Phys. Oceanogr., Vol. 9, No. 2, pp. 79-101 (1998) 9 1998.

Thermohydrodynamics of the Ocean The near-bottom boundary layer in the Black Sea: hydrological structure and modelling* V. N. EREMEEV, L I. IVANOV, A. S. SAMODUROV and M. DUMAN ~ The paper discusses the parameters derived through deep-sea precision CrD-probings, characterisdc of the structure of the near-bottom boundaries layer, specifically, the depth of the layer's upper boundary and the mean vertical potential temperature/salary gradients, as well as the density ratio over the layer of the near-bottom convection. The pe~i~fies of the parameters' spatiM distribution have been identifie& The conclusion derived from the analys~ of the model implles that the near-bottom boundary layer occurs, aside from the presence of the bottom geothermal heat flux, due to the strong dependence of the Bosphorus salt flux on stratification. The dependence of the Black Sea buoyancy flux and vertical diffusion coefficient on depth has been e~timated. Abstract

INTRODUCTION The typical vertical distribution of potential temperature in the Black Sea below the main thermocIine (Fig. I) is characterized by the general rising of t e m p e r a t u r e with depth. Within the 500-700-m layer, that regularity is violated due to the occurrence of a local minimum and a local maximum of potential temperature. Below 700m, potential temperature tends to rise up to the near-bottom convection layer characterized by the uniform distribution of both potential temperature and salinity. T h e thermohaline structure of that layer and its upper boundary is a focus of the present study. The results of deep-water measurements in the Black Sea have been repeatedly analysed from the viewpoint of describing the thermohaline structure of abyssal waters 8.82 350'

.

8.84 .

.

.

.

.

8.86 .

,

8.88 .

,

,

t

8.90 .

,

,

~

O,~

850

1350

H, rn

Figure I. The typical vertical distn'bu~on of the potential ~mpera~e in the Black Sea. "Translated by Vladimir A. lhichHn, U D K 551.46+551.46(262.5).

V.N.E.~uner,, ~

80

aL

and studying its likely spatio-temporal variability. The problem was discussed most intensively in the 1960s [1-3] in connection with the burial of radioactive wastes in the Black Sea near-bottom strata. From the data compiled at 115 deep-water stations occupied during the spring-stunmer seasons of various years, it was revealed in ref. 1 that the deep-water temperature and salinity in the central sea are larger by 0.05-0.10~C and 0.1-0.2~ respectively, than in the marginal areas. The subsequent investigations [4--8] did not support the inferences made in ref. 1 with regard to the regularities of the spatial temperature/salinity distribution in the near-bottom layer. In the evolution of temperature in the abyssal layers the major role belongs to adiabatic heating and bottom thermal radiation [1-3, 8]. Heat flux f~om the bottom ensures a saper-adiabatic rising of the potential temperature within the near-bottom layer. As a result of thermal convection, the near-bottom mixed layer is formed. The temperature drop needed for the convection to take place was found to equal 0.5~ [1]. The high homogeneity of the Black Sea abyssal waters, as well as the lack of the upto-date equipment required for conducting deep-water investigations and of the methods of conducting/n dtu precision measurements did not enable us to determine the thermohallne indices of the Black Sea abyssal and near-bottom waters with suffident accuracy and to confirm or to refute the conclusions made by the individual investigators regarding regularities of the spatio-temporal temperature/salinity changes within that layer [4]. Today, however, data are available which permit the thermohaline structure of abyssal waters and the near-bottom boundary layer to be described at a new depth level [4-7], DATA USED We have used the data compiled in the course of deep-water CTD-probings in the Black Sea carried out (i) during the Black Sea expedition of the R/V Knott in 1988 [6] (Fig. 2, Table 1); (ii) the data collected at the intercalibration stations occupied during the international experiments HydroBlack'91 [5], and CoMSBlack'92 [7]; (ill) during the cruise of the Turkish R/V Piri Reis in the south-eastern part of the Black Sea in March 1992 (the arrangement of the stations is shown in Fig.2); and (iv) during Cruises 30 and 33 of the R/V Professor Kolesnikov (Fig. 2).

••Kolesnikov'

4e~

44 o .

42 ~ .

28 ~

30 ~

32 ~

34 ~

36 ~

38 ~

40 ~ E

Figure 2. Schematicarrangementof the deep-waterstations occupiedfrom 1988to 1995.

The near-boftom boundary layer in the Black Sea

81

Table 1.

Information about the deep-water measurements implemented by the R/V Knott in 1988 Station .umber

1 3 5 7 1 7 10 18 26 30 9 20 21 22 26 27 6 8 12 15 16 21 23 6 8 16 24 28 43 47

Probing number 1 1 1 1 2 2 1

N E (degrees) (degrees)

1

41.804 43.162 42.980 42.392 41171 41786 42.742 42.935 43.104 43.084 42.839 42.802 42.842 42.844 41078 43.068 41.843 41.853 42.856 42.836 42.164 43.082 41755 43.089 43.099 43.098 43.081 43.083 43.079

I

43.084

I

1 1 1 1 I

1 2 1

1 1 1 1 1 2 1 2 2 2 I 1

Month

Date

Depth of probing(m)

Rp

21 22 24 26 15 18 19 21 23 24 5 7 7 7 10

1837 1976 2109 2069 1973 1975 ~Y74 2016 1971 2081 2057 1791

24 24 26 27 28 29 1 17 17 19 21 22 25

2.45 2.38 2.55 2.80 2.95 2-64 2.46 2.55 2.95 2.83 2.99 2.81 3.06 2-55 2.67 2-44 2.81 2.94 187 2.57 2.81 2.54 2.59 2.75 166

33.998 33.994

4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7

33.998

7

26

30.454 31.999 34.005 37.599 29.995 31.945 31.927 31.999 34.021 33.999 32.004 31.886 31.981 31.984 33.997 34.000 30.346 30.353 31.401 3L999 32.753 34.009 37.582 34.003 34.013 33.998 33,990

10

2061

1782 2158 1776 1823 1777 1825 2039 2066 2134 2028 2147 2139

H

~ma~L 1705 1675 1760 1735 1725 1725 1755 1710

1740 1725 1665 1685 1670 1715 1745 1745 1760 1720 1700 1685 1720 1770

21171

2.99

2141 2149 1973

768 2.73 2.49

1705 1755 1742 1753 1767 1778 1755

2150

160

1764

Rp denotes the density rado, and HNsst, is the upper border of the near-bottom boundary layer. C I ' D - m e a s u r e m e n t s from on board the R / V Professor Kole.mikov were conducted using the ISTOK-7 probe, while in the case of the R / V s P/r/Re/s and Knorr, as well during Cruise 33 of the R / V Professor Kolesnikov, SeaBird Electronics probes were employed. The basic evidence as to the adequacy and reproducibility of the m e a s u r e m e n t s data are submitted in the interealibration reports [5-7] and ref. 4. A survey carried out by the R / V Piri Reis in the south-eastern part of the Black Sea in 1992 is the only synoptic survey enabling one to gain insight into the spatial variability of the n e a r - b o t t o m boundary layer. As the precision of current velocity m e a s u r e m e n t s was not sufficient for the study of t e m p e r a t u r e / s a l i n i t y variability within the near-bottom b o u n d a r y layer, we do not have any idea about the possible range of variations of these parameters. Hence, it appears

82

V. iV. Eremeev et al.

appropriate to assume that T- and S-fluctuatious within the near-bottom boundary layer are the result of random errors of measurements. Relying on this assumption, we will evaluate the error of the measurements accomplished during the expedition of the R/V Piri Reis, where the temperature drop equalled 0.0013~ (the RMS deviation being 0.0007~ and the drop of salinity was 0.00160]00 (the RMS deviation being 0.00080/o0). Thus the error of temperature/salinity measurements during the cruise of the R]V P/r/ Re/s in 1992 was smaller than 0.001~ and 0.001~ respectively. METHODS OF DETERMINATION OF THE NEAR.BOTrOM BOUNDARY LAYER PARAMETERS We have used the available data to compute the following parameters characteristic of the structure of the near-bottom mixed layer and of the latter's upper boundary: the depth of the upper boundary of the near-bottom boundary layer (H~sL), the density ratio [Rp = (/30S/Oz)/(~ O0/Oz)] within the stratum overlying the near-bottom boundary layer, and the vertical temperature/salinity gradients over the upper boundary of the near-bottom boundary layer. The determination of the position of the upper boundary of the near-bottom boundary layer as a depth where the vertical gradient of the potential temperature/salinity turns to zero does not represent any difficulty. The vertical potential temperature/sallnity profiles exhibit a homogeneous layer bounded by the 1750 m depth (according to ref. 6, 1740m) and the bottom. Within that stratum, 0 = 8.893~ and S = 22.333~ [4]. Notwithstanding this, the identification of the upper boundary of the near-bottom boundary layer is not objective, and the possible 'error' of such a determination is about 5 m. The mean potential temperature vertical gradients within the 1100-1600m layer normally equal 4 to 5x 10-5~ approximately 50 to 100 m above the near-bottom convection layer, the potential temperature's vertical gradient increases by more than two times, attaining roughly 10• 10-5~ -1. A local maximum of potential temperature (A0 being about 0.001~ was observed at some stations fight above the mixed layer [4]. The mean vertical salinity gradient within the layer between 1100 and 1600 m equals 2 to 5 • 10-5 0/o0m-l, being slightly larger above the near-bottom convection layer. The potential temperature/sallnity vertical gradients, along with the density ratio, were determined for the layer of large vertical gradients, identified at the intersections of the tangents with the smoothed sections of the vertical profiles.

RESULTS The depth of the upper boundary of the near-bottom boundary layer, according to the data compiled by the R/V Knorr in 1988, varied, depending on the location of the station, from 1675 to 1735 m (Fig. 3, Table 1). The RMS deviation of that parameter from the mean value (1728m), by the data from all the measurements, was 31m, which is indicative not only of the significant spatial variability but also of the temporal one. The density ratio within the stratum overlying the near-bottom boundary layer changed from 2.38 to 3.06 (the mean value and the RMS deviation being, respectively, 2.70 and 0.18). The potential temperature/saHnlty vertical gradients within that layer were 7 to 12x 10-5~ -1 and 3 to 6x 10-5 ~ m -1, respectively. We will examine in more detail the results of the survey made in the south-eastern section of the sea during March 1992. In this area, the depth of the lower bound of the near-bottom boundary layer (Fig. 3b) changed from 1685 to 1888 m (the mean value

7he near-bottom boundary layer in the Black Sea

83

44 ~ -t 9 e 4,3 ~ -

(J

"

,

2a ~

1726

.~

~

.

172~.,b'~r~-~.~,.,,,~ ,., ,-'-,~ .."

31

32:33

'34

35

~

a,

~

~

,~~

(a)

+

' i

34 o

35 ~

36 ~

37 ~

38 ~

i

39 ~

f

40 ~

41 ~

42OE

(o) Figure 3. The spatial distribution of the depth d the upper boundary of the neat-bottom boundary layer (m), according to the data collected by (a) R/V/(non" in 1988 and Co) R/V/'/,'i Re/s in 1992.

and the RMS deviation being 1761 and 55 m, respectively) that is, it was situated at a larger depth than that indicated by the R/V Knorr data, and the general variability of the index was more pronounced. One can identify the general regularities of the spatial distribution of HNaaL. The largest depth of the near-bottom boundary layer was observed at the foot of the continental slope and in the vicinity of a bottom feature east of Cape Sinop. In the deep-water part of the area, far away from the bottom rise, the values of HNaaL ranged from 1685 to approximately 1750 m, that is, they were dose to the values obtained by the R/V Knorr, during whose expedition most of the stations were occupied in the abyssal part of the basin. Thus we have a domelike distribution of the upper boundary of the near-bottom boundary layer, with the depth of the upper boundary being larger near the continental slope. Figures 4a and 4b show the spatial distribution of the density ratios, as well as that of the potential temperature vertical gradients. In the Rp spatial distribution, two stations stand out in the vicinity of the bottom feature east of Cape Sinop (the values being 6.3 and 8.4). For the other stations, this value is 2.26 to 2.90 (the R/V Knorr-provided ratios being 2.38 to 3.06), with the smallest values occurring at the site,s where changes in the

84

V.N.E.remeev et aL

thickness of the near-bottom boundary layer and in the position of the latter's upper boundary were largest. An average density ratio for those stations equalled 2.50, and the RMS deviation was 0.15. Apparently, the reason why the R/V P/r/Re~-provided density ratio's was small was that the survey encompassed the larger part of the continental slope where the upper boundary of the near-bottom boundary layer deepened. The values of the potential temperature vertical gradient above the near-bottom boundary layer (Fig.4a), for the majority of the stations, equalled 6 to 22x 10-5~ -t (the largest gradients were documented in the areas where HNem. changed, as well as to the east of the upper boundary of the near-bottom boundary layer at a depth smaller than 1700 m). Two stations occupied over the bottom feature represented an exception, because the values of the vertical gradient 0 there were anomalously small, density ratios were very large, and the upper boundary of the near-bottom boundary layer was anomalously deep. The spatial distribution of the vertical salinity gradient within that layer displays specific features identical to the distribution of the potential temperature (the range of variability is 1 to 9x 10-5 ~ m-z). 44~

42~ . ~ - - . ~ ~

41~ 34~

~

,

9

35o

36 ~

370

38~ (a)

.

39~

,

40~

41~

420E

44~N

2.6 2.7 2.4

oo.

4~JO

2.6 2.4 8.4

'

34 ~

l

35 ~

'

i

36 ~

'

2.3

|

37~

~.~

I

38 ~

u

I

39 ~

'

I

40 ~

'

i

41~

i

42OE

(b) Figure 4. The spatial distribution of (a) the values of the potential temperature's vertical gradient and Co) density ratio.

The near-bottom boundary layer in the Black Sea

85

44"N

42r

41 ~

3,1~

,

35/0

f ~ 3fi

"# ~ .q7

,

=I0

,

~"

40 ~

41, ~

'

420E

F'gure 5. The spatial distn'butiun of the thickness of the near-bottom boundary layer.

As ref. 9 indicates, the values of the heat flux from the bottom are roughly equal throughout the sea area, slightly increasing near the continental slope in the southeastern section of the basin. Assuming the bottom's thermal radiation to be responsible for the occurrence of a super-adiabatic potential temperature gradient in the nearbottom layer and for the thermal convection, it may be antidpated that the thickness of the near-bottom boundary layer would slightly increase in the vicinity of the continental slope. However, in reality, the thickness of the near-bottom layer (i.e. part of the water column between the layer's upper boundary and the bottom) changed from 60 m in the shallows" up to 457 m in the deep-water part of the basin (Fig. 5). Hence, factors other than the bottom's thermal radiation basically determine the peculiarities of the spatial distribution of the near-bottom boundary layer's thickness and the position of the layer's upper boundary. Amongst these factors may be dynamic mechanisms. With the natural potential temperature/salinity variability within the near-bottom mixed layer assumed to be quasi-geostrophic and insignificant, the configuration of the layer's upper boundary governs the nature and the intensity of the relative drculation in the layer. As the conventional specific density above the layer's boundary decreases with depth (stable stratification), a dynamic peak and a dynamic trough indicate, respectively, the areas of deepening and shallowing of H~,L. Thus the near-bottom flux (i.e. not the absolute current velocity but the relative one, which is examined in terms of the dynamic method of current velocity determination) is oriented eastward along the foot of the continental slope and rounds the bottom elevation east of Cape Sinop, thereby generating an anticyclonic meander over the bottom rise and a cyclonic one behind it 6ee Fig. 3b). By comparing Figs 4a and 3b, we will see that the area where the potential temperature's vertical gradient above the near-bottom boundary layer coincides with the anticyclonic meander of the near-bottom current, and the largest values occur within the cyclonic meander. It is noteworthy that dynamle features in the near-bottom layer, identified by the thickness of the near-bottom mixed layer, are traceable over practically the entire water column, including the main pycnocllne. In the layer accommodating abyssal and intermediate waters, to the current's anticyclonic meander, given in the isopycuic coordinates, corresponded warm (salty) waters, and to the cyclonic meander, cold (less saline) waters.

86

V. fir.Eremeevct aL 8.880 1500 L . . . . .

1600

8.885 ~ ....

8.850 , ....

8.895 8.900 , .... , -_0,~

~

1700,

1800,

.

~oo

iI +

~'~'4+

t o

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X,m F l g u ~ 6. T h e ~ c ~ l

~,~

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II

\1'~ I

di~l~ulion of the potendal ~ m L ~ r a l u r e ' ~ i d ~ the n e ~ - b o t t o m layer. 8.880

1500

8.885

....

8.890

8.895

L , , , , , ....

8.900

, ....

~

e,~

1600. 1700. 1800,

i

H, m

(a)

22.320

22.325

22.330

+

1700

1800,

22.335 . . . .

s.+

" ~

[

St.5840 - ~ St..1955

--~--

1~.

~,m

St. 5975

(b)

Figure 7. Verticalprofilesof (a) the potentialtemperatureand Co) ~linity in the near-bottomlayer, accordingto the datacompiledduringCruise33 of the R/V ProfeJsor Koleanikov in 1995.

The nea~.bortom boundary layer in the Black Sea

87

Figure 6 displays a number of vertical distributions of the potential temperature within the near-bottom layer. The vertical distribution of 0, observed at the station occupied at 43~1fiN, 35~15'E, may be regarded as typical for the majority of the stations occupied at a large range from the bottom feature and continental slope (for most of the R/V Knorr stations, too). For the stations occupied over the bottom feature (42~ 36~ vertical gradients of the potential temperature above the nearbottom boundary layer are typically small, their changes are insignificant (the layer of large gradients is virtually absent), and the upper boundary of the near-bottom boundary layer lies at a large depth. At some stations (for instance, the stations having coordinates 42~ 35~ and 42~ 37 ~LS'E), potential temperature (and salinity) right above the near-bottom layer rapidly decreases and then increases. The positive anomaly of 0 has a vertical scale 100 to 200 m. Some regularities of the spatial distribution of the parameters at issue were identified using the data from one survey; the other measurements may be assumed to be single. However, it appears vital to obtain such single measurements data which would support the survey data collected by the R/V Pig Reis. Figure 7 shows the vertical distribution of the potential temperature and salinity in the abyssal layer observed at Stations 5840, 5955, 5975 and 6031, occupied by the R/V Professor Kolesnikov in December 1994 (St. 5840) and March 1995. The first station was occupied within the meander generated by the Black Sea rim current (which is indicated by the deepening of the pycnocLine); the second and the third stations were carried out within the eastern cyclonic gyre; and the fourth station was occupied within the western cyclonic gyre. The profdes distinctly show (save St. 5840) the homogeneous layer lying between the 1700-1750-m depth and the bottom, where 0 = 8.886~ and S = 22.3340/00 (30/00 at the western station), which is consistent with the data derived by the other researches. Density ratios for Stations 5955, 5975 and 6031 were 2.6-2.9, being dose to the ratios obtained during the expedition of the R/V Knorr, and at Station 5840, occupied south of the Crimea in the vicinity of the continental slope encompassed by the anticyclonic meander of the Black Sea rim current, it equalled 7. At Station 5840, one can also visualize a divergence in the ~.nlinltyvalues throughout the water column, equalling 0.01~ with the values of the potential temperature coinciding. It should be appropriately emphasized that seawater sampling intended to provide metrologlcal support for the salinity measurements, was conducted in such a way that the reliability of the acquired results raises no doubts. Thus, in the central sea, the near-bottom boundary layer is markedly pronounced; its depth is 1670-1780 m; and the density ratio above the layer is equal to about 2.7. Near continental slope (within the area of anticyclonic circulation), the near-bottom boundary layer parameters are non-unlformly distributed, the layer's upper boundary descends to a larger depth (in the limiting case, the layer may be absent), and the density ratio above the layers upper boundary increases by 2 to 3 times. MODELLING In modelling the near-bottom boundary layer, we win proceed from the assumption that the layer occurs due to the occurrence of a geothermal heat flux through the sea floor. According to ref. 9, the value of the specific heat flux HQ is uniformly distributed over the area in the deep-water part of the basin (being slightly larger in the margins) and may be evaluated as HQ ,~ 3x 10-2 Wm -2. Furthermore, it is assumed that when salt/heat fluxes propagating from the near-bottom boundary layer are equilibrated, they are controlled

88

v. IV. Eremeev el aL

by the double diffusion mechanism in the diffusive r e , me. The principal purpose of modelling is to identify the conditions facilitating the occurrence of a stationary nearbottom mixed layer in the Black Sea, as well as to determine the response of the layer parameters to the possible climatically induced changes in the salinity balance. RESULTS OF LABORATORY MODELLING As the steady density gradient in the Black Sea main pycnocline is basically governed by the salinity distribution, and the temperature's destabilizing contribution to stability over the larger part of the water column is modest, it appears appropriate to simulate the generation of the near-bottom boundary layer invoking the constant heating of the layer from below, with the constant salinity gradient being steady [10]. In general terms, the convective process develops as follows. Following the initial oscillatory stage of instability, as the temperature grows above the instability point, a well-mixed layer evolves over the bottom, whose boundary tends to rises upward. The evolution of the layer may take place in two ways: (i) temperature/salinity drops at the upper boundary are counterbalanced by density; and (ii) the mixing of convective motions in the mixed layer influences the adjoining stratified fluid. As a result of this, a steady density drop is produced at the upper boundary of the layer. The manifestation of some specific scenario is, obviously, determined by the values of the Reynolds and Richardson numbers near the layer's upper boundary. The first situation is, in large measure, characteristic of the laboratory modelling, while the second one depicts large-scale natural phenomena [10]. The processes of double diffusion in the diffusive regime play an important role in the evolution of the mixed layer. By virtue of this mechanism, at a certain point, the layer ceases to grow. A new layer emerges at its upper boundary, which develops in a similar fashion. As a result, a multi-layered structure, regulating heat and salt exchange, is generated in the near-bottom part of the water colunm. Let us scrutinize the model suggested by Turner [10] for the convection process. Assume a linear, hydrostatically stable salinity gradient in the gravity field, having the Brunt-VkisS.l[t frequency, N ~ = 9/9 d S / d z , to occur in a semi-i~finite basin bounded by the horizontal boItom. At the bottom, we prescribe a constant heat flux, HQ. At any time, t, temperature and salinity axe assumed to be uniformed distributed over the layer. Then HQt = U d A T u ,

9 ASL = 0.SaN ,

O)

where A T v and AS ~ indicate the drops of temperature and salinity, respectively, at the upper boundary of the layer, U denotes the thermal capacity per rn~ss unit, with pressure being constant; and d denotes the layer's thickness. Heat fluxes through the upper boundary are absent, l , order to determine the dependence of the layer's thickness upon time, d(t), it is necessary to prescribe one more relationship between the unknown quantities. In ref. 10, two limiting cases axe suggested for consideration. The first case reads as follows: aAT e = flAS L (2) with the temperature/salinity drops being equilibrated by density. The second case a A T v = 1/313AS L

(3)

implies that the process is taking place with the potential energy being unchanged. Relation (2) is dose to the laboratory modelling conditions. For both relations, dependence

The near-bottom boundary layer in the Black Sea

89

d(t) coincides with the accuracy of a constant factor. For instance, in the case of (3), it has the form d = (6)l/2B1/2N~1tl/2, (4) where B r = gaHQ/Cp is the buoyancy flux (Cp = pC) conditioned by the heat flux. Note that for condition (3), density ratio Rp is constant in time and close to the ratio observed at the upper boundary of the Black Sea near-bottom boundary layer: SAS L Rp = aAT------~ = 3.

Under the real conditions, the layer's upper boundary should not be regarded as a plane where temperature and salinity fluctuate in a jumplike fashion. As time goes on, a boundary layer emerges in the 'undisturbed' fluid due to molecular diffusion. If the near-bottom buoyancy flux is sufficiently significant, the contribution of salt at the boundary may be neglected, and we will derive instability conditions for the diffusive near-bottom thermal boundary layer. As soon as the instability condition is obtained, the near-bottom layer ceases to built up, and another layer evolves at its upper border. The boundary layer becomes unstable under the condition [10]

d=

=

(v Rae/ g~, )l14 B~.I4N,~2 ,

(5)

Here, Rar is the critical value of the Rayleigh number, and v and sz are the molecular viscosity and thermal conductivity coefficients, respectively. Obviously, this structure of the layers is unstable, as, aside from heat, salt is also transported across the layer's boundaries. This fact has been confirmed by the laboratory derived data. MODEL FOR THE BLACK SEA NEAR-BOTtOM BOUNDARY LAYER The/n s/tu data collected in the course of deep-water measurements in the Black Sea allow an assumption that the near-bottom boundary layer is stationary in time. The stability of such parameters as the depth of the layer's upper boundary and the densit), ratio support the supposition. The facts submitted above, indicating that dynamical processes in that layer are very intensive, confirm the hypothesis as to the layer's stationarity, became the observed flow (displacements) and vortical features do not upset the equilibrium. Furthermore, the estimates of the heat flux through the layer's upper boundary provide additional arguments in favour of the stationarity hypothesis. To this end, we will apply seml-empirical relations for the heat flux, derived in the course of simulating double diffusion processes:

& = Cv/a(O.32/Rz,)(gltc:ru)l/3~r(aAT)'/3 F o = Cp/a 3.2 x 10-3 cap (4.8/R~

[101,

(6) [11].

(7)

By substituting Rp = 2.6, AT = 5 x 10-3K, a = 1.3 x 10-4(K) -1, nr = 1.3 x 10-TmZs -I, v = 1.3x 10-6m2s -1, g = 9.Sins -2, and Cp = 4.2x 10SJm-3CK) -1 into relations (6) and (7), we will obtain the value of the two flows as 4.3 x 10-2 and 3.3 x 10-2 W m -2, respectively. Both estimates are satisfactorily consistent with the estimarion of the geothermal flux, particularly, in the case of relation (7), which is invoked to perform calculations when Rp is small In determining the characteristics of the stationary near-bottom boundary layer, we will apply Tumer's approach, adapting it to the Black Sea conditions. For the necessary

90

V.N. Eremeev et al.

model relationships to be unambiguously selected, we will examine the layer's evolution in more detail. Relation (1) implies that the layer's thickness changes very slowly: the characteristic relaxation time of the layer is much smaller than the characteristic time of the layer development, whence ensues, for instance, 10d 0-7 <

1 aE~

(8)

where Ek is the kinetic energy of convective motions per unit area, and BEk/t = ~, is the respective rate of energy dissipation. This provision appears to be reasonable. In fact, in order to obtain a crude estimate, by substituting the quantities calculated from the data compiled in the Black Sea, BT = 0.93 x 10-** m z s-3, Nsz = 2x 10-7s -z, and d = 350 m, into relation (4), we will obtain the layer's evolutionary period, t = 14 years. Let us consider energy evolution within the layer. Over the span of time at, the layer, having current thickness d, receives an influx of heat/~Q = HQat. The layer's thickness is expected to increase by at and will be equal to d' = d +/~d. The relation given below depicts one of the results of this forcing, in keeping with (1) +

= Od'(AT U +

Tu).

(9)

Write down the energy balance equation in the form as foUows: HQSt = C ~ S T U + C ~ d A T U - 5A + 5E~ + 5Ek + 6Era.

(10)

The terms in the right-hand side of equation (10) have the following meaning: //T u is the rising of temperature in the water column having a unit area and thickness d'; and /~A is the effect of gravity (buoyancy), constituted by two terms, namely, 6A § and/~A-, denoting the increasing and the decreasing of potential energy, owing to the mixing of the hydrostatically stable salinity gradient and to fluid warming, respectively. The quantity

5Ek = ~

6t

(11)

represents part of the energy needed to maintain convective motions transferring heat within layer d. By the absolute value, this part is equivalent to kinetic energy dissipation in the layer over the time ~t. Quantity 6E~ is part of the energy required to facilitate the generation of kinetic energy in the layer 5d. If, for the sake of simplicity, we assume the density of kinetic energy of convective motions per mlit volume to be constant

Ek + 6E~ d+Sd

Eh d '

then quantity 6E~ taken to an accuracy with increments of the second order of smallness will be as follows: Ek 0d = 7 6t. (12)

Surnmlng tip the right-handparts of relations(11) and (12),we have Ek 0t + d ~

Ek6t.

Whence, with inequality (8) being considered, ensues that we can ignore the fourth term in the right-hand side of equation (10) in view of its being small. Finally, the last term

7"he near-bottom boundary layer in ~te Black Sea

91

in the right-hand side of equation (10) depicts the loss of energy in the course of mixing, T h e growth of potential energy due to mixing is accompanied by the sink into the turbulent kinetic energy. The relation between these quantities is given by the equation

r

aEt at 6~I = Rj. Here, Rj is the effectiveness of mixing. In conformity with our supposition, the relaxation time of the system is relatively small. Hence, over time `Ht,all the kinetic energy fluctuations will be converted to heat, that is, they will induce an additional warming of the layer. That, in turn, leads to an additional compensating decreasing of the potential energy, `HA-. Hence, equation (10) can be rewritten as follows: HQ`Ht = C{`HT tr + C`HdAT v - (`HA + - ,HA-).

(13)

Summing (1) and (13), with (9) being considered, we obtain 6A = 6A + -6A-

=0,

whence ensues that the variation of the potential energy in the course of the layer's evolution is zero. In terms of the model under eomideration, the latter inference implies that the selection of relationship between thermal flux and the rise of temperature in the layer, given in the form of (1), requires meeting condition (3), or in the general case, AEp = 0, where AEp is the full increment of the potential energy when the layer reaches thickness d. Now let us consider the conditions governing the formation of the stationary nearbottom boundary layer. For the latter's parameters to be unchanging in time, it needs that heat, salt and buoyancy there be in equilibrium. We will write down this state in terms of the buoyancy fluxes: gaFT~ = Br,

gBF~ = Bs,

d = d,.

(14)

The leftand thc fight-hand sides of the equalitiescorrespond to the fluxes through the layer'supper boundary and from the Bosphorus to the near-bottom boundary layer and itslower border, respectively.An equilibrium sets in when the layer thickness d reaches its equilibrium state d~. The drops of the characteristicsat the layer'supper boundary are then also in equilibrium. From (14), we have the following relation: CtFTU

BT

at d = d~.

Assuming that fluxes through the layer's upper boundary axe governed entirely by the mechanism of double diffusion, we can apply the laboratory simulation data [10], whence it ensues that for the diffusive r e , me, the # F s / a F r ratio within the fairly broad range of variability of Rp is close to being constant and averages 0.15. We acquire then Bs/BT

= 7.

(15)

For the stationary state of the layer to be obtained, salt and the heat fluxes must be such that as a result of the evolution of the layer, they would be capable of adjusting to the sink parameters.

92

H N. E r e m e e v et aL

Z,

Z,

_ •

AS r

AS u

.(z) \ 1

!-I I I ro

I I

o

I

.

o

So

"~

Figure & Schematic formation of the near-bottom boundary layer.

Let us examine the layer's evolution in terms of the model discussed above. With the salt flux from the Bosphorus being considered, we will write down the governing equations for the buoyancy in the general form:

fo fo

t B r dt = g a A T U d ,

(16)

t B s dt = g # A S U d.

(17)

Applying the condition requiring that the layer's potential energy be constant, we will find the missing third equation. Density distribution reads as follows: p = poll - ~ ( y

- To) + # ( s

- So)].

Figure 8 schematically shows the evolution of the near-bottom boundary layer, where S = So + s (z) is the prescribed salinity distribution under the condition

fo ~s (z) dz

=

0.

For the equation being sought, we have

AEp = (1/2) 9pod2{-c~AT U + flAS u} - 9Po~

zs (z) dz = O.

(18)

In the case of salinity being linearly distributed over depth, equation (18) has the form A E e = (1/6)gpodz { - 3 a A T u + 3#AS v + B A S L} = O. (19) As quantities BT, Bs and a (z) are assumed to be given, to determine the unknown time-dependent functions d, AT u and AS u, we have equations (16)-(18). Furthermore, when an equilibrium thickness, d = d=, is reached, equalities (14) and (15) must be satisfied. The relation for the heat flux may be rewritten in the form

.f(R~)(~/xTu) ~/3 -- BT,

d -- d,,

(20)

where f is the known function of Rp. The left-hand side of equality (20) reflects the structure of the semi-empirical model relations for the heat fluxes [formulae (6) and (7)]-. The set of equations (14) and (15) has transformed into (19) and (20).

The near-bottom boundary ~

in the Black Sea

93

Obviously, the formation of the near-bottom boundary layer, starting from the moment when Marmara Sea waters penetrate into the Black Sea, appears to be rather complicated, and we will not be able to describe it in detail relying on the approach presented above. Therefore, we will take account of the basic aspects, using the data on the current state of the Black Sea. Assume the near-bottom geothermal thermal flux per unit area to be constant; and for the Bosphorus salt flux, we will examine the more reali.~tie model considering the latter's dependence on stratification We will present the buoyancy flux Bs emerging owing to the salt flux from the Bosphorus to the near-bottom boundary layer of variable depth d, in the form as follows:

Bs = bs(d)(1 - K,).

(21)

Multiplier bs(d) is linked with the occurrence of undisturbed fluid stratification outside the bounds of the near-bottom boundary layer. The dense Bosphorus water penetrating at the depth level z0 and flowing down the sloping bottom is partially mixed with the adjacent fluid. Thus, part of the mixed fluid, having reached density equilibrium, is retained there by virtue of the buoyancy forces. Then it spreads out isopycnically over the horizontal and then, due to the vertical turbulent diffusion, is transported to the surface layer and discharged into the Marmara Sea by the Bosphorus current. As a result, we have the dependence of the salt flux upon depth (stratification). Hence, as the near-bottom boundary layer's thickness increases with time, it receives an increasingly larger amount of salt per unit time, which is considered by the function bs(d). In fact, hundreds of years ago, the breakthrough of Marmara Sea waters into the Black Sea initiated the influence of salt fluxes and stratification upon one another, and today we witness their equilibrium. The current stratification in the Black Sea displays the following peculiarities. Beneath the surface layer, whose depth reaches several dozen metres, the density gradient conditioned chiefly by the salinity gradient is significant in the upper part of the main pycnocline and is essentially smaller in the lower part of the water column. This implies that the vertical salt flux, due to turbulent diffusion, is much larger in the upper part of the main pycuocline than in the deep one. Hence, salt flux per unit depth b(z), is expected to have the form of a function decreasing with depth. Let us determine the form of functions bs(z) and K,, relying on the following speculations. The buoyancy flux reaching the plane z (Fig. 9)

Bs = Bs - f ~ ~z) dz is partially 'absorbed' by the layer Az, with the remaining flux proceeding through that layer downward. Here, Bs is the full buoyancy flux from the Bosphorus per unit area. The flux 'absorbed' by the thin layer Az equals bAz. Assume the flux propagating toward the layer Az to be proportional to the flux propagating from above and to the density drop across the layer

7'

(22)

where k is the dimensionless proportionality coefficient Within the bounds Az ---, 0, we obtain g 2 b+f~bdz-Bs =0. (23) kN

94

V. N. E,remeev et al.

Ap A pb I I I

p~,~

I' I .~p

i I I I

'--I

I

~(~)

bAz z+Az

b (~)

IB,-~

.I F'tgure 9. Schematic salt balance in the Black Sea.

0.0 0

2;0 |

'

'

410 '

'

'

610 '

'

'

8i0 '

'

N,

cycle h-1

'

12~2 H, ml Figure 10. Approximation of the Brunt-V'ai..~ frequency vertical distribution, N = No(zo/z).

The near-bottom boundary layer in the Black Sea

95

By differentiating (23) over z, we have d--~ +

N2-

dz N -2 b = 0.

(24)

Through integrating (24), with the distribution of N ( z ) prescribed, one can derive dependence b(z). In the case of the Black Sea, dependence N(z) can be approximated by the function N = No(zo/z) (Fig. 10). Then (24) is transformed into the equation q+

dN

b = O,

q = k N~176 g

having solution b(z) = boN 2 exp (qN).

(25)

Constant bo is determined from the condition

and is equal to bo = g [exp (kr/zo) - exp ( k r / H ) ] '

r = ~#

(26)

By integrating b(z) within the bounds from H - d to H (Fig. 9), with (26) being considered, we find out the form of function bs(d): =

- exp

kr

.

(27)

This quantity determines the buoyancy flux occurring due to the Bosphorus salt flux to the near-bottom layer having thickness d, when convection is absent. The occurrence of convective processes in the near-bottom layer sharpens the density gradient at the layer's upper boundary, as compared with the background value. As a result, the amount of salt brought to the layer turns out to be smaller than in the case of an undisturbed layer of the same thickness. Part of the salt is retained, due to the effect of buoyancy forces, near the upper boundary, diffusing upwards as far as the upper boundary. The respective 'reflection coefficient' depends upon K,. In accord with (22), we have Bs -- bs(d) - bs(d) k(Apv/p),

hence, K , is #yen in the form If, = k a A T V ( R , - 1).

(28)

Here, a A T U ( R p - I) = ApV/po is the density drop at the upper boundary. By substituting (27) and (28) into relation (21), we define the form of function Bs. Relation (21) holds for the equilibrium state too, where, according to (15), we have an equality bs(d,)[1 - kaAT~U(R, - I)1 = 7BT. (29) Now, eliminating Rp from the set of equations (20) and (29), we can obtain dependence d, = d~(aAT~). The equilibrium values of d, and aAT~v, being sought, are found at the

V.N. Eremeev

96

~ aL

point of intersection of the curves for d~ = d~(aAT~) and d = d(cxAT~),which is derived by solving the determining system of equations (16-18). In this way, the problem on formation of an equilibrium near-bottom boundary layer, within the framework of the adopted model, may be completely resolved. In determining an equilibrium thickness of the near-bottom boundary layer, we restrict ourselves to equation (29) and to the evaluation of Kr, by expressing it through the known parameters and Rp, for instance, from relation (7). An estimate for Rp = ~(AS L + A S u ) / a A T u can be derived fxom the condition of potential energy conservation (18). In the case of linear density distn'bution (19), we have n , = 3 - 27 t',

(30)

where .~u = ~ A S L / a A T V . Density distribution over depth, corresponding to the model Brunt-V[fisglg frequency distribution, N = No(zo/z), may be given in the convenient form p ( z ) ; ~ A 5 'L , l n 4 _ l z + d

In4-1

"

(31)

Here, the z-axis is directed upwards. By substituting (31) into equation (18), we get Rp ~ 2.43 - 1.43 ~,v.

(32)

From equations (16), (1"/), and condition (15), we can readily obtain "ru < "/.-~ 0.15, whence we have for equations (30) and (32), respectively, 2.7
and

2.21
Both estimates are satisfactorily consistent with the mean Rp = 2.6 at the upper boundary of the near-bottom boundary layer. In order to elucidate the meaning and to assess the significance of the parameter k, we will return to relation (22). The reasoning for the inclusion of the latter into consideration was as follows. Assume that an amount of salt, .gls - Ms(z), reached the depth level z. The salt at issue is dissolved in some volume of fluid having nonuniform density. The complete density drop in the parcel of water, Ap~ = /r,,~h -- p(z) (Fig. 9), where/~,o~ indicates the density of the Bosphorus fluid, which reached the upper boundary of the halocline. Function ms, shown in Fig. 9, represents the function of salt distribution within Apb, normalized my Ms - Ms(z): /, m s d p = !.

(33)

Due to the effect of buoyancy, the salt contained in the parcel of water having the interval of density changing Ap, will be transported to the layer Az: (-f/Is - Ms(z)) re~

(34)

and the remaining part will penetrate to the deeper layers. Here, m ~ is the value of function m s at the origin of coordinates.

The near-bottom boundary layer in the Black Sea

97

The evolution of function m~ in Fig. 9, specifically, its decrease starting at the origin of coordinates, indicates that the volume of the fluid with the lesser density (salinity) is much larger than the volume of the dense fluid. This qualitative form of ms does not appear to be unexpected and is, apparently, realistic. In fact, the fairly reliable estimates of the geothermal flux and heat balance within the near-bottom boundary layer, given above, along with natural condition (15), indicate that less than 0.02% of the total amount of salt brought to the sea [below, see the estimates for salt fluxes (37)] is discharged to the relatively thick (300-400 m) near-bottom layer per unit time. The larger portion of salt is 'absorbed' by the main pycnocline's upper layer. Multiplying (34) by g~/Sas, where S'm is some average Black Sea area, and introducing function b(z), we obtain

-

f2bdz)pros\---_] ~ ( 'AP )p

= Azb.

(35)

From relations (35) and (22), we have ]g = prn~.

If the process of Bosphorus salt mixing over the vertical is self-similar, the quantity m ~ is constant. For the parameter m~r to be estimated, we will approximate function m ] by a rectangular, with condition (33) being preserved: r~s = (IIA'ppb).

Here, ~ p is some characteristic interval of density variation within a parcel of the transformed Bosphorus water. In the capacity of a rough estimate for -~/p, we adopt 10-3; then k ~ 102 and K, --- 10-3. A relation for dc will be derived from formulae (27) and (29): (36) In order to perform the calculations, we must choose the values of the parameters (36). As in deriving (36) we employed a stationary one-dimensional model of the Black Sea, the chosen parameters, by definition, are the mean climatic quantities averaged over the basin area. Assume z0 = 50m, H = 2000m, No = 10cycleh -1 [2,6], or 1.75x 10-2s -1, g = 9.8ms -2, and ~ = 0.15. Relations for the fluxes have the forms

BT =

gaHr Cp

'

/~s = g~345000 Sm

The numerical coefficient in the relation for ]~s reflects the 345 tons of salt axe discharged per second by the Bosphorus We will assume the Black Sea area, ~as, to be equal to 3.8 x 3• 102 W m -2 and t~ = 1.3• 10-4 (~ -I, we ultimately have 7BT /~s = 7.8 x 10 -9 m 2 s-3.

(37)

fact that approximately to the Black Sea [12]. 1011m 2. Taking HQ = = 1.4x 10-22 m 2 S-s and

98

V.N. Erem,evet al. 1200" dc, m

8OO

4O0

~

~o

~0o

~Ok

Figure 11. The dependence of the near-bottom boundary layer's equilibrium thickness upon k.

As we lack detailed data on the inflow of Bosphorus waters to the abyssal Black Sea, the calculations of d~ retain some ambiguity related, in the case given, to the value of the parameter k. Quantity k parameterizes the processes of salty Bosphorns waters inflow and mixing. Figure 11 shows the dependence (36) of the equilibrium thickness of the near-bottom boundary layer on parameter k. For the observed average thickness of the near-bottom boundary layer, de ,,, 350 m, we will take k = 3350. Quantity dc is rather sensitive to the choice of k. For k ranging within 1000--4000, d~ changes approximately by 18 times. DISCUSSION OF THE RESULTS Analysis of the /n ~'tu measurements, alongside the approach to describing specific features of the structure of abyssal Black Sea waters, should, apparently, be regarded as a preliminary diagnosis, which is not at bias with the hypothesis for the occurrence of a stationary near-bottom boundary layer. The inference that follows from the modelling results is that, aside from the propagation of the geothermal heat flux, the layer under consideration strongly depends on the stratification of the Bosphorus salt flux, at the layer's upper boundary, inclusively. In fact, if we take the specific buoyancy flux due to the salt flux, b(z), to be constant and apply equation (29), the value for d~ will turn out to be smaller than 50 cm. Besides, only the dependence of K, in equation (28) on density drop at the layers upper boundary, ( A p ~ / p ) = a A T U ( R p -- 1) allows one to simultaneously satisfy conditions (15) and (20), although is does not appreciably influence the thickness of equilibrium near-bottom boundary layer. Another Sis aspect contributing to the formation of the near-bottom boundary layer is the specific exchange in the near-bottom stratum. The prevalence of some mechanism for exchange, other than the mechanism for double diffusion, or the more essential role of the near-bottom friction would thoroughly modify the nature of structure generation in the considered area. Amongst the factors capable of influencing the stationary near-bottom boundary layer's parameters is a heat flux from the Bosphorus and a geothermal flux in the domain not encompassed by the near-bottom boundary layer, the effect of the heat/salt fluxes, propagating from the layer's upper boundary, upon the stratification of the adjacent layers, and the dependence of fluxes upon the current thickness of d when the layer is developing by virtue of the modification of the area of its upper boundary. Let us discuss some aspects of the acquired results.

The near-bottom boundary layer in the BlackSea

99

CAN A SYSTEM OF STATIONARY LAYERS OCCUR? When the formation of a stationary near-bottom boundary layer is completed, the latter's upper boundary proves to be in a state of dynamic equilibrium. Diffusive heat/salt fluxes propagating from the layer seek to expand the transition area between the layer and the overlying fluid. As the molecular heat diffusion coefficient is two orders of magnitude larger than the respective coefficient for salt, the thermal boundary layer tends to develop more rapidly, which eventually gives rise to its instability. A secondary mixed layer starts to evolve above the basic layer. It is readily demonstrated in the frame of the suggested model that the secondary layer is not capable of reaching an equilibrium state. In fact, the characteristics of the secondary layer are dictated by the heat/salt fluxes from the basic near-bottom boundary layer and by the additional salt flux coupled with quantity b(z), due to the expansion of the layer. For the fluxes travelling from the near-bottom boundary layer, we satisfy condition (15) fixing the ratio between the fluxes at the layer's upper boundary. The same condition must be satisfied at the upper boundary of the secondary stationary layer together with the heat/salt balance condition. When there is an additional influx of salt, this condition cannot be met. The flux of heat from the Bosphorus and sloping boundaries toward the undisturbed layer, not considered by the model, does not qualitatively change the result. Otherwise, that would merely imply that the near-bottom boundary layer has not yet reached an equilibrium state. At the same time, the spontaneously emerging and degenerating secondary layers or the combinations of layers are expected to play a vital role in the near-bottom boundary layer to the overlying fluid. Let us evaluate the vertical scale and the time scale of the secondary layer, relying on Tumer's speculations and on relations (4) and (5). Assuming Rac = 104,with the values of the remaining parameters, cited above being considered, and replacing, in accord with (3), the multiplier 1/4 for the brackets in (5), by 3/4, we obtain dr '-. 23 m, tc ,,, 22.5 day. (38) The estimation of the horizontal scale of the phenomenon, in terms of the model given, does not seem possible. The vertical scale in (38), by the order of magnitude, is dose to the mean value of the transitional layer at the upper border of the near-bottom boundary layer (h = 55 m), calculated, from the/n ~'tu measurements. Bearing in mind that the secondary layer's upper border may be eroded because of the generation of the new layers and because of the destruction of the existing ones, the agreement may be indicative of the possible contribution of stratification to the formation of the transitional layer h. Also note that the transfer of heat and salt upwards through convection, involving the formation of homogeneous layers, is not always the case. That mechanism ceases to function when Bs/BT = 1. We will determine the respective vertical scale by replacing 7BT/BS in (36) by BT/Bs. The scale thus acquired, dl -,- 1150m, corresponds to zl -,, 850 m, or roughly, to the upper border of the abyssal waters [4]. THE VERTICAL DIFFUSION COEFFICIENT FOR THE UPPER PART OF THE BLACK SEA HALOCLINE The Bosphorus Strait is a unique source of salt for the Black Sea. In keeping with the stationary condition, the salt transported by the Bosphorns undercurrent to the sea must be carried away from the basin by the Bosphorus current. A variety of processes

v.N. Eremeev et al.

10o

contribute to the formation of the vertical fluxes of heat, salt and passive impurities in the main pycnocline. Amongst these are shear flows and the overturning of internal waves, near-bottom friction, and the mechanism for double diffusion. The ultimate product of the action of those aspects must be the establishing of a salt balance in the sea. The application of the model under discussion enables one to evaluate the buoyancy flux and the vertical diffusion coefficient in the Black Sea, depending on depth or N as a result of the integrated action of the mechanisms responsible for vertical exchange. Assume that the down-oriented buoyancy flux occurs primarily due to the Bosphorus salt influx. For the sake of simplidty, we will ignore the other aspects, the effect of the near-bottom boundary layer being among them. Buoyancy flux toward the layer having thickness Az is constituted by b(z)Az, as well as by the contributions from the horizontal borders, Fa(z + Az) and Fe(z). The buoyancy balance equation has the form

b(z)Az = FB(=) - FB(z + a=). By dividing both parts of the equaLity by Az, we obtain within the bounds Az - , 0 b(z)

=

-

dFa dz "

With b(z) having been prescribed, one can determine the dependencies being sought. Adopting approximation N = No(zo/z), applied above, and prescribing b(z) in the form of (25), we have

Fs(~v) ~a =

N2

,

(40)

where tea is the vertical salt diffusion coefficient. The vertical buoyancy flux, Fa(N), equals zero at the bottom (z = H) and equals Bs, at z = z0. The dependence of ~r upon N (40) is shown in Fig. 12. ' As over the larger part of the main pycnocline, vertical stratification is dictated by the distribution of salinity, the fluxes of heat and impurities can be calculated by means of relation (40), except for the surface and the near-bottom layers, where this statement does not hold. Also note that ~r was calculated invoking the information about

0.12"/CBpC012S"I 0.10-

0.080.060'041 0.02 0.~

N, cydc h-I 0

Figure 12. The dependenceof the verticalsalt diffusioncoettidentupon stratification.

The near-bottom boundary layer in the Black Sea

101

the observed near-bottom boundary layer parameters. Hence, the derived estimate is expected to be rather accurate. This allows us to hope that relations (39) and (40) will prove to be useful. CONCLUSION Through the interpretation of deep-water probing data, using indirect methods, we have studied the peculiarities of the general dynamics and vorticity in the abyssal part of the Black Sea. Invoking the data on the p a r a m e t e r s of inflowing M a r m a r a Sea waters and on the current thermohaline structure of the Black Sea pycnocline, we have generated a model for the distribution of the Bosphorus salt over the Black Sea water column. It has been demonstrated that to m a k e possible the existence of a stationary nearbottom boundary layer in the Black Sea, at whose upper border exchange takes place by virtue of the mechanism for double diffusion, the concurrent propagation of the b o t t o m geothermal heat flux and the Bosphorus salt flux are distributed over depth surfaces. By applying the information about an average vertical scale of the current nearbottom boundary layer, in the frame of a unidimensional model, we have derived an analytical dependence of the vertical diffusion coefficient Black Sea in the main thermohalocline upon depth. REFERENCES 1. Vladlmirtscv, Yu. A. To the issue of deep-water circulation in the Black Sea. Okeanologia (1964) 4, 1013-1019. 2. Novitsky, V.P. Vertical structure of the Black Sea water column. Trady Azov-Black Sea .r~t. FLsk. Oceanogr. (1964) 23, 3-22. 3. Filippov, D.M. Carulation and Structure of Black Sea Waters. Moscow:. Nauka (1968). 4. Ivanov, L.I. and Shkvorets, L Yu. Thermohaline structure of abyssal and near-bottom waters of the Black Sea. Phys. Oceanoge. (1996) 7, 437-443. 5. Aubrey, D.G., Oguz, T., Dcmlrov, E., ~ al. HydroBlack-91. Report CrD Intcrcalibration Workshop. Woods Hole Ocoanogr. Inst. 1-10 December 1991. IOC Workshop Rep. (1993) No. 91. 6. Murray, J.M., Top, 7- and Ozsoy, F_ Hydrographic properties and ventilation of the Black Sea. DeepSea Res. (1991) 38, 663-689.

7. Oguz, T., Besiktcpc, S, Basmrlg O., eta/. CoMSBlack-92a. Physical and Chemical htercalibration Workshop. IOC Workshop Rep. (1993) No. 98. 8. Spencer, D.W. and Brewer, P.G. Vertical advectioa, diffusion and redox potentials as controls on the distribution of manganese and other trace metals dissolved in waters of the Black Sea. J. Geophys. Res. (1971) 76, 5837-5892. 9. Duchkov, A.D. and KaTantscv, S.A. Thermal flux ill the Black Sea trough. In: Geophysical Fielda of the Atlantic Ocean. Moscow:. Nauka (1988), pp. 121-130. 10. Turner, J.W. Buoyancy Effects in Fluids. New York: Cambridge University Press (1993). 11. Kelley, D.E. Fluxes through diffusive staircases: a mew formulation. I. Geophys. Res. (1990) 95, 3365-3371. 12. Uniuata, U., Oguz, T., Lati~ M.A., a aL On physical oceanography of the Turkish straits. In: The Physical Oceanography ~ Sea So~t.v. Ed. NATO/ASI Series. Kluwer. Deventcr, The Netherlands (1989).