean flow,

N

the

frequency. A s one can see i n f i g . 1, t h e experimental p o i n t s can

be approximated by a s t r a i g h t l i n e whose a n g u l a r c o e f f i c i e n t i s n e a r l y

1/2.

Thus, when we go from t h e domain of t h e upper e q u a t o r i a l c u r r e n t t o t h e opposing

122 102

wlZ 101

.

100

102

101

Richardson number Ri Fig. 1. The dependence of the dimensional relation scale Rt on the Richardson number.

E/bV,

and the turbulence

Tareev current, the dependences between the turbulence characteristics b E

and the parameters

where

c

- 4.

We can express

where

where

A

N

and

V,

and

have the following form:

It follows in fact from formula (1) that

E

with the help of

b

and the turbulence scale

:

is a universal dimensionless constant. Now from ( 2 ) we obtain that

Lo =

E’”

N-3/2

is the Ozmidov buoyancy scale. A dependence of the

123 turbulence s c a l e on t h e Richardson number i s represented i n f i g . 1. A s one could

Rt

expect, a general tendency t o a decreasing seen. Nevertheless, t h e c l e a r e s t dependence bounded region of

Ri

values between

1

with i n c r e a s i n g

Rt(Ri)

and

takes p l a c e i n a

1 0 . When

i t i s not l a r g e r than

formula ( 4 )

A/8

<<

10 - 15 cm.

i.e. a t

Ri < 1 ,

4-6 m ,

weak hydrodynamical s t a b i l i t y , t h e turbulence s c a l e reaches R i > 10

can be

Ri

and when

In view of t h e condition i n t h e

1 , t h e r e l a t i o n obtained between

Rt

and

shows t h a t

Lo

the c h a r a c t e r i s t i c s c a l e of t h e v e l o c i t y f i e l d v a r i a t i o n i s l e s s than t h a t of the d e n s i t y f i e l d . I t means t h a t t h e f i n e s t r u c t u r e i n t h e p r o f i l e of must be expressed more s t r o n g l y than i n t h e p r o f i l e of

N2(z)

V,(Z)

and must have a

smaller v e r t i c a l s c a l e .

Temperature

Fig. 2. The s e r i e s of repeated soundings with extremely f i n e - s t r u c t u r e o f temperature p r o f i l e .

T

("C)

layering

The s e r i e s of repeated soundings i n t h e region of t h e slope of t h e Mascaren ridge permited u s t o see successive s t a g e s o f development of extremely f i n e s t r u c t u r a l l a y e r i n g of t h e temperature p r o f i l e i n t h e depth range

2 1 5 - 250 m

(fig. 2 ) . The transformation of t h i s l a y e r , l o c a t e d i n t h e f r o n t a l zone under the temperature i n v e r s i o n , s t a b i l i z e d h y d r o s t a t i c a l y due t o s a l i n i t y , l e a d s t o t h e formation of a very t h i n l a y e r of water with t h i c k n e s s

50 - 100 cm;

t h e sign

of the temperature g r a d i e n t a l t e r n a t e s from one l a y e r t o another. The l e v e l of velocity f l u c t u a t i o n s within t h e compass of t h e l a y e r considered was markedly lower than a t i t s upper and lower boundaries, and t h e h o r i z o n t a l temperature gradient was about

3 l o w 6 'C/cm.

Our e s t i m a t e s show t h a t we have observed t h e

124 process of development of the fine-structure due to lateral convection. Long-term towing of the turbulimeter in the thermocline in the region of the propagation of intensive internal waves of large amplitude, which were discernible on the ocean surface as alternating strips of choppy surface waves or rips, permitted to find the relationship between the characteristics of the sea surface state, parameters of internal waves and changing of the level of smallscale velocity and electroconductivity fluctuations in the water body. It appeared that when a large internal solitary wave

or wave train passes, the

intensity of fluctuations of electroconductivity is sharply increased and the level of velocity fluctuations is changed relatively little. In many cases the regions of high values of electroconductivity fluctuations are in accordance with the moments of passing of strips of rips above the turbulimeter. Thus, in most cases, the passing of internal waves do not change the density of turbulent energy in space. When the horizontal temperature gradient in the thermocline changes sharply due to propagation of internal waves, the intensity of smallscale electroconductivity fluctuations, which is proportional to the value of this gradient, is also sharply changed.

125

VELOCITY FIELD FINE STRUCTURE AND SHEAR INSTABILITY OF CURRENTS I N EQUATORIAL REGIONS OF THE OCEANS.

R.V.

OZMIDOV,

M.L.

PYZHEVICH

Nunherous s i m u l t a n e o u s measurements o f t h e f i n 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 and v e l o c i t y f i e l d s i n t h e I n d i a n and P a c i f i c o c e a n s have been p e r f o r med i n t h e c o u r s e o f 22nd c r u i s e of R/V Dmitry Mendeleev i n 1979 (Ozmidov, 1979). The sounding, g i v i n g i n f o r m a t i o n on t h e f i n e v e r t i c a l s t r u c t u r e o f s a l i n i t y and temperature f i e l d s , h a s been u s e d a s w e l l as an a c o u s t i c measurement system f o r r e c o r d i n g t h e modulus and d i r e c t i o n o f t h e c u r r e n t v e l o c i t y v e c t o r . The measurements were performed w i t h v e r t i c a l sounding from a d r i f t i n g v e s s e l . The speed o f s o u n d i n g r a n g e d from

0.5 m/s

0.8 m / s

to

.

The d i s t a n c e between t h e

winches from which t h e measurements were t a k e n was e q u a l t o

70 m .

Data from r e p e a t e d s o u n d i n g s i n a number o f r e g i o n s i n t h e P a c i f i c show a d i f f e r i n g space-time v a r i a b i l i t y of c u r r e n t v e l o c i t y f i e l d f i n e s t r u c t u r e .

300"

300"

300'

305"

310"

315'

315'

325"

325'

320'

0

200

400

600

..E, N

5

B

40

40

40

35

42

37

40

40

40

40

..

0

45

0

30

cm/s

F ig . 1. P r o f i l e s of a b s o l u t e v a l u e s of flow v e l o c i t y ( d a s h e d l i n e ) and i t s d i r e c t i o n ( s o l i d l i n e ) , a c c o r d i n g t o t h e d a t a of numerous s o u n d i n g s a t s t a t i o n

1785.

126 1 shows t h e d a t a of

Fig.

10 successive measurements of absolute values of flow

v e l o c i t y and d i r e c t i o n , c a r r i e d o u t a t time i n t e r v a l s

40

minutes i n t h e North-

West p a r t of t h e P a c i f i c ocean a t s t a t i o n 1785 (Ozmidov, 1979). Note t h e r e l a t i v e l y s t r o n g time (more p r e c i s e l y , space-time) v a r i a b i l i t y of t h e flow d i r e c t i o n . But t h e p r o f i l e o f t h e absolute value of flow v e l o c i t y i s more p e r s i s t e n t here from sounding t o sounding. This bears evidence of o s c i l l a t i o n s of t h e flow v e l o c i t y v e c t o r r e l a t i v e t o some l o c a l a x i s . The measurements c a r r i e d o u t a t the equator a t s t a t i o n 1803, however, a r e more p e r s i s t e n t both i n t h e flow d i r e c t i o n and-absolute v e l o c i t y values; t h i s i s apparently c h a r a c t e r i s t i c , of

t h e systems

of e q u a t o r i a l c u r r e n t s ( f i g . 2 ) .

318"

~

U

350'

120

00

80"

60'

70'

200

400

f

\)

600

--

/

&

N

20

5

24

36

30

24

18

20

\

25

25

i? n

Fig. 2.

The same a s i n f i g . 1 f o r s t a t i o n 1808.

The s t r u c t u r e of v e r t i c a l p r o f i l e s of f l e l d s i n t h e ocean i s c h a r a c t e r i z e d by unordered a l t e r a t i o n , withdepth,of

l a y e r s with small and l a r g e values of

v e r t i c a l g r a d i e n t s ; t h e amplitudes of t h e s e non-uniformities vary l i t t l e with depth, a s d i s t i n c t from t h e non-uniformities of v e r t i c a l s t r u c t u r e of t h e temp e r a t u r e and s a l i n i t y f i e l d s which u s u a l l y have tendency t o decrease with depth. Table 1 g i v e s , as a t y p i c a l example, maximal, minimal and mean values of v e l o c i t y components, t h e i r v e r t i c a l d e r i v a t i v e s and t h e square of a b s o l u t e vel o c i t y values, computed using sounding no 5 a t s t a t i o n 1785. The t a b l e a l s o

127 TABLE 1

Signal moment Minimum Maximum Mean value Variance Asymmetry Excess

dV dZ

dU -

u

V

( 4 s )

(cm/s)

dZ

6’)

(S-3

dV dZ

(S-7

10’

- 5.3

- 4.2 1 0 - ~

9.1

8.2

3 . 3 10’

- 9.5

- 3.9 1 0 - ~

9.1 1 0 - ~

- 5.4

2 . 9 10’

- 2.1 1 0 - ~

- 1.4

1.1

2.7 1 0 - ~

- 1 . 9 10-3

1.3 1 0 - ~

1.4

-

- 2 . 2 10’

8.2

2.2

2.5

- 1 . 2 10’

- 7.3 1.0 10-2

9.8

2 . 1 10-2

2.5 1 0 - ~

7.6

3.0

5.3

gives t h e v a l u e s of v a r i a n c e , asymmetry and e x c e s s of t h e d i s t r i b u t i o n s of a l l these q u a n t i t i e s .

I

- 3

-2 l o g wave number

-1

k,

(m-’)

Fig. 3. S p e c t r a l d e n s i t i e s o f v e r t i c a l n o n - u n i f o r m i t i e s of z o n a l ( a ) and m e r i d i o n a l (b) f l o w v e l o c i t y components a c c o r d i n g l y t o t h e d a t a of t h e s o u n d i n g no 5 a t t h e s t a t i o n 1785. The v e r t i c a l l i n e r e p r e s e n t s t h e 9 5 % c o n f i d e n c e i n t e r v a l .

128 The i n t e r e s t i n g i n f o r m a t i o n on n o n - u n i f o r m i t i e s

o f t h e v e l o c i t y f i e l d gives

s p e c t r a l - d e n s i t y f u n c t i o n s . A s an example, f i g . 3 shows t h e s p e c t r a l d e n s i t y f u n c t i o n s o f v e r t i c a l n o n - u n i f o r m i t i e s o f z o n a l ( a ) and m e r i d i o n a l (b) v e l o c i t y t o t h e d a t a from sounding n o 5 a t s t a t i o n 1785, i n t h e

components, a c c o r d i n g d e p t h r a n g e from

20

to

664 m .

The c a l c u l a t i o n s were performed u s i n g a Fourier

transform of t h e c o r r e l a t i o n function with

26

d e g r e e s o f freedom. The range of

v e r t i c a l s c a l e s o f t h e v e l o c i t y f i e l d non-uniformities

8

to

140 m .

i n v e s t i g a t e d r a n g e s from

The s p e c t r a l c u r v e s f a l l u n i f o r m l y w i t h wave number

k,

,

with

- 3 ( i n l o g a r i t h m i c s c a l e ) , and f o r t h e z o n a l v e l o c i t y

mean s l o p e c l o s e t o

component t h i s s l o p e t e n d s t o d i m i n i s h w i t h i n c r e a s i n g

k,

.

For

k,

= 0.03

m-'

(which c o r r e s p o n d s t o t h e n o n - u n i f o r m i t y s c a l e - 3 3 m), t h e r e i s an i n f l e c t i o n o f t h e s p e c t r a l c u r v e . T h i s s c a l e , presumably,

can be a boundary l i n e between

log R i

-2 I

-1 I

1

2

3

L

100

200

'

s u

n

300

F i g . 4. An example o f v e r t i c a l p r o f i l e o f t h e l o g a r i t h m of t h e Richardson 10 m a p p r o x i m a t e l y . number w i t h d e p t h r e s o l u t i o n

129

a

Ri

d

C

0

10

20

30

40

50Ri

e

0

10

20

30

40

50

Ri Fig. 5. Histograms of distribution o f Ri and corresponding fitting curves of the exponential law with different values of X for five series of measurements.

130 n o n - u n i f o r m i t i e s w i t h d i f f e r e n t mechanisms o f f o r m a t i o n . Using t h e d a t a o f s i m u l t a n e o u s measurements o f t h e f i n e s t r u c t u r e of v e l o c i t y and d e n s i t y f i e l d s , t h e v a l u e s of t h e l o c a l Richardson number butions of

Ri

Ri

were c a l c u l a t e d . The v e r t i c a l d i s t r i -

show t h a t , i n a number of c a s e s , i n some t h i n l a y e r s , t h e condi-

t i o n s a r e c r e a t e d f o r t h e o n s e t o f s h e a r i n s t a b i l i t y and g e n e r a t i o n o f t u r b u lence (fig. 4).

I n p a r t i c u l a r , i t came o u t t h a t f o r a r e g i o n o f t h e I n d i a n Ocean

( n e a r Sumatra) t h e v a l u e s o f

log R i

30-40 m

Ri

l a y e r t h e value o f

ranged from

( l o g R i < - 0 . 6 ) . I n d e e p e r l a y e r s , t h e b u l k of t h e to

- 1.7

to

2.5

and i n t h e

w a s smaller t h a n t h e c r i t i c a l v a l u e

0.25

R i - v a l u e s r a n g e d from

1

15. I t i s shown t h a t t h e e m p i r i c a l d i s t r i b u t i o n s o f

Ri

can b e approximated

by t h e e x p o n e n t i a l - l a w c u r v e s

where

h

i s t h e parameter of t h e d i s t r i b u t i o n .

I t i s i n t e r e s t i n g t h a t i n s o m e r e g i o n s o f t h e ocean t h e r e may be,presumably,

a rather stable distribution of

Ri

with approximately c o n s t a n t values of

h .

Presumably t h e s e d i s t r i b u t i o n s can b e c o n s i d e r e d as a s u f f i c i e n t l y r e p r e s e n t a t i v e c h a r a c t e r i z a t i o n o f t h e f i n e s t r u c t u r e o f h y d r o p h y s i c a l f i e l d s i n a given r e g i o n o f t h e ocean.

REFERENCES

Ozmidov, R.V., 1979. 22nd c r u i s e o f R/V D m i t r y Mendeleev. Oceanology, v o l . no 5 , 948-954.

19,

131

TURBULENCE IN THE CORE OF THE EQUATORIAL UNDERCURRENT

CARL H. GIBSON Department of Applied Mechanics a n d Engineering Sciences a n d Scripps I n s t i t u tion of Oceanography, University of California a t San Diego, La J o l l a , California 92093 ABSTRACT

Estimates o f space time average velocity and temperature d i s s i p a t i o n r a t e s x from microstructure measurements a r e p a r t i c u l a r l y d i f f i c u l t in strongly s t r a t i f i e d ocean layers such as the equatorial undercurrent high velocity core and the seasonal thermocline because the turbulence in such layers i s extremely intermittent in time and patchy in space. I n the seasonal thermocline a t Ocean Station P , 50°N 145OW, x was found t o be lognormally d i s t r i b u t e d with variance u2lnx = 5.3, l a r g e r than values in t h e mixed l a y e r above and in l e s s s t r a t i f i e d layers below. A s i m i l a r pattern appears t o e x i s t in the equatorial undercurrent, with maximum u 2 l n x occurring near the depth of maximum s t r a t i f i c a t i o n in the h i g h velocity core. Large data samples must be averaged to r e l i a b l y e s t i mate X . The most probable X value f o r a short record, Xmode, i s l e s s than Xmea by a f a c t o r of exp(-1.5 cr21nX) i f X i s lognormal. Therefore, in the seasonar thermocline data mentioned, individual dropsonde x p r o f i l e s a r e l i k e l y t o and t h i s was observed. Combining underestimate xmean by a f a c t o r of 3.5 x a l l available X measurements in t h e core l a y e r of the equatorial undercurrent Clearly short X gives a u21nx value of about 7 a n d xmode/Xmean of 3 x records a r e subject t o extremely l a r g e sampling e r r o r s : several orders o f magnitude. Dropsonde measurements of x in the undercurrent core by Gregg (1976) are less than towed body measurements of Williams and Gibson (1974) by 2-4 orders of magnitude and dropsonde measurements o f E by Crawford (1976, 1982) and Osborn (1980) a r e l e s s t h a n towed body measurements of Williams and Gibson (1974) a n d Belyaev e t a l . (1975) by s i m i l a r l a r g e f a c t o r s . This discrepancy i s attributed t o l a r g e undersampling e r r o r s in the dropsonde x a n d F values which are based on much smaller sample s i z e s than the towed body values. I t i s important t o know the t r u e avera e F and X d i s s i g a t i o n r a t e s a t core depths. I f the dropsonde values o f 10-5 cm / ~ and 3 10-8 O C L / s a r e representatlve then the undercurrent core i s e f f e c t i v e l y nonturbulent and provides an insulating b a r r i e to vertical he t t r a n s f e r a t shallow depths. I f t h e towed body values of 10Cm2/s3 and lo-? oC*/s a r e c l o s e r t o t h e t r u e averages, then the equatorial undercurrent possibly plays a dominant r a t h e r than an unimportant r o l e in tropical heat and mass t r a n s f e r , and may therefore be an important f a c t o r in t h e determination of planetary climate.

E and

Y

r

132 1.

INTRODUCTION The i n t e n s i t y o f t u r b u l e n c e , m i x i n g and v e r t i c a l d i f f u s i o n as a f u n c t i o n of

d e p t h i n t h e e q u a t o r i a l u n d e r c u r r e n t i s i m p o r t a n t t o many oceanographic problems.

F o r example, t h e h e a t t r a n s f e r and h e a t s t o r a g e c a p a c i t y o f e q u a t o r i a l

w a t e r s i s i m p o r t a n t t o n u m e r i c a l models o f c l i m a t e , b u t t h e s e p r o p e r t i e s o f the f l o w depend c r i t i c a l l y on how r a p i d l y and t o what depths t u r b u l e n c e can d i f f u s e s o l a r h e a t i n g down from t h e s u r f a c e .

Because t h e c u r r e n t speeds and t u r b u l e n c e

l e v e l s a r e much l a r g e r t h a n i n s u r r o u n d i n g waters, t h e e q u a t o r i a l u n d e r c u r r e n t may c o n s t i t u t e t h e m a j o r mechanism o f h e a t t r a n s f e r and mass t r a n s f e r o v e r a wide band o f e q u a t o r i a l l a t i t u d e s , even though t h e c u r r e n t i t s e l f i s c o n f i n e d t o a narrow range w i t h i n a degree o r two o f t h e e q u a t o r .

F o r s i m p l i c i t y we s h a l l

r e f e r t o t h e u n d e r c u r r e n t s o f t h e A t l a n t i c and P a c i f i c as a s i n g l e f l o w . Several f a c t o r s suggest t h a t t u r b u l e n c e l e v e l s i n t h e u n d e r c u r r e n t a r e subs t a n t i a l l y above t h e o c e a n i c average.

The most s t r i k i n g evidence i s t h e broad-

e n i n g o f iso-oxygen c o n c e n t r a t i o n s u r f a c e s and i s o - s a l i n i t y s u r f a c e s about the undercurrent v e l o c i t y core.

I n t h e c e n t r a l P a c i f i c , where t h e c o r e l a y e r i s

about 110 m deep, i s o t h e r m s and iso-oxygen s u r f a c e s found a t 120 m depths a t

N'3

and 3's

a r e depressed t o depths o f 300-400 m w h i l e t h e s u r f a c e s a t 100 m

a r e pushed up t o o n l y 40 m o r so on t h e e q u a t o r .

I t has been suggested t h a t

t h e broadened s c a l a r p r o p e r t y p a t t e r n s may be a t t r i b u t e d t o g e o s t r o p h i c effects o r a d v e c t i o n from t h e s i d e s .

However, t h e e x c e p t i o n a l l y h i g h b i o l o g i c a l produc-

t i v i t y o f t h e r e g i o n , comparable t o t h a t o f c o a s t a l zones, suggests e x c e l l e n t v e n t i l a t i o n due t o u n d e r c u r r e n t t u r b u l e n c e i s p r e s e n t a t a l l depths i n t h e undercurrent.

T h i s i n c l u d e s t h e h i g h v e l o c i t y c o r e s i n c e , t o m a i n t a i n such a high

p r o d u c t i v i t y , n u t r i e n t s must somehow be t r a n s f e r r e d up t o t h e p l a n t s a t t h e surf a c e f r o m below t h e c o r e and oxygen must be t r a n s p o r t e d f r o m t h e s u r f a c e down t h r o u g h t h e c o r e t o s u p p l y t h e i n c r e a s e d b i o l o g i c a l oxygen demand a t a l l l e v e l s below.

T u r b u l e n t m i x i n g would seem t o be t h e most l i k e l y t r a n s p o r t mechanism.

W i t h o u t t u r b u l e n c e , s i d e a d v e c t i o n c o u l d broaden t h e s c a l a r p r o p e r t y p a t t e r n s , as observed, o n l y i f i t r e s u l t e d i n u p w e l l i n g above t h e c o r e and downwelling below. However, H a l p e r n has p r e l i m i n a r y evidence ( p r e s e n t e d a t t h e X I V LiGge colloquium) t h a t i n t h e P a c i f i c a t 0'

l l O o W t h e u p w e l l i n g d i v e r g e n c e o c c u r s a t 160 rn

depth, which i s w e l l below t h e c o r e , and t h a t t h e v e r t i c a l u p w e l l i n g may a c t u a l l y be a maximum n e a r t h e c o r e d e p t h o f 75 m r a t h e r t h a n zero.

F i g u r e 1 shows

t h e n o r t h - s o u t h c o n t o u r s o f s a l i n i t y , d e n s i t y and t e m p e r a t u r e a c r o s s t h e equat o r a t 155OW i n J u l y , 1972, f r o m Gregg (1976).

A h i g h s a l i n i t y tongue extends

133

I

T

S i l T i O H NO

SALINITY

F i g . 1.

N o r t h - s o u t h c o n t o u r s o f s a l i n i t y , d e n s i t y and temperature a t 155OW, J u l y 13-22, f r o m Gregg (1976).

Note t h e convergence o f l o w and h i g h

s a l i n i t y tongues a t 150 m d e p t h i n d i c a t i n g v e r t i c a l u p w e l l i n g may e x i s t a t t h e c o r e d e p t h o f 110 m.

The tongues broaden a t i 1.5'

when t h e y

encounter t h e u n d e r c u r r e n t and a r e a p p a r e n t l y mixed by t u r b u l e n c e a t a l l depths, i n c l u d i n g t h e v e l o c i t y c o r e .

Depth ranges of t h e s i x MSR

dropsonde d a t a r e c o r d s a r e shown a t t h e r i g h t .

toward t h e e q u a t o r f r o m t h e s o u t h and a l o w s a l i n i t y tongue extends toward t h e equator f r o m t h e n o r t h a t depths o f 140-170 m which i s below t h e u n d e r c u r r e n t

core depth o f 110 m e s t i m a t e d by Gregg (1976).

Both tongues t e r m i n a t e and

broaden a b r u p t l y a t t h e n o r t h e r n and s o u t h e r n u n d e r c u r r e n t boundaries a t

*

1.5'.

T h i s p a t t e r n a l s o suggests t h a t v e r t i c a l u p w e l l i n g a t t h e e q u a t o r begins a t a depth below t h e h i g h v e l o c i t y core, and t h a t an upward v e r t i c a l v e l o c i t y e x i s t s

a t core depths.

T h i s f l o w p a t t e r n has been modeled by W y r t k i (1982).

The cause o f t h e u p w e l l i n g i s u s u a l l y a t t r i b u t e d t o p o l e w a r d d i v e r g e n c e due

t o Ekman w i n d d r i f t , a l t h o u g h perhaps t h i s d i v e r g e n c e i s enhanced ( o r dominated) by an e s t u a r i n e - l i k e pumping due t o t h e l a r g e s u r f a c e buoyancy f l u x a t t h e equa-

tor, both f r o m r a i n f a l l and s o l a r h e a t i n g , i n c o m b i n a t i o n w i t h t h e enhanced mixi n g caused by t h e u n d e r c u r r e n t .

Such an e s t u a r i n e pumping has been suggested

by T u l l y and B a r b e r (1960) t o a c c o u n t f o r t h e v e r t i c a l s a l i n i t y d i s t r i b u t i o n northward o f t h e s u b - A r c t i c boundary i n t h e P a c i f i c ocean. v e r t i c a l u p w e l l i n g v e l o c i t y o f 20

*

1 0 m/year.

They e s t i m a t e a

Gammon e t a l . (1982) e s t i m a t e a

134

comparable v e r t i c a l upwelling r a t e ; t h a t i s , 12-14 mlyear in t h e same region from t h e v e r t i c a l freon d i s t r i b u t i o n . The magnitudes of the upwelling and diverging v e l o c i t i e s increase with t h e turbulent mixing r a t e . A t some level of turbulent mixing such e s t u a r i n e pumping must be considered a s a driving force f o r t h e undercurrent i t s e l f , b u t t h i s i s beyond t h e scope of t h e present paper. Without turbulent d i f f u s i o n , upwelling from below t h e core should cause the iso-concentration surfaces t o dome and crowd together a t the velocity core rat h e r than broaden and deepen as observed. Geostrophic e f f e c t s in such a complex meandering current system a r e d i f f i c u l t t o a s s e s s . Helm e t a l . (1980) have shown a well-defined separation between t h e high vel o c i t y core and t h e high s a l i n i t y core in the Atlantic equatorial undercurrent, with t h e s a l i n i t y core 15-40 m above t h e velocity core and about 10 nautical miles south when t h e velocity core was north of the equator. The separation i s a t t r i b u t e d t o an asymmetry in the s a l t fluxes from t h e s a l i n i t y core, with stronger turbulent mixing in the high velocity core than in the high shear layer above. I n the present paper we a l s o i n f e r a maximum mixing r a t e in the velocit y core, r a t h e r than a minimum as proposed by Osborn (1980) and o t h e r s . The f i r s t attempts a t d i r e c t measurements o f turbulence and turbulent mixing in the equatorial undercurrent were made using towed bodies. Williams and Gibson (1974) measured high frequency temperature f l u c t u a t i o n s in the Pacific equatorial undercurrent by towing k h z response sensors in the velocity core a t 0' and 1°N in April 1971, and Belyaev e t a l . (1975a,b) measured high frequency velocity f l u c t u a t i o n s by towing heated conductivity sensors a t several depths in the A t l a n t i c equatorial undercurrent during January-February of 1971. Subsequent microstructure s t u d i e s in the undercurrent have been c a r r i e d o u t with dropsonde mounted sensors. Gregg (1 976) reports s i x temperature microstructure p r o f i l e s through t h e P a c i f i c equatorial undercurrent a t 0' 155OW in June, 1972, with depth ranges shown in Figure 1 . Crawford (1976, 1982) has studied velocit y microstructure in both t h e Atlantic and P a c i f i c equatorial undercurrents in 1974 and 1979, respectively. Osborn (1980) and Osborn and Bilodeau (1980) discuss measurements of both velocity and temperature microstructure in the A t l a n t i c equatorial undercurrent a t 24-33OW from t h e 1974 GATE s t u d i e s . The r e s u l t s of t h e towed body and dropsonde attempts t o measure undercurrent turbulence and turbulent mixing parameters a r e q u i t e d i f f e r e n t a t a l l depths, b u t t h e most s t r i k i n g d i f f e r e n c e s occur a t the depth of t h e high velocity core. The purpose of t h e present paper i s t o review these differences and t o consider pos s i bl e expl ana t i ons . The explanation p u t f o r t h by Gregg (1976) and Crawford (1982) i s t h a t towed body turbulence sensors a r e s u b j e c t t o high noise l e v e l s due t o vibrations. However, the turbulence and temperature f l u c t u a t i o n l e v e l s detected by towed

135

bodies in the equatorial undercurrent a r e several orders of magnitude higher than noise l e v e l s of the instruments indicated by towing in o t h e r regions o u t side the undercurrent. Belyaev e t a l . (1975a) report spectra with E values as cm2/s3 compared t o 10-1 cm2/s3 measured in t h e undercurrent. low as Williams and Gibson (1974) spectra (shown in Figure 4 ) have noise peaks a t harmonics and subharmonics of t h e 60 Hz l i n e frequency, b u t do n o t i n d i c a t e any vibrational contamination. Gregg (1976) suggested vertical vibration of the sensors in the ambient v e r t i c a l temperature gradient could account f o r the measured s i g n a l , b u t Schedvin (1979) mounted accelerometers on the same towed body and found t h a t vibration l e v e l s in t h e d i s s i p a t i o n bandwidth a r e lower t h a n those required by Gregg's model by 7 orders of magnitude. Another possible explanation of t h e discrepancy i s t h a t the very high degree of turbulence intermittency a t t h e undercurrent core depth may bias the dropsonde estimates of mean turbulence and temperature d i s s i p a t i o n r a t e s F a n d 7, as discussed by Gibson (1981). These mean q u a n t i t i e s a r e dominated by a few, rare, intense patches in an i n t e r m i t t e n t turbulence l a y e r . Short data samples, such as only a few dropsonde p r o f i l e s t h r o u g h t h e i n t e r m i t t e n t l a y e r , will very probably not i n t e r s e c t the dominant patches a n d will therefore underestimate E and ? by l a r g e f a c t o r s i f t h e intermittency i s l a r g e . Because E and x appear t o be lognormal in s t r a t i f i e d ocean layers, we may estimate t h e bias, or " u n dersampling e r r o r " , by using t h e properties of t h e lognormal probability d i s tribution. I f only one small record i s a v a i l a b l e , i t s E and x represent "mode" values of t h e random v a r i a b l e s , by d e f i n i t i o n . However, i f x i s lognormal, then << x 'mode mean = xmode exp ( 1 . 5 o Z l n x ) . I f several independent data records a r e available, then the variance of u.2,nx may be estimated and t h e "undersampling

error f a c t o r " exp (1 . 5 o Z l n x ) computed. The best estimate of xmean i s then given xRean = exp p exp (0' 1 px/ 2 ) where p i s I n the following we discuss t h e d e f i n i t i o n s 07 F a n d x and compare measureh values and t h e d i s t r i b u t i o n o f X in the seasonal thermocline with those in the undercurrent core. The l a t t e r values a r e used t o estimate u Z l n x , 1-1 and xmean

by

F.

as a function of r e l a t i v e position in t h e undercurrent. Osborn (1980) divides the undercurrent i n t o t h r e e depth zones: t h e core, the shear zone above the core, and t h e shear zone below t h e core. We will t r e a t t h e undercurrents of the Atlantic and P a c i f i c as a s i n g l e flow and x as a lognormal random variable whose s t a t i s t i c a l properties do not vary from ocean t o ocean b u t depend only on the depth zones as c l a s s i f i e d by Osborn. Such a treatment i s very crude, ref l e c t i n g our primitive s t a t e of knowledge of t h e undercurrent and t h e fragmentary nature of the microstructure data. In t h e f i n a l section t h e v e r t i c a l d i f f u s i v i t y a n d heat t r a n s p o r t r a t e s indicated by t h e lognormal model a r e compared to smaller values o f Osborn (1980) and Gregg (1976) which do not account f o r

136 undersampling e r r o r s caused by t u r b u l e n c e i n t e r m i t t e n c y .

Very l a r g e d i f f e r e n c e s

a r e found, p a r t i c u l a r l y i n t h e h i g h v e l o c i t y c o r e l a y e r where t h e p r o b a b l e undersampling e r r o r i s o v e r f o u r o r d e r s o f magnitude. Evidence i s accumulating t h a t i s o l a t e d dropsonde p r o f i l e s o f q u i t e u n r e l i a b l e as e s t i m a t e s o f F and

2

E

and X may be

i n most ocean l a y e r s due t o such un-

dersampling e r r o r s . Gregg (1977) e s t i m a t e s a v e r t i c a l d i f f u s i v i t y o f o n l y 2 cm / s i n t h e main t h e r m o c l i n e o f t h e n o r t h P a c i f i c compared t o 1.2-1.3 2 cm / s e s t i m a t e d by Gamon e t a l . (1982) f r o m f r e o n p r o f i l e s . Gammon e t a l . (1982) p o i n t o u t t h a t i n t h e r e g i o n o f t h e i r measurements s i d e a d v e c t i o n w i l l 2 t e n d t o reduce t h e i r v e r t i c a l d i f f u s i v i t y e s t i m a t e , so 1.2-1.3 cm / s a c t u a l l y r e p r e s e n t s a l o w e r bound o f t h e t r u e v a l u e .

Gibson (1982) i n f e r s t h a t , based

on t h e l a r g e v e r t i c a l o v e r t u r n i n g s c a l e s measured by Gregg (1980), t h e Gregg (1977) m i c r o s t r u c t u r e i s f o s s i l t u r b u l e n c e i n an advanced s t a t e o f decay.

Con-

s e q u e n t l y , t h e space t i m e average ? and v e r t i c a l d i f f u s i v i t y K w i l l be undere s t i m a t e d by l a r g e f a c t o r s i f t h e Gregg (1977) values o f X and K a r e t a k e n as representative. dropsonde

x

I n s e c t i o n 4 an i n t e r c o m p a r i s o n t e s t between towed body and

measurements i s r e p o r t e d .

A v e r y l a r g e d i f f e r e n c e was found be-

tween i n d i v i d u a l X p r o f i l e s and average X p r o f i l e s , p a r t i c u l a r l y a t depths where t h e t u r b u l e n c e i s most i n t e r m i t t e n t .

T h i s i s c o n s i s t e n t w i t h t h e view

p r e s e n t e d i n t h e p r e s e n t paper t h a t t h e d i s c r e p a n c y between towed body and dropsonde

E

and

x

measurements i n t h e u n d e r c u r r e n t h i g h v e l o c i t y c o r e a r e due t o t h e

s c a t t e r induced by h i g h t u r b u l e n c e i n t e r m i t t e n c y i n t h i s l a y e r r a t h e r t h a n due t o any measurement n o i s e i n t h e towed body data. 2.

COMPARISON OF TOWED BODY AND DROPSONDE DISSIPATION RATES

E

AND

x

The most i m p o r t a n t parameters o f t u r b u l e n c e and t u r b u l e n t m i x i n g of temperat u r e a r e t h e viscous d i s s i p a t i o n r a t e

E

and t h e t e m p e r a t u r e d i s s i p a t i o n r a t e X.

V e l o c i t y f l u c t u a t i o n s a r e s t i r r e d down t o small s c a l e s and damped by v i s c o s i t y at a rate

Temperature f l u c t u a t i o n s a r e a l s o reduced t o s m a l l s c a l e s by t u r b u l e n t s t i r r i n g and a r e d i s s i p a t e d by m o l e c u l a r d i f f u s i o n a t a r a t e

where v and ly.

D a r e m o l e c u l a r v i s c o s i t y and d i f f u s i v i t y c o e f f i c i e n t s , r e s p e c t i v e -

Repeated i n d i c e s i n d i c a t e summation f r o m 1 t o 3, and commas i n d i c a t e grad-

i e n t s i n t h e d i r e c t i o n denoted by t h e i n d i c e s i o r j .

Both

E

and X a r e e n t r o p y

137

production terms which c h a r a c t e r i z e t h e cascade of turbulent kinetic energy and temperature variance over t h e f u l l range o f length scales from t h e scale of production, a t meters o r kilometers, t o t h e scales of d i s s i p a t i o n , a t centimet e r s o r mil 1 imeters . The s c a t t e r of E and x values measured by tow bodies and dropsondes i s shown in Figure 2 , along with t h e p r o f i l e s of eastward velocity, s a l i n i t y and temperature found a t 0' 15OoW in t h e P a c i f i c equatorial undercurrent in April, 1971,

10

12

I

3 B 0

14

16

I

18

20

I

1

22

24

26 Tl"C

34.9

35.0

35.1

35.2

35.3

35.4

39.5

3?.6

S,

20

40

60

80

100

110

120

140

"E m Isec

,.

I

I

I

I

400

40 80

E

120

a ILl

160

A 20c

.'.:'" .s. :,

k

I I

, /

:T

TOW BODIES

0A

DROPSONDES

8 A

FOSSILS

24C

El crn2/sec3

x,OC2/sec

Fig. 2.

S c a t t e r of

E

and

x

in a l l equatorial undercurrents.

Towed body

E

val-

ues (dark c i r c l e s ) a r e l a r g e r than dropsonde values (open c i r c l e s ) , e s p e c i a l l y a t core depths. Towed body x values (dark t r i a n g l e s ) in the core a r e much l a r g e r than dropsonde values (open t r i a n g l e s ) . Dropsonde f o s s i l temperature turbulence patches i n the core l a y e r shown in Fig. 3 imply previous E~ and x0 values a t f o s s i l i z a t i o n (crossed c i r c l e and t r i a n g l e ) c l o s e t o t h e values measured from two bodies. See t e x t f o r the sources of t h e data.

138

d u r i n g t h e A R I E S I V c r u i s e o f W i l l i a m s and Gibson (1974).

Values a r e grouped

by shear zone and r e p r e s e n t b o t h A t l a n t i c and P a c i f i c measurements.

Tow body

values of Belyaev e t a l . (1975a) i n t h e A t l a n t i c were c o n s t a n t i n a l l zones 2 3 a t about 0.1 cm / s and agree w i t h t h e W i l l i a m s and Gibson (1974) values a t E

1°N and 0'

i n t h e P a c i f i c a t 15OOW.

Dropsonde

E

values a r e from Osborn (1980)

and Crawford (1976) i n t h e A t l a n t i c , which g i v e cm2/s3 above t h e core, i n t h e c o r e and below t h e c o r e ; l o w e r than t h e tow body values by f a c t o r s of 10-1 Dropsonde x values f o r t h e c o r e l a y e r range f r o m 0 2 C / s from Gregg (1976) t o O C 2 / s f r o m t h e Osborn and B i l o d e a u (1980) measurements i n t h e A t l a n t i c . OC2/s a t 0'

Tow body X values o f

'C2/s

a t 1°N and

150°W were r e p o r t e d by W i l l i a m s and Gibson (1974), l a r g e r t h a n t h e

dropsonde X values by f a c t o r s o f 10'

- lo4.

Also shown i n F i g . 2 a r e " f o s s i l " dropsonde

and

E~

x0

values i n f e r r e d from

t e m p e r a t u r e m i c r o s t r u c t u r e patches d e t e c t e d by Gregg (1976) u s i n g t h e f o s s i l t u r b u l e n c e model e q u a t i o n s o f Gibson (1982).

These m i c r o s t r u c t u r e patches a r e

shown i n F i g u r e 3a,b and were i d e n t i f i e d by Gregg (1976) as " p u z z l i n g : although t h e Cox number i s low, t h e l i n e a r i t y o f t h e p r o f i l e s i s unusual and suggests strong v e r t i c a l mixing, e i t h e r present o r past."

The p a t t e r n i s t y p i c a l o f

f o s s i l t e m p e r a t u r e t u r b u l e n c e patches, as d i s c u s s e d by Gibson (1982), i n which t h e t u r b u l e n c e has been damped by t h e s t r a t i f i c a t i o n l e a v i n g a " f o s s i l t u r b u l e n c e " remnant i n t h e t e m p e r a t u r e f i e l d .

The f o s s i l p r e s e r v e s t h e v e r t i c a l

o v e r t u r n i n g s c a l e LT o f t h e p r e v i o u s t u r b u l e n c e a c t i v i t y , where

E

and X values

a t f o s s i l i z a t i o n a r e g i v e n by

E

2

0

= 2.8 LT N

3

(3)

and

x0

=

0.43 :L

(afiaz)'

N

b o t h e x p r e s s i o n s f r o m Gibson (1982).

(4) The patches a r e 1.7-2.3 m i n v e r t i c a l ex-

t e n t and l i e between t h e s a l i n i t y minimum a t 90 m and t h e s a l i n i t y maximum a t 119 m.

The two patches a t 100 m c o n t a i n numerous aT/az zero c r o s s i n g s , which

i n d i c a t e s i n t e r n a l d e n s i t y i n v e r s i o n s and a p r o b a b l e t u r b u l e n c e source s i n c e t h e ambient s a l i n i t y p r o f i l e i s s t a b l y s t r a t i f i e d . 1.4 x

lo-'

r a d / s and a f / a z i s about cm2/ s 3 and xo i s ( 1 - 3 ) x

about 0.1-0.4 ues.

OC/m.

The ambient N v a l u e i s about

From t h e s e v a l u e s and ( 4 )

OC'/s,

E~

The patches l i e i n t h e h i g h v e l o c i t y c o r e d e p t h range and suggest much

h i g h e r X v a l u e s were p r e s e n t a t p r e v i o u s t i m e s t h a n were observed by Gregg

(1 976).

is

c l o s e t o t h e towed body v a l -

139

dT > - "C -

T, "C

)(

2595 24 95

2545

I

t

dz

T, "C

m Zi

2600

-110 -111

-91

-I 12

-92

-114

-94

-115

-95

-116

-96

-117

-97

-I 18

-119

-98

LT

-99

w

-100

=

-113

-93

W

'm

26,30

-9c

OT

dT "C dz

p

-120

ZE

-121 -122

-101

-12: -102

-124

-103

-12f

-104

-12f

-105

-12;

-106

-I 21

-107

-12!

- 108

-131

t

-109 -I 10

Fig. 3.

Temperature and temperature gradient p r o f i l e s through t h e high velocity core l a y e r a t 0' 155OW, from Gregg (1976). Microstructure patches a t 100 m and 113 m a r e apparently f o s s i l temperature turbulence remnants of much stronger previous turbulence and mixing, with E~ and xo values shown in Fig. 2 .

140

COMPARISON OF TOWED BODY AND DROPSONDE TEMPERATURE SPECTRA AT CORE DEPTHS.

3.

Figure 4 shows a comparison between t h e Williams and Gibson (1974) towed body temperature spectra in t h e core a t 1°N and 0' with t h e Gregg (1976) dropsonde spectra in the same depth range. The dropsonde spectra were comput

&

-II

O

-5-

E

Q. 0

0 P

-4

n ,-. ... ..

B

k

-etn

-6 -

0 -

-7 -

-8: -9 -I

1

I

0

2

3

log k , cpm Fig. 4.

Temperature spectra from tow body and dropsonde in t h e core l a y e r of t h e P a c i f i c equatorial undercurrent. Tow body: Williams and Gibson (1974) 150°W; small squares, a t equator, 110 m; small c i r c l e s , 1°N, 99 m. Oropsonde: Gregg (1976) 155OW; c i r c l e s 90-99 m, t r i a n g l e s 99-108 m , squares 110-119 m.

141 from t h r e e 9 m r e c o r d s compared t o two 350 m r e c o r d s f o r t h e towed body s p e c t r a ,

o r about 4% as much d a t a . The dropsonde s p e c t r a show d i f f e r e n c e s i n a m p l i t u d e between themselves of almost t h r e e decades a t k = 10 cpm, much more t h a n t h e d i f f e r e n c e between t h e average dropsonde s p e c t r a l l e v e l and t h e towed body s p e c t r a l l e v e l s a t t h i s wavenumber.

Some o f t h e towed body s p e c t r a l bands a r e contaminated by l i n e

noise and a r e shown as d o t t e d p o i n t s .

Both t h e 1°N and ' 0 towed body s p e c t r a

show a prominent peak a t 60 Hz w i t h n e a r l y t h e same a m p l i t u d e .

However, most

1 cpm and many f o r k > 100 cpm were dominated by s i g n a l

spectral bands a t k

and a r e shown by s o l i d symbols. The main d i f f e r e n c e s between t h e towed body and dropsonde s p e c t r a o c c u r a t

l o w and h i g h wavenumber. numbers o f about k than 7 x

=

cm2/s3.

The dropsonde s p e c t r a i n d i c a t e d i f f u s i v e c u t o f f wave-

2 cpm o r l e s s , i n d i c a t i n g a d i s s i p a t i o n r a t e

E

o f less

T h i s i s l e s s t h a n t h e minimum necessary f o r t u r b u l e n c e 2 3 cm / s

t o e x i s t , which i s about 25 v N 2 a c c o r d i n g t o Gibson (1980) o r 6 x

if N i s 1 . 4 x

lo-'

rad/s.

T h e r e f o r e t h e m i c r o s t r u c t u r e observed by Gregg

(1976) i n t h e c o r e i s n o t t u r b u l e n t b u t f o s s i l t u r b u l e n c e a t a l l s c a l e s . This c o n c l u s i o n i s a l s o i n d i c a t e d by t h e l o w wavenumber dropsonde s p e c t r a , which f a l l w e l l below t h e l e v e l f o r t e m p e r a t u r e f l u c t u a t i o n s produced by s a t u rated i n t e r n a l waves

discussed by Gibson (1980, 1983), where i n ( 5 ) k i s measured i n radians/wavelength.

The s a t u r a t e d i n t e r n a l wave spectrum o f ( 5 ) i s shown i n F i g . 4 f o r

equatorial v a l u e s o f

aT/az

by t h e s o l i d l i n e w i t h s l o p e - 3 a t l o w k values.

If the m i c r o s t r u c t u r e patches i n a l a y e r a r e c l o s e l y spaced and c o m p l e t e l y t u r bulent t h e a s s o c i a t e d i n t e r n a l wave m o t i o n s h o u l d be s a t u r a t e d , and t h e temperature spectrum s h o u l d be g i v e n by ( 5 ) .

The e q u a t o r i a l towed body spectrum ap-

proaches t h e s a t u r a t e d wave s p e c t r a l l e v e l v e r y c l o s e l y as i s t o be expected i f small s c a l e i n t e r n a l waves a t k v a l u e s o f 1 cpm and l e s s a r e i n e q u i l i b r i u m w i t h f u l l y developed t u r b u l e n c e .

From t h e h i g h wavenumber c u t o f f a t about k = 200 2 3 cpm t h e v i s c o u s d i s s i p a t i o n E was e s t i m a t e d t o be about 0.1 cm / s and t h e temperature d i s s i p a t i o n r a t e x was about

OC2/s.

A c c o r d i n g t o t h e Gibson

(1980) f o s s i l t u r b u l e n c e model, m i c r o s t r u c t u r e i s f o s s i l t u r b u l e n c e when

E

5

E0

= (13/2)x0 N2/(aT/az)2z

E

~

z (13/2)~N~/(a?jaz)~

'

where e q u a l i t y shows t h e t u r b u l e n c e i s j u s t a t t h e p o i n t o f f o s s i l i z a t i o n , cated by o - s u b s c r i p t s .

S u b s t i t u t i n g t h e measured values o f X, N and

indi-

aT/az i n

142 (6) gives

E ~ '=

0.11 cm2/s3, which shows t h a t t h e t u r b u l e n c e p r o d u c i n g t h e mea-

s u r e d m i c r o s t r u c t u r e was c o m p l e t e l y a c t i v e b u t c l o s e t o t h e f o s s i l i z a t i o n p o i n t . Consequently, t u r b u l e n c e s h o u l d e x i s t f o r a l l wavelengths s m a l l e r t h a n about a meter, and s a t u r a t e d waves s h o u l d e x i s t f o r s c a l e s somewhat l a r g e r t h a n a meter, as observed. The spectrum f r o m t h e tow a t 1°N i s more d i f f i c u l t t o i n t e r p r e t . cous d i s s i p a t i o n r a t e 0.1 cm2/s3, b u t E

x

E

was o n l y about

' f r o m ( 6 ) i s 4.6 x 0

The v i s -

i n f e r r e d f r o m t h e d i f f u s i v e c u t o f f was a l s o about OC/cm, so

OC2/s and aT/az was 2.8 x

cm2/s3.

Because

E

>

E ~ ' ,i

f t h e t u r b u l e n c e were

c o n t i n u o u s one m i g h t i n f e r t h a t t h e t u r b u l e n c e i s so a c t i v e t h a t buoyancy e f f e c t s a r e u n i m p o r t a n t , even a t t h e l a r g e s t s c a l e s o f t h e t u r b u l e n c e . W i l l i a m s (1974) f o u n d compared t o

uZlnx

b l y q u i t e patchy.

x

However,

a t 1°N was e x t r e m e l y i n t e r m i t t e n t , w i t h u21nx > 5

< 2 f o r t h e e q u a t o r i a l data,

so t h e 1°N t u r b u l e n c e i s proba-

The s a t u r a t e d wave spectrum f o r t h e 1°N towed body d a t a i s

shown by t h e dashed l i n e which l i e s above t h e ' 0 l i n e shown i n F i g . 4 by a f a c t o r o f 6, r e f l e c t i n g t h e l a r g e r a'i/az

v a l u e a t 1°N f r o m ( 5 ) .

l o w wavenumber spectrum i s s u b s a t u r a t e d .

However, because t h e

x

Thus t h e 1°N r e c o r d i s very

i n t e r m i t t e n t t h e s u b s a t u r a t e d l e v e l o f t h e 1°N spectrum may o n l y be a conse2 3 quence o f a v e r a g i n g a few v e r y a c t i v e patches ( E : 0.1 cm / s ) w i t h l a r g e r e gions o f n o n t u r b u l e n t f o s s i l m i c r o s t r u c t u r e accompanied by s u b s a t u r a t e d i n t e r n a l wave m o t i o n s .

Note t h a t t h e

E

v a l u e i n f e r r e d f r o m t h e h i g h wavenumber c u t -

o f f of t h e t e m p e r a t u r e spectrum r e f l e c t s t h e maximum may be l a r g e r t h a n t h e average fraction)-';

E

E

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

f o r t h e r e c o r d by a f a c t o r o f o r d e r ( a c t i v e

p o s s i b l y a very l a r g e f a c t o r o f order 10 but probably l e s s than

100. 4.

INTERCOMPARISON OF TOWED

BODY AND

DROPSONDE x VALUES I N THE MILE M I X E D

LAYER EXPERIMENT Because t h e towed body and dropsonde

E

and X v a l u e s shown i n F i g u r e s 2 and

4 were measured a t v a r i o u s l o n g i t u d e s and t i m e s i t m i g h t be argued t h a t some o f t h e v a r i a b i l i t y i s n o t due t o t h e i n t e r m i t t e n c y o f t h e t u r b u l e n c e process i n t h e u n d e r c u r r e n t b u t due t o zonal v a r i a t i o n s o r s e a s o n a l i t y .

Therefore i t i s

useful t o examine t h e r e s u l t s of an i n t e r c o m p a r i s o n t e s t between a towed body and two d i f f e r e n t dropsonde systems d u r i n g t h e MILE mixed l a y e r experiment a t Ocean S t a t i o n P, 50°N 145OW i n August-September 1977, a p e r i o d d u r i n g which the m i x i n g processes and p r o p e r t y d i s t r i b u t i o n i n t h e upper ocean were r e l a t i v e l y stationary. F i g u r e 5 shows t h e r e s u l t s o f t h e i n t e r c o m p a r i s o n o f mean X v a l u e s as a f u n c t i o n o f d e p t h i n t h e upper 60 meters.

D i l l o n (1982) used a r a p i d l y deploy-

a b l e dropsonde t o c o l l e c t s i x p r o f i l e s d u r i n g p e r i o d s of l i g h t winds (Cast A)

143

x

9

OC*/S

0 16-8

CSD

10"7

Id-s

16-5

I

10-4

- DROPSONDE OSU - DROPSONDE

10

"LIGHT WIND" 20

E

*

I k W

30

n 40

50

DILLON ( 1982) CAST B, 15.5 M/S

LANGE ( I 9 8 I , Fig. 10, VMSR 25) 7.5 M/S

-

6(1 Fig. 5.

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

x(z) and x(z) f r o m dropsondes and tow body d u r i n g

MILE mixed l a y e r experiment, 50°N 145OW.

D i l l o n (1982): open c i r c l e s ;

h i g h (15.5 m/s) and l o w ( 5 . 5 m/s) winds; m u l t i p l e p r o f i l e s averaged o v e r d e p t h i n t e r v a l s shown, s t a n d a r d d e v i a t i o n i n t e r v a l shown f o r h i g h Lange (1981): s o l i d l i n e , wind 7.5 m/s, s i n g l e X(z) p r o f i l e UCSD tow body: open square shows space average 7 i n seasonal t h e r m o c l i n e , b a r shows range between xmode o f measured lognormal proba b i l i t y d e n s i t y f u n c t i o n and xmax, t h e maximum x i n a patch, wind

w i n d case. VMSR-25.

7 m/s.

-

Xo

i s t h e space average found i f a l l patches a r e assumed t o be

a t fossilization.

Note t h e l a r g e d i s c r e p a n c y between Lange's s i n g l e

p r o f i l e and t h e average

x

p r o f i l e , p a r t i c u l a r l y a t t h e depth o f maxi-

mum s t r a t i f i c a t i o n a t 30-40 m where i n t e r m i t t e n c y i s maximum.

7

144 The p r o f i l e s were d i v i d e d i n t o 56 s h o r t e r r e c o r d s

and h i g h winds (Cast B).

which were i n d i v i d u a l l y analyzed and t h e s t a t i s t i c s t a b u l a t e d . r e c o r d s were used t o compute t h e

x p r o f i l e s shown

t h e v e r t i c a l depth i n t e r v a l s shown.

The s h o r t e r

i n F i g . 5 by a v e r a g i n g o v e r

Standard d e v i a t i o n s about t h e means a r e

shown f o r t h e h i g h w i n d case. Both t h e h i g h w i n d p r o f i l e and t h e l o w w i n d p r o f i l e show t h a t

x i s a maximum

a t t h e depth o f maximum v e r t i c a l t e m p e r a t u r e and d e n s i t y g r a d i e n t , o r seasonal t h e r m o c l i n e , w h i c h o c c u r s a t about 30-40 m.

T h i s i s i n sharp c o n t r a s t w i t h t h e

p a t t e r n i n d i c a t e d by s i n g l e dropsonde p r o f i l e s r e p o r t e d by Lange (1981), u s i n g t h e same MSR dropsonde as Gregg (1976), an example o f which i s shown i n F i g . 5. The i s o l a t e d MSR p r o f i l e s t y p i c a l l y show minimum m o c l i n e even though t h e average

x profiles

x

values i n t h e seasonal t h e r -

i n d i c a t e d by D i l l o n (1982) a r e

3 maximum a t t h i s d e p t h w i t h values 1 0 - l o 5 t i m e s l a r g e r . The towed body average

2

i n t h e seasonal t h e r m o c l i n e was o b t a i n e d u s i n g a

m i c r o c o n d u c t i v i t y sensor t o d e t e c t h i g h f r e q u e n c y temperature f l u c t u a t i o n s , as d e s c r i b e d by Gibson (1981), Washburn and Gibson (1982) and Washburn (1982), and i s i n good agreement w i t h t h e D i l l o n (1982) r e s u l t s .

The p r o b a b i l i t y d e n s i t y

f u n c t i o n o f X measured by t h e towed body was c l o s e t o lognormal w i t h = 5.3 and Xmode = 4 x 1 0 - l ' OC2/s. Thus xmode i s c l o s e t o t h e Lange 1 nx (1981) i n d i v i d u a l p r o f i l e v a l u e s as m i g h t be expected. T h i s demonstrates t h e

u2

danger o f t r e a t i n g an i n d i v i d u a l

x

p r o f i l e as r e p r e s e n t a t i v e o f t h e mean p r o -

f i l e , e s p e c i a l l y i n a v e r y i n t e r m i t t e n t l a y e r such as t h e seasonal t h e r m o c l i n e . The towed body average was based on about 6 km o f data, o f which o n l y about 3% contained s i g n i f i c a n t microstructure a c t i v i t y .

The dominant m i c r o s t r u c t u r e

patches were f o s s i l t u r b u l e n c e a t t h e l a r g e s t s c a l e s .

An upper bound on t h e

space-time average X was e s t i m a t e d by c o r r e c t i n g each p a t c h t o i t s d i s s i p a t i o n rate X

a t fossilization,

0

g i v i n g the

yG

v a l u e shown i n F i g . 5.

Presumably the

t r u e space-time average l i e s somewhere between t h e space averages

7 and x0 '

F i g u r e 6 shows t h e i n d i v i d u a l m i c r o s t r u c t u r e p a t c h values f r o m t h e towed body and t h e D i l l o n (1982) h i g h and l o w wind p r o f i l e s compared t o t h r e e i n d i vidual

x

p r o f i l e s o f Lange (1981), a l l i n t h e 30-40 m depth range o f t h e sea-

sonal t h e r m o c l i n e .

The range o f values i s o v e r 5 decades, d e m o n s t r a t i n g t h e

extreme i n t e r m i t t e n c y p o s s i b l e i n such a s t r o n g l y s t r a t i f i e d l a y e r . ~ . a f u n c t i o n o f depth e s t i m a t e d f r o m t h e F i g u r e 7 shows a p r o f i l e o f u ~ , , ~ ,as

towed body as w e l l as t h e D i l l o n (1982) v a l u e s grouped by d e p t h i n t e r v a l . number o f l n x v a l u e s used t o compute a2

The

A l t h o u g h t h e r e i s consi-

a r e shown.

1nx d e r a b l e s c a t t e r i t seems c l e a r t h a t t h e i n t e r m i t t e n c y i s g r e a t e r i n t h e s t r o n g l y

s t r a t i f i e d seasonal t h e r m o c l i n e t h a n i n t h e mixed l a y e r above o r t h e l e s s s t r a T t i f i e d l a y e r s below.

E l l i o t t and Oakey (1980) found

d e p t h i n t e r v a l 30-130

m

d u r i n g GATE w i t h

u

x

was lognormal i n t h e

~ = 3.8, , ~ and~t h i s

v a l u e i s included

145 i n F i g . 7 f o r comparison.

3 -1 ; '

I

/'

/I

I

'

I

1

<

I \ \ I E / I 35A\ \\\\ , t/ a ,''" i/ /I 40-

I

'

I

I

I

b

o o

A

B

A 1

%

\

-

0 0

'\\

't

Fig. 6.

,

I

,','

N,;)

Range o f

x

0

oo 0

$3

k& OapsdBCIo

1

I

Dao

I -

v a l u e s i n seasonal t h e r m o c l i n e d u r i n g MILE.

t r i a n g l e s , h i g h wind; c i r c l e s , l o w wind. Lange (1981) X p r o f i l e s : dashed l i n e s . tend t o underestimate l a y e r (see F i g . 7 ) .

AA

D

x by l a r g e f a c t o r s

D i l l o n (1982):

UCSD tow body: squares.

Note t h a t i n d i v i d u a l p r o f i l e s i n t h i s very i n t e r m i t t e n t

146

0

2

I

0

I

I

I

10

0 1 :

3 I

x

I

2

5

4

6 I

I

4

3

P 8

-

E

2 20 a

W

n

4

30

2I

40

50 F i g . 7.

I n t e r m i t t e n c y oZlnx and p r o b a b l e undersampling e r r o r xmean/xmode = exp (1.5

versus depth.

D i l l o n ( 1 9 8 2 ) : c i r c l e s and t r i a n g l e s as i n

F i g . 6, d e p t h i n t e r v a l s and number o f p r o f i l e s averaged shown. tow body: square, 4292 1.1 m l e n g t h samples averaged.

UCSD

E l l i o t t and

Oakey (1980): d a r k i n v e r t e d t r i a n g l e , 30-130 m depths, d u r i n g GATE.

147

The undersampling e r r o r f a c t o r expected f o r a s h o r t d a t a r e c o r d , xmean/xmode= e x p ( l . 5 oZlnX),

i s shown on t h e i n t e r m i t t e n c y s c a l e .

F o r mixed l a y e r depths

down t o 25 m t h e expected undersampling e r r o r f a c t o r i s l e s s t h a n 10, a t t h e seasonal t h e r m o c l i n e i t i s o v e r 1000, and t h e r e i s perhaps some decrease i n l a y e r s below.

5.

ESTIMATES OF

x, DIFFUSIVITY AND

HEAT FLUX I N THE EQUATORIAL UNDERCURRENT

DEPTH ZONES FROM LOGNORMAL MODEL F i g u r e 8 shows a l l o f t h e a v a i l a b l e measurements o f X i n t h e c o r e l a y e r s o f

log

-8

-7

x:c/s 2 -6

-5

-4

0 40 E c

?a_

80

W

\OON

n

I20

I60

Fig. 8.

155OW

>t

x

measurements i n t h e h i g h v e l o c i t y c o r e o f t h e e q u a t o r i a l undercurrent. Osborn and Gregg ( 1 9 7 6 ) : crosses on d e p t h i n t e r v a l s o f MSR-3,4,7. B i l o d e a u (1980): d o t s on d e p t h i n t e r v a l s . crosses on d e p t h i n t e r v a l . the equator unless noted.

W i l l i a m s and Gibson (1974):

L o n g i t u d e s a r e shown, l a t i t u d e s a r e a t

148 t h e e q u a t o r i a l u n d e r c u r r e n t i n t h e A t l a n t i c and P a c i f i c . wide, c o v e r i n g n e a r l y 4 decades, b u t t h i s range

The s c a t t e r i s very

does n o t seem unreasonable i n

view o f t h e s c a t t e r observed i n t h e seasonal t h e r m o c l i n e shown i n F i g . 6. T r e a t i n g each o f t h e 11 samples shown as independent, and g i v i n g each equal w e i g h t g i v e s a mean l n x v a l u e p o f -14.51 and u21nx = 6.89.

x

T h e r e f o r e , assuming

lognormality, f o r t h e c o r e s h o u l d be about 1.6 x OC2/s based on t h i s da/2). T h i s v a l u e i s shown i n F i g . .A. t;l, where = exp u exp ( 5 * 1"XT a b l e 1 l i s t s e s t i m a t e s o f x f o r t h e t h r e e d e p t h zones o f t h e e q u a t o r i a l un-

<

d e r c u r r e n t i n d i c a t e d by t h e lognormal model.

I t s h o u l d be emphasized t h a t these

mean v a l u e s a r e based on a small number o f samples which have v a r i a b l e degrees o f s t a t i s t i c a l s i g n i f i c a n c e and do n o t t a k e i n t o account seasonal and zonal v a r i a b i l i t y which may be s u b s t a n t i a l .

The i n d i c a t e d mean X values i n t h e under-

c u r r e n t depth zones a r e about an o r d e r o f magnitude l a r g e r t h a n t h e correspondi n g mean values i n t h e seasonal t h e r m o c l i n e shown i n F i g . 5, which seems reasonable. Table 1.

E s t i m a t e s o f Xmean

i n Equatorial Undercurrent

Depth Zones - Lognormal Model

Samples

~i =

1n x

x = exp 11 exp(u2/2) IJ2

1 nx OC2/S

Shear l a y e r above c o r e Core l a y e r Shear l a y e r below c o r e

6

-13.16

2.72

7.5 x

11

-14.51

6.89

1.6

6

-14.81

2.05

1 . 0 x 10-6

F i g u r e 9 shows t h e v e r t i c a l eddy d i f f u s i v i t y K i n d i c a t e d by t h e dropsonde values of Gregg (1976), Osborn (1980) and t h e p r e s e n t work, where

u s i n g t h e Osborn and Cox (1972) model.

The most s t r i k i n g d i f f e r e n c e i s i n the c o r e l a y e r where t h e p r e s e n t lognormal model g i v e s K = (2-25) cm2/ s compared t o (1.5- 3) x

2

cm / s i n f e r r e d by Gregg (1976) and Osborn (1980).

The c o r r e s p o n d i n g values of v e r t i c a l h e a t f l u x Q a r e shown i n F i g u r e 10, where Q =

-

P

Cp K ( a T / a z ) = - P Cp ?/2

(aT/az)

149

log K

-2

-I

, cm2/s 0

I

2

1

1

K

a W

A

I

v>

W

nz

0

0 [r

a r v>

W

0GREGG (1976) OSBORN (I980) 0THIS WORK Fig. 9.

Vertical d i f f u s i v i t y K in various depth zones of t h e equatorial underc u r r e n t . Gregg (1976), squares. Osborn (1980), t r i a n g l e s . Average of a l l a v a i l a b l e values corrected f o r undersampling e r r o r using lognormal model, c i r c l e s .

150

log(- Q), W/m* I 2

3

4

nu

0GREGG (1976) L l OSBORN (1980) O T H I S WORK F i g . 10.

V e r t i c a l h e a t f l u x Q i n shear zones of e q u a t o r i a l u n d e r c u r r e n t .

Same

symbols as F i g . 9.

p

i s h e a t c a p a c i t y . V e r t i c a l t e m p e r a t u r e g r a d i e n t s were taken P OC/cm i n t h e c o r e and 5 x OC/cm i n t h e shear zones above and

i s d e n s i t y and C

t o be 1 x

below i n computing K and Q values i n F i g u r e s 9 and 10. The v e r t i c a l h e a t f l u x i n t h e c o r e zone i s l a r g e r t h a n i n t h e zones above and below, and i s about 2 o r d e r s o f magnitude l a r g e r t h a n i n f e r r e d by Gregg (1976) and Osborn (1980) and 1 o r d e r o f magnitude l a r g e r t h a n t h e upper bound of 10 2 W/m proposed by Crawford (1982). From t h e p r e s e n t work, Q i s about (0.2-2)

kW/m

2

downward a t t h e c o r e which i s l a r g e r t h a n t h e n e t s u r f a c e h e a t f l u x .

Therefore i t appears t h a t t h e u n d e r c u r r e n t may be c o l l e c t i n g h e a t by t u r b u l e n t

151 d i f f u s i o n f r o m warmer surface l a y e r s n o r t h and s o u t h o f t h e e q u a t o r (see F i g . 1 ) and m i x i n g t h e h e a t down t h r o u g h t h e c o r e t o deeper l a y e r s a t r a t e s 1-2 o r d e r s

o f magnitude h i g h e r t h a n t h e v e r t i c a l h e a t f l u x a t l a t i t u d e s o u t s i d e t h e underc u r r e n t in f l uence. 6.

SUMMARY AND CONCLUSIONS Estimates o f t h e t r u e space-time average

x,

K and Q values i n t h e v e l o c i t y

core o f t h e e q u a t o r i a l u n d e r c u r r e n t have been made from a l l a v a i l a b l e m i c r o Undersampl i n g e r r o r s due t o t u r b u l e n t p a t c h i n e s s and i n t e r m i t -

s t r u c t u r e data.

tency a r e t a k e n i n t o account by assuming t h e temperature d i s s i p a t i o n r a t e X i s lognormal.

Such undersampling e r r o r s appear t o be maximum i n s t r o n g l y s t r a t i -

f i e d l a y e r s such as t h e u n d e r c u r r e f l t h i g h v e l o c i t y c o r e and i n t h e seasonal thermocline a t h i g h e r l a t i t u d e s .

The range o f

x

v a l u e s measured i n t h e under-

c u r r e n t c o r e i s v e r y l a r g e , n e a r l y 4 decades as shown i n F i g . 8, b u t t h i s range i s l e s s t h a n t h e range observed i n t h e n o r t h P a c i f i c seasonal t h e r m o c l i n e , which covers n e a r l y 6 decades as shown i n F i g . 6. 1982) have suggested t h a t towed body c and

Gregg (1976) and Crawford (1976,

x

values i n t h e u n d e r c u r r e n t must be

contaminated by v i b r a t i o n a l n o i s e because t h e i r dropsonde values t e n d t o be orders o f magnitude s m a l l e r .

T h i s s u g g e s t i o n does n o t seem t o be j u s t i f i e d .

Rather, i t appears t h a t dropsonde

E

and

x

values g e n e r a l l y r e p r e s e n t t h e mode

of lognormal random v a r i a b l e s w i t h means s e v e r a l decades l a r g e r i n s t r a t i f i e d ocean l a y e r s such as t h e u n d e r c u r r e n t c o r e and t h e seasonal t h e r m o c l i n e . F o r the tow body-dropsonde i n t e r c o m p a r i s o n i n t h e seasonal t h e r m o c l i n e t h e upper end o f t h e range o f

x

v a l u e s shown i n F i g . 6 was measured f r o m a dropsonde by

D i l l o n (1982) r a t h e r t h a n t h e towed body.

No a t t e m p t was made t o e s t i m a t e t h e

i n t h e u n d e r c u r r e n t d e p t h zones because l e s s d a t a i s a v a i l a b l e , although i t seems l i k e l y t h a t t h e towed body v a l u e s i n t h e c o r e o f o r d e r 10- 1 2 3 cm / s shown i n F i g . 2 a r e c l o s e r t o t h e t r u e average t h a n t h e dropsonde values o f l o v 4 - l o m 5 cm2/ s 3 proposed as r e p r e s e n t a t i v e of t h e t r u e average b y Osborn

mean values of

E

(198R) w i t h o u t a c c o u n t i n g f o r i n t e r m i t t e n c y . The much h i g h e r

x, K and Q values

i n f e r r e d i n t h i s paper c a l l i n t o q u e s t i o n

the c o n c l u s i o n reached by Gregg (1976, p . 1195) t h a t " i n v i e w o f t h e small v o l ume of t h e u n d e r c u r r e n t system, i t i s of n e g l i g i b l e i m p o r t a n c e i n t h e g l o b a l balance o f t e m p e r a t u r e f l u c t u a t i a n s . " sumptions t h a t h i s dropsonde

x

Gregg's s t a t e m e n t was based on h i s as-

values of

the u n d e r c u r r e n t average i n t h e upper 200 f e r e n t t h a n average o c e a n i c

x

lov8m and

'C2/s were r e p r e s e n t a t i v e o f t h a t t h e s e were n o t much d i f -

values i n t h i s d e p t h range,

However, t h e p r e s e n t

analysis suggests 7 f o r t h e u n d e r c u r r e n t i s p r o b a b l y i n t h e range l o v 5 1 2 OC2/s, which may be 10 - 10 t i m e s l a r g e r t h a n t h e upper 200 m ocean average, which may a l s o be h i g h e r t h a n Gregg (1976) assumes.

Thus t h e u n d e r c u r r e n t may

152

c o n s t i t u t e a very important f a c t o r in tropical heat and mass t r a n s p o r t processes which a f f e c t planetary weather and climate. I t i s c l e a r t h a t t h e present information about turbulence, mixing and d i f fusion in t h e equatorial undercurrent system i s q u i t e incomplete: fragmentary might be a b e t t e r term. Much more data a t a l l scales i s needed t o e s t a b l i s h r e l i a b l e values of t h e relevant parameters on which t h e present r a t h e r crude a n a l y s i s depends. I t i s of p a r t i c u l a r importance t o measure the intermittency of t h e turbulence and mixing a t various depths, times and positions in order t o be a b l e t o evaluate any microstructure sampling procedure o r any p a r t i c u l a r d a t a s e t . P r o f i l e s of u 2 1 n x and u~~~~ a r e most d e s i r a b l e . Acknowledgements. The a u t h o r ' s attendance of t h e Liege colloquium was supported by a UNESCO travel g r a n t . Preparation of t h i s paper was supported by a grant from t h e UCSD Committee on Research. REFERENCES Belyaev, V . S . , A . N . Gezentsvey, A.S. Monin, R.V. Ozmidov and V T . Paka, 1975a . Spectral c h a r a c t e r i s t i c s of small-scale f l u c t u a t i o n s of the hydrophysical f i e l d s in the upper l a y e r of t h e ocean. Journal of Physica Oceanography, 5: 492-498. Belyaev, V.S., M . M . Lubimtzev and R . V . Ozmidov, 1375b. The r a t e of dissipation of t u r b u l e n t energy in t h e uoper l a y e r of t h e ocean. Journal of Physical Oceanography 5: 499-505. Crawford, W . B . , 1976. Turbulent energy d i s s i p a t i o n i n t h e A t l a n t i c equatorial undercurrent. Thesis, The University of B r i t i s h Columbia, Canada. Crawford, W.R. and T . R . Osborn, 1980. Microstructure measurements in the A t l a n t i c equatorial undercurrent during GATE. In: GATE-2, Equatorial a n d A-Scale Oceanography, Walter DL'ing, Ed., Pergammon, 285-308. Dillon, T . R . , 1982. Vertical overturns: a comparison of Thorpe and Ozmidov length s c a l e s . Journal of Geophysical Research, 87 ( C 1 2 ) : 9601-9613. E l l i o t t , J.A., and N.S. Oakey, 1980. Average microstructure l e v e l s and vertical diffusion f o r Phase 111, GATE. In: GATE-1, Equatorial and A-Scale Oceanography, Walter DL'ing, Ed. Pergammon, 273-293. Gammon, R . H . , 3. Cline and D . Wisegarvern, 1982. Chlorofluoromethanes in the northeast P a c i f i c ocean: measured v e r t i c a l d i s t r i b u t i o n s and application as t r a n s i e n t t r a c e r s o f upper ocean mixing. Journal o f Geophysical Research, 87 (C12): 9441-9454. Gibson, C . H . , 1980. Fossil temperature, s a l i n i t y , and y o r t i c i t y turbulence in the ocean. In: Marine Turbulence, J.C.J. Nihoul, Ed,, Elsevier, 221-257. Gibson, C . H . , 1981. Buoyancy e f f e c t s in turbulent mixing: sampling turbulence i n the s t r a t i f i e d ocean. AIAA Journal 19: 1394-1400.

153

Gibson, C . H . , 1982. Alternate i n t e r p r e t a t i o n s f o r microstructure patches in t h e thermocline. Journal of Physical Oceanography, 12:374-383. Gibson, C . H . , 1983. Internal waves, f o s s i l turbulence, and composite ocean mic r o s t r u c t u r e s p e c t r a . Submitted t o Journal of Physical Oceanography. Gregg, M . C . , 1976. Temperature and s a l i n i t y microstructure i n t h e P a c i f i c equat o r i a l undercurrent. Journal o f Geophysical Research, 81 :1180-1196. Gregg, M . C . , 1977. Variations in the i n t e n s i t y o f small-scale mixing i n the main thermocline. Journal of Physical Oceanography, 7 : 436-454. Gregg, M . C . , 1980. Microstructure patches in t h e thermocline. Physical Oceanography, 10: 915-943.

Journal of

Helm, R . , H . U . Lass and M . Sturm, 1980. Some p e c u l i a r i t i e s o f the A t l a n t i c equatorial undercurrent core s t r u c t u r e and i t s v a r i a t i o n i n time and space. I n : GATE-2, Equatorial and A-Scale Oceanography, Walter DUing, Ed., 249-259. Lanqe, R . E . , 1981. Observations of near-surface oceanic velocity s t r a i n - r a t e i a r i a b i l i t y during and a f t e r storm events. Journal of Physical Oceanography, 1 1 : 1272-1279. Osborn, T . R . , and C.S. Cox, 1972. Dynamics, 3: 321-345.

Oceanic f i n e s t r u c t u r e .

Geophysical Fluid

Osborn, T . R . , 1980. Estimates o f t h e local r a t e o f v e r t i c a l diffusion from dissipation measurements. Journal of Physical Oceanography, 10: 83-89. Osborn, T . R . , and L . E . Bilodeau, 1980. Temperature microstructure in t h e equat o r i a l A t l a n t i c . Journal of Physical Oceanography, lO(1): 66-82. Schedvin, J.C., 1979. from a towed body.

Microscale temperature measurements in t h e upper ocean Thesis, University o f California a t San Diego.

Tully, J . P . and F.G. Barber, 1960. An e s t u a r i n e analogy in the sub-Arctic Pacific ocean. J . Fish. Res. Bd. Canada 17 ( 1 ) : 91-112. Washburn, L . , a n d C.H. Gibson, 1982. Measurements o f oceanic temperature micros t r u c t u r e using a small conductivity sensor. Journal of Geophysical Research, 87(C6): 4230-4240. Washburn, L., 1982. Horizontal observations o f temperature microstructure within t h e seasonal thermocline. Thesis, University o f California a t San Diego. Williams, R . B . , and C . H . Gibson, 1974. Direct measurements o f turbulence in the Pacific equatorial undercurrent. Journal of Physical Oceanography, 4: 104108. Williams, R . B . , 1974. r i a l undercurrent.

Direct measurements o f turbulence i n the P a c i f i c equatoThesis, University of California a t San DiegQ,

Wyrtki, K., 1982. An estimate o f equatorial upwelling i n t h e Pacific. of Physical Oceanography, 1 1 : 1205-1214.

Journal

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155

ON THE INTERANNUAL WIND-DRIVEN RESPONSE OF THE TROPICAL PACIFIC OCEAN Antonio J. Busalacchi, Kensuke Takeuchi, 2 and James J. O'Brien Mesoscale Air-Sea Interaction Group Florida State University Tallahassee, Florida 32306 (USA) Present Affiliation:

Goddard Laboratory for Atmospheric Sciences NASAIGoddard Space Flight Center Greenbelt, MD 20771 (USA) Department of Geophysics Hokkaido University, Sapporo, 060 (JAPAN)

ABSTRACT A linear numerical model forced by ship-board wind estimates for each month from January, 1961 to December,1978, has been used to study the interannual variability of the tropical Pacific Ocean. Model pycnocline variations at several stations are similar to the observed sea level fluctuations. El Nino events are depicted as periods when the pycnocline is persistently deep along the eastern boundary. Remotely forced equatorial Kelvin waves are responsible for this response. The character of each simulated El Nino is strongly dependent on the relation between zonal wind stress changes in the western and central equatorial Pacific. A rapid shoaling of the pycnocline in the western tropical Pacific during each El Nino is caused by westwardpropagating Rossby waves. Interannual pycnocline displacements in the central equatorial Pacific are determined by the superposition of Kelvin waves excited to the west and first-mode Rossby waves generated to the east. INTRODUCTION The importance of the interannual variability of the tropical Pacific lies

in its relationship with the El Nino phenomenon.

In the strictest sense, El

Nino is a term used presently to represent the anomalous occurrence and persistence of warm sea surface temperatures (SST) along the coast of Ecuador and Peru.

It is used more loosely to represent anomalous high sea level and

deep thermocline periods in the eastern Pacific consistent and coincident with the SST changes.

An El Nino occurrence is not an isolated phenomenon, rather

it is one facet of global-wide climate anomalies characterized by changes in

the Southern Oscillation Index (Kidson, 1975).

With respect to the tropical

Pacific Ocean, one might expect that large perturbations to the mean state are

not unique to the eastern boundary region. Fortuitously, there are several island stations in key areas of the tropical Pacific (Fig. 1) from which sea level time series can be used to monitor the interannual variability. In the eastern Pacific, sea level changes at the Galapagos Islands are representative of the non-seasonal fluctuations at the equator and along the eastern boundary (Wyrtki, 1975; Hickey, 1975).

In the western tropical

156 Pacific, there is a drastic decrease in sea level and shoaling of the thermocline during the El Nino year (Hickey, 1975; Wyrtki, 1975, 1977, 1979; Meyers, 1982).

The largest drop in sea level occurs north of the equator. The

sea level record at Truk Island is representative of the variability in this region and is one of the longest time series available. A lagged cross correlation analysis (Hickey, 1975) indicates a maximum negative correlation of sea level between the eastern and western Pacific occurs when the eastern Pacific leads by several months.

In the central equatorial Pacific, sea level

data from Canton Island and Christmas Island indicate an anomalous rise in sea level during the latter half of the El Nino year.

The processes responsible

for the phase relations between the eastern, central equatorial, and western Pacific are not understood. Wyrtki (1975) has attributed El Nino to the excitation of Kelvin waves due to the interannual fluctuations of the southeast trade winds over the central equatorial Pacific. A statistical analysis by Barnett (1977) linked the variability of the zonal component of the southeast trades west of the dateline with sea level changes across the Pacific basin.

Numerical and

analytical models by Hurlburt et al., (1976) and McCreary (1976) simulated the excitation of an equatorially trapped internal Kelvin wave in response to changes in the zonal component of the wind stress.

Upon impingement with the

eastern boundary, the incoming Kelvin wave excited westward-propagating internal Rossby waves and poleward-propagating coastal trapped Kelvin waves. This is consistent with the theoretical work of Moore (1968) and Moore and Philander (1977).

Kindle (1979) demonstrated that the magnitude, duration and

timing of changes in the southeast trades over the central and western Pacific were important i n determining the character of a simulated El Nino response. O'Brien et al., (1981) discussed these aspects of Kelvin waves and El Nino i n a simpler physical context. This study uses the results of a linear numerical model to analyze the interannual variability of the tropical Pacific Ocean.

The model of

Busalacchi and O'Brien (1980) is forced by monthly estimates of the surface wind field based on ship-board observations over the tropical Pacific for 1961-1978.

The dense time and space coverage provided by such a model will be

used to provide insight into the causality of the wind-driven response in different parts of the basin.

Regions of important wind stress fluctuations

will be identified and the relevance to sea level/pycnocline responses in the eastern, central equatorial and western Pacific will be addressed.

Since the

model is simple, the wind induced variability can be interpreted easily in physical terms.

If the model results compare favorably with observations,

physical interpretation of the model response can be applied to the observed oceanic response.

157 THE MODEL AND WIND DATA The model utilized by Busalacchi and O'Brien (1980) is a 11/2 layer reducedgravity, linear transport model on an equatorial @-plane.

The model geometry Open

is an idealization of the tropical Pacific from 18ON to 12OS (Fig. 1).

boundary conditions at the northern and southern boundaries allow coastal A complete discus-

Kelvin waves to propagate freely out of the model domain.

sion of the model and its equations are included in the authors' previous work.

M0DEL GE0METRY

7.5.N 0

IsLtNo CHRISTMAS

2.8.N

4

-'. - _ - _ - _ - - - - _ _ .

'

0 '

B i

i

\

i

r

i

130E 140E 150E 160E 170E 180

i

i

i

i

i

i

i

i

i

i

170W 160W 150W 14OW 1301.1 1ZOW 110W 1OOW 9OW

8OW

i

70W

Fig. 1. Comparison of the model geometry with the tropical Pacific Ocean. The model basin extends from 180N to 120 S and 126'E to 77W. The dashed line represents an open boundary; all remaining boundaries are solid walls. Sea level data from the island stations indicated provide details of the interannual variability in different regions of the Pacific. For the present study, the upper layer thickness, H, is taken to be 300 m. This depth is sufficient to prevent any surfacing of the density interface during an 18-year integration. With H speed is 2.45 m s-l.

=

300 m the first baroclinic phase

This speed is the only dynamically important free

parameter in the model.

The Laplacian friction coefficient only cosmetically

smooths the very high wave number numerical noise. Details of the wind stress data base and a spectral analysis of that data for 1961-1970 were discussed by Goldenberg and O'Brien (1981).

Monthly

estimates of the surface wind stress based on ship observations over the tropical Pacific from January, 1961, to December, 1978, were subjectively analyzed onto a 2' by 2' mesh.

The resulting data set, continuous in time and

space, was input as a body force into the momentum equations of the model. Though the approach used in collecting and preparing the wind data is not the ultimate methodology for monitoring the wind field over the tropical Pacific Ocean, it has resulted in the

only data set available with spatial and

temporal resolution suitable for interannual modelling studies.

158 A new open boundary condition is implemented for this 18-year simulation. After 7 years of integration, the variant of the Hurlburt (1974) open boundary condition used in the previous study becomes unstable. The boundary condition at the northern and southern boundaries is replaced with an open boundary condition developed by Camerlengo and O'Brien (1980). This modification of the Orlanski (1976) open boundary treatment allows the model to be integrated for the full 18 years.

Prior to the onset of any instability, calculations with

the Hurlburt open boundary condition and those with the Camerlengo and O'Brien open boundary condition render the same solutions. The model is initiated using the results from year 4 of the seasonal calculation in Busalacchi and O'Brien (1980).

Thus, spin-up transients are confined essentially to the

first year of integration. EASTERN PACIFIC RESPONSE The 18-year period of the numerical simulation encompasses several notable eastern Pacific events of varying intensity. The strongest El Nino since 1957 occurred during 1972 (Quinn et al., 1978).

The associated environmental

changes resulted in the accelerated collapse of the Peruvian anchoveta fishery.

Sea surface temperatures (SST) off the coast of Ecuador and Peru

were up to 4OC warmer than the climatological monthly means (Fig. 2). level was at its highest point in years.

Sea

The sea level record at the

Galapagos Islands (Fig. 3) is a useful indicator of this interannual variability along the eastern boundary (Wyrtki, 1975; Hickey, 1975).

For the

1972 event, as opposed to previous Los Ninos, large anomalies were present during the middle of the year. June.

Positive SST anomalies peaked in March and

Sea level began to rise in late 1971 and reached a maximum in June.

Consistent with several previous El Nino events another peak in SST and sea level occurred at the end of the year. During 1965 and 1976, moderate El Nino conditions were present in the eastern tropical Pacific.

Sea surface temperatures were 2O-3OC above normal.

The 1965 event was characterized by warm SST and elevated sea level episodes at the beginning and end of the year.

For the 1976 El Nino, SST was

anomalously warm throughout the year.

Sea level began to rise late in 1975

and peaked in June similar to the 1972 occurrence. A secondary sea level maximum was present late in the year but was much smaller relative to the first peak than in the 1972 event. The weakest of the year-long warm events during this 18-year period were in 1963 and 1969.

1978).

Positive SST anomalies were less than 2.5OC (Quinn et al.

Once again sea level was elevated along the eastern boundary. However,

for the very weak event in 1963 the sea level anomaly at the Galapagos Islands was not truly representative of the anomalies at coastal stations.

Only at

m

P 'rl n d I W

rn

rl

a Ll

d

159

160

161 Galapagos was the sea level for 1963 higher than during the 1965 El Nino. At all the South American coastal stations monthly sea levels were higher in 1965. Another period worthy of attention is 1975 even though it was not an El Nino year. In 1974 it was noted that there was an ongoing decrease in the Southern Oscillation Index (Wyrtki et al., 1976).

Based on previous studies

linking a low Southern Oscillation Index with El Nino (Quinn, 1974), a weak El Nino was predicted for 1975. An expedition mounted to observe this event found anomalous conditions present off the coast of Ecuador and Peru in February and March of 1975.

The distribution of warm SST anomalies, changes

in thermocline depth, and elevated sea levels were similar to the onset phase of previous El Nino episodes. These conditions did not persist long enough and were not large enough in magnitude for 1975 to be recognized as an El Nino year.

By April and May the development of the warm episode had been aborted

and conditions were returning to normal. Interspersed among the El Nino episodes were periods of cool SST and depressed sea level. In this study of the linear wind-driven Pacific response the dynamics responsible for pycnocline and sea level changes during El Nino will be the same as in these non-El Nino events.

Most of the following

discussion of the model results will focus on the El Nino incidents since they often dominate the interannual variability, have important climatic implications, and have been the subject of previous observational and theoretical studies. The sea surface and pycnocline fluctuate 180Oout of phase in the model formulation used.

Meyers (1979) has shown, using sea level and interfacial

depth profiles, that the central and eastern Pacific act in a manner compatible with the dynamics implicit in this reduced-gravity approach. Since the model does not contain thermodynamics the results cannot give a direct indication of SST change. In general, there is no linear relation between upper layer thickness, sea level, or thermocline depth and SST.

Yet, in the

eastern tropical Pacific, warm (cold) SST anomalies are significantly correlated with elevated (depressed) sea level (Barnett, 1977; Enfield and Allen, 1980).

Modelling efforts including mixed-layer physics will provide

much needed information on such relations between thermocline depth, vertical velocity, and SST. A time series of the pycnocline height anomaly (PHA) at a location representing the Galapagos Islands (Fig. 4) depicts the vertical displacement

of the model pycnocline throughout the 18-year integration. The linear trend,

resulting from a mean background wind stress, has been removed. Upwelling and downwelling bursts of relatively short duration constitute the variability in the entire record. The model pycnocline is the deepest during 1963, 1965,

162

i

I

c _

4

I

0 I

(D

m -4

in

163 1969, 1972, and 1976; the five El Nino years. The double-peak El Nino signature found in the sea level record (Fig. 3 ) is present in the model results for 1965 and 1969.

During these years the upper layer becomes deepest at the

beginning and end of the El Nino year.

The onset of the 1972 El Nino is

preceded by a deepening of the pycnocline during the second half of 1971. The pycnocline reaches its maximum depth in June followed by a secondary maximum at the end of the El Nino year.

The 1976 El Nino is characterized by

downwelling from mid-1975 to early 1976, maximum pycnocline depths in June, and a deep pycnocline again in the latter half of the year.

The weak event of

1975 is represented by a downwelled pycnocline at the beginning of the year followed by a rapid upwelling leaving a shallow pycnocline for the remainder of the year.

The timing of major upwelling and downwelling events is similar

even though there are periods when the relative amplitude of observed sea level change and pycnocline displacement do not agree.

Changing the phase

speed of the model by 230% changes the phase of the eastern boundary response by less than one month.

When comparing with monthly mean observations this

shift in phase is not significant. A major difference between the model pycnocline fluctuations and observed sea level is the presence of more high frequency variability in the pycnocline time series.

The cross correlation of

pycnocline variability and observed sea level less the seasonal signals is maximum at zero lag with a correlation of 0.52 which is significant at the 99% level.

The degrees of freedom used in the significance test were determined

by dividing the total record length by the integral time period needed to obtain two independent realizations (Davis, 1976).

The number of equivalent

degrees of freedom was 51. The observed sea level and model pycnocline time series for the Galapagos Islands have been subjected to a 12-month, running-mean filter (Fig. 5).

This

provides a more graphic representation of the interannual variability during the 18-year period.

The similarities and differences between the model and

observations are clearly displayed.

The filtered data indicate a tendency for

the sea level and the model pycnocline to be elevated or depressed for spans of 10-30 months.

Discrepancies between the model and observations include the

phase of the response from mid-1961 through 1962, the relative amplitudes of the response from late-1967 to early-1968, and the amplitude in 1972.

The

cross correlation between these two filtered time series was .61. The model pycnocline variability at the location of Talara, Peru (Fig. 6) is very similar to that at the Galapagos Islands, except the maximum cross correlation (r = .98, significant at 99% level) occurs when the signal at Talara lags Galapagos by 1-3 days.

This lag increases when time series

further poleward along the coast are cross correlated with the Galapagos time series.

For example, the pycnocline time series at the location of Callao,

164 Peru (12OS) lags Galapagos by approximately one week and is highly correlated. The great degree of similarity between these time series attests to the large areal extent of the variability near the eastern boundary. The poleward increase in lag indicates a poleward propagation of information. Smith (1978), Enfield and Allen (1980), and Romea and Smith (1982) have reported on an observed poleward propagation along the coast.

Knox and Halpern (1982)

have observed eastward propagation along the equator from 152OW to 9l0W.

YEAR Fig. 5. Comparison of the model pycnocline height anomaly (solid) and observed sea level (dashed) at the Galapagos Islands filtered by a 12-month running-mean. The pycnocline displacement scale is in meters and sea level changes are expressed in cm. The pycnocline variability at the Galapagos Islands and Talara consists of discrete upwelling and downwelling events with a duration of several months. What is the mechanism responsible for these changes in depth of the pycnocline? A cross correlation of the pycnocline variability at the equatorial eastern boundary with all points west along the equator implies that the effects of internal Kelvin and Rossby waves are important.

The lag

structure of the pycnocline variability along the equator is illustrated in Fig. 7.

The most striking aspect is the linear increase in lag away from the

eastern boundary for high correlations. The solid line represents an eastward phase speed of 2.45 m s-l, corresponding to the phase speed for an internal, equatorially-trapped Kelvin wave in this model.

As a result, 50% of the

variability at the eastern boundary is accounted for by the variability along the Kelvin wave characteristic in the central Pacific. The linear increase in lead away from the eastern boundary (dashed line) represents the westward propagation of the lowest order Rossby waves excited

165

m

d h

5

m

U

rl

c x

a m

d

e

a

CL

a

i

IOOW

a

120 w

140W

l60W

I80

160 E

140E

- I8

- 12

-6

LAG EASTERN BOUNDARY LAGS

0 6 (MONTHS)

12

18

EASTERN BOUNDARY LEADS

Fig. 7. Contours of lagged cross correlation between the pycnocline variability at the equatorial eastern boundary and all points west. The slope of the solid line indicates an eastward propagation representative of equatorially trapped Kelvin waves. The solid line represents the westward propagation of Rossby waves excited at the boundary.

167 at the coast. These waves were excited by the impingement of Kelvin waves or local changes in the wind stress. These waves have a noticeable effect on the pycnocline variability westward to 160OW. The slope of the dashed line represents a phase speed of .82 m s-l, one-third the speed of the Kelvin wave. There is also a notable negative correlation when the eastern boundary leads the western boundary by several months. Away from the boundaries an equatorial Kelvin wave can only be generated by temporal fluctuations of the zonal wind stress symmetric about the equator.

A

test calculation was performed in which the model was only driven by the zonal wind stress for the period mid-1973 through 1977. This was intended to test the premise that the interannual events in the eastern part of the basin are remotely forced by Kelvin waves.

The time interval was chosen because it

contained several large changes in depth of the pycnocline. The resulting pycnocline response along the eastern boundary was essentially the same as the total response to zonal and meridional winds.

The cross correlation between

the zonal wind stress solution and the total forced case was .99 at zero lag. The pycnocline variability at the eastern boundary of this linear model is the integrated response to the zonal equatorial wind stress fluctuations to the west.

The evolution of significant events, e.g., El Nino occurrences, can

be traced back in time and space along the Kelvin wave characteristics. The

location of the forcing responsible for each event has been identified in this manner. We now describe the character of El Nino events from 1961-1978 depicted in this model as periods when the pycnocline was persistently deep. The period 1964-1965 is a good time frame within which to study the transformation from a non-El Nino regime to an El Nino regime. The semiannual pycnocline variability at the eastern boundary previously discussed by others (Meyers, 1979; Kindle, 1979; Busalacchi and O'Brien, 1980) has been associated with Kelvin wave signals excited between 180' and 12OoW. Evidence for this seasonal cycle is seen throughout the model integration (Figs. 4,6). The semiannual variability is typical of a non-El Nino year in the 1960's. From January, 1964, to April, 1964, the pycnocline in the eastern two-thirds of the equatorial Pacific is being upwelled (Fig. 8). This is a result of an upwelling Kelvin wave front excited during an October, 1963 to March, 1964 intensification of the easterlies between 18Oo-16O0W. The downwelling at the western boundary through June, 1964, is caused by a downwelling Rossby wave front excited by the same intensification of the easterlies between 180°-160OW. Another large amplitude upwelling Kelvin wave front is excited in the interior from July through September. Towards the end of a non-El Nino year a downwelling Kelvin wave front is excited in the central equatorial Pacific. A simulated seasonal El Nino along the eastern boundary is

168

Fig. 8. An X-T section along the equator for the upper layer thickness (ULT) during 1964-65. The phase speed of the downwelling Kelvin wave responsible for triggering the 1965 El Nino in the model is indicated by the slope of an imaginary line connecting a point at the western boundary for November, 1 9 6 4 , with a point at the eastern boundary for February, 1965. Such a line also indicates the end of the equatorial downwelling associated with the passage of the Kelvin wave.

169 associated with this downwelling Kelvin wave front.

Though the amplitude and

precise timing of these upwelling signals may vary amongst non-El Nino years, there is often an upwelling of the pycnocline early in the year. The upwelling is important because it causes the pycnocline to be upwelled following the seasonal downwelling of the pycnocline during the austral summer. The changes in pycnocline depth that typify the 1965 El Nino event have their roots in the western Pacific during the latter half of 1964.

A 0.4

dynes relaxation of the easterly wind stress between the western boundary and the dateline from August-November, i 9 6 4 , excites a downwelling Kelvin wave front. The slope of the downwelling signal in Fig. 8 represents the inverse phase speed of an internal Kelvin wave.

The equatorial pycnocline is

depressed as the wave front propagates eastward; terminating at the eastern boundary in January, 1965.

The timing of this wave is such that it greatly

enhances the normal seasonal downwelling during the Southern Hemispheric summer. The same sequence of events preceeds the 1969 El Nino. In addition to the downwelling Kelvin wave excited near the western boundary, the semiannual upwelling signals of 1965 are much weaker than those of non-El Nino years.

As a result, there is no mechanism to raise the deeper

than normal downwelled pycnocline present in early 1965.

The upwelling

signals are weaker than non-El Nino years because the intensification of the interior easterlies is not as strong.

This cessation of the normal semiannual

variability of the zonal wind stress also occurs during 1969.

Therefore, over

a one-year period of time the pycnocline is deeper than the long term mean. Towards the end of 1965 (Fig. 8), the seasonal relaxation of the interior easterlies excites a downwelling Kelvin wave front. This downwelling Kelvin wave is the cause of the downwelling at the eastern boundary at the beginning of 1966.

Though this Kelvin wave is associated with the seasonal

signal, it is atypical in the sense that it was excited at a time when the pycnocline was deeper than normal. Hence, there is a double-peak downwelling signature during 1965. The excitation of a large amplitude downwelling Kelvin wave west of the dateline, which then enhances the normal seasonal downwelling, and the concomitant cessation of the semiannual interior zonal wind stress is the scenario that describes the 1965 and 1969 El Nino events. The minor El Nino of 1963 is solely due to weakened seasonally varying zonal wind stress over the central equatorial Pacific. There were not any large amplitude downwelling Kelvin waves excited during late 1962. The events of the 1 9 7 0 ' s were somewhat different than in the previous decade.

Beginning in October 1971, there was a relaxation or weakening of the

trade winds west of the dateline (Fig. 9 ) .

This band of wind relaxation pro-

gressed eastward (Wyrtki, 1977) to 16OOW during the entire El Nino year.

170

F i g . 9 . Zonal wind s t r e s s a l o n g t h e e q u a t o r from 1971-1978. White a r e a s i n d i c a t e w e s t e r l y f l o w . Time p e r i o d s i n which t h e s t r e s s i s g r e a t e r t h a n 1 . 0 dynes cm-’ are shaded t h e d a r k e s t . Contour i n t e r v a l i s . 2 dynes cm-2.

171 Concurrent with the initial weakening in the west there was an intensification of the central equatorial easterlies, 130°W-1700W,

from mid-October until the

end of 1971. The combined effect of weakening winds in the west and intensifying winds in the central Pacific yielded average pycnocline depths in the east at the beginning of 1972 (Fig. 4 ) .

From January through April, at 12OoW-188,

there was a decrease in the zonal wind stress of more than .6 dynes cm-2. Thereafter, the winds in the central equatorial Pacific remained weak.

This

weakening of the easterlies excited a downwelling Kelvin wave front responsible for the deep model pycnocline (Fig. 4 ) corresponding with observed elevated sea level (Fig. 3 ) along the eastern boundary in June.

During the

latter half of the year an intensification-relaxation sequence at 1OOW-140W was responsible for the second downwelling peak at the end of 1972.

Recovery

from the 1 9 7 2 El Nino began with strengthening trades in January of 1973. The trade winds west of the dateline began decreasing in September of 1974 and continued until January, 1975. change appreciably.

The winds in the central Pacific did not

The resulting downwelling Kelvin wave front induced the

deep pycnocline in the east at the beginning of 1975.

As opposed to 1 9 7 2 , the

trades in the western and central Pacific did not continue to weaken.

An

intensification of the easterlies beginning west of the dateline in January and east of the dateline in March produced a rapid recovery from the downwelling at the beginning of the year.

A persistently deep pycnocline was not

present at the eastern boundary in 1975.

Consistent with observations, the

event in early 1975 never matured into an El Nino. The onset of the 1976 El Nino began when the winds west of 160°E started decreasing in October of 1975.

An eastward progression of this weakening

transpired similar to the wind changes in 1972.

A more rapid decrease in the

trades between 140°W and the dateline during the first four months of 1976 was again responsible for the large downwelling peak in June of the El Nino year. Continued weakening between 16OOW and 140°W produced the last downwelling pulse of the El Nino year.

The zonal wind stress remained weak up until

December. Recovery from the 1976 El Nino began with a short period of intensified easterlies between 14OoW and 180° (Wyrtki, 1 9 7 9 ) .

The subsequent

upwelling Kelvin wave front produced shallow pycnocline depths along the eastern boundary during the first half of 1977. Comparisons of the simulated El Nino events of 1972 and 1976 with those of 1965 and 1969 yield an important difference.

The model pycnocline variability

during Los Ninos of the 1 9 6 0 ' s were comprised of pycnocline depth maxima at the beginning and end of the El Nino year.

In the middle of the El Nino year

the pycnocline was not significantly deep.

On the contrary, during the 1972

and 1976 El Nino events the maximum pycnocline depth was attained in June. The reasons for this difference bear out the uniqueness of each El Nino.

172 The central equatorial easterlies during the 1970's had a significantly greater impact on the eastern boundary variability than in 1965 or 1969. The downwelling pulses at the beginning of 1965 and 1969 were due to weakening trades in the western Pacific during the four preceding months. During this same period the winds in the central Pacific did not intensify. Similar conditions were present at the beginning of 1975 and 1976; years in which the pycnocline was deep in January. A deep pycnocline did not exist at the beginning of 1972 because the easterlies in the central Pacific intensified in late 1971 while the winds west of the dateline were changing from easterly to westerly. From January to April of 1972 and 1976 the central equatorial easterlies decreased markedly. This resulted in the deep pycnocline along the eastern boundary in June.

During the first four months of 1965 and 1969 the

central equatorial trade winds did not weaken noticeably. Hence, the In 1975 the trade winds

pycnocline was not deep in mid-1965 or mid-1969.

intensified and were anomalously strong for the entire year resulting in a rapid upwelling from an initially deep pycnocline. WESTERN PACIFIC RESPONSE Since Wyrtki (1975) proposed a scenario of El Nino it has been thought that, due to strong easterlies, sea level in the'western tropical Pacific was deserving of attention in the year preceding El Nino. However, as Meyers (1982) recently reported, and, as shown in Fig. 10, the sea level change at Truk Island is much more dramatic in El Nino years themselves. The sea level record at Truk Island is presented because it is representative of the interannual changes in the western Pacific and is one of the longest time series available. In every year classed as an "El Nino year" for the period 1961-1978, a significant drop of the sea level is observed in the latter half of the year. Sustained significantly high sea levels are not necessarily observed in the year previous to every El Nino. Nino years have a common pattern.

The decreases in sea level at Truk during El They begin in late winter or spring

In most cases (1963, 1969, 1972 and 1976) an initial sea The lowest sea level, as low as 20 cm below the annual average, is reached at the end of the year. This is followed by a rapid recovery within the next few months, usually from January to April of the following year. Wyrtki (1979) examined the sea levels at widely scattered islands in the western Pacific Ocean for the 1976 El Nino event. Widespread low sea levels (February-May).

level minimum is attained in the middle of the year (June-September).

in the western tropical Pacific for the second half of the year were evident. The maximum sea level decrease was within a zonal band at 50N-10°N.

This

indicates that Truk Island is located in an advantageous position to monitor

173

m

m

P

I

d

m

iD

4 d

rd

5

H

m

d

F

5

m

m Q

i 0

174

_. m

d

m

ci

4

w

m

175 the sea level change during El Nino years.

The sea level excursions in the

Southern Hemisphere are much smaller. The time series of the model pycnocline displacement at the location of Truk Island is depicted in Fig. 11. several shallow pycnocline events.

The time series is characterized by Except for 1966, these events occur during

the latter half of an El Nino year and correspond well to the sea level time series at Truk (Fig. 10).

Note again a shallow pycnocline (positive PHA)

corresponds to low sea level.

A s expected from this comparison, the

correlation between the observed sea level and the model pycnocline at Truk has a maximum as high as 0.76 at zero lag. The spatial distribution of the anomalous model pycnocline depths in an El Nino year is also in agreement with the observations. Fig. 12 shows the difference in depth of the model pycnocline for the western Pacific between October, 1976 and October, 1975.

The spatial structure of the change in

pycnocline depth agrees with the observations shown by Wyrtki (1979, Fig. 7) except for the region close to the northern open boundary of the model. maximum pycnocline rise is also found around 50N-10°N.

The

A smaller maximum is

found in the southern hemisphere near the western boundary.

Fig. 12. The change in upper layer thickness from October, 1975 to October, 1976 in the western portion of the model domain. The stipled regions indicate where the pycnocline was shallower in October, 1976. Contour interval is 10 m. A Y-T diagram of the model pycnocline at 160°E for the period 1971 to 1977

(Fig. 13) is convenient for examining the meridional distribution of the shallow pycnocline during El Nino years.

The longitude 160°E is selected to

avoid the effects of the western boundary in the Southern Hemisphere.

It is

not considered inadequate to choose 160°E as being representative of the

176

Fig. 13. A Y-T section of the pycnocline height anomaly along 160°E for 1971 to 1978. White regions indicate the model pycnocline is shallower than the 18-year mean. Contour interval is 15 m.

171 western tropical Pacific since the model pycnocline variability at 7.S0N, 160°E, has a similar time series to that of Truk Island. In both the 1972 and 1976 cases the maximum positive pycnocline anomalies

take place around 7ON.

Anomalies in the Southern Hemisphere are smaller for

both El Nino events. Also common to both events are smaller positive anomalies found in both hemispheres 3-4 months prior to the main peaks.

The

latitudes of the smaller anomalies are 4 O to 6O from the equator depending on the event and the hemisphere, but always closer to the equator than the maximum anomalies. These earlier periods of shallow pycnocline depth are more symmetric to the equator than the latter ones and represent the initial shallowing of the pycnocline at Truk Island. The maximum positive anomaly at 7ON corresponds to the period when the pycnocline was shallow at Truk near the end of the El Nino year.

This pattern of pycnocline depth change is not as

evident in the El Nino events of the 1960's. For example, during the 1965 El Nino the maximum positive pycnocline anomalies are more symmetric to the equator. However, it can be stated that the Y-T pattern of the shallow pycnocline anomaly near 7ON late in the year is typical of an El Nino year for the 18-year record studied here. A matrix of lagged cross correlations between Truk Island and all points

along 7.5ON (Fig. 14) shows the pycnocline variability at Truk lagging that to the east.

The inclination of maximum positive correlations represents a

westward propagation of the pycnocline signal at approximately 40 cm s-'. This compares favorably with the 35 cm s-l phase speed for third latitudinal mode Rossby waves in this calculation. Projection of the meridional pycnocline structure onto the free modes of the system indicates the dominant response at Truk is due to third-mode Rossby waves.

Depending on the event, the

variability at Truk may also be influenced by first, second, and fourth mode Rossby waves. A s discussed in the previous section, relaxation of the easterlies takes

place in the central and western Pacific during El Nino.

It is suspected that

the wind changes that are responsible for high sea level in the eastern equatorial Pacific through the generation of equatorial Kelvin waves may also be responsible for low sea level in the western tropical Pacific through the generation of Rossby waves at the same time. McCreary (1977) showed that the onset of westerlies, which is equivalent to the relaxation of easterlies in linear theory, generates an eastwardpropagating, downwelling, equatorial Kelvin wave front and a westwardpropagating, upwelling, Rossby wave front which has minimum pressure on both sides of the equator. Therefore, it seems quite reasonable to attribute the decrease of sea level in the western tropical Pacific to the relaxation of the easterlies.

This would also explain the negative correlation between the

-18

- 12

-6

TRUK LAGS

0 6 LAG (MONTHS)

12

18

TRUK LEADS

Fig. 14. Contours of lagged cross correlation between the model pycnocline variability at Truk Island and all points east and west along 7.5ON.

179

equatorial eastern boundary and western boundary variability (Fig. 7).

The

maximum cross correlation between the non-seasonal model pycnocline signal at Truk and Galapagos is also negative and occurs when Galapagos leads by a few months. In McCreary's study, the wind stress and the resultant sea level distribu-

tion was symmetric to the equator. The observed sea level and the model pycnocline fluctuations, however, are not symmetric to the equator.

This

suggests that the relaxation of the easterlies may not be symmetric to the equator. To judge if this is true the meridional distribution of the wind stress variability is examined next. Only the zonal component of the wind stress is considered because it is more important in forcing low frequency motion in the equatorial ocean. This is supported by the test calculation when the model was forced only by the zonal wind stress. At Truk the pycnocline response to zonal forcing was very similar to that for the full model calculation forced by both zonal and meridional components. The meridional structure of the zonal wind stress variability is obtained by averaging the annual anomalies of the zonal wind stress between 160°E and 14OOW for 1971 to 1978 (Fig. 15).

The longitudinal

range is chosen to include the major wind stress changes in the El Nino years. The width of each wind event is 300-400 of longitude. The area west of 160°E is omitted because long Rossby waves generated there have no influence

eastward. The winds are predominantly easterly for the range 160E-l40W, so positive values in Fig. 15 indicate weakened easterlies. The seasonal variations are obvious and are basically out of phase between the hemispheres; the weakest easterlies occur in the second half of each year in the Northern Hemisphere and in the earlier half of each year in the Southern Hemisphere.

In 1972 and

1976, the weakening of the easterlies in the Northern Hemisphere was larger and the area of weakening (50N-10°N) was closer to the equator. The easterlies at the equator were also weaker than usual beyond March. Does such a distribution of decreasing easterlies cause the pressure field distribution found in Fig. 13? The response of the ocean to an idealized wind forcing event is calculated to determine this. An eastward wind stress which has a Y-T pattern shown in Fig. 16a, constant in the zonal direction between two meridions, and zero outside of it is assumed. The width of the region is taken to be 3300 km, corresponding to about 30° of longitude. This idealized forcing is a crude approximation of the relaxation and recovery phase of the northeast trades during the 1972 and 1976 Los Ninos. assumed to be at rest.

Initially the ocean is

The Y-T distribution of pressure along the meridion at

the west end of the forcing region is calculated and shown in Fig. 16b. The geostrophic balance is assumed for the zonal momentum equation. Forcing

180

Fig. 15. A Y-T diagram of the zonal wind stress averaged over 160°E-1400W for 1971-1978. White regions indicate the easterlies are weaker (westerly anomaly) than the lonq-term annual mean. Contour interval is .25 dynes cm-?.

181 functions for equatorial Rossby modes are calculated analytically and integrated numerically along the characteristics of each mode. The response to the idealized forcing (Fig. 16b) has some similarities with the modelled response of the western tropical Pacific in El Nino years (Fig. 13). The response has a peak in each hemisphere although the wind forcing is mostly in the Northern Hemisphere. The largest response is north of the equator. The minimum pycnocline depth appears around 7ON, about 1.5 months after the wind forcing minimum.

This supports the idea which

attributes sea level anomalies in the western tropical Pacific in the latter half of the El Nino year to the weakening of easterlies centered north of the equator.

-205 155

IOS

5s

EQ

5N

ION ISN 20N

Fig. 16. Idealized model of the response of the tropical ocean to the westerly wind stress anomaly confined within two meridians 30° apart. a) Y-T dia ram of the wind stress forcing function. Contour interval is .2 dynes cmb) Y-T diagram of the pycnocline response along the western edge of the forcing region. Contour interval is 10 m.

s.

The response of the model ocean is fairly sensitive to the location of the wind forcing.

If the center of the forcing shifts northward to around

182 l W N , similar to the location for the center of normal seasonal weakening, the lowlatitude response becomes considerably smaller and the maximum response

shifts northward more than the shift of the wind forcing (Fig. 17).

In this

case the forced motion is more like mid-latitude Rossby waves than equatorial Rossby waves. Also, it may explain why the relaxation of the easterlies found in the latter half of most years produces only a small response in the low latitudes of the western tropical Pacific except in El Nino years.

M F J

I

(6)PHA

20s 15s 10s 5s Fig. 17.

D

EQ

5N

ION 15N 20N

Same as Fig. 16 except the forcing is shifted northward by 3 O .

Four or five months prior to the main weakening of the northeast trades, weakened easterlies exist about the equator in both 1972 and 1976 (Fig. 15). Since the wind anomalies are maximum near the equator, the response of the ocean should be symmetric to the equator. Late in the El Nino year the relaxation of the northeast trades is followed by strong westward anomalies. The switch from eastward to westward anomalies takes place very rapidly. This rapid recovery of the easterlies, along with the earlier eastward anomalies near the equator, might provide a more complete description of the typical sea

183 level change at Truk Island during an El Nino event, i.e.,

a two-step drop in

sea level during the El Nino year with lowest sea level occurring at the end of the year followed by a rapid rising.

20s 15s

IOS

5s EQ

5N

ION

15N 20N

20s 15s

IOS

5s

5N

ION

15N 20N

EQ

Fig. 18. Similar to Figure 16 but the forcing function is now preceeded by an equatorial relaxation sequence and followed by an intensification of the trades (stipled) late in the year. Another idealized forcing calculation is performed in which there are minimum easterlies at the equator in April, minimum northeast trades in September, followed by a rapid strengthening yielding anomalously strong northeast trades in the following January and February (Fig. 18a).

The

resulting pycnocline response (Fig. 18b) is initially symmetric about the equator with minimum pycnocline depths at ?5' in May-June. The remainder of the response is not symmetric to the equator whereby the pycnocline depth minimum is located at 9 ' N

in November. This compares favorably with the

shallow pycnocline depths of the 1972 and 1976 events depicted in Fig. 13. The pycnocline response (Fig. 18b) at 7.5%

is also similar to that at Truk Island

184 during an El Nino year (Fig. 11).

There is an initial shoaling of the

pycnocline from March to May, followed by a few months during which there is a slight increase in pycnocline depth, further rising of the pycnocline until October-November, and a final rapid increase in pycnocline depth. CENTRAL EQUATORIAL RESPONSE The two previous sections have demonstrated that for 1961-1978 the variability in the eastern tropical Pacific may be influenced by equatorially trapped Kelvin waves and the western tropical Pacific may be influenced by westward-propagating Rossby waves.

In the central equatorial Pacific there

are not many long-term observations. The sea level data at Canton and Christmas Islands are among the few available. Unfortunately, the time series are not continuous and do not cover the entire 18 years of interest. Furthermore, data is missing during several El Nino events. Nonetheless, the most significant features are high sea levels at both islands during the second half of an El Nino year.

Smaller high sea level peaks are often found

at the begining of an El Nino year. A lagged cross correlation with the model pycnocline time series is impossible because of the data gaps in the sea level record. A zero lag cross correlation can be performed if the sea level observations are concatenated and then correlated with the corresponding points in time for the model pycnocline record.

The zero lag cross

correlations are 0 . 4 0 at Canton and 0.67 at Christmas Island. Instead of comparing the observed sea level and model pycnocline variations, it is of interest to know the relationship of these variations at Christmas and Canton to those in the eastern and western Pacific discussed in the previous sections. This may aid future analyses of sea level records when complete time series become available. The location of these two islands are opportune for two reasons. First, longitudinally the islands are in a region where there are important wind stress changes to the east and west.

The sea

levels at these islands may therefore be affected by both Kelvin waves generated west of the islands and Rossby waves generated east of the islands. Second, latitudinally these islands are situated where both Kelvin waves and first-mode Rossby waves have relatively high amplitudes in the pressure field. For the baroclinic phase speed chosen in this study the equatorial radius of deformation is 327 km.

At the latitudes of Christmas, 1°59'N, and Canton,

2O48'S, sea level variations due to an equatorial Kelvin wave are 80% and 64% of that at the equator, respectively.

At low frequencies, the first-mode

equatorial Rossby wave has its maximum pressure field amplitude at f3.6O from the equator.

The amplitude of Rossby wave pressure variations at Christmas

and Canton are 80% and 95% of the maximum, respectively. Therefore, it is suggested that the sea level variations at these islands are strongly

185 influenced by both Kelvin and first-mode Rossby waves.

It is impossible to

separate Kelvin and Rossby signals from the observed sea levels at these islands. Fortunately, the model pycnocline variability is similar at times with the observed sea level.

It is possible to get some hint of the

contributions of Kelvin and Rossby waves to the sea level variations by projecting the model pycnocline structure onto the Kelvin and Rossby wave components. In Fig. 19 and 20, Kelvin and first-mode Rossby wave components of the model pycnocline are plotted for the 1965 El Nino event at Canton and Christmas. Most of the variations of the model pycnocline at both islands are attributed to Kelvin waves and first-mode Rossby waves.

The pycnocline

variability at Christmas Island contains more Kelvin wave signal than at Canton. islands.

This can be explained by considering the locations of the two Since Christmas Island is located closer to the equator than Canton,

if the amplitudes of the Kelvin waves at the longitudes of these islands are

the same, Christmas Island would experience a stronger Kelvin wave signal than would Canton.

In addition, the longitudinal location of these islands can

also lead to stronger Kelvin signals at Christmas since the Kelvin waves

generated between the longitudes of Canton and Christmas only reach Christmas Island. By similar reasoning, Canton Island is likely to receive larger Rossby signals than Christmas if the Rossby waves generated between the islands add constructively. For the 1965 El Nino, the downwelling peak at the beginning of the year The shallow

at both islands is primarily due to the Kelvin wave component.

pycnocline in March-April is greatly influenced by the upwelling Rossby wave front discussed in the previous section. occurs in the second half of the year.

Another deep pycnocline episode However, in this latter downwelling

event, the first-mode Rossby wave component shares the role of depressing the pycnocline. At Christmas Island, the downwelling peaks of the Kelvin wave component and first-mode Rossby wave component have a slight time lag and result in a double peak in the pycnocline variability.

This feature is also

present in the observed sea level record. The temporal variation of the Kelvin wave component at these two islands is similar at a slight time lag. The variability at Galapagos Island is also similar at a lag of about 1.5 months.

The downwelling peak of the Kelvin wave

component at the beginning of the year does not change much in amplitude as it passes Canton, Christmas, and Galapagos.

The peak later in the year grows in

amplitude as it passes Canton, Christmas, and Galapagos. This suggests the forcing region of the Kelvin wave front responsible for the deep pycnocline in the beginning of the year is west of the forcing region for the Kelvin wave front excited later in the year. This is common among many El Nino events in

186 I 1 I I I I I 1 I I I

I

I I I I I I I I I I I 1 I 1 I II I I I I I I

(A 1 KELVIN t I ST ROSSBY-

1 (C) I ST

64

ROSSBY

65

66

Fig. 19. Kelvin and first-mode equatorial Rossby wave components (solid) of the model pycnocline signal (dashed) at Canton Island for 1964 to 1966. a) Kelvin plus first-mode Rossby wave compared with the pycnocline signal. b) Kelvin wave compared with the pycnocline signal. c) First-mode Rossby wave compared with the pycnocline signal.

( A ) KELVINt I ST ROS 20

M O -20 20

M O -20

1 (C) I S T ROSSBY

Fig. 20.

Same as Fig. 19 except at Christmas Island.

4

187 this 18-year period and consistent with the previous identification of the forcing regions. The 1972 El Nino event (Fig. 21) provides another interesting example of the relationship between the effects of the Kelvin waves and the Rossby waves. In this event the Kelvin wave component exhibits two downwelling peaks: the beginning and middle of the year.

at

The initial downwelling Kelvin wave

signal of 1972, which emanates in the west, has little influence on the pycnocline depth at Galapagos because of intensified easterlies in the central Pacific. This intensification, from mid-October until the end of 1971, is responsible for a downwelling Rossby wave response at Canton at the beginning of 1972.

The Kelvin wave peak later in the year is not found in the total

pycnocline signal at Canton because the Kelvin wave component is canceled out by an upwelling first-mode Rossby wave contribution. At Galapagos, this second Kelvin wave signal is no longer affected by a Rossby wave and thereby contributes to a deep pycnocline in June.

The large downwelling at the end of

1972 is mainly a Rossby wave response.

I-

k

Fig. 21.

-I

(C) I ST ROSSBY

Same as Fig. 19 except from 1971-1973.

It appears there may be great difficulty in interpreting the sea level data at Canton and Christmas Islands due to the interplay between Kelvin waves and Rossby waves from one event to the next.

This is also evident if

the 18-year pycnocline records for all points along a longitude representative

188 of Canton or Christmas Island are correlated with the model pycnocline variability at Galapagos. At Zo-3O

from the equator the influence of the

Kelvin waves have been reduced enough that the resulting maximum positive correlation when the central Pacific leads Galapagos is comparable to the maximum negative correlation due to Rossby waves when the central Pacific variability lags Galapagos. At times the sea level data of these islands can be used to discuss the passage of Kelvin waves.

However, the present study

suggests a strong influence of the first-mode equatorial Rossby waves at these islands. In order to fully understand the processes responsible for the observed sea level variability at these islands, it is necessary to know the sea level and wind stress variability to the east and west or the meridional structure of the sea level variability.

SUMMARY AND CONCLUSIONS The results of a linear, wind-driven, numerical model have been used to study the interannual variability of the eastern, central equatorial, and western Pacific for a span of 18 years.

The model was forced by monthly

estimates of the observed surface wind field over the tropical Pacific for 1961-1978.

Such a model provides a straightforward way of assessing the

basin-wide response to the overlying wind field in a manner that would not be possible by studying the wind field variability. period of study were several Los Ninos.

Of interest during the

The character of these events in the

model results and the nature of the forcing were described. The model pycnocline variability in the eastern Pacific was induced by internal equatorially trapped Kelvin waves excited by fluctuations in the zonal wind stress at the equator in the western and central Pacific. The model pycnocline variability at the Galapagos Islands was remarkably similar to the observed sea level variability there.

Cross correlation between the

model pycnocline variability and observed sea level indicated a maximum significant correlation at zero lag.

One important discrepancy between the

model pycnocline time series and observed sea level was the presence of more high frequency fluctuations in the pycnocline record.

This is to be expected

since the temporal resolution of the model pycnocline time series is much greater than the monthly sea level record.

Furthermore, in this single mode

calculation the time scales of the upwelling and downwelling episodes in the east are indicative of the time and spatial scales of the wind changes to the west.

The addition of slower higher order vertical modes may lead to longer

duration events. Another possible reason for this discrepancy may be that the wind estimates used have more power at high frequencies than the actual wind field.

189

The five Los Ninos years of 1963, 1965, 1969, 1972 and 1976, were depicted as years when the pycnocline was anomalously deep.

Los Ninos of 1965 and 1969

have been classified as being the strongest for the 1960's.

The variability

of the southeast trades on both sides of the dateline was the cause of these events in the model.

The onset of El Nino was due to the excitation of a

large amplitude downwelling Kelvin wave front west of 180O. This Kelvin wave front was excited by a 0.4 dynes cm-2 relaxation of the easterly wind stress during the latter half of the year preceding El Nino.

The relaxation in 1964

and 1968 was so large that the zonal wind stress changed from easterly to westerly. The timing of this Kelvin wave is such that it enhanced the remotely forced seasonal downwelling at the eastern boundary. Besides the initial downwelling impulse, the El Nino year was characterized by the persistence of a downwelled pycnocline. The pycnocline remained deep because the seasonal intensification of the central Pacific easterlies was not as strong as during non-El Nino years. The upwelling Kelvin waves excited were small in amplitude. Hence, the pycnocline was not significantly upwelled.

This lack of a normal seasonal upwelling kept

the pycnocline deeper than normal throughout the El Nino year.

Towards the

end of the El Nino year the semiannual variability of the interior easterlies was reestablished. The resulting downwelling Kelvin wave front generated towards the end of the year created the second major downwelling pulse of the El Nino year. This completed the double-peak downwelling signature characteristic of the 1965 and 1969 El Nino events.

In contrast, the minor El Nino of 1963 was only influenced by the wind During 1962 there was not a large

stress variability east of 180'.

relaxation of the wind field west of the dateline. After the seasonal downwelling at the beginning of 1963 there was a cessation of the semiannual intensification of the southeast trades. The pycnocline remained depressed throughout 1963 and did not recover until 1964. Anomalous changes in the wind field leading up to the model expression of the 1972 El Nino began with an eastward progression of weakening trade winds west of the dateline in late 1971.

A nearly simultaneous intensification of

the central equatorial easterlies negated any influence from the west.

This

resulted in mean annual pycnocline depths at the eastern boundary in early 1972.

From January through April a significant decrease of the zonal wind

stress between 120% and 180" excited a downwelling Kelvin wave front responsible for deep pycnocline depths at the eastern boundary in June. Observations indicated unusually high sea level for the same period.

Late in

the year, a relaxation of the easterlies at 10OoW-14O0W created a second downwelling episode, smaller relative to that in June.

A second peak in sea

190 level was observed at the end of the year.

Intensification of the trade winds

in January of 1973 led to a recovery from the 1972 El Nino. Wind changes and their effects associated with the 1976 El Nino were similar to 1972. An eastward progression of weakening trade winds began west of 160°E in late 1975 and generated a downwelling Kelvin wave front.

As

opposed to late 1971, the winds in the central Pacific did not intensify. Thus, the model pycnocline was deep along the eastern boundary at the beginning of 1976.

A decrease in the equatorial easterlies between 14OoW and

180° during the first several months of 1976 was once again responsible for the deep model pycnocline at the eastern boundary in June of the El Nino year. Additional weakening of the wind stress in the central Pacific produced a final downwelling burst later in the year.

The recovery phase began with

intensified easterlies in December. There was one major difference between the simulated Los Ninos of the 1970's and those of 1965 and 1969. For the 1960's events, observed sea level was highest and the model pycnocline was deepest towards the beginning and end of the El Nino year in the eastern Pacific.

During the 1972 and 1976 El Nino

occurrences, elevated sea level and maximum pycnocline depth were in June.

Common to all these events was a weakening of the trade winds west of the dateline late in the preceding year.

The model pycnocline was deep in June of

1972 and 1976 because the central equatorial easterlies had decreased considerably from January to April.

The pycnocline was not deep in mid-1965

or mid-1969 because the trade winds in the central Pacific did not weaken during the first four months of the year.

Thus, during the 1970's the

easterlies in the central equatorial Pacific had more of an active role in the evolution of El Nino than in the previous decade.

This in turn implies there

are important differences in the location and timing of the wind changes responsible for each El Nino. The season in which an anomalously deep pycnocline occurs might have important ramifications for determining the size of anomalous SST.

For the El

Nino events of the 1960's the model pycnocline was anomalously deep during the periods of seasonal warming in the Southern Hemisphere. For the El Nino events of the 1970's the pycnocline was deepest during the cool SST season and SST anomalies were larger than in the previous decade.

Does a depression of

the thermocline during the auroral fall and winter result in a larger positive SST anomaly than a thermocline depression in summer? Modelling efforts including thermodynamics will provide the information needed to understand relations between thermocline depth, vertical velocity, and SST. The El Nino sequence of initial wind relaxation west of the dateline followed by weakening or quiescent winds in the central Pacific did not apply to 1975. This event began when winds west of the dateline decreased in late

191 1974 similar to the type of relaxation prior to an El Nino. A downwelling Kelvin wave was excited and resulted in a deep pycnocline at the eastern boundary in early 1975.

The similarity with an El Nino event stopped there.

After the initial weakening, the winds intensified and remained anomalously strong for the remainder of the year. At the eastern boundary, there was a rapid upwelling and the model pycnocline remained shallow. Hydrographic observations in the eastern Pacific indicated El Nino type conditions were present at the beginning of 1975 but soon deteriorated (Wyrtki et al., 1976). The interannual variability in the western tropical Pacific was characterized by a shoaling of the model pycnocline and an observed drop in sea level in all El Nino years. Maximum changes in model pycnocline depth and observed sea level occurred at 50N-10°N. Truk Island at 7.5ON, 151.9OE is in a strategic position to monitor these fluctuations. The model pycnocline time

series at Truk was highly correlated at zero lag with the observed sea level record. A majority of the pycnocline variability at Truk was due to westwardpropagating, third latitudinal mode Rossby waves. The shallow pycnocline and low sea level at the end of the El Nino year was attributed to an upwelling Rossby wave front excited by a decrease in the trade winds to the east. Related wind changes at the equator were responsible for downwelling at the eastern boundary in the middle and end of the El Nino year.

This accounts for the out of phase relation between the eastern and

western tropical Pacific during the El Nino simulations. The meridional structure of the zonal wind stress variability between 160E and 140W indicated that the largest perturbation to the wind field during El Nino was not symmetric about the equator and involved the northeast trades. The seasonal weakening of the northeast trades was larger in area and closer to the equator (5'N-10°N)

during the 1972 and 1976 Los Ninos.

A simple

analytical model forced by an idealization of this weakening yielded an upwelling Rossby wave response in both hemispheres west of the forcing with maximum upwelling at 7ON, 1.5 months after the minimum wind forcing.

When the

idealized forcing consisted of decreasing southeast trades symmetric about the equator at the beginning of the El Nino year, followed by the El Nino weakening of the northeast trades, and a subsequent recovery of the northeast trades, the response at 7°N-80N was in qualitative agreement with the pycnocline variability at Truk during the 1972 and 1976 events. The oceanic response is strongly dependent on the location of the weakened trade winds. This may account for differences between the seasonal and nonseasonal response in the western tropical Pacific. When the center of the northeast trade wind forcing was shifted to 10°N, similar to the normal location of the maximum seasonal weakening, the low-latitude response was considerably smaller and the maximum response was displaced northward more than the shift of the forcing.

192

In the central equatorial Pacific, limited sea level records were available for Canton Island and Christmas Island. This is an area for which there are important wind changes to the east and west during E l Nino.

These

islands are therefore subject to the influence of equatorially trapped Kelvin waves excited to the west and long Rossby waves generated to the east. these islands are located 2 O - 3 0

Since

from the equator, the Kelvin wave amplitude is

reduced and the Rossby wave amplitude is increased relative to that at the equator.

Decomposition of the model pycnocline variability at these islands

indicated that almost all of the signal was due to Kelvin waves and first latitudinal mode Rossby waves.

The superposition of Kelvin and Rossby waves

during E l Nino changes from one event to another depending on the location and timing of the forcings. Analysis of sea level variability in the central equatorial Pacific is therefore difficult because Kelvin wave signals generated in the west and ultimately causing pycnocline displacements in the east may be masked temporarily by a superposition with Rossby waves of opposite sign. Even though all Los Ninos events are unique, a few generalizations are in order. The results of the numerical model demonstrate that interannual changes of the zonal wind stress in the central and western Pacific are very important in determining the sea level/pycnocline responses of El Nino.

For

most Los Ninos during the period of study the onset phase was linked to perturbations to the zonal wind field in the western Pacific. How the El Nino event progressed and matured was subsequently determined by the nature of the wind field in the central Pacific. Recently, it was noted (Keen, 1982) that there is often a greater incidence of tropical cyclone pairs in the western Pacific prior to El Nino.

A succession of these disturbances, at times

penetrating east of 1800, results in strong eastward perturbations to the wind field several times per month.

In the future it will be necessary to

determine how these high frequency disturbances affect the wind field monthly It would be of interest to know how the model results would change if

means.

there was a greater temporal resolution of the wind field. The results of this numerical simulation have also provided some information regarding monitoring the tropical Pacific wind field. In view of the correlations between the model results and observations at several locations, important fluctuations in the low-latitude surface wind field must have been large enough in space and time to have been resolved by ship-board estimates. Admittedly, there are several problems with this method of observing the wind field. Yet it is the only data set available suitable for interannual modelling studies. Nonetheless, this study has demonstrated a definite need for continuous monitoring of the detailed structure of the entire tropical Pacific wind field.

193

With respect to real-time wind monitoring, the simulations of the El Nino events for 1961-1978 indicate that a predictive capability for El Nino will not be straightforward. At the present time, persistence of anomalous conditions in the tropical atmosphere cannot be predicted.

An example of why

this is important is the aborted event of 1975 when the winds in the western Pacific initially weakened in a manner similar to the onset of previous El Nino events. Shortly thereafter the winds abruptly intensified and remained strong. Monitoring a significant wind relaxation without knowledge of a subsequent intensification may lead to an erroneous El Nino prediction. Furthermore, equal weight must be given to all regions when monitoring the tropical Pacific wind field.

As illustrated by the conditions during the

first several months of 1972, an anomalous decrease in the trade winds in the western Pacific may be followed by an intensification of the winds in the central Pacific.

The net result of such circumstances being no change in the

eastern Pacific. The wind-driven modelling results presented here have shown that a significant amount of the observed interannual sea level variability in the eastern, central equatorial, and western Pacific can be accounted for by linear theory when reasonable estimates of the wind field are provided. Internal Kelvin and Rossby waves play important roles in determining the variability throughout the tropical Pacific.

Drastic shoaling of the

pycnocline in the western Pacific during El Nino may be induced by Rossby waves excited by changes in strength and position of the northeast trades.

In the eastern tropical Pacific, remotely forced Kelvin waves generated in the central and western equatorial Pacific are responsible for the El Nino pycnocline displacements.

By definition El Nino is associated with warm SST

but at present the cause and effect relation of a Kelvin wave induced deep thermocline and SST is not understood. ACKNOWLEDGMENTS This work was supported by the National Science Foundation under grants ATM7920485 and OCE8119052.

Computations were performed at the National Center

for Atmospheric Research and the Florida State University Computation Center. We gratefully acknowledge the many persons involved in the wind data analysis. Special thanks to Pat Teaf for manuscript preparation. kindly provided by Dewey Rudd and Roberta Scott.

Drafting services were

Contribution number 187 of

the Geophysical Fluid Dynamics Institute, The Florida State University, and contribution number 15 to PEQUOD.

194

REFERENCES Barnett, T. P., 1977. An attempt to verify some theories of El Nino. J. Phys. Oceanogr., 7: 633-647. Busalacchi, A. J., and J. J. O'Brien, 1980. The seasonal variability in a model of the Tropical Pacific. J. Phys. Oceanogr., 10: 1929-1951. Camerlengo, A. L., and J. J. O'Brien, 1980. Open boundary conditions in rotating fluids. J. Comp. Phys., 35: 12-35. Davis, R. E., 1976. Predictability of sea surface temperature and sea level pressure anomalies over the North Pacific Ocean, J. Phys. Oceanogr., 6: 249-266.

Enfield, D. B., and J. S. Allen, 1980. On the structure and dynamics of monthly mean sea level anomalies along the Pacific coast of North and South America. J. Phys. Oceanogr., 10: 557-578. Goldenberg, S. B., and J. J. O'Brien, 1981. Time and space variability of tropical Pacific wind stress. Mon. Wea. Rev., 109: 1190-1207. Hickey, B., 1975. The relationship between fluctuations in sea level, wind stress and sea surface temperature in the equatorial Pacific, J. Phys. Oceanogr., 5: 460-475. Hurlburt, H. E., 1974. The influence of coastline geometry and bottom topography on the eastern ocean circulation. Ph.D. dissertation, Florida State University, 104 pp. Hurlburt, H. E., J. C. Kindle and J. J. O'Brien, 1976. A numerical simulation of the onset of El Nino. J. Phys. Oceanogr., 6: 621-631. Keen, R. A., 1982. The role of cross-equatorial tropical cyclone pairs in the Southern Oscillation, Mon. Wea. Rev., in press. Kidson, J. W., 1975: Tropical eigenvector analysis and the southern oscillation, Mon. Wea. Rev., 103: 187-196. Seasonal and El Kindle, J. C., 1979. Equatorial Pacific Ocean variability Nino time scales. Ph.D. dissertation, Florida State University, 134 pp. Knox, R. A., and D. Halpern, 1982. Long range Kelvin wave propagation of transport variations in Pacific Ocean equatorial currents, J. Mar. Res.,

-

4 0 : 329-339.

McCreary, J., 1976. Eastern tropical response to changing wind systems: with application to El Nino. J. Phys. Oceanogr., 6: 632-645. McCreary, J., 1977: Eastern ocean response to changing wind systems, Ph.D. dissertation, University of California, San Diego. Meyers, G., 1979. Annual variation in the slope of the 14 C isotherm along the equator in the Pacific Ocean. J. Phys. Oceanogr., 9: 885-891. Meyers, G., 1982. Annual and interannual variation in sea level near Truk Island, J. Phys. Oceanogr., 12: 1161-1168. Moore, D. W., 1968. Planetary-gravity waves in an equatorial ocean. Ph.D. thesis, Harvard University, 201 pp. Moore, D. W., and S . G. H. Philander, 1977. Modeling of the tropical oceanic circulation. The Sea, Vol. 6, E. Goldberg, et al., Eds., Wiley-Interscience, 319-361. O'Brien, J. J., A. Busalacchi and J. Kindle, 1981. Ocean models of El Nino. In: Resource Management and Environmental Uncertainty: Lessons from Coastal Upwelling Fisheries. M. H. Glantz and J. D. Thompson, Eds., Wiley-Interscience, 159-212. Orlanski, I., 1976. A simple boundary condition for unbounded hyperbolic flows. J. Comp. Phys., 21: 251-269. Quinn, W. H., 1974: Monitoring and predicting El Nino invasions, J. Appl. Meteor.. 13: 825-830.

195 Quinn, W. H., D. 0 . Zopf, K. S. Short, and R. T. W. Kuu Yang, 1978. Historical trends and statistics of the Southern Oscillation, El Nino and Indonesian droughts. Fish. Bull., 76: 663-678. Romea, R. D., and R. L. Smith, 1982. Further evidence for coastal trapped waves along the Peru coast. Submitted to J. Phys. Oceanogr. Smith, R. L., 1978. Poleward propagating perturbations in currents and sea levels along the Peru coast. J. Geophys. Res., 83: 6083-6092. Wyrtki, K., 1975. El Nino - the dynamic response of the equatorial Pacific Ocean to atmospheric forcing. J. Phys. Oceanogr., 5: 572-584. Wyrtki, K., Sea level during the 1972 El Nino, J. Phys. Oceanogr., 6: 779-787, 1977.

Wyrtki, K., The response of sea surface topography to the 1976 El Nino. J. Phys. Oceanogr., 9: 1223-1231, 1979. Wyrtki, K., Stroup, E., Patzert, W., Williams, R., and Quinn, W., Predicting and observing El Nino, Science, 191: 343-346, 1976.

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197

ON WESTWARD PROPAGATION OF SEA-SURFACE TENPERATURE ANOMALIES IN THE EQUATORIAL PACIFIC ERIC B. KRAUS and HOWARD P. HANSON Cooperative Institute for Research in Environmental Sciences University of Colorado/NOAA, Box 4 4 9 , Boulder, Colorado, USA 80309

ABSTRACT

Sea-surface temperature anomalies in the tropical Pacific, both in the Eastern Pacific coastal areas and in the Central Pacific, have been the focus

of much attention in recent years, the former because of impacts on South American fisheries and the latter as a possible modulator of the North American climate.

The westward spreading of warm anomalies from the South American

coast occurs at speeds of around three times the mean advection rate; the mechanics of this spreading must therefore be associated with dynamic phenomena which propagate westward substantially faster than the surface current.

More-

over, the strength of the anomalies suggests that ocean-atmosphere interactions cannot be ignored as a feature of the overall process. The westward spreading is discussed here in terms of a simple mixed-layer model in the context, first, of a non-rotational equatorial channel model and, second, of the dynamics of the equatorial beta plane.

Model results indicate

substantial enhancement of westward propagation due primarily to the effect on the mixed layer of anomalous air-sea heat fluxes.

Limitations and implications

of the model are discussed, and the need for finite-amplitude (numerical)

investigations is indicated. 1.

INTRODUCTION The so-called Southern Oscillation, specified by a see-saw between the sur-

face pressure anomalies in

the region of Indonesia and Northwest Australia on

the one hand, and those in the Southeast Pacific (Tahiti, Rapa, Easter Island) on the other, is best interpreted as a symptom or index of a global energy

relaxation cycle.

It seems that it involves a quasi-cyclical voiding and fil-

ling of a large oceanic and atmospheric reservoir of thermal and available potential energy.

Though relatively large, the signal associated with the

198 cycle is obscured to some extent by non-linear interactions associated with other energy sources and sinks and by the general climatic noise. no two sequences or episodes are exactly identical. ever, sufficiently pronounced

to

permit

As a result,

The similarities are, how-

the construction of a "typical"

sequence from the composite of a number of cycles.

This was done by Rasmusson

and Carpenter (1982) for the tropical Pacific (30N-30s) sea surface temperature and wind fields.

The characteristic sequence of events in the Western Pacific

has been discussed

by Donguy and Herrin (1980).

Among many other relevant

diagnostic studies, one might quote Julian and Chervin (1978), Horel and Wallace (1981) or Pazan and Meyers (1982). One particular link in the whole sequence of events is the appearance of pronounced warm sea surface temperature anomalies throughout the Central Equatorial

Pacific.

The

climatological importance of

these warm

anomalies has been discussed by Horel and Wallace (&

tit.).

equatorial On the basis

of analytical computations by Hoskins and Karoly (1981), they demonstrated the existence of long wave trains in the upper atmosphere that appear to be forced in the first instance by the anomalous (latent) heat flux from the equatorial ocean. These waves not only modify the tropospheric pressure patterns in a rather persistent manner, but they also can contribute to the transport of atmospheric potential energy in the meridional direction. The appearance of sea surface temperature (SST) anomalies in the Central Equatorial Pacific is commonly (but not always) preceded by the appearance of a pronounced warm anomaly in the Eastern Pacific along the South American coast

--

the so-called El Nizo.

After the high temperatures are observed in the sur-

face waters off Peru, the anomaly seems to spread westward at a rate of about -1 0.5-1.0 m (Rasmusson and Carpenter, loc. cit.). The positive anomalies continue to increase in the Central Equatorial Pacific for 3-6 months following their maximum off the Peru coast.

During the final stages of such a warm

episode, a negative SST anomaly propagates westward from the South American coast at about the same rate as the earlier warm anomaly.

It is with this

westward propagation of sea surface temperature anomalies that this paper is essentially concerned. It seems unlikely that the westward propagation of the anomaly is simply due to advection.

The westward drift of the surface water above the eastern

setting Equatorial Undercurrent has a mean velocity of only about 0.25 m s-l Or less (Bruce Taft, personal communication), which is substantially less than the spreading rate of the anomaly.

It is also very shallow.

At a depth of about

20 m the water tends to move eastward with the Undercurrent.

heat which can be advected westward is correspondingly small.

The amount of If one assumes

that the heat loss to the atmosphere which would be associated with a warm SST

199 anomaly of, say, 3C amounts to no more than 40 IT m-2, reservoir in the top 20 m of 1500 km.

one finds that the heat

will have been practically exhausted over a distance

The distance from the coastal areas off Peru to the dateline is

more than 10,000 km.

It follows that warm anomalies in the Central and Western

Pacific cannot have been kinematically advected there from the South American region.

Their existence and westward propagation must be due to dynamic or

thermodynamic effects. Temperature anomalies can be propagated by waves.

In particular, they can

travel with the phase speed of an "odd" Rossby wave, provided there is a sufficient meridional temperature gradient across the Equator. meridional

In general, the

temperature gradient is too weak to account for the observed

phenomenon, which can involve anomalies of more than 3C.

Anomalies can be pro-

pagated westward also, however, by gravity waves and by "even" Rossby waves, which produce westward moving undulations of the isotherms.

The interpretation

of the westward propagating sea surface temperature changes simply in terms of the phase speed of these waves leaves, however, also a number of problems unanswered. Firstly, the longitudinal extent of the anomalies along the Equator changes with time.

The phenomenon seems to correspond to the spreading of a warm sur-

face layer from the coastal regions of South America until it covers all the Eastern and Central Equatorial Pacific.

Subsequently something like a cold

front appears to move through the same area until the more common equatorial cold tongue has been restored.

While it may be possible to account for these

phenomena in terms of groups o f Rossby waves, we are not aware that this has been done

so

far; it may be difficult to do

so

because part of the group may be

found to carry energy eastward. A second difficulty arises from the fact that the vertical advection velo-

city associated with the waves must become zero at the sea surface.

Surface

temperature changes can therefore be produced only either by horizontal advection or by non-adiabatic processes.

In particular, if the propagating tempera-

ture anomalies are to be associated with westward propagating even Rossby waves, concomitant changes in the vertical heat flux convergence and mixing have to be invoked. wave theory (e.g.,

It is not possible to do this in the framework of linear Moore and Philander, 1977) and the stipulation of a struc-

ture with a variable surface mixed layer becomes convenient in this case. When the mixed layer is deep, entrainment tends to be reduced and the heating by solar radiation of equatorial surface layers i s then enhanced.

When the

mixed layer is shallow, entrainment tends to be more vigorous and the entrained cold

water

is mixed

into a

thinner layer with enhanced cooling.

These

processes imply negative feedback and increased dissipation of the energy of

200 waves associated with vertical displacements at the bottom of the mixed layer. Other feedbacks associated with air-sea interaction processes can independently produce a westward propagation of surface temperature anomalies.

One such

feedback could be caused by changes in the stress and the surface heat flux associated with the passage of the wind over the anomalies.

It is with this

process that the present paper is concerned. We model the ocean's

response to stress and surface heat flux variations

which are associated with a steady easterly wind in the presence of variations in the sea-air temperature difference. typically of the order 5 et al., 1977; O'Brien

The mean zonal wind along the Equator,

s - l , exerts a stress of some 0.04 kg m-l s-2

and Goldenberg, 1982).

friction velocity of about 0.6

cm s-l.

(Katz

This corresponds to an oceanic

At these relatively low wind speeds,

the friction velocity is very sensitive to changes in the air-sea temperature difference, as shown in Fig. 1.

The easterly wind, in passing over the eastern

boundary (Fig. 2, right) of a patch of warm equatorial water, increases the stress, causing divergence, upwelling and also increased wind stirring and entrainment. The resulting cooling will cause the boundary to shift westward. On the westward side of the patch the stress must decrease as the wind moves from a warmer to a

colder

surface, causing divergence and

downwelling.

Entrainment is suppressed, and a new shallower mixed layer is formed and heated by solar radiation, producing a gradual westward extension of the anomaly. Changes in the flux of latent and sensible heat greatly reinforce the mechanical process.

A s cold and relatively dry air moves in over a warmer sur-

face along the eastern boundary, the water below will be cooled by enhanced conduction and evaporation. entrainment.

The resulting convection also can reinforce the

The opposite happens at the western boundary where the air moves

from a warmer to a colder surface. The response of the ocean to these processes is discussed here based on, first, results of a simple non-rotational channel model including mean currents and wind stress variations and, second, the behavior of Rossby waves on the equatorial beta plane as modified by heat flux feedbacks.

Based on the heuris-

tic descriptions of the feedback processes outlined above, one might expect the speed of westward propagating sea surface temperature anomalies to be increased due to the air-sea heat and momentum exchange.

The strength of the ocean's

response would seem to be directly related to the strength of the air-sea coupling; a less obvious, but highly important, parameter measures the strength of the vertical coupling within the ocean (which controls the vertical mixing rate).

In linear equatorial wave theory this is a friction coefficient or eddy

viscosity; in the mixed layer model it is the entrainment rate. siderations anticipate results below.

These con-

A more subtle aspect of the ocean's

201

7-

-5

-4

-3

-2

-I

0

I

2

3

4

5

TS-TA (C)

Figure 1.

Variation of oceanic friction velocity vs.

difference, for various wind speeds, after Kondo's

sea-air

temperature

(1975) parameterization.

From Kraus and Hanson ( 1 9 8 3 ) .

Figure 2.

Schematic diagram of air-sea interaction associated with an anomo-

lous patch of warm water.

gence (C),

divergence (D),

Arrows and symbols represent perturbation conver-

-

and associated vertical motion w

fluxes (F). From Kraus and Hanson ( 1 9 e 3 ) .

,

and heat

202

response involves the interplay of the two quantities which determine the upper-ocean heat content; i.e.,

the upper ocean temperature (the SST in a mixed

layer model) and the mixed layer depth.

Combined, they determine the relevant

pressure variable appearing in the momentum budgets.

However, assumptions

involved in their analytic combination are shown here to mask a response that is significant to westward SST anomaly propagation. 2. 2.1

A NON ROTATIONAL MODEL The Basic State Flow We first consider the efficacy of the processes discussed above in modify-

ing SST anomaly propagation by neglecting cross-equatorial displacements, and focus attention on forces and velocities in the equatorial plane without rotation or meridional motion. The layered structure we use consists of a two-layer ocean with a welldefined surface mixed layer.

This convenient approximation is never exactly

realized along the Equator, where shear turbulence tends to produce a gradual transition from the shallow surface layers to the Undercurrent (Hayes, 1981; Crawford and Osborn, 1979).

The last quoted authors have established, however,

that most of the shear-generated turbulence is dissipated again at the base of the mixed layer.

Because of this they found that a vertically quasi-uniform

temperature distribution tends to exist in the surface layer above.

In our

model the lower layer is infinitely deep with a constant temperature.

Balance

between the zonal pressure gradient and frictional forces allows for an Undercurrent to be driven eastward with a zonally-uniform velocity ub.

The mixed

layer zonal velocity u , depth h and temperature T are assumed to vary.

The

constant lower layer temperature is used as a reference; thus T represents the temperature difference between the two layers.

The flux of buoyancy downward

through the sea surface (F*) represents the sum of the latent, sensible and radiative fluxes; in general at the Equator, the sea is heated and F*

>

0. A t

the interface between the two layers, the entrainment velocity V* is found following Niiler and Kraus ( 1 9 7 7 ) : 3

w*

2Mu, =

c

2

-

[ I - h/L*]

(h/L* < 1)

s(u-ub)

The symbol C represents the velocity of the long internal gravity waves in the

layer, and is proportional to its heat content (hT),

and

203

L"

i s a g e n e r a l i z e d Monin-Obukhov the

fraction

of

mechanical

3

(2)

= -2Mu*/F*

length.

The e m p i r i c a l f a c t o r s M and S measure

e n e r g y which,

after local

dissipation,

remains

a v a i l a b l e f o r l a y e r s t i r r i n g by t h e work of t h e s h e a r s t r e s s e s a t t h e s u r f a c e and t h e l a y e r i n t e r f a c e , r e s p e c t i v e l y .

<

A s u r f a c e l a y e r can be m a i n t a i n e d o n l y i f L*

1.

It f o l l o w s t h a t t h e f a c -

t o r M h a s t o be f a i r l y l a r g e t o g e t a r e a s o n a b l y deep mixed l a y e r when t h e wind i s weak.

Following Turner (1969) we s e t M

v a l u e s proposed by v a r i o u s a u t h o r s .

=

8, r a t h e r on t h e h i g h end of

We a l s o s e t S = 0.1,

90% of t h e t u r b u l e n c e which i s produced by s h e a r a t

which i m p l i e s t h a t

t h e bottom of

t h e mixed

l a y e r i s d i s s i p a t e d and t h a t 10% i s c o n v e r t e d i n t o p o t e n t i a l energy by e n t r a i n ment of d e n s e r w a t e r .

Davis e t a l .

(1981) d e r i v e d v a l u e s of S from t h e Mixed

Layer Experiment r e s u l t s i n t h e North P a c i f i c which v a r i e d between 0. and 0.67. The h i g h v a l u e w a s a s s o c i a t e d w i t h t h e o n s e t of

a s e v e r e storm, and t h e low

v a l u e s corresponded t o p e r i o d s of r e l a t i v e l y low wind.

I t i s t h e l a t t e r case

which i s r e l e v a n t f o r t h e e q u a t o r i a l problem c o n s i d e r e d h e r e .

Lie n o t e t h a t ,

inasmuch a s t h e r e i s r e a l l y no s h a r p v e l o c i t y jump between t h e t o p of t h e Equat o r i a l Undercurrent and t h e s u r f a c e l a y e r , t h e e n t i r e f o r m u l a t i o n i s somewhat unrealistic.

W e have simply t a k e n M and S t o be a d j u s t a b l e p a r a m e t e r s , which

a r e f i t t e d t o p r o v i d e a n a d e q u a t e r e p r e s e n t a t i o n of t h e b a s i c s t a t e . Assuming h y d r o s t a t i c b a l a n c e ,

t h e e q u a t i o n s f o r volume, h e a t and momentum

c o n s e r v a t i o n can be w r i t t e n

-aT =

at

aT ax +

-u-

F*/ag h

- W*T

(4)

204 where a and g are the thermal expansion coefficient ( 3 . x 10-4C-1 and gravity ( 9 . 8 1 m s-'), respectively. The entrainment velocity W* can be eliminated between the last two equations, and, since C2 = qghT, the equations reduce to

&[(~-~~)h]

=

- a

[u(u-ub)h]

- + h

a(c2)

u*2 - R(u-ub). 2

ax

The factor R in the momentum equations (5,5')

(5')

measures the efficacy of loss of

easterly momentum from the upper layer by the downward radiation of internal waves. Rather than integrating Eqs.

(1-5) with appropriate eastern and western

boundary conditions, we find the basic state in the interior, which can then be perturbed by traveling waves, by setting

with analogous formulae for u,T and W*.

Taking the x-axis directed westward

from an mid-oceanic origin, we assume for ho

70 m, uo

=

=

0.25 m s-',

-1

and -1

To = 4. C at x = 0. We further stipulate = -1.2 m s 9 u* = 0.6 cm s (corresponding to a mean surface wind of about 5 m s-l under neutral conditions

-

~ i 1) ~ and . F* = 3 .

about 50. W m-2).

s - ~(corresponding to a mean surface heat input of

These values give W,* = 2.10-6

-1

m s

at

x = 0.

A s long as W* remains finite the layer continues to deepen.

In the present

case, if the wind and surface flux are assumed to remain constant everywhere, the layer deepens asymptotically from ho = 70. m at x = 0. to ho x =

00.

= 120.

m at

On the other hand, a wind speed only 20% lower could not maintain 70.m

deep mixed layer at all, and a new layer about 50.m deep would form. This new

205 i n t e r i o r mixed l a y e r would w a r m up r a p i d l y because t h e e n t r a i n m e n t would be

small and t h e h e a t i n p u t would o c c u r o v e r a s h a l l o w e r l a y e r . 5 i n s t e a d y s t a t e shows t h a t t h e f i r s t and f o u r t h

A scale a n a l y s i s of Eq.

terms a r e more t h a n a n o r d e r of magnitude s m a l l e r t h a t t h e wind s t r e s s t e r m f o r realistic

values

of

h, = 10 m/1000 km = outside

the

gnh0(Th),/uf

boundary =

the second

mean a mean

region

(smoothed)

thermocline

slope.

(see,

e.g.

Fuglister,

1960),

the

With K m-l

t e m p e r a t u r e g r a d i e n t Tx = 0.3

ratio

of

Though t h i s i s n o t i n s i g n i f i c a n t , i t does i n d i c a t e t h a t

0.3.

which

term,

the and

represents

s m a l l e r t h a n t h e s u r f a c e stress.

the pressure force,

remains

considerably

I t f o l l o w s t h a t t h e i n p u t of momentum by t h e

wind must be balanced i n t h i s model l a r g e l y by i n t e r n a l wave r a d i a t i o n l o s s e s a t t h e b a s e of t h e mixed l a y e r . late R = 1.2

U s e of

On t h e b a s i s of t h i s c o n s i d e r a t i o n , w e s t i p u -

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

t h e c o n s t a n t s as d e r i v e d

above a l l o w s t h e e q u a t i o n s t o be s o l v e d f o r t h e f i r s t - o r d e r l o n g i t u d i n a l v a r i a t i o n s i n u , T, h and W* ( i . e . ,

ul,

etc.

Such a c a l c u l a t i o n y i e l d s a

i n (6)).

mixed l a y e r which deepens, warms and d e c e l e r a t e s toward t h e w e s t , i n agreement with o b s e r v a t i o n s .

The model p l a c e s r a t h e r t o o l a r g e a n emphasis on t h e i n t e r -

nal wave r a d i a t i o n as a f r i c t i o n a l mechanism ( t h e f a c t o r R b e i n g l a r g e ) ; t h i s

i s due t o t h e model’s Hanson,

1983).

c o n f i n e d geometry and n e g l e c t of u p w e l l i n g (Kraus and

I n any e v e n t ,

t h e l i n e a r i z a t i o n below t r a n s f o r m s t h e p r o c e s s e s

a t t h e b a s e of t h e mixed l a y e r i n t o t h e u s u a l Newtonian c o o l i n g and Rayleigh friction.

2.2.

Feedback The s t e a d y b a s i c s t a t e of t h e p r e v i o u s s e c t i o n , found by i n t r o d u c i n g obser-

v a t i o n a l p r e j u d i c e i n t o t h e e q u a t i o n s (1-5)

i n order t o evaluate the necessary

e m p i r i c a l f a c t o r s , p r o v i d e s a n environment i n which waves can propagate i n t e r a c t w i t h t h e atmosphere a s d e s c r i b e d i n t h e I n t r o d u c t i o n .

and

Our c h o i c e of

an a t m o s p h e r i c model i s made on t h e b a s i s of s i m p l i c i t y and i n o r d e r t o i s o l a t e the ocean as much as r e a s o n a b l y p o s s i b l e . the atmosphere are n o t dynamical model of

included;

Large-scale

d e s c r i p t i o n of

t h e atmosphere.

c i r c u l a t i o n changes i n

such phenomena

An example of

requires

a

a s i m p l e atmosphere-ocean

model w i t h a t m o s p h e r i c dynamics h a s been d i s c u s s e d by Lau (1981).

We l i m i t o u r

a t t e n t i o n h e r e t o t h e thermodynamic changes a s s o c i a t e d w i t h a v a r i a b l e a i r - s e a temperature

difference.

Due t o

its

lower

thermal

inertia,

the

atmosphere

responds t o v a r i a b l e h e a t i n g on much s h o r t e r t i m e scales t h a n t h e ocean; we therefore

ignore

effects

of

changing h e a t

atmospheric t e m p e r a t u r e i s presumed

storage i n

t h e atmosphere.

The

t o ad j u s t o v e r d i s t a n c e s of hundreds of

k i l o m e t e r s t o h e a t i n g a t i t s lower boundary due t o ocean t e m p e r a t u r e changes (the d i s t a n c e being an a d j u s t a b l e parameter). preted s y m b o l i c a l l y a s

T h i s a d j u s t m e n t can be i n t e r -

206

where CT is the surface exchange coefficient and UA and HA are the zonal wind velocity and the atmospheric boundary layer depth.

Bo is a Bowen ratio to be

interpreted here as the net amount of latent heat flux into the atmosphere below HA which is condensed locally. yields a length scale

The combination of dimensional parameters

Y , which is the adjustment scale for 8

.

Note that

because of the wind speed term on the right side of ( 7 ) and the velocity term on the left, y is not necessarily positive. proportional to exp(ikx)

Atmospheric temperature changes

take the form

where

f =

k/(k-iy)

is the sea-air transfer function. In order to estimate the effects on the ocean of the feedback, the forcing terms (F*',u;

) in the perturbation equations are set proportional to the air-

sea temperature difference perturbations using (8b). thermodynamic equation ( 4 ) becomes

The heat flux term in the

207

where T' is the sea-surface temperature perturbation and the time scale for the mixed layer to adjust to surface heat flux changes can be estimated from

The friction velocity perturbations appear as both the wind stress ( E q .

mechanical energy input ( E q .

1).

4 ) and

They are found via linearization of the

parameterization in Fig. 1 to be

where the changes in surface stability scale changes in friction velocity by the factor

The derivative is averaged about neutral conditions in Fig. 1, and T o is taken from the previous section. The feedback processes discussed in the Introduction are therefore formulated in terms of the simple transfer function (8b). A more complex atmospheric model would produce a transfer function analogous to large-scale changes in UA to T.

f

and another relating

The latter would appear in (5) with (loa) and

likely dominate. 2.3.

Irrotational Waves A perturbation analysis of E q s .

(1-5),

using the basic state and feedback

derivations above, can be formulated as a 3x3 matrix eigenvalue problem; the determinant represents the dispersion relation for the system.

The non-

208 linearities in the system (1-5) lead to a large number of terms, many of which can be eliminated as small in a post-hoc analysis. The important terms can then be reduced to

2 + at*

25 fT - CEh s

=

au - lJEu + Co( 2 s+ aT at* ax

0

+

1-1 fT

=

0.

Here the time derivative is Doppler shifted with respect to the mean current

am* (T;h)

E aiat =

+

aiax

(T'/To;h'/ho).

T

and The drag term

vE

and

h

are

non-dimensionalized

is associated with the (linearized)

internal wave radiation, and CE is the effect of entrainment on h and T.

The

perturbation entrainment rate has been included in (11) and (12); this accounts for the feedback in (11) and the factor of 2 in (12).

A s before, (11) and (12)

can be combined to give

a(c2) + -aU+ at* ax

5 fT s

=

0.

In the absence of any feedback or drag, the system reduces to

(14)

209

and the two gravity waves are Doppler shifted

wfk

= u

i Co.

With feedback and drag terms, it is necessary to solve the three equations (11-13).

Without feedback, initial disturbances in the 3 equation set, in

addition to generating the gravity waves above, are advected downstream at a rate uo (Kraus and Hanson, 1983).

.3-No

Feedback

.2-

.-

.I

.I

Figure 3.

.2 k (10'5m-')

.3

.4

Speed of "wave" due to oscillation between mixed-layer depth and

temperature, for various atmospheric adjustment scales. Hanson (1983).

From Kraus and

210 The presence of feedback decouples the continuity and thermodynamic equations and a third "wave" appears due to the oscillation between T and h. ure 3 shows the resulting phase speed (real part of adjustment scales y

.

Fig-

w /k) for a variety of

The air-sea interaction enhances the propagation speed

of the low wavenumber disturbances by as much as a factor of 2 over the mean current for certain adjustment scales.

Examination of the details of this

enhanced propagation reveals that it is almost entirely due to the heat-flux feedback terms; the wind-stress terms have relatively little effect in this linear model.

The drag terms at the mixed layer interface, however, cause

decay of initial disturbances on time scales of weeks for the enhanced propagation. Air-sea interaction therefore causes propagation rates for sea surface temperature anomalies which are increased over the mean advection speed.

The

heuristic description of the mechanism in the Introduction is borne out in the context of a simple channel model without rotation, although the dissipation rates are rather too large.

This may be due to the importance placed on the

internal wave drag (the factor R) in the present formulation; numerical calculations are required to resolve this issue. equatorial beta-plane can be

The role of these processes on the

investigated analytically; first results are

described in the following section. 3.

ROTATIONAL EFFECTS The key to the enhanced propagation in the previous section was the decou-

pling of the mixed layer depth and temperature; it follows that studies which consider only the layer heat content as a variable (i.e.

use only Eq. 14 in

some form) cannot reproduce this result of air-sea interaction.

Although

number of models of ocean circulation on the equatorial beta

plane has

appeared, each has used

a

variant of Eq. 1 4 , with feedback included, in a few

cases, by replacing the temperature in the last term with the heat content. This despite the fact that surface fluxes depend on the surface temperature. Therefore it seems useful to extend the results of the previous section to include rotational effects. Introducing the meridional direction y (and concomitant motion v) increases the complexity of the model to fourth order.

We report here results from

a

simple formulation which retains the essential aspects of the new physical processes introduced above and neglects potential complexities.

In particular,

the interfacial drag terms in the momentum equations and the mean current are ignored, and only the heat-flux feedback is considered. The model therefore represents a single baroclinic mode of the classical theory (e.g., Moore and Philander, 1977) with an equivalent depth hE =@T, h = c2/g = 8.4 cm; this is roughly the third baroclinic mode. The 0

0

211 shear terms are not included in the entrainment rate (Eq. 1). tions are (1-4)

The basic equa-

and the v-momentum equation; with some manipulation they become

z+ 25 at

-at aU-

fT - 5 h = 0

E

2 aT ah B y v + C 0 ( -ax + - ) ax

=

0

and, as before, ( 1 6 ) and ( 1 7 ) combine to give

(The non-dimensionalization and linearization of T and h imply C f 2 = C : ( T Using (18), ( 1 9 ) and (20) without feedback and defining

+

h).)

212 l e a d s t o t h e m e r i d i o n a l s t r u c t u r e r e p r e s e n t e d by t h e H e r m i t e f u n c t i o n s i n the v a r i a b l e y*; f o r o r d e r m t h e d i s p e r s i o n i s

w2

where m

2 1 for

-

2 Cok(k-B/w) - (2m+l)BCo = 0

t h e (westward p r o p a g a t i n g ) Rossby wave modes.

I n t h e previous

s e c t i o n i t was s e e n t h a t t h e feedback i s e f f e c t i v e o n l y a t low wavenumbers; t h i s is t h e case a l s o with r o t a t i o n .

F i g u r e 4 shows t h e no-feedback

diagram f o r f r e q u e n c i e s of i n t e r e s t .

I t s f e a t u r e s have been d e s c r i b e d by Moore

and P h i l a n d e r (1977).

dispersion

The K e l v i n wave (m = -1) has phase speed Co.

3

'4 0 -1.6

-1.2

-8

-.4

0

.4

.8

1.2

1.6

I m ( k ) [10-5m-']

Figure 4.

Low-frequency

regime of waves on t h e e q u a t o r i a l b e t a p l a n e f o r an

e q u i v a l e n t d e p t h of 8.4 cm.

213 I n o r d e r t o a s s e s s t h e e f f e c t s of r o t a t i o n of t h e s e waves, t h e f o u r equat i o n s (16-19)

must b e s o l v e d .

T h i s p r e s e n t s no g r e a t d i f f i c u l t y due t o t h e

simple form of ( 1 7 ) ; t h e r e s u l t s can b e c a s t i n t h e c l a s s i c a l form by d e f i n i n g (Hanson, 1983)

where t h e n e t e f f e c t of t h e f e e d b a c k i s c o n t a i n e d i n t h e complex f a c t o r

The d i s p e r s i o n of t h e Rossby waves i s found by s o l v i n g ( 2 2 ) w i t h Co r e p l a c e d by I t should be noted t h a t CF i s s t i l l t h e Kelvin wave speed; t h e form of Z

CF-

i m p l i e s t h a t i t h a s become d i s p e r s i v e .

--

Note a l s o t h a t t h e " e q u i v a l e n t depth"

t h e v e r t i c a l s e p a r a t i o n c o n s t a n t i n t h e three-dimensional

frequency dependent. T h i s i s a post-hoc

problem

--

i s now

j u s t i f i c a t i o n of o u r u s e of a l a y e r e d

model; e x p a n s i o n i n t o v e r t i c a l modes w i l l n o t work f o r t h e feedback problem.

It

is at

adjustment

t h i s point

in

s c a l e becomes

the analysis

important.

that

the

s i g n of

t h e atmospheric

I n t h e previous s e c t i o n a l l q u a n t i t i e s

were c o n v e n i e n t l y d e f i n e d a s p o s i t i v e toward t h e west w i t h o u t ambiguity.

With

r o t a t i o n , waves p r o p a g a t e i n b o t h d i r e c t i o n s and (16-20) a r e f o r m u l a t e d i n t h e u s u a l right-handed c o o r d i n a t e system.

y

that

<

0 (see 7).

The e a s t e r l y t r a d e winds t h e r e f o r e imply

I n f a c t , from t h e h e u r i s t i c d i s c u s s i o n of t h e feedback

mechanism g i v e n i n t h e I n t r o d u c t i o n , one might e x p e c t waves t r a v e l i n g upwind t o be slowed.

T h i s can be e a s i l y t e s t e d f o r t h e Rossby waves by presuming a wes-

t e r l y wind, s o t h a t Figure

y

>

0.

5 shows phase

speeds

for

the

low wavenumber m = 1 Rossby

waves

w i t h o u t feedback ( d a s h e d ) , f o r t h e feedback s c a l e s i n Fig. 3 , and f o r one c a s e with

y

>

0.

The low wavenumber phase speed l i m i t f o r t h e m = 1 wave i n t h i s

c a s e i s ( w / k ) = 0.30 m s-l; feedback enhances t h i s by about 50% f o r an atmosp h e r i c a d j u s t m e n t s c a l e of -500 km ( i . e . ,

e a s t e r l y wind).

The i m p l i e d w e s t e r l y

214 Comparison of Figs. 3 and 5

case decelerates the wave speed, as expected. indicates that rotation constrains the model's

response somewhat.

In the non-

rotational case, the low-wave number disturbances were free to propagate as fast as the match of

(thermal exchange) scales allowed; with rotation the

Rossby dynamics competes with this exchange and the low-wavenumber propagation enhancement is decreased. If the phase speeds in Fig. 5 are superimposed on the mean current of Secone arrives at a propagation rate between about 0.5

tion 2.1,

-

1.0 m s-l f o r

SST anomalies in the Equatorial Pacific, the exact rate depending

wavenumber and the atmospheric adjustment scale.

on the

This is the range of propaga-

tion speeds deduced by Rasmusson and Carpenter (1982) from the composite of warming events.

Wavelength (lo3 krnl 20 I

.7

10 25 I I

5

4

3.5

3

2.5

2

1.5

I

l

l

1

I

I

I

.6 .5

--.4 'm

E

-a

73 .2 rn = I Rossby Wave

.I

.2

.3

.4

.5

- k,(~o-W I

Figure 5.

Phase speed of low wavenumber m = 1 Rossby wave

various atmospheric adjustment scales.

VS.

wavenumber for

215 4.

DISCUSSION

The results above indicate the potential importance of the role played by air-sea interaction in the westward propagation of equatorial SST anomalies. In the linear model used here, the dominant process

is the sea-air heat

exchange; in a non-linear model it is to be expected that the stress coupling through variable surface stability (Fig. 1) would become important also.

For

several reasons, non-linear modeling should be considered relevant to the study

of this phenomenon. For example, in reality the mixed layer depth may not be a continuous variable.

A new shallower mixed layer will be formed whenever h

>

L* that is, when

there is not enough mechanical energy available for entrainment of colder dense water.

The formation of a new shallower mixed

layer could considerably

accelerate the warming to the west of a warm anomaly and therefore the rate of anomaly propagation.

In the linear analysis here, we have only considered

anomalies which had everywhere and at all times a mixed layer depth h which remained smaller than the generalized Monin-Obukbov length L*

.

In other words

we did not consider the intermittent cessation of the entrainment process.

In

a realistic, finite amplitude model this intermittent cessation would have to be considered. Another reason for numerical modeling concerns the realistic description of the air-sea

interaction processes themselves.

The stress variability with

sea-air temperature difference is clearly non-linear (Fig. 1).

Moreover, our

highly simplified atmospheric model neglects non-linearities associated with variable irradiance in addition to atmospheric circulation changes. One important aspect of the enhanced propagation speeds shown in Fig.

5

(discussed more fully in Hanson, 1983) that is revealed in this linear study 2

concerns the response of the mixed layer heat content (C ) to the heat-flux feedback.

Analysis of

the components of the heat content shows that the

enhanced propagation at the very low wavenumbers is almost entirely due to a temperature response, with the mixed-layer depth showing very little change. Toward increasing wavenumbers, where the propagation rate is less, a mixed layer depth response begins to dominate with the temperature response becoming smaller.

The heat content thus changes in two distinct regimes: a slower ther-

mal response and a faster pseudo-mechanical response.

It is the thermal

response that is associated with the increased sea-surface temperature anomaly propagation rates in the linear model.

The decoupling of h and T (in Eqs. 16

and 1 7 ) allows these separate responses; a model using only the heat content equation (20) would not exhibit this characteristic.

That the thermal response

occurs on large space and long time scales makes it all the more relevant for climate studies.

216 In the present study we have simply tried to show that air-sea interaction can cause or contribute to the displacement of thermal boundaries. we have considered a constant wind in the free atmosphere.

To do

so,

This is not

entirely consistent with our allowing for adjustment of the atmospheric temperature field.

In fact, it was the observed or stipulated changes in the

atmosphere which largely generated the present interest in the study of the Equatorial Pacific region.

There is reason to believe that the atmospheric

changes are at least as energetic as those observed in the ocean. The two media interact.

A complete understanding of the phenomenon will eventually require

the development of a realistic, truly interactive ocean-atmosphere model.

We

consider this an ultimate goal, toward which the present work leads. ACKNOWLEDGEMENT The studies published in this paper were supported by the National Science Foundation with Grant ATM 80-23334 and by the National Oceanic and Atmospheric Administration as part of the Equatorial Pacific Ocean Climate Studies program. REFERENCES Crawford, W.R.

and T.R.

Osborn, 1979: Microstructure measurements in the Atlan-

tic Equatorial Undercurrent during GATE. Deep-sea Res.,

26A

(GATE Suppl.

11), 285-308.

Davis, R.E.,

R. DeSzoeke and P. Niiler, 1981: Variability in the upper ocean

during MILE.

Part 11: Modeling the mixed layer response.

Deep-sea Res.,

-

28A, 1453-1475.

Donguy, J.R.

and C. Henin, 1980: Climatic teleconnections in the Western South

Pacific with El Nix0 phenomenon. J.

x. Oceanogr., lo,

1960: Atlantic Ocean Atlas of Temperature

Fuglister, F.C.

1952-1958.

Salinity Profiles

----

and Data from the International Geophysical Years of 1957-1958.

WHO1 Atlas

Series, V. 1. Woods Hole, Mass., 209 pp. Hanson, H.P.,

1983: Equatorial waves in the presence of sea-air heat exchange.

To appear in J. Phys. Oceanogr. Hayes, S.P., Geophys.

1981: Vertical fine-structure in the Eastern Equatorial Pacific J .

k.,E, 10983-10999.

Horel, J.D. and J.M. Wallace, 1981: Planetary-scale atmospheric phenomena associated with the Southern Oscillation.%. Hoskins, B.J.

-.

K.,109,813-829.

and D.J. Karoly, 1981: The steady linear response of a spherical

atmosphere to thermal and orographic forcing. J. Atmos.

x., 38, 1179-

1196.

Julian, P.R.

and R.M.

Walker Circulation. Katz,

E.J.

and

Chervin, 1978: A Study of the Southern Oscillation and

5. Weath.

collaborators,

Rey.,

1977:

106,1433-1451. Zonal

pressure

gradient

along

the

217

Mar. %.,35,

Equatorial Atlantic. J . Kondo, J.,

1975:

Boundary-= Kraus, E.B.

293-307.

Air-Sea bulk transfer coefficients in diabatic conditions. 9

Yeteorol.,,,

91-112.

and H.P. Hanson, 1983: Air-Sea interaction as a propagator of equa-

torial ocean surface temperature anomalies. J.

w. Gceanogr., 2 , (1) in

press. Lau, K-PI., 1981: Oscillations in a simple equatorial climate system. J. Atmos.

s., 38, 248-261. Moore, D.W.

Philander, 1977: Modeling of the tropical ocean circula-

and S.G.H.

tion. In The Sea,

v. A,

ed. Goldberg et al. Wiley Interscience, pp. 319-

361.

Niiler, P.P.

Kraus, 1977: One-dimensional models of the upper ocean.

and E.B.

In: Modeling

&

Prediction

of

the Upper Layers of the Ocean, ed. E.B.

Kraus. Pergamon. pp. 143-173. O'Brien, J.J.

Goldenberg, 1982: Tropical Pacific Wind-Stress Atlas,

and S.B.

Florida State University Press, Tallahassee. Pazan, S. and G . Meyers, 1982: Interannual fluctuations of the Tropical Pacific wind field and the Southern Oscillation. Mon. Weath. Rasmusson, E.M. temperature

and J.H. and

surface

Oscillation/El NiKo. Turner, J . S . ,

g . ,110,587-600.

Carpenter, 1982: Variations in tropical sea-surface

&.

wind

fields

Weath. Rev.,

associated

with

the

Southern

110,354-384.

1969: A note on wind-mixing at the seasonal thermocline. Deep-sea

Res., 16 (Suppl.), -

297-300.

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219

VARIABILITY OF COASTAL ZONES I N LOW LATITUDES ( w i t h a p p l i c a t i o n t o t h e Somali C u r r e n t , t h e G u l f o f Guinea and t h e E l Nino Current)

P . DELECLUSE' and S.G.H.

PHILANDER*

Abstract S o u t h e r l y winds i n low l a t i t u d e s d r i v e v e r y i n t e n s e c u r r e n t s a i o n g t h e west e r n c o a s t and much s l o w e r c u r r e n t s a l o n g t h e e a s t e r n coast. J u s t under t h e s u r f a c e l a y e r , t h e c u r r e n t s a r e o p p o s i t e t o t h e wind i n t h e e a s t e r n p a r t ( t h e y flow upwind, f o l l o w i n g t h e p r e s s u r e g r a d i e n t f o r c e ) ; t h e y are i n t h e same d i r e c t i o n a s t h e s u r f a c e f l o w a i o n g t h e w e s t e r n c o a s t . These d i f f e r e n t p r o p e r t i e s are due t o t h e Ekman d r i f t i n t h e s u r f a c e l a y e r , which i s maximal w i t h i n 3' off the e q u a t o r and d r i v e s s t r o n g z o n a l c u r r e n t s t h a t g i v e o u t e r c o n d i t i o n s t o c o a s t a l c u r r e n t s . Non l i n e a r i t i e s i n t e n s i f y t h e w e s t e r n c u r r e n t s b u t have s m a l l e f f e c t s on t h e e a s t e r n s i d e . When t h e wind r e l a x e s , southward c u r r e n t a p p e a r s a l o n g t h e c o a s t . The r e l e v a n c e o f t h e s e r e s u l t s f o r t h e Somali C u r r e n t , t h e Gulf o f Guinea and t h e e a s t e r n P a c i f i c c u r r e n t s i s examined.

1.

INTRODUCTION Coastal c u r r e n t s i n l o w l a t i t u d e s p r e s e n t v e r y d i f f e r e n t aspects a l o n g t h e

western s i d e and a l o n g t h e e a s t e r n s i d e . E a s t e r n boundary c u r r e n t s a r e broad and slow. T h e i r v a r i a b i l i t y i s h i g h because t h e y h a r d l y p e r s i s t a few weeks as t h e y are r a p i d l y d i s p e r s e d by l o n g westward p r o p a g a t i n g Rossby waves. D u r i n g most p a r t o f t h e y e a r , s o u t h e r l y winds blow o v e r t h e e a s t e r n p a r t o f e q u a t o r i a l oceans ; i n February

-

March, t h e winds weaken and warm southward c u r r e n t s have been

n o t i c e d a t t h i s p e r i o d , a l o n g t h e w e s t e r n c o a s t o f A f r i c a ( H i s a r d , p e r s o n a l comm u n i c a t i o n ) and a l o n g t h e c o a s t s o f Peru and Ecuador. These c u r r e n t s f l o w upwind during the wind r e l a x a t i o n . Along t h e w e s t e r n s i d e of t h e ocean, v e r y i n t e n s e c u r r e n t s e x i s t . I n t h e I n dian ocean, f o r i n s t a n c e , t h e southwest monsoon d r i v e s a c o a s t a l c u r r e n t t h a t p r e sents some p e c u l i a r c h a r a c t e r i s t i c s as shown i n F i g u r e 1, d u r i n g t h e FGGE exper i m e n t i n 1979 (Duing, M o l i n a r i and Swallow, 1980 ; Brown, Bruce and Evans, 1980)

1. L a b o r a t o i r e d ' O c & a n o g r a p h i e Physique /MNHN, P a r i s , F r a n c e . 2. Geophysical F l u i d Dynamics Laboratory/NOAA, P r i n c e t o n , U . S . A .

220

JUNE 6 -JULY 30,1979

-

40" E

100 CMISEC

42'

44"

46"

48'

50"

52"

54'

56"

Fig. 1 : The d i s t r i b u tion o f s u r f a c e currents between 6 June and 30 July 1979 o f f the eastern coast o f Africa. Current arrows a r e centered on the point of observation. After Du ing, Molinari and Swallow (1980). The southern branch of the c u r r e n t veers offshore around 4" N (and t h i s separat i o n i s marked by an upwelling) ; then, the coastal current seems t o be part of an anticyclonic gyre s i t u a t e d between 4" N and 10" N and a second upwelling appears a t 10" N. The monsoon winds increase from t h e equator t o 12"N b u t there is no special f e a t u r e s of the wind around 4" N .

I n the following p a r t , we t r y t o explain why the Somali current leaves the ' N and why the e a s t e r n and western coasts e x h i b i t such d i f f e r e n t becoast a t 4 haviours. Part I 1 describes the l i n e a r response of a n equatorial ocean t o a southerly wind s t r e s s ; p a r t I11 extends the r e s u l t s t o a non l i n e a r ocean and t o t h e relaxation of the wind. F i n a l l y , in p a r t IV, the Somali current i s examined i n view of the previous r e s u l t s and the e a s t e r n boundary currents are discussed. A description of the numerical model used i n t h i s paper i s presented in the appendix. For a more d e t a i l e d discussion of some of the r e s u l t s described here, the reader i s r e f e r r e d t o Philander and Delecluse (1983)

221

2.

THE LINEAR RESPONSE TO A SOUTHERLY WIND STRESS Away f r o m t h e c o a s t , a s o u t h e r l y u n i f o r m wind s t r e s s o v e r t h e ocean d r i v e s a

n o r t h w a r d c u r r e n t a t t h e e q u a t o r , an eastward c u r r e n t n o r t h o f t h e e q u a t o r and a westward c u r r e n t s o u t h o f i t . The l i n e a r p r o b l e m , i n a s h a l l o w w a t e r ocean, has been i n v e s t i g a t e d by Moore and P h i l a n d e r (1977). The Ekman t r a n s p o r t Ty/f TY

(where

i s t h e m e r i d i o n a l wind s t r e s s component and f i s t h e C o r i o l i s parameter)

grows q u i c k l y as t h e e q u a t o r i s approached. The Ekman t r a n s p o r t becomes s i n g u l a r a t t h e e q u a t o r where t h e balance i s ensured by t h e p r e s s u r e g r a d i e n t f o r c e :

The maximum o f t h e Ekman t r a n s p o r t ( w h i c h corresponds t o t h e maximum o f zonal c u r r e n t s ) i s o b t a i n e d w i t h i n a d i s t a n c e equal t o t h e r a d i u s o f d e f o r m a t i o n o f f t h e e q u a t o r . I n a s t r a t i f i e d model, t h e response i s m o d i f i e d as t h e wind d r i v e n response p r e s e n t s a v e r t i c a l p r o f i l e d i f f e r e n t f r o m t h e oceanic s t r a t i f i c a t i o n s t r u c t u r e . I n t h e f o l l o w i n g s t u d y , o n l y s p i n - u p motions above t h e t h e r m o c l i n e a r e c o n s i d e r e d . Long t e r m e q u i l i b r i u m o f an ocean i n response t o a s o u t h e r l y wind s t r e s s have been d e s c r i b e d i n P h i l a n d e r and Pacanowski (1981) and Cane (1979) I n t h e numerical approach, surface winds d r i v e c u r r e n t s c o n f i n e d i n t h e f i r s t l a y e r (25m) and subsurface c u r r e n t s a r e s i t u a t e d between t h e f i r s t l a y e r and t h e t h e r m o c l i n e . The w i n d s t r e s s a c t s as a body f o r c e i n t h e f i r s t l a y e r . A

u n i f o r m s o u t h e r l y w i n d s t r e s s d r i v e s c r o s s e q u a t o r i a l f l o w downwind,

depresses t h e t h e r m o c l i n e n o r t h o f t h e e q u a t o r and r a i s e s i t south. A s t r o n g p r e s s u r e g r a d i e n t f o r c e e x i s t s j u s t under t h e s u r f a c e , which d r i v e s southward r e t u r n c u r r e n t a t t h e e q u a t o r , westward c u r r e n t n o r t h o f t h e e q u a t o r and eastward c u r r e n t s o u t h o f i t , a t r i g h t a n g l e t o t h e p r e s s u r e f o r c e . T h i s m e r i d i o n a l c i r c u l a t i o n i s d e p i c t e d i n F i g u r e 2 where a m u l t i l e v e l numerical model, d e s c r i bed i n t h e appendix, i s d r i v e n by a u n i f o r m s o u t h e r l y w i n d s t r e s s , a c t i n g on t h e f i r s t 25 meters. The t i m e r e q u i r e d t o r e a c h an e q u i l i b r i u m i s e s t i m a t e d by: T = ( B N H ) - ' I 2= 2 days

where H i s t h e t h e r m o c l i n e depth, N i s t h e mean B r i i n t VaTsalX frequency f o r t h e s u r f a c e l a y e r s and B i s t h e v a r i a t i o n o f t h e C o r i o l i s parameter

with latitude.

The zonal c u r r e n t s a r e s i t u a t e d ' w i t h i n a d i s t a n c e L o f f t h e e q u a t o r : L = (NHB-')1/2

= 200 km

222

Ullluot

-

UlllUDt

-

F i g . 2 : A m e r i d i o n a l s e c t i o n o f t h e two h o r i z o n t a l v e l o c i t y components and temp e r a t u r e a l o n g a m e r i d i a n i n t h e c e n t e r o f t h e b a s i n . The f i e l d s were averaged o v e r t h e 13 day p e r i o d f r o m day 34 t o day 46 i n o r d e r t o e l i m i n a t e t h e Rossbyg r a v i t y o s c i l l a t i o n s . (The winds s t a r t t o blow on day z e r o . ) Along t h e w e s t e r n and t h e e a s t e r n boundaries t h e e v o l u t i o n i s d i f f e r e n t . A t m i d l a t i t u d e s , t h e c o a s t a l c u r r e n t a l o n g t h e western boundary a c c e l e r a t e s u n t i l t h e a r r i v a l o f K e l v i n waves p r o p a g a t i n g equatorward, which a r e e x c i t e d a t the boundaries o f t h e domain ( A l l e n , 1976). T h i s e x p l a i n s why t h e c u r r e n t becomes s t e a d y f i r s t a t m i d l a t i t u d e s i n F i g u r e 3 . B u t i n low l a t i t u d e s , K e l v i n waves have

d i f f e r e n t p r o p e r t i e s as t h e y t r a n s f e r t h e i r energy t o equa-

t o r i a l waves. Along t h e e a s t e r n boundary, poleward K e l v i n waves a r e r e g u l a r l y e x c i t e d by e q u a t o r i a l

mixed Rossby g r a v i t y waves ; t h i s r e s u l t s i n t o o s c i l l a t i o n s

o f the coastal c u r r e n t . The s t r u c t u r e o f c u r r e n t s and temperature w i t h d e p t h i s presented i n Figure

4 and c l e a r l y shows t h e d i f f e r e n c e s between t h e two boundaries. Along t h e east e r n s i d e , t h e impact o f t h e eastward j e t on t h e boundary i n c r e a s e s t h e thermoc l i n e d e p r e s s i o n i n t h e n o r t h e r n hemisphere and i n t h e s o u t h e r n hemisphere the u p w e l l i n g i n c r e a s e s a l o n g t h e c o a s t as t h e westward c u r r e n t leaves t h e coast. This contributes t o t h e p r e s s u r e f o r c e a n d t e n d s t o r e d u c e t h e s u r f a c e c u r r e n t a n d t o c r e a t e s t r o n g southward c u r r e n t j u s t under t h e s u r f a c e l a y e r . As t h e e q u a t o r i s approached f r o m t h e south, t h e m e r i d i o n a l l y i n t e g r a t e d Ekman t r a n s p o r t o f f s h o r e grows and t h e c o a s t a l c u r r e n t i n t e n s i t y r e v e r s e s : there

w i l l be a c u r r e n t minimum a t t h e e q u a t o r . Along t h e western boundary, t h e coast a l c u r r e n t d r a i n s w a t e r f r o m t h e westward c u r r e n t (and t h e r e w i l l be downwelling south o f the equator along t h e coast) b u t n o r t h o f t h e equator i t leaves the

223

coast t o feed the eastward current,where the Ekman transport i s maximum,creating a strong coastal upwelling. The pressure gradient force i s then northward a n d contributes t o increase the northward current i n the surface layer and below the surface. As the meridionally integrated Ekman transport toward the coast increases as i t approaches the equator and decreases north of the equator, a current maximum e x i s t s a t the equator.

50

.J

O.

1J

30

Y5

20

IJ

10

LATITUDE

-

LATITUDE

-

f i g . 3 : The evolution of the meridiotial velocity comoponents a t the surface, 60 km from the eastern and western coasts respectively. In order t o reach an equilibrium, f r i c t i o n must be considered i n the equation, I t s typical time scale i s around two weeks : T = (p2A,)-

1’3

The importance of f r i c t i o n for western boundary adjustment was already noticed by Munk (1950) for mid-latitudes; H u r l b u r t and Thompson (1976) in a simulation of the Somali current w i t h a two layer model showed i t s role i n equatorial area.

224

WEST

EAST

Fig. 4 : Meridional s e c t i o n s o f t h e alongshore v e l o c i t y component and temperatur e 60 km from t h e western ( ( a ) and ( c ) ) and eastern ( ( b ) and ( d ) ) coasts. The f i e l d s were averaged over a 13 day p e r i o d , from day 34 t o 46, i n order t o f i l t e r o u t the dominant o s c i l l a t i o n s . The flow i s southward i n shaded regions.

3.

NON LINEAR RESPONSE AND EFFECT OF A RELAXATION

The same model, r u n n o n - l i n e a r l y ,

shows i n t e r e s t i n g m o d i f i c a t i o n s o f the cur-

r e n t s t r u c t u r e . Due t o t h e p o t e n t i a l v o r t i c i t y conservation, a p a r t i c l e moving from t h e equator t o h i g h e r l a t i t u d e s gains eastward momentum ; f a r from the coast, t h e eastward c u r r e n t i s s t r o n g l y i n t e n s i f i e d and the westward current i s now slow and broad ( F i g . 5 ) . The downwelling area, n o r t h o f t h e equator, i s s t r o n g and narrow ; t h e subsurface c u r r e n t s a r e consequently m o d i f i e d : the westward c u r r e n t t h a t was under t h e eastward surface c u r r e n t moves toward t h e equa-

225

t o r and j o i n t s t h e s u r f a c e westward c u r r e n t ; t h e subsurface eastward c u r r e n t s o u t h o f t h e e q u a t o r s t r e n g t h e n s . These m o d i f i e d c i r c u l a t i o n p a t t e r n s may be seen i n F i g u r e 6.

7; .......

.. ..

1oc

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V .. .. .......

20c

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

yi\ .......

u ( y , z ) cm/sec

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

1 S

LATITUDE

-

. . . . ... ... ... ... .... .. .. .. .. . . .. .. .. .. .. . . . . . 1 :. . . . . . .. .. ... ... 5--r . . . . . . . . . . ..... .. .. .. .. .. .. .. .. .. . . . . .. ... ... .. .. . . . . .. .. .. .. .. . . . . . . . . . . . ... ... .. .. . . . .. .. .. .. .. .. . . .. .. .. .. .. .. . . . . . .. .. .. .. ... ... . .. .. .. .. .. ... ... ... .. . ... ... I:. ... ... ... ... .. .. .. . .. .. .. .. ... ... .. .. .. .. .. .. .. .. .. .. .. . . . . . .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... .. .. .. ... ... ... ... ... ... ... ... .. .. ... .. .. .. .. .. ........ 1......... . . . ..... . .: .:.:.:.. :.. :.. .:. .:...:....... ... ... ............. ... .. .. .. .................. ......................

1

I:

I:::: I::

:::: : : : : : :: :::::: : : :

10"N

Fig. 5 A m e r i d i o n a l s e c t i o n o f t h e z o n a l v e l o c i t y component - i n shaded r e g i o n s , t h e m o t i o n i s westward - The n o n l i n e a r model i s f o r c e d w i t h winds of i n t e n s ty 0.5 dynes/ct$.

226

IO'N

E?'

LONClIUDt

-

Fig. 6 : The horizontal velocity vectors a t depths o f ( a ) 12.5 m and ( b ) 37.5 m, and the temperature a t a depth of 12.5 m , in a nonlinear model 50 days after the wind started t o blow.

227

Along the e a s t e r n c o a s t , non l i n e a r e f f e c t s a r e l i g h t ; b u t along the western c o a s t , t h e r e i s a strong advection of the coastal current core i n t o the northern hemisphere and the associated upwelling i s very well developed (Fig. 7 ) . An a n t i cyclonic c e l l e x i s t s now j u s t under the s u r f a c e , n o r t h of the equator, along the coast.

fq

LATITUDE

-

I O ' N

IJ , 100s

Eq

LATITUDE

-

I IO'N

Fig. 7 : The evolution of t h e alongshore flow and temperature, a t t h e surface, 60 km from t h e western c o a s t , when the winds s t a r t t o blow a t day zero and suddenly relax a t day 35, over a nonlinear model. After 35 days, the wind-stress was relaxed w i t h a cosine taper of f i v e days in order t o avoid t h e e x c i t a t i o n of strong i n e r t i a g r a v i t y waves. As the wind decays, the water surges following the pressure g r a d i e n t forces and the surface flow i s southward a t the equator from the i n t e r i o r t o t h e eastern boundary. Currents i n t h e surface l a y e r and the second l a y e r (Fig. 8) a r e very s i m i l a r . Non l i n e a r e f f e c t s allow the c u r r e n t s t o persist longer and they decay slowly by friction.

228

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LONGITUDE

-

F i g . 8 : The h o r i z o n t a l v e l o c i t y v e c t o r s a t d e p t h s o f ( a ) 1 2 . 5 m and ( b ) 37.5 m, f i f t e e n days a f t e r the wind had s t o p p e d blowing. (The wind t u r n e d on a t day zero and t u r n e d o f f a t day 3 5 ) .

229

.. .

,, .

.,

,, . .

:: ,, ,. ..: :., .. ,,. . .

LONGITUDE

--.

Fig. 9 : The horizontal velocity vectors and temperature a t depth of 12.5 m in a non linear model, 50 days a f t e r the southwesterly wind started t o blow.

23 0

4.

4.1

DISCUSSION

The Somali c u r r e n t The i m p o r t a n t p o i n t demonstrated above i s tClat t h e s e p a r a t i o n p o i n t of t h e

northward c u r r e n t from t h e c o a s t i s determined by t h e o f t s h o r e Ekman t r a n s p o r t and depends s t r o n g l y on e q u a t o r i a l dynamics. I n a l i n e a r model, t h i s p o i n t i s s i t u a t e d around 4" N . When non l i n e a r e f f e c t s a r e added, i t moves n o r t h w a r d as t h e w i n d i n t e n s i f i e s ( i t reaches 6" N f o r a w i n d o f 0.5 dyne/cm2). S o u t h e r l y winds d r i v e a westward f l o w a t t h e e q u a t o r (see F i g u r e 6 ) ; when w e s t e r l y winds blow, t h e c u r r e n t a t t h e e q u a t o r i s an eastward j e t ( P h i l a n d e r and Pacanowski, 1980). C o n s i d e r i n g t h e southwest monsoon, t h e r e w i l l be v e r y l i t t l e zonal flow a t t h e e q u a t o r and t h e l a t i t u d e o f t h e eastward j e t i s l o w e r t h a n i n case of pur e l y s o u t h e r l y wind. V e l o c i t y and t e m p e r a t u r e f i e l d s a r e p r e s e n t e d i n F i g u r e 9, f o r a southwest wind s t r e s s o f 0 . 5 dyne/cm2 and i t i s c l e a r t h a t t h e i n c l i n a t i o n of t h e wind t e n d s t o i n h i b i t t h e p e n e t r a t i o n o f t h e c o a s t a l j e t i n t o t h e nort h e r n hemisphere ( t h e l a t i t u d e o f s e p a r a t i o n i s around 4" N ) . A more r e a l i s t i c s i m u l a t i o n o f t h e Somali c u r r e n t i s r e a l i z e d by t a k i n g i n t o

account t h e c o a s t l i n e i n c l i n a t i o n . There t h e s e p a r a t i o n occurs around 3" N and t h e u p w e l l i n g tongue i s s t r o n g l y marked around 4" N ( F i g . 1 0 ) . The c h a r a c t e r i s t i c s o f t h e s o u t h e r n tongue a r e w e l l r e p r e s e n t e d (compare F i g . 1 and F i g . l o ) , c o n s i d e r i n g t h e crude assumptions r e q u i r e d by t h e numerical model. An i m p o r t a n t p o i n t i s m i s s i n g i n t h a t model : t h e a n t i c y c l o n i c g y r e centered a t 8" N. T h i s g y r e must be due t o t h e s p a t i a l s t r u c t u r e o f t h e wind ( Anderson, 80). There i s , i n f a c t , a s t r o n g i n t e n s i f i c a t i o n o f t h e monsoon wind offshore

around 12" N. I n o r d e r t o g e t a complete s c e n a r i o f o r t h e Somali c u r r e n t , a det a i l e d d e s c r i p t i o n of t h e wind f i e l d i s r e q u i r e d ( t h e w i n d may be h i g h l y variable f r o m one y e a r t o t h e o t h e r ) and a good knowledge o f temperature and s a l i n i t y s t r u c t u r e i s needed because t h e I n d i a n ocean i s n o t a t r e s t when t h e monsoon s t a r t s and i t e v o l v e s f r o m a g i v e n d e n s i t y s t a t e .

4.2

The e a s t e r n boundaries Very few measurements have been made a l o n g t h e e q u a t o r i a l e a s t e r n c o a s t and

no s t r o n g c u r r e n t s have been r e p o r t e d t h e r e . E a s t e r n boundary c u r r e n t s a r e slow and broad. I n t h e e a s t e r n p a r t o f t h e G u l f o f Guinea, t h e winds a r e m o s t l y sout h e r l y and t h e y r e l a x d u r i n g t h e months o f F e b r u a r y - A p r i l . I n t h e numerical mod e l , c u r r e n t s a r e weak a l o n g t h e e a s t e r n boundary and o s c i l l a t e around a mean v a l u e w h i c h i s n o r t h w a r d a t t h e s u r f a c e and southward i n subsurface. When t h e w i n d r e l a x e s , t h e f l o w r e v e r s e s a t t h e s u r f a c e and goes southward d u r i n g a few

231

10'

10'

-

LONGITUD~

Fig. 10 : T h e horizontal v e l o c i t y vectors a t depths of ( a ) 12.5 m and ( b ) 11.5 m , 50 days a f t e r t h e onset of southwesterly winds of i n t e n s i t y 1.0 dyne/cm2 over a basin with a western coast t h a t i s inclined t o meridians.

23 2

Fig. 11. T r a j e c t o r i e s of MARISONDE buoys B 10 ( s o l i d l i n e ) from 26 July 1978 t o 1 February 1979 and B 37 (dashed l i n e ) from 20 January t o 10 July 1979 in the Gulf o f Guinea.

233

weeks

.

T h i s scheme i s c o h e r e n t w i t h 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 Guinea :

d u r i n g most o f t h e y e a r , t h e r e i s s t a g n a t i o n i n t h e e a s t e r n p a r t ( H i s a r d ' s p e r sonal communication) and some d r i f t i n g buoys t r a j e c t o r i e s ( F i g . 1 1 ) observed d u r i n g t h e f a l l and w i n t e r 78-79 c o n f i r m

t h i s c i r c u l a t i o n ( P i t o n , 1982). I t i s

i n t e r e s t i n g t o p o i n t o u t t h a t , i n March 79, one o f t h e buoy, a l o n g t h e e a s t e r n coast s t a r t s t o move southward d u r i n g a b o u t a week and then, i t r e v e r s e s . T h i s w i n d r e l a x a t i o n happens a l s o i n t h e P a c i f i c ocean and may cause

the

warm southward c u r r e n t t h a t appears d u r i n g a few weeks a l o n g t h e c o a s t of Ecuador and Peru a t t h e b e g i n n i n g o f S p r i n g . C u r r e n t s a l o n g t h e e a s t e r n c o a s t s cannot p e r s i s t l o n g e r t h a n a few weeks because t h e y a r e d i s p e r s e d by l o n g westward p r o p a g a t i n g Rossby waves. Thus v a r i a b i l i t y i s l i k e l y t o be h i g h i n t h e s e areas. Moreover, remote e f f e c t s may i n c r e a s e this variability.

In t h i s p e r i o d range ( a week

-

a month), K e l v i n waves and m i -

xed Rossby g r a v i t y waves a r e e a s i l y e x c i t e d and t h e y b o t h c o n t r i b u t e t o t r a n s p o r t t h e energy eastward. They may g r e a t l y modify t h e c o a s t a l phenomena. F u r t h e r l o n g t e r m measurements a r e r e q u i r e d t o understand t h e dynamics o f these boundaries.

Appendix : The n u m e r i c a l model The e q u a t i o n s o f m o t i o n and t e m p e r a t u r e ( t h e p r i m i t i v e e q u a t i o n s ) a r e s o l v e d n u m e r i c a l l y f o l l o w i n g t h e method and schemes d e s c r i b e d by Bryan (1969). The equat i o n o f s t a t e i s assumed o f t h e f o r m : P =

PO(^

where

p

-4 i s the density,

T

i s t h e temperature,

a = O.O002/"C

i s t h e coef-

f i c i e n t of thermal expansion, and p,, = 1 g / c m 3 . The c o e f f i c i e n t s o f h o r i z o n t a l vH and v e r t i c a l vv eddy v i s c o s i t y , and t h e thermal d i f f u s i v i t y x a r e a s s i gned t h e v a l u e s :

vv

=

10 cm2/s

vH = 2

%

=

1 cm2/s

xH = 107 cm2/s

x

107 cm2/s

vH and xH 20 i n o r d e r t o dampen westward p r o p a g a t i n g K e l v i n

except i n t h e neighbourhood o f zonal boundaries where t h e v a l u e s o f are i n c r e a s e d by a f a c t o r o f waves a l o n g those c o a s t s . The

ocean i s 3 000 m deep and has a f l a t bottom, i t i s r e p r e s e n t e d by 1 6 g r i d

p o i n t s i n t h e v e r t i c a l . P r o f i l e s o f t h e i n i t i a l t e m p e r a t u r e and s t r a t i f i c a t i o n and d i s t r i b u t i o n o f t h e upper g r i d p o i n t s a r e d e p i c t e d i n F i g . 12.

234 The model ocean i s a r e c t a n g u l a r box which s t r e t c h e s f r o m 11" S t o 16" N, and which has a l o n g i t u d i n a l e x t e n t o f 4 600 km. The l a t i t u d i n a l g r i d spacing i s 5.6 km ; t h e l o n g i t u d i n a l g r i d s p a c i n g i s 111.2 km i n t h e i n t e r i o r o f t h e b a s i n b u t t h i s decreases t o 22.4 km n e a r t h e e a s t e r n

and western c o a s t s . (The h o r i -

z o n t a l g r i d s p a c i n g i s r e p r e s e n t e d on t h e frame i n F i g u r e 1 2 ) .

No s l i p c o n d i t i o n s a r e a p p l i e d a l o n g t h e v e r t i c a l w a l l s and a t t h e bottom. u = v =

TA

= 0

a l o n g t h e m e r i d i o n a l boundaries

u = v =

Tcp

= 0

a l o n g t h e zonal b o u n d a r i e s .

The ocean i s a t r e s t i n i t i a l l y and i s f o r c e d by a n u n i f o r m n o r t h w a r d winds t r e s s o f i n t e n s i t y 0.5 dyne/cm2. The winds a r e s e t up w i t h a c o s i n e t a p e r over a p e r i o d o f f i v e days i n o r d e r t o f i l t e r o u t i n e r t i a - g r a v i t y waves. I n t h e case where t h e winds r e l a x a f t e r b l o w i n g s t e a d i l y f o r 35 days, t h i s happens a g a i n o v e r a p e r i o d o f f i v e days. The h e a t f l u x across a l l boundaries, i n c l u d i n g t h e surface,

i s z e r o . When t h e v e r t i c a l g r a d i e n t o f d e n s i t y becomes u n s t a b l e , con-

v e c t i v e a d j u s t m e n t between a d j a c e n t l a y e r s r e s t a b l i s h e s t h e e q u i l i b r i u m . TEMPERATURE ( " C ) 0

100

-E

1

200

I +

0. W

7

a

1

300

AOC

50C

F i g . 12. The i n i t i a l temperature and B r u n t - V a i s a l a frequency i n t h e upper 500 m o f t h e model. A t g r e a t e r depths t h e temperature decreases l i n e a r l y t o z e r o . The v e r t i c a l s p a c i n g o f g r i d p o i n t s i s i n d i c a t e d .

235

REFERENCES A l l e n . J.S. (1976) : Some aspects o f t h e f o r c e d wave response o f s t r a t i f i e d coast a l r e g i o n s . J: Phys. Oceanogr., 6, 113-119. Anderson, D.L.T., : The Somali C u r r e n t ( u n p u b l i s h e d m a n u s c r i p t ) Brown, D.B.. J.G. Bruce and R.H. Evans, (1980) : E v o l u t i o n o f sea s u r f a c e temp e r a t u r e - i n t h e Somali B a s i n d u r i n g - t h e s o i t h w e s t monsoon o f 1979. Science,

(m)

209. 595-597 B r y K ’ K . (1969) : A numerical method f o r t h e s t u d y o f t h e w o r l d ocean. J. Comp. Phys., 4, 347-376 Cann.A.-(1979) : The response o f an e q u a t o r i a l ocean t o s i m p l e w i n d - s t r e s s p a t t e r n s : 11. Numerical r e s u l t s . 3. Mar. Res., 37, 253-299 Charney, J.G., (1955) : The g e n e r a t i o n o f i c e % i T F c u r r e n t s by winds. J. Mar. Res.

14. 477-498. D u i K , W . , R.L. M o l i n a r i and J.C. Swallow, (1980) : Somali c u r r e n t : e v o l u t i o n o f t h e s u r f a c e f l o w . Science, 209, 588-590 H u r l b u r t , H.E. and J.D. Thomson, m 6 ): A numerical model o f t h e Somali C u r r e n t J. Phys. Oceanogr., 6, 646-664 Moo%,-[TTW. and S.G.H. P h i l a n d e r , (1977) : M o d e l i n g o f t h e t r o p i c a l oceanic c i r c u l a t i o n i n The Sea, V o l . V I . , W i l e y I n t e r s c i e n c e , NY. pp. 319-361 Munk, W.H., ( 1 9 m n n t h e w i n d - d r i v e n ocean c i r c u l a t i o n . J o u r . of Meteo. Vol 7, n o 2 . P h i l a n d e r , S.G.H. and R.C. Pacanowski, (1980) : The g e n e r a t i o n o f e q u a t o r i a l c u r r e n t s . J . Geoph. Res., 85, 1123-1136 P h i l a n d e r , S . G . H X R T Pacanowski, (1981) : The oceanic response t o c r o s s e q u a t o r i a l winds ( w i t h a p p l i c a t i o n t o c o a s t a l u p w e l l i n g i n l o w l a t i t u d e s ) . l l u s , 33, 201-210 -T e_ P h i l a n d e r , S.G.H. and P. Delecluse,(l983) : Coastal c u r r e n t s i n low l a t i t u d e s . Deep Sea Research, I n press.

This Page Intentionally Left Blank

231

REFLECTIONS O F LOW FREQUENCY E Q U A T O R I A L WAVES O N PARTIAL B O U N D A R I E S

Y. du P E N H O A T

1

,

M.A.

CANE2

and R . J .

PATTON2I3

' A n t e n n e ORSTOM - C e n t r e O c e a n o l o g i q u e d e B r e t a g n e , B P 3 3 7 , 29273 B r e s t cedex, France LDepartment o f Meteorology and P h y s i c a l C a m b r i d g e , MA 0 2 1 3 9 , U . S . A .

Oceanography, M.I.T.

3 P r e s e n t a d d r e s s : Dynamics T e c h n o l o g y , T o r r e n c e , C A 9 0 5 0 5 , U.S.A.

22939 H a w t h o r n e B l v d ,

ABSTRACT

We d e v e l o p a l i n e a r t h e o r y f o r t h e e f f e c t s o f p a r t i a l b o u n d a r i e s the kind thought t o be important i n the seasonal and i n t e r a n n u a l v a r i a t i o n s of t h e e q u a t o r i a l c i r c u l a t i o n . The w e s t e r n p a r t i a l b o u n d a r y c a s e ( e . g . B r a z i l ) d i f f e r s f r o m t h e e a s t e r n o n e ( e . g . , t h e G u l f o f G u i n e a ) by t h e p r e s e n c e o f s h o r t Rossby w a v e s t r a p p e d a l o n g t h e n o r t h - s o u t h p a r t o f t h e b o u n d a r y which f o r m a b o u n d a r y c u r r e n t a c c o m p l i s h i n g t h e r e q u i r e d m e r i d i o n a l r e d i s t r i b u t i o n o f t h e z o n a l mass f l u x . T h e r e i s a d i s c o n t i n u i t y i n the dynamic topography a t t h e c o r n e r o f t h e e a s t - w e s t c u r r e n t a t t h i s point. Calculations f o r t h e world's e q u a t o r i a l ocean b a s i n shapes a r e d i s c u s s e d . C a l c u l a t i o n s c a r r i e d o u t f o r e q u a t o r i a l i s l a n d s show t h a t p r o p a g a t i o n o f s u c h low f r e q u e n c y w a v e s w i l l n o t b e a f f e c t e d s i g n i f i c a n t l y by a n y i s l a n d o f t h e r e a l e q u a t o r i a l o c e a n .

o n low f r e q u e n c y w a v e s o f

INTRODUCTION

The d y n a m i c a l e f f e c t o f

t h e r e v e r s a l s i g n of

a t t h e e q u a t o r makes i t a v e r y

the Coriolis force

e f f e c t i v e wave g u i d e w h i c h s u p p o r t s

p l a n e t a r y waves unique t o t h e t r o p i c s .

P l a n e waves s o l u t i o n t o li-

nearized equations have a f a s t e r propagation near t h e equator than l a t i t u d e . A s a consequence,

they h a v e a t h i g h e r

the equatorial

ocean e x h i b i t s a s t r o n g a n d r a p i d r e s p o n s e t o s e a s o n a l a n d i n t e r annual v a r i a t i o n s

i n t h e wind s t r e s s .

We d e v e l o p a c o m p l e t e l i n e a r t h e o r y f o r t h e e f f e c t s o f p a r t i a l b o u n d a r i e s o n t h e low f r e q u e n c y w a v e s w h i c h p l a y a n i m p o r t a n t r o l e

i n these variations.

By p a r t i a l b o u n d a r i e s ,

presents discontinuities north-south

coast.

w e mean a c o a s t w h i c h

( o r c a p s ) and which is n o t a s t r a i g h t

F o r e x a m p l e , w e may t h i n k o f

t h e c o a s t of

the

238 Gulf

o f Guinea and B r a z i l

i n t h e A t l a n t i c ocean,

t h e New G u i n e a

c o a s t i n t h e P a c i f i c and t h e Somali c o a s t i n t h e I n d i a n ocean. thermore,

Fur-

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

p a r t i a l boundaries. Our i n t e r e s t i s i n t h e e f f e c t o f s u c h b o u n d a r i e s on t h e wave motions

e s s e n t i a l t o b a s i n w i d e a d j u s t m e n t r a t h e r t h a n o n d e t a i l s of

the perturbations near the boundaries.

solve t h e l i n e a r s h a l l o w w a t e r e q u a t i o n s a p p r o p r i a t e t o

We w i l l

a s i n g l e b a r o c l i n i c mode u s i n g t h e u s u a l e q u a t o r i a l s c a l i n g , ly,

the length scale

: L

( g H / B 2 ) l l 4 ( t h e e q u a t o r i a l r a d i u s of

=

f o r m a t i o n ) and t h e t i m e s c a l e T = depth of

8

t h e b a r o c l i n i c mode,

the meridional

namede-

(gHB2)-1/4 w i t h H t h e e q u i v a l e n t

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

derivative of

the Coriolis parameter.

S i n c e we a r e i n t e r e s t e d i n low f r e q u e n c y m o t i o n ,

t h e frequency

i s s m a l l compared t o t h e e q u a t o r i a l s c a l i n g f r e q u e n c y s o t h a t :

-

1

The m i x e d g r a v i t y wave a n d s h o r t R o s s b y w a v e s c a n n o t p r o p a -

g a t e very 2

-

f a r into the i n t e r i o r before f r i c t i o n destroys

Geostrophic balance holds i n the meridional

them.

direction.

3 - The w e s t w a r d p r o p a g a t i n g l o n g R o s s b y w a v e s a r e a p p r o x i m a t e l y non d i s p e r s i v e . We c h o o s e a s o u r c a n o n i c a l p r o b l e m t h e l a r g e t a s y m p t o t i c f l o w t h a t r e s u l t s when a wave s o u r c e i s s w i t c h e d o n a t t = 0 a n d r e m a i n s steady thereafter

a s d i s c u s s e d i n Cane and S a r a c h i k

;

(19761, t h e

s o l u t i o n f o r a p e r i o d i c f o r c i n g o r a n y f o r c i n g c a n b e d e d u c e d from t h e s o l u t i o n t o t h i s problem. Cane and S a r a c h i k

(1976)

( s e e a l s o Anderson and Rowlands,

h a v e shown t h a t f o r l a r g e t , t h e a s y m p t o t i c m o t i o n s a r e o f kinds

:

( i ) E q u a t o r i a l K e l v i n waves, and h p r o p o r t i o n a l t o

JI,

=

1976)

3

71

-1/4

e-Y2/2

.

J,

0’

propagating energy eastward with u

t h e zeroth o r d e r Hermite function

:

The l a r g e t r e s p o n s e i s s t e a d y f o r a n H ( t )

t i m e dependence and i s i n d e p e n d e n t

( i i ) Long R o s s b y w a v e s ,

of x . .

p r o p a g a t i n g energy westward.

The e q u a -

t o r i a l K e l v i n wave h a s v = 0 a n d t h e l o n g R o s s b y w a v e s h a v e v both s a t i s f y the geostrophic r e l a t i o n yu Again,

+ ah aY

= 0

t h e l a r g e t a s y m p t o t i c form i s i n d e p e n d e n t o f

( i i i ) S h o r t Rossby waves wave)

of

t h e form

t and

X.

( i n c l u d i n g t h e mixed R o s s b y - g r a v i t y

( s e e Cane a n d S a r a c h i k ,

1977 p 4 0 4 ) .

0 ;

239 s

( u ,

V

s

hs)

,

Note t h a t a s

=

t+m,

[ - -a , ay

a ax

t

Y]

J o ( 2 & ) d

{ J o ( 2 G )

6(x)

; a

X(Y)j

s u m o f s u c h modes i s a n

ever t h i n n i n g boundary l a y e r trapped a t x = 0 . The u s u a l b o u n d a r y c o n d i t i o n s p r e s c r i b e d a t t h e e a s t e r n a n d w e s t e r n f u l l b o u n d a r i e s must b e c a r e f u l l y a p p l i e d t o t h e c a s e o f p a r t i a l boundary t o e n s u r e c o n s e r v a t i o n o f mass. no n o r m a l f l o w e x i s t s a t t h e l o n g i t u d e o f

For a f u l l boundary,

t h e boundary,

but i f

boundary does n o t extend a c c r o s s a l l l a t i t u d e s i n t h e b a s i n ,

the

the

c o n d i t i o n o f no n o r m a l f l o w c a n no l o n g e r b e a p p l i e d i n t h e o p e n ocean region. The p l a n o f tion 2,

t h e remainder of

we s o l v e t h e p r o b l e m o f

parately,

t h i s paper

i s as follow

:

in sec-

a K e l v i n wave a n d R o s s b y w a v e s s e -

f o r an e a s t e r n p a r t i a l boundary.

The c a s e f o r a w e s t e r n

p a r t i a l b o u n d a r y w i l l d i f f e r f r o m t h e e a s t e r n o n e by t h e p r e s e n c e of

s h o r t Rossby waves t r a p p e d a l o n g t h e n o r t h - s o u t h

boundary and i s d i s c u s s e d i n s e c t i o n 3 . tend the r e s u l t s

p a r t of

In section 4,

t o a more c o m p l e x g e o m e t r y

the

we w i l l e x -

( f o r example a " z i g z a g "

s t e p c o a s t ) . I n s e c t i o n 5 , we s u m m a r i z e o u r r e s u l t s a n d c o n s i d e r t h e i r a p p l i c a b i l i t y t o t h e world ocean.

EASTERN P A R T I A L B O U N D A R Y C A S E

I n c o m i n g K e l v i n wave

W e f i r s t consider the case of p i n g i n g on a p a r t i a l

a u n i t a m p l i t u d e K e l v i n wave i m -

c o a s t a t X = XB e x t e n d i n g from t h e l a t i t u d e

y = b a t south t o i n f i n i t y a t north

(see figure

1 ) . The p a r t o f t h e

wave n o r t h o f y = b w i l l b e r e f l e c t e d a s a s e t o f as i n the case of

a f u l l boundary.

t r a n s m i t t e d K e l v i n wave o f

l o n g Rossby waves

South of b and e a s t of

amplitude

X

B' a TK a n d s h o r t Rossby waves a r e

allowed t o propagate. Therefore west of

u

W

=

UR

X B , we may w r i t e

:

+ $o ( Y ) , (3)

while e a s t of X

B

240 where

(uR, h ) R

a r e components of

a r e components o f

(us,

hs)

s h o r t Rossby waves.

X B and s o u t h of t h e c o r n e r , t h e matching c o n d i t i o n s a r e

=

X

A t

l o n g Rossby waves and

t h a t u and h b e c o n t i n u o u s a t X = X

E'

y < b s o t h a t uE = uw

h E = hW

a t X = XE, y < b . Making u s e o f

h"

( y ) + yx.

= TKJio

Since yields

(2),

(5)

(uw, hw) s a t i s f i e s

(l),

substituting (5) into

(3)

:

s i n c e t h e K e l v i n wave i s a l s o g e o s t r o p h i c ,

or,

-

Y

Therefore

+

Ga i Y X l

x

= 0 for

= 0

y < b ; t h a t means

t h e r e i s no r e f l e c t e d

short

R o s s b y wave a n d o n l y R o s s b y w a v e s a n d K e l v i n wave a r e r e f l e c t e d and t r a n s m i t t e d . Integrating

( 1 ) a c r o s s t h e boundary longitude y i e l d s

b+

L-

yudy

+

h(b+)

-

h(b-)

:

= 0

T h e r e f o r e t h e r e c a n b e no jump i n h a t y = b .

We now s u m m a r i z e c o n d i t i o n s t h a t m u s t b e s a t i s f y a t a n e a s t e r n p a r t i a l boundary

:

( a ) h and u must b e c o n t i n u o u s i n x a t t h e boundary l o n g i t u d e . South of

t h e boundary,

t h e R o s s b y modes m u s t c o n s p i r e t o c a n c e l

t h e untransmitted p a r t of

t h e K e l v i n wave t o e n s u r e c o n t i n u i t y

n

x : hR = uR =

(TK - l)Jio

( b ) Above t h e b o u n d a r y , f u l l boundary, UR

=

namely,

f o r y
(6

t h e c o n d i t i o n s a r e t h e same a s f o r a

no normal f l o w a n d t h e t o t a l h a c o n s t a n t :

-JIo

hR = DK

-

JIo

for

y>b

(7)

241 ( c ) h i s c o n t i n u o u s i n y a t t h e c o r n e r X = XB, y = b . expressions south hR(b) =

( 6 ) and

-

(TK

K

T $,(b)

or

north 1)$,(b) = D

= DK

- Jl0(b)

= hR(b)

K

(8)

( d ) The R o s s b y w a v e s g e n e r a t e d t o t h e w e s t o f o r t h o g o n a l t o t h e K e l v i n mode dix A ) .

Using t h e

(7) for h t h i s implies

t h e boundary a r e

( s e e Cane a n d S a r a c h i k ,

T h i s c o n d i t i o n may b e e x p r e s s e d

1 9 7 9 , Appen-

i n t h e form

where t h e i n n e r p r o d u c t i s d e f i n e d by

Substituting

( 6 ) and

(7) into

(9) yields

+m

Finally using

Equations problem.

[J

( 8 ) and t h e n o r m a l i z a t i o n c o n d i t i o n

( 6 ) , (7),

( 8 ) and

$:

=

13,

-m

(10) give t h e e n t i r e s o l u t i o n f o r t h e

We p o s t p o n e d i s c u s s i o n a f t e r t h e i n c o m i n g R o s s b y wave c a s e

has been solved.

I n c i d e n t R o s s b y wave m o t i o n

Another p o s s i b l e s i t u a t i o n is t o have a s e t of

l o n g Rossby waves

p r o p a g a t i n g from t h e e a s t and e n c o u n t e r i n g t h e c o r n e r a t y = b .

Let

B a n d Ii b e t h e c o m p o n e n t s o f t h e i n c o m i n g R o s s b y w a v e s ( O b ) .S i n c e it i s madeup of holds so,

l o n g Rossby waves, t h e g e o s t r o p h i c r e l a t i o n

as before,

we may c o n c l u d e

waves g e n e r a t e d a t t h e b o u n d a r y . o f a K e l v i n wave the boundary.

(1) s t i l l

t h a t t h e r e a r e no s h o r t R o s s b y

However,

there is the possibility

R

( o f a m p l i t u d e T 1 b e i n g r e f l e c t e d e a s t w a r d from

Hence f o r X > X B ,

uE

=

'rR$o -k B

s o l u t i o n t h e r e m u s t b e s o l e l y Rossby waves

+ h.

a n d hE = TR$

On t h e o t h e r h a n d t h e r e c a n b e no K e l v i n wave w e s t o f

(uR, h R ) .

XB

; the

242

t

coast

b ..........__ ...

O0 iE Figl:Diagram of partial boundary near equator used i n calculating transmission coetficients of reflected planetary waves.

I .:

I

0.5

Fig.2: Transmission coefficients of Kelvin mode and height constants along upper wall for partial boundary a s functions of distance b from the equator t o the zonal coast T k transmission coefficient far incident Kelvin waves, T' transmission coefficient for incident Rossby modes with unit amplitude a t corner, Dk height c o n s t a n t set-up f o r incident Kelvin waves, D' height c o n s t a n t f o r incident Rossby waves.

.

243 S i n c e t h e r e i s n o i n c i d e n t z o n a l v e l o c i t y a b o v e t h e b o u n d a r y , we have

:

u

R

= o

h R = DR = c o n s t a n t

w h i l e c o n t i n u i t y i n x below

u

t h e boundary means:

0'

+

a t X = XB

.

TR$

R

= h(b)

+

(12)

Y
c a s e h must b e continuous

i n y a t the corner: (13)

TRJlo(b).

West o f X B , t h e K e l v i n w a v e a m p l i t u d e i s z e r o . a K e l v i n wave o n t o t h e s o l u t i o n w e s t o f (13) gives

Finally,

R

or T

(11)

= i i + T $

i n the previous D

B'

R

R

hR = h As

f o r y>b a t X = X

=

Therefore projecting

t h e boundary using

(12) and

:

solving for T

j

R

, we rm

get

:

m

- r i ( b ) ~ ~ tJo(Y)dY

We note t h a t T t h i s case)

R

b

R

and D

( a n d b y e x t e n s i o n t h e e n t i r e s o l u t i o n for

depend o n l y on t h e v a l u e o f

mode a t y = b ,

i.e.

t h e h e i g h t of t h e R o s s b y

o n Fi(b).

Results

Figure 2 displays

the solution coefficients

T

and D f o r a n inco-

m i n g K e l v i n wave a n d f o r a n i n c i d e n t R o s s b y w a v e m o t i o n of u n i t h e i g h t a m p l i t u d e a t t h e Corner. F o r t h e K e l v i n wave c a s e , w e o b t a i n t h e s u r p r i s i n g r e s u l t t h a t t h e K e l v i n wave t r a n s m i s s i o n c o e f f i c i e n t g r e a t e r than one

: the

curve asymptotes

cedes t o i n f i n i t y t o t h e north

is

t o one from above as b r e -

(b>O), b u t T

K

goes t o i n f i n i t y as b

244 i n c r e a s e s south of south of

the equator

t h e e q u a t o r a n d b+-m).

(i.e.

as the corner is s i t u a t e d

To u n d e r s t a n d t h i s b e h a v i o r ,

we must

c o n s i d e r t h e e n t i r e mechanism. First,

t h e t r a n s m i t t e d e q u a t o r i a l K e l v i n wave c a n b e c o n s i d e r e d

as a c o a s t a l K e l v i n wave.

To s e e t h a t t h e two a r e t h e s a m e , we n o r -

m a l i z e t h e e q u a t o r i a l K e l v i n wave t o b e o n e a t y = b a n d d e f i n e

-

rl = y

rl

b,

t h e d i s t a n c e from t h e c o a s t .

Therefore

:

i s s m a l l and eis liked a

l/b

(scaled) radius of deformation a t y = b ,

wave a m p l i t u d e b e h a v e s The a m p l i t u d e o f

l i k e the usual f-plane

so the

c o a s t a l K e l v i n wave.

t h i s wave m u s t b e s u c h a s t o make i t s h e i g h t a t

t h e c o r n e r m a t c h t h e c o n s t a n t h e i g h t s e t up among t h e b o u n d a r y a s

(8).

g i v e n by

I n t h e o t h e r hand,

a s b goes south

( b - + - m ) , t h e r e f l e c t e d Rossby

w a v e s h a v e t h e same s t r u c t u r e a s t h e y w o u l d i f finite.

In particular,

the barrierwerein-

t h e h e i g h t s e t s u p t o h a v e t h e same v a l u e

a s f o r an i n f i n i t e c o a s t l i n e case.

The p r o c e s s

up h a s b e e n d i s c u s s e d by A n d e r s o n a n d Rowlands

that brings this set

( 1 9 7 6 ) a n d C a n e and

( 1 9 7 7 ) . Mass i s c a r r i e d t o w a r d s t h e p o l e s i n a m e r i d i o n a l

Sarachik

c u r r e n t t h a t i s l i k e a c o a s t a l K e l v i n wave a n d i s g e o s t r o p h i c a l l y balanced.

The t r a n s p o r t i n t h i s c u r r e n t a t y = b i s g i v e n by

I f we now c a l c u l a t e t h e t r a n s p o r t u n d e r

t h e b o u n d a r y c a r r i e d by

t h e t r a n s m i t t e d K e l v i n , we f i n d by a s y m p t o t i c e x p a n s i o n s that

:

a s b+m,

:

The mass

t r a n s p o r t around t h e c o r n e r i s j u s t what t h e c o a s t a l

K e l v i n wave u n d e r t h e b o u n d a r y i s a b l e t o s u p p l y . As b

goes north

(b++m), t h e a m p l i t u d e o f

t h e t r a n s m i t t e d Kelvin

wave g o e s t o o n e a n d t h e h e i g h t a l o n g t h e n o r t h - s o u t h zero.

c o a s t goes t o

T h e r e i s no t r a n s m i t t e d Rossby wave.

F o r a n i n c o m i n g R o s s b y wave m o t i o n u n d e r the equator t o t h e north, h e i g h t of

the corner,

away from

t h e h e i g h t along t h e w a l l i s simply the

t h e i n c i d e n t R o s s b y modes a t t h e c o r n e r a n d no K e l v i n

245 wave i s r e f l e c t e d .

This is

t o be expected since the height along

t h e w a l l w i l l have a n i n c r e a s i n g s m a l l e r p r o j e c t i o n on t h e equator i a l K e l v i n mode a s t h e b o u n d a r y r e c e d e s

from t h e e q u a t o r .

T H E WESTERN PARTIAL B O U N D A R Y CASE

I n c o m i n g K e l v i n wave

We now d e a l w i t h a w e s t e r n p a r t i a l b o u n d a r y e x t e n d i n g f r o m y =

t o y = b a t a l o n g i t u d e X = Xw

-m

( f i g u r e 3 ) . The o n l y p o s s i b l e

m o t i o n g e n e r a t e d a t t h e c o r n e r a r e l o n g Rossby waves t o t h e w e s t (above t h e east-west s h o r t Rossby waves West o f

c o a s t ) , and K e l v i n waves p l u s boundary-trapped

t o the e a s t of

t h e s o l u t i o n i s made up o f

t h e l o n g i t u d e Xw,

ming K e l v i n wave

the corner. t h e inco-

(assumed t o have u n i t a m p l i t u d e ) , and a s e t o f

l o n g Rossby waves r e f l e c t e d a t t h e b o u n d a ry a t Xw.

The p a r t o f

the

K e l v i n wave n o t r e f l e c t e d i n R o s s b y w a v e s i s t r a n s m i t t e d w i t h a n amplitude T

K

. Equations

continuous i n x,

( 3 ) and

so that u

E

=

W

u

( 4 ) s t i l l hold.

Both u and h a r e

and hE = hw f o r y > b . S i n c e u and

h a r e i n g e o s t r o p h i c b a l a n c e a t X = Xw y > b , we c a n s a y a s i n s e c t i o n 2 t h a t t h e r e i s no d i s t u r b a n c e c r e a t e d b y s h o r t R o s s b y w a v e s and hR = uR = A t X = Xw

(TK

-

l)q0(y)

and y
This condition leads t o

c and h

E

= x(-m)

= 0

E

= 0

; hence

:

;

K

= T ~ l ~ ( y ) + Y T'J'

-m

$,(y)

at

=

xw

Y
Discontinuities i n h a r e thus possible a t y = b. t h e boundary u and h a r e i n g e o s t r o p h i c b a l a n c e a l l o w f o r t h e p o s s i b i l i t y on a n i n f i n i t e

S i n c e w e s t of

f o r a l l y , we m u s t

zonal velocity a t y = b

246 t o b a l a n c e t h e jump i n h

: i.e.

u = A6(y - b ) a t Y = b .

Hence

X B , we h a v e

w e s t of

Using t h e o r t h o g o n a l i t y and c o m p l e t n e s s p r o p e r t i e s o f f u n c t i o n s of

t h e shallow water equations,

wave o n t h e s o l u t i o n

e a s t of

u s i n g t h e f a c t t h a t y$

= -$,

the barrier

t h e eigen

we may p r o j e c t t h e K e l v i n :

a n d i n t e g r a t i n g t h e l a s t t e r m by

parts leads t o :

Note t h a t i t f o l l o w s from

I--

(2),

(15) and

(18) t h a t

V ( y = b ) d x = -A

xW

That i s ,

t h e eastward t r a n s p o r t A i n t h e boundary c u r r e n t a t the

c o r n e r i s a l l c a r r i e d southward by t h e boundary c u r r e n t a l o n g t h e north-south

coast.

T h e r e i s no n e t f l u x i n t h i s b o u n d a r y l a y e r

( s e e Cane a n d S a r a c h i k ,

1977)

; its

only r o l e i s t o r e d i s t r i b u t e

z o n a l l y t h e m a s s f l u x s o t h a t t h e K e l v i n wave may c a r r y i t o f f . P r o j e c t i n g t h e K e l v i n wave w e s t o f

t h e boundary where t h e

K e l v i n wave a m p l i t u d e i s known t o b e o n e l e a d s t o

:

I n c i d e n t R o s s b y wave m o t i o n s

I n t h i s s e c t i o n , we a r e l o o k i n g a t t h e e f f e c t s o f

t h e western

c o r n e r on a n i n c o m i n g R o s s b y w a v e . Again, s e t of

t h e only p o s s i b l e motions generated a t t h e corner a r e a

l o n g Rossby waves t o t h e w e s t ,

boundary-trapped vious section,

r e f l e c t e d K e l v i n wave and

s h o r t Rossby waves t o t h e e a s t .

As

i n t h e pre-

t h e r e i s no p e r t u r b a t i o n c r e a t e d b y s h o r t Rossby

waves above t h e l a t i t u d e o f

the corner

(x

= 0 for

y > b ) . We w r i t e

247 the solution as

(20)

Y’b

-?.&

uE = o = f i + T R $ h E = I i + TR $

Therefore,

Y
uE = 0 o n t h e w a l l i m p l i e s

in

As

a t X = XW

+ yo x

the

previous

section,

,

there is a discontinuity for

h a t y = b and a n i n f i n i t e s i m a l l y t h i n boundary c u r r e n t must b e allowed f o r t o balance it

u R = ii

+

TR$,(y)

h R = FI

+

TR $ , ( y )

h E = fi

+

T ~ $ , ( Y )+ YJ

+

B6(y

b

:

-

b)

(fi + T R J l o ) d y

-a

P r o j e c t i n g t h e K e l v i n wave o n t h e s o l u t i o n e a s t o f leads t o

t h e boundary

:

t h e K e l v i n wave o n t h e R o s s b y w a v e s w e s t o f

The z e r o p r o j e c t i o n o f t h e boundary l e a d s t o

:

Results

F i g u r e 3 shows t h e r e s u l t s o b t a i n e d f o r t h e w e s t e r n b o u n d a r y case.

F o r a n i n c o m i n g K e l v i n wave,

AK t h e a m p l i t u d e o f

t h e boundary

248

0 .:

b

4

0.:

-I

Fig.3: Transmission coefficient (TI and amplitude of the zonal current (A) at the latitude of the western corner as function of the latitude of the zonal coast. Subscript (k) applies to an incident Kelvin wave and subscript ( r ) for an n = l incident Rossby wave.T- i s the value o f T k a s b-+a

249

c u r r e n t a t t h e c o r n e r i s maximum when t h e c o r n e r i s s i t u a t e d a t t h e e q u a t o r a n d b e c o m e s n e g l i g i b l e when t h e p o s i t i o n o f t h e c o r n e r is of

the order of

two r a d i i o f d e f o r m a t i o n

:

for b S -2,

t h e equa-

t o r i a l K e l v i n wave d o e s n o t f e e l t h e c o r n e r a n d p r o p a g a t e s f u r t h e r 1).

f a r w i t h o u t s i g n i f i c a n t c h a n g e i n a m p l i t u d e (TK c r e a s e s northward

from t h e e q u a t o r ,

t h e amplitude of

As b

in-

t h e boundary

c u r r e n t and t h e t r a n s m i s s i o n c o e f f i c i e n t b o t h d e c r e a s e v e r y r a p i d l y a t f i r s t becoming n e g l i g i b l e by b

2.

By t h i s l a t i t u d e ,

there

i s a l m o s t no e q u a t o r i a l K e l v i n wave a n y m o r e . The r e s u l t s i n f i g u r e 3 a r e f o r t h e n = 1 R o s s b y wave a n d h a v e t o t h e v a l u e o f TR a t i n f i n i t y ,

been normalized

- -'/'

TR when

t h e boundary e x t e n d s from

2

T:

71-1/4111 Q d y

to

-m

+m.

i.e.

t h e value of

A s b goes t o

: a s t h e b a r r i e r becomes

+-,

i n f i n i t e a l l of

t h e i n c i d e n t m a s s f l u x i s r e t u r n e d i n t h e r e f l e c t e d K e l v i n wave ( s e e Cane and S a r a c h i c k ,

1 9 7 7 ) . The n o r t h - s o u t h

boundary c u r r e n t

r e d i s t r i b u t e s m e r i d i o n n a l l y t h e i n c o m i n g m a s s f l u x t o make t h i s p o s s i b l e ; i t h a s no n e t m a s s f l u x . boundary case, depends

In contrast to the eastern

where t h e a m p l i t u d e of

t h e r e f l e c t e d K e l v i n wave

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

boundary case i s q u i t e c o m p l i c a t e d . A s n o t e d above, becomes i n f i n i t e ,

t h e a n s w e r d e p e n d s o n t h e t o t a l z o n a l mass f l u x .

For a p a r t i a l b a r r i e r ,

( 2 5 ) shows t h a t t h e r e s p o n s e d e -

equation

pends on t h e s t r u c t u r e of

t h e i n c i d e n t m o t i o n s a s w e l l a s on t h e

Zonal mass f l u x i n c i d e n t o n t h e b a r r i e r .

Note t h a t t h e f i r s t term

i s s m a l l f o r b > > 1 s i n c e JI

i n t h e numerator

the western

as t h e b a r r i e r

i s then s m a l l .

It is

0

a l s o s m a l l f o r b < < -1 b e c a u s e t h e o r t h o g o n a l i t y o f

t h e Kelvin and

R o s s b y modes t h e n i m p l i e s t h a t t h e i n t e g r a l i s s m a l l . T o know how w e l l

t h e nth

mode i s t r a n s m i t t e d p a s t t h e c o r n e r ,

we a l s o c o m p u t e t h e t r a n s m i s s i o n e n e r g y i n t h e nth

f a c t o r y t h a t i s t h e r a t i o of

i s t h e c o m p a r a b l e m e a s u r e f o r t h e K e l v i n wave c a s e .

(TK)'

t i n g t h e nth

the

mode w e s t o f t h e c o r n e r t o t h e i n c i d e n t e n e r g y . Projec-

R o s s b y mode o n t h e s o l u t i o n w e s t o f t h e c o r n e r , w e ob-

tain :

(fi2

2

+

li ) d y

+

BQ(b)

+

T

Y = J+*(fi'

+

S2)dy

--m

F i g u r e 4 shows t h e t r a n s m i s s i o n c o e f f i c i e n t f o r t h e f i r s t 6 Rossby modes. b

-

(2n

+

F o r t h e nth

1)1'2

mode,

t h e v a l u e approaches

zero a s

which i s t h e t u r n i n g l a t i t u d e . A t t h a t l a t i t u d e ,

250

. 4 (a)

-

0.7-

0.6.-

(25-.

-

0.4.

0.3-

0.2.0.1.-

-3 Fig.4(a)-4(b):

-2

-I

The transmission factor

0 4tb)

8

1

2

for the first 6 Rosby waves in

the case of western partial boundary in function of the latitude b of the corner. (a) symetric m o d e s , n odd (b) antisymetric modes, n even

251 the barrier

i s e x t e n d e d enough t o b l o c k t h e i n c i d e n t m o t i o n .

bumps i n t h e c u r v e s a r e d u e t o t h e o s c i l l a t o r y n a t u r e o f compo n e n t

the

The U

.

GENERALIZATION

The c o n f i g u r a t i o n o f coastline)

oceanic coastline

t h e South A m e r i c a

c a n n o t b e drawn s c h e m a t i c a l l y w i t h o n l y one s t e p b u t ,

more r e a l i s t i c a l l y ,

with several steps.

waves i m p i n g i n g on a n o r t h - s o u t h

The c a s e o f

the previous sections.

a p a r t i a l westward boundary i s c o n s t i t u t e d of

north-south

extension ai+l

-

low f r e q u e n c y

z i g z a g c o a s t can b e deduced i n a

s t r a i g h t f o r w a r d wayfrom t h e r e s u l t s o f If

(e.g.

a , , i = 1, N,

N

s t e p s of

we g e t f o r a n i n c o m i n g

K e l v i n wave t h e e x p r e s s i o n :

K

with T .

the amplitude of

number o f

steps,

i =

t h e t r a n s m i t t e d K e l v i n wave a n d i t h e

1, N.

The t r a n s p o r t i n t h e w e s t - e a s t

b o u n d a r y c u r r e n t i s g i v e n by

:

L+ 1

In t h e case of tude of

a n i n c o m i n g Rossby wave,

t h e r e f l e c t e d K e l v i n wave

(in t h i s case,

we g e t f o r t h e a m p l i -

:

t h e s u b s c r i p t i c o u n t s t h e number o f

east t o west ; see f i g u r e 5 ) .

s t e p s from

252 and t h e e a s t - w e s t

transport a t the corner i

:

/ / /

/ /

- - N- /-/ / /-/ A- - - - - - - - - - - - - - - 4

---

6

--

2

/

Equator Ocean

/

//////// /

/ / /

Fiq.5 S t e p structure u s e d to schematize the B r a s i l c o a s t

S i m i l a r arguments have been used t o compute t h e s o l u t i o n of f r e q u e n c y waves i m p i n g i n g on a t h i n i s l a n d o r c h a i n o f

( s e e Cane a n d du P e n h o a t , v a r i a t i o n e a s t of

1982). W e have found a c o n s t a n t depth

the island,

t e r n s i d e of t h e i s l a n d s . i s s k e t c h e d i n f i g u r e 6.

low

islands

two b o u n d a r y c u r r e n t s o n t h e e a s -

T h e s o l u t i o n f o r a n i n c o m i n g K e l v i n wave

253

h=hT+oI

I

xwt-l

I

I

$1

,,'u=AS(y

/

I

/ /

/

u'

/

i=h=i+ho*

ncoming Celvin wave

I

,boundary current of width wt-l

3

I u=h=O

I I I

I I

.

I

\ \

\

I

I

1

I

\

I

I I I I

I

I

I

I I

\ u=h \ = T$o 7 ' 1

\ \ \ \

I

If

I

I q u = h=Tqbo Transmitted Kelvin wave

\

Fig.

1 I

0

h=D

/

/ / + x u - -t

I I 1

'

S k e t c h o f t h e s o l u t i o n f o r a n i n c o m i n g K e l v i n wave on a t h i n island. For t > > l , t h e asymptotic solution holds o u t t o a l o n g i t u d e x - t , t h e f a r t h e s t e a s t w a r d t h e K e l v i n wavc t r a v e l s i n t i m e . To t h e w e s t , it a p p l i e s behind a f r o n t w i t h a form x - - 1 / 3 t near t h e equator and x - y b 2 t f o r high latitude.

6

an i s l a n d i s small

a and b

latitude of

(i.e.,

a - b < < 1 radius of deformation,

t h e n o r t h and south t i p o f

the i s l a n d ) , then

low f r e q u e n c y waves p a s s i t a l m o s t u n d i s t u r b e d w i t h t h e mass f l u x i n c i d e n t on t h e upstream s i d e flowing around it about equally t o t h e n o r t h a n d s o u t h a n d c o n t i n u i n g o n d o w n s t r e a m i n t h e lee island.

If

the island is large

of

the

( l a i r Ibl >,2 r a d i i o f d e f o r m a t i o n ) ,

t h e n t h e p r i n c i p a l r e s p o n s e i s o r g a n i z e d a s i t would be i f t h e island b a r r i e r w e r e meridionally infinite.

254 DISCUSSION

W e now a p p l y o u r r e s u l t s t o t h e r e a l o c e a n . the c o a s t of t h e Gulf of Guinea

e f f e c t of north)

I n the Atlantic the

( r o u g h l y a t 5" l a t i t u d e

i s v e r y s m a l l f o r e i t h e r low f r e q u e n c y Rossby waves o r t h e

K e l v i n wave.

2 f o r n = 1 , a 2 2 i n non d i m e n s i o n a l u n i t s ,

(see fig.

a n d f o r h i g h e r b a r o c l i n i c modes a 2 2 ) . up on the n o r t h - s o u t h

I n the case of

coast,

t h e South A m e r i c a coast,

schematically by 3 s t e p s

between 0 . 2 0

constant height is set

w e add f r i c t i o n ,

c o a s t and i f

boundary c u r r e n t along t h e east-west

represented

A

(fig.

i n t h e A t l a n t i c ocean,

5)

:

t h e f i r s t corner

S and 3 S a f f e c t s t h e long e q u a t o r i a l

w i t h an i n t e n s e westward t h e two o t h e r s t e p s ,

current a t this point

t h e amplitude of

there is a

which widens westward.

K e l v i n wave

(see t a b l e 1 ) . For

t h e t r a n s m i t t e d K e l v i n wave

d e c r e a s e s o n l y s l i g h t l y a n d r e s u l t s w i l l n o t c h a n g e b y a d d i n g more

s t e p s : low f r e q u e n c y w a v e s w i l l n o t f e e l a more d e t a i l e d c o a s t v e r y much.

F o r t h e n = 1 R o s s b y mode,

only approximately

63

%

of

t h e e n e r g y i n t h e f i r s t h o r i z o n t a l mode i s t r a n s m i t t e d t h r o u g h t h e 3 steps.

TABLE 1 Parameter values f o r t h e c o a s t of South A m e r i c a (a) f o r an incid e n t K e l v i n wave, ( b ) f o r n = 1 Rossby wave. The e q u a t o r i a l l e n g t h s c a l e R1 e t R 2 a r e f r o m C a n e a n d M o o r e ( 1 9 8 1 ) .

Y

TK

BK

f i r s t b a r o c l i n i c mode

-0.113

0.727

0.412

Equatorial length scale R1 = 3 2 6 km

-1.022

0.693

0.142

- 1.704

0.687

0.057

Second b a r o c l i n i c mode

-0.149

0.704

0.465

-1.344

0.688

0.099

-2.240

0.687

0.016

Equatorial R2

length scale

= 2 4 8 km

255

n = 1 Rossby wave

Y

First baroclinic mode R1 = 3 2 6 km

Second baroclinic mode R 2 = 2 4 8 km

TR

BR

Y

-1.704

0.001

0.09

0.95

-1.022

0.01

0.111

0.79

-0.1136

0.06

-2.24

0.0001

0.043

0.99

-1.344

0.004

0.114

0.88

-0.149

0.061

-0.064

0.63

-0.078

0.63

We have computed the different coefficients for the coast of New Guinea

(Pacific ocean) schematically represented with 6 steps

(table 2 ) .

For an incident Kelvin wave, the amplitude of the trans-

mitted wave is greater than 0 . 7 3

for the first and second barocli-

nic modes and more steps will not change it significantly. For the n = 1 Rossby wave, 6 4

%

of the energy is transmitted in this mode

pass the last step. For higher horizontal mode (not shown), this value decreases.

TABLE 2 Parameter values for the coast of New Guinea

(a) for an incident

Kelvin wave, (b) for n = 1 Rossby wave.

Y First baroclinic mode

R1

= 3 5 7 km

-0.155

TK 0.877

BK 0.193

-0.465

0.780

0.214

-0.933

0.754

0.097

-1.245

0.735

0.104

- 1.867

0.733

0.041

-3.112

0.733

0.001

256

R

n = 1 R o s s b y wave

Y

F i r s t b a r o c l i n i c mode

R1

-3.112

357 km

=

Y

BR

T

0.005

-0

0.999

-1.867

J ~ I O - ~ 0.076

-1.245

0.006

0.117

0.860

-0.933

0.009

0.104

0.773

-0.465

0.027

0.018

0.671

-0.155

0.031

0.075

0.643

0.971

i s s i t u a t e d a t t h e c o n n e c t i o n b e t w e e n t h e I n d i a n and

New G u i n e a

P a c i f i c oceans and t h e flow through t h i s c o n n e c t i o n c o u l d t u r n o u t t o h a v e c o n s i d e r a b l e s i g n i f i c a n c e i n t h e e x h a n g e b e t w e e n t h e two o c e a n s a n d i t s p o s s i b l e r e l a t i o n s t o E l Nin;. u s i n g C a n e a n d du P e n h o a t ' s z a t i o n of

%

of

crude calculation,

(1982) r e s u l t s a n d a r o u g h s c h e m a t i -

t h e a r e a shows t h a t f o r a n =

only l e s s than 9

A

I

i n c i d e n t Rossby wave,

t h e incoming energy i s t r a n s m i t t e d p a s s

Borneo i s l a n d and t h a t Java-Sumatra

i s l a n d s a c t almost a s an i n f i -

n i t e b a r r i e r f o r low f r e q u e n c y e q u a t o r i a l R o s s b y w a v e s . C a l c u l a t i o n s c a r r i e d o u t f o r e q u a t o r i a l i s l a n d s show t h a t no island,

i n t h e world ocean,

w a v e s v e r y much,

because

i n f l u e n c e s low f r e q u e n c y

their

north-south

compared t o t h e e q u a t o r i a l r a d i u s o f du P e n h o a t ,

s l i g h t l y enhanced i s thickened mode).

deformation

1982). West o f t h e i s l a n d ,

equatorial

extension i s t o o small ( s e e Cane a n d

the sea level signal is

(and c o n s t a n t a t t h e c o a s t ) and t h e thermocline

( a s s u m i n g i t t o b e d e s c r i b e d by t h e s e c o n d b a r o c l i n i c

E a s t of

the island,

t h e t h i c k n e s s decreases toward t h e

equator due t o t h e presence of Galapagos archipelago, c i e n t o v e r 0.98

s h o r t Rossby waves.

Even f o r t h e

our theory p r e d i c t s a transmission coeffi-

f o r t h e f i r s t a n d s e c o n d b a r o c l i n i c mode K e l v i n

waves,

s o t h a t t h e i s l a n d s do n o t a f f e c t t h e p r o p a g a t i o n o f t h e s e

waves.

T h i s r e s u l t a g r e e s w i t h Yoon's

tions.

An i n c i d e n t R o s s b y wave i s t r a n s m i t t e d w i t h o u t m a j o r

of

(1981) n u m e r i c a l c a l c u l a -

e n e r g y a n d t h e r e i s o n l y a weak r e f l e c t e d K e l v i n wave.

loss

In fact,

i t s p r o p a g a t i o n w i l l b e more s e v e r e l y i n f l u e n c e d by t h e mean c u r r e n t system

(Philander,

1978). C a l c u l a t i o n s c a r r i e d o u t f o r t h e

M a l d i v e s i s l a n d s show t h a t t h e y do n o t a c t a s a s i g n i f i c a n t b a r rier,

because,

although they have a g r e a t e r l a t i t u d i n a l extension,

257 the islands close t o t h e equator a r e small.

We c o n c l u d e t h a t i s l a n d s i n t h e r e a l e q u a t o r i a l o c e a n s w i l l n o t a f f e c t t h e Fropagation of

low f r e q u e n c y w a v e s s i g n i f i c a n t l y a n d

t h a t perturbations w i l l occur only i n t h e i r vicinity.

The i r r e g u -

l a r i t i e s i n t h e B r a z i l i a n c o a s t have a n o t i c e a b l e e f f e c t b u t litt l e i s g a i n e d r e p r e s e n t i n g t h e m by more t h a n a s i n g l e s t e p . G u l f o f G u i n e a h a s l i t t l e e f f e c t on i n c o m i n g K e l v i n w a v e s t h e response along i t s c o a s t i s of s a k e ) and t h e complex,

course of

The

(though

i n t e r e s t f o r i t s own

ragged boundary i n t h e western P a c i f i c i s

a n e f f e c t i v e b o u n d a r y f o r s u c h low f r e q u e n c y w a v e s .

REFERENCES

A b r a m o w i t z a n d S t e g u n , 1 9 6 5 . Handbook o f m a t h e m a t i c a l f u n c t i o n s . D o v e r , N e w York, 1046 p p . Anderson, D.L.T. and Rowlands, P.B., 1 9 7 6 . The r o l e o f i n e r t i a g r a v i t y a n d p l a n e t a r y waves i n t h e r e s p o n s e o f a t r o p i c a l o c e a n t o t h e i n c i d e n c e o f a n e q u a t o r i a l K e l v i n wave o n a m e r i d i o n a l b o u n d a r y . J . Mar. R e s . , 34: 295-312. Bye, J . A . T . and Gordon, A . H . , 1982. S p e c u l a t e d c a u s e o f i n t e r h e m i s p h e r i c o s c i l l a t i o n . N a t u r e , 296: 5 2 - 5 4 . a n d Moore, D . , 1 9 8 1 . A n o t e o n low f r e q u e n c y e q u a t o r i a l Cane, M.A. b a s i n modes. J . P h y s . O c e a n o g r . , 1 1 : 1 5 7 8 - 1 5 8 4 . Cane, M.A. and du Penhoat, Y . , 1 9 8 2 . The e f f e c t s o f i s l a n d s o n low f r e q u e n c y e q u a t o r i a l m o t i o n s . J . Mar. R e s . ( i n p r e s s ) . and S a r a c h i k , E.S., 1 9 7 6 . F o r c e d b a r o c l i n i c o c e a n moCane, M.A. t i o n s : I . The l i n e a r e q u a t o r i a l u n b o u n d e d c a s e . J . Mar. R e s . , 34: 629-665. Cane, M.A. and S a r a c h i k , E.S., 1 9 7 7 . F o r c e d b a r o c l i n i c o c e a n mot i o n s : 11. The l i n e a r e q u a t o r i a l b o u n d e d c a s e . J . Mar. R e s . , 35: 395-432. Cane, M.A. and S a r a c h i k , E.S., 1 9 7 9 . F o r c e d b a r o c l i n i c o c e a n mot i o n s : 111. The l i n e a r e q u a t o r i a l b a s i n c a s e . J . Mar. R e s . , 37: 366-398. and S a r a c h i k , E.S., 1 9 8 1 . The r e s p o n s e o f a l i n e a r b a Cane, M . A . r o c l i n i c e q u a t o r i a l o c e a n t o p e r i o d i c f o r c i n g . J . Mar. R e s . , 39: 652-693. G i l l , A.E., 1 9 7 5 . Model o f e q u a t o r i a l c u r r e n t s . Symposium o n numer i c a l m o d e l s o f o c e a n c i r c u l a t i o n . N a t . A c a d . S c i . , Durham, N.H., U.S.A., OCt. 17-20-72. Patton, R.J., 1981. A n u m e r i c a l model o f e q u a t o r i a l waves w i t h app l i c a t i o n t o t h e s e a s o n a l u p w e l l i n g i n t h e Gulf o f Guinea. 1 2 0 pp. MS t h e s i s , M . I . T . , Pedlosky, J . , 1965. A n o t e on t h e w e s t e r n i n t e n s i f i c a t i o n of t h e o c e a n i c c i r c u l a t i o n . J . Mar. R e s . , 2 3 : 2 0 7 - 2 1 0 . P h i l a n d e r , S.G.H., 1979. E q u a t o r i a l waves i n t h e p r e s e n c e o f t h e e q u a t o r i a l u n d e r c u r r e n t . J . P h y s . O c e a n o g r . , 9 : 254-262. P h i l a n d e r , S.G.H. a n d P a c a n o w s k i , 1 9 8 0 . The g e n e r a t i o n o f e q u a t o r i a l c u r r e n t s . J . Geophys. R e s . , 8 5 ( C 2 ) : 1123-1136. 1981. Evidence o f e q u a t o r i a l t r a p p e d Ripa, P. a n d Hayes, S . P . , waves a t t h e G a l a p a g o s I s l a n d s . J. Geophys. R e s . , 86: 6509-6516. 1 9 8 1 . The f l o w o f e q u a t o r i a l K e l v i n w a v e s a n d t h e Rowlands, P . G . , e q u a t o r i a l u n d e r c u r r e n t a r o u n d a n i s l a n d . J . Mar. R e s . i n p r e s s .

258

Wirtky, K., 1 9 6 1 . P h y s i c a l o c e a n o g r a p h y o f t h e S o u t h e a s t A s i a n wat e r s . Naga r e p o r t , v o l u m e 2 - The U n i v e r s i t y o f C a l i f o r n i a S c r i f f s I n s t i t u t i o n s o f o c e a n o g r a p h y , La J o l l a , C a l i f o r n i a . Yoon, 1 9 8 1 . E f f e c t s o f i s l a n d s o n e q u a t o r i a l w a v e s . J . G e o p h y s . R e s . , 86: 10913-10920.

259

COASTAL EFFECTS ON UPWELLING.

P a s c a l e DELECLUSE L a b o r a t o i r e d ' O c 6 a n o g r a p h i e physique/MNHN, P a r i s , F r a n c e

Abstract S t e a d y wind p a r a l l e l t o t h e c o a s t g e n e r a t e s u p w e l l i n g and t h e i n f l u e n c e 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 wind o r t h e c o a s t a l i n d e n t a t t i o n s must b e t a k e n i n t o a c c o u n t i n t h e d e t e r m i n a t i o n o f t h e l i f t i n g of t h e t h e r m o c l i n e . A s h a l l o w w a t e r model i s used t o d i s p l a y t h e r e s p o n s e o f t h e ocean around a c a p e . The r e s p o n s e t o s t e a d y wind f o r c i n g i s d e s c r i b e d i n ( 2 ) . A s p a t i a l l y uniform wind, v a r y i n g w i t h t i m e a c c o r d i n g t o t h e r e a l wind r e c o r d s i n Dakar, i s t h e n used t o f o r c e t h e o c e a n and t h e r e s p o n s e ' i s examined o f f - s h o r e and a l o n g t h e c o a s t f o r d i f f e r e n t f r e q u e n c y bands ( 3 ) . Ekman pumping d o m i n a t e s o f f s h o r e f o r i n t e r m e d i a t e r a n g e f r e q u e n c i e s ( 2 0 - 3 d a y s ) and t h e c o a s t a l dynamics i s d r i v e n by Kelvin waves e x c e p t f o r v e r y h i g h and v e r y low f r e q u e n c i e s . The r e l e v a n c e o f t h e s e r e s u l t s f o r Dakar i s d i s c u s s e d i n ( 4 ) .

1.

INTRODUCTION

R e c e n t l y s a t e l l i t e p i c t u r e s have shown s y n o p t i c maps of t h e SST (Sea S u r f a c e Temperature) i n t h e area of Dakar and u p w e l l i n g w a s c l e a r l y v i s i b l e n o r t h and s o u t h o f t h e c a p e ( C i t e a u , G u i l l o t and Roy, p e r s o n a l communication). The p u r p o s e

of t h i s p a p e r i s t o d e m o n s t r a t e t h a t t h e p r e s e n c e of a cape may a f f e c t t h e l o c a l dynamics. The Dakar area w a s chosen b e c a u s e t h e coast i s mainly n o r t h - s o u t h w i t h a s m a l l c a p e a t Dakar. During a l o n g p a r t o f t h e y e a r ( e x c e p t t h e summer months),

Dakar i s s i t u a t e d i n t h e t r a d e winds and u p w e l l i n g a p p e a r s . The area i s w e l l documented by t h e work done by ORSTOM ( R o s s i g n o l , 1973; Merle, 1981;

...) .

Dakar i s l o c a t e d a t

15'N,

1973; P o r t o l a n o ,

v e r y c l o s e t o t h e e q u a t o r i a l band and

Rossby waves can e v a c u a t e e f f i c i e n t l y t h e e n e r g y away from t h e e a s t e r n boundary. I n p a r t 2 , a r e v i e w o f a n a l y t i c a l r e s u l t s f o r u p w e l l i n g i s g i v e n and t h e academic problem o f t h e u p w e l l i n g d r i v e n by a n u n i f o r m wind stress i n p r e s e n c e of a cape i s solved numerically.

Then, i n p a r t 3, t h e wind r e c o r d e d a t t h e

Dakar a i r p o r t i s u s e d t o d r i v e t h e model d u r i n g one y e a r . A d e s c r i p t i o n o f t h e o c e a n i c r e s p o n s e i s g i v e n , c o n s i d e r i n g t h e d i f f e r e n t f r e q u e n c i e s o f t h e wind f o r c i n g . F i n a l l y p a r t 4 c o n t a i n s t h e d i s c u s s i o n o f t h e r e s u l t s and t r i e s t o es-

timate t h e i r r e l e v a n c e t o t h e r e a l o c e a n i c r e s p o n s e .

260 2.

UPWELLING I N PRESENCE OF A CAPE FOR AN UNIFORM W I N D FORCING

2.1

Analytical r e s u l t s D e s p i t e t h e f a c t t h a t t h e u p w e l l i n g e v e n t i s a 3-dimensional phenomenon

(Halpern, 1 9 7 6 ) , a r e a s o n a b l y good d e s c r i p t i o n of t h e p h y s i c a l p r o c e s s e s can be o b t a i n e d w i t h a t w o - l a y e r model. Many a u t h o r s have s t u d i e d a n a l y t i c a l l y and num e r i c a l l y t h e c o a s t a l response of a two-layer ocean t o simple wind-stress p a t t e r n s ( A l l e n , 1976; Charney, 1955; Csanady, 1975; CrGpon and R i c h e z , 1982;

...)

and have shown t h a t t h e c o n t r i b u t i o n o f t h e b a r o c l i n i c t e r m s t o t h e t h e r -

mocline e l e v a t i o n w a s e s s e n t i a l . I n o r d e r t o d e s c r i b e t h e o c e a n i c c i r c u l a t i o n around a c a p e , i t i s u s e f u l t o g i v e a b r i e f r e v i e w o f t h e a n a l y t i c a l r e s u l t s o b t a i n e d by Crdpon and Richez (1982). L e t

h

d e n o t e t h e i n t e r f a c e e l e v a t i o n from i t s i n i t i a l p o s i t i o n ;

T (Tx,Ty), t h e a p p l i e d wind-stress; t h i s analysis); d e e p l a y e r and

where

c

Ap c = (--

Ap p

,

f

,

t h e C o r i o l i s parameter (constant f o r

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

t h e r e f e r e n c e d e n s i t y ; t h e i n t e r n a l r a d i u s of deformation i s

i s t h e p r o p a g a t i o n s p e e d o f t h e i n t e r n a l mode gH)

:

112

The s u r f a c e l a y e r t h i c k n e s s

H

i s c o n s i d e r e d n e g l i g i b l e compared t o t h e deep

l a y e r t h i c k n e s s . With t h e Boussinesq and t h e h y d r o s t a t i c a s s u m p t i o n s , t h e l i n e a r i z e d e q u a t i o n s t h a t govern t h e dynamics a r e t h e s h a l l o w water e q u a t i o n s

-au a t-

f v = - g

Ap 7

ax +

Tx

A p r o p a g a t i o n e q u a t i o n c a n be deduced f o r

The e q u a t i o n f o r

h

:

h :

i s s o l v e d by F o u r i e r t r a n s f o r m i n s p a c e and Laplace

t r a n s f o r m i n t i m e and a s y m p t o t i c s o l u t i o n s are c a l c u l a t e d f o r s p e c i f i c wind forcing. L e t u s c o n s i d e r t h e case o f an u n i f o r m wind blowing o v e r an ocean l i m i t e d by

two s o l i d b o u n d a r i e s a t r i g h t a n g l e s a t t h e e a s t e r n edge and a t t h e s o u t h e r n edge. Two d i f f e r e n t cases must be c o n s i d e r e d . F i r s t , l e t u s assume t h a t t h e wind blows southward ( f i g . 1 ) [ t h i s case w i l l be c a l l e d Bay A ] .

261

1.

Fig.

Bay A .

Away from t h e c o r n e r , a l o n g t h e e a s t e r n boundary

(x = 0 )

t h e wind c r e a t e s

a boundary c o a s t a l j e t growing l i n e a r l y w i t h t i m e . Upwelling compensates f o r t h e Ekman d r i f t away from t h e c o a s t . Along t h e s o u t h e r n boundary

(y

=

O), a

s m a l l downwelling due t o t h e wind normal t o t h e c o a s t , bounded w i t h t i m e , a p p e a r s . A K e l v i n f r o n t i s c r e a t e d i n t h e c o r n e r f o r t h e c u r r e n t t o match t h e boundary c o n d i t i o n s ( n o f l u x t h r o u g h b o u n d a r i e s ) . T h i s f r o n t p r o p a g a t e s poleward a l o n g t h e e a s t e r n boundary and compensates e x a c t l y t h e a c c e l e r a t i o n due t o t h e wind stress. A f t e r i t s p a s s a g e , t h e f l o w i s s t e a d y and t h e u p w e l l i n g i s s t a b i lized. The a n a l y t i c a l s o l u t i o n a l o n g t h e e a s t e r n c o a s t t h a t summarizes t h i s mechanism i s : T

h

=

Y

PCf

where

x

. xp

(3 {[ft R

- (ft +

4 R

ac(ct-y)I - (1 -

1

1 + Ict-yl

-

1 K(ct -y)

1

i s t h e Heaviside f u n c t i o n .

The t e r m

0

r e p r e s e n t s t h e a c c e l e r a t i n g flow and t h e K e l v i n f r o n t . The t e r m

@ shows t h e e f f e c t o f t h e s m a l l downwelling and i t s p r o p a g a t i o n northward as a K e l v i n f r o n t . The l o n g t e r m a s p e c t of t h e s o l u t i o n i s a c o n s t a n t p r e s s u r e g r a -

d i e n t a l o n g t h e e a s t e r n c o a s t i n e q u i l i b r i u m w i t h t h e wind f o r c i n g . L e t c s now c o n s i d e r t h e same wind b u t assume a d i f f e r e n t geometry. The ocean

i s l i m i t e d by two s o l i d b o u n d a r i e s a t i t s n o r t h e r n edge and i t s e a s t e r n edge (Bay B, f i g . 2 ) .

F i g . 2.

Bay B.

262 A f t e r t h e w i n d ' s o n s e t , t h e r e i s an u p w e l l i n g a l o n g t h e e a s t e r n c o a s t and no mechanism w i l l p r e v e n t i t from growing. A s m a l l bounded u p w e l l i n g a p p e a r s a l o n g t h e n o r t h e r n coast (due t o t h e e f f e c t o f wind f o r c i n g normal t o t h e c o a s t l i n e ) b u t t h i s s i g n a l i s q u i c k l y masked by t h e a r r i v a l of a K e l v i n f r o n t , g e n e r a t e d i n t h e c o r n e r , t h a t p r o p a g a t e s t h e f l o w a c c e l e r a t i o n westward i n o r d e r t o f e e d t h e i n c r e a s i n g e a s t e r n t r a n s p o r t . A p r e s s u r e g r a d i e n t i s slowly e s t a b l i s h e d a l o n g t h e c o a s t ( i n balance with t h e c o a s t a l c u r r e n t ) . This system i s c o n t i n u o u s l y growing w i t h t i m e . The m a t h e m a t i c a l e x p r e s s i o n o f t h e s o l u t i o n a l o n g t h e northern c o a s t i s t h e following : h

=

-k exp PCf

(% R

[(ft

+

&) R Jf(ct+x)

+

1

0 The t e r m

0

1

(1 -

+

Ict+x(

7 -

1 JE(ct+x)l

0

r e p r e s e n t s t h e K e l v i n f r o n t t h a t a c c e l e r a t e s t h e flow and t h e term

@ i s t h e small u p w e l l i n g due t o t h e d i r e c t wind e f f e c t a l o n g t h i s c o a s t . Symmet r i c a l s o l u t i o n s can be deduced f o r d i f f e r e n t c o a s t d i r e c t i o n s and o t h e r wind d i r e c t i o n s . The same approach i s now u s e d t o o b s e r v e t h e e f f e c t 0 f c a p e s . A ~prev i o u s l y , t h e r e are two d i f f e r e n t classes. F o r t h e c a s e Cape A ( f i g . 3) which i s similar t o Bay A , a s m a l l bounded upw e l l i n g a p p e a r s a l o n g t h e s o u t h e r n c o a s t and t h e l i n e a r l y growing u p w e l l i n g , a l o n g t h e e a s t e r n c o a s t , i s s t a b i l i z e d by a Kelvin f r o n t g e n e r a t e d i n t h e comer.

aaa a a fig. 3.

Cape A.

f i g . 4.

Cape B.

F o r t h e c a s e Cape B ( f i g . 4 ) , similar t o Bay B, t h e r e i s c o n t i n u o u s l y increas i n g u p w e l l i n g a l o n g t h e e a s t e r n c o a s t and t h e f l u x i s d e v i a t e d as a Kelvin f r o n t a r o u n d t h e c o r n e r . T h i s f r o n t c a n c e l s t h e weak downwelling and c r e a t e s an u p w e l l i n g l a t e r a l o n g t h e n o r t h e r n c o a s t where a p r e s s u r e g r a d i e n t w i l l balance t h e coastal c u r r e n t . A l l t h e p r e v i o u s r e s u l t s can b e summarized t o d e s c r i b e t h e r e s p o n s e of t h e

ocean a r o u n d a c a p e ( f i g . 5 ) .

263

a

Cape

F i g . 5.

The p o s i t i o n

@)

i s an example o f Bay A . A Kelvin f r o n t i s g e n e r a t e d i n

and c r e a t e s 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 c o a s t

C1

stress f o r c i n g and a r r e s t s c u r r e n t a c c e l e r a t i o n .

In

, t h a t b a l a n c e s t h e wind@,

r e s u l t s o f Cape B can

be a p p l i e d . A Kelvin f r o n t w i l l r a i s e t h e t h e r m o c l i n e a l o n g a c c e l e r a t i o n along t h e bay

C1.

The c a p e

0

@)

C2

and restore t h e

w i l l c r e a t e a s t a b i l i z i n g Kelvin f r o n t b u t

@ w i l l f i n a l l y r e - e s t a b l i s h t h e a c c e l e r a t i o n a l l along t h e c o a s t l i n e .

T h i s i s a b r i e f summary o f t h e mechanism; s e c o n d a r y e f f e c t s a p p e a r (bounded mot i o n s due t o t h e wind normal t o t h e c o a s t , c o u p l i n g w i t h i n e r t i a l motions) t h a t

are d i s c u s s e d i n t h e p a p e r o f Biju-Duval and C h a r t i e r ( 1 9 8 2 ) . The i m p o r t a n t r e s u l t i s t h a t , a f t e r a t i m e l o n g enough f o r a Kelvin f r o n t t o reach t h e c o a s t

C1

,

coming from

@,

t h e u p w e l l i n g e x i s t s everywhere b u t i s

s l i g h t l y weaker on t h e n o r t h e r n c o a s t b e c a u s e i t h a s been s t o p p e d t w i c e d u r i n g t h e t i m e it t a k e s f o r a Kelvin wave t o p r o p a g a t e from @

2.2

to

0.

The n u m e r i c a l approach F i n i t e d i f f e r e n c e schemes ( i n s p a c e and t i m e ) were u s e d t o w r i t e n u m e r i c a l l y

t h e g e n e r a l i z e d s h a l l o w water e q u a t i o n s on a s p h e r e , w i t h n o n - l i n e a r

t e r m s . The

code, d e s c r i b e d i n t h e Appendix, can s e r v e t o s o l v e many d i f f e r e n t problems. The p r e s e n t one i s a spin-up problem and o n l y a few d a y s o f s i m u l a t i o n are r e q u i r e d t o g i v e t h e s o l u t i o n p a t t e r n s . F o r s u c h a s m a l l t i m e i n t e g r a t i o n , c u r r e n t s do n o t r e a c h v e r y h i g h s p e e d and it i s n o t n e c e s s a r y t o keep t h e n o n - l i n e a r

terms.

The s p h e r i c a l t e r m s and e s p e c i a l l y t h e b e t a e f f e c t w i l l n o t b e i n c l u d e d i n t h e computation f o r t h e s a m e reason. A southward w i n d - s t r e s s

0 . 5 dyn/cm2

of

i s a p p l i e d uniformly over t h e ocean,

s t a r t i n g from r e s t . The wind i s s l o w l y i n c r e a s i n g from z e r o t o i t s f i n a l v a l u e with a cosine t a p e r o f

100

t i m e s t e p s . The i n t e r f a c e i s p r e s e n t e d d u r i n g f o u r

f o l l o w i n g d a y s i n f i g . 6. I t i s r a p i d l y r i s i n g a l o n g t h e c o a s t l i n e s and t h e K e l v i n f r o n t s , g e n e r a t e d i n each c o r n e r a t

a l l p r o p a g a t e a t t h e same s p e e d

c =

AP 112 (7 gH)

=

1 m/s

:

t = 0 ,

are c l e a r l y v i s i b l e . They

264 with 2 .

- =

and

H = 50 rn

F i g . 6. I n t e r f a c e d e p t h d u r i n g f o u r foll.owing d a y s . The c o n t o u r i n t e r v a l i s 150 m and s t i p p l e d a r e a i n d i c a t e s u p w e l l i n g .

Even t h e s e c o n d a r y downwelling e f f e c t a l o n g t h e c o a s t

C2

can be e x h i b i t e d . The

motions a r e c o n f i n e d a l o n g t h e c o a s t w i t h i n t h e r a d i u s o f d e f o r m a t i o n R =

C

--26km f

The e x p o n e n t i a l p r o f i l e o f t h e v e l o c i t y i s n o t i c e a b l e i n f i g . 7 .

:

265

200

15'

10'

5 O

Longitude

100

'I

Fig. 7. Velocity v e c t o r s f o r t h e same experiment a f t e r four days.

The b e s t way t o o u t l i n e t h e f r o n t propagation i s t o p r e s e n t t h e contours of h

a s f u n c t i o n s of space and time along t h e e a s t e r n c o a s t . This i s done i n

f i g . 8. Lines p a r a l l e l t o t h e space a x i s mean growing upwelling (when they a r e e q u i d i s t a n t , t h e growth i s l i n e a r ) and l i n e s p a r a l l e l t o t h e time a x i s represent s t a b l e s i t u a t i o n ( c o n s t a n t v a l u e s ) . The four Kelvin f r o n t s a r e represented with dashed l i n e s i n t h e northern p a r t . Other c o n f i g u r a t i o n s of capes have been t e s t e d with t h e f i n i t e element model w r i t t e n by Lien Hua e t a l .

This model allows a good d e s c r i p t i o n of i r r e g u l a r

c o a s t s . Trapezoidal, t r i a n g u l a r and even rounded capes were p u t i n t h e model with about t h e same dimensions and t h e r e s u l t s were t h e following

:

f o r t h e r e c t a n g u a l r cape, both numerical models ( t h e f i n i t e d i f f e r e n c e model and t h e f i n i t e element model) give t h e same r e s u l t s i n p e r f e c t agreement with t h e a n a l y t i c a l approach;

266

F i g . 8. Space-time diagram o f t h e i n t e r f a c e d e p t h a l o n g t h e e a s t e r n c o a s t . The c o n t o u r i n t e r v a l i s 2 . 5 0 m and t h e c e n t r a l s t r i p r e p r e s e n t s t h e c a p e . Dashed l i n e s d e p i c t t h e Kelvin f r o n t propagation.

f o r o t h e r s h a p e s , i t i s more and more d i f f i c u l t t o d i s t i n g u i s h t h e d i f f e r e n t f r o n t s and where e x a c t l y t h e y a r e g e n e r a t e d ; b u t however t h e s h a p e , t h e f i n a l r e s u l t i s t h e same : t h e u p w e l l i n g e x i s t s everywhere a f t e r a w h i l e b u t i s weaker a l o n g t h e n o r t h e r n p a r t b e c a u s e o f t h e d e l a y due t o K e l v i n f r o n t p r o p a g a t i o n a l o n g t h e f a c e s o f t h e c a p e normal t o t h e wind.

(Compare f i g . 6 and f i g . 9 where

t h e s o l u t i o n f o r a t r i a n g u l a r cape with t h e f i n i t e element i s p r e s e n t e d . ) I n t h e n e x t s e c t i o n , s i m u l a t i o n s w i l l be c a r r i e d on w i t h a w i n d - s t r e s s

uni-

form i n s p a c e b u t h a v i n g a r e a l t i m e v a r i a b i l i t y . The f i n i t e d i f f e r e n c e model, w i t h a r e c t a n g u l a r c a p e , w i l l be u s e d f o r t h e f o l l o w i n g r e a s o n : it i s much c h e a p e r t h a n t h e f i n i t e e l e m e n t model;

i t h a s been shown t h a t t h e e v e n t s a l o n g t h e n o r t h e r n and s o u t h e r n c o a s t s were s i m i l a r , however t h e s h a p e o f t h e cape.

(The K e l v i n f r o n t s g e n e r a t e d i n e a c h

c o r n e r , c a n c e l each o t h e r two by t w o . ) ; t h e f i n i t e d i f f e r e n c e model w i l l keep t h e s p h e r i c a l t e r m b e c a u s e , r u n , Rossby waves a r e r e q u i r e d t o t r a n s p o r t t h e e n e r g y westward.

for a long

267

F i g . 9. val i s

3.

I n t e r f a c e d e p t h a t day

1

b e f o r e a t r i a n g u l a r c a p e . The c o n t o u r i n t e r -

2.00 m .

SIMULATION WITH A TIME V A R Y I N G W I N D

3.1

D e s c r i p t i o n o f t h e wind f i e l d The wind u s e d i n t h e s i m u l a t i o n h a s been r e c o r d e d by t h e ASECNA (Cgence pour

A e r i e n n e ) a t t h e Dakar a i r p o r t . D i r e c t i o n and aml a E m i t 6 de l a N a v i g a t i o n p l i t u d e a r e e s t i m a t e d e a c h t h r e e h o u r s and t h e s e r i e s were n e a r l y c o m p l e t e . The w i n d - s t r e s s a c t i n g on t h e ocean was e s t i m a t e d w i t h t h e b u l k formula : =

-

pa

cD ~2

Ty =

-

pa

CD U2 c o s D

T,

where D

pa

sin D

is the a i r density,

CD

t h e drag c o e f f i c i e n t ,

U

t h e wind a m p l i t u d e ,

t h e wind d i r e c t i o n ( g i v e n w i t h t h e m e t e o r o l o g i c a l c o n v e n t i o n ) . C a r e f u l a n a l y s e s o f t h e wind i n t h e Dakar a r e a have been done f o r s p a c e and

t i m e v a r i a b i l i t y by P o r t o l a n o ( 1 9 8 1 ) . The y e a r chosen (1973) h a s t h e main char a c t e r i s t i c s o f t h e mean c l i m a t i c y e a r and was w e l l sampled f o r t h e wind

(2

%

of missing v a l u e s ) . Compared t o t h e o t h e r c o a s t a l s t a t i o n s , Dakar seems t o be t h e most r e p r e s e n t a t i v e f o r t h e wind o v e r t h e o c e a n . No o t h e r measurement ( n e i t h e r on a p i e r n o r

268

... )

a lighthouse

was a v a i l a b l e . S y n o p t i c maps d i d n o t e x i s t f o r l o n g p e r i o d s .

To o b t a i n a s p a t i a l c o v e r a g e o f t h e area, s a t e l l i t e methods combined w i t h assim i l a t i o n t e c h n i c s i n GCM ( G l o b a l C i r c u l a t i o n Model) a r e r e q u i r e d . Such winds a r e a v a i l a b l e f o r t h e FGGE y e a r 1979 and w i l l be soon i n t r o d u c e d i n t h e model. Nevertheless,

t h e i r r e l e v a n c e f o r c o a s t a l dynamics i s q u e s t i o n a b l e .

The wind p a t t e r n i n Dakar i s c l o s e l y r e l a t e d t o t h e p o s i t i o n o f t h e ITCZ

( I n t e r T r o p i c a l Convergence Zone) which moves m e r i d i o n a l l y back and f o r t h during t h e y e a r . Two s e a s o n s a p p e a r : t h e b o r e a l w i n t e r when t h e I T C Z i s f a r s o u t h . Dakar i s s i t u a t e d i n t h e t r a d e winds ( n o r t h e r l y t o n o r t h - e a s t e r l y w i n d s ) . T h e i r a m p l i t u d e i s i m p o r t a n t ( 5 m / s ) and t h e y a r e r e l a t i v e l y r e g u l a r . These winds can e a s i l y i n d u c e c o a s t a l upwelling; t h e b o r e a l summer when t h e I T C Z i s n o r t h of Dakar. I t s p o s i t i o n i s n o t very

w e l l d e f i n e d . The wind i s weak and v a r i a b l e , mainly s o u t h e r l y , s o u t h - e a s t e r l y .

S p e c t r a of t h e wind stress component. The t h i n l i n e r e p r e s e n t s t h e F i g . 10. z o n a l component and t h e d a r k l i n e r e p r e s e n t s t h e m e r i d i o n a l component.

I n b o t h s e a s o n s , a s t r o n g d i u r n a l c y c l e i s superimposed t o t h e wind. I n f i g .

10, s p e c t r a l power f o r

T,

and

Ty

are p r e s e n t e d ( f o r p e r i o d s l o n g e r than two

d a y s ) . The most i m p o r t a n t p o i n t t o n o t i c e i s t h e e n e r g y e x c e s s o f

Ty

on

T,

a t a l l f r e q u e n c i e s . There i s no w e l l d e f i n e d p e a k i n b o t h s p e c t r a , j u s t a s l i g h t l y h i g h e r amount o f e n e r g y f o r

3.2

Ty

between

40

and

50

days.

The o c e a n i c r e s p o n s e The ocean model d e s c r i b e d i n p a r t 2 w a s run l i n e a r l y on a s p h e r e d u r i n g a

year (with

72

t i m e s t e p s p e r day) w i t h a c o n t i n u o u s l y v a r y i n g wind stress ( t h e

269 wind i n p u t w a s m o d i f i e d e a c h t h r e e h o u r s ) . The e a s t e r n coast o f t h e model had and t h e rec-

t h e same o r i e n t a t i o n t h a n t h e S e n e g a l c o a s t (mainly n o r t h - s o u t h )

t a n g u l a r c a p e emphasized t h e c a p e of Dakar. Mean k i n e t i c e n e r g y (KE) and mean a v a i l a b l e p o t e n t i a l e n e r g y f o r t h e ocean (APE) a r e r i s i n g u n t i l t h e b e g i n n i n g o f May where a f t e r 150 d a y s of run ( t h e run s t a r t s on t h e 1 s t o f J a n u a r y 1973) a peak e x i s t s ( f o r APE and K E ) . T h e r e seems t o be a d e l a y ( a b o u t

25

days)

between t h e maximum o f t h e e n e r g y r e s p o n s e i n t h e ocean and t h e wind i n p u t (fig. 11).

1

JAN

'

FEE

'

MAR

'

APRIL

'

MAY

'

JUN

'

JUL

'

AUG

'

SEP

'

OCT

'

TlllW NOV

'

DEC

F i g . 11. Wind stress modulus ( t h i n l i n e ) , mean k i n e t i c e n e r g y (dashed l i n e ) and mean a v a i l a b l e p o t e n t i a l e n e r g y ( d a r k l i n e ) i n f u n c t i o n o f t i m e d u r i n g t h e one-year r u n .

To j u s t i f y t h i s p o i n t , t h e f o l l o w i n g argument i s p r o p o s e d : t h e wind d r i v e s c u r r e n t s i n t h e ocean b u t two k i n d s o f ocean r e s p o n s e s e x i s t . The f i r s t one i s t h e l o c a l r e s p o n s e ( f o r i n s t a n c e , c o a s t a l c u r r e n t s w i l l r e a c h t h e i r maxima s i m u l t a n e o u s l y w i t h t h e l o c a l w i n d ) ; t h e second one i s t h e remote r e s p o n s e due t o waves ( c o a s t a l K e l v i n waves a r e e x c i t e d and p r o p a g a t e t h e e n e r g y poleward; Rossby waves c a r r y t h e e n e r g y westward, away from t h e e a s t e r n b o u n d a r y ) . The p r e s e n c e o f t h e s e waves may i n t r o d u c e a d e l a y i n t h e o c e a n i c r e s p o n s e . F o r KE, a n o t h e r peak i s r e a c h e d i n September and t h e n i n November. The APE i s d e c a y i n g

f r o m A p r i l t o September and rises as t h e t r a d e s blow a g a i n i n t h e f a l l . The a n n u a l c y c l e i s much more n o t e w o r t h y on t h e APE t h a n on t h e K E .

270

F i g . 12. I n t e r f a c e depth ( t h e contour i n t e r v a l is d a y s . Dashed a r e a s are u p w e l l i n g a r e a s .

2 . 0 0 m) f o r t h r e e d i f f e r e n t

F i g u r e 1 2 p r e s e n t s t h e t h e r m o c l i n e d e p t h a t t h r e e d i f f e r e n t t i m e s ( 2 0 0 days, 280 d a y s and 360 d a y s ) . The s p a t i a l v a r i a b i l i t y i s v e r y h i g h b u t Rossby waves p r o p a g a t i o n i s n o t i c e a b l e a c r o s s t h e domain ( i n c l i n e d f r o n t s o f e q u a l

h

value

a p p e a r b e c a u s e t h e wave speed depends on t h e l a t i t u d e and i s l a r g e r along t h e s o u t h e r n b o u n d a r y ) . Two space-time

diagrams have been s e l e c t e d i n o r d e r t o out-

l i n e t h e waves i m p o r t a n c e i n t h i s model ( f i g . 1 3 ) . The f i r s t one p r e s e n t s

h

a l o n g t h e e a s t e r n coast as a f u n c t i o n o f l a t i t u d e and t i m e and shows t h e success i o n o f c o a s t a l K e l v i n f r o n t s p r o p a g a t i n g p o l e w a r d s . The second p i c t u r e i s a

271

a

b

F i g . 13. Space-time d i a g r a m s . a ) I n t e r f a c e d e p t h a l o n g t h e e a s t e r n boundary. b ) Zonal v e l o c i t y i n f u n c t i o n o f l o n g i t u d e j u s t s o u t h o f t h e c a p e .

s e c t i o n t a k e n a c r o s s t h e b a s i n j u s t s o u t h o f t h e cape. Kelvin waves a p p e a r a l o n g t h e c a p e b u t t h e p r o p a g a t i o n a c r o s s t h e o c e a n i c i n t e r i o r i s done t h r o u g h Rossby waves. From t h i s p i c t u r e , t h e i r speed i s e s t i m a t e d around

3 cm/s

which i s a

r e a s o n a b l e v a l u e f o r Rossby f r o n t a t t h i s l a t i t u d e . The l a s t a n a l y s i s performed w i t h t h e s e d a t a i s t h e s p e c t r a l a n a l y s i s . Auto spectra f o r t h e zonal v elo cit y

u

and t h e m e r i d i o n a l v e l o c i t y

v

o f t h e s o u t h e r n h a l f o f t h e b a s i n show t h a t f o r p e r i o d s between 40

i n t h e middle

3

d a y s and

d a y s t h e r e i s a n e x c e s s i n e n e r g y f o r t h e z o n a l component compared t o t h e

m e r i d i o n a l component ( f i g . 1 4 ) b u t f o r lower and h i g h e r f r e q u e n c i e s , t h e i r l e v e l s

a r e s i m i l a r . T h i s c a n be e x p l a i n e d , a t h i g h f r e q u e n c i e s (around two d a y s ) , b y t h e e x i s t e n c e o f a s t r o n g i n e r t i a l peak: a t low f r e q u e n c i e s , t h e e n e r g y e q u i p a r t i t i o n may be j u s t i f i e d by t h e p r e s e n c e o f Rossby waves which c o n t r i b u t e e f f i c i e n t l y t o i n c r e a s e t h e e n e r g y l e v e l i n t h a t r a n g e . F o r t h e medium r a n g e , it i s e a s y t o v e r i f y t h a t t h e o c e a n i c t r a n s p o r t i s d i r e c t e d t o t h e r i g h t o f t h e wind, i n agreement w i t h t h e Ekman t h e o r y . The c o h e r e n c e between the

95

%

v

and

Ty

i s above

l e v e l o f c o n f i d e n c e ( f i g . 15) and t h e p h a s e l a g i s z e r o . A s m a l l e r

c o h e r e n c e i s found between

u

and

Tx

( t h i s wind component i s smaller t h a n t h e

m e r i d i o n a l component) b u t t h e p h a s e l a g i s s t a b l e around

180'.

Along t h e c o a s t , spectra are d i f f e r e n t ( f i g . 1 4 ) . I n t h e r a n g e

3 -100 days,

k i n e t i c e n e r g y f o r t h e m e r i d i o n a l component i s two d e c a d e s h i g h e r a l o n g t h e

coast t h a n i n t h e middle o f t h e b a s i n . A l l t h e c o a s t a l p o i n t s show a s i m i l a r spectrum. The d i r e c t e f f e c t o f t h e wind s t r e s s and o f t h e p r o p a g a t i o n o f c o a s t a l

;-02

.rnE-Ol

. m E +oo

.IWE+OI

. m E +02

F i g . 14. K i n e t i c e n e r g y d e n s i t y s p e c t r a f o r t h e m e r i d i o n a l v e l o c i t y a l o n g t h e c o a s t a t 1 2 O N ( d a r k l i n e ) , f o r t h e m e r i d i o n a l v e l o c i t y ( t h i n l i n e ) and t h e z o n a l v e l o c i t y (dashed l i n e ) a t 12.12' N and 5' W . Coherence

Coherenu

PhaW Lop

T

m-

I

i

I

I

i

I

So0 .

-w

-

-1WA

a

b

Fig.

b)

Coherence and p h a s e l a g a t and T X .

15. u

12.12' N , 5 O W , between

:

a)

v

and

T

~

;

273 waves i s c l e a r l y v i s i b l e . I n o r d e r t o p r o v e t h e wave e x i s t e n c e , t h e c o h e r e n c e was c a l c u l a t e d between d i f f e r e n t p o i n t s a l o n g t h e c o a s t (9.56" N ,

13.73' N ,

16.27' N ,

17.88'N).

12.12' N ,

The l e v e l o f c o h e r e n c e was v e r y h i g h a t a l l f r e -

q u e n c i e s and t h e p h a s e l a g a n a l y s i s r e v e a l e d t h a t t h e c o a s t a l K e l v i n waves p r o p a g a t i o n was r e s p o n s i b l e f o r t h e h i g h c o h e r e n c e l e v e l . I n f i g u r e 1 6 , t h e phase l a g between d i f f e r e n t p o i n t s i s p r e s e n t e d a s a f u n c t i o n o f f r e q u e n c y . The dashed l i n e i s t h e t h e o r e t i c a l s t r a i g h t l i n e o b t a i n e d by assuming t h a t two p o i n t s , s e p a r a t e d by a d i s t a n c e a t t h e speed

c

( 2 m/s

f u n c t i o n o f frequency

L

cp ( r a d i a n s ) = ( 2 r -)

L ,

are c o r r e l a t e d by Kelvin waves p r o p a g a t i n g

f o r t h i s r u n ) . The p h a s e l a g can be e x p r e s s e d a s a w :

w

Fig. 16. Phase l a g i n f u n c t i o n o f p e r i o d f o r t h e m e r i d i o n a l v e l o c i t y a t d i f f e rent points along t h e coast : a ) 9.56" N and 12.12' N ; b) 9.56' N and 13.73' N ; c) 9.56" N and 16.27O N ; d) 16.27"N and 1 7 . 8 8 " N . The dashed l i n e s r e p r e s e n t t h e t h e o r e t i c a l c u r v e s .

214 The agreement i s v e r y good i n t h e medium r a n g e between p o i n t s s i t u a t e d e i t h e r i n t h e n o r t h e r n h a l f o f t h e domain o r i n t h e s o u t h e r n h a l f . I t i s s t i l l v a l i d between one p o i n t n o r t h o f t h e cape and one s o u t h o f i t b u t w i t h a s m a l l e r l e v e l of confidence.

4.

DISCUSSION I t w a s shown, i n t h e p r e v i o u s p a r t , t h a t f o r a l a r g e band p e r i o d

300 d a y s ) which c o r r e s p o n d s t o a wavelength band (500 km

to

( 3 days t o

5000 km)

,

t h e pre-

s e n c e o f a c a p e , t h e d i m e n s i o n s o f which a r e b i g g e r t h a n t h e r a d i u s o f d e f o r m a t i o n , a l l o w s t h e p r o p a g a t i o n of c o a s t a l Kelvin waves w i t h o u t a f f e c t i n g t h e i r properties.

Secondary waves a r e g e n e r a t e d by t h e c a p e i t s e l f b u t t h e y c a n c e l

one a n o t h e r . For s m a l l e r p e r i o d ( a n d s m a l l e r w a v e l e n g t h s ) t h e coherence l e v e l

i s n o t h i g h enough f o r t h e p h a s e l a g t o be s i g n i f i c a n t : c o a s t a l phenomena appear u n c o r r e l a t e d f o r p e r i o d s smaller t h a n t h e i n e r t i a l p e r i o d . The c o h e r e n c e l e v e l i s n o t determined e i t h e r f o r very long p e r i o d s ( s u p e r i o r t o

30

d a y s ) . Away

from t h e c o a s t , t h e Ekman t h e o r y i s w e l l v e r i f i e d f o r p e r i o d s between

3

days

and a few weeks. But, o u t s i d e t h i s band, wave dynamics dominates. With a m u l t i - l e v e l n u m e r i c a l model, v e r t i c a l s t r u c t u r e would have been obtained.

Such a s i m u l a t i o n d i s p l a y s t h e c o a s t a l and t h e v e r t i c a l t r a p p i n g as

shown by Yoon and P h i l a n d e r ( 1 9 8 2 ) . But t h e b a s i c a d j u s t m e n t , t h r o u g h c o a s t a l Kelvin waves, i s s i m i l a r t o t h e one o b t a i n e d w i t h a s h a l l o w w a t e r model; consid e r i n g t h e s t r a t i f i c a t i o n o f f s h o r e o f Dakar, it i s r e a s o n a b l e t o assume t h a t t h e f i r s t b a r o c l i n i c mode i s r e s p o n s i b l e f o r t h e l a r g e s t p a r t o f t h e adjustment and t h a t t h e reduced g r a v i t y model r e p r o d u c e s t h e main p a t t e r n s o f t h e mixed l a y e r . A s t r a t i f i e d model w i l l a l s o be a b l e t o p r e s e n t t o p o g r a p h i c e f f e c t s due t o t h e c o n t i n e n t a l margin. C o a s t a l t r a p p e d waves a r e g e n e r a t e d w i t h speed comp a r a b l e t o K e l v i n waves s p e e d and t h e y p r o p a g a t e poleward

( s e e S u g i n o h a r a , 1982).

I n t h e o c e a n , a l l t h e c o a s t i n d e n t a t i o n s , cape o r b a y , l a r g e r t h a n 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 , a r e a b l e t o c r e a t e s e r i e s o f t r a p p e d waves t h a t may canc e l one a n o t h e r . A r t h u r

(1965) h a s c o n s i d e r e d a d i f f e r e n t problem: i n h i s ap-

p r o a c h , t h e r e e x i s t s a c o a s t a l boundary l a y e r where t h e v e l o c i t y goes t o zero and t h e dimensions o f t h e cape a r e smaller t h a n t h e r a d i u s o f d e f o r m a t i o n . Thus, t h e v a r i a t i o n of v o r t i c i t y around t h e cape i s n o t n e g l i g i b l e .

But i t does n o t

a p p l y i n t h e p r e s e n t model where t h e cape i s l a r g e and t h e v e l o c i t y h i g h along t h e c o a s t . Long Kelvin waves w e r e p r e s e n t i n t h e model though open boundary cond i t i o n s were a p p l i e d ; t h e y may r e p r e s e n t g l o b a l phenomena coming from e q u a t o r i a l r e g i o n . The s a l i n i t y c a n n o t b e i n t r o d u c e d i n t h e r e d u c e d g r a v i t y model and i t s v a r i a t i o n may p l a y a r o l e i n t h i s a r e a and c r e a t e i m p o r t a n t l o c a l v a r i a b i l i t y . The p h a s e l a g s c a l c u l a t e d i n t h e model are n o t d i r e c t l y comparable w i t h measurements b e c a u s e coastal topography and s t r a t i f i c a t i o n w i l l a l t e r t h e wave s p e e d and 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

( t h e t r a p p i n g s c a l e for i n s t a n c e ) but

275

with this simple numerical approach, basic features were outlined. The next step will require the input of spatially varying wind-stress that will excite a large wave spectrum in the ocean and add some remote effects. The coast will not be the only source of vorticity. Then, the non-linear problem will be studied. The addition of non-linear terms will modify slightly wave properties but the currents are not very strong and this will not introduce completely different results.

REFERENCES Allen, J.S., 1976. Some aspects of the forced wave response of stratified coastal regions. J. Phys. Oceanogr., 6, 1: 113-119. Arthur, R.S., 1965. On the calculation of vertical motions in the eastern boundary currents from determination of horizontal motion. J. of Geoph. Res., vol. 70, no 12: 2799-2803. Biju-Duval, N. and Chartier, M., 1982. Effets d'un cap sur les upwellings. Solution numerique & partir d'une methode aux elements finis. Projet no 127, Ecole Nationale Superieure de Techniques Avancees. Charney, J.G., 1955. The generation of ocean currents by wind. J. Mar. Res., 14, 4: 477-498. Camerlengo, A.L. and O'Brien, J.J., 1980. Open boundary conditions in rotating fluids. Jour. of Computational Physics, vol. 35, no 1: 12-35. Crepon, M. and Richez, C., 1982. Transient upwelling generated by two dimensional atmospheric forcing and variability in the coastline (submitted to J. Phys. Oceanogr.) Csanady, G.T., 1975. The coastal jet conceptual model in the dynamics of shallow seas. In :Goldberg, MC Cave, O'Brien and Steele (Eds.), The Sea, vol. 6, Marine Modelling, pp. 117-144. Wiley Interscience Publ., New York. Halpern, D., 1976. Structure of a coastal upwelling event observed off Oregon during July 1973. Deep-sea Res., 23, 6: 495-508. Hua, B.L., 1981. Modelisation numerique d'upwellings cdtiers 2 l'aide d'une m6thode d'616ments finis. Application au golfe du Lion. These de doctorat d'Etat Ps Sciences physiques, Universite Pierre et Marie Curie et Museum National d'Histoire Naturelle, Paris, 18 mai 1981. Merle, J., 1973. Hydrologie saisonniere dans la region de Dakar (unpublished document). Portolano, P., 1981. Contribution & l'btude de l'hydroclimat des cdtes sen6galaises, CRODT - ORSTOM. Rossignol, M. and Meyrueis, A.M., 1962. Campagne oceanographique du "Gerard Treca", CROD'I - ORSTOM. Rossignol, M., 1973. Contribution 5 1'Btude du complexe guineen, ORSTOM. Suginohara, N., 1982. Coastal upwelling : onshore-offshore circulation, equatorward coastal jet and poleward undercurrent over a continental shelf slope. J. of Phys. Oceanogr., vol. 12, no 3: 272-284. Yoon, J.H. and Philander, S.G.H., 1982. Formation of the coastal undercurrent. Submitted to the J. Oceanogr. SOC. Japan.

.

APPENDIX -DESCRIPTION OF THE NUMERICAL MODEL The equations used to study the dynamics of the upwelling event in the numerical model are the reduced-gravity equations in the shallow water approximation

au at +

:

(U.V)U

+

f k

A

u

=

- g' Vh

+

D

276

where

represents the horizontal velocity vector,

U

layer,

f

t h e C o r i o l i s parameter,

v e r t i c a l normalized v e c t o r .

Ap

g

h

t h e thickness of the

t h e a c c e l e r a t i o n o f g r a v i t y and

k

the

i s t h e d e n s i t y d i f f e r e n c e between t h e mixed-

D r e p r e s e n t s t h e e x t e r n a l f o r c e s (wind

l a y e r and t h e deep m o t i o n l e s s l a y e r and

...) .

stress f o r c i n g , f r i c t i o n ,

F o r s o m e e x p e r i m e n t s , a l i n e a r v e r s i o n o f t h e above s y s t e m o f e q u a t i o n s w i l l be used :

ah + H

at

H

= 0

VU

i s t h e i n i t i a l t h i c k n e s s o f t h e l a y e r . C o n s i d e r i n g t h i s s y s t e m i n t e r m s of

v e r t i c a l modes, a e q u i v a l e n t d e p t h can b e e s t i m a t e d : he =

ap P

when

H = 10 c m

i s equal t o

Ap/p

.

2

and

H

50 m .

to

The h o r i z o n t a l p h a s e speed

r e l a t e d t o t h i s b a r o c l i n i c mode i s e q u a l t o c = ( g he)"'

=

1 m/s

Without f o r c i n g , t h e n o n - l i n e a r torial operators

momentum e q u a t i o n s w i l l b e w r i t t e n w i t h vec-

:

The v e c t o r i a l o p e r a t o r s can b e e x p r e s s e d i n a t e n s o r i a l form, i n v a r i a n t i n any c u r v i l i n e a r o r t h o g o n a l b a s e t r a n s f o r m a t i o n . Let

be t h e l a t i t u d e ,

[p

center of the earth. L e t

i

A and

t h e l o n g i t u d e and j

the v e r t i c a l a x i s give the t h i r d direction. of

r

t h e d i s t a n c e from t h e

d e s c r i b e t h e h o r i z o n t a l d i s c r e t e mesh and [p

is a function of

j

,

and

A

i .

Let

x ,

y

and

z

d e n o t e t h e d i s t a n c e s i n a frame r e f e r r e d t o t h e c e n t e r

of the earth. [p(j)

cos A ( i )

y = r cos q ( j )

sin X ( i )

x = r cos

z = r sin q ( j )

Assuming fined :

a

t o be t h e r a d i u s o f t h e e a r t h , a new frame

(x',y',z')

i s de-

277 dx'

a di

=

dy' = a d j dz'

dr

=

The i n f i n i t e s i m a l d i s p l a c e m e n t s i n b o t h frames

(x,y,z)

and

(x',y',z')

are

equal :

(as)'

(dx)'

=

+ (dy)' + (dz)'

The c o e f f i c i e n t s

ex,

,

= ( e x #d x ' ) '

+

(eyg d y ' ) '

+

(ezt

e z , are e a s i l y c a l c u l a t e d

ey, and

dz')'

:

These a r e t h e i m p o r t a n t p a r a m e t e r s , t y p i c a l o f t h e t r a n s f o r m a t i o n , t h a t app e a r i n t h e e x p r e s s i o n of t h e c o v a r i a n t and c o n t r a v a r i a n t c o o r d i n a t e s o f a vector.

-

V

Let

(Vxe , V y t , V z t )

VK = eK VK

(K = x '

b e a v e c t o r . The c o v a r i a n t components a r e d e f i n e d by

,

y'

or

z')

or

z')

and t h e c o n t r a v a r i a n t component 4

VK =

K '

-

(K = x '

,

y'

eK

The v e c t o r i a l o p e r a t o r s have an i n v a r i a n t e x p r e s s i o n i n f u n c t i o n o f t h e s e coefficients. Let

b

ex, x e

be t h e p r o d u c t

r

W e now assume t h a t

Y

The c o n t i n u i t y e q u a t i o n g i v e s :

ax

and, s e t t i n g -a p + a p z +

at

ax

a (hb?) aY

P = hb,

a p f j = o aY

x

i s equal t o

t o simplify t h e expressions.

a (hb) + a (h b 8 ) + 5

I

= 0

ezg

a

and

A

a scalar quantity

and t h e i n d i c e s

'

w i l l b e dropped

218

-

i s t h e mass f l u x .

Pz

F o r t h e momentum e q u a t i o n , l e t

With t h e s e n o t a t i o n s , t h e e q u a t i o n s f o r t h e m e r i d i o n a l and z o n a l v e l o c i t y components a r e e a s i l y deduced :

The shape t a k e n by t h e s e e q u a t i o n s i s v e r y i n t e r e s t i n g b e c a u s e t h e y a r e i n t r i n s i v a l l y c o n s i s t e n t f o r any c u r v i l i n e a r o r t h o g o n a l t r a n s f o r m a t i o n . They allow t h e u s e of v a r i a b l e g r i d - s p a c i n g s . The e q u a t i o n s w i l l b e d i s c r e t i z e d i n a s t a g g e r e d a r r a y P

U

V

P

P

U

P

U

P

V U

P

7 Let

K = i , j

Assuming

5 = 6,:

-

6 ii

and

1

0 = g'h

+ 2

---x

(u2

-v

+ v2

)

t h e d i s c r e t e s e t of e q u a t i o n i s

219

T h i s scheme c o n s e r v e s p o t e n t i a l e n t r o p h y . I n t h e f o r c i n g t e r m s wind stress and f r i c t i o n a r e i n c l u d e d . The wind stress

i s a p p l i e d as a body f o r c e i n t h e mixed s u r f a c e l a y e r and t h e l a t e r a l f r i c t i o n i s e x p r e s s e d i n f u n c t i o n o f a L a p l a c i a n o p e r a t o r ( n o t e t h a t t h e L a p l a c i a n oper a t o r i s d e f i n e d o n l y f o r t h e s c a l a r q u a n t i t i e s and t h e c o r r e c t e x p r e s s i o n f o r t h e f r i c t i o n a l o p e r a t o r h a s t o be c a l c u l a t e d u s i n g t h e g e n e r a l i z e d form o f t h e v e c t o r i a l o p e r a t o r s and t h e r e l a t i o n s h i p :

The c o e f f i c i e n t o f l a t e r a l f r i c t i o n The e x t e n t o f t h e domain i s centered a t

15" N

i n l a t i t u d e and

3"

11'

AH

i s e s t i m a t e d t o be

i n l o n g i t u d e and

15'

10' m's-'

.

i n l a t i t u d e . I t is

and t h e e a s t e r n boundary i s t h e c o a s t l i n e . The cape i s

2'

i n l o n g i t u d e i n t h e middle o f t h e e a s t e r n boundary. A f r e e

s l i p c o n d i t i o n i s a p p l i e d along a l l t h e l a t e r a l boundaries except t h e southern and t h e n o r t h e r n w a l l s where open boundary c o n d i t i o n s a r e a p p l i e d (Camerlengo and O ' B r i e n ,

1 9 8 0 ) . Along t h e w e s t e r n w a l l a sponge boundary c o n d i t i o n i s used

i n o r d e r t o damp t h e e n e r g y coming from t h e e a s t e r n p a r t w i t h Rossby waves. The r e s o l u t i o n o f t h e g r i d - s p a c i n g ( 6 km) and d e c r e a s e s toward t h e w e s t .

2 7 km

i s v e r y h i g h a l o n g t h e e a s t e r n boundary In l a t i t u d e , t h e r e s o l u t i o n i s about

around t h e cape.

The t i m e d i f f e r e n c e scheme i s a l e a p f r o g scheme f o r t h e i n t e r n a l dynamics and a f o r w a r d scheme f o r t h e e x t e r n a l f o r c e s . S o l u t i o n s a t odd and even t i m e s t e p s a r e r e g u l a r l y mixed t o g e t h e r t o a v o i d t i m e s p l i t t i n g and t h e t i m e s t e p used i s

20 m n .

This Page Intentionally Left Blank

281

MODEL OF THE GULF OF GUINEA UPWELLING. INFLUENCE OF THE COAST'S IRREGULARITIES.

Jacques C.J. NIHOUL and A. BAH

1.

INTRODUCTION Every summer, for a period from early July through September, upwelling is

an important feature along the Gulf of Guinea coast (fig. 1). According to Houghton (19761, the cold water found along the northern boundary of the Gulf

is local in origin and not advected into the ared by the Benguela current. The coldest water is always found east of Cape Palmas and Cape Three Points. There is no correlation between local winds and nearshore temperatures or changes in the local ocean circulation.

Dakar

Fig. 1. Schematic map of the Gulf of Guinea, showing the region of upwelling and subsurface (--) currents (shaded area) and the presumed surface (-) (after Houghton, 1976).

282

Observations, during Gate, by the Soviet Ship RV. Parsat seemed to suggest a forcing of oceanic origin and O'Brien (e.g. O'Brien et al., 1978; Adamec and O'Brien, 1978) hypothesized that a baroclinic Kelvin wave is excited in the western Atlantic by the onset of the southeast trades in May-June. This long wave, strong upwelling impulse, propagates eastward across the Atlantic. It then propagates poleward as a coastal Kelvin wave and produces the upwelling event along the Gulf of Guinea coast. With a non-linear numerical model, using the

f3 -plane approximation in an

ocean initially at rest, Adamec and O'Brien (1978) calculated the first baroclinic modal response of the ocean to a sudden increase of the wind stress and succeeded in reproducing the main features of the observations with a very good agreement of both amplitude and time scales. In all the applications of their model, however, the coast was assumed rectilinear and the possible effect of capes on the upwelling's intensity could not be studied. The effect of capes is often discussed in terms of local conditions such as the orientation of the coast with respect to the local wind or the deflection of the coastal circulation. An approximate calculation made by Bah (1980)*, using current results of a numerical model similar to that of Adamec and O'Brien (1978), showed a possible amplification of the upwelling east of Cape Three Points, without being strongly conclusive. In the following, the influence of Cape Palmas and Cape Three Points is investigated, using an improved version of Bah's model, with a numerical grid which takes into account the coastal irregularities. It is shown that a Kelvin wave generated upwelling, of the type hypothesized by O'Brien et al. (1978), can explain, along a non-linear coast such as the northern coast of the Gulf of Guinea, the kind of amplification of upwelling's intensity which is observed east of the capes.

2.

DESCRIPTION OF THE MATHEMATICAL MODEL Fig. 2 shows the model geometry with the irregular coastline. The governing equations are derived from the Boussinesq equations (e.9.

Nihoul, 1982). Assuming two layers of uniform densities pz

p1

(upper layer) and

(lower layer) and zero pressure gradient in the bottom layer, one can write,

in the

@-plane approximation, the equations for the transport

u

in the upper

layer, in the form aH +v.u at

= 0

* Some misprints in the equations used for the calculation make this part of the paper difficult to understand. The reader is advised to enquire into the corrigenda.

283

Fig. 2.

$+

The model geometry with t h e i r r e g u l a r c o a s t l i n e .

v.(H

-1

uu)

+ Bxz(e3

A

u)

=

-

g'H Vh

P1

+ T +

A

V2U

where

H=Ho+h

Ho

(3)

i s t h e undisturbed t h i c k n e s s o f t h e upper l a y e r

t u r b a t i o n o f t h e upper l a y e r ' s t h i c k n e s s and of t h e upper l a y e r .

A

H

-

(Ho

50 m),

h

t h e per-

t h e t o t a l (disturbed) thickness

i s a h o r i z o n t a l d i f f u s i o n c o e f f i c i e n t t a k i n g i n t o account

turbulence and shear e f f e c t ,

T

i s t h e wind s t r e s s ,

The d e t a i l s of t h e numerical model ( d i s c r e t i z a t i o n scheme, s t a b i l i t y c r i t e r i a , boundary c o n d i t i o n s ,

3.

. .. )

a r e given i n (Bah, 1980).

APPLICATION

O'Brien e t a l .

(1978), Adamec and O'Brien (1978) and Bah (1980) have inves-

t i g a t e d s e v e r a l cases of oceanic responses t o impulsive changes of t h e wind s t r e s s , over p a r t o f t h e a r e a . One o f t h e s e c a s e s assumes a sudden i n c r e a s e of ward wind s t r e s s over t h e western

1500 km

0.0125 Nm-*

of t h e basin.

i n t h e west-

284

Fig. 3.

Elevation of the interface

10

days after the onset of the wind.

Fig. 4.

Elevation of the interface

20

days after the onset of the wind.

285

Fig. 5.

Elevation of the interface

30

days after the onset of the wind.

Fig. 6.

Elevation o f the interface

40

days after the onset of the wind.

286

,

I

50

Fig. 7.

Elevation of the interface

50

days after the onset of the wind.

Fig. 0 .

Elevation of the interface

60

days after the onset of the wind.

287

Fig. 9.

Fig. 10.

Elevation of the interface

Elevation of the interface

70

80

days after the onset of the wind.

days after the onset of the wind.

288

Fig. 11.

Elevation of the interface

90 days after the onset of the wind.

This case has been simulated using the model described in section 2. Figs. 3 to 1 1 show the propagation of the Kelvin wave generated upwelling 10,

20,

...,

90 days after the onset of the wind.

An

amplification of the

upwelling's intensity east of Cape Three Points is apparent. On fig. 12, the elevation of the interface in the Gulf of Guinea after

90

days is compared with the interface elevation which is found when one assumes a linear coast line. The effect of the shape of the coast on the distribution of the upwelling's intensities is indicated by the position of the

10 m

elevation-curve. The Kelvin wave model appears thus to be able to reproduce the main features of the upwelling in the Gulf of Guinea including the amplification of its intensity east of the capes on the northern boundary.

4. REFERENCES Adamec, D. and O'Brien, J.J., 1978. The seasonal upwelling in the Gulf of Guinea due to remote forcing. J. Phys. Oceanogr., 8: 1050. Bah, A., 1980. Upwelling in the Gulf of Guinea. In: J.C.J. Nihoul (Editor), Ecohydrodynamics, Elsevier Publ., Amsterdam, pp. 99-140. Houghton, R.W., 1976. Circulation and hydrographic structure of the Ghana continental shelf during the 1974 upwelling. J. Phys. Oceanogr., 6: 909-924. Nihoul, J.C.J., 1982. Hydrodynamic models of shallow continental seas, Riga Publ., Liege, 198 pp. O'Brien, J.J., Adamec, D. and Moore, D., 1978. A simple model of upwelling in the Gulf of Guinea. Geophys. Res., 5: 641-644.

289

Fig. 12. Elevation of t h e i n t e r f a c e c a l c u l a t e d by t h e model f o r a r e c t i l i n e a r c o a s t l i n e (above) and a r e a l i s t i c c o a s t l i n e t a k i n g t h e capes i n t o account (below). The r e s u l t s f o r a l i n e a r c o a s t l i n e a r e s i m i l a r t o those of O'Brien e t a l . (1978), Adamee and O'Brien (1978) and Bah (1980).

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291

THE EFFECT OF ZONAL CURRENTS ON EQUATORIAL WAVES

P. Ripa and S . G .

Marinone

Centro de Investigaci6n C i e n t i f i c a y de Educaci6n Superior de Ensenada, Ensenada, B.C.,

Mgxico

Abstract The i n t e r a c t i o n between a zonal c u r r e n t and e q u a t o r i a l waves i s s t u d i e d i n t h e framework of an one-layer 6-plane model. The eigenvalue problem i s solved by expanding t h e p e r t u r b a t i o n over t h e s o l u t i o n s of t h e l i n e a r problem (which form an orthogonal and complete b a s i s ) . Analytic expressions f o r t h e f i r s t o r d e r correct i o n t o t h e waves' frequency and numerical s o l u t i o n s of t h e s u i t a b l e truncated eigenvalue problem a r e presented. Both s t a b l e and unstable s o l u t i o n s a r e d e s c r i bed. Growing p e r t u r b a t i o n s a r e found f o r flows such t h a t only one of t h e two s t a b i l i t y c o n d i t i o n s (Miyata, 1981; Ripa, 1982b) i s v i o l a t e d ; w k . , a s u b c r i t i c a l flow with p o t e n t i a l v o r t i c i t y extrema, o r a j e t w i t h a monotonic p o t e n t i a l v o r t i c i t y p r o f i l e which i s s u p e r c r i t i c a l i n a neighborhood of t h e equator. The l a t t e r case i s t h a t of a westward j e t with t h e meridional s t r u c t u r e of a Kelvin wave.

1.

INTRODUCTION

The e q u a t o r i a l oceans are c h a r a c t e r i z e d by a system of zonal c u r r e n t s with strong v e r t i c a l and meridional s h e a r s and, a t t h e same time, t h e equator a c t s a s a waveguide (Matsuno, 1966).

These c u r r e n t s and e q u a t o r i a l waves i n t e r a c t , re-

s u l t i n g i n a form of Doppler s h i f t of t h e waves' frequency (Philander, 1979; McPhaden and Knox, 1979) and t h e c u r r e n t s may a l s o become

unstable (Philander,

1976, 1978; KUO, 1978; Hughes, 1979, 1981). Miyata (1981) and Ripa (198233) showed t h a t f o r an e q u a t o r i a l flow ( o r any current

system f o r which t h e quasi-geostrophic approximation cannot be used) t o be

Stable hJ0 d i f f e r e n t conditions must be m e t .

The f i r s t one i s a s o r t of c r i t i c a -

l l y of t h e flow and t h e second one involves t h e g r a d i e n t of p o t e n t i a l v o r t i c i t y . The p o s s i b i l i t y of unstable c u r r e n t s f o r which only one of t h e two s t a b i l i t y cond i t i o n s i s v i o l a t e d i s i n v e s t i g a t e d here. The c l o s e a p p l i c a b i l i t y of t h i s model t o a r e a l i s t i c oceanographic s i t u a t i o n

is questionable, because it has only one l a y e r and t h u s it r e q u i r e s t h a t t h e perturbations

have

t h e same v e r t i c a l s t r u c t u r e than t h e fundamental flow.

The

discussion of model p r e d i c t i o n s based on experimental d a t a is t h e r e f o r e postponed u n t i l i t s g e n e r a l i z a t i o n t o t h e f u l l y three-dimensional case is completed. I n Section 2 t h e model equations are reviewed and t h e method of s o l u t i o n of

292 t h e eigenvalue problem i s presented.

The p a r t i c u l a r case of a j e t with a Gaussian

meridional p r o f i l e is discussed i n Section 3 , while Section 4 i s devoted t o the Summary and Conclusions.

An Appendix

is added with t h e d e t a i l s of t h e evaluation

of t h e matrix elements.

2

MODEL EQUATIONS

W e work i n an one-layer reduced g r a v i t y model i n t h e unbounded e q u a t o r i a l 6-

plane.

The e v o l u t i o n equations of t h e model a r e ( s e e , f o r i n s t a n c e , Ripa 1982a)

where 1 = (u,v) and V =

( a ,a X

)

are t h e h o r i z o n t a l v e l o c i t y and g r a d i e n t operator,

Y

rl i s t h e v e r t i c a l d i l a t a t i o n f i e l d , and c i s t h e s e p a r a t i o n constant.

Eastward

and northward coordinates a r e denoted by ( x , y ) . The f i e l d rl i s defined i n such a way t h e t t h e l a y e r t h i c k n e s s , a t any p o s i t i o n and time, i s equal t o i t s mean value times ( 1 by d e f i n i t i o n , i d e n t i c a l l y zero.

+ n ) ; thus t h e meanvalue

(The dynamic p r e s s u r e i s c2n.)

of

n is,

The a c t u a l val-

ues of t h e reduced g r a v i t y and t h e average layer-thickness

a r e not important: on-

dedineo

{The d e f i n i t i o n of

l y t h e i r product,

which

t h e value c2, i s relevant.

t h e s e p a r a t i o n constant i n terms of t h e

is t i m e invariant. t o define c.

mean depzh. i s

most appropiate, because it

Philander (1976, 1978), though, uses t h e depth a t t h e equator

McPhaden and Knox (1979) s t a r t with a c e r t a i n parameter, say c o n

which they equate t o c while d e a l i n g with i n e r t i a - g r a v i t y waves, but t h e y make co

f c i n t h e i r t r e a t m e n t of Kelvin waves.

These f a c t s should be born i n mind

when comparing t h e r e s u l t s of t h i s work and those p a p e r s . )

The v a l u e s of c and

B a r e used t o e v a l u a t e t h e e q u a t o r i a l deformation r a d i u s ,

which i s t h e e-folding half-width of l i n e a r Kelvin waves. c = 2.4 ms-'

,

R = 460 km,

PcY~,tWcfiatiflneXpanAifln.

2 r R = 2.9 M m ,

and

(For, s a y ,

2nR/c = 14 days.)

The dynamic v a r i a b l e s can be grouped i n a v e c t o r f i e l d

as

which i s expanded i n s e r i e s as

293

with

<
E

i s an e x a c t s o l u t i o n of t h e model equations and

The f i r s t term, Go,

t h e r e s t r e p r e s e n t s a small p e r t u r b a t i o n of O C E ) .

The equations of t h e model a t

t h e lowest o r d e r a r e

vo = 0 , fuo

+

c2a

Y

no

= 0,

t h e fundamental flow i s zonal and it i s i n qeostrophic balance.

i.e.,

To t h e

next o r d e r , equations ( 1 ) and ( 2 ) y i e l d

D

~

-U

D

~

V + f~u l

Donl

( f~ - a u 0 ) v 1 Y

+

+ c2aXnl

= 0,

c2a n 1 = 0 , Y

+ V ' { ( l + n o ) ~ l =~ 0 ,

where Do =

at +

uoax.

The law of p o t e n t i a l - v o r t i c i t y

conservation i s , t o f i r s t

order,

Do(axvl

- aY u l

- q o n l ) (i+n,,)-l

+

vlayqo = 0 ,

where

i s t h e p o t e n t i a l v o r t i c i t y of t h e fundamental flow.

Equations (8) through (10)

can be r e p r e s e n t e d i n t h e form

where i L c o n t a i n s t h e l i n e a r o p e r a t o r , and i C t h o s e p r o p o r t i o n a l t o uo and

no.

The equations a t second o r d e r are

Sh7b-y a such t h a t

conditioYL.5.

Ripa (398213) has shown t h a t , i f t h e r e exists any number

294

then t h e f i r s t o r d e r p e r t u r b a t i o n ly) s t a b l e .

i s bounded i n t i m e , and t h u s Oo i s ( l i n e a r -

Weaker s t a b i l i t y conditions a r e

E i g e n v a h e pfiobletn.

Since t h e c o e f f i c i e n t s i n (13) a r e time independent,

SO-

l u t i o n s can be sought f o r 01, of t h e form

When (19) i s s u b s t i t u t e d i n ( 1 3 ) , t h e following equation i s obtained

i . e-. ,

t h e u a r e t h e eigenvalues of t h e o p e r a t o r L

+

C.

Some eigenvalues may be

complex, with I m ( u ) > 0 , i n d i c a t i n g t h a t t h e f i e l d Q0 i s u n s t a b l e . The e i g e n s o l u t i o n s of (20) i n t h e absence of c u r r e n t s ’ {ao =

a r e t h e e q u a t o r i a l waves (Matsuno, 1966). number k

(-m

< k <

m),

01,

GZ.,

The l a b e l ‘ a ‘ denotes t h e zonal wave

t h e meridional quantum number n ( = -1, 0 , 1 , 2 ,

...) , and

a d i s c r e t e index r t h a t numbers t h e d i f f e r e n t s o l u t i o n s f o r each value of k These eigenfunctions form a corn@&?

&

n.

b a s i s (Ripa, 1982a) and t h u s it i s possible

t o make t h e expansion

where

and t h e expansion f u n c t i o n s a r e normalized so t h a t

295

if n

= nb and

ra = rb, and vanishes otherwise ( t h e symbol

s e complex conjugate).

+

r e p r e s e n t s transpo-

This technique i s s i m i l a r t o t h a t used by Kasahara (1980),

who expands i n Hough f u n c t i o n s , because he works on t h e sphere i n s t e a d of on t h e @-plane. In o r d e r t o avoid confusion, h e r e a f t e r we w i l l r e f e r t o t h e eigensolutions of t h e problem with t h e b a s i c flow,

(20), a s ‘waves’ and t o those of ( 2 1 ) a s

‘components‘. Thus, u denotes t h e frequency of a wave, and w t h a t of a component. S u b s t l t u t i n g of ( 2 2 ) i n (201, premultiplying by

gb+,

i n t e g r a t i n g i n 5 , and us-

i n g ( 2 1 ) and ( 2 4 ) we o b t a i n

(Wa

- a) xa +

1cabs =

0,

b

a r e t h e m a t r i x elements of C , i . e . , where C ab Cab = J d 2 x GafC

e,.

I t can be shown t h a t

Cab = 2716(ka-kb)

(c/5l1I2

R

ab‘

where

i s a r e a l and ( g e n e r a l l y ) non-symmetric matrix and y ’ = (@/c)’/’y. see t h a t only s t a t e s with t h e same v a l u e of k a r e coupled, because dent of x.

In ( 2 7 ) we Lpo

i s indepen-

Moreover, i f Lpo(y) = Oo(-y), then modes with d i f f e r e n t meridional

+ n b = odd. a With t h i s formalism, w e can r e p r e s e n t (25) i n t h e form

p a r i t y a r e decoupled, i.e.,

(Wa

-

U)X

+

1 nab%

Cab = 0 f o r n

= 0,

n r b b

and t h u s CI i s t h e eigenvalue and X t h e eigenvector of an a l g e b r a i c problem. t h e Appendix it i s shown t h a t

In

296

nab

-

-

= /dy'{kuo(2v *.v - a *

+

+

+

c2Ga *Gb)

- u *n

-

c2w Q ;i *i w u b o a b b o a

b

From t h e phases of t h e components of real.

(B/wa)UO
}.

(30)

6 , Eq..

(All,

it follows on t h a t

nab

is

The l a s t t h r e e terms i n t h e inteqrand a r e not symmetric and t h u s may re-

s u l t i n complex eigenvalues u i n ( 2 9 ) .

Equations ( A 1 2 ) through (A141 give prac-

t i c a l formula f o r t h e e v a l u a t i o n of fi

ab'

If

0

i s r e a l , t h e r e may be

m

C

d

e c c t i t u d a , where

(11) t h a t , a t a c r i t i c a l l a t i t u d e , e i t h e r

v1 = 0

D,

= 0.

It follows from

(regular solution) o r

u1

has a logarithmic s i n g u l a r i t y . Both kinds of s o l u t i o n s a r e needed f o r t h e comp l e t e n e s s of t h e eigenfunctions of (20) (Drazin and Howard, 1966).

The d i s c r e t e

eigenmdes r e p o r t e d h e r e , obtained V h a s u i t a b l e t r u n c a t i o n of fi

i n ( 2 9 ) , are

ab

of t h e f i r s t , r e g u l a r , type.

(Due t o t h e t r u n c a t i o n , t h e node i n v1 and

nl

is

found near-but not e x a c t l y a t - t h e c r i t i c a l l a t i t u d e . ) The dynamic f i e l d s ul, v1 and

n1

a r e given by

where

and t h e normalization i s such t h a t

F L U X ohdm

do.&d&h?A.

I f t h e b a s i c s t a t e i s 'weak' enough, t h e s o l u t i o n s of

(29) a r e e q u a t o r i a l waves s l i g h t l y modified by t h e fundamental c u r r e n t and l a y e r depth s t r u c t u r e .

I n t h e l i m i t u,,,

no

+ 0 , t h e e i g e n s o l u t i o n s a r e given by {see

f o r i n s t a n c e Courant and H i l b e r t (19531, pp.

343-3463

f o r each s t a t e ' a ' , where t h e summation i s c a r r i e d over (nb,rbl t i c e t h a t u i s real i n (34a).

# (n ,r

).

NO-

a a T h i s approximation is v a l i d a s long a s t h e correc-

t i o n t o t h e f r e e f i e l d s i n (34b) i s small;

i . ~f o.r ,I S j a l

<<

I (ma

-

Wb)

1.

297 With ( 3 4 a ) , it follows t h a t i f t h e f i r s t o r d e r s o l u t i o n s a r e v a l i d , t h e correct i o n t o t h e free-frequency i s small compared t o t h e s e p a r a t i o n between frequencies. I n o r d e r t o i l l u s t r a t e t h e meaning of (34a) l e t us consider a few examples:

a)

S h o d in&-gmuaq

i n (AS) w e get N ( f )

%

w a u U and K & v h - w v U .

1, N(T)

%

0, N(0)

%

Taking t h e l i m i t s c

+

0 , where t h e upper (lower) s i g n s

respond t o eastward (westward) propagating i n e r t i a - g r a v i t y waves.

?1 COr-

Using t h i s i n

(A121 and (A13) we g e t f o r (34a)

W e recall that

<m/rlglm>

and

c m / u g / m > a r e average values of '10 and u o , weigh-

t e d with t h e square of t h e p a r a b o l i c c y l i n d e r f u n c t i o n of o r d e r m [cf. (A6b) and

( A 1 4 ) I . For a Kelvin wave ( s c : 1) we o b t a i n (35) with t h e a t t h e f i r s t o r d e r , Kelvin waves remain non-dispersive,

+

u/k

s i g n , n + 1 = O ; thus, =

constant.

The second term i n t h e r i g h t hand s i d e of (35) i s c l e a r l y an C h d C C ~ U CDoppler s h i f t , whereas c ( 1

+

1 / 2 < q 0 > ) i s an e f f e c t i v e value of t h e separation constant

(because t h e mean depth ' s e e n ' by t h e wave i s < l + n o >t i m e s t h e average over t h e e n t i r e @-plane of t h e layer-thickness,

and <1+qo>1/2% 1 + 1 / 2 < Q 0 > )

-

McPhaden and Knox (1979) made, f o r t h e Kelvin wave, an expansion Of c o 2 i n powers of t h e s t r e n g t h of uo &

no

{see t h e i r Eq.

(14) 1, obtaining

which i s equivalent t o (32) up t o O ( Q 2 ) {Eq. (36) corresponds t o t h e i r Eqs. and ( 2 4 e ) l .

U &

(24d)

I n t h i s expression, t h e e f f e c t i v e Doppler s h i f t and change of t h e

value of c a r e presented s e p a r a t e l y . b) 0,

S h o d Rohhbq WavU.

INCO)

we get

where

I

%

1 i n (A5).

These correspond t o s c << -2n-1,

Using t h i s r e s u l t and w

*

-B/k

which y i e l d s N(?)"'

in (A12),

(A13) and (34a)

298 w2 = Bc/(l-sc),

k = sw

(--m

< sc

<

(39)

3).

Notice t h a t (38) reduces t o (351, with t h e

+

sign, for s c

‘L

1, and t o (37) f o r

s c << -1. Equations (37) and (38) p r e d i c t w waves).

under t h e a c t i o n of a westerly. %

2B2c-l(na

-

I%/). 3

%

k f o r s c +

-m

( u l t r a s h o r t Rossby

I f t h i s were v a l i d , t h e s e waves could have an eastward phase-propagation However,

Gab

%

k = O(k) and w

a

-

w

b

n ) k - 3 = O ( k - 3 ) , t h e approximation (34) breaks down k-4 < O(B-’c b

SOLVTIONS FOR A GAUSSIAN PROFILE S o l u t i o n s to (29) w e r e found f o r t h e symmetric zonal c u r r e n t f i e l d

and, i n v i r t u e of Eq. ( 7 ) ,

where

Any Gaussian j e t i s then parametrized by two non-dimensional

/ c and B = (L/R)’.

numbers:

A = uoCO)

The parameters of t h e s t a b l e j e t s , as guaranteed by (17) and

(18), a r e shown i n Fig. 1 ; t h e d e t a i l s of t h e c a l c u l a t i o n a r e given by Ripa (1982b) ( t h e parameters

A and 1-1 used i n t h a t paper a r e equal t o

X

=

AB,

W e approximate t h e s o l u t i o n s of (29) by those of a f i n i t e submatrix of

= B-l)

n,

choosing t h e b a s i c s t a t e s so t h a t any added component has l e s s than 0.5% of t h e t o t a l energy. ( 8 ) , (9)

T y p i c a l l y , w e use 40 components.

and (10) i s w r i t t e n a s R1

+

R2

+

I f each of t h e t h r e e equations

R3 = 0 , then t h e accuracy of t h e

solu-

t i o n w a s f u r t h e r checked by a s s u r i n g t h a t

IlRl

+

R,L

+

R,I2dy in-2

with t h e i n t e g r a t i o n c a r r i e d over a region of appreciable amplitude.

S-tabLe

ho~m‘ion5

For a yi eIds

Kdwh Wwe,

w = kc and n = - 1 .

The f i r s t o r d e r s o l u t i o n (34a)

299

5

4

3

2

I

0 -2

0

-I

I

,

A = uo ( O ) / c Fig. 1 . - S t a b i l i t y zone of a Gaussian j e t centered a t t h e equator. uo(O1 i s t h e e q u a t o r i a l zonal v e l o c i t y and I, i s t h e e-folding half-width of t h e j e t . For val u e s of A and B i n t h e shaded a r e a t h e flow i s s t a b l e , a s guaranteed by equations ( 1 7 ) and ( 1 8 ) ; t h e s e two c o n d i t i o n s a r e v i o l a t e d beyond t h e s o l i d and dashed l i n e s , respectively.

where C = {2B/(1+2B) ) ' I 2 .

(44)

The expansion ( 3 6 ) , made by McPhaden and Knox (.1979), t a k e s t h e form

which coincides with (43) up t o O C A 2 ) . i n s t e a d of c , t o nondimensionalize

0

Unfortunately, McPhaden and Knox used c o ,

and k and t h u s one of t h e nonlinear e f f e c t s

i s hidden i n t h e p l o t - s c a l e of t h e i r d i s p e r s i o n diagram. Figure 2 shows t h e d i s p e r s i o n r e l a t i o n of Kelvin waves, f o r d i f f e r e n t values

of

A & B.

The s o l i d curves a r e t h e s o l u t i o n of (291 ( c a l c u l a t e d t a k i n g a s u f f i -

c i e n t l y high number of s t a t e s ) , whereas t h e dashed l i n e s g i v e t h e f i r s t o r d e r

300 approximation ( 4 3 ) . of k & A, say,

The l a t t e r i s a reasonable approximation f o r moderate values

lkRAl < 0.8, b u t f o r l a r g e r s l o p e s i t i s n o t , and i n f a c t t h e

Kelvin wave becomes s l i g h t l y d i s p e r s i v e . For a

mixed Ronnby-Gtravay

W U L J ~n , = 0 , t h e f i r s t order correction

( 3 8 ) , yields

5

4

crR

3

C

2

/

a

I

0.8

I

1.0

C

I

0.2

I

0.16

I

/

d 1-06 1 0 . 1 5 0

I

I

I

I

1

2

3

4

k R Fig. 2.- Dispersion r e l a t i o n of a Kelvin wave, f o r d i f f e r e n t v a l u e s of A and B. The dashed and s o l i d l i n e s correspond t o t h e e x a c t , ( 2 9 ) , and approximate, (431, s o l u t i o n s r e s p e c t i v e l y . Note t h e d i s p e r s i v e c h a r a c t e r f o r kRAl > 0.8.

I

For l a r g e Ikl

= w

+

, short

waves, we have

k c AC f o r sc << 1 .

(47)

which corresponds t o t h e Rossby mode l i m i t , Eq.

U

= kc{l

+

AC(1

+

B/2)

1

(37), or

f o r sc + 1 ,

which corresponds t o t h e g r a v i t y mode l i m i t , E q .

(48)

(35).

Figure 3 shows t h e dis-

persion r e l a t i o n , comparing t h e r e s u l t s of (29) and ( 4 6 ) ,

f o r two values of A

301 with B fixed.

I n t h e Rossby wave l i m i t t h e phase propagates westward, a s found

by Philander (1979), even €or A > 0 , u n l i k e what t h e f i r s t o r d e r approximation (47) i n d i c a t e s .

A t low f r e q u e n c i e s , t h e c u r r e n t s have a strong e f f e c t due t h e

comparable values of t h e phase speed and t h e p a r t i c l e s v e l o c i t y i n t h e b a s i c s t a t e (Philander 1979, Philander and Pacanowski 1981), but t h e e f f e c t i s not s t r o n g enough t o reverse t h e d i r e c t i o n of phase-propagation. Figure 4 shows t h e d i s p e r s i o n r e l a t i o n of t h e g r a v e s t waves, obtained by solving (29) f o r t h e Q0 f i e l d given by A = B = 0.15 { f o r t h e s e v a l u e s , t h e flow i s s t a b l e according t o ( 1 7 ) and ( 1 8 ) ) .

We s e e t h a t t h e e f f e c t of t h e c u r r e n t i s

s t r o n g e r f o r t h e Rossby than f o r t h e i n e r t i a - g r a v i t y waves, because t h e former have phase v e l o c i t i e s t h a t a r e comparable t o u o ( y ) , and f o r small B t h e change of

B = 0.15

u \ [r

b

-5

-4

-3

-2

-1

0

1

2

3

Fig. 3 . - Dispersion r e l a t i o n of t h e mixed Rossby-gravity waves f o r B = 0.15. The s o l i d and dashed l i n e s correspond t o t h e e x a c t , (29), and approximate, ( 4 6 ) , solutions respectively .

302 depth i s not important.

The Rossby waves p r e s e n t a reduction of t h e i r maximum

frequency. Figure 5 shows t h e d i s p e r s i o n r e l a t i o n f o r A = -0.35

and B = 0.15.

The e f f e c t

on t h e Rossby waves i s s t r o n g e r than i n t h e case of an eastward c u r r e n t (Fig. 4 ) .

Dymh2

~ ~ d &Examples .

of t h e amplitudes 8 = {U(y) ,V(y) ,Z(y)

>

a r e shown in

Figs. 6 , 7 and 8 f o r t h e Rossby (n = Z ) , mixed Rossby-gravity (n = 0) and Kelvin n = -1) waves f o r A = kO.15 and B = 0 . 1 5 . corresponding s t r u c t u r e s f o r A = 0 .

is real.

A l s o shown, f o r comparison, a r e t h e

The amplitudes U and Z a r e imaginary and V

The l a r g e s t departure from t h e A = 0 case i s found on t h e maximum shear

zone of t h e b a s i c s t a t e {the normalization i s f i x e d by Eq.

(33)).

Note t o o the

appearence of a meridional v e l o c i t y component f o r t h e Kelvin wave (Fig. 8 ) .

p 1,

A-O.i5 B = 0.15

I I

I I I

-4

-3

-2

-I

I

I

I

I

2

3

Fig. 4.- Dispersion r e l a t i o n of t h e e q u a t o r i a l waves modified by t h e e f f e c t of an eastward narrow c u r r e n t ( A = B = 0.15) The parameter n corresponds t o t h e mer i d i o n a l quantum number of each mode i n t h e l i m i t A -+ 0. S o l u t i o n s with (k,U): real between t h e heavy s o l i d l i n e and t h e u = 0 a x i s have c r i t i c a l l a t i t u d e s .

.

303 UlznRabfk bVkI,7%lzn GROW% tuL7k.

The maximum of I m ( o ) of t h e unstable waves is shown i n Fig. 9

f o r two values of B (0.15 and 0.5)

f o r A between -2 and 0.

with A < 0 & B < 2 - l I 2 must s a t i s f y A < -B;

Unstable s o l u t i o n s

a t l e a s t f o r narrow e a s t e r l i e s , (17)

seems t o be a l s o a MeCUbdtcy s t a b i l i t y condition, i n t h e sense t h a t A = -B is t h e t h r e s h o l d f o r i n s t a b i l i t y . Eastward c u r r e n t s a r e more s t a b l e than t h e westward ones i n t h e sense t h a t :

a) t h e m i n i m u m value of l u o ( 0 )

I

for instability

i s g r e a t e r f o r t h e eastward c u r r e n t s , and b) t h e maximum growth r a t e

is greater

f o r A < 0 than f o r A > 0 ( n o t shown), f o r t h e same value of \ A \ . These r e s u l t s coincide with t h o s e presented by Philander ('1976). The curvature, o r & e f f e c t , has a s t a b i l i z i n g influence i n t h e sense t h a t , f o r f i x e d A , Im(o) i s g r e a t e r f o r s m a l l e r values of B (Fig. 9 ) .

This e f f e c t has been

noted before by Chamey (1947) and Pedlosky (1964) i n a n a l i t i c a l models f o r mid-

I

I I

A = - 0 . 15 B = 0 . 45

I I I I I

i

I I

I

/

I

,

-3

Fig. 5.-

-2

-1

I

1

2

3

A s i n F i g . 4 , f o r a westward c u r r e n t (-A = B = 0.15).

4

304 l a t i t u d e s , and KUO (1978) i n a numerical model.

% 5 p m i o n diagtram.

Here we p r e s e n t d i s p e r s i o n r e l a t i o n s which include un-

s t a b l e s o l u t i o n s , f o r A = -0.6

& B=

t o 0 . 4 times t h a t of a Kelvin mode)

0.15 ( t h i s represent a j e t with a width equal

,

F i g . 1 0 , and f o r A = -0.9

& B =

1 (i.e.,

t h e same width a s t h a t of a Kelvin wave), Fig. 11. I f t h e flow i s u n s t a b l e , t h e r e i s no value of u such t h a t conditions (15) and (16) a r e simultaneously s a t i s f i e d .

For B = 0.15, condition (151 (with, say, a =

0 ) i s s a t i s f i e d , t h e flow i s s u b c r i t i c a l , but condition (16) i s v i o l a t e d because

t h e g r a d i e n t of p o t e n t i a l v o r t i c i t y i s negative i n a neighborhood of t h e equator (more p r e c i s e l y , i n IyI < .5606L f o r A = - 0 . 6 ) . ayqo

: B

For B = 1 , on t h e o t h e r hand,

f o r any value of A , and t h e r e f o r e condition (16) i s s a t i s f i e d f o r

u 2 max(u,,); unstable flows a r e r e l a t e d t o t h e v i o l a t i o n of (15) : e.g., equator,

a t the

u = AC = - 0 . 9 ~but c ( I + n ) l / * = c ( l + A B ) l i 2 = 0 . 3 2 ~ .

In t h e f i r s t case (Fig. l o ) , t h e complex eigenvalues a r e found where two curves (which i n t h e l i m i t A + 0 correspond t o t h e mixed Rossby-gravity ond Rossby waves) coalesce.

and sec-

However, t h e i n s t a b i l i t y is not s o l e l y due t o the

i n t e r a c t i o n of t h e s e two modes w h t h e fundamental flow, a s Fig.

10 might suggest.

Namely, i f t h e m a t r i x (29) i s t r u n c a t e d down t o j u s t t h e s e two s t a t e s , t h e sol u t i o n i s s t a b l e (Fig. 12) :

I n o r d e r t o o b t a i n u n s t a b l e s o l u t i o n s it is neces-

s a r y t o have s e v e r a l components i n t e r a c t i n g with t h e b a s i c s t a t e . Ripa (1982b) showed t h a t i f energy and pseudomomentum W e h t e x a c t l y quadratic approximation), then t h e flow with B = 1

( a s they a r e i n t h e quasi-geostrophic would be s t a b l e f o r

any value of

A.

H e f u r t h e r argued t h a t i f t h e flow i s

unstable (which can only happen f o r A < -0.62

o r A > 1) then:

1) The amplitude

of t h e flow must be l a r g e enough f o r t h e terms higher than t h e q u a d r a t i c t o be important, i n t h e energy and pseudomomentum i n t e g r a l s .

2)

The Kelvin component

i n t h e expansion ( 2 2 ) of t h e p e r t u r b a t i o n must be r e l a t i v e l y e n e r g e t i c .

We did

not f i n d complex eigenvalues f o r A > 1; t h e d i s t o r t i o n of t h e d i s p e r s i o n diagram of A = -0.9,

Fig.

11, as compared with t h e A = 0 (no c u r r e n t s ) case is an indi-

c a t i o n t h a t t h e amplitude required f o r i n s t a b i l i t y i s indeed q u i t e l a r g e . {Notice t h a t i n Fig.

1 1 t h e r e i s l i t t l e i n d i c a t i o n of t h e Kelvin wave.

In f a c t , consid-

e r i n g only t h e i n t e r a c t i o n among Kelvin modes, (Boyd 1980, Ripa 1982a, o r Eq. (43) with B = 1 ) t h e phase speed of t h e Kelvin wave would be {1+A(3/2)1/2}c, which is equal t o - 0 . 1 ~f o r A = -0.9.1

D y d C @d~!5.

The amplitudes U, V and Z corresponding t o t h e f a s t e s t growing

s o l u t i o n shown i n F i g . 10 (B = 0.151

a r e presented i n Fig. 13.

phase i s f i x e d by making V r e a l a t t h e equator.

The r e l a t i v e

Similary, i n F i g . 14 we show

t h e amplitudes of t h e most unstable s o l u t i o n from Fig.

1 1 (B = 1 ) .

Since t h e

s o l u t i o n i s made up of odd states, t h e phase i s f i x e d by making U imaginary a t t h e equator.

305 B =

L2

R2

,

= 0.15

uo ( 0 )

-=

Curve a : A =

Curve b : A = 0 Curve

:

,

0.15

IJ =

,

A = - 0.15

CR

,

u = 0.28

0 . 3 1 cR 0 =

-1

-1

0.39

, CR

cR

-1

n = 2

-1

... .

: ... ,

-

C

k = - 2.56

I

T

I

I

I

I

I

I

Fig. 6.- Amplitudes U , V and Z as a f u n c t i o n of l a t i t u d e , f o r t h e second Rossby mode modified by Gaussian flows and i n t h e absence of c u r r e n t s . The normalizat i o n of t h e f i e l d s is given by Eq. ( 3 3 ) . Note t h a t f o r small values of B ( i . e . ,

c u r r e n t s narrower than t h e Kelvin

mode) t h e s t r o n g e s t i n s t a b i l i t y happens through even p e r t u r b a t i o n s i n v (meand e r s ) , while f o r B = 1 t h e f a s t e s t growing disturbance has even u (varicose mode) ; t h e former w a s a l s o found by Philander (1976)

, whereas

t h e l a t t e r i s con-

3 06 B =

0.15

,

Curve a : A =

R

,

= 0.49

0.15

Curve b : A = 0 Curve c : A =

-1

k = - 2.56

,

- 0.15

0

a = 0.63 c R

,

IJ =

cR

-1

-1

0.74 c R

,

n = 0

-1

C

0

I

I

I

I

I

I

I

1

2

3

4

5

6

7

Fig. 7.- A s i n F i g . 6 f o r t h e mixed Rossby-gravity wave.

s i s t e n t with t h e need f o r a Kelvin component i n t h e growing p e r t u r b a t i o n , a s mentioned above. In t h e d i s p e r s i o n r e l a t i o n of Fig. 1 1 , t h e complex eigenvalues appear i n t h e modes t h a t , i n t h e l i m i t A

-f

0 , a r e t h e n = 7 & 9 Rossby waves, b u t t h e corre-

sponding dynamic f i e l d s look more l i k e t h o s e of a Kelvin wave, and t h e major p a r t

307

,

B = 0.15

_ _ ---___a ~ - -_

-..

Fig. 8.-

k = - 2.56 R

Curve a

:

A

Curve b

:

A = 0

Curve c

:

A

=

=

0.15

,

0.15

,

IJ =

- 2.76 C R

u = - 2.56 C R

,

U

=

,

n

=

- 1

- 2.36 c R

--..... --____ . ...

As i n Fig. 6 f o r t h e Kelvin wave.

of t h e energy is a l s o concentrated i n t h e Kelvin component. have a f i n i t e v1 f i e l d , absent i n a pure Kelvin wave.)

( H e r e , though, we

This i s similar t o the

wave discussed by Hughes (1979, 1981).

4

SUMMARY AND CONCLUSIONS

The e f f e c t of a zonal c u r r e n t on t h e e q u a t o r i a l waves is s t u d i e d i n a one-lay-

308

M A X I M U M GROWTH RATE B = L2/R2 0.5

-

0.4

-

0.3

-

0 \

oz b-

0.2

0.1

-

0.0

-

-

-I

A

.o

-0.5

0.0

u,(O)/c

Fig. 9.- Maximum growth rate of t h e e q u a t o r i a l i n s t a b i l i t y a s a function of t h e c u r r e n t amplitude, f o r two values of i t s width.

er reduced g r a v i t y model i n t h e e q u a t o r i a l @-plane. The normal-modes problem i s solved expanding t h e p e r t u r b a t i o n in t h e s o l u t i o n s of t h e l i n e a r system.

Both

s t a b l e and unstable s o l u t i o n s a r e found f o r Gaussian j e t s with amplitude and width i n agreement with t h e s t a b i l i t y c r i t e r i o n derived by Ripa (198233). An a n a l i t i c a l expression i s derived f o r t h e frequency s h i f t t o f i r s t order i n

t h e amplitude of t h e j e t .

This c o r r e c t i o n i s r e a l and ( i n t h e cases of Kelvin,

s h o r t Rossby and s h o r t g r a v i t y waves) p r o p o r t i o n a l t o t h e zonal wavenumber. Howe v e r , t h e s o l u t i o n of t h e complete equation shows t h a t t h e Kelvin waves becomes d i s p e r s i v e i n t h e presence of s t r o n g c u r r e n t s .

I t i s a l s o found t h a t , f o r a l l

t h e waves, westward c u r r e n t s produce, i n g e n e r a l , a s t r o n g e r Doppler s h i f t than eastward ones do. Unstable s o l u t i o n s a r e found f o r j e t s such t h a t only one of t h e two s t a b i l i t y conditions i s v i o l a t e d ;

V ~ Z . ,a

s u b c r i t i c a l and narrow j e t with p o t e n t i a l vor-

t i c i t y extrema, o r a s u p e r c r i t i c a l j e t with t h e shape of a Kelvin mode.

309 r /’ /

/

/

I

//I /

,/’

-5

-4

I

-1

-2

-3

2

kR Fig. 10.- As in Fig. 4 for B ponds to the imaginary part of

=

a

0.15

.

and

A = - 0.6. The dotted line corres-

Comparing westward and eastward jets with the same strength and width, it is found that the former are more unstable (larger maximum growth rate for the perturbation).-The energetics of both types of instability are discussed in a companion publication (Marinone and Ripa, 1 9 8 3 ) .

Acknowledgements We are grateful to Sergio Ramos for drafting the figures, to Antoine Badan and Cuauhtgmoc Nava for comments, and to Dolores Peralta for typing the manuscript.

310

2

0-

-3

-2

-1

2

0

3

4

kR Fiq. 11.- A s i n Fig. 10 f o r A = - 0 . 9 same w i d t h of a Kelvin mode).

and

B = 1

(i.e., a c u r r e n t w i t h t h e

311 L

2 -

A =-0.6

B

-4

-3

0.15

-2

-i

0

I

2

3

4

kR Fig. 12.- Eigenvalues of ( 2 9 ) including only t h e mixed Rossby-gravity and t h e The parameters A and B a r e t h e same t h a t those of second Rossby components. Fig. 10; however, t h e frequencies a r e r e a l , i n d i c a t i n g t h a t more than two components a r e needed i n o r d e r t o g e t t h e i n s t a b i l i t y .

312

\

13 =

( 1 . 0 8 , 0.35)cR-'

k =

-

2.56 R

-1

z(Yl

0.5

0.0

-0.5 0

1

2

3

4

5

6

7

Fig. 13.- Complex amplitude of t h e dynamic f i e l d s ul, v1 and n I corresponding t o t h e f a s t e s t graving s o l u t i o n of Fig. 10. The s o l i d and dashed l i n e s correspond t o t h e real and imaginary p a r t s of t h e amplitude.

313

- - 0.9

A=--C

u

=

k

= -

( 0 . 7 7 , 0.034)cR

\ \ \

2.22 R

-1

\

0.5

0.0

-0.5

0

1

2

3

Y/L Fig.

14.-

A s i n Fig.

1 3 , f o r t h e f a s t e d growing s o l u t i o n o f F i g .

11.

-1

314 APPENDIX. MATRIX ELEMENTS O F C. The expansion f u n c t i o n s t a k e t h e form

where y ' = ( B / c ) ' / ~ Y , (Miller,

and Y a r e t h e normalized p a r a b o l i c c y l i n d e r functions

The eigenvalues w and e i g e n c o e f f i c i e n t s N a r e more e a s i l y w r i t -

1966).

t e n using t h e zonal slowness,

s = k/w

(A2)

as a parameter.

The expression a r e (Ripa, 1982a)

w = kc

(n = - 1 ; N(+)

= 1, N(-)

= N(0)

s c = 1)

,

(A3)

= 0

f o r t h e Kelvin component,

f o r t h e mixed Rossby-gravity components ( s c < 1)

for the inertia-gravity

Q = {4n+2

Na(+)2

+

,

and

( - 1 < sc < 1 ) and Rossby ( s c < -2n-1)

components, where

S C { ~ - ( S C ) ~ } } The ~ / ~ normalization . is

+ Na(-)2

which implies

+

m

Na(0)2 = 1 ,

-i IY(m,y')2dy'

= 1,

( A6a, b)

315 The matrix elements Cl

ab

a r e defined by ( 2 8 ) , where i C is t h e o p e r a t o r involv-

ing uo and q o i n (8) through ( 1 0 ) .

Expanding t h e integrand i n (281 we obtain

.

The f i r s t term i n t h e expression between

{

1 comes from t h e advection by t h e

flow u o ; t h e second one i s due t o t h e c o n t r i b u t i o n of t h e shear 2 u o t o t h e Y C o r i o l i s term i n ( 8 ) ; f i n a l l y , t h e t h i r d one corresponds t o t h e e f f e c t of t h e

no,

topography of t h e b a s i c flow,

i n t h e mass conservation law ( 1 0 ) .

The i n t e -

g r a l i n (A8) may be s i m p l i f i e d using t h e following p r o p e r t i e s of t h e eigenfunct i o n s of (21) :

t o eliminate e x p l i c i t derivatives.

(These two equations a r e t h e l i n e a r i z e d con-

s e r v a t i o n l a w s of p o t e n t i a l v o r t i c i t y and m a s s . ) I n t h e f i r s t term i n (A8),

( ay

a

*)uo;

b

+

a

r(

G

may be replaced by i k .

<*

and G are then evaluated from b

In t h e t h i r d and l a s t term, V. (q

+ 'loV-$,

which i s s i m p l i f i e d using ( 7 ) and (A10).

(V * * G +

C2~a*~b),

YOb (A81 a r e t h u s replaced by

1: iku

-?J

0-a

2: uo{i(k+B/w ); * a a 3: - f u

+

fGa*}G

b

The second term may be

i n t e g r a l obviously v a n i s h e s , minus

*uoaycb; t h e y - d e r i v a t i v e s of

(A91 and ( A I O ) , r e s p e c t i v e l y .

a

aX

(u *uocb), whose meridional ~a

a

written as

+

uo;

a

*(-iw ?l + ikGb), b b

G

O-b

)

i s equal t o

The t h r e e terms i n

(A1 1

ii *V + c2n i w ii *-

Oa

b

0

b a 'lb'

Adding t h e s e t h r e e expressions we f i n a l l y g e t Eq.

(30).

The expressions ( A l ) are replaced i n (30) f o r t h e p r a c t i c a l e v a l u a t i o n of t h e matrix elements, which y i e l d s

where

316

and

For t h e Gaussian j e t (40) t h e s e i n t e g r a l s a r e evaluated using t h e a n a l y t i c expressions derived

by Busbridge (1948), i n t h e form

where p = 1/2+B and h = ( m ' + m ) / 2

( A must be a non-negative i n t e g e r ) , and

a r e t h e gamma & hypergeometric functions.

r

&

F

F i n a l l y , it follows from (41) t h a t

D(i,j) = (B/c)U(i,j).

REFERENCES

Boyd, J . P . , 1980. The nonlinear e q u a t o r i a l Kelvin wave. J . Phys. Ocean., 10: 1-1 1 . Busbridge, I . W . , 1948. Some i n t e g r a l s involving H e r m i t e polynomials. J . London Math. SOC., 23: 135-141. 1947. The dynamics of long waves i n a b a r o c l i n i c westerly curChamey, J . G . , 135-163. r e n t . J . Meteor., 4: Courant, R. and D. H i l b e r t , 1953. Methods of mathematical physics. I n t e r s c i e n c e , New York, 561 pp. Drazin, P.G., and L . N . Howard, 1966. Hydrodynamic S t a b i l i t y of P a r a l l e l Flow of I n v i s c i d F l u i d . I n 'Advances i n a p p l i e d Mechanics', Academic P r e s s , New York, 9: 1-89. Hughes, R . L . , 1979. On t h e dynamics of t h e e q u a t o r i a l undercurrent. T e l l u s , 31: 447-455. , 1981. On i n e r t i a l i n s t a b i l i t y of t h e e q u a t o r i a l undercurrent. T e l l u s , 33: 291-300. Kasahara, A . , 1980. E f f e c t of zonal flows on t h e f r e e o s c i l l a t i o n s of a b a r o t r o p i c atmosphere. J . Atmos. S c i . , 37: 937-929. Kuo, H . L . , 1978. A two-layer model study of t h e combined b a r o t r o p i c and baroJ. A t m o s . S c i . 35: 1840-7860. c l i n i c instability i n the tropics. Marinone, S.G., and P . Ripa., 1983. Energetics of t h e i n s t a b i l i t y of a depth independent e q u a t o r i a l j e t . In p r e p a r a t i o n . Matsuno, T . , 1966. Quasi-geostrophic motions i n t h e e q u a t o r i a l a r e a . J. Meteor. SOC. Japan, 44: 25-43. and R.A. Knox, 1979. E q u a t o r i a l Kelvin and Inertio-Gravity McPhaden, M . J . , waves i n zonal shear flow. J. Phys. Ocean., 9: 263-277. Miller, J.C.P., 1966. P a r a b o l i c c y l i n d e r f u n c t i o n s . I n 'Handbook of Mathemati c a l T u n c t i o n s ' , M. Abramowitz and I . A . Stegun, e d i t o r s . Dover P u b l i c a t i o n , Inc. chap. 19, pp. 685-720.

317 Miyata, M . , 1981. A c r i t e r i o n f o r b a r o t r o p i c i n s t a b i l i t y a t t h e e q u a t o r . (Unpublished m a n u s c r i p t ) . T r o p i c a l Ocean-Atmosphere N e w s l e t t e r , 5 , J a n u a r y . P e d l o s k y , 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 o c e a n s . P a r t . I. J. A t m o s . S c i . , 27: 201-219. 1976. I n s t a b i l i t i e s of z o n a l e q u a t o r i a l c u r r e n t s . J . Geophys. Philander, S.G.H., R e s . , 81: 3725-3735. , 1978. I n s t a b i l i t i e s of z o n a l e q u a t o r i a l c u r r e n t s , 2. J . Geophys. R e s . , 83 : 3679-3682. , 1979. E q u a t o r i a l waves i n t h e p r e s e n c e of e q u a t o r i a l u n d e r c u r r e n t . J. Phys. Ocean., 9 : 254-262. , and R.C. Pacanowski, 1981. Response of e q u a t o r i a l o c e a n s t o p e r i o d i c 1903-1916. f o r c i n g . J. Geophys. R e s . , 86: Ripa, P . , 1982a. N o n l i n e a r wave-wave i n t e r a c t i o n s i n a o n e - l a y e r reduced gravi t y model on t h e e q u a t o r i a l B-plane. J . Phys. Ocean., 12: 97-111. , 198233. G e n e r a l s t a b i l i t y c o n d i t i o n s f o r z o n a l f l o w s i n a o n e - l a y e r model on t h e B-plane o r t h e s p h e r e . J . F l u i d . Mech., i n p r e s s .

This Page Intentionally Left Blank

319

THEORY OF FREQUENCY SPECTRA OF EQUATORIALLY TRAPPED WAVES.

W.

FENNEL and H.U. LASS

1.

INTRODUCTION

I n t h e l a t e 1960's t h e o r e t i c a l i n v e s t i g a t i o n s of b a r o c l i n i c motions i n a l i n e a r i n v i s c i d e q u a t o r i a l ocean on a

B-plane revealed t h e p o s s i b i l i t y of

e q u a t o r i a l trapped waves. For a h i s t o r i c a l review of t h e t h e o r i e s see e . g . Wunsch (1978). By s e p a r a t i o n of v a r i a b l e s i n case of f r e e motion, t h e s t r u c t u r e of meridional modes and t h e d i s p e r s i o n r e l a t i o n , c l a s s i f y i n g Rossby-,

inertial-gravity

and t h e

mixed Rossby-gravity waves, can be discussed. Current and water l e v e l measurements a t various p o i n t s i n t h e e q u a t o r i a l oceans,performed during t h e 1970's,gave experimental evidence of e q u a t o r i a l trapped motion coherent over l a r g e zonal d i s t a n c e s . Since most of t h e measured time s e r i e s a r e expressed i n terms of frequency s p e c t r a a t a f i x e d p o s i t i o n , i t would be d e s i r a b l e t o c a l c u l a t e t h e frequency s p e c t r a of t h e dynamic v a r i a b l e s from t h e equation of motion f o r an adequate comparison of theory and measurements. This has been t r i e d by Wunsch and G i l l (1976). However, t h e i r r e s u l t s depend on a pseudo-dissipation parameter which does not appear i n t h e b a s i c equation they used and, moreover, they d i d n o t d e r i v e closed expressions f o r t h e frequency s p e c t r a i n t h e whole range of p o s s i b l e frequencies. The aim of t h e p r e s e n t paper i s t o determine t h e power s p e c t r a of Eulerian measurements of v e l o c i t y and p r e s s u r e i n t h e e q u a t o r i a l wave guide,on t h e b a s i s of a Greenfunction technique. W e consider v e r t i c a l standing mode o r e q u i v a l e n t l y a two layered l i n e a r ,

h y d r o s t a t i c and i n v i s c i d ocean on an e q u a t o r i a l ding

dissipation

6 - p l a n e . Although i n c l u -

processes should be possible,we consider an i n v i s c i d theory

j u s t f o r s i m p l i c i t y . Moreover, t h e main d i s s i p a t i o n processes of t h e ETW's have not been i d e n t i f i e d a t p r e s e n t . This i s a f u r t h e r reason t o consider a theory which avoidsmore o r less a r t i f i c a l d i s s i p a t i o n terms. In t h e second s e c t i o n we d i s c u s s some a s p e c t s of t h e f r e e motions.

In s e c t i o n

three,some general p r o p e r t i e s of t h e Green functions and t h e i r s p e c t r a l represent a t i o n s w i l l be i n v e s t i g a t e d . C l e a r l y , i n an i n v i s c i d t h e o r y , t h e c a u s a l i t y i s n o t accounted f o r e x p l i c i t l y . By means of t h e s p e c t r a l r e p r e s e n t a t i o n s , which a r e compact r e p r e s e n t a t i o n s of t h e i n i t i a l c o n d i t i o n s t h e c a u s a l i t y w i l l be insured.

320 In t h e f o u r t h s e c t i o n , t h e r e s u l t s w i l l be a p p l i e d t o t h e c a l c u l a t i o n of power s p e c t r a . T h i s i m p l i e s t h e a s s u m p t i o n o f f o r c i n g f u n c t i o n s . The ocean f l u c t u a t i o n s can b e e x c i t e d i n p r i n c i p l e by d e t e r m i n i s t i c o r s t o c h a s t i c atmospheric fluctuations.

W e c o n f i n e o u r s e l v e s t o two d e t e r m i n i s t i c examples o f

f o r c i n g , a b r o a d band and a s m a l l band f o r c i n g i n t h e z o n a l wavenumber domain. T h i s i s m o t i v a t e d by t h e f o l l o w i n g f a c t s

:

( i ) The d e s c r i p t i o n o f s t o c h a s t i c f l u c t u a t i o n s i n t e r m s o f t h e i r moments re-

q u i r e s t h e s t o c h a s t i c p r o c e s s t o b e s t a t i o n a r y and homogeneous. However, Weisberg and Hortgan (1981) found e v i d e n c e f o r a s e a s o n a l modulation o f t h e ETW's. Moreover, t h e l o n g wave l e n g t h o f t h e ETW's makes any assumption o f homogeneity q u e s t i o n a b l e . ( i i )Very l i t t l e i n f o r m a t i o n i s a v a i l a b l e f o r t h e wavenumber s t r u c t u r e o f t h e

a t m o s p h e r i c f o r c i n g f i e l d above t h e e q u a t o r i a l ocean. T h e r e f o r e , i t seems t o b e r e a s o n a b l e t o t r y some examples o f f o r c i n g f u n c t i o n s . n = 0

The c a l c u l a t i o n o f t h e s p e c t r u m o f t h e

mode on an e q u a t o r i a l B - p l a n e

w i l l b e d i s c u s s e d i n s e c t i o n f i v e . I n t h e s i x t h s e c t i o n , we summarize t h e res u l t s o f o u r c a l c u l a t i o n s and compare them w i t h measurements.

2.

FREE MOTION

F i r s t l y w e c o n s i d e r some s p e c i a l a s p e c t s o f t h e f r e e motion problem. For t h e m e r i d i o n a l c u r r e n t w e have t h e well-known boundary v a l u e problem (see e . g . Moore and P h i l a n d e r ,

with

v

and

Ah

a2

0

-+

1977).

for

y

+

* -.

i s t h e h o r i z o n t a l Laplacian

Ah=----+ax2

a2 ay2

u

The z o n a l component

o r , equivalently

- y

U t

D(x,y,t) is the d i f f e r e n t i a l operator

+ uxy

Y Px - P t y =

=

V t t

V t t

- vyy

- y

2

and t h e p r e s s u r e

p

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

v

according t o

321 For

v

w e make t h e u s u a l s e p a r a t i o n m

where

are t h e n o r m a l i z e d H e r m i t e f u n c t i o n s

$,(y)

From ( 1 ) and ( 7 ) f o l l o w s

-

i Dn(w,k) Sn(w,k) = 0

where

Dn(w,k)

Dn(w,k) = w 3

-

i s t h e d i s p e r s i o n polynomial (2n+ l ) w

I t c a n b e shown t h a t

-

k20 - k

Dn(w,k) h a s t h r e e d i s t i n c t r e a l r o o t s

on,(k)

(j = 1 , 2 , 3 )

with t h e p r o p e r t i e s

T h e r e f o r e w e may rewrite (9) i n t h e form

The g r a p h i c a l r e p r e s e n t a t i o n o f t h e r o o t s of

(9) w i t h r e s p e c t t o

kn1,2 = -

1

[1 f 2

wnj

may be found u s i n g t h e r o o t s

k

d(u2- 4 ~( w 2) - &R)]

(11)

The v a l u e s

a re t h e p o i n t s o f z e r o group v e l o c i t y ( f i g . 1 ) . x 6(x) = 0

Generalizing t h e relation

(8) and ( 1 0 ) t h e s p e c t r a l f u n c t i o n

Sn(w,k)

o f D i r a c ' s 6 - f u n c t i o n w e f i n d from t o be

S i n c e w e d e a l w i t h a t h i r d o r d e r d i f f e r e n t i a l e q u a t i o n w i t h r e s p e c t to three constants

A , B

and

C

a p p e a r i n t h e s o l u t i o n ( 1 3 ) . Choosing t h e

t

,

322

Fig. 1.

The dispersion diagram of equatorialiy trapped waves for

n

2

1.

pseudo-initial conditions Vn(X,O) = Vnt(X,O) = 0

(14)

vntt(x,O) = 6(x)

(15)

or, equivalently

we find, inserting (13) in (16) and (17), a linear system

and it f o l l o w s that

323 or

I n t h e u s u a l d i s c u s s i o n o f t h e f r e e motion,

-

vn(x,t) where

w

e

vn

i s g i v e n i n t h e form

- i o t + ikx

and

a r e c o n n e c t e d by a d i s p e r s i o n r e l a t i o n

k

w = wnj(k)

.

I t is

e a s y t o show t h a t s u c h a r e p r e s e n t a t i o n i m p l i e s i n i t i a l c o n d i t i o n s o f t h e t y p e vn(x.O) = v n t ( x , O )

=

vn(w,k)

w 2 vn(w,k)

vntt(x,O)

= e

ikox

w e have

i n t h e w-k-domain

I I-

,

0

=

I-

dw 2n

i w vn(w,k)

=

do 2n

= o

2n 6 ( k - ko)

T h i s c o r r e s p o n d s t o an i n i t i a l s m a l l band f o r c i n g i n t h e k-domain.

The r e s u l t i s

A f t e r F o u r i e r t r a n s f o r m a t i o n , one o b t a i n s

Thus, w e see t h a t t h e u s u a l s o l u t i o n s o f t h e f r e e motion problem d e s c r i b e t h e ikox response of t h e ocean to a p u l s e l i k e f o r c i n g w i t h a s p a t i a l p a t t e r n l i k e e

.

The p h y s i c a l meaning o f t h e s p e c t r a l f u n c t i o n

i s t h e following

:

Sn(w,k)

Sn(w,k)

a c c o r d i n g t o eq. (18a)

i s t h e F o u r i e r t r a n s f o r m o f a wave p r o c e s s

vn(x,t)

which i s a n a l y t i c a l l y c o n t i n u e d i n t h e n e g a t i v e t i m e domain. T h i s f u n c t i o n c o n t a i n s no i n f o r m a t i o n a b o u t t h e d i s t u r b a n c e s o f t h e " s w i t c h on" p r o c e s s a t

t = 0

and, t h e r e f o r e ,

Sn(w,k)

m i r r o r s t h e p u r e p r o p e r t i e s o f t h e wave p r o -

cess. I n o t h e r words w e may c o n s i d e r process t h a t w a s forced a t

t = -

Sn(w,k)

m .

t o be t h e s p e c t r a l f u n c t i o n of a

T h i s becomes e v i d e n t i n t h e d i s c u s s i o n o f

t h e Green f u n c t i o n i n t h e f o l l o w i n g s e c t i o n . I n t h e f o l l o w i n g w e c o n s i d e r o n l y t h e modes

n t 1

.

we may express t h e

The mode u-

and

n = 0

w i l l be d i s c u s s e d i n s e c t i o n 5 . For

p - f i e l d i n t e r m s of

Sn(w,k)

n t 1

i n t h e u s u a l manner

324

3.

GREEN FUNCTIONS AND SPECTRAL REPRESENTATIONS

Including a f orci n g function D(XrY,t)

F(x,y,t)

,

w e have, i n s t e a d o f eq.

(1) :

V(x,y,t) = F(x,Y,t)

(21)

W e c o n f i n e o u r s e l v e s t o two examples o f f o r c i n g f u n c t i o n s , f i r s t a b r o a d band

f o r c i n g g i v e n by D i r a c ' s 6 - f u n c t i o n s F(X,y,t)

6(t-t')

6(y-y')

= ~ ( X - X ' )

(22)

and, s e c o n d , t o a s m a l l band f o r c i n g i n t h e wave number domain

( 2 1 ) and ( 2 2 ) w e have t o d e t e r m i n e t h e Green f u n c t i o n o f

C l e a r l y , with eqs.

o u r boundary v a l u e problem

T h i s f u n c t i o n i s o f s p e c i a l i m p o r t a n c e s i n c e it l e a d s i n p r i n c i p l e t o a f o r m a l s o l u t i o n o f t h e g e n e r a l problem ( 2 1 ) by means o f v(x,y,t) = Let

I

dx' dy' d t ' G ( x , y , t ; x ' , y ' , t ' )

K(x,y,t;x',y',t')

F(x',y',t')

b e t h e s o l u t i o n o f t h e problem ( 2 1 ) and ( 2 3 ) . T h i s

f u n c t i o n i s a l s o a Green f u n c t i o n D(x,y,t) K(x,y,t;x',y',t') To c a l c u l a t e t h i s f u n c t i o n , Hermite-functions G(xry,t;X' , Y ' p t ' )

= S(y-y')

w e expand

i k , (x - x' )

6(t-t')

e

G , K

and

6(y-y')

(24b) i n t e r m s of

Jln ( y ) =

C Gn(Xrt;X'tt')

Jln(Y) Jln(YO

n K(X,y,t;X'rY',t')

=

1K n ( X , t ; X ' , t ' )

Jln(Y) $ n ( Y ' )

n

~(Y-Y') =

1Jln(y)

$n(y')

n From e q . and

( 2 ) , it follows t h a t

t-t'

w e have

.

G

and

K

depend o n l y on t h e d i f f e r e n c e s

After Fourier transformation with respect to

x-x'

and

x-x'

t-t'

,

where

(9).

i s t h e d i s p e r s i o n polynomial

Dn(w,k)

The t r a n s f o r m a t i o n o f e q s .

(25a) and (25b) i n t h e

x,t-domain c o n s t i t u t e s

a problem s i n c e t h e s e f u n c t i o n s p o s s e s s p o l e s on t h e r e a l w-axis a t

w = wnj

( j = 1 , 2 , 3 ) . Due t o t h e d i f f e r e n t k i n d s o f Green f u n c t i o n s which r e s o l v e e q s . (24a) and (24b) t h e r e a r e v a r i o u s p o s s i b i l i t i e s t o go around t h e s e p o l e s . The p r e s c r i p t i o n how t o go around t h e p o l e s f o l l o w s from t h e p r i n c i p l e o f c a u s a l i t y . To show t h i s w e c o n s i d e r t h e r e t a r d e d Green f u n c t i o n s

O(T) T

i s t h e s t e p f u n c t i o n [@(T)

< 01. I n s e r t i n g e q s .

Ghom and and

Khom

for

= 1

T

> 0

and

@(r)

=

0

for

( 2 4 a , b ) , r e s p e c t i v e l y , we see t h a t

(27a,b) i n eqs.

a r e t h e s o l u t i o n s o f t h e homogeneous problems

DGhom = 0

with t h e i n i t i a l conditions

DKhom = 0

We see t h a t t h e F o u r i e r t r a n s f o r m o f

Ghom

i s j u s t t h e s p e c t r a l f u n c t i o n (18a)

d i s c u s s e d i n t h e p r e v i o u s s e c t i o n . T h i s i s clear s i n c e t h e i n i t i a l v a l u e p r o blem f o r

Ghom i s i d e n t i c a l w i t h t h a t g i v e n by e q s .

S i m i l a r l y , w e f i n d , u s i n g eq.

( 1 ) and (141, ( 1 5 ) .

(18b),

Now w e make u s e o f t h e c o n t o u r i n t e g r a l r e p r e s e n t a t i o n o f t h e s t e p f u n c t i o n

(E +

E

+

0)

(30)

i s a p o s i t i v e i n f i n i t e s i m a l q u a n t i t y . C o n s i d e r w t o b e a complex v a r i a b l e . 1 h a s a s i m p l e p o l e i n t h e lower h a l f p l a n e a t w = - is

The f u n c t i o n

+ 0

(see f i g . 2 ) . F o r

1E T

> 0

a c c o r d i n g t o J o r d a n ' s Lemma, w e can complete t h e

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

R +

m

i n t h e lower

3 26

Fig. 2 . I n t e g r a t i o n p a t h of t h e contour i n t e g r a l r e p r e s e n t a t i o n of t h e s t e p f u n c t i o n f o r T < 0 and T > 0 .

h a l f p l a n e . Applying t h e r e s i d u e theorem, t h e i n t e g r a l i s found e q u a l t o For n e g a t i v e

T I

1

.

w e must u s e a s e m i c i r c u l a r c o n t o u r i n t h e u p p e r h a l f p l a n e (30) i s i n f a c t a r e p r e s e n t a t i o n o f

and t h e i n t e g r a l v a n i s h e s . T h e r e f o r e e q . t h e s t e p f u n c t i o n . With eq.

dw'

( 3 0 ) , i t f o l l o w s from e q s .

( 2 9 a ) and (29b)

271 6 ( k - k o ) S n ( w ' , k ) w - w' + ic

These are t h e s p e c t r a l r e p r e s e n t a t i o n s o f t h e r e t a r d e d Green f u n c t i o n s

and

Gr

Kr.

Using D i r a c ' s f o r m u l a - -1

w + i c

P - . - + 171 6 ( w ) w

where t h e l e t t e r

1 i

P

dwv

Sn(W',k)

2n

w - w'

dOv i

<(w,k)

d e n o t e s a Cauchy p r i n c i p l e v a l u e , we have

= P

-

S,(w',k)

i

Sn(w,k) 2

271 6 ( k - k , )

w

-

0'

These are t h e g e n e r a l s o l u t i o n s of e q s .

- i v Sn(w,k) 6 ( k - k,)

(24a) and ( 2 4 b ) , r e s p e c t i v e l y , which

c o n s i s t of t h e g e n e r a l s o l u t i o n s o f t h e homogeneous problems

217 6 ( k - k , )

Sn (w,k)

(33b)

Sn(w,k)

and

and t h e s p e c i a l s o l u t i o n s of t h e non-homogeneous problems

327 i n t e r m s o f t h e p r i n c i p l e v a l u e i n t e g r a l s . From e q s .

(33a) and ( 3 3 b ) , w e s e e

that 1

k) = - S n ( w , k )

2 Im - G ; ( w + i ~ , 2 Im

51 K i ( w + i E , k)

(E

+

0)

= - ZIT 6 ( k - k o ) Sn(w,k)

Now w e can s e e how t h e f o r m a l s o l u t i o n s ( 2 5 a , b ) must be modified i n o r d e r t o be c o n s i s t e n t w i t h t h e i n i t i a l c o n d i t i o n s ( 2 8 a , b ) and t h e p r i n c i p l e o f causality i D n ( w + i E , k)

G:(w'k)

P a r t i a l f r a c t i o n expansion y i e l d s

Taking from eq.

(35),

The r e s u l t f o r

Ki

Im

1

r

T Gn

i s sim:ly

,

one f i n d s u s i n g eq.

(32) t h e r e l a t i o n

found by m u l t i p l y i n g e q .

W e n o t e t h a t t h e s p e c t r a l f u n c t i o n s are a l r e a d y g i v e n by e q s .

(34a).

2n 6 ( k - k o )

(35) by

.

(18a,b). Clearly

t h e p r e s c r i p t i o n how t o go around t h e p o l e s i s g i v e n by means of t h e p o s i t i v e infinitesimal

E

.

The d i s c u s s i o n a l o n g t h o s e l i n e s i s w e l l known i n o t h e r b r a n c h e s o f t h e o r e t i c a l physics [e.g.

quantum f i e l d t h e o r y o r many p a r t i c l e t h e o r y , see e . 9 .

Wu

and Omura (1962) o r M a r t i n and Schwinger ( 1 9 5 9 ) l . Of c e n t r a l i m p o r t a n c e i s t h e

f a c t t h a t c a u s a l i t y and s p e c t r a l r e p r e s e n t a t i o n s a r e i n t i m a t l y c o n n e c t e d . T h e r e f o r e w e can c o n c l u d e t h a t s u c h r e p r e s e n t a t i o n s a l s o e x i s t f o r t h e z o n a l v e l o c i t y and f o r t h e p r e s s u r e f i e l d . Using t h e s p e c t r a l f u n c t i o n s and

pn(w,k,y)

un(w,k,y)

g i v e n by eqs. (19) and (20) and d e n o t i n g t h e c o r r e s p o n d i n g

Green f u n c t i o n s

Un

and

Pn

,

we have

f o r t h e b r o a d band f o r c i n g c a s e ( 2 2 ) . I n t h e s m a l l band f o r c i n g case, e q s . and (37) must b e m u l t i p l i e d by

4.

271 6 (k - k o )

(36)

.

SPECTRA OF EULERIAN TIME SERIES N o w w e c o n s i d e r a t i m e series o f

Gi(x,t)

a t fixed

a . W e choose

a m e r i d i o n a l c u r r e n t component, s a y

x = x'

without l o s s of g e n e r a l i t y . In t h e

328 w-k-domain

Gg(w)

t h i s i s e q u i v a l e n t l y t o a k - i n t e g r a t i o n of

G,’(w,k)

i s j u s t t h e frequency spectrum of t h e c u r r e n t amplitude. Introducing

t h e correlation function

where t h e l e n g t h o f t h e t i m e series i s assumed t o b e l a r g e

(T +

m ) ,

w e have

a f t e r Fourier transformation

Now w e may i n s e r t

G,’

according t o eq.

( 3 3 a ) and f i n d

F o r o u r f u r t h e r d i s c u s s i o n , it i s n e c e s s a r y t o e s t i m a t e

To t h i s end, w e u s e t h e s p e c t r a l f u n c t i o n ( 1 8 a ) . I t i s r e a d i l y s e e n t h a t n o t h i n g

i s changed by t h e i n t r o d u c t i o n o f s t e p f u n c t i o n s

-

wn2 - wnl

Here t h e r e l a t i o n s

are v a l i d f o r a l l

2T 6 ( w - w n 3 ) @ ( - 0 - WnG)

k

> 0

1 (Wn3 ,

Wnl)

wn3 - wnl

( f i g . 1) were u s e d . N o w

(Wn3 - W n 2 )

< 0

w a s used. T h i s g i v e s , r e s p e c t i n g eq.

(ll),

wn3 - wn2 < 0

which

w e may w r i t e w,k)l

where t h e 6 - f u n c t i o n r e l a t i o n

and

I

(39)

329

The spectrum o f eq.

(40a) i s t h e frequency spectrum of t h e meridional c u r r e n t

components of t h e ETW which a r e e x c i t e d by a broad band f o r c i n g , long before our "time s e r i e s " s t a r t e d . I n t h i s case we may assume t h a t t h e ETW f o r g o t t h e d i s turbances of t h e "switch on" processes. Then t h e corresponding power spectrum is

If t h e f o r c i n g occured within our time s e r i e s , t h e power spectrum w i l l be

smeared o u t . This p r o c e s s i s accounted f o r by t h e p r i n c i p l e value i n t e g r a l i n eq.

(33a) and, t h e r e f o r e , i n eq.

(38).

Thus

Now we determine t h e p r i n c i p l e value i n t e g r a l i n eq.

( 4 2 ) . With r e s p e c t t o

one can w r i t e

l o Thus t h e power spectrum i s e x p l i c i t l y

otherwise

330 We see t h a t t h e e f f e c t of t h e "switch on" process i s t o f i l l t h e gap between t h e two peaks which occur i n t h e spectrum of eq. process which was forced a t w

large

and f o r small

Eqs.

m .

t h e spectrum decreases l i k e

1 = 4T

RX(w)

t = -

1

large

7 w

(41) of t h e q u a s i steady wave

W e note some p r o p e r t i e s of eq. w

( 4 3 ) . For

-4

w

(44)

it follows t h e law

( 4 4 ) and (45) a r e v a l i d f o r a l l mode numbers

n .

Obviously, t h e spectrum'

of t h e meridional component i s peaked a t t h e frequencies o f zero group v e l o c i t y f o r a l l mode numbers

n

2

1 . The y-dependence of t h e power s p e c t r a (43) o r (41)

may be obtained by multiplying t h e s e formulas by R:(w,y)

= R:(w)

jii(y)

$A(y) (46)

Now we e s t i m a t e t h e power s p e c t r a of t h e zonal c u r r e n t and of t h e p r e s s u r e field.

From eqs.

( 3 6 ) , (37) t o g e t h e r with eqs.

wing i n t e g r a l s must be c a l c u l a t e d

and

where

Sn(w)

i s given by eq. (40a)

(19) and ( 2 0 ) , we s e e t h a t t h e f o l l o -

33 1 I n s e r t i n g eqs.

( 4 9 ) t o (52) i n e q s .

(47) and ( 4 8 ) , one f i n d s

(53a) Both f o r small and f o r l a r g e

o , eq. ( 5 3 a ) v a r i e s l i k e

w

-2

. Clearly,

eqs.

(43a)

and (53a) are due t o t h e b r o a d band f o r c i n g case. I n t h e case o f t h e s m a l l band f o r c i n g [eq. d e r a b l y s i m p l i f i e d . The k - i n t e g r a t i o n o f e q .

( 2 3 ) ] , t h e c a l c u l a t i o n s are consi(18b) y i e l d s

t

Thus, f o r a t i m e s e r i e s o f a p r o c e s s e x c i t e d a t spectrum. The p e a k s o c c u r a t

.If

w = wn,(ko)

+

- - , w e have a l i n e

the forcing occurs within t h e

c o n s i d e r e d t i m e series, w e f i n d t h e power s p e c t r u m by i n s e r t i n g e q .

eq.

(18b) i n

(38)

The power s p e c t r u m i s peaked a t t h e f r e q u e n c i e s persion curves i n t e r s e c t t h e l i n e

k = ko

.

w

=

wn,(ko)

where t h e d i s -

C l e a r l y , t h e s e are g e n e r a l l y n o t t h e

p o i n t s o f z e r o group v e l o c i t y . The power s p e c t r u m (43b) d e c r e a s e s l i k e t h e f r e q u e n c y l i m i t and i s c o n s t a n t f o r s m a l l

w.

w-6

in

Thus t h e peak f r e q u e n c i e s as

w e l l as t h e s p e c t r a l slope a t h i g h f r e q u e n c i e s d i f f e r s i g n i f i c a n t l y i n t h e cases

of small and b r o a d band f o r c i n g . The c o r r e s p o n d i n g power s p e c t r a o f t h e z o n a l c u r r e n t and t h e p r e s s u r e i n t h e

s m a l l band f o r c i n g case f o l l o w s i m p l y from e q s .

(47) and (48) u s i n g e q s .

and (37) w i t h t h e s p e c t r a l f u n c t i o n s ( 1 9 ) and ( 2 0 ) m u l t i p l i e d by The r e s u l t i s

(36)

2 n 6 (k - ko)

.

332 For l a r g e

5.

as w e l l as for s m a l l

w

w

,

becomes i n d e p e n d e n t o f

R”:

t h e b r o a d f o r c i n g case. With =

.

n = 0

THE MODE

Now we d i s c u s s some p r o p e r t i e s o f t h e mode

BO(0)

w

n = 0 ,

from eq.

n = 0 .

Here w e c o n s i d e r o n l y

(40a), we get

2 1-2w2

(54)

( 4 3 a ) , w e have

and from eq.

(55)

Although t h i s r e s u l t seems

1

b e v e r y r e a s o n a b l e , w e mus

b e aware t h a t t h e

t h r e e r o o t s o f t h e d i s p e r s i o n polynomal Do(w,k)

=

-

w3

w

- k2w

-

k

must b e t a k e n i n t o a c c o u n t i n o r d e r t o f i n d e q s . d i n g s p e c t r a l f u n c t i o n s f o l l o w s from e q s .

(54) and ( 5 5 ) . The c o r r e s p o n -

( 1 8 a ) , ( 5 6 ) and ( 5 7 ) .

or, equivalently, 1

SO(w,k) = -

2n 6 ( w + k ) -

2~ 6 ( w - - - k )

2 w 2 - 1

(58)

2 w 2 - 1

Defining (1) = 2n 6 ( w + k ) SO

1 - 2 w 2

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

uL1) (w,k,y)

=

f i v i

pA1) (w,k,y)’ =

where

6(w+k) [Jil

- 2

w(l

6T w(l

6(w+k)

i

-

2

(Y) +

(w2

-

+)

$(Y)l

(59)

$(Y)l

(60)

w2)

02)

[$l(Y)

-

1 ( 2 - T)

333

vanishes only f o r

y

-f

+

For

m .

y

+

-

$(y)

a ,

varies like

eV2” a n d ,

6 - p l a n e a p p r o x i m a t i o n f a i l s . The o n l y e x c e p t i o n s

therefore, the equatorial are the points

which d e f i n e t h e i n t e r s e c t i o n s o f t h e d i s p e r s i o n c u r v e s (55) and (57) a n d , moreover, t h e c u r v e w = - -

1 2k

which i s t h e l o c u s o f z e r o group v e l o c i t y p o i n t s . On t h e o t h e r hand it i s known t h a t t h e i n t r o d u c t i o n o f c h a n n e l boundary c o n d i t i o n s r e s o l v e t h i s problem (see e . g . P h i l a n d e r , 1977 and Dickey, 1978) v = O

for

y

=

Then t h e e i g e n v a l u e s

f

~

vn

a r e no l o n g e r i n t e g e r s . The e i g e n f u n c t i o n s may be

e x p r e s s e d i n t e r m s o f Kummer-functions tends t o

n

(Dickey, 1 9 7 8 ) . F o r

and t h e u s u a l problem f o l l o w s . For

s i o n c u r v e a r e o n l y s l i g h t l y m o d i f i e d . But f o r f o l l o w s q u i t e s i m i l a r y t o t h e h i g h e r modes ( n

vo

s i o n r e l a t i o n s ( 5 6 ) and ( 5 7 ) f o r u V O G and

+

0 .

vn

with

n = 0 2

the

L +

n t 1

the disper-

a d i s p e r s i o n diagram

1) which a p p r o a c h e s t h e d i s p e r -

Then t h e z e r o group v e l o c i t y p o i n t s

u y O R w i l l n e a r l y come t o g e t h e r and a s p e c t r u m l i k e eq.

(55) f o l l o w s .

T h e r e f o r e w e may c o n c l u d e , t h a t t h e d i f f i c u l t i e s a r i s i n g from e q s . ( 6 0 ) a r e due t o t h e l i m i t

nal velocity the l i m i t

n + 0 n

-f

0

o r , equivalently,

vo

-f

0.

(59) and

I n t h e meridio-

p r o d u c e s no problems a n d , t h e r e f o r e , w e may

p o s t u l a t e t h e power s p e c t r u m o f e q .

6.

vn

(55).

SUMMARY AND COMPARISON WITH MEASUREMENTS Employing t h e l i n e a r i n v i s c i d e q u a t i o n s o f motion on an e q u a t o r i a l

6 -plane,

c l o s e d e x p r e s s i o n s f o r t h e E u l e r i a n power s p e c t r a o f t h e dynamical v a r i a b l e s a t

a f i x e d p o i n t have been c a l c u l a t e d u s i n g a G r e e n f u n c t i o n t e c h n i q u e under c o n s i d e r a t i o n o f t h e p r i n c i p l e o f c a u s a l i t y . A v e r t i c a l modal s t r u c t u r e o r a t l e a s t a two l a y e r e d ocean h a s been assumed.

The s h a p e o f t h e s p e c t r a depends on t h e t y p e of f o r c i n g ( s m a l l o r broad band f o r c i n g i n t h e wave number domain) and whether o r n o t t h e f o r c i n g o c c u r s d u r i n g t h e t i m e o f o b s e r v a t i o n . F o r c i n g e v e n t s which o c c u r e d b e f o r e t h e t i m e o f measurements c a u s e t h e s p e c t r a t o have narrow p e a k s and s p e c t r a l gaps governed by t h e dispersion r e l a t i o n . Forcing events during t h e t i m e of observation f i l l t he s p e c t r a l g a p s and s p r e a d t h e p e a k s i n t h e f r e q u e n c y domain.

334 In t h e case o f s m a l l band f o r c i n g i n t h e wave number domain, t h e p e a k s o f t h e f r e q u e n c y s p e c t r a a r e l o c a t e d a t t h e f r e q u e n c i e s o f t h e f r e e waves f o r t h e g i v e n wave number. During b r o a d band f o r c i n g t h e p e a k s o f t h e s p e c t r a o c c u r a t f r e q u e n c i e s o f v a n i s h i n g h o r i z o n t a l group v e l o c i t y and, a s i n t h e c a s e

n = 0

a t o t h e r h i g h e r o r d e r z e r o t h o f t h e d i s p e r s i o n r e l a t i o n . S p e c t r a o f broad band f o r c i n g have been d i s c u s s e d i n d e t a i l . The power s p e c t r a f o r d i f f e r e n t merid i o n a l modes o f t h e m e r i d i o n a l c u r r e n t component, shown i n f i g . 3 , are c h a r a c t e r i z e d by a c o n s t a n t l e v e l a t l o w f r e q u e n c i e s , r e s o n a n t p e a k s a t f r e q u e n c i e s o f z e r o group v e l o c i t y f o r Rossby- and i n e r t i a l g r a v i t y waves, a r e s o n a n t peak at w

=A

f o r t h e Yanai-wave and a s t e e p d e c r e a s e o f s p e c t r a l e n e r g y a t h i g h f r e q u e n c i e s

.

like

\ \

\

..

I .

'\

\ \

2

10-1

-

100

fIcpdl

F i g . 3. T h e o r e t i c a l power s p e c t r a o f t h e f i r s t t h r e e m e r i d i o n a l modes independent of the location.

Power s p e c t r a o f d i f f e r e n t modes o f t h e z o n a l v e l o c i t y component and t h e p r e s s u r e f i e l d are r e d f o r l o w and h i g h f r e q u e n c i e s l i k e f o r modes

n t 1

,

w-2

and h a v e , a t l e a s t

t h e same p e a k s a s t h e m e r i d i o n a l component s p e c t r a ( f i g . 4 ) .

335

10:

5

2E

\ \ \

10'

* v)

3

\ \ \ \ / \ \ f

10' c

*-

c,

B

c

8 10I

5

-n - 1 --n = 3

\

W= rns-' aty = 0

* ficpdl

10-

Fig. 4. T h e o r e t i c a l power s p e c t r a of t h e f i r s t and t h i r d modes o f t h e zonal c u r r e n t component a t t h e equator.

Comparing measured c u r r e n t s p e c t r a with our r e s u l t s we may expect t h e b e s t agreement with c u r r e n t s p e c t r a i n t h e s u r f a c e l a y e r . In o r d e r t o dimensionalize t h e frequency of t h e c a l c u l a t e d s p e c t r a we must assume values f o r t h e f i r s t v e r t i c a l eigenvalue. For t h e A t l a n t i c we follow Moore and Philander (1977) and

2,4 m/s

take

c1

with

c1 = 3 m / s

=

,

f o r t h e P a c i f i c we adopt t h e value of Ripa and Hayes (1981)

.

The general shape of t h e p r e s s u r e s p e c t r a given by Wunsch and G i l l (1976) and Ripa and Hayes (1981) agrees q u i t e well with t h a t of our c a l c u l a t e d s p e c t r a assuming a summation of t h e s p e c t r a of d i f f e r e n t meridional modes. The shape of the

v - s p e c t r u m given by Weisberg (1979) a l s o agrees with t h a t given i n f i g . 3 .

The

u - s p e c t r a of Weisberg (1979) and Lass and Fennel (1981) behave i n t h e high

frequency range l i k e by our c a l c u l a t e d

u-3

which i s a somewhat s t e e p e r slope than t h a t p r e d i c t e d

u-spectrum.

Eriksen (1980) r e p o r t s a

w - ~ to

w-3

high

frequency slope o f energy s p e c t r a . The shape of k i n e t i c energy s p e c t r a i s dominated by t h e most e n e r g e t i c component which i s ,

i n our c a s e , t h e

u-spectrum.

However, caution m u s t be given comparing our s p e c t r a with t h a t of Eriksen (1980) because h i s spectrum i s based on observations i n t h e deep sea where v e r t i c a l l y propagating waves a r e observed. Concerning t h e peak frequencies a t zero group v e l o c i t y f o r meridional modes n 2 1

and a t

336 w

=&-

(which c o r r e s p o n d s t o a p e r i o d of

14

days i n t h e A t l a n t i c and

t h e P a c i f i c r e s p e c t i v e l y ) f o r t h e Yanai-mode

12

days i n

t h e r e i s a l o t o f experimental

e v i d e n c e . See Wunsch and G i l l ( 1 9 7 6 ) , Weisberg ( 1 9 7 9 ) , F e n n e l and L a s s (19791, Horigan and Weisberq ( 1 9 8 1 ) , Ripa and Hayes (19811, Duing e t a l . Fahrbach and Meincke (19811, J a r r i g e and Rual

(19751,

(1981) and Bubnov (1981) f o r de-

t a i l s of t h e o b s e r v a t i o n s . Q u a l i t a t i v l y w e have a q u i t e good agreement between

770

o u r t h e o r y and t h e s p e c t r a from a Halpern

(1982) [ f i g s . 5 and 6 ; D.

-

-95

day r e c o r d i n t h e P a c i f i c g i v e n by

H a l p e r n , p r i v a t e communication].

20.0W

PERCEN4

100

.001

.Ol

.1

FREQUENCY (CYCLES/DRY)

F i g . 5. Spectrum o f t h e z o n a l c u r r e n t component a t depth 20 m ( C o u r t e s y o f D. H a l p e r n . )

.

110" W on t h e e q u a t o r a t a

From t h e comparison o f t h e o b s e r v e d s p e c t r a w i t h o u r c a l c u l a t e d power s p e c t r a f o r s m a l l and b r o a d band f o r c i n g i n t h e wave number domain w e c o n c l u d e t h a t t h e

r e a l e q u a t o r i a l ocean seems t o b e e x c i t e d by f o r c e s which have a b r o a d band c h a r a c t e r i n t h e frequency-wave number domain.

337

-

-95

.OOl

20.OM/

I

PERCENT

.Ol

.l

1

FREQUENCY (CYCLES/ORY) F i g . 6. Spectrum o f t h e m e r i d i o n a l c u r r e n t component a t a t a d e p t h o f 20 m . ( C o u r t e s y of D. H a l p e r n . )

l l O o W on t h e e q u a t o r

Acknowledgement The a u t h o r s w i s h t o e x p r e s s t h e i r t h a n k t o D r . D. Halpern f o r t h e d e l i v e r y of t h e s p e c t r a o f t h e two y e a r t i m e series i n t h e t r o p i c a l P a c i f i c .

REFERENCES Duing, W . , H i s a r d , P . , K a t z , E . , Meincke, J . , M i l l e r , L . , M o r o s h i k i n , K . V . , P h i l a n d e r , G . , Rybnikov, A . , V o i g t , K. and Weisberg, R . , 1975. Meanders and l o n g waves i n t h e e q u a t o r i a l A t l a n t i c . N a t u r e , 257: ( 5 5 2 4 ) , 280-284. E r i k s e n , C . , 1980. Evidence f o r a c o n t i n u o u s s p e c t r u m o f e q u a t o r i a l waves i n t h e I n d i a n Ocean. J o u r n a l of G e o p h y s i c a l R e s e a r c h , 85: 3285-3303. E r i k s e n , C . , 1981. E q u a t o r i a l waves w i t h p e r i o d s from a few d a y s t o a few weeks i n t h e P a c i f i c and I n d i a n Oceans. P a p e r p r e s e n t e d a t t h e SCOR WG 47 Meeting i n V e n i c e / I t a l y from 27-30 A p r i l 1981. E r i k s e n , C . , 1981. Deep c u r r e n t s and t h e i r i n t e r p r e t a t i o n as E q u a t o r i a l t r a p p e d waves i n t h e Western P a c i f i c Ocean. J . Phys. O c e a n o g r . , 11: 1 , 48-70. F a h r b a c h , E. and Meincke, J . , 1981. Moored c u r r e n t m e t e r measurements i n t h e E q u a t o r i a l A t l a n t i c d u r i n g FGGE. P a p e r p r e s e n t e d a t t h e SCOR WG 47 Meeting i n V e n i c e / I t a l y from 27-30 A p r i l 1981. F e n n e l , W. and L a s s , H . U . , 1979. On t h e v e r t i c a l e i g e n v a l u e problem o f e q u a t o r i a l t r a p p e d waves. G e r l a n d s B e i t r a g e z u r Geophysik ( L e i p z i g ) , 88: 279-293.

338 G a r r e t t , C. and Munk, W . , 1972. Space t i m e s c a l e s o f i n t e r n a l waves. G e o p h y s i c a l F l u i d Dynamics, 2 : 225-264. J a r r i g e , F. and R a u l , P . , 1981. Measurements i n t h e e q u a t o r i a l c u r r e n t s o f t h e A t l a n t i c and P a c i f i c Oceans. P a p e r p r e s e n t e d a t t h e SCOR WG 47 Meeting i n V e n i c e / I t a l y from 27-30 A p r i l 1981. L a s s , H . U . and F e n n e l , W . , 1981. C u r r e n t o b s e r v a t i o n s i n t h e e q u a t o r i a l wave g u i d e a t 28'40' W d u r i n g FGGE ( u n p u b l i s h e d m a n u s c r i p t ) . Lighthill, M.J., 1969. Dynamic r e s p o n s e o f t h e I n d i a n Ocean t o o n s e t o f t h e s o u t h w e s t monsoon. P h i l . T r a n s . Roy. SOC. London, A 265: 45-92. M a r t i n , P . and Schwinger, J . , 1959. Theory o f many p a r t i c l e s y s t e m s . P h y s i c a l Review, 115: 1342. Moore, D . and P h i l a n d e r , S . G . , 1977. M o d e l l i n g o f t h e t r o p i c a l o c e a n i c c i r c u l a t i o n . I n : The S e a , Wiley, N e w York, p p . 319-361. P e d l o s k y , J . , 1979. G e o p h y s i c a l F l u i d Dynamics. S p r i n g e r , N e w York, 624 pp. Ripa, P. a n d Hayes S . P . , 1981. Evidence f o r e q u a t o r i a l t r a p p e d waves t h e Galap a g o s I s l a n d s . J o u r n . Geophys. R e s . , 86: 6509-6516. 1979. E q u a t o r i a l waves d u r i n g GATE and t h e i r r e l a t i o n t o t h e Weisberg, R . H . , mean z o n a l c i r c u l a t i o n . Deep Sea R e s e a r c h , 26 (Supplement 11): 179-198. Weisberg, R.H. and H o r i g a n , A . M . , 1981. Low-frequency v a r i a b i l i t y i n t h e equat o r i a l A t l a n t i c . J o u r n a l o f P h y s i c a l Oceanography, 11: 913-920. Wunsch, C . and G i l l , A . E . , 1976. O b s e r v a t i o n s o f e q u a t o r i a l t r a p p e d waves i n P a c i f i c sea l e v e l v a r i a t i o n s . Deep Sea R e s e a r c h , 23: 371-390. 1976. M a t h e m a t i c a l methods f o r p h y s i c s . Benjamin I n c . , N e w York, Wyld, H . W . , 628 pp. Wu, T.Y. and Ohmura, T . , 1962. Quantum Theory of S c a t t e r i n g . P r e n t i c e - H a l l I n c . , N e w York.

339

INSTABILITY ON THE EQUATORIAL BETA-PLANE J O H N P. BOYD AND ZAPHIRIS D. CHRISTIDIS

1.

INTRODUCTION

S i n c e b o t h t h e t r o p i c a l atmosphere and t h e e q u a t o r i a l ocean are r e g i o n s of s t r o n g l a t i t u d i n a l s h e a r , i t i s i m p o r t a n t t o s t u d y t h e hydrodynamic i n s t a b i l i t i e s which are p o s s i b l e a t t h e s e low l a t i t u d e s . s t u d i e d t h e t r a d i t i o n a l b a r o t r o p i c , Rossby wave-like, ties.

P h i l a n d e r (1978) h a s Rayleigh-Kuo

instabili-

Dunkerton (1981) and Stevens (1982) have i ndependent l y anal yzed t h e

i n e r t i a l i n s t a b i l i t i e s a n d f o u n d t h e c r i t i c a l shear f o r z e r o wavenumber. ( 1 9 8 2 ) h a s g e n e r a l i z e d t h e Rayleigh-Kuo c r i t e r i o n f o r i n s t a b i l i t y .

Ripa

I n s p i t e of

t h e s e i n t e r e s t i n g b e g i n n i n g s , h o w e v e r , t h e p r e s e n t a u t h o r s a r e embarked upon t h e f i r s t s y s t e m a t i c and c o m p r e h e n s i v e s t u d y o f s h e a r i n s t a b i l i t i e s i n equat o r i a l flows.

I n t i m e , we hope t o a p p l y o u r r e s u l t s t o b o t h t h e o c e a n and

a t m o s p h e r e i n a r t i c l e s p l a n n e d f o r b o t h t h e J o u r n a l o f P h y s i c a l Oceanography and the J o u r n a l o f t h e Atmospheric Sc ie n c e s. progress report.

T h i s p a p e r i s o n l y a modest

N o n e t h e l e s s , enough i s a l r e a d y known t o show t h a t e q u a t o r i a l

i n s t a b i l i t i e s a r e a l i k e l y p r o s p e c t and t h a t t h e i r dynamics i s s t r i k i n g l y d i f f e r e n t from t h o s e of t h e m id d le l a t i t u d e s . O u r r e s u l t s t o d a t e a r e a m i x t u r e o f t h e a n a l y t i c a l and n u m e r i c a l .

s m a l l z o n a l wavenumber k , i t i s p o s s i b l e t o employ t h e "long-wave''

For

a n d "gamma-

p l a n e " a p p r o x i m a t i o n s t o c l e a r l y i d e n t i f y t h e d i f f e r e n t s t a b l e and u n s t a b l e e q u a t o r i a l modes and f o r some t o c a l c u l a t e t h e g r o w t h r a t e s i n a p p r o x i m a t e c l o s e d form.

T h i s a n a l y s i s i s g i v e n i n o u r j o i n t l e t t e r (Boyd and C h r i s t i d i s ,

1982) and w i l l n o t be r e p e a t e d h e r e .

I n s t e a d , w e w i l l m e r e l y summarize i t s

c o n c l u s i o n s a n d c o n c e n t r a t e i n s t e a d upon e x p l a i n i n g and d i s p l a y i n g some o f o u r most r e c e n t n u m e r i c a l r e s u l t s .

2.

MODEL AND METHODS The e q u a t i o n s w e s o l v e a r e t h o s e o b t a i n e d by s e p a r a t i n g v a r i a b l e s i n a

c o n t i n u o u s l y s t r a t i f i e d f l o w u n d e r t h e a s s u m p t i o n t h a t t h e mean wind U i s a f u n c t i o n of l a t i t u d e o n l y .

N o n d i m e n s i o n a l i z i n g a s i n Boyd ( i 9 8 0 ) so t h a t t h e

e q u i v a l e n t d e p t h i s e q u a l t o 1, w e o b t a i n

i k [U(y) - c] u

-

[y - dU/dyl v + ik@ = 0

i k [u(y) - cl v + yu + @

Y

(2)

0

=

i k [U(y) - c] @ + iku + v Y

(1)

=

0

(3)

where k is the zonal wavenumber, c the phase speed, subscript y denotes differentiation with respect to y, @ is the height and U(y) the mean wind or current.

These are almost the nonlinear shallow water wave equations (linearized

about a zonal current U(y)) except for the absence of some terms in (3) which are proportional to the variable mean depth.

The set (1)-(3) is the natural

choice for modelling the atmosphere, and while it lacks the pseudomomentum conservation law of the shallow water wave equations (linearized about a zonal current U(y)) except for the absence of some terms in (3) which are proportional to the variable mean depth.

The set (1)-(3) is the natural choice for modelling

the atmosphere, and while it lacks pseudomomentum conservation law of the shallow water set, these "stratified flow" equations can be analyzed via the "gamma-plane" approximation while the shallow water wave equations cannot. Our numerical results indicate instabilities of roughly the same qualitative nature for either set (although there are the expected quantitative differences and our comparisons are still in progress), so in the rest of this paper, as in Boyd and Christidis(l982), we shall discuss the "stratified flow" equations (1)-(3) only. We employed two different algorithms to solve (1)-(3): (i) a Chebyshev pseudospectral/aZ method and (ii) a shooting method.

The Chebyshev method is

quite sensitive to critical latitude singularities and is therefore ineffective for near-neutral modes.

It is also rather costly since the operation count is

proportional to the cube of N where N is the number of polynomials in the expansion.

However, the QZ eigenvalue matrix algorithm does not require a first

guess, so our method is useful for verifying that we have not missed modes or overlooked strong instabilities in some region of parameter space. The shooting method involved marching in from either computational boundary and matching the two numerical solutions at the equator.

Since equatorially

trapped waves are exponentially increasing as we march towards the equator, this double shooting method avoids numerical "stiffness" and a simple fourthorder Runge-Kutta algorithm could be used for the marching.

Because the ex-

pense is only linearly proportional to the number of grid points, this shooting method is very cheap.

Newton's method was used to vary c until the two solu-

tions matched at the equator, and this has the disadvantage that it will not converge unless a good first quess for c is available. We met this need by employing the "continuation" method.

Beginning with a known equatorial wave

341 f o r e i t h e r zero shear o r zero wavenumber, o r occasionally from c ' s c a l c u l a t e d by t h e Chebyshev program, w e s y s t e m a t i c a l l y increased t h e shear o r wavenumber i n small s t e p s , using previous r e s u l t s t o l i n e a r l y e x t r a p o l a t e a f i r s t guess f o r t h e next v a l u e of shear o r wavenumber i n t h e sequence. To cope with c r i t i c a l l a t i t u d e s i n g u l a r i t i e s ( t h e s e t (1)-(3) i s s i n g u l a r where U ( y )

=

c , which occurs f o r r e a l y when c i s r e a l ) , t h e d i f f e r e n t i a l

equations were i n t e g r a t e d using a p a t h of i n t e g r a t i o n i n t h e complex y-plane which dipped below t h e r e a l y-axis a s shown i n Fig. 1.

This makes it p o s s i b l e

t o follow t h e modes r i g h t up t o t h e n e u t r a l curve without d i f f i c u l t y .

One can

i n f a c t compute t h e modes even when t h e imaginary p a r t of t h e phase speed i s negative.

A s shown i n t h e f i g u r e , however, t h e p a t h of i n t e g r a t i o n i m p l i c i t l y

f o r c e s u s t o draw t h e branch-cut

from t h e c r i t i c a l l a t i t u d e s i n g u l a r i t y t o

i n f i n i t y i n such a way t h a t t h e branch-cut c r o s s e s t h e r e a l y-axis when t h e imaginary p a r t of t h e phase speed i s negative.

(This i s necessary because t h e

shooting procedure computes a s o l u t i o n which i s smooth and continuous on t h e p a t h of i n t e g r a t i o n , which i s p o s s i b l e i f and only i f t h e branch-cut does not c r o s s t h e p a t h of i n t e g r a t i o n ) .

The f a c t t h a t t h e branch-cut c r o s s e s t h e r e a l

y-axis implies t h a t t h e modes we compute a r e discontinuous f o r some r e a l l a t i tude y , and t h e r e f o r e a r e unphysical. Fi9.2 shows t h e r e a l and imaginary p a r t s of t h e phase speeds of t h e n = l Rossby wave i n a l i n e a r shear a s computed using t h i s complex p a t h of i n t e g r a tion.

The imaginary p a r t of t h e phase speed i s everywhere n e g a t i v e , which shows

t h a t t h e s e d i s c r e t e modes a r e unphysical. t h e r e a l y-axis

What happens i f one i n t e g r a t e s along

i n s t e a d i s t h a t , as i s known from s t u d i e s of Rossby waves i n

shear i n t h e middle l a t i t u d e s , a continuous spectrum of n e u t r a l Rossby waves occurs. The Kelvin wave, however, i s a d i f f e r e n t c l a s s of wave with a phase speed Of t h e o p p o s i t e sign.

O u r c a l c u l a t i o n s show t h a t it i s u n s t a b l e , i . e . ,

imaginary p a r t of t h e phase speed which i s p o s i t i v e .

has an

Such modes have c r i t i c a l

l a t i t u d e s above r a t h e r than below t h e r e a l y-axis and t h u s can be smooth and continuous on t h e r e a l a x i s and have a p h y s i c a l e x i s t e n c e a s d i s c r e t e modes.

3.

NUMERICAL RESULTS Three major s p e c i e s of i n s t a b i l i t y have been i d e n t i t i f i e d so f a r :

(i)

b a r o t r o p i c i n s t a b i l i t y (ii) i n e r t i a l i n s t a b i l i t y and (iii)Kelvin wave i n s t a b i l i t y , which has no c o u n t e r p a r t f o r non-equatorial

flows.

Barotropic i n s t a b i l i -

t y has a l r e a d y been s t u d i e d (Philander, 1978), so our d i s c u s s i o n w i l l be conf i n e d t o t h e remaining two types.

Because t h e most i n t e r e s t i n g e f f e c t s a r e

observed f o r l i n e a r shear U(Y) =

s

Y

(4)

342

)r

v

E

H

Kelvin

Real (y)

Fig. 1 The complex y-plane with t h e path of numerical i n t e g r a t i o n f o r l i n e a r shear shown looping below t h e r e a l a x i s . The branch c u t s from t h e c r i t i c a l l a t i t u d e t o i n f i n i t y a r e a l s o shown schematically a s cross-hatched l i n e s f o r a Rossby and a Kelvin wave.

343

S-

0.6

-0.1

- 0.2 - 0.3 - 0.4 -0.5

- 0.6 -0.7

Fig. 2 The v a r i a t i o n o f t h e real and i m a g i n a r y p a r t s o f t h e p h a s e s p e e d c f o r t h e n = l e q u a t o r i a l Rossby wave w i t h l i n e a r s h e a r U(y)=Sy as computed u s i n g t h e complex p a t h o f i n t e g r a t i o n shown i n F i g . 1. S i n c e t h e i m a g i n a r y p a r t o f c i s n e g a t i v e , t h i s computed mode i s d i s c o n t i n u o u s a t the l a t i t u d e where t h e branchc u t c r o s s e s t h e real y - a x i s and i s n o t p h y s i c a l . The c o m p u t a t i o n shows t h a t no d i s c r e t e Rossby modes e x i s t which are c o n t i n u o u s a t a l l l a t i t u d e s .

344 where S is a constant, we shall concentrate upon this simple case, but instability is observed for a wide range of shear profiles and we shall display results for a parabolic wind shear at the end. Inertial instabilities have been known since the early part of the century and normally take the form of axisymmetric disturbances, i.e., zero wavenumber.

Independently, Dunkerton (1981) and Stevens (1982) showed that

one could use the equatorial "gamma-plane" approximation (Boyd, 1978) to exactly solve (1)-(3) for the special case of (a) linear shear and (b) zero wavenumber.

Stevens (1982) gives a particularly clear and careful descrip-

tion of the physical causes of the instability.

Both found that instability

occurs only for IS1 > 2 and that the unstable/damped pair of modes both have the structure of n=O equatorial gravity waves. Boyd and Christidis (1982) show that, in contrast to all other known cases of inertial instability, on the equatorial beta-plane the growth rates are largest for non-zero values of the .zonal wavenumber k.

In addition, insta-

bility is possible for finite wavenumber below the critical shear S=2 calculated by Dunkerton and Stevens for k=O.

These surprises show that equa-

torial instability has to be considered as a separate sub-area of hydrodynamic instability theory; blind application of misconceptions based on other stability problems can only lead to embarrassment. maximum growth rate is relatively small (k for larger

S)

=

However, the wavenumber of

0.27 for S=2 and smaller values

and growth rates for non-zero k are only 30% or so larger than

for k=O except for shears close to 2.

Further, graphs of the eigenfunctions

show shapes very similar to those given in Boyd (1978) for the "gamma-plane" approximation, so there is no doubt that these unstable modes are indeed inertial instabilities. Equatorial instability, however, is far more than just this single mode. There are two unstable modes, each of which has at least two distinct regimes with the modes exchanging identities in the transition regime, and there are at least two physically distinct mechanisms of instability. In strong shear, it is therefore necessary to be careful about precisely what one means by "Kelvin" wave and "gravity" wave.

Boyd and Christidis (1982)

apply these labels in accordance with the so-called "long-wave" and "gammaplane" approximations which apply for small wavenumber to different classes Of waves.

The "long-wave" equations, for example, filter out gravity waves to

permit only Kelvin and Rossby waves, which have finite phase speeds in the limit k

+

0.

The Rossby modes have negative real and imaginary parts Of the

phase speed and therefore are always stable as discussed in Sec. 2,

so there

is no danger of confusing them with the Kelvin wave, for which the imaginary part and (usually) the real part of c are both positive.

Thus, it is sensible

345 to define "Kelvin" wave to mean that solution of the "long-wave" equations which is unstable. Similarly, the "gamma-plane" approximation is applicable only to gravity waves (including inertially unstable ones), so it is reasonable to define "gravity wave" to mean a wave that can be approximated, however crudely, via the "gamma-plane", or as the analytic continuation of such a wave as the wavenumber k is increased numerically in small steps.

The "continuation" method

makes it possible to define a mode through the simple process of computing its phase speed through small steps in S or k from some known solution for either zero shear or wavenumber.

Thus, there is no real ambiguity in either

labelling a wave regime as "Kelvin" or "gravity" or in identifying a single continuous mode as having distinct regimes where different labels must apply. The dominant mode of instability is what Boyd and Christidis (1982) name the "mixed Kelvin/inertial mode".

For small shears

(S

< 2), this mode is an

unstable Kelvin wave width the real part of the phase speed roughly equal to one as for a neutral Kelvin wave in the absence of shear.

One remarkable discovery

is that the imaginary part of the phase speed for the Kelvin wave can be approximated to within an error of 8 % on the interval 0.4 c S

1.15 by the

curve-fit formula Im(c) = 13.56 exp(-5.34/S)

(5)

For S < 0.4, the imaginary part of c is too small to be accurately computed, but the form of (5) suggests that there is instability for all values of the shear, however small, although growth rates are very small unless S > 1.

This

absence of a "critical shear" has not been seen in any other similar instability problem that the authors are aware of, but it is suggestive that the Kelvln wave instability is a critical latitude effect (like ordinary Rayleigh-Kuo barotropic instability) since the location of the critical latitude is inversely proportional to S so that the amplitude of the Kelvin wave at the critical latitude is an exponential function of 1/S.

The inertial instability, in

contrast, occurs (for small wavenumber) only for waves with very large c the critical latitude is very distant from the

SO

equator at a location where the

wave has no appreciable amplitude. Thus, there appear to be two distinct, physically different mechanisms for instability on the equatorial beta-plane for linear shear, and three for those other current profiles for which barotropic instability is also possible. Boyd and Christidis(l982) show using the "uniform gamma-plane" approximation that in the vicinity of S = 2, which is the critical shear for the zero wavenumber inertial instability found by Dunkerton and Stevens, the wave types exchange identities.

In particular, for very small k, the Kelvin wave suddenly

346

hecnmns neutral with a negative real phase speed for

S > 1.9 and for larger

shear merges with the negative frequency, n=O neutral gravity wave to become the inertially unstable mode and its complex conjugate.

For larger wavenumber,

the two modes do not actually merge, but instead the imaginary part of the phase speed of the Kelvin wave dips to a non-zero value and then begins to rise rapidly as the shear is increased.

It is still true, however, that for S > 2 ,

this mode is well-approximated via the "gamma-plane'' and equally well by the "long-wave" equations for

S

< 2.

In the transition zone, S

=

2, this mode is

truly a hybrid of Kelvin and inertial wave, and neither label is appropriate alone. The other unstable mode is the "mixed gravity/Kelvin" mode. ,*

this is the positive frequency n=O gravity wave.

For small shear,

Like the Kelvin wave (and

unlike the negative frequency gravity wave which is always neutral), this mode is weakly unstable even for weak shear.

Growth rates are always very small,

however, and this mode would likely be suppressed by viscous damping in most physical situations.

For S > 2, this mode becomes an unstable Kelvin wave and

growth rates grow rapidly for

S

> 2.4.

However, for all values of

S,

growth

rates are small in comparison to those for the Kelvin/inertial mode, so the latter is always the dominant mode of instability. Great care is thus needed in interperting numerical results correctly, The "long-wave'' equations reveal two branches of Kelvin wave instability with a region of neutrality around S = 2 in between them as shown in Fig. 1 of Boyd and Christidis(l982).

What can only be seen by careful analysis and numerical

continuation is that these two branches belong to physically distinct modes: the lower branch Kelvin wave cannot be smoothly continued to the upper branch Xelvin wave (by repeated numerical solution with small steps in S , for example) because the "long-wave'' approximation inevitably fails in a neighborhood of

s

= 2.

In summary, we have a weakly unstable "mixed gravity/Kelvin wave" whose real part of c is always large and positive and whose imaginary part is always small plus a strongly unstable "mixed Kelvin/inertial" wave whose real part of phase speed is small but may be of either sign.

Fig. 3 displays contour plots of the

nondimensional growth rate for the dominant "mixed Kelvin/inertial" in linear shear.

The mode does not exist on the equatorial beta-plane for large values

of the wavenumber because when S > l/k, one can show by analyzing the asymptotic behavior as y goes to infinity of the set (1)-(3) that this counterbalances the equatorial trapping created by the variations of the Coriolis parameter, and the mode is no longer latitudinally confined. the figure is left blank.

Consequently, a portion of

347

w.u

I

0.2

I

1

I

0.4 0.6 0.8 WAVENUMBER k

I

1

1.0

1.2

Fig. 3 Contours of constant growth r a t e (imaginary p a r t of nondimensional frequency) f o r t h e mixed K e l v i n - i n e r t i a l mode i n l i n e a r s h e a r , p l o t t e d a s a f u n c t i o n of s h e a r s t r e n g t h S and zonal wavenumber k. This i s t h e Kelvin-like regime; t h e i n e r t i a l - l i k e regime i s 9 . 2 and i s n o t shown.

348 The shear p r o f i l e U(y) = S ( 1 - e

-y2/10 (6)

)

i s approximately equal t o t h e simple parabola

U(Y) = (S/10) y

2

(7)

f o r s m a l l y, b u t i s bounded f o r l a r g e y so t h a t t h e modes a r e always equatoriThe p r o f i l e i s b a r o t r o p i c a l l y unstable when S > 5.

a l l y trapped.

t h e growth r a t e s f o r t h e unstable Kelvin wave f o r p o s i t i v e S.

i s found f o r negative S . )

Fig. 4 shows

(No i n s t a b i l i t y

The Kelvin wave appears t o be unstable f o r a l l

values o f t h e s h e a r s t r e n g t h ( s o long a s t h e sign i s r i g h t ) , b u t growth r a t e s a r e r a t h e r s m a l l u n t i l one has crossed t h e b a r o t r o p i c s t a b i l i t y b a r r i e r .

We

have n o t y e t made d e t a i l e d comparisons of t h e Kelvin and b a r o t r o p i c i n s t a b i l i t y i n t h e parametric region where they c o - e x i s t , b u t it i s s t r i k i n g t h a t Kelvin waves can again grow with time where c l a s s i c a l s t a b i l i t y p r e d i c t s only a continuous spectrum of b a r o t r o p i c a l l y s t a b l e Rossby waves. Neither of t h e two p r o f i l e s w e have discussed i s unduly r e a l i s t i c , but they suggest t h a t more complicated c u r r e n t s which a r e n e i t h e r symmetric nor antisymmetric about t h e equator w i l l have u n s t a b l e Kelvin waves, t o o , and i f t h e shear i s s t r o n g enough, b a r o t r o p i c and i n e r t i a l i n s t a b i l i t i e s as well.

In

t h i s model, we have ignored v e r t i c a l s h e a r , b u t when it i s included, b a r o c l i n i c i n s t a b i l i t y i s possible also.

I t i s c l e a r t h a t much f u r t h e r research i s need-

ed. 6.

VISCOSITY AND INSTABILITY IN THE OCEAN Dunkerton(1981) p o i n t s o u t t h a t t h e nondimensional s h e a r S i s r e l a t e d t o t h e

dimensional shear S* v i a

2 2

where E = 4 fi a

/ ( g H ) i s "Lamb's parameter" w i t h H t h e "equivalent depth", Q

t h e a n g u l a r frequency of t h e e a r t h ' s r o t a t i o n , and a t h e r a d i u s of t h e planet. Since E i s p r o p o r t i o n a l t o t h e square of t h e v e r t i c a l mode number m,

it follows

t h a t t h e nondimensional s h e a r i s a monotonically i n c r e a s i n g f u n c t i o n of m. This i n t u r n l e a d s t o t h e absurd p r e d i c t i o n t h a t t h e ( i n v i s c i d ) i n s t a b i l i t y

w i l l have l a r g e s t dimensional growth r a t e s f o r i n f i n i t e m and t h e r e f o r e i n f i n i t e l y small v e r t i c a l and h o r i z o n t a l length s c a l e s . Dunkerton noted t h a t t h e r e s o l u t i o n o f t h i s c o n t r a d i c t i o n i s t h a t viscous e f f e c t s i n c r e a s e n o t a s t h e q u a r t e r power o f E b u t r a t h e r a s E i t s e l f .

There-

f o r e , as t h e v e r t i c a l mode number m i n c r e a s e s , S i n c r e a s e s a s t h e square r o o t

of m b u t viscous e f f e c t s a s m squared.

For s u f f i c i e n t l y l a r g e m -- how l a r g e

349

0.

0

k

0.0

.oo .oc ,000

.ooo

Fig. 4 C o n t o u r s of c o n s t a n t growth r a t e f o r t h e K e l v i n mode i n t h e q u a s i p a r a b o l i c s h e a r d e s c r i b e d i n t h e t e x t . The wavenumber i s p l o t t e d on a l o g a r i t h m i c s c a l e ; t h e s h e a r s t r e n g t h on a l i n e a r s c a l e . The flow i s b a r o t r o p i c a l l y u n s t a b l e f o r S>5.

350 depends on both the dimensional shear and the viscosity

--

the damping must win

and dimensional growth rates must level off and then decrease as the mode number increases still further. Thus, equatorial instabilities will occur at finite vertical and horizontal scales, but the reason is depressing in that one cannot know exactly what these scales or the e-folding time of the wave are unless one knows both the shear and the viscosity.

The former is highly variable and mostly concentrated in the

Equatorial Undercurrent (in the oceanic case) instead of being independent of depth all the way to the botton, as implicitly assumed in our model and those of Dunkerton, Stevens, and Ripa.

The viscosity is also highly variable, even

harder to measure, and raises the unpleasant issue of whether the dissipation can be approximated by a linear eddy viscosity at all, or whether some more complex nonlinear damping might be more appropriate. The results of our inviscid model must therefore be interperted with much caution when applied to the real ocean.

It is still worthwhile, however, to

attempt at least an order-of-magnitude estimate. For the first baroclinic mode, let us take H=40 cm so that the nondimensional units have dimensional equivalents of 1.7 days (time), 300km (length), and 2.0 m/s (velocity). S = 2 for linear shear, which is the dividing line between

the "Kelvin" and "inertial" instability regimes, then requires a current of

1 m/s (-1 m/s) 75 km north (south) of the equator.

This is a very strong shear,

so it seems unlikely that inertial instability will be seen for the lowest baroclinic mode.

At the depth where the latitudinal shear is a miximum, the

Equatorial Undercurrent can be crudely modelled by a constant plus a parabola of the form of (6) with a nondimensional shear of

S = 20:

This is enough to

allow barotropic instability, but it is far more than is needed to create unstable Kelvin waves as well as shown in Fig. 4. Thus, barotropic and Kelvin wave "instability" are likely for low baroclinic modes; inertial instability can occur only for high order baroclinic modes.

Only further work can determine

which form of instability is dominant. 5.

SUMMARY

The simple, latitudinal-shear-only model has shown that unstable Kelvin waves will occur for rather arbitrary wind profiles at shear strengths below those needed for the previously studied inertial and barotropic instabilities. In linear shear, the dominant unstable mode is a "mixed Kelvin/inertial" wave which we have so named because it is an unstable Kelvin wave for weak shear but an inertially unstable n=O gravity wave for strong shear.

In parabolic shear,

inertial instability does not occur, but unstable Kelvin waves form in shears too weak for barotropic instability. The neglect of vertical shear and viscosity are serious limitations on the

351 model.

Nonetheless, there is every reason to expect that unstable Kelvin waves

can be generated by the Equatorial Undercurrent.

Only nulti-level, three-

dimensional numerical models can hope to resolve the competion between the unstable Kelvin waves discussed here, the familiar inertial and barotropic instabilities, and baroclinic instability for the role of generating unstable WAVCS

in the equatorial ocean.

It is altogether possible that two Or more

Or

these mechanisms operate simultaneously. ACKNOWLEDGEMENTS.

This work was supported by the National Science Foundation

through grant OCE8108530.

We thank S. Jacobs, T. Dunkerton, J. Kindle, and

D. Stevens for helpful comments. REFERENCES Boyd, J.P., 1978. Part I:

The effects of latitudinal shear on equatorial waves.

Theory and methods.

J. Atmos. Sci., 35: 2236-2258.

Boyd, J.P., 1980. The nonlinear equatorial Kelvin wave.

J. Phys. Oceangr.,

10: 1-11.

Boyd, J.P., and Z.D. Christidis, 1982. equatorial beta-plane.

Low wavenumber instability on the

Geophys. Res. Lett., 9: 769-172.

Dunkerton, T.J., 1981. On the inertial stability of the equatorial middle atmospher.

J. Atmos. Sci., 38: 2354-2364.

Philander, S.G.H., 1978.

Instabilities of zonal equatorial currents, 2.

J. Geophys. Res., 83: 3679-3682.

Ripa, P . ,

1982.

A qeneralizaticn of the Kayleigk-KLc critericn to the

equatc,rial beta-plane. Stevens, D.E., 1982. near the equator.

To be published.

On symmetric stability and instability of zonal mean flows

J. Atmos. Sci., 39: in press.

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353

ON THE GENERATION OF ROSSBY SOLITONS DURING EL N I N O

J O H N C.

KINDLE

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 , M S 39529

USA

ABSTRACT The e x c i t a t i o n of e q u a t o r i a l Rossby s o l i t o n s during E l Nino i s s t u d i e d numerically using a one-layer reduced-gravity formulation. an i d e a l i z a t i o n of t h e t r o p i c a l P a c i f i c

km meridionally.

-

The model b a s i n

-

extends 15,000 Ian zonally and 3,000

Forcing i s a p p l i e d as a p a t c h of zonal wind stress repreIt is

s e n t i n g t h e r e l a x a t i o n of t h e e q u a t o r i a l e a s t e r l i e s preceding El Nino.

shown t h a t a r e l a x a t i o n of t h e e q u a t o r i a l winds g e n e r a t e s i n t e r n a l Rossby s o l i t o n s subsequent t o t h e r e f l e c t i o n of an e q u a t o r i a l Kelvin wave f r o n t from t h e e a s t e r n boundary.

The meridional s t r u c t u r e of t h e s o l i t o n i s t h a t of a

f i r s t l a t i t u d i n a l mode Rossby wave.

The simple E l Nino simulations r e s u l t i n

t h e e x c i t a t i o n of two o r t h r e e s o l i t o n s separated by approximately 3,000 km. The r e s u l t s of t h i s study suggest t h a t i n t e r n a l Rossby s o l i t o n s a r e most l i k e l y t o be observed i n t h e c e n t r a l and western P a c i f i c during a major E l Nino year.

1.

INTRODUCTION

I f E l Nino i s i n i t i a t e d by a remotely forced i n t e r n a l Kelvin wave f r o n t

(Wyrtki, 1975; Hurlburt e t a l . , 1976; McCreary, 1976) then t h e r e f l e c t i o n of t h i s wave should r e s u l t i n a set of westward propagating Rossby waves emanating from t h e e a s t e r n boundary (Moore, 1968).

Along t h e equator t h e f i r s t

l a t i t u d i n a l mode Rossby wave would have t h e l a r g e s t amplitude.

Theoretical

s t u d i e s of remotely forced E l Nino events r e v e a l such a wave response ( e . g . , McCreary, 1977; Kindle, 1979; Busalacchi and O'Brien, 1981).

I n d i r e c t obser-

v a t i o n a l evidence e x i s t s i n t h e form of westward propagating sea s u r f a c e tempe r a t u r e (SST) anomalies a t a speed c o n s i s t e n t with a f i r s t l a t i t u d i n a l mode Rossby wave (Barnett, 1977; Ramussen and Carpenter, 1982; Weare, 1982).

I t is

t h e t h e s i s of t h i s paper t h a t t h e f i r s t l a t i t u d i n a l m o d e Rossby wave r e s u l t i n g from E l Nino may evolve i n t o one o r m o r e e q u a t o r i a l Rossby s o l i t o n s .

These

robust nonlinear waves may provide an important mechanism for t h e westward propagation of E l Nino e f f e c t s along t h e equator. Nino and Rossby s o l i t o n s a r e provided below.

Brief i n t r o d u c t i o n s t o E l

354 1.1 E l Nino

Bjerknes (1966) was t h e f i r s t t o a s s o c i a t e E l Nino with t h e l a r g e s c a l e weakening of t h e s o u t h e a s t t r a d e s .

Wyrtki (1975) suggested t h a t t h e relaxa-

t i o n of t h e zonal component of t h e e q u a t o r i a l t r a d e s i n t h e c e n t r a l and western P a c i f i c i n i t i a t e d t h e event by e x c i t i n g an e q u a t o r i a l l y trapped i n t e r n a l Kelvin wave.

This hypothesis was supported by t h e t h e o r e t i c a l work of

Hurlburt, e t a l .

(1976) and McCreary (1976, 1977).

Busalacchi and O'Brien

(1981) forced a l i n e a r numerical model with observed winds and found t h a t E l Nino events i n t h e 1960's were most l i k e l y i n i t i a t e d by wind events i n t h e western P a c i f i c .

Kindle (1979) examined E l Nino from i t s o n s e t t o t h e

termination phase using a nonlinear model forced by an i d e a l i z e d representat i o n of t h e seasonal and inter-annual wind v a r i a b i l i t y a s s o c i a t e d with E l Nino. In t h a t study, t h e f i r s t mode Rossby wave r e s u l t i n g from t h e incidence of t h e E l Nino Kelvin wave a t t h e e a s t e r n boundary propagated across t h e b a s i n and

r e f l e c t e d as an e q u a t o r i a l Kelvin wave.

The relative timing of t h e r e f l e c t i o n

of t h e wave from t h e western boundary and t h e r e - i n t e n s i f i c a t i o n

of t h e t r a d e

winds determined t h e c h a r a c t e r of t h e s o l u t i o n a t t h e e a s t e r n boundary during t h e year following a major E l Nino.

Due t o t h e s p a t i a l averaging applied t o

t h e s o l u t i o n , t h e e f f e c t s of t h e Rossby wave's n o n l i n e a r i t y w e r e obscured and no s o l i t o n s were observed. Rasmussen and Carpenter (1982) and Weare (1982) r e c e n t l y analyzed h i s t o r i c a l d a t a s e t s of t r o p i c a l s e a s u r f a c e temperatures.

The r e s u l t s of both t h e s e

s t u d i e s , which a r e c o n s i s t e n t w i t h previous d e s c r i p t i o n s ( e - g . , Hickey, 1975; B a r n e t t , 1977; Wyrtki, 1977), show t h a t t h e warming a s s o c i a t e d with E l Nino a t t h e e a s t e r n boundary begins near t h e f i r s t of t h e year and reaches a maximum around May.

Subsequently, t h e warm SST anomalies propagate westward a t a speed

of .5 t o 1 m/sec.

By t h e end of t h e E l Nino y e a r , warm SST anomalies along

t h e equator a r e w e l l e s t a b l i s h e d from t h e c o a s t s of Ecuador and Peru t o t h e dateline.

The above normal e q u a t o r i a l s u r f a c e temperatures a r e b e l i e v e d t o be

r e l a t e d t o climate anomalies throughout t h e t r o p i c s and higher l a t i t u d e regions (e.g.,

Bjerknes, 1966; Namais, 1976; J u l i a n and Chervin, 1978; Wright, 1979;

Horel and Wallace, 1981).

1.2

E q u a t o r i a l Rossby S o l i t o n s S o l i t o n s e x i s t when t h e tendency of a w a v e t o d i s p e r s e i s balanced by

its nonlinearity.

The t h e o r e t i c a l e x i s t e n c e of e q u a t o r i a l Rossby s o l i t o n s

was demonstrated by Boyd (1980) who examined t h e nonlinear form of t h e shallow w a t e r wave equations on an e q u a t o r i a l beta-plane.

H e utilized the

method of m u l t i p l e s c a l e s t o study only Rossby waves i n an unbounded ocean.

355 The l a t i t u d i n a l dependence of t h e eigenfunctions of t h e system a r e t h e c l a s s i c e q u a t o r i a l modes (e.g.,

Moore and Philander, 1977).

The zonal-

temporal behavior i s governed by t h e one-dimensional Korteweg-de V r i e s (KdV) equation.

I t has been w e l l e s t a b l i s h e d t h a t t h e s o l u t i o n t o t h e KdV equation

f o r a v i r t u a l l y a r b i t r a r y i n i t i a l condition y i e l d s a f i n i t e number of s o l i t o n s and a d i s p e r s i v e wavetrain (Gardener, e t a l . , solitons are the & s t a b l e

1967).

Hence, a s t

s o l u t i o n t o t h e KdV equation.

+ m,

Boyd demonstrated

t h a t i n t e r n a l Rossby s o l i t o n s could be generated by very g e n e r a l i n i t i a l c o n d i t i o n s provided t h a t t h e i n i t i a l f e a t u r e r e p r e s e n t s a depression of t h e thermocline.

Along t h e e q u a t o r , t h e l a r g e s t amplitude s o l i t o n has a meri-

d i o n a l dependence of a f i r s t l a t i t u d i n a l mode Rossby wave. Kindle (1982) examined t h e generation of Rossby s o l i t o n s by e q u a t o r i a l wind events.

Using a one-layer reduced g r a v i t y numerical model of t h e

t r o p i c a l P a c i f i c , he found t h a t even a modest r e l a x a t i o n of t h e e q u a t o r i a l t r a d e s could g e n e r a t e e q u a t o r i a l Rossby s o l i t o n s .

The time s c a l e of t h e

wind event could vary from a few weeks t o months.

I f t h e d u r a t i o n of t h e

event i s longer than two months, more than one s o l i t o n can evolve from t h e f i r s t l a t i t u d i n a l mode Rossby wave f r o n t emanating from t h e e a s t e r n boundary. The ease with which e q u a t o r i a l Rossby s o l i t o n s develop i n t h e a n a l y t i c a l work of Boyd and t h e numerical experiments of Kindle suggest t h a t t h e s e c u r i o u s nonlinear waves may p l a y an important r o l e i n t h e dynamics of t h e equatorial Pacific. The approach of t h i s paper i s s i m i l a r t o t h a t of Kindle (1982). Section 2 t h e numerical model i s described.

In

Section 3 demonstrates t h e

a b i l i t y of e q u a t o r i a l wind e v e n t s t o generate Rossby s o l i t o n s .

The f i n a l

experiments a r e simple r e p r e s e n t a t i o n s of E l Nino events; it w i l l be shown t h a t Rossby s o l i t o n s a r e most e a s i l y e x c i t e d by a prolonged weakening of t h e e q u a t o r i a l t r a d e s such a s during E l Nino.

2.

The Model The numerical model i s t h a t which i s described by Kindle (1979, 1982).

The governing system i s t h e e q u a t o r i a l beta-plane, equations with t h e i n c l u s i o n o f eddy v i s c o s i t y . f o r one a c t i v e l a y e r .

The model geometry

-

shallow water wave

The equations a r e solved

an i d e a l i z a t i o n of t h e t r o p i c a l

P a c i f i c - i s r e c t a n g u l a r i n shape and extends 1 5 , 0 0 0 km i n t h e zonal direction. The northern boundary, which i s open i n order t o permit t h e e x i t of c o a s t a l Kelvin waves, i s l o c a t e d 1 , 5 0 0 km from t h e equator.

Because only l a t i t u -

d i n a l l y symmetric modes a r e examined, t h e s o l u t i o n i n t h e southern hemisphere

i s t h e r e f l e c t i o n of t h a t i n t h e northern h a l f .

3 56 The e x p l i c i t numerical scheme employs leapfrog time d i f f e r e n c i n g and centered space d i f f e r e n c i n g ; t h e viscous terms a r e lagged i n time.

A

staggered g r i d which i n c o r p o r a t e s t h e "C" s t e n c i l (Mesinger and Arakawa, 1976) i s u t i l i z e d .

The g r i d spacing i n t h e zonal d i r e c t i o n v a r i e s from 20

?a near t h e boundaries t o 165 km i n t h e i n t e r i o r ; t h e meridional spacing

i s 25 i m throughout t h e domain.

3.

Numerical Results In t h i s s e c t i o n , t h e r e s u l t s of seven experiments are described.

In

Cases 1 and 2 , t h e model i s i n i t i a l i z e d with t h e a n a l y t i c a l s o l u t i o n f o r an e q u a t o r i a l Rossby s o l i t o n derived by Boyd (1980).

In Cases 3 and 4 , a

p a t c h of zonal wind stress (meridionally uniform) i s impulsively applied f o r 30 days i n o r d e r t o demonstrate t h e generation of Rossby s o l i t o n s by equa-

t o r i a l wind events. E l Nino events.

from rest.

Cases 5, 6 , and 7 a r e very simple r e p r e s e n t a t i o n s of

Except f o r t h e f i r s t two experiments, t h e model i s s t a r t e d

The i n i t i a l t h i c k n e s s of t h e upper l a y e r i s 150 meters and t h e

d e n s i t y s t r a t i f i c a t i o n between t h e two l a y e r s i s 3Ot u n i t s .

In Cases 1 and

2 , t h e i n i t i a l l a y e r t h i c k n e s s i s 100 m e t e r s and 40t u n i t s .

The model is i n i t i a l i z e d with Boyd's s o l u t i o n f o r t h e f i r s t l a t i t u d i n a l mode e q u a t o r i a l Rossby s o l i t o n (Fig. 1). C a s e 1 i s t h e l i n e a r s o l u t i o n . The e f f e c t s of d i s p e r s i o n cause t h e i n i t i a l f e a t u r e t o evolve i n t o a wavet r a i n (Fig. 2 a ) .

In C a s e 2 t h e nonlinear terms are included; Fig. 2b r e v e a l s

t h a t t h e i n i t i a l d i s t u r b a n c e propagates across t h e b a s i n with very l i t t l e change i n shape o r amplitude.

C l e a r l y , t h e nonlinear terms balance t h e

tendency t o d i s p e r s e , t h u s demonstrating t h a t t h e model reproduces t h e behavior of t h e e q u a t o r i a l Rossby s o l i t o n derived a n a l y t i c a l l y by Boyd. In t h e experiments described below, wind stress f o r c i n g i s applied t o t h e model ocean i n o r d e r t o demonstrate t h e e x c i t a t i o n of s o l i t o n s by wind events.

The f o r c i n g i s i n t h e form of a patch of zonal wind stress with a

uniform meridional d i s t r i b u t i o n and a top-hat zonal shape.

The wind i s

d i r e c t e d from w e s t t o e a s t and r e p r e s e n t s a relaxation of t h e mean e q u a t o r i a l trades.

A s described by McCreary (1977) and Kindle (1979), t h e wind patch

r a d i a t e s packets of Kelvin and Rossby waves.

The Kelvin waves, which have

a much l a r g e r amplitude than t h e Rossby waves, propagate a downwelling p u l s e towards t h e e a s t e r n boundary.

The r e f l e c t i o n of t h i s downwelling p u l s e

i n i t i a t e s westward-propagating

Rossby waves.

The subsequent d e s c r i p t i o n

focuses on t h e response of t h e f i r s t l a t i t u d i n a l mode Rossby wave created by t h e e a s t e r n boundary r e f l e c t i o n .

357

0

10" KM

15

Figure 1. Initial condition for Cases 1 and 2 - the prototype Rossby soliton derived by Boyd. (a) Zonal velocity component. The contour interval is 5 cm/sec. (b) Model pycnocline surface as viewed from the southwest Pacific. The maximum amplitude of the initial depression is 25 meters. ( f r m Kindle, 1982)

358

DQY

DAY

160

120

Figure 2. (a) Nodel pycnocline s u r f a c e f o r Case 1 ( l i n e a r s o l u t i o n ) . 2 (nonlinear s o l u t i o n ) . (from Kindle, 1982)

(b) C a s e

359 I n Case 3 , t h e wind stress has a zonal width s c a l e of 2,000 km and an amplitude of - 5 dyne/cm

2

.

from t h e e a s t e r n boundary. o f f a t Day 30.

The e a s t e r n edge of t h e patch i s located 6,500 km The f o r c i n g i s a p p l i e d impulsively and switched

Figure 3 p r e s e n t s t h e r e s u l t s of t h e l i n e a r c a l c u l a t i o n .

As

t h e f i r s t mode Rossby wave propagation westward, it w o l v e s i n t o a wavetrain. Although n o t a s pronounced as i n Case 1, t h e e f f e c t s of d i s p e r s i o n a r e very The nonlinear c o u n t e r p a r t t o t h i s experiment (Case 4) i s shown i n

evident.

The f i r s t mode Rossby wave propagates a c r o s s t h e b a s i n and e x h i b i t s

Figure 4.

only s l i g h t changes i n i t s shape and amplitude.

C l e a r l y , t h e nonlinear e f f e c t s

a r e balancing t h e tendency of t h e wave t o d i s p e r s e and causing t h e peak t o be l a r g e r and sharper than i n t h e l i n e a r experiment.

I t i s i n t h i s sense t h a t

w e d e s c r i b e t h e f i r s t mode Rossby wave as having evolved i n t o a s i n g l e Rossby soliton. The preceding experiments demonstrated t h a t e q u a t o r i a l s o l i t o n s could develop from wind events i n which t h e e q u a t o r i a l t r a d e s relax f o r periods of approximately one month.

Kindle (1982) revealed t h a t Rossby s o l i t o n s could

be e x c i t e d by wind e v e n t s whose d u r a t i o n s vary from a few weeks t o months. In t h e following experiments w e w i l l examine t h e response t o a prolonged r e l a x a t i o n of t h e e q u a t o r i a l wind.

It has been hypothesized (Wyrtki, 1975:

Hurlburt, e t a l . , 1976; McCreary, 1976) t h a t j u s t such events a r e responsible f o r i n i t i a t i n g E l Nino; t h e c o a s t a l Kelvin wave caused by t h e i n c i d e n t downwelling e q u a t o r i a l Kelvin wave c r e a t e s an i n t r u s i o n of abnormally warm s u r f a c e w a t e r along t h e c o a s t s of Peru and Ecuador.

Hence, it i s of i n t e r e s t t o

examine whether e q u a t o r i a l Rossby s o l i t a r y waves a r e a s s o c i a t e d with t h i s In f a c t , Boyd (1980) suggests t h a t E l Nino would be a l i k e l y mechanism

event.

f o r t h e generation of Rossby s o l i t o n s . The extended p e r i o d of anomalously weak e q u a t o r i a l t r a d e s a s s o c i a t e d with E l Nino are represented very simply i n t h e experiments below. i d e n t i c a l t o Case 2 except t h a t t h e f o r c i n g i s not switched o f f .

They a r e This permits

a c l e a r e r examination of t h e response subsequent t o t h e r e f l e c t i o n of a Kelvin wave f r o n t . I n t h e f i r s t experiment, t h e nonlinear terms a r e neglected. v e l o c i t y f i e l d i s shown i n Fig. 5.

The zonal

Although, no wavetrain has developed a s

i n t h e l i n e a r prototype experiments (Fig. 2 a ) . t h e e f f e c t s of d i s p e r s i o n a r e evident.

The wavefront a s s o c i a t e d w i t h t h e f i r s t mode Rossby wave has elon-

g a t e d and evolved i n t o a double peak s e p a r a t e d by a s l i g h t saddle. s o l u t i o n s a r e s i m i l a r t o t h e l i n e a r one-dimensional conducted by Boyd (Fig. 7, 1980).

initial-value

The experbents

SI

m COI 0 5'1-

s-1-

09E

361

0

10" Khi

-1.s 1s

0

10" Khi

0

10" KM

-1.5

0

IS 10" KM

( a ) Same a s Figure 3 except f o r C a s e 4 (nonlinear s o l u t i o n ) . Figure 4. (b) Zonal v e l o c i t y a t Day 200 f o r Case 4. E q u a t o r i a l s o l i t o n i s c l e a r l y e v i d e n t a t x = 4000 km. (from Kindle, 1982)

362

EOURTBR

0

103 KM

-1.5 15

0

103 KM

15

0

103 KM

Figure 5. Zonal v e l o c i t y component f o r l i n e a r E l Nino experiment (Case 51. ( a ) Solution a t Day 120. The f i r s t mode Rossby w a v e r e s u l t i n g from t h e Kelvin (from Kindle, wave r e f l e c t i o n i s a t x -,1 2 , 0 0 0 km. (b) Solution a t Day 2 2 0 . 1982)

Figure 6 i l l u s t r a t e s t h e r e s u l t s of t h e corresponding

nonlinear case.

Note t h a t a t Day 120. t h e s o l u t f o n i s v i r t u a l l y i d e n t i c a l t o t h e l i n e a r case. Hence, t h i s r e p r e s e n t a t i o n of E l Nino i s v i r t u a l l y l i n e a r through t h e o n s e t I f t h e incoming Kelvin wave and i t s r e f l e c t i o n a r e e s s e n t i a l l y

of t h e event.

l i n e a r , t h i s may h e l p t o explain t h e r e l a t i v e l y c l o s e agreement between t h e l i n e a r experiments of Busalacchi and O'Brien of t h e onset of E l Nino.

(1981) and t h e observations

B u t e q u a t o r i a l Rossby s o l i t o n s r e q u i r e only a

balance between weak n o n l i n e a r i t y and weak d i s p e r s i o n . Figure 6b, r e v e a l s t h a t t h e presence of weak n o n l i n e a r i t y can a l t e r t h e c h a r a c t e r of t h e s o l u t i o n dramatically. evolved i n t o

two d i s t i n c t

The f i r s t mode Rossby wave has

Rossby s o l i t o n s .

The l a r g e s t amplitude s o l i t o n

t r a v e l s t h e most r a p i d l y ; a s time progresses t h e two s o l i t o n s w i l l continue t o separate.

This i s a l s o c o n s i s t e n t with t h e work of Boyd (1980) who found

t h a t f o r an i n i t i a l condition w i t h a "top-hat" zonal shape, m u l t i p l e s o l i t o n s could develop.

The amplitudes of t h e i n d i v i d u a l peaks decrease monotonically

away from t h e l e a d s o l i t o n . I n t h e f i n a l experiment, t h e amplitude of t h e E l Nino event i s increased by extending t h e zonal width s c a l e of t h e wind patch by 50%. The patch of zonal wind stress now extends f r m x = 5,500 km t o x = 8,500 km. amplitude of t h e wind event remains a t .5 dynes/cm'. zonal v e l o c i t y a t Days 120 and 220.

The

Figure I d e p i c t s t h e

During t h i s period t h e s o l u t i o n i s very

s i m i l a r t o t h a t of C a s e 6 except t h a t t h e amplitude is approximately 50% greater.

Figure 8 , however, r e v e a l s t h e development of a t h i r d s o l i t o n which,

by Day 280, i s w e l l i n f r o n t of t h e m = 3 Rossby wave ( a t x = 9,000 kml. C l e a r l y , t h e number &- I$

amplitude of t h e s o l i t o n s a r e p r o p o r t i o n a l t o t h e

amplitude of E l Nino event.

I t should be noted t h a t n o n l i n e a r i t y appears t o

have a dramatic e f f e c t on t h e s o l u t i o n s a t t h e western boundary.

Even though

an i n t e n s e eddy f i e l d develops i n t h a t region, numerical experiments ( n o t shown) demonstrate t h e s o l i t o n s reflect a s Rossby waves and e q u a t o r i a l Kelvin waves.

4.

This r e f l e c t i o n process w i l l be t r e a t e d i n f u t u r e work.

Summary The wind e x c i t a t i o n of e q u a t o r i a l Rossby s o l i t a r y waves during E l Nino

has been i n v e s t i g a t e d numerically using a n o n l i n e a r , one-layer, g r a v i t y model of t h e t r o p i c a l P a c i f i c .

reduced-

The model b a s i n , which i s rectangular

i s shape, extends 15,000 km z o n a l l y and 1,500 km on e i t h e r s i d e of t h e equator. The northern and southern boundaries a r e open.

The model is forced by patches

of zonal wind stress r e p r e s e n t i n g e q u a t o r i a l t r a d e wind events.

364

0

103 KM

-1.5

0

0

EOUATBR

103 m

-1.5 0

1s

10" K M

Figure 6. Same as Figure 5 except f o r nonlinear s o l u t i o n . evident i n (b). (from Kindle, 19821

Two s o l i t o n s a r e

365

0 103

KM

0

103 KM

-1.5

1s

0

103 KM

Figure 7. (Case 7 ) .

Zonal velocity component f o r large amplitude E l Nino experihlent a ) Day 1 2 0 ; b) Day 220

366

a)

1.5

0

:OURT0R

lo3 KM

-1.5 0

15

1 0 3 KM

b)

1.5

0

lo3 KM

-1.5

15

0

1 0 3 KM

Figure 8. As in Figure 7, a) Day 260; h) Day 280. The third soliton is evident in a) at x = 7,500 km. Ky Day 280, it has intensified and propagated to x = 6,000 km.

361

A prolonged relaxation of the equatorial trades, such as that associated with El Nino, generates a soliton train subsequent to the reflection of the Kelvin wave front at eastern boundary.

Even a very

modest event in which the amplitude of the relaxation is .5 dynes/cm

2

over

a 2,000 km patch generates two Rossby solitons which effect a thermocline depression of 30 meters. A major El Nino event would create a significantly larger response, including three or more first mode Rossby solitary waves. The ease with which the numerical model yields solitons for the prolonged wind events suggests that Rossby solitary waves may be most easily observed following a major El Nino.

5.

Acknowledgements I would like to thank Drs. John Boyd, Harley Hurlburt, and Dennis Moore

for their helpful comments. Appreciation is extended to Charlene Parker for typing the manuscript.

The computations were performed on the two-pipeline

Texas Instruments Advanced Scientific Computer at the Naval Research Laboratory in Washington, D.C.

REFERENCES

Barnett, T. P., 1977: An attempt to verify some theories of El Nino. J633-647. Phys. Oceanogr., Barnett, T. P., 1981: Statistical relations between ocean-atmosphere fluctuations in the tropical Pacific. J. Phys. Oceanogr., 2 (81,

z,

1043-1058.

Bjerknes, J., 1966: A possible response of the atmospheric Hadley circulation to equatorial anomalies of ocean temperature. Tellus, 1 8 ,820-829. Boyd, John P., 1980: Equatorial solitary waves. Part 1: Rossby solitons., J. Phys. Oceanogr., lo, 1699-1717. Busalacchi. A. and J. J. O'Brien. 1981: Interannual variabilitv of the equatorial Pacific in the 1 9 6 0 ' s . J. Geophys. Res., 86, 10901-10907. Gardner, C. S . , J. M. Greene, M. D. Kruskal and R. M. Miura, 1 9 6 7 : Method for solving Korteweq-de Vries equation. Phys. Rev. Lett., 19,1095-1097. Hickey, B., 1975: The relationship between fluctuations in sea level, wind stress and sea surface temperatures in the equatorial Pacific. J. Phys. Oceanogr., 5, 460-475. Horel, J. D. and J . M. Wallace, 1981: Planetary scale atmospheric phenomena associated with the Southern Oscillation. Mon. Wea. Rev., 813-829. Hurlburt, H. E., J. C. Kindle and J. J. O'Brien, 1 9 7 6 : A numerical simulation of the onset of El Nino. J. Phys. Oceanogr., 6, 621-631. Julian, P. R. and R. M. Chervin, 1978: A study of the Southern Oscillation and Walker Circulation phenomenon. J. Atmos. Sci., 106, 1433-1451. Kindle, J. C., 1979: Equatorial Pacific Ocean Variability seasonal and El Nino time scales. Ph.D. thesis, Florida State University, 1 3 4 pp. Kindle, J. C., 1982: A numerical study of equatorial Rossby solitons, JPhys. Oceanogr., In Press.

*,

-

368 McCreary, J. P., 1976: Eastern tropical ocean response to changing wind systems: With application to El Nino. J. Phys. Oceanoqr., 6, 632-645. McCreary, J. P., 1977: Eastern ocean response to changing wind systems, Ph.D. Dissertation, Univ. of California, San Diego. Mesinger, F., and A . Arakawa, 1976: Numerical methods used in atmospheric models. Garp. P u b l . Ser., No. 17, WMO. Moore, D., 1968: Planetary-gravity waves in an equatorial ocean. Ph.D. Thesis, Harvard University. , and S. G. H. Philander, 1977: Modeling of the tropical oceanic circulation, The Sea, VL, ed. by E. D. Goldberg, I. N. McCave, J. J. O'Brien and J. H. Steele, 319-362, John Wiley & Sons, New York. Namias, J., 1976: Some statistical and synoptic characteristics associated with El Nino. J. Phys. Oceanogr., 6, 130-138. Rasmussen, E. M. and T. H. Carpenter, 1982: Variations in tropical sea surface temperature and surface wind fields associated with the Southern Oscillation/El Nino. Mon. Wea. Rev., 110,354-384. Weare, B. C., 1982: El Nino and tropical Pacific Ocean temperatures. JPhys. Oceanogr., 2, 17-27. Wright, P. B., 1979: A simple model for simulating regional short-term climatic changes. Mon. Wea. Rev., 107 ( 1 2 ) , 1567-1580. Wyrtki, K., 1975: El Nino - The dynamic response of the equatorial Pacific Ocean to atmospheric forcing. J. Phys. Oceanoyr., 5, 572-584. Wyrtki, K., 1977: Sea level &ring the 1972 El Nino. J.Phys. Oceanogr.,

7, 779-787.