Synoptic Scale Variability of Hydrophysical Fields in the Baltic Proper on the Basis of CTD Measurements

433

SYNOPTIC SCALE VARIABILITY OF HYDROPHYSICAL

FIELDS I N THE BALTIC PROPER ON THE B A S I S OF CTD MEASUREMENTS A. Aitsam, J. Elken I n s t i t u t e o f Thermophysics and Electrophysics Academy o f Sciences o f t h e Estonian S.S.R. ABSTRACT The r e s u l t s o f CTD surveys i n t h e ' B a l t i c Proper on r e c t a n g u l a r g r i d s w i t h spacing o f 5 n a u t i c a l m i l e s a r e analyzed.

Eddylike p e r t u r b a t i o n s o f

t h e r e l a t i v e dynamic topography (ROT), w i t h diameters equal t o 2 t o 5 t i m e s t h e i n t e r n a l Rossby r a d i u s o f deformation Rd (E 10 km), are described.

The

t y p i c a l m i g r a t i o n speed o f these p e r t u r b a t i o n s i s a few cm/sec and i t 5 s d i r e c t e d along t h e averaged isobaths w i t h shallower water on t h e r i g h t .

It

i s shown t h a t t h e speed and d i r e c t i o n of m i g r a t i o n o f t h e eddies can be e x p l a i n e d i n terms of topographic waves.

The hypothesis t h a t some o f t h e

observed eddies might be generated by b a r o c l i n i c i n s t a b i l i t y o f sheared mean f l o w s i s discussed on t h e b a s i s o f a simple model. estimate absolute v e l o c i t i e s method.

An attempt i s made t o

using a generalization o f the beta-spiral

Synoptic s c a l e processes i n t h e B a l t i c a r e compared t o t h e i r ocea-

n i c counterparts.

INTRODUCTION Synoptic eddies (Koshlyakov and Monin, 1978; Woods and Minnett, 1979) o r "mesoscale" eddies ( t h e l a t t e r term i s w i d e l y used by t h e MODE Group, 1978) a r e a common phenomenon i n t h e open ocean as w e l l as near f r o n t a l currents.

The B a l t i c Sea i s one o f t h e most thoroughly i n v e s t i g a t e d semi-

enclosed seas (Jansson, 1978); y e t , s y n o p t i c scale v a r i a b i l i t y has n o t been s t u d i e d here as much as i n t h e ocean.

Previous observations worth mention-

i n g i n c l u d e t h e s e c t i o n o f thermocline anomaly observed by Keunecke and Magaard (1974)

u s i n g a towed t h e r m i s t o r s t r i n g ; i n t e r e s t i n g data from the

s i x t i e s i n t h e Arcona Basin (Kielmann e t a l . , (Sustavov

e t al.,

1978);

1973) and i n t h e Gotland Basin

and r e s u l t s o f t h e B a l t i c - 7 5 experiment i n t h e

Bornholm Basin (Kielmann e t a l . ,

1976).

As f o r numerical model s t u d i e s ,

e d d y l i k e motions can be s i m u l a t e d i f t h e r e s o l u t i o n o f t h e model i s s u f f i c i e n t (Simons, 1978; Kielmann, 1978). The aim o f our s t u d i e s i s t o broaden our knowledge o f t h e three-dimens i o n a l s t r u c t u r e o f s y n o p t i c s c a l e p e r t u r b a t i o n s and o f t h e i r e v o l u t i o n . The f i e l d experiments described i n t h e n e x t s e c t i o n t o o k p l a c e mainly i n t h e

BOSEX area.

434

I n t h i s paper, we consider t h e r e s u l t s o f v e r t i c a l CTD c a s t s obtained d u r i n g several surveys.

A t t h e present time, t h i s i s t h e o n l y p o s s i b l e way

t o achieve s u f f i c i e n t s p a t i a l coverage and r e s o l u t i o n t o document l o w f r e quency motions f r o m t h e surface down t o t h e bottom l a y e r s .

The complete

l i s t o f measurements a l s o i n c l u d e s d i r e c t c u r r e n t measurements a t various mooring s t a t i o n s ,

and CTO p r o f i l e s obtained w i t h an u n d u l a t i n g underwater

u n i t towed i n t h e upper l a y e r .

U n f o r t u n a t e l y , t h e most i n t e n s i v e d e n s i t y

anomalies were n o t covered by d i r e c t c u r r e n t measurements.

Some o f t h e

r e s u l t s o f t h i s complex p r o j e c t a r e described i n another paper

earlier

(Aitsam e t a l . , 1981). METHODS

A l a r g e number o f hydrographic measurements has been made i n t h e ocean as w e l l as i n t h e B a l t i c Sea d u r i n g t h e l a s t century.

However, h i s t o r i c a l

data are t o o sparse i n space and t i m e t o r e s o l v e t h e s y n o p t i c s c a l e motions.

A q u a l i t a t i v e l y new approach was implemented i n t h e course o f s p e c i a l l y designed p r o j e c t s , such as POLYGON-67 (Koshlyakov e t a l . , (Koshlyakov

and Grachev,

1973),

MODE (McWilliams,

1970), POLYGON-70

1976) and POLYMODE; i n

these experiments, hydrographic casts were o b t a i n e d a t s t a t i o n s c o v e r i n g a r e g u l a r g r i d w i t h proper g r i d spacing.

We have no i n f o r m a t i o n about s i m i l a r

measurements i n t h e B a l t i c Sea and our t a s k was t o apply "oceanic" methods and h i s t o r i c a l experiences t o t h e B a l t i c . simply a reduced model o f t h e ocean,

However, t h e B a l t i c Sea i s n o t

so t h a t t h e a p p l i c a t i o n o f oceanic

r e s u l t s t o t h e B a l t i c case r e q u i r e s caution. For t h e design o f an oceanographic experiment, t h e optimal sampling r a t e and t h e optimal c o n f i g u r a t i o n and spacing o f s t a t i o n s can be found i f t h e c o r r e l a t i o n and s p e c t r a l c h a r a c t e r i s t i c s are known ( B r e t h e r t o n e t a l . , 1976).

The s p a t i a l c o r r e l a t i o n f u n c t i o n s were n o t known a t t h e s t a r t o f our

i n v e s t i g a t i o n s , so we e l e c t e d t o make measurements on a r e c t a n g u l a r g r i d w i t h a spacing o f 5 n a u t i c a l m i l e s between g r i d p o i n t s .

The l a t t e r choice

was based on t h e hypothesis t h a t the scales o f t h e eddies and o f t h e i n t e r n a l Rossby r a d i u s o f deformation, Rd,

a r e s i m i l a r i n t h e ocean and i n t h e

I n t h e B a l t i c , Rd i s about 10 km.

Baltic.

We s e l e c t e d experimental areas

w i t h r e l a t i v e l y smooth bottom slopes, and w i t h depths g r e a t e r than 80 m i n order

to

include the halocline.

The o r i e n t a t i o n o f t h e g r i d was chosen

according t o t h e p e c u l a r i t i e s o f t h e bottom topography.

The number o f

s t a t i o n s was l i m i t e d t o ensure t h a t surveys c o u l d be completed i n two days o r less. The v a r i o u s surveys w e r e performed d u r i n g c r u i s e s o f t h e R/V "Ayu-Dag". Most surveys were conducted i n t h e BOSEX area (Aitsam and Elken, 1980), and some t o o k p l a c e i n t h e Bornholm Basin and i n t h e Gotland Basin t o t h e n o r t h

435 1).

o f t h e BOSEX a r e ( F i g .

The surveys are l i s t e d i n Table 1.

I n this

t a b l e , t h e f i r s t i t e m o f t h e survey number denotes t h e c r u i s e number o f t h e

R/V "Ayu-Dag".

The l e n g t h s ( i n n a u t i c a l m i l e s ) o f t h e sides o f t h e g r i d s i n

t h e x- and y - d i r e c t i o n s are t a b u l a t e d under t h e heading "Survey area". x-

and y-axes

a r e d i r e c t e d eastward and northward:

1981 surveys; t h e axes a r e r o t a t e d 30' 1980.

respectively,

The

f o r the

clockwise f o r t h e surveys o f 1979 and

The lower l e f t and upper r i g h t coordinates d e f i n e the geographical

coordinates

o f t h e working area;

they correspond t o t h e corners o f t h e

"boxes" shown i n F i g u r e 1. I n t h e BOSEX area t h e bottom topography i s s l o p i n g mainly i n t h e x - d i r e c t i o n (see t h e maps i n Aitsam e t a l . ,.,' 1981, and i n Aitsam and Talpsepp. On t h e l e f t s i d e o f t h e area t h e slope exceeds 5-10-3, i n t h e cen-

1980).

t r a l p a r t t h e slope i s more moderate, r a n g i n g from 5-10-4 t o t h e r i g h t s i d e t h e depth decreases.

and on

A t y p i c a l depth i s 100 m.

The i n s t r u m e n t used i s t h e N e i l Brown Mark I11 CTD-profiler, c h a r a c t e r i s t i c s a r e described elsewhere (Laanemets and L i l o v e r , 1981).

whose The

d a t a were c o l l e c t e d on a REVOX audio tape recorder, and subsequently t r a n s f e r r e d t o a HP-9825A microcomputer f o r p r e l i m i n a r y data processing and s t o r age on HP-9885 f l e x i b l e d i s k s . I n t h e p r e l i m i n a r y data processing phase, temperature and c o n d u c t i v i t y data a r e i n t e r p o l a t e d a t pressure i n t e r v a l s o f 0.1 dbar; s a l i n i t y and density

values

(1981).

are

then

c a l c u l a t e d as described i n Laanemets and L i l o v e r

To f a c i l i t a t e f u r t h e r analyses, temperature,

s a l i n i t y and d e n s i t y

values a t s e l e c t e d pressure l e v e l s as w e l l as temperature,

s a l i n i t y and

pressure values a t s e l e c t e d d e n s i t y l e v e l s are compiled i n e a s i l y r e t r i e v a b l e format.

Also some i n t e g r a t e d p r o p e r t i e s , such as t h e r e l a t i v e dynamic

e. t h e d i f f e r e n c e o f dynamic h e i g h t s ) , henceforth denoted RTD, topography (i. a r e c a l c u l a t e d between s e l e c t e d pressure l e v e l s .

The RDT i s c a l c u l a t e d

according t o t h e formula:

where p1 and p2 denote pressure values ( i n dbars i n t h e argument o f RDT, w i t h p1 < p2); g, water;

and D(p2,

t h e a c c e l e r a t i o n due t o g r a v i t y ; p , t h e d e n s i t y o f t h e

p,),

t h e RDT i n cm, o r w i t h t h e accuracy o f

g in

dynamic cm. The d a t a i n pressure coordinates and t h e RDT have minor instrumental e r r o r s f o r s y n o p t i c scale s t u d i e s , except f o r t h e s a l i n i t y i n t h e thermoc l i n e l a y e r where n e g a t i v e spikes can occur. v e r t i c a l coordinate,

When d e n s i t y i s used as t h e

s p e c i a l care must be taken.

For long-term processes

436

I

Figure 1.

i

Basic areas f o r CTD surveys i n 1979, 1980 and 1981 (boxes), w i t h

depth contours (dashed l i n e s ) labeled i n meters. t h e water ii assumed t o be s t a b l y s t r a t i f i e d .

However, d e n s i t y inversions

are present i n some o f the observed p r o f i l e s .

These i n v e r s i o n s are removed

t o guarantee one-to-one correspondence o f pressure and density.

The e s t i -

TABLE 1.

L i s t o f the CTD surveys

Survey Number

day

Time month year

13/1 13/2 13/3 13/4 13/5 15/1 15/2 16/1 17/1 18/1 18/2 18/3 19/1 20/1 20/2 22/1 22/2 23/1 23/2 23/3 23/4 23/5

27 28 29-30 2-3 10-11 5-6 15-16 25-26 8-9 30-31 8-9 10-11 1-3 10-11 2-3 25-26 29-30 3-5 15-16 21-22 26-27 4-5

05 05 05 06 06 08 08 09 05 05 06 06 07 08 09 04 04 06 06 06 06 07

79 79 79 79 79 79 79 79 80 80 80 80 80 80 80 81 81 81 81 81 81 81

Duration (hrs)

Survey area

Number o f casts

18 21 34 20 20 24 20 23 24 32 33 27 39 37 30 34 32 44 26 26 25 25

20x20 20x20 30x20 20x20 20x20 20x20 20x20 20x20 20x25 20x25 20x25 25x20 20x25 25x25 20x25 25x25 25x25 25x30 20x20 20x20 20x20 20x20

21 21 38 21 21 21 21 21 30 30 30 27 30 36 30 36 36 42 25 25 25 25

Geographical Coordinates Lower l e f t Upper r i g h t Latitude Longitude Latitude Longitude 50'14.5'N 50'14.5'N 50'14.5'N 50'14.5'N 50'14.5'N 50'14.5'N 50'14.5'N 50'14. 5'N 56'03.4' N 56'03.4'N 56'03.4" 56'05.4' N 56'03.4" 56'03.4'N 56'03.4' N 55'00. O ' N 55'00.O'N 56'31.0'N 56'31. O'N 56'31.0'N 56'31.0'N 56'31. O ' N

18'21.3'E 18'21.3' E 18'21.3' E 18'21.3' E 18'21.3' E 18'21.3'E 18'21.3' E 18'21.3' E. 18'18.8'E 18'18.8'E 18'18.8'E 18'31.1' E 18'18.8' E 18'18.8 ' E 18'18.8' E 15'30.O'E 15'30. O ' E 18'55.4 ' E 18'55.4' E 18'55.4' E 18'55.4' E 18'55.4' E

56'21.1'N 56'21.1' N 56'15.7" 56'21.1" 56'21.1'N 56'21.1" 56'21.1'N 56'21.1' N 56'14.8" 56'14.8' N 56'14.8 ' N 56'09.3'N 56'14.8' N 56'12.1" 56'14.8" 55'25. O'N 55'25.0' N 57'01.0 ' N 56'51.0'N 56'51. O ' N 56'51.0' N 56'51. O'N

19'11.1' E 19'11.1'E 19'25.0' E 19'11. 1'E 19'11.1' E 19'11.1' E 19'11.1' E 19'11.1' E 19'12.4' E 19'12.4' E 19'12.4'E 19'27.8'E 19'12.4'E 19'20.1' E 19'12.4' E 16'13.4' E 16'13.4' E 19'40.7 ' E 19'32.1' E 19'32.1' E 19'32.1'E 19'32.1'E

438 mates o f t h e measurement e r r o r based on " t o t a l d i f f e r e n c e " type expressions are n o t good because t h e p r o f i l e s can be t o o jagged w i t h i n t h e d e n s i t y e r r o r intervals.

The e r r o r on t h e q u a n t i t y $ (temperature, s a l i n i t y o r pressure)

a t t h e d e n s i t y value

at

i s determined as f o l l o w s .

i n s t r u m e n t a l e r r o r s on $ and at, and l e t 41(a,) t h e measured p r o f i l e s o f

$(p)

w i t h i n the density i n t e r v a l Then t h e t r u e value o f $ a t

(at

at

at

be t h e

Consider a l l t h e values o f $

and ot(p).

- Aat,

L e t A$ and Aut

be t h e r e l a t i o n obtained from

+ Aut),

and f i n d

i s between t h e l i m i t s

(qmin

-

and. , , ,$

+ A$),

A$,

and i t should be determined i n d i v i d u a l l y every t i m e . The t y p i c a l v e r t i c a l s t r a t i f i c a t i o n o f t h e B a l t i c waters i s w e l l known. The upper boundary o f t h e h a l o c l i n e i s l o c a t e d between 60 and 80 m,.,'and separates t h e upper c o l d / f r e s h

it

waters from t h e l o w e r warm/salty waters.

D u r i n g summer, a very steep thermocline a t a depth o f 1 5 t o 30 m separates t h e warm upper "quasi-homogeneous''

l a y e r and t h e c o l d i n t e r m e d i a t e l a y e r .

When i n t e r p o l a t i n g nonsimultaneous and nonaveraged measurements on a horizontal grid,

i t i s n o t easy t o e x t r a c t t h e synoptic s c a l e component o f

the v a r i a b i l i t y .

Among the several p o s s i b l e i n t e r p o l a t i o n and f i l t r a t i o n

techniques, t h e optimal i n t e r p o l a t i o n (Gandin, "mesoscal e" oceanographers

1965) has t h e f a v o r o f most

(McWi 11iams , 1976).

For s p e c i a l

purposes,

if

s t a t i s t i c s are n o t w e l l known, t h e l e a s t squares polynomial f i t t i n g ( N i k i t i n and Vinogradova, 1980) c o u l d be u s e f u l . Whatever t h e technique,

t h e s i g n a l t o n o i s e r a t i o i s a v e r y important

parameter which i n d i c a t e s how j u s t i f i e d t h e i n t e r p o l a t i o n procedure can be. I n t h e a l g o r i t h m o f optimal i n t e r p o l a t i o n , t h e e r r o r norm ( r a t i o o f t h e d i s p e r s i o n s o f n o i s e and s i g n a l ) i s e x p l i c i t l y c a l c u l a t e d , and i f t h e value o f t h i s norm i s c l o s e t o one, t h e maps c o n s t r u c t e d by t h e i n t e r p o l a t i o n method are o n l y s l i g h t l y i n f l u e n c e d by t h e measurements. I n order t o estimate t h e e r r o r norms, we c o l l e c t e d s e r i e s o f p r o f i l e s a t given stations

i n d i f f e r e n t seasons.

measure t h e e r r o r d i s p e r s i o n s was one day, casts one hour.

The d u r a t i o n o f each s e r i e s t o and t h e t i m e i n t e r v a l between

During h o r i z o n t a l surveys, t h e d u r a t i o n and t h e t i m e i n t e r -

v a l were about t h e same, b u t t h e measurements were made a t d i f f e r e n t s t a tions.

The e r r o r d i s p e r s i o n ,

E',

i n c l u d e s t h e random measurement e r r o r s and

t h e h i g h frequency n o i s e ( i n t e r n a l waves), a l l y .stationary, contamination trends

of

i n the

which can be assumed s t a t i s t i c -

homogeneous and u n c o r r e l a t e d i n space; "instantaneous"

synoptic

it also includes

p a t t e r n s due t o d i u r n a l

scale p e r t u r b a t i o n s .

The

variations

l a t t e r factor

and

imposes

c e r t a i n l i m i t a t i o n s on t h e survey d u r a t i o n and on t h e number o f s t a t i o n s . Our experience i n d i c a t e s t h a t maps obtained from surveys t a k i n g more t h a n two

days

cannot

be considered

instantaneous,

and some dynamical

and/or

439

statistical

The s i g n a l d i s p e r s i o n , u

time c o r r e c t i o n s are required.

determined from t h e d e v i a t i o n s from the mean of

2

,

is

t h e data obtained i n t h e

h o r i z o n t a l surveys; u2 i n c l u d e s b o t h t h e d i s p e r s i o n o f t h e "cooled" synoptic s c a l e p e r t u r b a t i o n s , and i t s t i m e contamination and h i g h frequency noise. 2 2 Some t y p i c a l d i s t r i b u t i o n s o f t h e e r r o r norm3, q = E /u , f o r t h e summer s t r a t i f i c a t i o n

i n t h e BOSEX area are presented i n F i g u r e 2, w i t h

e i t h e r pressure o r d e n s i t y as t h e " v e r t i c a l " coordinate.

Note t h a t q can be

l a r g e r than one due t o s t a t i s t i c a l u n c e r t a i n t i e s and because t h e i m p l i c i t hypothesis o f s t a t i s t i c a l homogeneity and s t a t i o n a r i t y i s n o t always v a l i d . F i g u r e 2 shows t h a t , when t h e pressure i s used as t h e v e r t i c a l c o o r d i nate, t h e d e n s i t y , temperature and s a l i n i s y p r o f i l e s above t h e 70 dbar l e v e l above t h e h a l o c l i n e ) a r e d i s t u r b e d by " e r r o r s " ; hence i t i s n o t poss-

(i.e.

i b l e t o t r y t o "separate"

o r i d e n t i f y "cooled" p a t t e r n s i n such data.

This

c o n c l u s i o n does n o t apply t o t h e s a l i n i t y i n t h e l a y e r above t h e thermoc l ine

which i s n o t d i s t u r b e d by v e r t i c a l displacements o f i n t e r n a l waves

and d u r n a l heat exchange v a r i a t i o n s .

1eve1 a r e 0 . 1 t o 0.2,

T y p i c a l values o f q below t h e 70 dbar

i n d i c a t i n g t h a t h o r i z o n t a l low frequency inhomogene-

i t i e s dominate over s h o r t - t e r m temporal v a r i a t i o n s i n t h e h a l o c l i n e . he e r r o r norms f o r t h e p r o f i l e s o f pressure, temperature and s a l i n i t y as f u n c t i o n s o f d e n s i t y a r e s m a l l e r than those c a l c u l a t e d i n p-coordinate.

F o r t h e pressure, t y p i c a l values o f q are 0.3-0.5 5.5-6.5), layer,

and 0.1-0.2

i n t h e thermocline (ut =

i n t h e h a l o c l i n e (ut = 7.5-8.5).

I n t h e intermediate

t h e h i g h e r v a l u e o f q can be explained by measurement e r r o r s :

v e r t i c a l d e n s i t y g r a d i e n t i s small i n t h a t l a y e r .

the

As t o t h e temperature and

s a l i n i t y p r o f i l e s i n at-coordinate,

they should t h e o r e t i c a l l y be f r e e o f t h e

kinematic e f f e c t o f i n t e r n a l waves.

The r e l a t i v e l y higher values o f q above

t h e ut = 7.5 l e v e l can be e x p l a i n e d by measurement e r r o r s r a t h e r than by p h y s i c a l processes.

I n these l a y e r s the temperature and s a l i n i t y v a r i a t i o n s

(due t o t h e f i n e s t r u c t u r e ) w i t h i n each d e n s i t y e r r o r i n t e r v a l can be compara b l e t o t h e t h e r m o c l i n i c i t y e f f e c t s described by Woods (1979). cline

(below at

= 7.5),

thermoclinicity

I n t h e halo-

c l e a r l y dominates and q i s very

small. The values o f q f o r t h e r e l a t i v e dynamic topography (RDT) sented i n t h e f i g u r e .

are n o t pre-

I f t h e thermocline and/or t h e h a l o c l i n e l i e between

t h e l i m i t s o f i n t e g r a t i o n , t h e RDT anomalies are caused mainly by t h e t o t a l v e r t i c a l displacement o f these t r a n s i t i o n l a y e r s , and t h e m a n i f e s t a t i o n s o f fine-scale/short-term procedure.

phenomena a r e e l i m i n a t e d v i a t h e v e r t i c a l i n t e g r a t i o n

T y p i c a l values o f q a r e 0.2-0.5

than 0 . 1 f o r t h e h a l o c l i n e .

f o r t h e thermocline, and l e s s

Note t h a t f o r t h e MODE r e g i o n t h e e r r o r norms

a r e w i t h i n t h e range o f 0.1-0.3

(McWilliams, 1976).

I

__ .--0-

/

100: dbar

dbar'

"t\

9.0 F i g u r e 2.

"A

9.0

9.0

V e r t i c a l d i s t r i b u t i o n o f t h e e r r o r norms, q =

as function o f pressure (above); (below).

2

......

-z

'2,

E

2/u 2 , o f d e n s i t y (ut), temperature (T) and s a l i n i t y ( S )

e r r o r norms o f pressure ( p ) ,

The s o l i d l i n e s represent d a t a from survey 20/1,

IA

temperature and s a l i n i t y as f u n c t i o n o f d e n s i t y

t h e dashed l i n e s d a t a from survey 20/2.

441 From t h i s study o f t h e e r r o r norms, we conclude t h a t , i n t h e h a l o c l i n e , t h e amp1 i t u d e o f t h e "cooled"

p a t t e r n s o f synoptic scale p e r t u r b a t i o n s i s

l a r g e r t h a n t h a t o f t h e s h o r t - t e r m v a r i a t i o n s ( w i t h p e r i o d s i n f e r i o r t o one day);

i t i s t h e r e f o r e meaningful t o map t h e observed f i e l d s .

A t t h e same

t i m e we doubt t h a t i t would be j u s t i f i e d t o p l o t , h o r i z o n t a l maps ( o r sections)

o f t h e temperature,

s a l i n i t y o r d e n s i t y f i e l d s a t any given depth

(pressure) l e v e l above 70 m (dbar) when more than a f e w hours elapse between neighbor s t a t i o n s . The knowledge o f t h e s p a t i a l c o r r e l a t i o n f u n c t i o n s i s r e q u i r e d t o draw maps u s i n g t h e optimal i n t e r p o l a t i o n techniques (Gandin,

1965).

Unfortun-

a t e l y , no d a t a o t h e r than those c o l l e c t e d d u r i n g t h e v a r i o u s surveys are a v a i l a b l e f o r determining these c o r r e l a t i o n f u n c t i o n s .

When o n l y a f e w data

p o i n t s from one survey a r e used, t h e s t a , t i s t i c a l u n c e r t a i n t i e s a r e l a r g e , b u t v a r i a t i o n s from survey t o survey are g r e a t e r than t h e estimated c o n f i dence i n t e r v a l . F i g u r e 3 shows an example o f t h e c o r r e l a t i o n f u n c t i o n of D (70,30),the RDT between 30 and 70 db ( i . e . t h e h a l o c l i n e anomalies), s i n g l e survey

(lower

I n t h e a n a l y t i c a l f i t t i n g t h e a n i s o t r o p y was taken i n t o account

by t h e c o r r e l a t i o n e l l i p s e s . i n t h i s example,

The c o r r e l a t i o n r a d i i a r e more than 10 miles

so t h e g r i d spacing chosen f o r t h e measurements (5 m i l e s )

i s almost o p t i m a l exceed 20%.

and t h e average c o r r e l a t i o n s over 6 surveys

The c o r r e l a t i o n s were c a l c u l a t e d i n f o u r d i r e c t i o n s w i t h 45'

(upper panel). increment.

panel)

f o r t h e data o f a

i n terms o f i n t e r p o l a t i o n e r r o r s :

t h e l a t t e r do n o t

However, some o f t h e o t h e r RDT d a t a gave t o o s h o r t c o r r e l a t i o n

l e n g t h s i n comparison w i t h t h e g r i d spacing.

As a r u l e , t h e parameters

which have l a r g e e r r o r norms a r e u n c o r r e l a t e d a t t h e d i s t a n c e o f t h e g r i d spacing. Various experiments show t h a t t h e i n t e r p o l a t e d maps are v i s u a l l y n o t very sensitive t o the variations o f the c o r r e l a t i o n functions.

However,

t h i s c o n c l u s i o n does n o t apply t o t h e study o f t h e s p a t i a l d e r i v a t i v e s and t h e dynamical equations.

Generally, f o r repeated surveys (close i n t i m e t o

each o t h e r ) t h e averaged c o r r e l a t i o n f u n c t i o n s were used.

For some cases

t h e c o r r e l a t i o n l e n g t h s were increased t o o b t a i n more e f f e c t i v e p o i n t s f o r the interpolation.

SYNOPTIC SCALE DISTRUBANCES The r e l a t i v e dynamic topography (RDT),

c a l c u l a t e d by formula (l), i s

t h e main o b j e c t o f our i n t e r e s t f o r two reasons. small

error

norms

and s u f f i c i e n t l y l a r g e c o r r e l a t i o n l e n g t h s t o ensure

correct interpolation. property:

it i s

F i r s t , t h e RDT has f a i r l y

Second, and more i m p o r t a n t l y , t h e RDT i s a dynamical

t h e geostrophic

stream f u n c t i o n o f r e l a t i v e c u r r e n t s .

442

a)

1

1

0

0

-1

-1

1

30 -1 -

Figure 3. Spatial correlation functions of the r e l a t i v e dynamic topography (RDT) between 30 and 70 d b , D (70,30), in four directions (indicated by subscripts). Circles represent data points, vertical bars indicate the 90% confidence l i m i t s , and solid l i n e s are the r e s u l t s of two-dimensional analyt i c a l f i t s . Upper panel shows the average correlation functions over s i x 1980 surveys; lower panel shows r e s u l t s of the single survey 18/2.

443

Indeed, f o r t h e nondimensional parameter values c h a r a c t e r i s t i c o f the B a l t i c Proper,

t h e c o n d i t i o n s f o r t h e quasi-geostrophic approximation t o be v a l i d

a r e s a t i s f i e d i n t h e low frequency range.

However, i t should be emphasized

t h a t t h e r e f e r e n c e l e v e l f o r geostrophic c a l c u l a t i o n s o f t h e absolute veloc i t y by t h e dynamical method i s n o t w e l l known. proposed (Fomin, currents.

Several methods have been

1964), b u t i n t h i s s e c t i o n we s h a l l o n l y discuss r e l a t i v e

I f t h e RDT i s c a l c u l a t e d by (l), i t represents t h e v e l o c i t y o f

t h e upper l a y e r r e l a t i v e t o t h a t o f t h e l o w e r l a y e r i n t h e t r a d i t i o n a l sense o f a stream f u n c t i o n .

An RDT change o f 1 dyn.cm over 5 m i l e s corresponds t o

a r e l a t i v e c u r r e n t speed o f 8.65 cm/sec.

I f t h e isopycnals are displaced

upward, t h e RDT anomaly i s negative, and'vice versa. Three examples o f t h e e v o l u t i o n o f e d d y l i k e phenomena can be described on t h e b a s i s o f r a p i d l y succeeding surveys i n t h e BOSEX area. The d a t a o f August 1979 show an e d d y l i k e p e r t u r b a t i o n o f t h e RDT w i t h a The l e f t - h a n d s i d e o f Figure 4 shows t h r e e RDT

diameter o f 20 km (9 2Rd). i n t e g r a l s between d i f f e r e n t

levels

for

survey

15/1; t h e r i g h t - h a n d side

shows t h e same i n t e g r a l s f o r survey 15/2 t e n days l a t e r . o f t h e thermocline [D(30,10)]

The deformations

and o f t h e h a l o c l i n e [D(90,30)]

have the same

s i g n , and b o t h r e f l e c t an upward displacement from t h e mean p o s i t i o n i n t h e center o f the perturbation.

The d i f f e r e n c e i n geostrophic c u r r e n t s above

and below t h e h a l o c l i n e i s 5 t o 7 cm/sec.

The comparison o f t h e two s e r i e s

o f maps shows t h a t t h e eddy migrates 10 m i l e s along t h e average isobaths i n

10 days ( m i g r a t i o n speed the r i g h t .

3

2 cm/sec),

w i t h t h e shallower water remaining on

I t can a l s o be seen t h a t t h e a x i s o f t h e eddy i s n o t v e r t i c a l

( t h e c e n t e r s do n o t c o i n c i d e i n t h e h a l o c l i n e and thermocline maps) and i t appears t h a t t h e thermocline p e r t u r b a t i o n migrates f a s t e r than t h a t o f the halocline. dent:

The i n t e n s i f i c a t i o n o f the h a l o c l i n e p e r t u r b a t i o n i s a l s o e v i -

t h e r e l a t i v e r o t a t i o n a l speed doubles i n 10 days. The maps o f surveys 1 3 / 1 t o 13/4 (Figure 5) show a p o s i t i v e e d d y l i k e

RDT p e r t u r b a t i o n o f weak i n t e n s i t y i n t h e upper c e n t r a l p a r t o f t h e area. The p e r t u r b a t i o n appears in t h e ha1o c l ine o n l y , because no thermocl ine has developed y e t .

On t h e b a s i s o f a s i n g l e survey,

i t c o u l d be hypothesized

t h a t t h e p e r t u r b a t i o n i s caused by i n t e r n a l waves.

However, t h e presence o f

t h e p e r t u r b a t i o n on t h r e e successive d a i l y maps (13/1-3) i s convincing e v i dence t h a t t h e p e r t u r b a t i o n ( l o w e r i n g o f isopycnals, w i t h axes

Rx z 1 5 km,

R E 20 km) i s a s y n o p t i c f e a t u r e . The speed o f t h e p e r t u r b a t i o n d r i f t i s Y o f t h e o r d e r o f 1.5 cm/sec w i t h t h e shallower water on t h e r i g h t . Although t h e c u r r e n t speeds a r e t o o weak f o r a c o r r e c t comparison,

the r e l a t i v e

c u r r e n t s a t t h e c e n t r a l s t a t i o n , determined on t h e b a s i s o f mooring s t a t i o n data and averaged over 5 days, correspond s a t i s f a c t o r i l y t o t h e geostrophic

444

1 ( 90,lO)

1511 5.-6.08.79

I(90,301

1511: 5.-6.08.79

D (90101

1512:15.-16.08.:

D (90,30)

1512 : 15-16.08:

03

N30,lO)

1512:15.-16.08.7!

1511: 5.-6.08.79.

0

F i g u r e 4.

5

10

6 miles

Maps o f RDT anomalies ( i n dynamic cm) f o r surveys 15/1 (on t h e

l e f t ) and 15/2 (on t h e r i g h t ) .

The contour i n t e r v a l i s 0 . 1 dyn.cm.

445

D(90,30)

F i g u r e 5.

1313 : 29.0579

Maps o f RDT anomalies ( i n dynamic cm) f o r surveys 13/1-4.

contour i n t e r v a l i s 0 . 1 dyn.cm.

The

446

v e l o c i t y determined f r o m RDT.

On t h e r i g h t s i d e o f t h e area, t h e edge o f a

l a r g e negative RDT anomaly can be observed.

An e x t e n s i o n

of survey 13/3

a l l o w s us t o document t h e scales .and shape o f t h i s p e r t u r b a t i o n .

The halo-

c l i n e i n t e r s e c t s t h e bottom slope a t t h e r i g h t edge o f t h e survey extension (decreasing depth).

The anomaly i s t o n g u e l i k e i n shape, and i t extends 40 The streamlines o f D(90,30) remain unclosed along

km i n t h e y - d i r e c t i o n .

t h e l i n e where t h e h a l o c l i n e disappears because o f decreasing depths. The data o f surveys 18/1 t o 18/3 ( e a r l y summer 1980) show an i n t e n s i v e and l a r g e e d d y l i k e p e r t u r b a t i o n .

The isopycnals a r e d i s p l a c e d upward by

more than 20 m i n t h e c e n t e r o f t h e eddy.

The t o t a l depth i s about 100 in.

The diameter o f t h i s eddy i s more than t w i c e as l a r g e as t h a t o f the,.eddies p r e v i o u s l y observed; i t exceeds 40 km.

The d i f f e r e n c e i n geostrophic c u r -

r e n t between t h e 60 m and 90 m l a y e r s i s about 20 c d s e c . o f D(70,30) f o r t h r e e d i f f e r e n t surveys ( F i g . perturbation.

I n 9 days ( i . e .

The contour maps

6) show t h e e v o l u t i o n o f t h e

between survey 18/1 and 18/2), t h e c e n t e r o f

t h e p e r t u r b a t i o n moves 5 t o 10 m i l e s eastward across t h e isobaths, and i t "escapes"

t h e survey area.

A t t h e p e r i p h e r y o f t h e eddy, t h e l i n e s o f con-

s t a n t RDT become more d i s t o r t e d than i n p r e v i o u s surveys; t h e contour l i n e s on t h e l e f t - h a n d s i d e o f t h e area tend t o become p a r a l l e l t o t h e isobaths, Survey 18/3 (which covers a d i f f e r e n t

w i t h shallower water on t h e r i g h t .

area s e l e c t e d on t h e b a s i s o f t h e observed m i g r a t i o n o f t h e eddy c e n t e r , and which was completed immediately a f t e r survey 18/2) r e v e a l s a " s p l i t t i n g " o f t h e l a r g e eddy i n t o two s m a l l e r ones w i t h diameters o f about 20 km. t i m e o f t h e l a s t survey,

A t the

t h e s p l i t t i n g i s n o t f u l l y completed and t h e p e r -

t u r b a t i o n s have a common area.

I t must a l s o be p o i n t e d o u t t h a t t h e t i m e

e v o l u t i o n o f such an i n t e n s i v e p e r t u r b a t i o n i s uneven.

Between surveys 18/1

and 18/2, t h e time e v o l u t i o n was moderately slow, b u t survey 18/3 shows a "collapse-like

behavior",

i . e changes i n t h e isopycnal depths occur much

f a s t e r than d u r i n g p r e v i o u s days.

This r a p i d s p l i t t i n g o f t h e p e r t u r b a t i o n

leads t o a rearrangement o f t h e v e r t i c a l s t r u c t u r e o f t h e d e n s i t y anomalies. The

isopycnals

gether" f o r 7.5

observed d u r i n g surveys

5

ut

5

18/1 and 18/2 a r e d i s p l a c e d " t o -

8.5, and t h e c r o s s - c o r r e l a t i o n between pressure a t ut

= 7.0 and RDT D(70,30)

i s l a r g e r than 0.95.

For t h e d a t a o f survey 18/3,

t h e l a t t e r c o r r e l a t i o n i s reduced t o 0.8 and l e s s . .We f i n d i t a l s o i n t e r e s t i n g t o analyze t h e temperature f i e l d on given isopycnal surfaces. (above t e h a l o c l i n e )

F i g u r e 7 shows temperature maps on t h e s u r f a c e at = 6.5 f o r surveys 18/1 and 18/2.

Because t h e c o r r e l a t i o n

r a d i i a r e f a i r l y small, these maps were n o t c o n s t r u c t e d by optimal i n t e r p o lation,

b u t by s p l i n e

c e n t e r o f t h e eddy;

interpolation.

t h e l o c a l minimum,

The temperature i s maximum a t t h e l o c a t e d a t a d i s t a n c e o f about 10

447

D(70.301 18/1: 30.-31.05.80

0

Fig.

6.

5

10

15 miles

Maps o f ROT anomalies ( i n dynamic cm) f o r surveys 18/1 to 18/3.

The contour i n t e r v a l surveys 18/2 and 18/3.

i s 0.2 dyn.cm f o r survey 18/2, and 0 . 1 dyn.cm f o r

448

Fig. 7.

15 miles

10

5

0

Maps o f temperature on t h e isopycnal s u r f a c e ut = 6.5 f o r surveys

18/1 and 18/2. The contour i n t e r v a l i s 0 . 5 O C . miles, i s not r e f l e c t e d i n the density f i e l d .

This l o c a l minimum seems t o

have a s t a b l e o r i e n t a t i o n w i t h respect t o t h e c e n t e r o f t h e eddy. v a r i a t i o n s i n temperature a r e l a r g e ( Z 4°C

w i t h e r r o r z 1°C)

The

compared t o

oceanic d a t a (see Woods and M i n n e t t , 1979, who r e p o r t v a r i a t i o n s o f about 0.1"C.)

The temperature d i s t r i b u t i o n on at-surfaces

can be considered a

t r a c e r under t h e assumption t h a t t h e process r e s p o n s i b l e f o r t h e f o r m a t i o n o f t h e anomalies i s slow.

I n such a case, t h e water i n t h e c e n t e r o f t h e

eddy should m i g r a t e w i t h t h e eddy, and t h e e d d y l i k e p e r t u r b a t i o n c o u l d n o t be o f wavelike o r i g i n s i n c e mass i s a c t u a l l y t r a n s p o r t e d i n t h e d i r e c t i o n which would be t h a t o f t h e phase speed.

The o t h e r p o s s i b i l i t y i s t h a t t h e

eddy permanently generates t h a t k i n d o f anomalies.

Another f e a t u r e o f

survey 18/1 i s t h a t t h e s a l i n i t y above t h e h a l o c l i n e i s markedly h i g h e r a t t h e c e n t e r o f t h e eddy than elsewhere (,in pressure coordinate); vides

evidence t h a t

pumping o r m i x i n g processes

upwell

t h i s pro-

salty halocline

waters. F i g u r e 8 shows maps o f RDT D(70,30) o f t h e s i n g l e surveys,

number 19/1.

and temperature a t ut = 6.5 f o r one

A n e g a t i v e RDT p e r t u r b a t i o n i s l o c a t e d

i n t h e upper r i g h t corner o f t h e area, b u t t h e contour l i n e s a r e n o t closed.

449

0

F i g . 8. at

= 6.5

~~

‘15 miles

10

5

Maps o f RDT ( l e f t panel) and temperature on t h e isopycnal surface ( r i g h t panel)

for

The contour i n t e r v a l s a r e 0.1

survey 19/1.

dyn.cm f o r RDT and 0.5OC f o r temperature. Assuming t h a t t h e p e r t u r b a t i o n i s e d d y l i k e , r o u g h l y equal t o 30 t o 40 kin.

t h e diameter appears t o be

The displacements o f t h e thermocline and

h a l o c l i n e appear t o have t h e same sign.

The p a t t e r n o f t h e temperature

f i e l d ( r i g h t panel) i s s i m i l a r t o t h a t o f surveys 18/1 and 18/2:

t h e tem-

p e r a t u r e i s maximum a t t h e c e n t e r o f t h e p e r t u r b a t i o n and a l o c a l minimum i s observed nearby. Some o t h e r p e r t u r b a t i o n s have been observed d u r i n g some o f t h e s i n g l e surveys conducted i n t h e BOSEX area.

The RDT D(70,30) o f survey 17/1 i n d i -

cates a j e t l i k e anomaly (contour l i n e s almost p a r a l l e l t o t h e isobaths) i n t h e western p a r t o f t h e area.

As observed i n t h e surveys o f s p r i n g and

e a r l y summer o f 1980, t h e isopycnals are deeper a t t h e western edge o f the area where t h e water i s shallower. l i k e p e r t u r b a t i o n s with’diameters

The data o f survey 20/1 show t w o eddyo f about 20 km (2Rd).

depressed a t t h e c e n t e r o f b o t h p e r t u r b a t i o n s ,

The thermocline i s

b u t t h e h a l o c l i n e i s de-

pressed i n one case and u p l i f t e d i n t h e other. The processing o f t h e 1981 d a t a i s n o t completed y e t . d e s c r i b e some o f t h e p e r t u r b a t i o n s w i t h o u t f i g u r e s .

Hence, we s h a l l

450

Two surveys

- 22/1

and 22/2

-

were c a r r i e d o u t i n t h e Bornholm Basin a t

t h e end o f A p r i l 1981.

The h a l o c l i n e i n t h e Bornholm Basin i s sharper than

i n t h e B a l t i c Proper.

The Bornholm Basin and t h e S t o l p e Furrow ( i n t h e

e a s t e r n p a r t o f t h a t basin) are t h e regions through which t h e s a l t y N o r t h Sea waters e n t e r t h e B a l t i c Proper i n t h e bottom l a y e r s .

Several d e n s i t y

and ROT anomalies were observed i n the Bornholm Basin, b u t t h e i r s t r u c t u r e i s more complicated than i n t h e BOSEX area.

A c h a r a c t e r i s t i c feature i s the

r a i s i n g o f the isopycnals i n t h e shallower p a r t s o f t h e working area; t h e converse was observed i n t h e BOSEX area.

I n t h e c e n t r a l p a r t of t h e working

area, t h e c r o s s - c o r r e l a t i o n s between t h e displacements o f d i f f e r e n t isopycn a l s are poor:

some displacements even change s i g n over small

v e r t i c a l i n t e r v a l s w i t h i n a given p e r t u r b a t i o n .

(5-;10

m)

Hence, i t i s hard t o be-

l i e v e t h a t t h e observed p e r t u r b a t i o n s are synoptic scale eddies.

Unfortu-

n a t e l y , no e r r o r norm estimates are a v a i l a b l e . I n June o f 1981, f i v e surveys were performed i n t h e Gotland area ( n o r t h

o f t h e BOSEX area) d u r i n g t h e j o i n t Soviet-German Physical/Chemical ment.

maps o f surveys 23/3 t o 23/5. b a t i o n i n RDT D(80,50)

I n survey 23/3 a p o s i t i v e , t o n g u e l i k e p e r t u r -

appears i n t h e upper l e f t p a r t o f t h e area;

p e r t u r b a t i o n extends 20 km i n t h e x - d i r e c t i o n . 23/4),

Experi-

Two d i s t i n c t p e r t u r b a t i o n s and t h e i r e v o l u t i o n can be f o l l o w e d on t h e the

Over t h e n e x t 5 days (survey

t h e p e r t u r b a t i o n seems t o expand along t h e isobaths:

the t i p o f the

tongue migrates 20 km i n t h e y - d i r e c t i o n and t h e tongue widens t o 30 km i n the x-direction.

I n t h e upper p a r t o f t h e p e r t u r b a t i o n , a s l i g h t e d d y l i k e

c e n t e r begins t o t a k e shape.

On the map o f survey 23/5 (8 days l a t e r ) , t h e

w i d t h o f t h e p e r t u r b a t i o n has decreased t o 20 km i n t h e x - d i r e c t i o n , and t h e eddylike center i s stretched out i n the y-direction.

The o t h e r disturbance

i s a n e g a t i v e e d d y l i k e p e r t u r b a t i o n , 15 t o 20 km i n diameter, l o c a t e d i n t h e right-central 23/4,

p a r t o f t h e map o f survey 23/3.

Between surveys 23/3

and

we c o l l e c t e d data along a s e c t i o n o f t h e eddy w i t h a p r o f i l i n g i n t e r -

val o f 1 mile.

The r e s u l t s show t h a t t h e RDT v a r i e s smoothly between t h e

g r i d s t a t i o n s o f t h e survey and t h a t i n t e r p o l a t i o n gives n e a r l y t h e same p i c t u r e as do measurements on a f i n e h o r i z o n t a l scale. 23/4,

On t h e map o f survey

t h e eddy i s a t t h e same place, b u t i n t h e upper l e f t p a r t o f t h e eddy

t h e s t r e a m l i n e s o f t h e r e l a t i v e v e l o c i t y have become denser because t h e positlve

RDT p e r t u r b a t i o n described above i s impinging on t h e negative

eddylike perturbation.

A f t e r 8 days (survey 23/5),

t h e eddy has migrated

about 11-14 km along t h e isobaths towards t h e n o r t h e a s t e r n corner o f t h e area, i . e . w i t h shallow water on t h e r i g h t .

M i g r a t i o n along t h e isobaths i s

c h a r a c t e r i s t i c o f b o t h p e r t u r b a t i o n s i n s p i t e o f t h e f a c t t h a t t h e average bottom slopes have completely d i f f e r e n t o r i e n t a t i o n s below t h e d i f f e r e n t perturbations.

451

THEORETICAL INTERPRETATION G e n e r a l l y speaking, t h e t h e o r y o f s y n o p t i c scale motions i s complicated and needs f u r t h e r study.

The f i r s t eddies observed i n t h e ocean were i n t e r -

p r e t e d as t h e s u p e r p o s i t i o n o f l i n e a r b a r o t r o p i c and b a r o c l i n i c Rossby waves (Koshlyakov and Grachev, 1973; McWilliams and F l i e r l , 1976).

I n t h i s sec-

t i o n , we do n o t t r y t o develop general t h e o r i e s , b u t we l o o k f o r t h e simpl e s t p o s s i b l e quasi-geostrophic

motions c o n s i s t e n t w i t h parameter values

c h a r a c t e r i s t i c o f t h e B a l t i c Sea, and we p o i n t o u t some d i f f e r e n c e s between t h e l i n e a r regimes o f t h e oceans and o f deep seas.

I n p a r t i c u l a r , some

p e c u l a r i t i e s o f topographic waves and b a r o c l i n i c i n s t a b i l i t y o f sheared mean c u r r e n t s a r e discussed i n connection wifih observational r e s u l t s . L e t x,y,z and n o r t h ,

be C a r t e s i a n coordinates w i t h x and y d i r e c t e d t o t h e e a s t

and z p o i n t i n g down w i t h z = 0 a t t h e undisturbed surface.

sketch o f t h e model i s presented i n Figure 9. sloping i n the x-direction,

i.e.

A

Consider a b a s i n w i t h bottom

w i t h depth H = Ho + a x , and assume t h a t a

<< 1, so t h a t as a f i r s t approximation t h e d i f f e r e n c e between H and Ho can be neglected f o r moderate h o r i z o n t a l scales except i n terms i n v o l v i n g t h e depth g r a d i e n t s .

L e t us assume t h a t t h e water column c o n s i s t s o f two l a y e r s

o f thicknesses hl

and h2 r e s p e c t i v e l y , and constant ( b u t d i f f e r e n t ) V a i s a l a

frequencies N1 and N2. a t the interface.

A t t h e same time t h e d e n s i t y i s assumed continuous

Consider a l s o a mean f l o w

i s c o n s t a n t i n t h e upper l a y e r (Vs) (Vs

-

Vb)/hp,in

t h e lower l a y e r .

v(z) i n t h e y - d i r e c t i o n , which

and has a constant v e r t i c a l g r a d i e n t ,

The E a r t h ' s r o t a t i o n i s taken i n t o account

by t h e usual 8-plane approximation, f = f o + By, where t h e d i f f e r e n c e between t h e C o r i o l i s parameter f and t h e constant f o can be neglected except i n t h e y - d e r i v a t i v e o f f.

The l i n e a r i z e d quasi-geostrophic

equation ex-

p r e s s i n g t h e c o n s e r v a t i o n o f p o t e n t i a l v o r t i c i t y can be w r i t t e n as f o l l o w s

:ig.

9.

Sketch o f t h e t w o - l a y e r model.

452

where JI i s t h e stream f u n c t i o n , t denotes t h e t i m e v a r i a b l e and A Laplace's The s u b s c r i p t k = 1,2 i d e n t i f i e s t h e upper and lower l a y e r r e -

operator. spectively.

The v e r t i c a l boundary c o n d i t i o n s w i l l be g i v e n l a t e r .

Their

form depends on t h e s o l u t i o n one i s l o o k i n g f o r , and t h e i r p h y s i c a l meaning i s t h e requirement o f zero normal v e l o c i t y a t t h e surface and a t t h e bottom and o f c o n t i n u i t y a t t h e i n t e r f a c e . A

Topographic

Waves

L e t us f i r s t consider t h e case o f topographic waves (Rhines, w i t h o u t mean f l o w

= 0).

model (hl waves.

(i = 0).

1970)

and, f o r s i m p l i c i t y , l e t us analyze a one-layer

The s u b s c r i p t s can then be o m i t t e d f o r these topographic

We l o o k f o r wave s o l u t i o n s o f t h e form

JI = O(z) exp [ i ( k x where $(z)

+

ly

-

wtll

(3)

i s t h e v e r t i c a l s t r u c t u r e f u n c t i o n , k and 1 a r e t h e wavenumbers The s u b s t i t u t i o n o f (3) i n t o equation (2) g i v e s t h e

and w i s t h e frequency.

f o l l o w i n g e q u a t i o n f o r $(z): d

2

5

- (q2 (?9) dz f

where q2 = k2 + 1'.

*dz= o

+

E) $ w

= 0,

The boundary c o n d i t i o n s are

a t z = ~ ,

2 !!t=-T@ atz=H. dz The 'system (4).

(5), (6)

has two classes o f s o l u t i o n s depending on

whether q2 + pk/w i s p o s i t i v e o r negative. 2 I f 0 + pk/w > 0, t h e s o l u t i o n i s

453

and t h e transcendental equation d e f i n i n g w i s

Parameter values c h a r a c t e r i s t i c o f t h e BOSEX area are: sec-l,

N =

lo-'

sec-l,

I Axl = I AY I

H = 100 m,

01

f = 1.25~10-~

= 5 ~ 1 0 - ~p , = 1.3~10-'~ cm-l sec-l, and

= 40 km, where Ax = 2n/k, and A = 2n/l. For these y- 2 values, t h e second term under t h e r a d i c a l i s o f order 10 . A s long as t h e parameters vary w i t h i n reasonable l i m i t s , t h e r o l e o f p does n o t increase

wavelengths

considerably.

Therefore,

i n t h e Ba1tj.c Sea, t h e p - e f f e c t can be neglected

f o r t h e " f a s t b a r o c l i n i c " waves (Rhines,

1977), and equation (8) takes t h e

form o f t h e well-known d i s p e r s i o n r e l a t i o n f o r topographic waves

I n t h e l i m i t NrlH/f

>> 1, (9) reduces t o t h e d i s p e r s i o n equation f o r

bottom-trapped topographic waves, w = -N a s i n e , where 0 i s t h e angle between t h e wave v e c t o r and t h e bottom slope. For NqH/f << 1, equation (9) 2 becomes w = - a l f / r l H , a p p r o p r i a t e f o r b a r o t r o p i c waves. Since f3 has no e f f e c t on t h e s o l u t i o n ,

t h e o r i e n t a t i o n o f t h e bottom slope and o f t h e

c o o r d i n a t e axes can be a r b i t r a r y . I f q2 + pk/w < 0, t h e s o l u t i o n describes slow b a r o c l i n i c waves.

p-effect

dominates t h a t o f t h e bottom slope;

The

t h e presence o f a slope i s

i m p o r t a n t , b u t t h e v a r i a t i o n o f i t s magnitude has o n l y minor i n f l u e n c e .

For

t h e parameter values corresponding t o t h e B a l t i c Sea, t h e p e r i o d s o f these waves are l o n g e r than years.

Therefore, such waves a r e n o t r e l e v a n t t o t h e

study o f s y n o p t i c v a r i a b i l i t y . Consequently, i n t h e absence o f a mean shear f l o w and w i t h a l i n e a r l y s l o p i n g bottom,

only bottom-intensified o r nearly barotropic ( f o r

wavelengths) topographic waves can e x i s t .

large

These waves have no modal s t r u c -

t u r e and a s i n g l e frequency w corresponds t o each p a i r o f wavenumbers k and 1.

As l o n g as d+(z)/dz

does n o t change i t s ( p o s i t i v e ) s i g n i n t h e v e r t i c a l

d i r e c t i o n , t h e displacements o f t h e f r e e surface and o f t h e isopycnal surfaces have t h e same sign.

This i s t h e reason why no attempt was made t o

d i s t i n g u i s h cyclones and a n t i c y c l o n e s i n t h e d e s c r i p t i o n o f t h e experimental data. then,

I f t h e eddies a r e formed by a s u p e r p o s i t i o n o f topographic waves, u n l i k e t h e oceanic case,

an a n t i c y c l o n e has a c o l d c e n t e r i n the

t h e r m o c l i n e and a s a l t y c e n t e r i n t h e h a l o c l i n e ; a cyclone has warm and

454

f r e s h c e n t e r s r e s p e c t i v e l y i n t h e thermo- and h a l o c l i n e . Since

N # constant f o r t h e observed s t r a t i f i c a t i o n , t h e problem consis-

t i n g o f equations ( 4 ) , d i f f e r e n c e method.

(5),

i s homogeneous, so t h a t ,

quency

ui

( 6 ) was a l s o solved n u m e r i c a l l y u s i n g a f i n i t e

The system o f l i n e a r equations f o r d i s c r e t e @(z) values i n order t o obtain n o n t r i v i a l solutions, the f r e -

has t o be such t h a t t h e determinant o f t h e system i s equal t o zero.

F i g u r e 10 shows v a r i o u s p r o f i l e s o f $(z) summer s t r a t i f i c a t i o n . of A

Y

calculated f o r a typical

The v a r i o u s p r o f i l e s correspond t o d i f f e r e n t values

(we assume k = 0), and t h e y are normalized by t h e c o n d i t i o n

F i g . 10.

V e r t i c a l s t r u c t u r e f u n c t i o n o f topographic waves, $(z),

August s t r a t i f i c a t i o n .

f o r the

The v a r i o u s curves correspond t o d i f f e r e n t values o f

The wavenumber i n t h e x - d i r e c t i o n , A,,. cases.

k,

i s s e t equal t o zero i n a l l

455

S i n c e g(z) r e p r e s e n t s t h e a m p l i t u d e o f t h e stream f u n c t i o n , i t i s p r o F o r A = 1 0 km, we f i n d t h a t t h e Y There a r e no v e r t i c a l shear i n

portional t o the horizontal velocity.

motion i s concentrated i n t h e bottom layers. the

horizontal

velocity

and

no

displacements o f

the

isopycnals

i n the

thermocline. F o r A = 200 km, t h e f u n c t i o n g(z) corresponds t o t h e baroY t r o p i c regime, and t h e whole w a t e r column moves w i t h t h e same v e l o c i t y . For i n t e r m e d i a t e wavelengths,

t h e r e a r e v e r t i c a l shears o f v e l o c i t y i n b o t h t h e

t h e r m o c l i n e and t h e h a l o c l i n e .

The i s o p y c n a l displacements i n t h e thermo-

5

A < 80 km. y .The o b s e r v a t i o n s p r e s e n t e d i n F i g u r e 4 can be modeled by t h e superposi-

c l i n e a r e l a r g e s t f o r 20 km t i o n o f two p l a n e waves, km. are:

F o r such a model,

+

c = (0;

( k , 1) and (-,k,l),w i t h Ax = 40 km, and A = -40 Y t h e n u m e r i c a l l y d e t e r m i n e d phase speed and p e r i o d

3 ) c d s e c ; T = 15.6 days.

The e s t i m a t e d m i g r a t i o n speed o f

t h e RDT p e r t u r b a t i o n between surveys 1 5 / 1 and 15/2 i s 2 cm/sec. a c c o u n t t h e u n c e r t a i n t i e s a f f e c t i n g t h e parameter v a l u e s , between t h e model and t h e o b s e r v a t i o n i s n o t s i g n i f i c a n t . t h e speed o f m i g r a t i o n o f t h e RDT p e r t u r b a t i o n ,

Taking i n t o

the difference

The d i r e c t i o n and

as w e l l as t h e presence o f

g e o s t r o p h i c v e l o c i t y shears i n t h e t h e r m o c l i n e and i n t h e h a l o c l i n e , c o r respond s a t i s f a c t o r i l y t o t h e t o p o g r a p h i c wave model. The o b s e r v a t i o n s shown i n F i g u r e 5 can be i n t e r p r e t e d i n a s i m i l a r way.

t

U s i n g e s t i m a t e d wavelengths Ax = 25 km and A = -40 km, t h e t h e o r y y i e l d s Y = (0; 1.9) cm/sec and T = 23.8 days. On t h e b a s i s o f t h e e x p e r i m e n t a l d a t a , t h e m i g r a t i o n speed o f t h e RDT p e r t u r b a t i o n i s 1 . 5 cm/sec.

Hence, we be-

l i e v e t h a t t h e c o n c l u s i o n o f t h e p r e v i o u s paragraph i s a l s o v a l i d i n t h i s case. B.

Baroclinic i n s t a b i l i t y L e t us now c o n s i d e r e q u a t i o n (2)

with

p =

0, a p p l i e d t o a t w o - l a y e r

f l u i d w i t h o u t d e n s i t y jump, i n t h e presence o f a sheared mean f l o w , i ( z ) , described a t t h e beginning o f t h i s section.

as

We assume t h e s o l u t i o n t o b e o f

t h e form

$k = Re ($,(z) where b o t h gk(z)

exp[il(y

-

ct)]]

s i n kx

and t h e phase speed,

s a t i s f i e s t h e equation

c,

, a r e complex.

(10) The f u n c t i o n g k

4 56

s u b j e c t t o t h e f o l l o w i n g boundary c o n d i t i o n s : a t z = 0,

dz

The general s o l u t i o n o f equation (11) i s a sum o f h y p e r b o l i c s i n e and cosine, where t h e c o e f f i c i e n t s must be determined so as t o s a t i s f y t h e boundary c o n d i t i o n s (12)-(15).

The system o f l i n e a r equations f o r t h e determin-

a t i o n o f t h e c o e f f i c i e n t s i n t h e general s o l u t i o n i s homogenous; i n o r d e r t o o b t a i n a n o n t r i v i a l s o l u t i o n , t h e phase speed c must be such t h a t t h e d e t e r minant i s equal t o zero.

Therefore, c must s a t i s f y a q u a d r a t i c equation.

I n some parameter range, t h e phase speed has a nonzero imaginary p a r t ; t h e corresponding s o l u t i o n s describe unstable waves.

The c a l c u l a t i o n s r e p o r t e d

here were made by M. Pajuste. I n t h i s paper, we p r e s e n t o n l y t h e r e s u l t s f o r t h e one-layer case (hl

0).

(The s o l u t i o n s f o r t h e two-layer

cated.)

=

b u t more compli-

The phase speed i s given by

vs c =

case a r e s i m i l a r ,

+ Vb + c 0 2

--vs Y

vb [ ( V s

vs

-

Vb 2

t

{(

-

Vb)(coth y

+

co 2

1

1 - -1 1(

-

co ( t a n h y

-

y ) I l +i

,

where co i s the phase speed o f topographic waves w i t h o u t mean f l o w (co < 0 if

c1

> 0) and y = NrlH/f.

In general, t h e phase speed i s complex, c = c r

t h e stream f u n c t i o n , JI. i s

+ ic

i' The s o l u t i o n f o r

JI = Re((@, + iQi) e x p [ i l ( y - c r t ) ] ] s i n kx exp(1 cit) = I $I cos (Icy - c r t + e(z)]) s i n kx exp(1 tit),

457 where (Iand , Oi f u n c t i o n $(z),

a r e t h e r e a l and imaginary p a r t s o f t h e v e r t i c a l s t r u c t u r e

I $1

2 4 , and t h e z-dependent phase, e ( z ) , = ($, 2 + (I~)

i s given

by

I f t h e phase speed has a nonzero imaginary p a r t , ci

# 0, we a l s o have

Q i # 0; t h e waves a r e then unstable, and t h e i r amplitude increases w i t h t i m e as exp(1

tit).

The phase i s n o t constant v e r t i c a l l y , and t h e axes o f eddy-

l i k e p e r t u r b a t i o n s are i n c l i n e d w i t h re?pect t o t h e v e r t i c a l . The t w o - l a y e r model w i t h p = 0 contains, as p a r t i c u l a r cases, t h e model o f Tang (1975) (corresponding t o a = 0, Vb = O), and t h e b a r o c l i n i c i n s t a b i l i t y model o f Eady (1949) ( a = 0, Vb = 0, hl = 0). For t h e c a l c u l a t i o n s described h e r e a f t e r , we used t h e f o l 1owing param e t e r values:

2.5-10-2 s e c - l ;

H = 100 in,

hl

= 60 m, h2 = 40 m, N1 = lo-* sec-’,

f o r t h e one-layer case, we chose N = 1.25.10

2

sec-l.

N2

=

Since

t h e observed RDT anomalies were almost c i r c u l a r , o n l y waves f o r which Ax = A

Y

( o r k = 1) were s t u d i e d . The i n s t a b i l i t y r e g i o n f o r a = 0, h

1

= 0 i s independent o f t h e mean

d e r i v e d by Eady (1949).

(A > 2.6 f l Rd) a l l t h e waves are unstable, as Y The same r e s u l t holds f o r 01 = 0, hl # 0, b u t t h e

critical

equal

and f o r y < 2.399

flow,

values.

wavelength

is

to

44.5

km f o r t h e above-given

parameter

I f a > 0, t h e i n s t a b i l i t y r e g i o n depends on b o t h t h e wavelength and

t h e mean flow,

b u t waves a r e more unstable i f Vs

-

Vb > 0.

I n other words,

t h e s t a b i l i t y domain i s s m a l l e r when t h e d i r e c t i o n o f t h e upper l a y e r mean f l o w r e l a t i v e t o t h e bottom c u r r e n t i s opposed t o t h a t o f t h e phase speed o f t h e topographic waves. Two-folding times f o r t h e amplitudes o f t h e unstable waves are presented i n F i g u r e 11 as f u n c t i o n o f t h e wavelength A o f t h e mean c u r r e n t Vs and t w o - l a y e r

-

Vb.

f o r d i f f e r e n t shears Y’ For a = 0, t h e r e s u l t s obtained from t h e one-

models a r e close,

r e q u i r e s much g r e a t e r values of Vs model.

b u t f o r a = 5.10-4

-

t h e one-layer model

Vb f o r i n s t a b i l i t y than t h e two-layer

According t o t h e two-layer model, f o r a mean c u r r e n t d i f f e r e n c e o f

2.5 cm/sec between t h e s u r f a c e and bottom l a y e r s , t h e amplitude o f t h e most u n s t a b l e waves doubles i n 10 days. B a l t i c Sea. t o 5 Rd).

Both values are q u i t e r e a l i s t i c f o r t h e

These most u n s t a b l e waves correspond t o A ?? 50 t o 60 km (E 4 Y The dominating wavelength o f t h e RDT p e r t u r b a t i o n observed d u r i n g

surveys 1 8 / 1 and 18/2, estimated by t h e c o r r e l a t i o n f u n c t i o n , i s 80 t o 90 km; t h i s i s somewhat l a r g e r t h a n t h e scale o f t h e most unstable waves calcul a t e d from t h e b a r o c l i n i c i n s t a b i l i t y theory.

This d i f f e r e n c e , however, i s

4 58

I

a)

C)

(days) T2

241

I

16

i

8-

\. -.-.-.-.-.10.0

d)

i g . 11.

Two-folding times (T2)

f o r the amplitudes o f t h e u n s t a b l e waves as

The v a r i o u s curves correspond t o d i f f e r e n t ‘unctions o f t h e wavelength A Y’ Panels a and b show t h e r e s u l t s ,slues o f t h e mean v e l o c i t y shear Vs - Vb. t h e one-layer model, panels c and d those o f t h e t w o - l a y e r model. 4 lottom slope ci = 0 f o r panels a and c, and CY = 5.10 f o r b and d.

If

The

459

reasonably small, and we suggest t h a t t h i s RDT p e r t u r b a t i o n was generated by When t h e amplitude o f t h e wave reaches some c r i t i -

baroclinic instability. cal

value,

describe

t h e l i n e a r i z e d t h e o r y presented above ceases

the

further

development o f t h e waves:

growth p r e d i c t e d by (17)

t o be v a l i d t o

t h e i n f i n i t e amplitude

i s l i m i t e d by nonlinear,processes.

The data o f

survey 18/3 show t h e s p l i t t i n g o f a l a r g e and i n t e n s i v e eddy i n t o two s m a l l e r ones,

and t h a t i s one p l a u s i b l e mechanism which would l i m i t the

amp1 itude growth.

I t must be p o i n t e d o u t t h a t such quasi-geostrophic waves i n t h e presence o f shear mean f l o w a r e v e r y s e n s i t i v e t o parameter v a r i a t i o n s . i n c l i n a t i o n o f the v e r t i c a l

oceanic (Koshlyakov and Grachev, the theoretical

Some

a x i s o f p e eddy i s c h a r a c t e r i s t i c o f both 1973) and B a l t i c f i e l d observations, b u t

phase d i s t r i b u t i o n e(z)

v e r t i c a l g r a d i e n t s o f b o t h signs.

o f t h e unstable waves can have

I n the one-layer model, t h e amplitude

o f t h e unstable waves above a s l o p i n g bottom has maxima a t t h e surface and a t t h e bottom.

I n t h e two-layer

model,

( 0I

i s maximum a t t h e i n t e r f a c e

(upper boundary of t h e h a l o c l i n e ) , and t h e amplitude decreases more r a p i d l y towards t h e bottom than towards t h e surface. solutions

for

the

above-mentioned models.

For s t a b l e waves t h e r e are t w o I n the one-layer

model,

one

v e r t i c a l s t r u c t u r e f u n c t i o n $ ( z ) decreases monotonously w i t h depth, whereas t h e o t h e r increases.

For t h e two-layer model, b o t h $(z)

are very s i m i l a r ;

t h e y a r e maximum a t t h e i n t e r f a c e and decrease f a s t e r towards t h e bottom t h a n towards t h e s u r f a c e (as f o r t h e unstable waves o f t h i s model). The l i n e a r quasi-geostrophic f e r e n t f r o m t h a t o f t h e ocean.

regime o f t h e B a l t i c Sea i s somewhat d i f I n t h e B a l t i c , t h e e f f e c t o f t h e bottom

slope overwhelms t h e p l a n e t a r y p - e f f e c t i n t h e constant slope model, b u t the r o l e o f t h e Rossby deformation r a d i u s as determinator o f t y p i c a l h o r i z o n t a l scales i s common t o b o t h t h e B a l t i c and t h e oceanic cases.

The mean c u r r e n t

shear i n t r o d u c e s new types o f waves, b u t they a r e s t i l l i n f l u e n c e d by the s l o p i n g bottom.

It should be emphasized t h a t t h e assumption o f a constant

bottom slope i s a s i m p l i f i c a t i o n , l i s parameter,

and t h a t t h e r e a l bottom topography i s

t h i s i s i n c o n t r a s t t o t h e r e g u l a r v a r i a t i o n o f t h e Corio-

very i r r e g u l a r :

which dominates ocean dynamics.

The p e r t u r b a t i o n s o f t h e

bottom topography and o f t h e atmospheric f o r c i n g , which can be important c o n t r i b u t o r s t o t h e dynamics o f synoptic scale motions, a r e n o t considered here. ON THE ESTIMATION

OF ABSOLUTE VELOCITIES

The c l a s s i c a l dynamic method (Fomin,

1964) allows t h e c a l c u l a t i o n o f

r e l a t i v e geostrophic c u r r e n t s from d e n s i t y data.

For t h e determination o f

a b s o l u t e v e l o c i t i e s , i t i s necessary t o know t h e c u r r e n t a t some reference

460

l e v e l e i t h e r from d i r e c t measurements (McWilliams,

1976) o r as a r e s u l t o f

The o l d i d e a t h a t deep water v e l o c i t i e s are small does n o t f i t

speculation.

i n t o d a y ' s conceptions.

S c h o t t and Stommel (1978) proposed t h e b e t a - s p i r a l

method t o overcome t h e problem o f the r e f e r e n c e l e v e l v e l o c i t y f o r l a r g e scale currents.

T h i s method uses t h e geostrophic r e l a t i o n s t o g e t h e r w i t h

t h e l i n e a r equation o f v o r t i c i t y conservation on a p-plane and i t assumes the immiscibility o f the density s t r a t i f i c a t i o n . The s y n o p t i c eddies cannot be t r e a t e d by t h e p - s p i r a l method, b u t t h e g e n e r a l i z a t i o n proposed by Korotayev and Shapiro (1978) a l l o w s t h e c a l c u l a t i o n o f t h e a b s o l u t e v e l o c i t y o f n o n s t a t i o n a r y quasi-geostrophic c u r r e n t s and eddies.

I n t h i s s e c t i o n , we use t h e method o f Korotayev and s a p i r o

w i t h a s l i g h t l y d i f f e r e n t formulation.

We choose t o use d e n s i t y as t h e

v e r t i c a l coordinate, w i t h t h e hope t h a t these "Lagrangian" coordinates m i g h t l e a d t o b e t t e r v e r t i c a l r e s o l u t i o n than " E u l e r i a n " pressure coordinates f o r t h e case o f t h e v e r y sharp d e n s i t y l a y e r i n g observed i n t h e B a l t i c . For t h e v e r t i c a l d i s c r e t i z a t i o n , consider a m u l t i - l a y e r e d water column consisting o f N layers o f constant densities.

The p o t e n t i a l v o r t i c i t y con-

s e r v a t i o n equation, which holds f o r each l a y e r , has t h e form

where u k and vk are t h e v e l o c i t i e s , o f the k-th layer.

Decompose t h e

6,

t h e v o r t i c i t y , and hk t h e t h i c k n e s s

By d e f i n i t i o n ,

i n t o a reference

leve

value, denoted by an overbar, p l u s a value r e l a t i v e t o t h a t r e f e r e n c e

velocities

and t h e v o r t i c i t y

eve1

denoted by a prime, as f o l l o w s : Uk=

-u +

Vk=

i

u;(

+ v;(

, ,

t,=E+t;,. Note t h a t t h e reference l e v e l values a r e independent o f depth ( o r l a y er).

ti

I f t h e d a t a o f two r a p i d l y succeeding surveys a r e a v a i l a b l e , uk, v '

k'

and hk as w e l l as t h e i r t i m e and space d e r i v a t i v e s can be c a l c u l a t e d

u s i n g t h e geostrophic r e l a t i o n s f o r t h e v e l o c i t i e s and t h e d e f i n i t i o n o f relative vorticity. S u b s t i t u t i n g (19) can be o b t a i n e d

i n t o (18),

the f o l l o w i n g system o f l i n e a r equations

461 5

Xi + Fk = 0,

2 Aki i=l

where t h e Xi's

k = l,N

a r e f u n c t i o n s o f t h e unknown reference l e v e l values

and where t h e Aki's

and F k ' s depend o n l y on t h e r e l a t i v e values o f t h e

v a r i a b l e s (which a r e known from t h e observations):

I n order t o solve

(ZO), one must t a k e N 2 5.

c l u d e t h e s u r f a c e and/or

There i s no need t o i n -

bottom l a y e r s among t h e l a y e r s s e l e c t e d f o r t h e

s o l u t i o n o f t h e system. I f t h e o b s e r v a t i o n a l d a t a are w i t h o u t e r r o r s and (18) holds e x a c t l y ,

and i f N > 5, o n l y 5 equations a r e l i n e a r l y independent and t h e remaining (N

-

5)

equations a r e l i n e a r combinations o f t h e former.

because o f e r r o r s and s m a l l - s c a l e noise, (20)

I n practice,

i s overdetermined f o r N > 5,

and t h e s o l u t i o n can be found by a l e a s t squares method, i . e . by m i n i m i z i n g t h e sum

R =

N

5

t ( 2 Aki Xi

k=l

i=l

+ Fk)

2

.

(23)

T h i s procedure i s f o l l o w e d a t every p o i n t x, y o f t h e d a t a g r i d . values o f

i,

and ag/ax,

&ay

The

are calculated separately despite the f a c t

Z9P

Fig.

12.

Estimated a b s o l u t e v e l o c i t i e s f o r t h e near-surface l a y e r ( l e f t )

and on t h e ut = 8.5 surface ( r i g h t ) f o r survey 18/1.

An arrow whose l e n g t h

equals t h e i n t e r p o l a t i o n s t e p corresponds t o a v e l o c i t y o f 10 cm/sec. t h a t t h e y a r e r e l a t e d through s p a t i a l d e r i v a t i v e s . enormously complicated

if

the horizontal

But t h e problem becomes

f i e l d s are g i v e n as numerical

t a b l e s and t h e equations solved f o r a l l p o i n t s simultaneously. For a t e s t o f t h e method, we chose t h e data o f surveys 1 8 / 1 and 18/2 f o r which t h e t i m e i n t e r v a l i s 9 days.

The pressure values as f u n c t i o n s o f

d e n s i t y were i n t e r p o l a t e d by optimal i n t e r p o l a t i o n t o a denser g r i d (spacing o f 0.25 at u n i t s ) and t h e values o f Aki

and Fk were c a l c u l a t e d .

The t i m e

d e r i v a t i v e s were c a l c u l a t e d by one-sided d i f f e r e n c e s and t h e space d e r i v a t i v e s by c e n t r a l d i f f e r e n c e s , t h e l a t t e r from t h e d a t a o f survey 18/1. The r e f e r e n c e l e v e l was chosen a t t h e surface, involved only intermediate layers w i t h

b u t t h e m i n i m i z a t i o n o f (23)

N = 8 t o 11.

The estimated a b s o l u t e v e l o c i t i e s a r e presented i n F i g u r e 12 f o r t h e s u r f a c e l a y e r and on t h e ut = 8.5 surface, which i s i n t h e middle o f t h e halocline.

The d i r e c t i o n s o f t h e v e l o c i t y v e c t o r s r e p l i c a t e t h e p a t t e r n o f

463 t h e RDT p e r t u r b a t i o n shown i n F i g u r e 6, c i e n t l y smooth.

However,

and the v e l o c i t y f i e l d i s s u f f i -

we t h i n k t h a t t h e magnitudes o f t h e reference

l e v e l (surface)

c u r r e n t s are underestimated,

should be weaker

or even reverse.

and t h a t t h e bottom c u r r e n t s

I n m i n i m i z i n g (23), t h e dominant t e r m s o f t h e system (20) were Ak4X4 and Ak5X5,

which represent t h e advection o f reference l e v e l v o r t i c i t y by t h e

r e l a t i v e velocity. a r e one order

The o t h e r terms o f (20),

o f magnitude s m a l l e r .

a f t e r l e a s t squares f i t t i n g ,

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

r e s u l t s were

o b t a i n e d by Korotayev and Shapiro (1978), b u t they estimated t h e absolute v e l o c i t y a t one l o c a t i o n only.

Our l a r g e r h o r i z o n t a l data s e t allows us t o

compare "independently" estimated values,. o f

The c o r r e l a t i o n between these values i s bad, v o r t i c i t y g r a d i e n t s being s y s t e m a t i c a l l y higher.

Hence,

we

are unable t o estimate t h e balance o f

terms i n t h e v o r t i c i t y c o n s e r v a t i o n equation and t o determine which t e r m s are t h e most i m p o r t a n t c o n t r i b u t o r s t o t h e dynamics o f synoptic s c a l e processes. Nevertheless, we t h i n k t h a t our attempt t o estimate absolute v e l o c i t i e s f o r s y n o p t i c s c a l e processes was p a r t i a l l y successful and t h a t t h e s h o r t comings a r e due t o t h e q u a l i t y o f t h e d a t a r a t h e r than t o t h e method.

The

data were n o t c o l l e c t e d w i t h t h e d i r e c t purpose o f e s t i m a t i n g t h e absolute v e l o c i t y , and t h e temporal and s p a t i a l r e s o l u t i o n s were probably n o t optimal f o r t h e c a l c u l a t i o n o f t h e high-order d e r i v a t i v e s which are necessary f o r t h e method. DISCUSSION AND CONCLUSIONS

First,

l e t us summarize t h e p u r e l y experimental r e s u l t s obtained from

t h e CTD surveys:

1)

t h a t t h e s t r a t i f i c a t i o n o f t h e B a l t i c Proper i s

It i s evident

d i s t u r b e d by low-frequency motions.

Such motions can be d i s t i n c t l y sepa-

r a t e d from s h o r t - t e r m v a r i a t i o n s ( w i t h p e r i o d s s h o r t e r than one day),

es-

p e c i a l l y i n the halocline.

2)

The most common s p a t i a l s t r u c t u r e o f t h e s y n o p t i c scale perturba-

t i o n s c o n s i s t s o f "mountains" and " v a l l e y s " o f isopycnal surfaces.

For many

p e r t u r b a t i o n s t h e geostrophic streamlines o f r e l a t i v e v e l o c i t y are closed, being nearly c i r c u l a r .

For t h a t reason we can consider them t o be eddies.

I n t h e most d i s t i n c t i v e eddies, perturbation.

t h e isopycnals r i s e i n t h e center o f t h e

464

3)

The t y p i c a l h o r i z o n t a l dimensions o f t h e eddies a r e o f t h e o r d e r

o f 2 t o 6 Rd (Rd E 1 0 km). the vertical.

4)

The eddy a x i s can be i n c l i n e d w i t h r e s p e c t t o

,

The usual d i r e c t i o n o f m i g r a t i o n o f t h e eddies i s along t h e aver-

aged isobaths w i t h shallower water on t h e r i g h t .

The t y p i c a l m i g r a t i o n

speed i s a few cm/sec. 5)

The v e r t i c a l s y n o p t i c s c a l e displacements o f t h e isopycnals can be

more than 20 m.

The r e l a t i v e c u r r e n t s i n t h e eddies can exceed 10 t o 1 5

cm/sec.

6)

The t y p i c a l l i f e t i m e o f t h e eddies i s more t h a n 10 days.

The

i n t e n s i f i c a t i o n o f an eddy was documented, as was t h e s p l i t t i n g o f a l a r g e and i n t e n s i v e eddy i n t o two s m a l l e r ones.

7)

In

The l a r g e and i n t e n s i v e eddies r e v e a l s i g n i f i c a n t t h e r m o c l i n i c i t y .

t h e i n t e r m e d i a t e l a y e r between the thermocl ine and t h e h a l o c l ine,

the

temperature d i s t r i b u t i o n on a f i x e d d e n s i t y s u r f a c e can have v a r i a t i o n s o f up t o 4 O C .

8)

The eddies and o t h e r s y n o p t i c s c a l e p e r t u r b a t i o n s t e n d t o have

l a r g e r dimensions along t h e averaged isobaths than along t h e bottom slope. The s t r e a m l i n e s o f r e l a t i v e c u r r e n t s can i n t e r s e c t t h e bottom contours where t h e depth decreases.

From the section e n t i t l e d "theoretical interpretation",

the following

p o i n t s can be made:

1)

The speed and t h e d i r e c t i o n o f m i g r a t i o n o f t h e eddies can be

e x p l a i n e d i n terms o f topographic waves.

Also,

t h e v e r t i c a l shears o f t h e

h o r i z o n t a l c u r r e n t s i n t h e thermocline and i n t h e h a l o c l i n e may correspond to

those

o f topographic waves.

The magnitude o f

the current

shear

is

g r e a t e r i n t h e h a l o c l i n e t h a n i n t h e thermocline, f o r topographic waves, and t h e shear has t h e same s i g n i n b o t h l a y e r s .

2)

I n t h e simple model o f b a r o c l i n i c i n s t a b i l i t y , t h e wavelengths o f

t h e most u n s t a b l e waves agree w e l l w i t h t h e dimensions o f t h e l a r g e r eddies.

A v e r t i c a l shear o f t h e mean f l o w o f t h e order o f a few cm/sec can produce reasonable growth r a t e s f o r unstable waves. t h a t t h e observed eddies can be generated

T h i s leads us t o t h e hypothesis by b a r o c l i n i c

instability o f

sheared mean flows. Comparing our r e s u l t s t o those o b t a i n d f o r t h e ocean, we note t h a t t h e nondimensional diameters o f t h e eddies ( w i t h Rd as t h e s c a l e u n i t ) a r e t h e same i n t h e B a l t i c and i n t h e ocean. a reduced model o f t h e ocean.

The B a l t i c Sea, however, i s n o t simply

The m i g r a t i o n and t h e e v o l u t i o n o f t h e eddies

a r e c o n t r o l l e d by t h e bottom topography r a t h e r t h a n by t h e p l a n e t a r y effect.

From a t h e o r e t i c a l p o i n t o f view,

p-

i t i s only f o r the barotropic

465

case t h a t t h e p - e f f e c t ( i n t h e ocean) can be simply replaced by the i n f l u ence o f t h e bottom slope ( i n t h e B a l t i c ) .

I n t h e s t r a t i f i e d water o f t h e

B a l t i c , t h e e f f e c t o f bottom topography completely dominates t h a t o f beta, and many o f t h e oceanic t h e o r e t i c a l r e s u l t s cannot be d i r e c t l y a p p l i e d t o t h e B a l t i c case.

The o t h e r c o m p l i c a t i o n i s t h a t , in,,contrast t o t h e r e g u l a r

v a r i a t i o n o f t h e C o r i o l i s parameter, t h e bottom topography i s very i r r e g u lar,

and t h e assumption o f a constant slope i s o n l y v a l i d i n a few cases.

Disturbances o f t h e bottom topography on a scale comparable t o t h a t o f t h e eddies can a l s o be important. The

limitations

of

the

experiments

d i d not allow t o

"oceanic" q u e s t i o n o f whether t h e eddies ,,are "closed-packed" Monin, 1978) o r s i n g u l a r (Nelepo and Korotayev, 1979).

answer

the

(Koshlyakov and

I n t h e l a t t e r paper,

t h e authors a s s e r t t h a t eddies are s i n g u l a r n o n l i n e a r phenomena, between which e x i s t s a background o f Rossby waves.

They show t h e o r e t i c a l l y t h a t t h e

n o n l i n e a r eddies m i g r a t e westwards l i k e Rossby waves. Woods (1980) d i s t i n g u i s h e s between wavelike motions t h a t r a d i a t e energy and momentum, and a d v e c t i v e - l i k e motions (eddies and f r o n t s ) t h a t t r a n s p o r t momentum and energy by advection o f water p a r t i c l e s .

A t t h e present time,

we a r e n o t a b l e t o c l a s s i f y t h e observed eddies ( d e f i n e d otherwise l i k e Woods) i n those terms. The c u r r e n t s i n t h e B a l t i c Sea are considered t o be m o s t l y wind-induced (Jansson, 1978).

With t h e h e l p o f a l i n e a r numerical model, Kielmann (1978)

shows t h a t f l u c t u a t i n g winds can generate topographic eddies.

The computa-

t i o n s o f Simons (1978), based on a n o n l i n e a r model, i n d i c a t e t h a t t h e eddies a r e n o t r e l a t e d i n a s t r a i g h t f o r w a r d manner t o t h e wind f o r c i n g .

Our obser-

v a t i o n s i n d i c a t e t h a t t h e storm which occurred between surveys 18/1 and 18/2 had no obvious i n f l u e n c e on t h e RDT p a t t e r n s . Numerous i n t e r e s t i n g phenomena were observed, not e n t i r e l y clear.

t h e nature o f which i s

From our p o i n t o f view, cooperative experiments such as

BOSEX i n 1977 should be u s e f u l t o complement t h e knowledge o f t h e dynamics

o f t h e B a l t i c Sea.

REFERENCES Aitsam, A. and Elken, J., 1980.

Results o f CTD surveys i n t h e BOSEX area o f

t h e B a l t i c Sea ( i n Russian).

In:

T o n k a y a ' s t r u k t u r a i sinopticheskaya

izmenchivost morei, T a l l i n n , pp. 19-23. Aitsam,

A.,

Elken.

J., Pavelson, J. and Talpsepp, L., 1981.

Preliminary

r e s u l t s o f the investigation o f spatial-temporal characteristics o f the B a l t i c Sea s y n o p t i c v a r i a b i l i t y .

In:

The I n v e s t i g a t i o n and M o d e l l i n g

o f Processes i n t h e B a l t i c Sea, P a r t I,pp. 70-98.

466

Aitsam,

A.,

and Talpsepp,

synoptic

scale

Russian).

In:

L.,

1980.

currents

in

Investigation o f the v a r i a b i l i t y o f

the

Central

Baltic

in

1977-1980

(in

Tonkaya s t r u k t u r a i sinopticheskaya izmenchivost morei,

T a l l i n n , pp. 14-18. Davis, R.E.

B r e t h e r t o n , F.P.,

and Fandry, C.B.,

A technique f o r ob-

1976.

j e c t i v e a n a l y s i s and design o f oceanographic experiments a p p l i e d t o

MODE-73. Eady, E . T . , Fomin, L.M.,

23:

Deep-sea Research,

1949.

559-582.

Long waves and cyclone waves.

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