Fine structures in the seasonal thermocline during JASIN

lh,~7>,'~¢aRe'search, VO[. ~3. No. 9, pp. 11(17 lib{I, 19b;6.

{tltYS il149/sl, $31nl ~ II Ipll PCfg~IIIIOII hltllllal[ ~. ] td

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Fine structures in the seasonal thermocline during JASIN M I ( ' I I A E L A KNOI.I.:;:

( Recei~'ed 1 N o v e m b e r 1985: in rel'zsed l~.'m 12 March 19,%: acc~7~led 13 Marc/; 1986)

A b s t r a c t - - F i n e strtteturcs and their g e n e r a t i n g p r o c e s s c s o b s e r v e d in the s e a s o n a l t h c r m o c l i n c o l the n o r t h e a s t A t l a n t i c d u r i n g J A S I N were analysed. A c o m p a r i s o n of the t e m p e r a t u r e and d e n s i t y lields as well as the stratilication p a r a m e t e r s s h o w e d the d o n f i n a n c e of vertical p r o c e s s e s . p a r t i c u l a r l y i n t e r n a l wave strain or t u r b u l e n t mixing. Intrusive and d o u l q c - d i f f t N v e p r o c e s s e s were seldom observed. In eonlparison to nunlel'OtlS intrusioiln i11 tile 111tli11 thernlocJinc o l the' J A S I N area, the vertical scales o f the' line structure in the seasonal t h e r m o c l i n e were smalh:r. F h c ratio oI' the vertical to the h o r i z o n t a l scales was I: I[II). To d i s c r i m i n a t e b e t w e e n r e v e r s i b l e and irreversibh_' line s t r u c t u r e , data sets were c o m p a r e d with different t h e o r e t i c a l m o d e l s . ] ' h e m e a s u r e m e n t s from R.V. Me;e<," a l o n g an o c e a n i c front s h o w e d n u l n e r o u s i r r e v e r s i b l e line strt~cturcs, while the o b s e r v a t i o n s of R.V. l'hmct o u t s i d e the lront s h o w e d nlolC r e v e r s i b l e struelttres.

INTROI)U('TION

FINE structures, characterized by the fluctuations of the vertical gradients with scales of 1-100 m, have been studied mostly in the main thermocline. Their origin has been ascribed to several processes. In addition to intrusions along isopycnals, lateral mixing near oceanic fronts and double-diffusive processes (WooDs et al., 1977: Jovc~, 1977: TtTrNH< 1981), the internal wave field is of main importance for their generation. internal waves can produce reversible as well its irreversible fine structures. The latter can originate from vertical mixing either due to shear instabilities (GAm~ErF and MtNK, 1972) or to the breaking of internal gravity waves (ORI..aNSKV and Br3aX, 1969). WooI3s (1968) analysed irreversible fine structures in the seasonal thermocline near Malta. Like most of the authors, he described the temperature field by a set of layers with small vertical gradients separated by sheets of high stability. The temperature changes were found mainly across the sheets, and were based on mixing events occurring randomly in space and time. McKEAN (1974) looked at the temperature and density structure as a Poisson process with the vertical extent of the mixing event being a random wmable. Assuming a Poisson distribution, HAVES et al. (1975) presented the probability density function of the vertical temperature gradient, while JovcE and DVS.atJBIES (1977) described the probability density function of the layer thickness, Reversible fine structures can be produced by the deformation of the temperature field due to internal waves. These deformations are caused by the internal wave strain, for the vertical displacement changes with depth. DESAtmIF.S and GrE~;¢; (1981) described the probability density

' l n s t i t u t fi.ir M e c r e s k u n d e , 23 Kicl, F . R . G . 1167

1168

M. KNoI.I.

function of the vertical temperature gradient assuming an initial linear temperature profile distorted by nonlinear internal waves. During the Joint Air Sea Interaction Project (JASIN) 1978 in the northeast Athmtic Ocean numerous fine structures of temperature and salinity were observed in the seasonal thermocline. Most of those fine structures were real and not artificially produced by ship rolling (T~uMP, 1983), as individual hlyers could be pursued in successive CTD profiles. The aim of this paper is to describe those fine structures and to determine the dominant generating processes. Therefore the observed temperature field is compared with simple theoretical models for reversible and irreversible fine structures. II Y l) 17,() (; R A I ) II

The JASIN experiment took place from July to September 1978 in the Rockall Trough in the northeast Atlantic Ocean. Several mesoscale eddies and fronts were observed in that region. Warm and salty water masses south of the observation area were separated by a front from colder and fresher Modified North Athmtic Water in the north (ELLHT et a/., 1983). To resolve smaller scale processes coordinated intensive multiship experiments were carried out. The following fine structure investigation is based on the CTD observations from the German research vessels Meteor and Planet recorded every 5 rain down to a depth of 10() m during the second multiship experiment. This experiment took place on 2 and 3 September next to the mooring H2 (59°25'N, 12°30'W). Four ships held their positions relative to H2 while three ships steamed around a square circuit enclosing the fixed ships and H2 (Fig. 1). Throughout the period of this experiment the southeasterly winds were light. A weak thermohaline front was observed in the mixed layer separating warm and salty water masses in the west from colder and fresher ones in the east. The front, predominantly lying north-south, belonged to an anticyclonic eddy with a diameter of about 85 kin. Its center was situated north of the observation area of the second multiship experiment (MINNETT et al., 1983). At the mooring H2~ equipped with seven vectoraveraging current meters and two acoustic current meters in the upper 60 m, a mean

0 I I

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Fig. I.

Positions of the mooring H2 (59°25'N, 12°3(1'W) and ()I" Ihc lixcd and mobile ships during the second multiship experiment.

Fine structures in the seasonal thermoclinc during JAS1N

J 169

current was measured in the mixed layer of about 21 cm s -~ to the south. It was superimposed by an east-west oscillation with a tidal (12.4 h) or inertial (13.8 h) period. The amplitude of this oscillation caused a 3 km zonal displacement of the water masses, while the southward displacement was about 10 km during a tidal/inertial period. Below the mixed layer this oscillation was very weak, and the mean current flowed to the south with 19 cm s i at 60 m depth. T o g e t h e r with this oscillation the front in the mixed layer moved to the west until 15:00 G M T and then again to the east until 21:30 G M T . In the morning of 2 September, the beginning of the experiment, the front passed the R.V. Meteor and later R.V. Poseidon, but was not advected as fi~r west as R.V. Planer On its return, the front passed R.V. Meteor again, leaving the R.V. Meteor in the same water mass as R.V. Planet at about 21:00 G M T (Fig. 2). The changes of t e m p e r a t u r e and salinity across the front in the mixed layer were 0.32°C and 0.08. The front had only a (o)

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1170

M. KNOll

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Time series of t e m p e r a t u r e vs pressure (a, c)
slight signature in the density field because the horizontal t e m p e r a t u r e gradient was nearly c o m p e n s a t e d by salinity, and it did not affect the depth of the mixed laver or the thickness of the seasonal thermocline. The density structure as well as the mixed layer depth were mainly influenced by the internal wave field. At the eastern side of the front a cold and less saline water body was observed m the range of cs, = 26.65-26.90 kg m ~. T o g e t h e r with the front, it passed the R.V. Meteor twice, at about 13:05 and 16:5{) G M T . Assuming a mean southward current of 21 cm s i the water body extended more than 2 km along the front. STA l ISTI('AI.

l) E S(" I,I I P ' l l () N

During the second multiship experiment 151 C T D profiles were obtained by R.V. Meteor, while 229 C T D profiles were recorded on R.V. Phmet (SmDH.:R and Z[£NK,

Fine structures in the seasonal thermocline during ,IASIN

1171

1980). These profiles, obtained every 5 min with a vertical resolution of 0.5 dbar, showed numerous fine structures in the seasonal thermocline (KNot,L, 1983). The upper and lower boundary of the seasonal thermocline was determined by the absolute vertical temperature gradient over 1.5 dbar, which had to be <>0.05°C dbar -~ fl~r several times. Furthermore the vertical gradient calculated from differences over 15 dbar had to be >0.03°C dbar I or several times <0.05°C dbar ~. Quasi-homogeneous layers in this area were recorded where the absolute temperature gradient over 1.5 dbar was <0.05°C dbar ~. The boundaries of the seasonal thermocline and of the quasi-homogeneous layers in it, calculated by these limits, corresponded to the visual impression of the profiles. The mean vertical temperature gradient in the seasonal thermocline calculated over 1.5 dbar was about -0.1°C dbar i. Due to instrument resolution only the quasihomogeneous layers thicker than I m were registered. Only 40% of those layers were found in the upper and lower part of the seasonal thermocline, while 60% were situated in the middle. This corresponded to the position of the maximum of the Vfiisfil/i frequency and therefl~re of the largest vertical shear (GARrLTT and Mt~nk, 1972). The Vfiis/:ilii frequency in the seasonal thermocline varied between 6 and 12 cph. Only a few temperature inversions observed during an intrusive process were recorded. Therefore a direct overturning of a breaking internal gravity wave was not observed. The degree of mixing can be described by the ratio of the actual increase in potential energy PE and the maximum increase, given by the initial ~: and actual 9-- density gradients: A P E / m a x ( A P E ) = ( p ~ - p:)/~_ (Di..sat;m~s and Gm(~(;, 1981 ). Onlv (I.5'!4, of the profiles in the seasonal thermocline were totally mixed and only 6% were mixed up to 80%. This means that the actual vcrtical density gradicnt was <0.2 times the initial gradient in the seasonal thermocline. For the resolved vertical scales, irreversible line structures were apparently produced by shear rather than by convective instabilities because most of the quasi-homogeneous layers occurred in the region of maximum shear: but temperature inversions and complete mixing processes were seldom observed. For vertical scales < 1 m, however, overturning processes might be important. The number of the quasi-homogeneous layers in a single CTD profile varied from 0 to 5, with a mean wduc and a standard deviation of 1.3 + 1.1 per profile during the second multiship experiment. The R.V. Meteor data set showed that west of the mixed layer front (1.7 + 1).7 quasi-homogeneous layers per profile occurred, while on the eastern side 1.1 _+ 1.2 layers per profile were recorded. Individual layers could be pursued in successive CTD profiles, and thicker ones could be observed for a hmger time, sometimes up to 9(1 rain. Assuming that those layers were transported with the mean velocity of 20 cm s ~ to the south, their horizontal extensions were calculated. The ratio of the vertical to the horizontal extent varied between 7 × 10 ~ and 2 × 10", with a mean value of 1 × 11) ". This corresponded to the ratio predicted by Wool>s (1973) for lhe line structure in the seasonal thermoclinc resulting from gcostrophic turbulence. Many observations in the main thermocline and theoretical predictions of (Lxrr~i i and Mt,N~, (1972) (concerning mixing processes due to shear instabilities of internal gravity waves) yielded a ratio of 1(I ~. Furthermore, the frequency of those quasi-homogeneous layers in lhe seasonal thermocline decreased exponentially with increasing laver thickness. (II_Nt{RA IIN(~ I ' R ( ) ( ' t SNIPS

l , ternal waves, intrusions a , d double-d~[l?lsive l)rocexses In the literature several methods have been presented to discriminate between different processes generating fine structures. Most methods are based on a comparison

M. KnoI.[

1172

between the variations of the different parameter fields. The internal wave strain as well as turbulent mixing deforms the temperature, salinity and density field uniformly, while intrusive and double-diffusive processes change the T-S relationship. Assuming an unperturbed mean profile, different generation mechanisms can be recognized by variations in the T-S diagram (GARGEI3", 1978). If fine structure is influenced by several processes, however, this method cannot compare their individual contributions. To eliminate the processes which equally deform the different parameter fields, GrE(i(; (1980) presented temperature and salinity vs density instead of pressure. JOI~NSON et al. (1978) separated the same processes by comparing the vertical displacement profiles of temperature and density relative to an undistorted mean profile, if fine structure is only generated by internal wave strain or turbulent mixing, displacement profiles of temperature, salinity and density will be equal. To recognize the dominating generating processes in the seasonal thermocline during JASIN, temperature vs density as well as differences between the displacement profiles of temperature and density were calculated. The undistorted profile was obtained by averaging over an inertial period. The first period (Fig. 3a-c) demonstrates a typical situation observed in most of the CTD measurements, where the displacement profiles in the seasonal thermocline are nearly equal and the temperature vs density is very smooth (Fig. 2b). One exception is shown in the second period (Fig. 3d-f) during which a temperature inversion was observed. It was recorded while a relatively cold and less saline water body on the eastern side of the mixed layer front was passing R.V. M e t e o r . {o II

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Fig. 3. T e m p e r a t u r e profiles vs pressure (a, d) and density (h, e) and the differences hetv,'een the displacement profiles of temperature and density vs pressure (c, t). The successi~ e prolile~, ~Lre displaced by 2°C and 2(I dbar, respectively. The cl~na sels were recorded hv R.V. l'lum,I on 3 September 1978, 0:05-0:35 G M T (a, b, c) and by R.V. M e t e o r on 2 Seplcmher 197~. 16:3517:05 G M T (d, c, I).

1174

M. KNOI.L

The difference between the displacement profiles in the depth of the t e m p e r a t u r e inversion as well as the t e m p e r a t u r e curve vs density indicate a change in the T - S relationship. At the lower boundary of this intrusion conditions for diffusive instabilities occurred, since the value of the density ratio R 0 = ~T=/I3T= with ~t = -1/p(Op/OT) and [] = 1/p(Op/OS) varied between 0.5 and 1 (S('ttMITT and GEORGI, 1982). Most of the C T D m e a s u r e m e n t s recorded by R.V. Meteor and R.V. Planet showed that both t e m p e r a t u r e and salinity contributed to the stability of the stratification in the seasonal thermocline. Intrusive and double-diffusive processes were hardly observed.

Spectral analvsis The stratification p a r a m e t e r m = S'/T', the ratio of the salinity and t e m p e r a t u r e fluctuations, also can indicate the different processes generating fine structure (PIN(;REk, 1972). For strictly vertical or horizontal processes, m corresponds to ,S_/T_ or ~,/~P,, the ratios of the mean vertical or horizontal gradients of salinity and temperature. In the case of advection or mixing along isopycnals, rn is equal to ~/~, while for double-diffusive processes m corresponds to the ratio of the salt and heat fluxes. JovcE (1976) transferred the stratification p a r a m e t e r into the vertical w a v e n u m b e r space k to examine the T - S relation on different vertical scales. Supposing a relationship of S(k) = re(k) • T(k), two different estimations of m yield

ml = CT.s(k)/Frr(k) m~ = sign(Cr.s(k) )(Fs.s(k)lFTr(k) )" with the spectra FTT and Fs.s of temperature and salinity fluctuations, respectively, and the co-spectrum CTS. The coherence between the t e m p e r a t u r e and salinity fluctuations is equal to 1, while the quadrature spectrum is 0 and the phase corresponds to 0 ° or 180 ° depending on the sign of m. If two independent processes characterized by different stratification parameters rn, and ml, are involved, the coherence can be rather low and the values of inj and m : will be between m,, and m;,. But if one process dominates, the coherence will be close to I and the values of mt and m , will pass into the corresponding stratification p a r a m e t e r (VAN A~EN, 1981). To investigate the influence of noise on the t e m p e r a t u r e signal (and therefore also on salinity calculated from conductivity C) two independent processes were assumed. The first one was characterized by m , = .'~_/fL = -0.08°C -~ describing a vertical process in the seasonal thermocline during JAS1N. while the second one represented the temperature-induced noise with

OC / OC

m;, = ~/-bTgS = - I ° C

i

"

With the aid of the observed t e m p e r a t u r e and salinity fluctuation spectra and the supposed stratification p a r a m e t e r s m,, and m;,, the spectrum of t e m p e r a t u r e noise n r was calculated (Fig. 4a). The fluctuations were calculated relative to a mean profile averaged over an inertial period. The spectra as well as the stratification p a r a m e t e r (Fig. 4) show that the noise in the temperature signal can be neglected in the analysed wavenumber range. The spectra of the t e m p e r a t u r e and salinity fluctuations, covering a vertical w a v e n u m b e r range of 0.06 cpdbar ~
Fine structures in the seasonal thermocline during JASIN

1175

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Fig. 4. Measurements of R.V. P l a n e t on 2 September 1978. 11:30-17:25 GMT. (a) Mean vertical wavenumber spectra of temperature F;.;. and salinity l-ss fluctuations and temperature noise nT. (b, c) Mean vertical wavenumber spectra of the coherence (b) and phase (c) between temperature and salinity fluctuations. (d) Dependency of the stratitication parameters mj and m, on the vertical wavcnumbcr k. i n t e r n a l w a v e s (GREGG, 1977). D u r i n g s o m e o b s e r v a t i o n p e r i o d s the m e a n s p e c t r a l s l o p e was n e a r to - 2 . 5 o r even close to - 3 . I n v e s t i g a t i o n s in the m a i n t h e r m o c l i n e o f v a r i o u s r e g i o n s in the o c e a n s h o w e d a s p e c t r a l s l o p e o f - 2 m a i n l y up to a w a v e n u m b e r o f 0.1 c p d b a r , while for l a r g e r w a v e n u m b e r s the s l o p e c h a n g e d to - 3 d u e to the influence of i r r e v e r s i b l e fine s t r u c t u r e (GREcG, 1977). T h e c o h e r e n c e b e t w e e n t e m p e r a t u r e a n d salinity f l u c t u a t i o n s slowly d e c r e a s e d with i n c r e a s i n g w a v e n u m b e r s , b u t was o b v i o u s l y

1176

M. KNOLL

above the 95'/o significance limit (Fig. 4b). The phase varied between 175° and 21(1° (Fig. 4c). The stratification parameters ml and me were compared with the values of tz/6, ~{,/T, and S,/]e, (Fig. 4d). For this purpose the horizontal gradients were estimated by transferring successive CTD profiles into horizontal distances by assuming a mean velocity of 20 cm s-~ to the south. For the analysed wavenumber range, the values of m~ and m, enclosed the ratio of the vertical gradients. This was observed in nearly all measurements of R.V. Meteor and R.V. Planet during the second multiship experiment. The stratification parameters never corresponded to the values of ~t/[3. The previous investigations showed that vertical processes, such as internal wave strain or turbulent mixing, were more important in the seasonal thermocline for fine structure generation than intrusive or double-diffusive processes. While internal wave strain produces reversible fine structure, irreversible fine structure is obtained bv turbulent mixing, To decide which one of those two processes was dominant, the temperature structure was compared with simple theoretical models for reversible and irreversible fine structure. Irreversible .line structure

To produce irreversible fine structure in a stably stratified fluid, kinetic energy is needed to break up the stratification. In the region of the thermocline such energy often originates from internal waves which locally can intensify the already existing vertical shear. If instabilities arise, they will lead to turbulent mixing events occurring randomly in space and time. Therefore the temperature structure consisting of sheets and layers is described by a Poisson process, where the vertical extent of the mixing events is a random variable. The probability of obtaining n sheets in the vertical distance y is P(n) = e-~-v(~ty)"/n!, where ~ is the average number of sheets per metre. Hence it follows that the probability density function of the layer thickness Hi is p(Hi) = ~ e -~'(H'-H', with

( ~ p ( H i ) d H i = 1, J

H I

H/ is the smallest thickness possible for instrument resolution (Jov('F. and DESAt;I~n:S, 1977). For the analysed data set H/corresponds to 1 m. The mean thickness of the quasihomogeneous layers la-j can be derived from the mean as well as the variance of Hi, since / ~ i = H I + ta-n

and

V a r ( H i ) = ~-~.

The data set of R.V. Planet yields a mean thickness I,L-~ of 2.2 and 2.3 m, respectively, calculated from the mean and the variance of H~, while the measurements of R.V. Meteor deliver values of 1.8 and 1.9 m, respectively. DESAU~IE:.Sand GRFG(~ (1981) state that the calculated mean thickness of the quasi-homogeneous layers increases with the differencing interval 8 used for the calculation of the vertical temperature gradient. This dependency, predicted as/a -~ = (3 to 4)8, was not observed in the present data sets which were based on a different definition of the layer thickness. Proceeding from the observed frequency h of the individual layer thickness Hi, the probability density distribution p(H~) was calculated for the data sets of R.V. Planet (Fig. 5a) and R.V. Meteor (Fig. 5b), For a finite number of independent observations rn the relative frequency h/m, being a maximum likelihood estimation of the probability, can

Fine structures in thc seasonal thcrmoclinc during JASIN O. 60

O. 60

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Fi~. 5. Probability dcnsitv lunction and thc 95% confidence inlcrva]s ol the c u a s i - h o m o g c . . . ncous laycr thickness compared with a . thcorctical cxp~clti I dec c sc F(It,) = ~. c it I I I givcn by the dashcd line. Thc bcst lit was obtained by using 1-t ~ = 2.2 m fin lhc data sct of R.\". Plam'l (a) and It I = 2.0m Ior the data set of R.V. Meteor (b) rccordcd during the second multiship experiment. d e v i a t e f r o m the real p r o b a b i l i t y P. T h e c o n f i d e n c e interval is given by t'L <~ P <~ P2 with h + (q2/2) -T- q [ h ( m - h ) / m + (q2/4)]1/2 Pl,2 =

I11 + q2

F o r a 5 % p r o b a b i l i t y of P not lying b e t w e e n t h e s e limits the level of significance q is e q u a l to 1.96 (TAUBENtlEIM, 1969). This c o n f i d e n c e interval was t r a n s f e r r e d to the p r o b a b i l i t y d e n s i t y d i s t r i b u t i o n s h o w n in Fig. 5. T h e d a t a sets fit q u i t e well with the t h e o r e t i c a l m o d e l o f J()YCE! a n d DESAUIHES (1977). T h e c h i - s q u a r e g o o d n e s s - o f - f i t test m a k e s it p o s s i b l e to e x a m i n e the e q u i v a l e n c e b e t w e e n an e m p i r i c a l f r e q u e n c y d i s t r i b u t i o n hi a n d a h y p o t h e t i c a l o n e ei. T h e o b s e r v a t i o n s only consist o f M d i f f e r e n t results. If the v a l u e Z2 =

M ~,

( h , . - ei) 2

i= I

ei

e x c e e d s a given limit o f significance, t h e n the d i f f e r e n c e b e t w e e n the o b s e r v e d a n d

1178

M. KNOLL

theoretical frequencies are significant and not random. The best fit between the data set of R.V. Meteor and the theoretical probability density function was obtained by using !u-j = 2.0 m. For a 5% level of significance the hypothesis of equivalence was accepted and the differences between the empirical and hypothetical frequencies were only random. For the data set of R.V. Planet a value of p-~ = 2.2 m was used for the best fit, but the results were not so definite compared to R.V. Meteor's data. For a 5% level of significance the value of Z2 just exceeded the given limit and therefore the differences between the observed and theoretical frequencies seem to be significant. The probability distributions of the vertical temperature gradient over 1.5 dbar in the seasonal thermocline also were calculated. Both distributions covering a range of +0.03 to -0.48°C dbar -~ were skewed (Fig. 6). The mean temperature gradient was -0.10°C dbar -~ with a standard deviation of 0.07°C dbar -~. If the temperature structure consists of sheets and layers, the probability distribution of the vertical temperature gradient should be bimodal for differencing intervals ;6 being smaller than the thickness of the sheets (DEsAUBIES and GRE~;C,, 19811. Due to instrument resolution the sheets could not be resolved. By increasing 8 the bimodal distribution will be replaced by a skewed one, which at last will pass into a Gaussian

0.I0

_

(a) /\

A O. I--"

{L

0.05

o._o9.50 u

I l t l l l J l [ I J

I I I I l l

-0.40

-0.30

iii

-0.20

-0.10

0.00

Tp [°C/dbar] 0 . 1 0 - (b)

/

/\

o.os

i i i I i i i u

O. _0~.50

i l i I I

-0.40

i I. I.I,

"

- 0 .,.~ 30

-0.20

- 0 . I0

0 . 0 0 ,,

Tp [°C/dbar] Fig. 6. Probability function and the 95% conlidencc intervals of the vertical temperature gradient calculated over 1.5 dbar in the seasonal thermoeline. A comparison with theorelical models for reversible (---) and irreversible (--) fine structure is given. The data scts were recorded by R.V. Phmet (a) and R.V. Meteor (b) during the second multiship experimcm.

Fine structures in the seasonal thermocline during JASIN

1179

distribution. On the premise that the vertical temperature structure could be described by a Poisson process, HAYES et al. (1975) presented a gamma distributed probability density function of the vertical temperature gradient T~, p(r,,)

-

!a6/7"/' (laSTp) ("~-l) e-~T,' with Tt, = Tp/~Pp

The best fit between this model and the sampled data of R.V. Planet (Fig. 6a) and R.V. Meteor (Fig. 6b) was obtained for i,t-I = 0.56 and 0.63 m, respectively, with a mean gradient of 7",, = -0.10°C dbar -1 and 8 = 1.5 dbar. These results of the mean layer thickness considerably differed from the values obtained by the model of JovcE and DESAUBIES (1977). Again a Z2 goodness-of-fit test was carried out, and for a 1% level of significance differences occurred between the theoretical and empirical frequencies observed by R.V. Meteor as well as R.V. Planet. Strong deviations especially occurred for small absolute temperature gradients, because the model did not consider temperature inversions, and the inaccuracy of the measurements was most critical there. Neglecting the range of absolute temperature gradients below 0.04°C dbar -l, the differences between the hypothetical frequencies and those obtained by R.V. Meteor were random for a level of significance of 5% (Fig. 6b).

Reversible fine structure A completely different description of the temperature structure was made by DESAU~IES and GREGO (1981). They did not assume a vertical Poisson process, but referred the fine structure to the deformation of a mean gradient. An initial linear temperature profile was distorted by a nonlinear Gaussian distributed internal wave field, Based on an analytical model they developed the probability density function of the temperature gradient

p(Tp) = 8 L,-'(2x) ,/2

{(

s"+

(s + (~Y-Y)S')2) e I/2( (6 ")/s)e} 7

/

"

"

s(y) = Z {2(1- ¥(y))}1/2 is the standard deviation of the differences between the displacement of two isotherms separated by a mean distance of y = 8 T~,/ ~,- 7(Y) = (¢l¢2)/Z 2 is the correlation of the displacements, while ¢ corresponds to the vertical component of the displacement with a variance of Z 2 = (~) = (~2). An analytical expression for the correlation y(y) was obtained from the cosine transform of the wavenumber spectrum of displacement qb(k) presented by DESAI1BIES (1976) with

7(y) = Z -2

cos(ky)do(k)dk = e -k*'' 0

~)(k) = 2 1 u ' k , Z 2 ( k 2 + k.2,)-' .

The internal wave field is described by the variance Z 2, being proportional to the energy level, and by the band width k, which is the inverse of the correlation length. Due to the nonlinearity of the internal waves, the Gaussian distribution of the temperature gradient is replaced by a skewed one for decreasing 8. The shape of the distribution is very sensitive to the choice of Z and k, (DESAUBIES and GREGG, 1981). The best fit between

1180

M. KN()I.I

the data sets and this analytical model for reversible fine structure was obtained by using k , = 10-2 m -~ and Z = 5 m. But the X2 goodness-of-fit test still showed significant differences between the m e a s u r e m e n t s of R.V. Meteor as well as R.V. Planet and the theoretical probability distribution. The differences may originate from irreversible processes which were not considered. A further assumption of this model, namely that the t e m p e r a t u r e gradient is a random variable and therefore that successive measurements are independent, was not fulfilled. Also t e m p e r a t u r e inversions and horizontal terms were not considered in this model. While the model of HAYES et al. (1975) considered random mixing events generating Poisson distributed irreversible fine structures, the model of DESAUBIES and GREG(; (1981) only regards reversible fine structures caused by nonlinear internal waves. The shape of the observed distributions of the vertical temperature gradients resembles the model distributions, but deviations are significant. Especially for small absolute temperature gradients neither model fits the observed data sets. Nevertheless, differences between the fine structures obtained by R.V. Meteor and those predicted by the model of HAYES et al. (1975) are essentially smaller (Fig. 6b) compared to those predicted by the model of DESAUBIES and GREG(; (1981). In contrast to this, for temperature gradients in the range o f - 0 . 0 2 to --0.50°C dbar -l, the deviations between the measurements of R.V. Planet and the model for reversible fine structure are smaller than for irreversible fine structures (Fig. 6a).

CONCLUSIONS

Based on C T D measurements, fine structures in the seasonal thermocline during J A S I N were examined. To discriminate between different generating processes the variations of the t e m p e r a t u r e and density fields were c o m p a r e d and the stratification p a r a m e t e r s were calculated. The results indicate the dominance of vertical processes, such as internal wave strain and turbulent mixing, in the seasonal thermocline. In spite of the existence of a mixed layer front, intrusions and double-diffusive processes were rarely observed. The spectra of the t e m p e r a t u r e fluctuations often showed a dependency close to k 2 corresponding to the influence of internal waves. Sometimes the spectral slope was near to -2.5 or even close to -3, referring to irreversible fine structure. The vertical scales of the fine structure in the seasonal thermocline were essentially smaller than those found in the deeper ocean of the J A S I N area, where many intrusions occurred (~AN AKEN, 1981). On the premise that the fine structure was advected with the mean current, the ratio of the vertical to the horizontal scales was 1:100. To decide if reversible or irreversible fine structures dominated the seasonal thermocline, the measured temperature structure was compared with different theoretical models, describing the probability distributions of the layer thickness and of the vertical t e m p e r a t u r e gradients (HAYESel al., 1975; JoY('ri and DESAUBIES, 1977; D~':SAUBlt~Sand GRE(;(;, 1981). For the irreversible fine structures, which were apparently produced by shear rather than by convective instabilities, a Poisson distribution was assumed. The comparison between the measured t e m p e r a t u r e structure and those models showed that in the data set of R.V. Meteor in the region of an oceanic front irreversible fine structures were often observed, while the measurements of R.V. Planet outside the front corresponded more closely to the model for reversible structures.

Fine structures in the seasonal thcrmoclinc during JASIN

1 181

Acknon'ledgemems--I wish to acknowledgc the assistance of my thesis supervisor G. Sicdler and of thc staff o1 lhc Marinc Physics G r o u p at the hlstitut Il.ir M c c r c s k u n d c in Kicl. F.R.G. This work was supportcd b,, thc Dcutschc Forschungsgcmeinscha ft. R [{ I"1{ R E N ('t{S I)t SM:IHI{S "Y. J. F. (1976) Analytical rcprcscntalion o f internal wave spcctrn..l~;m'md ol Phv~iual (kcam,k, ruphv, 6, 97(~-9~1. Ill S,\UBll.S g . J. F. and M. C. (}1.{I (;(; (IO8l) Revcrsihlc and irrc',crsiblc Ihlc-structtn-c. ,Iota'rod ,I I'hv,,iual Oceam~k,raphy. I I. 541-556. El [1{II 1). ,I., P. KRtlSl MAN, G. ,I. PRAN(iS[',IA, R. T. POll ARD, tt. M. VAN A M X. A. Era\ \IdeS, tt, 1). I)()()l.I "~ and W. J. O o u I J ) (1983) Water masses ~llld nlcsoscalc circulation of North Rockall Trough waters during .IASIN 1978. Pllilos'ophical Tran.sacdo;zs of the Royal ,~'ocit'ty ¢4 l.¢mdcm. A308. 231 252. (;.\l~,(i[:ll A. E, (1978) Microstructurc and line slructurc in iii1 upper ocean Irontal r e g i m e . . h m r H o l o/ GeoplLwical Reseats'h, 83, 5123-5134. (M~,kEIq" C. and W. MUNK (1972) Oceanic mixing by breaking mtcrnal waves, l)e~7*-Sea Research, 19,823-832. (iRI (;(; M. ('. (1977) Variations in the intensity of small-scalc mixing in the inaill thcrmoclmc..IOlllTitl/ O/ Physical Oceam~graphy, 7,436-454. (}Rt ¢;¢; M. ('. (19811) The three-dimensional nlapping ol a small thcrmohalinc intrusion. ,lomvm/o/l'hvs'ica/ Oceam~raphy, 10, 1468-1492. It,\~ Is S. P.. T. M. Jo'~('l and R. C. M[II ARI) (1975) M c a s u r c m c n t s of vertical lmc Sll'tlCttll-C ill lilt Sm-gasso S e a . . h m r m d of Geophysical Research. 811.314~319. .l()llNS()y C. L., ('. S. ('()x and B. GAI.I A(;III R (1978) 1"he scparalion of x~avc-induccd ;rod in|l-tlSi\c occamc tinestructurc. Jotlrnal of Physi¢'al Oceanogrgq~hy, 8, 846-8(~0. .1()',{I T. M. (197fl) Large-scale variations in small-scale temperature/salinity [incstructurc in lhc main thcrmocline of the northwest Athmtic. De~7~-Sea Research, 23, 1175 1186. J~)',{l T. M. (1977) A note on the lateral mixing of water masses. Joltrltal r{t l'hysiual Oceam~vraphv. 7, (~2¢'~ 629. Jov('r; T. M. and Y. J. F. DESAUBIES (1977) Discrimination between internal waves and tcmpcrature linestructurc. Jmtrnal of Physical Oceanowaphy, 7, 22 32. KNOl I M. (1983) ( ' T D and current protiler data fronl .IASIN 197N. -Mewor'" l"ol;chmtys'erk, t,httis.sc ,.1,'11, 24. 25-4{1. M¢KI AN R. S. (I 974) Interpretation of intcrnal wave mcasttrcments in the prcscncc ol [hie-structure..lore'rod ¢~1'Physical Oceanography, 4, 211(>213. MINNEII P. J.. R. T. Pt)I.,.a}~l), D. S. C()l.l INN. A. tto,{(',, ;rod M. K~,(>l I (1983) The structurc of it weak thcrmohaline Iront. PhilosoF,hical Transactions of the Royal Society ol London. A308. 359 375. ()RI ANSKI I. lind K. BI,~'~AN (1969) Fornlation o f thc thcrmoclinc step structure hy Ill-go-amplitude internal gravity waves. Jomm.d of Geol?h)'sical Research. 74, fl975-6983. PI~q(ip,l I R. D. (1972) Mixing in the deep stratilied ocean. Deep-Sea Research, 19. 549-5~'~2. S(ll\llll R. W. and D. T. GI!()R(II (1982) Fincstructurc and microstructtlrc in thd North Atlnntic Ctll-lClll. .Iota'hal of Marine Research, 4111(Suppl.), 659-705. SII I)I.ILR G. and W. ZINK (1980) JASIN 1978 licld activities on thc rcscarch vessels "Meteor'. "l'hmut', "Po.seidem" and thc rcscarch aircraft D - C M E T . "'Melt,of" t:ot:sdmnk,.ser~tt'httis.sc. A21, 25 48. I'.\IrI~I:NIIEI~,I J. (1969) Statistische A u s w c r t u n g gcophysikalischcr und mctcoroh)gischcr Datcn. Akadcmischc Vcrlagsgcscllschaft Geest t, nd Portig K.-(i., Leipzig, 383 pp. "[RtMI' C. L. (1983) Effects of ship's roll on the quality of prccision ( ' T D datH. DUel>Sea lCevearch. 30. 1173 1183. Tt RNI:I ?. J. S. ( 1981 ) Small-scale mixing processes. In: Evohttion qlphys'i<'al o<'eanovraphy. B. /\. W' \m::l x and ('. W u y s ( II, editors, Thc MIT Press, Cambridge, MA, pp. 23(~2<~2. V.\N AKIN H. M. (1981) Thc thermohalinc tint structure in the Norlh Rockall Trough. PhD thesis, [ !nivcrsitv IJtrccht, Netherlands, 161 pp. W()<)l)S J. D. (1968) Wave-induced shcar instability in the s u m m e r thcrmoclinc..lrmrmd ol Htfid Muuhani<~. 32, 791-800. W{x~i)s J. D. (1973) Space-time charactcristics of turbulcncc in thc scasonal thcrmoclinc. Memoirc~ dc la ,S'oci('le Rovale de.~ Sciences de Lie t,,<', ser. 6, Vol. 6. 1(19-130. WOODS J. D., R. L. WILEY and M. G. BRlsCov (1977) Vertical circulation at fronts in the upper ocean. In: A voyage ql'discovet3', Supplement to DetT>Sea Re.search, M. Angel. editor, Pergamon Prcss. Oxford, pp. 253-275.