Ventilation of Black Sea pycnocline by the Mediterranean plume

Ž .Journal of Marine Systems 31 2001 77–97www.elsevier.comrlocaterjmarsys

Ventilation of Black Sea pycnocline by the Mediterranean plume

E.V. Stanev) 1, J.A. Simeonov 2, E.L. PenevaDepartment of Meteorology and Geophysics, Faculty of Physics, UniÕersity of Sofia, 5 James Bourchier Street, 1126 Sofia, Bulgaria

Received 30 September 1999; received in revised form 17 January 2000; accepted 25 April 2001

Abstract

We present here results of numerical simulations with reduced gravity model of the Mediterranean plume intruding intothe Black Sea. The model has horizontal resolution of 600 m. The scenarios analyzed in the paper aim at quantifying thesensitivity of the plume to the ambient stratification and the fluxes of mass, momentum and buoyancy through the BosphorusStraits. The simulated plume characteristics are compared against observations. It is found that the mixing of Mediterraneanand Black Sea water, as well as the termination depth of the plume, are very sensitive to specific combinations of thegoverning parameters. The behavior of gravity currents on the shelf and on the continental slope is also studied and the role

Ž .of topographic control is demonstrated. The relatively large entrainment rate ;10–12 compared to the one in the AtlanticŽ .ocean ;2–3 , shallow penetration and small deflection to the right caused by the earth rotation are explained as a result of

the specific combination of governing parameters, topography routing and ambient stratification. A simple two-componentchemical model for the interaction between H S and O is coupled with the dynamical model in order to investigate the2 2

Ž .impact of the Bosphorus plume rich in O on the oxidation of anoxic water. q 2001 Elsevier Science B.V. All rights2

reserved.

Keywords: Gravity currents; Entrainment; Oxidation of hydrogen sulphide

1. Introduction

Gravity currents provide an important mechanismcontributing to the ocean water mass formationr

Ž .transport Price and Baringer, 1994 . Most of therecent studies are focused on the Mediterranean out-

Žflow Price et al., 1993; Baringer and Price, 1997a,b;.Jungclaus and Mellor, 2000 and on the outflows

Žthrough the North Atlantic straits Jungclaus and.Backhaus, 1994 . In the case of some semi-enclosed

) Corresponding author. Tel.: q359-2-62561x289; fax: q359-2-962-5276.

Ž .E-mail address: [email protected] E.V. Stanev .1 Present affiliation: ICBM, University of Oldenburg, Germany.2 Present affiliation: Florida State University, Tallahassee, FL,

USA.

Žbasins characterized by limited exchange with the.ocean , the conditions for deep water formation are

too different from the oceanic case, and the corre-sponding processes themselves have much smallerspace-scales but are of paramount importance. Thismotivates us to address the evolution of a buoyancyplume originating from a strait separating oceanbasins with very different thermohaline character-istics. We focus on the Black Sea, which gives aunique test case, characterized by extremely sharp

Žsalinity difference with the neighboring basin theMediterranean Sea surface salinity is ;36 vs. ;18

.in the Black Sea , very strong vertical stratificationŽsalinity of ;18 at sea surface vs. 21.5 at ;300.m , and variable topography in the outflow area

Žshallow shelf of ;50 m and abrupt change of the.depth up to 2000 m in 10–50 km only, Fig. 1 .

0924-7963r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0924-7963 01 00048-3

( )E.V. StaneÕ et al.rJournal of Marine Systems 31 2001 77–9778

Ž .Fig. 1. The Black Sea and the Bosphorus outflow area with rectangle .

The Black Sea is a typical example of an estuar-ine basin where the large river discharge and thelimited exchange with the Mediterranean Sea createsan extremely stable vertical stratification, controlledby the density differences between the two seas. Theobservations do not indicate substantial ventilation ofthe deep layers, supporting speculations that the deepwater has been formed a long time ago, and that thedeep layers are currently unaffected by the sinkingplume. One major focus in the present paper is thedependence of the termination depth and the entrain-ment in the Black Sea on the external forcing andstratification.

It is known from the theory of geostrophic cur-rents flowing on a sloped bottom that after exiting

Žthe strait, the stream deflects to the right in the.northern hemisphere , closely following the isobaths.

Most observations have failed to trace the Mediter-ranean plume to the east of the Bosphorus Straits

Žexit that is to the right looking in the direction of.the outflow , but there is clear evidence that it

persistently takes a northwest track within the shelfŽ . ŽTolmazin, 1985 . Recent observations Yuce, 1990;Latif et al., 1991; Oguz and Rozman, 1991; Di Iorio

.and Yuce, 1999 explain the westward deflection ofthe plume as due to the guidance by a narrowunderwater channel. It is worth noting here that in

Ž .the presence of bottom friction or any drag , theflow tends to cross the isobaths, thus descending intothe deeper layers. Also important is the fact that the

Ž .width of the plume, when it exits the strait ;2 km ,

is much smaller that the deformation radius; there-fore, its subsequent adjustment and spreading on theshelf is significantly ageostrophic. However, the fun-

Ž .damental issue of why there is: 1 no pronouncedturn to the right after the plume reaches the continen-

Ž .tal slope, and 2 no further propagation along iso-Žbaths as this is the case with the Mediterranean

.plume leaving the Gibraltar Straits is still not re-solved. In the present study, we answer this questionby showing that after the shelf break, the plumedynamics is dominated by entrainment. In the ex-

Žtreme case of very strong drag e.g., the entrainment.occurring beyond the shelf break in our model , this

descent will dominate and there will be little propa-gation along the isobaths.

Another fundamental issue concerning the mixingmechanisms arises from the fact that the verticaldiffusion by itself could hardly explain the mixing in

Žthe stagnant intermediate layers Murray et al., 1991;¨ .Ozsoy et al., 1993 . Now, it is widely accepted that

Ž .the Mediterranean Sea Water MSW entrains coldsurface or near-surface water and forms the BlackSea deep water. The importance of entrainment wasproved in a very convincing way by Buesseler et al.Ž . Ž .1991 and Staneva et al. 1999 , who analyzed theobservations and model simulations of Chernobyltracers. The above findings give enough argumentsto conclude that the entrainment and the lateralintrusions dominate the penetration of MSW into theinterior basin and provide an important mechanismfor internal mixing. However, there is still a large

( )E.V. StaneÕ et al.rJournal of Marine Systems 31 2001 77–97 79

Ž .uncertainty see the beginning of Section 4 aboutthe rates of entrainment and the depth of injections

Žof MSW. The scales of the outflow it spreads.several tens of kilometers from the strait; see Fig. 1

dictates a separate study addressing the small-scaleprocesses governing the gravity currents along theshelf and on the continental slope. The detection ofthe plume is difficult, particularly when the modifiedMSW approaches the properties of the Black Sea

Ž . ŽWater BSW on the continental slope Oguz andRozman, 1991; Gregg and Ozsoy, 1999; Di Iorio and

.Yuce, 1999 .The numerical simulation of gravity currents pre-

sents an important complement to observations, help-ing to quantify the dominating physical balances.

Ž .Although stream tube models Smith, 1975 are stillŽapplied to the outflows from marginal seas Price

.and Baringer, 1994 , reduced gravity modelsŽJungclaus and Backhaus, 1994; Simeonov et al.,

.1997 or fully 3D primitive equation modelsŽGawarkiewicz and Chapman, 1995; Chapman and

.Gawarkiewicz, 1995; Jungclaus and Mellor, 2000give a more complete view of the dynamics ofsinking plumes under realistic conditions. As demon-

Ž .strated by Simeonov 1996 and Simeonov et al.Ž .1997 , the use of reduced gravity model in theBlack Sea conditions gives a description of the pro-cesses over realistic topography, which is more ade-quate than the one obtained with stream tube models.At the same time, the reduced gravity model con-sumes much less computer resources than the fully3D models, which make it possible to run it with

Ž .very high resolution 600 m in our case . We willillustrate that our model provides a tool-to-traceMSW in the areas where existing observations aresparse and their accuracy is low. Our objectives here

Ž .is to focus on: 1 the phenomenology of the plumeŽ .as simulated by the model, and 2 the entrainment

and ventilation depth as dependent on external condi-tions, such as the magnitude of the fluxes in the straitand the vertical stratification. The third objective isto extend the research beyond the pure physicalapproach by including chemical processes, which arefundamental in the Black Sea. There are indicationsthat the Bosphorus plume and the signals originatingfrom the strait can be clearly detected in the chemi-cal composition of sea water; therefore, the analysisof the spatial distribution of chemical tracers like O2

is very useful when studying the termination depthof gravity plumes and ventilation processes. Thismotivates us to address here the role of the Bospho-rus inflow in the process of oxidation of anoxicwater.

In Section 2, we describe the numerical modeland the details of individual simulations. The spatialcharacteristics of the simulated plume are analyzedin Section 3. The mixing of MSW and BSW isaddressed in Section 4, followed in Section 5 by thedescription of coupled dynamical–chemical modeldesigned to study the spatial characteristics of theventilation of deep water in the vicinity of theBosphorus Straits. The paper ends with short conclu-sions.

2. The model and scenarios

2.1. The numerical model

The numerical model is essentially the same asthe one described in the paper by Jungclaus and

Ž .Backhaus 1994 , where it has been used for studieson the outflow through the Denmark Strait. Thegoverning equations of the model are given in Ap-pendix A. The model consists of a turbulent lower

Ž .layer of height H the plume , underlying an upperlayer at rest. The outflow is a density-driven bottomcurrent accelerated by the local gradients of topogra-

Ž .phy. Bottom friction tending to decelerate the flowobeys a quadratic drag law. The corresponding coef-

y2 Ž .ficient rs3=10 see Appendix A has beenchosen after carrying out a number of calibrationexperiments with friction coefficient ranging from3=10y3 to 3=10y2 and is in the ranges deter-

Žmined from observations in the same region Di.Iorio and Yuce, 1999 . The major difference between

simulations with small and enhanced friction is thatin the second case, the flow slightly slows down.However, the model sensitivity to this parameterseems to be much weaker than the sensitivity to thecoefficient c , which controls the interfacial ex-L

change. The model entrainment ensures that the ex-change at the interface between the plume and theambient water depends on the Richardson number,which becomes significant if the current is acceler-ated by the sloped topography. The coefficients of


turbulent exchange and diffusion are taken as A sh

ATs50 m2 sy1, respectively.h

The lateral extent of the plume is determined bythe movable boundary technique, described by Jung-

Ž .claus and Backhaus 1994 . In the shelf regions oftidal seas, where the local water depth is smaller thanthe tidal range, some grid points may become AdryBin the ebb period. The same can be applied to theBosphorus outflow—wherever it is absent, the inter-face depth and the sea bottom depth coincide. Whenthe density currents reach some point, the interfaceleaves the bottom and this point is further considered

Žas AwetB point. In the opposite case a retreat of. Ždensity current , the AwetB model area decreases the

.model can simulate even multiple connected plumes .For more details on the numerical formulation of thistechnique, we refer to the paper by Jungclaus and

Ž .Backhaus 1994 . The Black Sea set-up of the model,as well as the analysis of the dominating balances is

Ž .described by Simeonov 1996 and Simeonov et al.Ž .1997 . The sensitivity of the model response todifferent topographies and bottom roughness is ana-

Ž .lyzed by Peneva and Stanev 2000 .

2.2. The model domain and boundary conditions inthe control run

Ž .The model domain Fig. 2 is resolved with ahorizontal grid interval of 600 m. The topography istaken from the bathymetric maps of Latif et al.Ž .1991 , showing that the strait of Bosphorus has anunderwater extension in the shelf area of ;10 km.The channel has the same orientation as the strait inthe first 8 km. Then it turns to the north, and afterthat to the northwest, reaching the wide and flat shelf

Ž .area Fig. 2b with a slope of ;1:500. The conti-nental slope has orientation from northwest to south-east and an abrupt change of the depth between 100and 1000 m occurs in ;10 km only. The modelarea has almost solid boundary to the south, with asmall opening, where the characteristics of the straitoutflow are prescribed. The other three boundariesare open. The model area is extended towards the

Žbasin interior with a buffer zone 10 points in each.direction , where the horizontal grid size increases

linearly up to a maximum value of 27.7 km. Thisbuffer zone is not shown in the figures and is alsoexcluded in the presentation of model results.

ŽAt the open boundaries the boundaries of the.large model domain , we prescribe zero normal gra-

dients,

ES ET Eus0, s0, s0,

En En EnL L L

EÕ Ezs0, s0, 1Ž .

En En LL

where L corresponds to eastern, northern and west-ern boundaries, which allows free propagation of the

Ž .plume for the notations, see Appendix A .ŽAt the solid boundary M M corresponds to the

.southern boundary :

< <U s0, V s0. 2Ž .M M

The initial width of the plume is limited by theŽ .straits opening three grid elements , which is smaller

Žthan the baroclinic radius of deformation ;10–20.km in the Black Sea . The thickness of the plume at

the straits exit is specified such that the simulatedŽ 4transport was comparable to the observed one 10

3 y1 . Žm s ; Unluata et al., 1990 . This value corre-3 y1.sponding to a net annual outflow of 310 km year

is reached in the model when the thickness of theplume at the boundary is prescribed as 26 m. Thesalinity in the inflow points is set to 37. This large

Ž .value double the ambient salinity provides the neg-ative buoyancy flux and maintains the slope convec-tion in the model. The temperature in the inflow is

Ž14 8C Yuce, 1990; Murray et al., 1991; Oguz et al.,¨ .1990; Ozsoy et al., 1993 .

The heat and salt fluxes at the interface are de-fined as the product of the entrainment velocity andthe temperaturersalinity differences between the

Ž .plume and its environment see Appendix A . Theevolution of these fluxes in time shows that themodel reaches quasistationary state after ;20 daysof integration. Most of this adjustment to forcing andenvironmental conditions is reached in ;5 days.

The ambient stratification corresponds to the an-nual mean profiles of temperature and salinity, and isresolved with a vertical discretization of 10 m. Thesedata are used for the entire model domain and arekept constant in time during the integration. The twomajor topographic features in the outflow zone, theunderwater channel and the shelf break are wellpronounced in Fig. 2b. Practically, the ambient fluid


Ž .Fig. 2. a Bottom salinity corresponding to the ambient stratification, contours are plotted from 18 to 22 by 0.5. The data from Latif et al.Ž . Ž .1991 are superimposed along the core of the plume. The dash curves are the 60-, 80-, and 100-m isobaths. b Model topography, the

Ž . Ž .contour interval is 10 m in the shelf region full lines and 100 m on the continental slope dashed lines .

acts as a motionless sponge, where the intrusionsfrom the plume terminate. Thus, our results providediagnostics of different types of penetration of MSWunder predetermined stratification. This one-way ex-change is an important model simplification.

2.3. Model scenarios

Our study addresses the question of how thecharacteristics of outflowing water depend uponsource water properties and oceanic conditions. We


Žvary boundary conditions temperature, salinity and.thickness of the outflow in some ranges correspond-

ing to present-day conditions, as well as to condi-tions that could have dominated the water massformation in the past. Thus, we create differentcombinations of governing parameters by varyingMSW temperature and salinity, the thickness of theplume, as well as the ambient stratification, assign-

Ž . Ž .ing to them realistic R and test T values. EveryŽ .individual experiment Table 1 is identified by the

combination of three such letters in the followingorder: ambient stratification, initial thickness of theplume, and MSW salinity. The smallest number ofexperiments needed to study the individual and col-lective impact of boundary conditions on the behav-ior of the plume is 23. We will refer to the experi-

Ž .ment RRR as to control run CR .ŽThe increase of salinity contrast between the

.MSW and the Black Sea ambiance and the thick-ness of the outflow at the same time leads to unreal-istically large transport. Normally, these parametersare negatively correlated; therefore, in the T experi-ments, we decided to use salinity values that are twotimes smaller that the ones in the control run. The Rand T stratifications are shown in Fig. 3a,b. Tocreate T-profile, we just decrease the salinity differ-ence between each level and surface level two times.This case of decreased stability of stratification couldroughly represent the oceanographic conditions inthe paleo-Black Sea, which were established under

Ž .different from present-day freshwater flux and straitexchange. The extreme of this experiment is the one

Table 1Experiments’ nomenclature and major forcing and ambient fluidparameters

Identification dSrd z h SB

RRR R 26 37RRT R 26 27RTR R 13 37RTT R 13 27TRR T 26 37TRT T 26 27TTR T 13 37TTT T 13 27HRR H 26 37

R, real; T, test; H, homogeneous.

Ž . Ž .Fig. 3. Ambient fluid stratification: a salinity solid and temper-Ž . Ž .ature dashed line in RRR experiment; b density in R-experi-Ž . Ž .ments full line and in T-experiments dashed line .

with homogeneous vertical stratification and is de-Žnoted as HRR Homogeneous ambient fluid, R-thick-

ness of the plume and R-salinity contrast in the.outflow location . This experiment aims at simulat-

ing the bottom boundary currents in the transitionperiod after the reestablishment of the connectionwith the Mediterranean Sea. At this time, the BlackSea was almost a freshwater lake with oxic condi-tions and deep ventilation. The weak stratificationdid not present an obstacle for the gravity currents


originating from the strait, and the MSW reached thedeepest levels. We admit that the processes in the

Žreal sea could have developed quite differently with.very slow increase of the undercurrent ; however,

there are recent speculations about possible catas-Ž .trophic scenarios Ryan et al., 1997 , and the experi-

ment HRR roughly corresponds to such a situation.We calibrate the model parameters in the controlŽ .run see Section 2.1 and Appendix A in a way to

Žobtain the best agreement with observations the data.from observations are given with stars in Fig. 2a .

Ž .These results taken from literature sources areprobably not enough for precise model tuning, butthey could give us at least a first-order estimate forsuch important parameters of the plume as width,thickness, extension, salinity contrast. Thus, the sim-ulations in RRR are supposed to be the AperfectBones, to which we will compare the results of our

Ž .sensitivity experiments Table 1 . The model param-Ž .eters friction and mixing coefficients are kept the

same in all experiments.

3. Spatial characteristics of the plume

The plume has the form of a thin wedge with welldefined boundaries along the underwater canyon andon the continental shelf. The thickness ranges from 1m at the edge of the plume to 17 m in the channelŽ .Fig. 4c . These values might seem slightly different

Žfrom the estimates based on observations 10 m in.the channel; Latif et al., 1991 , but we must keep in

mind that in the reduced gravity model, the tempera-ture and salinity are homogeneous in the vertical andare bounded by material interface, whereas in theobserved data, there is a continuous transition be-tween the dense bottom layer and the ambient fluid.Thus, the calculation of the interface depth is subjectto interpretation.

To give an idea about the agreement betweenobservations and simulations, we refer to Fig. 2awhere some bottom salinity values measured by

Ž .Latif et al. 1991 are given, as well as their esti-mates about the most probable path of MSW. Bothindependent estimates show good agreement, indicat-ing that the model is well tuned to the observations.The plume turns to the right on the flat shelf, whichis an indication that the Coriolis force starts to

Ždominate the solution in this region compare alsowith Fig. 11 of Yuce, 1990, Fig. 4 of Latif et al.,

.1991, and Fig. 4 of Di Iorio and Yuce, 1999 . Thecurvature of the right turn is comparable to the onecorresponding to the Rossby radius of deformation.The effluent is thin in this area, reaching ;3 m in

Ž .the simulations Fig. 4c vs. 2 m in the observationsŽ .reported by Latif et al. 1991 . Taking into account

the number of model simplifications, this agreementseems rather good.

As the current flows onto the continental slopeŽ .steepness ;1:10–20 , its topographic acceleration

Ž .increases Fig. 4d , which is accompanied by strongentrainment. The result is a further reduction of the

Ž .plume salinity Fig. 4a , but an increase in its thick-Ž .ness Fig. 4c . The loss of density contrast on the

slope is followed by a deceleration of the plume.However, unlike the case with the Gibraltar outflow,

Žwe do not distinguish in the RRR experiment and.also in the observations a situation where the bot-

tom current follows the isobaths as a quasi-geostrophic flow.

The model plume does not reach the modelŽ .boundaries Fig. 4 , supporting the observational evi-

dence that it cannot be found to the west of 28850XEŽ .Oguz and Rozman, 1991 . According to these au-thors, the plume is almost undetectable on thecontinental slope, which is due to the very smalldifferences between the plume and ambient waterproperties. In the deeper levels, lateral intrusionsdominate the penetration of the MSW, but theseprocesses are not well represented in our model sincethe plume is arrested to the bottom. For vanishingly

Žsmall values of density contrast between the plume.and ambient fluid , the plume looses its identity and

simulations are not representative for a gravity cur-rent. A similar problem exists in the stream tubemodels: if the current vanishes, the layer thicknessmust become infinite in order to conserve the flux ofwater. The loss of identity below some small value

Žof the density difference Dr s0.3 density units;crit.Fig. 4e might serve as a criterion to trace the

boundary beyond which the results of the model losecredibility. This number was chosen after analyzingthe sensitivity of results against this parameter, and itroughly corresponds to values, beyond which theplume is difficult to be observed in the natural

Ž .conditions Gregg and Ozsoy, 1999 .


ŽThe simulated entrainment velocity see Eqs.Ž . Ž . Ž . Ž ..A6 – A9 and A11 – A13 and heatrsalinity fluxshow clearly that there are two regions where the

Ž .mixing is well pronounced Fig. 5 . The first regionis in the underwater channel and just after it, and isdue to the large contrast between MSW and BSWŽ . Ž .Fig. 5d . The second and major one is close to theshelf edgercontinental slope. Thus, three characteris-tic areas are noteworthy: the two areas where thesalinity fluxes, and hence the effects on plume dilu-

Ž .tion by entrainment is increased Fig. 5a,d , and theone situated on the flat shelf, where both salt andwater exchange with the ambient fluid are relativelysmall.

In the case of homogeneous stratification, theŽgravity plume penetrates much deeper and farther

.from the strait . This result may serve as a proof thatŽunder specific but unrealistic for the present day

.Black Sea conditions, the model plume can behaveŽsimilarly to other well known ocean plumes e.g., the

.one exiting from the Strait of Gibraltar . Note thatthe temperature and salinity patterns in the outflowarea are completely dominated by the plume dynam-

Ž .ics Fig. 4a , which is demonstrated by the fact thatbottom patterns are completely different from the

Ž .ones of ambiance stratification at bottom Fig. 2a .By integrating the heat and salinity exchange

between the plume and ambiance over the interfaceŽ .in the area of the validity of model , we obtaingeneralized information about the depth ranges wherethe mixture of Mediterranean and Black Sea surface

Ž .water is formed Fig. 5e,f . The dynamic control isextremely strong and both signals follow the samepath. The ratio between the corresponding fluxes of

Žbuoyancy due to salinity and heat dashed line in.Fig. 5e ranges between 70 in the upper layers and

15 below 100 m, demonstrating the dominating roleof salinity. The main conclusion from Fig. 5e,f isthat the exchange between the plume and ambianceconstantly increases on the shelf, reaching a maxi-

mum at ;100 m. This is actually the shelf edge,which is plotted with the full-contour line in Fig.5a,d. Below this depth, the interaction between thegravity plume and environment gradually weakens,but small fluxes are still observed down to ;350m.It is noteworthy that the large net values of exchangeon the shelf are mostly due to the large extension ofarea of the plume at these depths, while the largevalues beyond the shelf edge are mostly due to thelarge entrainment. Though the above results show

Žsome sensitivity to the parameter Dr see thecrit.dashed and dotted line in Fig. 5f , the major conclu-

sions about the regime of interaction between theMediterranean and Black Sea waters do not changewhen different values of Dr are used, particularlycrit

in the upper 250 m, where most of the exchangebetween the plume and ambiance occurs.

In the context of further analyses on the modelentrainment, it is noteworthy that the plume can bewell identified over a large part of the continentalslope by its density contrast with surrounding water.The latter is presented in Fig. 4e, where the area

Žbounded by the isoline Dr s0.3 the density con-crit.trast, which is physically well resolved by the model

and isobath 100 m coincides with the area of en-Ž .hanced mixing on the continental slope Fig. 5 . In

this area of relatively large contrasts, the thickness ofŽthe plume is still relatively small less than 15 m, as

.seen in Fig. 4c , and the model produces physicallycorrect results. However, the simulations are subject

Ž .to some caveats since in the deep sea the real basin ,the plume is not necessarily arrested at the bottomŽ .as it is the case in the model but mixes with theambiance water at smaller depths. Thus, the limita-tions introduced by the Dr value actually excludecrit

from the analyses of simulations the depths, belowwhich the real plume cannot be observed on thebottom. In the experiments listed in Table 1, thepatterns are similar to those in the control run, butthe horizontal gradients, or the contrast at the plume

Ž .Fig. 4. Simulations in experiment RRR after 6 days of integration. Dash curves are the 60-, 80-, 100- and 500-m isobaths. a BottomŽ . Ž .salinity, the contours are 18–36 by 2 salinity units; b bottom temperature, the contours are 8–14.5 by 0.5 8C; c thickness of the plume,

Ž . y1 Ž .the contours are 2–26 by 2 m; d gravity currents, the scale is 0.4 m s ; e difference between plume an ambient density, the contours areŽ .1–13=1 s-unit. Masking is done where the density difference is less than 0.3. The area here and in all following horizontal plots

coincides with the area in Fig. 2; therefore, the geographic coordinates are not plotted.



interface change in different experiments. We willnot analyze the individual patterns in all T-cases, butin the next section, we will rather focus on somegeneral characteristics that are specific for each ex-periment.

4. Mixing and ventilation depth

The idea that the MSW mixes on the shelf signifi-cantly with surface water and does not sink to the

Žbottom but to some intermediate depths Bogdanova,


.1961 was widely used to estimate the entrainmentrates, defined as the entrained water versus theBosphorus inflow. The estimates of different authors

Ž .vary in large ranges—4:1 in Ostlund 1974 , 1:4 inŽ .Boudreau and Leblond 1989 , 3.3:1 according to

Ž .Murray et al. 1991 , 10:1 in the work of BuesselerŽ .et al. 1991 . Most of them give much larger values

than what is currently agreed about the entrainmentŽof MSW in the Atlantic ocean 2–3, Baringer and

.Price, 1997a . This suggests that the mechanisms ofthe spreading of dense MSW into the two basinsŽ .Atlantic ocean and Black Sea might differ substan-tially. One of the aims of the present paper is toanalyze the dependency of model entrainment on theforcing and environmental conditions, and to givebetter understanding on the processes controlling theventilation of Black Sea anoxic waters.

If we assume that Q km3 sy1 Mediterraneanb

water with salinity S entrains Q km3 sy1 coldb eŽ .intermediate layer CIL water with salinity S ande

forms a mixture with salinity

S i , j H i , jŽ . Ž .Ýp

S s ,p H i , jŽ .Ýp

Žwhere Ý is a sum over the plume points see alsop.Appendix A , then

Q S qQ S s Q qQ S . 3Ž . Ž .b b e e b e p

The ratio between Q and Q can be used to quan-b e

tify the entrainment. If we take for the Mediterraneansalinity S s37.0 for the salinity in the CIL S s19b e

Žand for the salinity of the mixture S s21.5 wep

assume that this is the salinity value, below which.we cannot detect the plume; see Fig. 4a , then Q rQe b

is ;6. If we assume that S s20, which would alsoe

Ž .include mixing with deeper waters see Fig. 3a , thisfactor would increase to 10.3. These numbers ob-tained with the classical methods used in oceanogra-phy give us only rough estimates of the entrainmentrate. However, they are fundamental for the interpre-tation of deep ocean mixing. With decreasing thedensity contrast between the simulated plume andambiance, the simulated entrainment rate tends toincrease because mixing with deeper water is in-cluded, which is similar to the case in the above bulkestimates.

Our sensitivity analysis demonstrated that by inte-grating the entrainment velocity over the plume in-terface, we obtain more precise idea about the modelentrainment than by using simple bulk approaches.

Ž .The evolution of entrainment rate in time Fig. 6shows that 20 days are sufficient for the plume to

Žreach quasistationary state this is achieved usually.much earlier .

In the following, we will analyze mixing proper-ties of the plume and their dependence on forcingparameters and ambient stratification. We define theglobal entrainment rate as the area integrated waterflux entrained at the interface between the plume andthe ambient fluid normalized by the outflow magni-tude:

k

w l D xD yŽ .Ý Ý ei , j ls1

E k s , 4Ž . Ž .Qb

where the integration is taken over the interfaceŽ .between the sill depth and the model level z k .

Ž .The increase of E k with depth takes placeŽ .mainly in the upper 110–300 m Fig. 7 ; thus, the

depth reached by the sinking plume can be roughlyestimated as the depth below which the global en-

Ž y1 Ž . Ž .. Ž . Ž .Fig. 5. Entrainment velocity w at the interface of the plume in m h , see Eq. A8 – A11 . a Experiment RRR. b Experiment HRR.eŽ . w y2 y1 2 x Ž . w y2 y1 y4 xc Heat flux in experiment RRR J m s =10 . d Salt flux in RRR experiment kg m s =10 . Dashed contours represent60-, 80- and 500-m isobaths. The 100-m isobath is shown with a solid line. Averaged in the different depth intervals over the plume

Ž . w y1 7 x Ž . w y1 x Ž .interface area fluxes of e heat J s =10 and f salt kg s . The dashed line in e gives the ratio between buoyancy fluxes caused byŽ . y4 y1 y4 y1salinity and temperature R sygbQ rgaQ r r c , where as1.3=10 8C and bs7.5=10 psu are the thermalST S T 0 w

Žexpansion and saline contraction coefficients, Q and Q are the heat and salt fluxes for convenience, the ratio is shown with opposite signT S. Ž . Ž .on graph . The numbers for the ratio x-axis read as non-dimensional. The dashed and dotted lines in f give an idea about the sensitivity

Ž .of presentation of results against parameter Dr . These lines non-dimensional number give the ratio between entrained water and thecritŽ .inflowing from the strait Mediterranean water further in the text, we call that ratio entrainment number . Long-dashed line corresponds to

Dr s0.5, short-dashed line to Dr s0.3, dotted line to Dr s0.1.crit crit crit


Ž .Fig. 6. The establishment of quasistationary state in a RxxŽ .experiments and b in Txx experiments.

trainment does not increase substantially anymoreŽ .see also the results in Fig. 5f . For brevity, we willrefer further to this depth as Atermination depthB.Note that the increase of entrainment is small on the

Ž .flat part of the shelf ;2 in the first 100 m in RRR .The maximum salt flux in Fig. 5f occurs above thedepth below which the validity of model could be-come questionable, which ensures the credibility ofthe major conclusions regarding the Black Sea mix-ing characteristics.

The model simulates a trend of decreasing depthreached by gravity currents under stronger stratifica-

Ž .tion Fig. 7 . Though the entrainment values in threeof the experiments plotted in Fig. 7b are higher thanwhat is commonly agreed nowadays about the en-trainment in Black Sea, these results are instructiveabout the consequences which are to be expected

Ž .under different from the present day stratificationand outflow conditions. We could roughly say that ifthe salinity and the outflow thickness were equal to

Žor greater than 37 and 26 m, respectively the combi-nation Ss37 and hs27 m provides strong forcing

.in the straits exit , and if the stratification were atŽ .least half the present stratification experiment TRR ,

the plume would reach the very deep bottom. In the

Ž Ž .. Ž .Fig. 7. Global entrainment rate see Eq. 4 in: a Rxx experi-Ž . Ž .ments and b Txx experiments x is R, or T .


following text, we will analyze the global entrain-ment rate in the individual Txx and Rxx experi-ments, where the index ‘x’ denotes either T or R.

In all Rxx experiments, the termination depth isŽsmaller than in the Txx experiments stratifica-

.tion weaker than in the present ; however, thisdependency changes in a complicated way fromexperiment to experiment. Similar clearly defineddependence of termination depth on the inflow char-

Ž .acteristics also exists: 1 the depth in all xTx experi-Ž .ments initial thickness smaller than in the present is

smaller than the one in the corresponding xRx exper-Ž .iments; 2 this depth is smaller in all xxT experi-Ž .ments initial salinity smaller than in the present

relative to the one in the xxR experiments. Theabove results could be expected from general theo-retical considerations since the deepening of the

Ž .plume increases as: 1 the stability of stratificationŽ .decreases, 2 the salinity of the outflow increases,

Ž . Žand 3 the thickness of the outflow increases Fig.

.8 . However, this dependency is far from linear, asseen from the results of our eight experiments. Thisis partially explained by the fact that the physics ofsinking plumes is governed by the fluxes at the straitexit. The rate of increase in termination depth de-pends in a complex way on the ambient stratificationand the thickness of plume in xxT and xxR experi-

Ž .ments Fig. 8 . The sensitivity is strongest for weakerŽstratification and thicker outflows changing depth.from 300 m in TRT to bottom in TRR . This depen-

dence is much weaker for conditions that are closerŽto a contemporary stratification regime the depth

changes from 150 m in RRT to 300 m in RRR.and from 125 m in RTT to 180 m in RTR . This

demonstrates that without changing substantially thevertical stratification, one cannot expect substantialchange of the depth of penetration of gravity currentsin the Black Sea.

The above values of the depth of penetration ofŽ .gravity currents see also Table 2 approach in some

Fig. 8. Schematic representation of the dependency of entrainment and termination depth on the stratification and outflow parameters. TheŽ .eight corners of the cube represent the eight combinations of the governing parameters the first eight experiments listed in Table 1 .

Ž . Ž .Stratification changes to the AeastB increase of stability , the thickness of the outflow changes to the AsouthB decrease of thickness , theŽ .salinity contrast between the outflow and ambient water changes AupwardsB decrease of contrast . The arrows on the axes give the direction

in which the depth of sinking increases. At each corner of the cube, the values of entrainment and sinking depth are also given.


Table 2Simulated plume characteristics in different experiments

3 y1 3 y1 4 y2w x w x w x w xExperiment Q m s E z m QDS 10 kg s QU m s

Ž .RRR 9976 11.2 2.3 300 190 2126Ž .RRT 6590 4 2.3 150 59 928Ž .RTR 2825 10 3.9 180 53 341Ž .RTT 1838 5 3 125 16 144Ž .TRR 10,013 25 2 )500 90 2142Ž .TRT 6646 11 1.9 300 60 943Ž .TTR 2842 20 3.5 288 54 345Ž .TTT 1862 8 3.5 160 17 148Ž .HRR 13,092 40 2 bottom 406 3662

Entrainment numbers in parentheses are for the upper 100-m water column.

experiments the depth beyond which the model isnot applicable for present conditions. In the case ofRRR experiment, the error is not large, as seen fromFig. 5f. Unfortunately, there is no observational evi-dence that could serve as criteria for model validityunder a quite wide range of parameters examinedhere. This could motivate further studies with moreadequate models. Therefore, the analysis below givesthe general trends of sensitivity to forcing, the pre-cise numbers are subject to further investigation.

The increase of termination depth in xTx relativeŽto xRx experiments the transition from the front to

.the back side of the cube in Fig. 8 shows a strongdependency on the stratification and salinity of theoutflow. The sensitivity is stronger under weak strat-ification and when the plume is thicker at the out-flow location. This is illustrated in Fig. 8 by the

Žarrow on the initial height axis the direction ofstrongest increase of the termination depths is shown

.by the arrows on the main axes .Now, we will examine the change of termination

depth in Rxx relative to Txx experiments. This ratedecreases for thinner outflows and when the contrastbetween outflow and ambient salinity is smaller. The

Ž .most dramatic sinking down to the bottom is ob-served when switching from RRR to TRR. On thecontrary, the stratification does not affect substan-

Ž . Ž .tially the transition RTT 125 m –TTT 160 m . Thisindicates the following very important result. The

Ž .weak outflows for the magnitudes, see Table 2simulated when thin plumes with small salinity con-trast intrude the Black Sea shelf are diluted at thevery shelf. They rapidly lose potential energy, anddo not reach deep levels, even under much weakerstratification than what exists nowadays.

In the following, we will analyze the dependenceof model entrainment on the governing parametersŽ . ŽTable 2 . In vertically homogeneous fluid experi-

.ment HRR , as well as under weak stratificationŽ .experiment TRR , the total amount of entrained

Ž .water increases monotonically with depth Fig. 7 .This increase is almost linear in the two experiments,but larger in HRR. In most of the experiments listedin Table 2, there is a good correlation between thedepth reached by density currents and the entrain-ment. In all experiments, the entrainment numberusually decreases with decreasing thickness of theplume and its salinity at the exit of the strait, andincreasing the stratification. The effect of outflowsalinity and ambience stratification almost compen-sate each other in TRT experiment, resulting inentrainment, which is almost equal to the one inRRR. Note, however, that the transports are ;50%

Ž .larger in RRR Table 2 than in the relatively lessenergetic experiment TRT.

The entrainment does not always increase withincreasing the initial thickness of the plume as canbe seen in the transition between RRT and RTT.Unlike most of the experiments where the entrain-ment increases when passing from the front side ofthe cube to the back one, the transition between RRT

Ž .and RTT experiments has inverse direction Fig. 8 .The bottom boundary currents reach shallower depthin RTT, while the entrainment in this experiment islarger than in the RRT. Recall that the potentialenergy provided in RTT is much smaller than inRRT and the transports in the two experiments differconsiderably. This trend changes the balances in themain driving terms and, consequently, the majorphysical characteristics of the plume.


The compensation of mutually opposing factors iswell demonstrated by comparing the results of RTRand TTT experiments, as well as the results of RRR

Ž .and TRT experiments Table 2 . The major differ-ence between these experiments is their energy levelŽthe outflow at the exit in the first two experiments isseveral times smaller than that in the second pair;

.Table 2 . Increased stratification in the RTR experi-ment compensates for the effect of strong salinitysignature of the outflow, thus seen from the view-point of transportrentrainment these experiments aresimilar. The same is valid if the plume in the strait

Ž .exit is thicker RRR and TRT experiments . In thelatter case, however, the transport is much larger and

Ž .the plume reaches larger depths Fig. 8 .

5. Oxidation of anoxic water in the outflow region

The formation and evolution of Black Sea anoxiczone is governed by complicated biochemical reac-tions. However, the problem of their representationin the models is not fully resolved at present. Forsimplicity, we address here only the process of H S2

Ž .oxidation. According to Cline and Richards 1969 ,the interaction between H S and O could be param-2 2

eterized with a kinetic reaction of second order.Thus, a two-component chemical model for the evo-lution of H S and O is coupled here with the2 2

dynamical model. The corresponding equations areŽsimilar to these of temperature and salinity see

.Appendix A and are identical to ones used in theŽ .basin-wide model of Stanev 1989 :

w x w x w xE H S E H S E H S2 2 2qu qÕ

Et Ex E y

w x w xH S y H S2 2 aqwe H

ATh w x w x w xs = H= H S yK H S O , 5Ž .Ž .2 H S 2 22H

w x w x w x w x w xE O E O E O O y O2 2 2 2 2 aqu qÕ qwe

Et Ex E y H

ATh w x w x w xs = H= O yK O H S , 6Ž .Ž .2 O 2 22H

w x w xwhere H S and O are concentrations of hydro-2 2w xgen sulphide and oxygen in the plume and H S2 a

w x Ž .and O are the ambient properties Fig. 9a . The2 a

Ž . w xFig. 9. a Vertical ambient profiles of H S and O mM on2 2Ž . w x Ž . w xsigma-levels. b Bottom values of H S mM and c O mM ,2 2

corresponding to the ambient stratification. The dash curves withŽ . Ž .labels in b and c are the 60-, 80-, and 100-m isobaths.


Ž . w x Ž . w x Ž . w x Ž .Fig. 10. Tracer patterns in CR: a bottom H S mM ; b bottom O mM ; c difference between ambient and plume H S mM ; d2 2 2w x Ž . w 2 x Ž .difference between ambient and plume O mM ; e the product of ambient H S and O concentrations mM ; f the product of plume2 2 2

w 2 x Ž .H S and O concentrations mM . The results are shown for the area of model validity Dr)Dr . The isobaths are plotted as in Fig. 5.2 2 crit


H S and O ambient profiles present adequately the2 2

onset of anoxic zone. The corresponding bottomvalues calculated from these profiles show clearly

Ž .the decoupling between surface oxygenated andŽ .deep anoxic water, which occurs on the steep

continental slope. The decay term in the right-handside parameterizes the oxidation in the model. Fol-

Ž .lowing Cline and Richards 1969 and the simula-Ž .tions of Stanev 1989 , the constants in the decay

terms are set to K s0.5=10y3mMy1 hy1 andH S2

K s3K .O H S2 2

The boundary conditions are similar to those forthe temperature and salinity, i.e. we assume zero

Ž Ž ..normal gradients at the open boundary Eq. 1 . Theplume concentration of H S and O at the strait2 2

opening is prescribed as 0 and 300 mM, respectively.The bottom patterns of H S and O after the 6th day2 2

Žof integration by this time the stationary state is.reached; Fig. 6 are presented in Fig. 10a,b. The

Ž .differences between ambient properties Fig. 9b,cand plume concentration of H S and O are also2 2

given. Obviously, there are similarities betweenŽchemical and dynamical properties compare with

.Fig. 4 , in particular for the oxygen. The largestdifferences between ambience and plume values areobserved on the continental slope where the mixingintensifies the process of oxidation, thereby Aflush-ingB the H S below 100–200 m. Note that the2

patterns in Fig. 10b,d are very similar to the entrain-Ž .ment patterns Fig. 5 , proving that the chemical

tracers could be used to detect important physicalprocesses. This is demonstrated by the product of

Žoxygen and hydrogen sulfide concentrations Fig..10e,f , showing the area of most intense oxidation. It

is clear that the flow of rich oxygen surface water,originating from the strait, displaces the zone ofmaximum oxidation on the continental slope todeeper levels.

In the context of studies on the ventilation ofBlack Sea anoxic waters, it is instructive to analyzethe fluxes of O at the plume interface, calculated as2

the entrainment velocity multiplied by the differencebetween concentration of tracers in the plume andambiance. The integrated value of oxygen flux in thewhole water column is 2.9=1011 M yeary1. Thisvalue is ;3 times larger than the amount of oxygenpenetrating into the Black Sea with the Bosphorus

Žunderflow see the formulation of boundary condi-

.tions for oxygen and Table 2 for the outflow rate .Ž .Our vertical profiles Fig. 11c are in a qualitative

agreement with the profiles presented in the study of

Ž . Ž . w y2 y1 y5 xFig. 11. Fluxes of a H S and b O M m s =10 . The2 2Ž . w y1 xisobaths are plotted as in Fig. 5. c Fluxes of O M s2

integrated in the different depth intervals over the plume interfacearea.


Ž .Konovalov et al. 2001 ; the latter are based oncalculations using a much simpler 1D inverse model.However, the profiles obtained by our simulationsare sharper and the flux associated with plume dy-namics does not affect depths larger than 350 m. Thedifference between the estimates based on two dif-ferent approaches is indicative for the impact of local

Žprocesses physics governed by gravity currents over.realistic topography . Thus, we could speculate that

the mixing in the deep layers simulated in the 1DŽ .models might not be only directly linked to the

Ž .signals originating from the strait, but also to thediapycnal mixing associated with the circulation,which shapes the vertical stratification basin wide.

The results presented above demonstrate the po-tential of simulations as a valuable complement toobservations when addressing the mechanisms ofmixing between Mediterranean and Black Sea wa-ters. The local maxima below 250 m could indicatean intermittence of mixing, which is caused by therugged topography of the continental slope. Thesmall extensions of the area where most of theexchange of plume water and anoxic water from the

Ž .ambiance occurs Fig. 11a indicate the need toincrease the horizontal resolution in further simula-tions when addressing the details of chemical inter-

Žactions in the region of the Bosphorus outflow see.also Fig. 10e .

6. Conclusions

The formation of deep water is a fundamentalissue in the physical oceanography of the Black Sea,having important implications for internal mixing,circulation mechanisms and biogeochemical fluxes.This issue is crucial for the understanding of thesensitivity of water masses to external climatic andantropogenic impacts. The changing terminationdepth of MSW could give an illustration of theevolution of Black Sea physical system from a statetypical for a freshwater lake to its present stagnantstate. We have analyzed the dependence of this depthon the ambient stratification and parameters of theMediterranean outflow. Our model simulations showan encouraging agreement with observations. Thecomparison with other well known oceanic outflowsdemonstrates the unique behavior of the Mediter-

ranean plume in the Black Sea. Though this outflowis characterized by much denser source water thanthe Gibraltar one, it sinks to a much shallower depth.With the results of a number of sensitivity experi-ments, we explained the shallow sinking by the factthat the outflow entrains substantial amount of CIW.This entrainment reduces the salinity of the plumeand its density, so that the neutral buoyancy depth isreached at 200–400 m.

The model simulations could help in elucidatingthe regional physical balances, and to quantify thenumber of subtle characteristics of the plume. The

Žbest agreement with observations thickness of the.plume, bottom temperature and salinity, pathways

are simulated when the entrainment of CIW by theŽ .MSW is ;1: 10–12 . This entrainment rate corre-

Žlates with other independent estimates Buesseler et.al., 1991 , proving that the model is adequately

calibrated, and ensures a good agreement betweenthe simulated plume phenomenology and the resultsfrom observations. The agreement is better on theshelf and on the shelf edge, where most of thetransformation of MSW occurs.

The fundamental difference between the behaviorof the Mediterranean plumes in the Black Sea and inthe Atlantic ocean is that in the former case, theabsence of a pronounced turn to the right after the

Žplume reaches the continental slope and further.propagation along isobaths is due to the extremely

large entrainment, which causes a rapid loss of po-tential energy of the plume on the shelf.

We showed that, without substantially changingthe vertical stratification in the Black Sea, one can-not expect substantial change of the depth of penetra-tion of gravity currents. Changing the salinity differ-ence between the Black Sea and Mediterranean Sea

Ž .two times under present day stratification can onlylead to changing about two times the depth of pene-tration of the signal from the strait. Thus, it is hard tobelieve that oscillations in the source salinity maynowadays reach the abyssal plane. Another important

Ž .result is that when weak outflows thin plumes arediluted at the Black Sea shelf, they rapidly losepotential energy and cannot reach deep levels, evenunder much weaker stratification than the one whichexists at present.

Some important properties of gravity currents arewell illustrated by the simulations of the oxidation of


H S by oxygen-rich surface water. The active dy-2Žnamics intense mixing on the continental slope

.caused by the accelerated plume results in a dis-placement of the zone of maximum oxidation to

Ž .larger depths Fig. 10e relative to the case of noŽ .outflow dynamics Fig. 10f . The simulations seem

to be a useful complement to other independentstudies on the chemical ventilation of Black Sea. Theratio between the entrained flux of oxygen and thedirect oxygen flux from the Strait of BosphorusŽ .;3 is several times smaller than the correspondingratio for water fluxes, thus illustrating the pro-nounced differences in the efficiency of penetrationof different tracers into the deep layers. We remind

Ž .here that the maximum oxygen flux Fig. 11c occursŽ;50 m deeper than the maximum of salt flux Fig.

.5f , which might be due to the differences in theambient stratification of physical and chemical trac-ers.

Admittedly, there are simplifications in the pre-sent study. Some of them are related to the model,

Ž .e.g., 1 Aarresting the plume at the bottomB, orŽ .considering it as fully mixed in the vertical, 2

assuming that the upperlying layers are at rest, andŽ .3 using very simple chemical model. Other as-sumptions are related to the formulation of model

Ždriving we have chosen the simplest driving config-.uration here . Further model development has to deal

with improving the resolution, which is still insuffi-cient in the strait exit area, and combining strait andshelf physics in one model.

Acknowledgements

We thank J. Backhaus and J. Jungclaus for pro-viding us with the numerical model and for theuseful comments. Thanks are due also to the anony-mous reviewers for their useful suggestions andcomments. This study was supported by the CECproject AVentilation of the Black Sea anoxic watersBŽ .Contract IC15-CT96-0113 .

Appendix A. Model equations

We define first the integrated transports:yz yz™

Vs U,V , Us ud z , Vs Õd z , A1Ž . Ž .H HyD yD

and averaged velocities:

U Vus , Õs , HsDyz . A2Ž .

H H

The model equations in vertically integrated formread:

EU U U™q=P V yA H= y f Vh

Et H H

Ez gH 2 Er t b xXsyg H y y , A3Ž .Ex 2r Ex ro o

EV V V™q=P V yA H= q f UhE t H H

Ez gH 2 Er t b yXsyg H y y , A4Ž .E y 2r E y ro o

where A is the coefficient of horizontal turbulenth

exchange,ryraXg s g A5Ž .ro

is the Areduced gravityB, subscript ‘a’ denote ambi-ent quantities, and r is the reference density. Theo

continuity equation reads:

Ez EU EVq q sw , A6Ž .e

Et Ex E y

where w is the entrainment velocity, parameterizinge

the entrainment of ambient water into the turbulentflow. Bottom stress in the model obeys a quadraticdrag law:™t b ™™< <sr v v, A7Ž .ro

where r is the dimensionless friction coefficient.Integrated conservation equations for heat and saltread:

ET ET ET TyT ATa h

qu qÕ qw s = H=T ,Ž .eEt Ex E y H H

A8Ž .

ES ES ES SyS ATa h

qu qÕ qw s = H=S ,Ž .eEt Ex E y H H

A9Ž .


where AT is the coefficient of horizontal turbulenth

diffusion. The density,

rs f T ,S , A10Ž . Ž .

is calculated using a linear equation of state. For theentrainment velocity w , we use the parameterizatione

Ž .given by Jungclaus and Backhaus 1994 :

X2c g HL 2 2w s u qÕ q , A11Ž .(e Sm Sm

where, c s0.086 is a proportionality constant andL

Sm is the turbulent Schmidt number. The last isdefined by the formula given by Mellor and DurbinŽ .1975 :

RiSms ,

2'0.725 Riq0.186y Ri y0.316 Riq0.0346Ž .A12Ž .

gXHRis A13Ž .

2 2u qÕ

is the Richardson number.

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Ventilation of Black Sea pycnocline by the Mediterranean plume

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