Eddy Processes in Semienclosed Seas: a Case Study for the Black Sea

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Eddy Processes in Semienclosed Seas: A Case Study for the Black Sea

NICKOLAY H. RACHEV AND EMIL V. S TANEV Department of Meteorology and Geophysics, University of So®a, So®a, Bulgaria (Manuscript received 14 December 1994, in ®nal form 29 November 1995)

ABSTRACT The enclosed boundaries and small scales of some seas lead to the formation of speci®c physical balances, which motivates the oceanographic interest in studying the dynamics of semienclosed ocean basins. The focus in the paper is on the speci®c appearances of eddy processes when the basin scales and the ones of the topographic features are comparable with the baroclinic radius of deformation. The Black Sea is used as a test basin. Eddy variability is analyzed using simulation results and compared with existing observations. The Bryan±Cox model with horizontal resolution ⌬␸ ϭ 1/10Њ and ⌬␭ ϭ 1/6Њ is forced with annual-mean wind stress data. Buoyancy ¯ux at the sea surface is proportional to the deviation of the model density from the annual-mean climatological data. Sensitivity studies on different forcing and on the topographic control are carried out. Synoptic periods are estimated to be about 0.5 yr. Eddies form in the eastern Black Sea and propagate westward with a speed of about 3 cm sϪ1. The narrow section of the Black Sea, between the Crimea Peninsula and the Turkish coast, strongly affects eddy propagation. Dissipation increases in the western basin, where eddies slow down and their scales become small. This process is dependent on topography, which is dominated by a large shelf area in the western basin. Eddy kinetic energy exceeds the kinetic energy of the mean motion over large areas. Energy transfer between external and internal modes shows that the topographic control and the nonlinear transfer almost compensate each other. Energy spectra indicate that an inverse cascade may occur.

1. Introduction to the very small exchange with the Mediterranean Sea. Experiments and theory have shown remarkable The freshwater input from rivers and the net balance progress in the past two decades, resulting in elucidation between precipitation and evaporation tend to decrease of some important physical processes, which govern the salinity in surface layers. The input of more saline water mesoscale/synoptic eddies. A large amount of knowl- through the Strait of Bosphorus compensates the salinity edge already exists for the Gulf Stream, Kuroshio, Ant- de®cit at the sea surface, and an extremely stable strat- arctic Circumpolar, and equatorial currents. However, i®cation is formed down to 200±300 m. It tends to de- the impact of large-scale turbulence and baroclinic increase the vertical mixing and favors the unique envi- stability on the circulation in semienclosed seas is not ronment of the Black Sea, which is manifested by the well understood. Regional studies could be of general existence of an anoxic layer occupying 90% of its vol- oceanographic interest, showing speci®c physical bal- ume. ances in areas where the Rossby radius of deformation The Black Sea can be regarded as a two-layer basin is comparable to the basin scales. Decreasing resolution in which the deep layer is much thicker than the upper to about 1/10Њ, or less, and integrating models for suf- one (Fig. 2). Synoptic scales are larger than the corre- ®ciently long times, are realistic with present computers sponding scales in the neighboring Mediterranean Sea for entire (enclosed) basins if their size is small enough. [eddy diameters could reach 200 km (Latun 1990)] and In the present study we use the Black Sea as a test basin. may approach the width of the narrow section between Therefore, a short introduction to the physical ocean- the Crimea and Sinop (later in the text we refer to this ography of this sea is given below with a focus on the simply as the Black Sea narrow section). The growth topics discussed in the paper. of instabilities in this small basin is sometimes limited The Black Sea (Fig. 1a) is a typical example of an by the basin scales, which could give more relative ocean basin where the vertical strati®cation is dominated weight to the basin or subbasin mode oscillations. by salinity. This is due to the speci®c water balance and The Black Sea has a relatively simple coastal line in contrast to the Mediterranean Sea. The con®guration of the deep sea is geometrically even simpler, and the deep bottom topography is rather smooth. The continental Corresponding author address: Prof. Emil V. Stanev, Department of Meteorology and Geophysics, University of So®a, 5, J. Bourchier slope is steep in the southern and eastern Black Sea, Street, 1126 So®a, Bulgaria. and rather ¯at between the Crimea and the Bulgarian E-mail: [email protected]®a.bg coast (Fig. 1b), where depths less than 100 m dominate.

᭧1997 American Meteorological Society

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FIG. 1a. The Black Sea. Isobaths for 100, 500, 1000, and 2000 m are plotted. The straight zonal line across the sea and the points A, B, and C give the position of the cross section and of the isolated points where model data are analyzed. The thick lines show the sections where bottom pro®les are shown in Fig. 1b.

Thus, regional conditions for the synoptic processes are Dynamic computations initiated early this century quite different over large areas in the deep sea than over (Knipovich 1932; Filippov 1968; Bogatko et al. 1979) the continental shelf. This motivates us to address in established the concept of a basinwide circulation gyre the paper the penetration of the synoptic eddies from (named recently in some studies Rim Current), with two the eastern to the western part of the sea, focusing on centers in the eastern and western basin, named ``Kni- the impact that the basin shape and bottom topography povich spectacles.'' Much less is known about the space have on their mobility. and time variability of the Black Sea circulation with

FIG. 1b. Bottom pro®les along the thick section lines in Fig. 1a, plotted with different vertical discretization. The capital letters at each pro®le correspond to the section line from the coast to the open sea location (A, B, or C) in Fig. 1a. To more clearly illustrate the differences in the topographies, which are signi®cantly larger on the shelf and on the continental slope, the section lines are limited to the isobath 1400 m. Full lines correspond to coarse-resolution, dash lines correspond to ®ne-resolution (details on the resolution of the topography are given in section 2b).

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velopment and analyses. In this paper, our interest is focused on the temporal dynamics, which is one of the most important issues of the Black Sea oceanography. We hope that elucidation of the regional dynamics could be of general oceanographic interest, showing possible results that may be expected in other basins whose scales are comparable to the Rossby radius of deformation. In the next sections we present a description of the model, analyses on the model phenomenology and on its phys- ics, followed by discussion.

2. Description of the model a. The numerical model and boundary conditions The model is based on the primitive equation numerical model of Bryan (1969) in the version documented by Cox (1984). The momentum equations, the equation of quasistatics, and the equation of continuity, written in spherical coordinates (␭, ␸, z) are FIG. 2. Mean vertical density pro®le (␴ units) for the Black Sea; U ٌpץ t solid line corresponds to initial density, dash line corresponds to h n ϩ L(Uhh) ϩ f ϫ U ϭϪ ϩA hh⌬U t ␳0ץ .density at the end of the integration

ϩAvhU, (1) synoptic scales, though large surveys were carried out zz recently (Oguz et al. 1994) with a very dense coverage pz ϭϪ␳g, (2) of the entire basin. Numerical modeling has resulted in some progress in L(1) ϭ 0. (3) the study of the Black Sea eddy ®eld too, but much still In the above equations U ϭ (u, ␷,w) is the velocity remains to be done. The horizontal resolution was ®rst vector, Uh its horizontal component, f ϭ 2⍀ sin(␸)k, k reduced to 20 km for the entire Black Sea in the non- ϭ (0, 0, 1), p and ␳ are the pressure and density, n ϭ linear diagnostic model of Bulgakov and Korotaev 1 for Laplacian mixing, and n ϭ 2 for biharmonic mix- (1987), which is rather coarse for eddy resolution in this ing. The advection operator L(␮) and the Laplacian ⌬␮ basin. The Bryan and Cox GCM with horizontal reso- are de®ned as lution ⌬␸ ϭ 1/6Њ and ⌬␭ ϭ 1/3Њ was later applied by Ϫ1 Stanev (1988, 1989b, 1990) to study the variability of L(␮) ϭ {sec(␸)a [(u␮)␭␸ϩ (␷␮/sec(␸)) ] the circulation. Forcing functions with seasonal oscil- ϩ(w␮) } (4) lations (wind stress, heat ¯ux, precipitation minus evap- z Ϫ1 Ϫ1 oration, river runoff, and exchange through the Strait ⌬(␮) ϭ sec(␸)a {sec(␸)␮␭␭ϩ [␮ ␸sec (␸)]␸}, (5) of Bosphorus) were used in different combinations to study the response of the model sea to external forcing. where ␮ is any scalar quantity, a is the radius of the Some of the topics, addressed in these studies, to be earth, and subscripts ␭, ␸, and z denote differentiation. reconsidered in the present paper are 1) the sensitivity Numerical experiments carried out by Stanev (1990) of the circulation to horizontal and vertical resolution, showed that the buoyancy due to temperature has sec- 2) mean versus time dependent circulation, and 3) model ondary effect on the general circulation of the Black energetics. Sea. Therefore, the density is used here as a thermo- In the recent paper of Oguz et al. (1995) the individual dynamic variable so that the corresponding conservation impact of the mechanical and thermohaline forcing on equation reads ␳ץ -the model simulations was studied, using ®ner resolu n tion (variable in the horizontal, with grid intervals be- ϩ L(␳) ϭ Khvzz⌬ ␳ ϩ K ␳ . (6) tץ tween 5 and 15 km) than in the previous studies. The novelty in this work is the more precise formulation of The coef®cients of turbulent diffusion for momentum the effects of buoyancy forcing on the barotropic cir- and density are Ah,v and Kh,v, respectively, where h is culation. This was achieved by using active free surface horizontal and v vertical. Convection is introduced in dynamics. the model using the convective adjustment procedure of Though some important topics related to the eddy Bryan (1969). ®eld in the Black Sea were addressed before, there are As in the standard Cox (1984) code, the lateral bound- some principal items requiring systematic model de- aries are insulating and nonslip, and the bottom is taken

Unauthenticated | Downloaded 09/26/21 06:08 AM UTC 1584 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 to be insulating and free slip. The model assumes the the Black Sea, the model resolution has to be better than following boundary conditions at z ϭ 0: ®ve kilometers. With coarser resolution in the horizontal, the Black Sea continental slope looks like a vertical ␳ A U ϭ ␶, (7) 0 vhz wall, independent of the vertical resolution, Fig. 1b. However, the pro®les for the shelf region differ one from Kvz␳ϭ␩(␳*Ϫ␳)⌬z, (8) another in the coarse- and ®ne-resolution case (the me- where ␶ is the wind stress, ␳* is the climatological den- ridional pro®le between the coast and location A, Fig. sity, ␩ is an inverse timescale, and ⌬z is the thickness 1b). It is shown later that this difference, along with the of the ®rst model layer. The numerical algorithms are insuf®cient resolution of the continental slope in the documented in Bryan (1969) and Cox (1984). western Black Sea, could have a very strong impact on the eddy dynamics. b. Model geometry and parameters Mixing and diffusion in the horizontal are parame- terized with biharmonic operators, with coef®cients Ah The model resolution is 1/10Њ in latitude and 1/6Њ in 19 4 Ϫ1 19 4 Ϫ1 ϭϪ0.1 ϫ 10 cm s and Kh ϭϪ0.4 ϫ 10 cm s longitude, giving almost square grid elements in the (see also Cox 1985; Holland 1989; and BoÈning and horizontal with a grid size of about 11±13 km. The Budich 1992), which are just suf®cient to prevent noise. present study aims to provide estimates for some im- For horizontal resolutions of about 10 km, as in the portant physical processes in the Black Sea rather than present case, the ¯ow dependency on the biharmonic a detailed reproduction of large number of circulation coef®cient is small (Barnier et al. 1991), which is sup- features. This is one of the motivations to make some ported by our preliminary sensitivity experiments. The model simpli®cations, including the minimum neces- 2 Ϫ1 vertical mixing coef®cient, Av ϭ 1.5 cm s , and the sary resolution. Nonuniform resolution is used in the 2 Ϫ1 vertical diffusion coef®cient, Kv ϭ 0.1 cm s , are cho- vertical with ⌬z chosen as 40, 60, 80, 160, 320, and sen small enough not to create unrealistically strong 880 m. We remind here that Hecht et al. (1988) showed mixing in the deep layers. We admit that the parame- that for the deeper (and more complicated in strati®- terizations of the subgrid-scale processes, the model dis- cation) Mediterranean Sea eight levels are suf®cient to sipation, or the numerical formulations could affect describe the major features of the vertical strati®cation. model estimates; therefore further studies, including Also, Barnier et al. (1991) conclude that the number of vertical modes that require high resolution tends to be model intercomparisons, are needed. limited. In their six-layer experiments with a resolution In the present study, the Strait of Bosphorus is closed of 10 km the dynamical role of the modes 5 and 6 seems [the impact of the salt balance on the model circulation to be of secondary importance. Following the idea that is discussed by Stanev (1988, 1990) and more recently the model resolution has to be consistent in the three by Oguz et al. (1995) and Stanev et al. (1997)]. Since dimensions, we assume that with our coarse vertical grid the focus in this paper is not on the climatic but rather we do not neglect more detail (relevant to baroclinic on the synoptic processes, we carry out the integration instability) than we do with the ®ne 11-km horizontal for relatively short periods (less than decade), not al- grid. lowing substantial changes in the vertical baroclinic The above arguments do not neglect the need to more structure. As it is known from tracer studies (OÈ stlund precisely resolve the bottom topography, particularly 1974) and from numerical model experiments (Stanev over the shelf and in the shelf±open sea transition zone 1988), the timescale related to the exchange with the (Fig. 1b). In the present study, the topography is dis- Mediterranean Sea is about 102±103 years. The vertical cretized from the bathymetric map of UNESCO with strati®cation remains close to the initial during the rel- the model resolution. With this rather coarse vertical atively short integration in the present study (Fig. 2), resolution we capture the most important topographic which shows that the errors resulting from closing the features (the shelf area, the sharp bottom slope, and the strait are small. ¯at interior). The comparison between bottom topography resolved with a limited number of vertical levels and the topography resolved with much ®ner resolution c. Model forcing is shown in Fig. 1b for several sections across the shelf and on the continental slope. In the ®ne resolution case There is a strong uncertainty in the quality of the we use 22 vertical levels. The thickness of each of the existing forcing functions for the Black Sea (Staneva ®rst four levels is 5 m, of the following seven levels 10 and Stanev 1997), but no studies on the response of the m, and it constantly increases in the deep layers as fol- model eddies to different mechanical forcing have been lows: 30, 40, 50, 60, 80, 100, 130, 170, 240, 310, and carried out before. Therefore, we run several experi- 340 m. No pronounced differences are seen between the ments, aimed to illustrate the sensitivity of the model two topographies on the steep continental slope. This Black Sea to data from different origin: atmospheric agrees with the results of Oguz et al. (1995), showing analysis data and ship observations. The ®rst dataset is that to accurately resolve the steep continental slope in calculated from the U. S. National Meteorological Cen-

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ter1 (NMC) twice daily (at 0000 and 1200 UTC) me- two experiments: The ®rst is forced with the annual- teorological analysis of the sea surface wind compo- mean wind stress of Rachev et al. (1991), (Wind Rachev

nents Wx, Wy for the period 1980±89, with resolution of et al. 1991 hereafter WR91) experiment and the second 1Њ. This period corresponds to the period of integration is forced by the NMC annual-mean wind stress, WNMC used by Stanev et al. (1995), which enables intercom- (Wind NMC) experiment (Table 1). The integration parisons between the results using similar forcing, but starts from rest in both experiments. The initial density different horizontal resolution. is taken from the annual-mean data. ␭ ␸ Using the bulk formula (␶ , ␶ ) ϭ ␳␣CDͦWͦ(Wx, Wy), The volume mean kinetic energy reaches a quasiper- where C 1.3 103, we calculate the wind stress D ϭ ϫ iodic state after 2±3 years, Fig. 4. The curves, corre- components ␶␭ and ␶␸ from the annual-mean wind mag- sponding to the WNMC and WR91 experiments, are nitudes and directions. The computed values are inter- polated onto the model grid. The wind stress curl, Fig. very different. The energy is higher in the WR91 ex- 3a, is positive in the eastern and southwestern Black periment, due to the stronger forcing, and the oscilla- Sea and negative in the rest of the basin, which does tions (160-day period) are very pronounced. The am- not seem to correlate well with other climatic data (see plitudes in the WNMC experiment are negligibly small. below). Since both experiments are initialized from the same Climatic data for the wind stress, originating from initial conditions, but the temporal variability is too dif- ship observations (Sorkina 1974) were compiled and ferent, we conclude that the quasiperiodic solution is analyzed by Rachev et al. (1991). The corresponding dominated by the forcing and the resulting internal dy- annual-mean wind stress curl pattern, Fig. 3b, is very namics, and not (or negligibly) by the initial data. The different from the one corresponding to the NMC cli- vertical strati®cation at the end of the integration is not mate. Wind stress curl reaches 40 ϫ 10Ϫ8 Pa mϪ1 in the changed signi®cantly, Fig. 2, which indicates that the eastern Black Sea (close to the Caucasian coast), where- mean Rossby radius of deformation remains unchanged as in the NMC climate the maximum is about 5 ϫ 10Ϫ8 throughout the experiments. Pa mϪ1, and it is located in the southern Black Sea. The The next experiment is forced with double the wind corresponding extrema for the anticyclonic curl are Ϫ27 stress of Rachev et al. (WR91D experiment), which en- Ϫ8 Ϫ1 ϫ 10 Pa m in the climatic data of Rachev et al. ables one to better understand the model response to Ϫ8 Ϫ1 (1991) and Ϫ5 ϫ 10 Pa m in the NMC climate. For increased winds. The corresponding curve in Fig. 4 has more details on the mechanical forcing we refer to the about 2±3 times higher mean value, the amplitude of paper by Staneva and Stanev (1997). It is well known that linear Sverdrup dynamics have the oscillations is about 5 times larger, and they are more little effect in a small basin; therefore wind stress is also irregular than in the WR91 experiment. shown in Figs. 3a,b to better illustrate the mechanical To study the effect that bottom relief has on the cir- forcing. In both datasets wind stress is higher in the culation we performed two additional experiments western Black Sea than in the remainder of the basin. forced with the wind stress of Rachev et al. (1991). In Due to the coarse resolution in the NMC analysis data, the ®rst we set a ¯at bottom (WR91F experiment) at wind stress patterns are very smooth. Pronounced dif- depth 1540 m equal to the maximum depth in the WR91 ferences in the wind stress direction are observed in the experiment. In the second additional experiment we use western Black Sea. These strong differences could result much ®ner vertical resolution (WR91VR) with 22 lev- in substantial changes in the circulation and in the phys- els. This permits better resolution of the continental ical balances, which will be shown later. slope and the continental shelf. Climatological temperature and salinity data for the We will analyze the performance of the present model Black Sea are analyzed in Blatov et al. (1984), Stanev by comparing our results with some estimates of earlier et al. (1988), and Stanev (1989a). From the monthly studies. With a horizontal resolution of 1/4Њ (which does mean climatic data we calculate annual-mean sea sur- not resolve eddies in the Black Sea), but with essentially face density ␳*, Fig. 3c, which enters in the restoring the same model, Stanev et al. (1995) and Staneva and term in Eq. (8). The relaxation time 1/␩ is chosen as Stanev (1997) studied the oceanic response to different 10 days. Sensitivity analyses on the model response to types of forcing functions, which included seasonal, as changing ␩ in the range 10±300 days showed that this parameter has small impact on the eddy dynamics (at well as short periodic variability. The sensitivity of the least for the relatively short integration time). model simulations to the horizontal resolution was pre- viously addressed for the Black Sea by Stanev (1988, 1990), who used two different resolutions: 1/2Њ and 1/6Њ. d. Model experiments Since the same numerical model was used in these stud- To study the sensitivity of the model circulation to ies, we will try to revise some of the past results, taking mechanical forcing by different sources we performed into account the effects resulting from the ®ner resolution in the present study. When no reference to the experimental nomenclature is given further in the text, 1 National Centers for Environmental Prediction. we imply the WR91 experiment.

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FIG. 3. Model forcing. (a) Annual-mean wind stress and wind stress curl, calculated from the NMC analysis data for the period 1980±89. The contour interval is 10Ϫ8 Pa mϪ1, solid lines correspond to positive values, and dash lines correspond to negative values. (b) Annual mean wind stress and wind stress curl calculated from the wind data of Sorkina (1974). The contour Ϫ8 Ϫ1 interval is 5 ϫ 10 Pa m . (c) Annual-mean sea surface density ␴t. The contour interval is 0.1

␴t units.

3. Analysis on the model-simulated circulation eddies are quasi-permanent or transient features. By analyzing time-averaged simulation results, we will try to a. Time-averaged ®elds answer this question. In the following we will also il- The available information from hydrographic surveys lustrate the sensitivity of the circulation to different me- is not suf®cient to decide whether some of the observed chanical forcing, bottom relief, and vertical discretiza-

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TABLE 1. List of the numerical experiments. Experi- Mechanical ment forcing Topography WR91 Annual-mean wind stress Variable, coarse vertical from Rachev et al. (1991) resolution WNMC Annual-mean wind stress Variable, coarse vertical derived from twice daily resolution NMC analysis data WR91D Annual-mean wind stress Variable, coarse vertical from Rachev et al. (1991) resolution with double magnitude WR91F Annual-mean wind stress Flat from Rachev et al. (1991) WR91VR Annual-mean wind stress Variable, ®ne vertical from Rachev et al. (1991) resolution tion. The averaging is carried out over at least ®ve eddy periods (eight periods in WR91). The analysis on the periodicity of the oscillations (monochromatic oscillations, see further in the text) and on the stability of the estimates as a function of the length of the averaging FIG. 4. Kinetic energy (cm2 sϪ2) during the integration. The legend shows that averaging for ®ve eddy periods gives quite in the ®gure refers to the experiment nomenclature; see Table 1. stable results. Comparison between mass transport streamfunction in WNMC and WR91, Figs. 5a and 5b, and between the corresponding wind stress curls, Figs. 3a and 3b, the eastern subbasin, reaching about 4.5 Sv. Some of reveals rather low correlation (large part of the western the quasi-permanent eddies, which we ®nd in Fig. 5a, subbasin is dominated by anticyclonic wind stress in disappear; others intensify (e.g., the Sakarya eddy) or Fig. 3a and by cyclonic mass transport in Fig. 5a), in- their locations become more realistic (e.g., the Batumi dicating that the circulation is far from the Sverdrup eddy). The peculiarity of the mass transport in the north- balance. The physical balance in the 1/4Њ resolution ex- western Black Sea simulated in the WNMC experiment, periments (Stanev et al. 1995) was rather different, and Fig. 5a (but not supported by observations), disappears there was a good correlation between the patterns of the in the WR91 experiment, Fig. 5b. The circulation in the wind stress curl and of the total transport streamfunc- WR91 experiment has much in common with the di- tion. This important difference between the coarse- and agnostic and prognostic calculations of the annual-mean ®ne-resolution simulations is an indication that in the circulation (Bogatko et al. 1979; Blatov et al. 1984; case of nonlinear dynamics the Black Sea circulation Bulgakov and Korotaev 1987; Stanev et al. 1988; Oguz depends substantially on the basin shape and topogra- et al. 1994). The anticyclonic eddy seaward of the Sa- phy, which governs the propagation of coastal trapped karya canyon (Oguz et al. 1993) is simulated in all waves rather than on the wind stress curl. This seems experiments, with some differences due to different plausible if we have in mind that the relatively small forcing and topography. It seems that this is one of the scale of the sea could act as a limiting factor for the most stable subbasin-scale quasi-permanent features of magnitude of annual-mean wind stress curl. the circulation. The basin interior in the WNMC experiment is dom- Doubling the wind forcing in the WR91D experiment inated by cyclonic circulation with mean transport of drastically changes the circulation pattern, compared to about 1 Sv (Sv ϵ 106 m3 sϪ1). There are several quasi- that in the WR91 experiment, Fig. 5d. The circulation permanent anticyclonic eddies between the coast and in the eastern basin intensi®es, and the transport max- the main gyre. The comparison with the observations imum reaches 7 Sv. The circulation in the western basin (Kaz'min and Sklyarov 1982; Stanev et al. 1988; Oguz weakens (particularly in the westernmost part of the et al. 1992; Oguz et al. 1993) shows an agreement in sea). The anticyclone off the Sakarya canyon is shifted the positions of the Kaliakra, Bosphorus, Sinop, and farther toward the open sea, and the quasi-permanent Batumi quasi-permanent eddies. However, the circula- Batumi eddy is not simulated. The pronounced differ- tion in the northern Black Sea seems not to be realis- ence between the simulations in the WR91D and WR91 tically simulated. experiments shows that the similarity in the patterns of There is only qualitative agreement between the cir- mechanical forcing (double the wind stress) does not culation patterns simulated in WNMC and WR91 ex- result in similar circulation patterns, which indicates that periments in the basin interior. The circulation in the the circulation might be dominated by nonlinear pro- second experiment intensi®es (Fig. 5b), particularly in cesses. The discrepancy between the simulations in the

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FIG. 5. Time-averaged streamfunction of the vertically integrated mass transport. Solid lines correspond to positive values, dash lines correspond to negative values. The contour interval in the ®rst plot is 0.2 Sv; in the rest of the ®gures it is 0.5 Sv. (a) WNMC experiment, (b) WR91 experiment, (c) WR91 experiment; the relaxation parameter ␩ from Eq. (8) is set to 1/300 days, (d) WR91D experiment, (e) WR91F experiment, and (f) WR91VR experiment.

WR91D experiment and the existing concepts for the and 5e indicates that the anticyclonic eddies along the general circulation in this sea shows clearly that using Turkish coast are more pronounced in the ¯at-bottom inappropriate mechanical forcing in the eddy-resolving experiment, which compares better with observations models could lead to severe inconsistencies. This sen- (Oguz et al. 1993). This could serve as an indication sitivity is an important modeling problem since existing that with a resolution of about 12 km the slope area is datasets for the mechanical forcing in the Black Sea not accurately resolved, which could result in under- show large differences (Staneva and Stanev 1997). We estimation of the coastal/topographic control. We re- have to admit here that the above results could depend mind here that 5-km resolution in this extremely steep on the friction in the model. area is also not suf®cient for accurate simulations (Oguz The intensity of the circulation in the WR91F ex- et al. 1995). Assuming vertical wall along the southern periment (Fig. 5e) is comparable to the one in the coast seems to better approximate the real topography WR91D experiment, but the decoupling of the circu- with the model resolution. lation in both parts of the sea disappears (the maximum Model sensitivity with respect to the relaxation co- moves from the eastern Black Sea into its westernmost ef®cient in Eq. (8) and with respect to different vertical zone). The anticyclonic circulation is localized in the resolution is illustrated by the comparison of Fig. 5c northern (now deep) area and along the southern coast. (relaxation time 300 day) and Fig. 5f (WR91VR ex- The Batumi quasi-permanent eddy disappears in the ¯at- periment) with Fig. 5b (central experiment WR91). bottom experiment, which shows that this important cir- Even with unrealistically large relaxation time of 300 culation feature is rather sensitive to changes in the days, compared to the one of 10 days in WR91, the model topography. The comparison between Figs. 5b streamfunction patterns change insigni®cantly. How-

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FIG. 6. Snapshots of the vertically integrated mass transport streamfunction. Time interval between the snapshots (in alphabetical order) is 30 day; the contour interval is 1 Sv. Solid lines correspond to positive values, dash lines correspond to negative values. ever, increasing the vertical resolution has much more movie of the experiments, reveal a regular periodic cy- pronounced impact. It is better observed in the western cle; thus Fig. 6 is representative for the whole integra- Black Sea, where the differences between the model tion in the WR91 experiment. Eddies form in the east- topographies are stronger (Fig. 1b). The time-averaged ernmost Black Sea (once every six months) and con- circulation intensi®es in WR91VR due to the more ac- stantly grow with time. After about 12 months they enter curate resolution of the topography and to the resulting the western Black Sea and dissipate. There are some changes in the dissipation. regularities in the eddy evolution, which are different for cyclonic and anticyclonic eddies. Anticyclones have almost equal scales zonally and meridionally at the ini- b. Model eddies tial phase of their evolution. Five months after they We will demonstrate the eddy generation, evolution, appear (at this time the eddy center reaches about 37Њ and dissipation, trying to ®nd the common features be- E), anticyclonic eddies start to elongate in the meridi- tween the present estimates and the observations. Dif- onal direction and become sandwiched between two cy- ferently from the mean circulation patterns in Fig. 5, clonic eddies. The cyclonic eddy to the west is still the streamfunction snapshots, Fig. 6, are dominated by intense but its westward velocity starts to decrease in eddies and give quite a different view of the circulation. the narrow section; the one to the east intensi®es, moves The systematic analyzes of Blatov et al. (1984) and of rather rapidly to the west, and ``¯attens'' the anticy- Golubev and Tuzhylkin (1990) show that the Black Sea clone. The elongated anticyclone moves farther west, eddies have diameters ranging from 30 to 220 km. With but its meridional extension starts to decrease when it our model resolution of about 11±13 km we capture the enters the narrow section between Sinop and Crimea. medium and large size eddies. Next, its pathway turns to the southwest (towards the Analyses of a large number of snapshots, that is, a Bosphorus Strait). In such a way the anticyclonic cir-

Unauthenticated | Downloaded 09/26/21 06:08 AM UTC 1590 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 culation in this area (the Sakarya eddy) is constantly (Fig. 7b). After two months, the circulation in the area maintained. The cyclones continue to the west and of this meander closes, which indicates that a ring is merge with the weak, but permanent, cyclonic eddy; formed (Fig. 7c). The ring formation process and sim- thus they contribute to maintaining the cyclonic circu- ulated magnitudes of the surface currents compare well lation in the western Black Sea. with observations (Oguz et al. 1994). The pathways of the cyclones and anticyclones in the There is good correlation between the circulation pat- eastern Black Sea coincide in the WR91 experiment, terns and the horizontal anomalies in the density ®eld. whereas the anticyclones tend to propagate to the south As seen from the comparison between the time-averaged from the cyclones in the WR91F experiment. This ex- pattern, Fig. 8a, and the two snapshots, Figs. 8b and 8c plains the higher anticyclonic rotation along the Turkish (corresponding to Figs. 7b and 7c), these anomalies dis- coast in the WR91F experiment (compare Fig. 5e with appear in the time-averaged pattern. The density anom- Fig. 5b). alies in the cyclonic eddies correlate with the mean up- The comparison of model and survey data reveals ward transport in the basin interior and associated down some similarities in the dynamics of the anticyclonic welling in the coastal areas. eddies in the central Black Sea (Altman et al. 1984; The southern part of the main gyre (¯ow to the east) Latun 1990). Observed eddies are less elongated than is more unstable than the part of the gyre along the those in the model simulations before entering the Black Caucasian coast (¯ow to the northwest). This result is Sea narrow section. However, their shape becomes sim- in good agreement with the earlier theoretical analyses ilar to that of the model simulated eddies in the narrow (Blatov et al. 1984) of the baroclinic instability of the section. Moving farther west these eddies again become Black Sea currents as a function of their direction. Sim- symmetric. The vertically integrated transport, estimat- ulated current patterns indicate that the instabilities (me- ed for this eddy by Golubev and Tuzhylkin (1990), rang- anders) are created in the area of the Batumi quasi- es from 1.2 to 3.3 Sv. The corresponding numbers es- permanent eddy and propagate against the gyre (to the timated from the model are between 3 and 5 Sv, when west). The excitation of the Sinop anticyclonic eddy the eddy is within the area of the narrow section. could be regarded as stimulated by the growing insta- The comparison between the mean patterns and the bility moving to the west. In about 2±3 months the large snapshots could give information on the dominating anticyclonic meander reaches the narrow section and modes in the simulated circulation. Mean patterns are evolves into a ring (Fig. 7). Though possible conclusions dominated by one or two gyres, with scales of the order based on the correlation between the transport patterns of the basin scales [modes with wavenumbers nϭ1 and of suspended matter and plankton derived from satellite nϭ2; see Eremeev et al. (1992)]. Snapshots are domi- observations, and the model simulated patterns are ques- nated by 4±5 eddies, with scales on the order of the tionable, we refer to the results of Sur et al. (1994). The width of the narrow section (wavenumbers 4, 5, and 6). comparison demonstrates that the horizontal scales and From the comparison between the magnitudes of the the speed of propagation of the eddies/meanders west mean and eddy transports we see that the subbasin-scale of the Caucasian coast are comparable in the model modes start to dominate the solution. This accumulation simulations and in the observations. of energy in the higher wavenumbers is due to the spe- Unlike some theoretical estimates (e.g., Blatov et al. ci®c physical mechanisms of the model (see section 4). 1984, no dissipation included), the numerical model Sea surface velocities, Fig. 7, reach maxima of about does not indicate increased baroclinic instability close 45 cm sϪ1, which is in a good agreement with the ob- to the Bulgarian coast. However, the change in the dis- servations compiled by Blatov et al. (1984). The max- sipation mechanisms in the WR91F experiment changes ima decrease with increasing depth to about 25±30 cm completely the results. The decreased dissipation in the sϪ1 at 70 m, and to 5±10 cm sϪ1 at 1100 m. No strong western basin (due to the absence of the shelf) enables indications could be found from the model results that the eddies to reach the westernmost Black Sea, thus the circulation reverses in deep layers. However, the intensifying the variability and the instabilities in this Sakarya and Batumi anticyclones are better pronounced area (see section 4). in the deeper layers. The model estimates support recent observational results of Oguz et al. (1994), showing that the mesoscale features are coherent down to 500 m. We 4. Physical analyses ®nd vertical coherency down to the bottom, particularly a. Time variability in the areas ®lled with strong eddies. In contrast to the vertically averaged streamfunction We begin the analysis on the time variability by ex- patterns, current patterns are dominated not only by ed- amining the velocity components and density at points dies but also by pronounced meandering of the main A, B, and C, marked in Fig. 1a. The oscillations have gyre. Some meanders increase in amplitude and form large amplitudes and are very regular in the eastern and rings, which is the case illustrated in Fig. 7. We see in central subbasins; amplitudes are smaller and more cha- Fig. 7a an anticyclonic meander south of the Crimea otic in the western subbasin, Figs. 9a±c. Model data Peninsula. It constantly grows and moves to the west show good correlation between the surface values and

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FIG. 7. Snapshots of the horizontal velocities at the sea surface, corresponding to the ®rst three streamfunction snapshots in Fig. 6. those at the depth of the halocline (260 m) in the eastern western subbasin (Fig. 9a) where periods of 145, 160, and central subbasins. Statistical analysis of the simu- 205, and 288 days are observed. The coherency between lated data in the same regions shows that the main pe- the processes in the surface layer and at 260 m is less riodicity (160 days) dominates the spectra for velocity pronounced in western subbasin than elsewhere in the and density in surface and deep layers. Velocities at sea sea. The trend of decreasing periodicity in the western surface and at 260 m show maximum coherency at about basin is even stronger in the WNMC experiment. 145 days and much lower secondary peak at about 20 From the above considerations it follows that there days. It is dif®cult to ®nd pronounced regularities in the are two very different regimes dominating the circula-

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FIG.8.Density(␴tunits) at 260 m in the WR91 experiment. (a) Time-averaged ®eld; (b) snapshot, corresponding to the velocity pattern in Fig. 7b; (c) snapshot, corresponding to the velocity pattern

in Fig. 7c. The contour interval is 0.02 ␴t units. The shallow part of the sea is shaded. tion: a wavelike regime in the eastern and central Black line labeled by asterisks in Fig. 9a (oscillations of the Sea and a turbulentlike regime in the western basin. The meridional velocity at location A for the WR91VR exchange of the oscillations from monochromatic in the periment) reveals slightly better regularity than the cor- eastern basin to chaotic in the western basin is clearly responding curve resulting from the WR91 experiment. illustrated by the hodographs (Figs. 9d±f). This sensitivity is very strong [note the similarity of the The regularity of the oscillations in the western Black bottom pro®les when the topography is differently re- Sea is affected also by the resolution of the shelf. The solved (Fig. 1b) and the difference in the amplitudes of

Unauthenticated | Downloaded 09/26/21 06:08 AM UTC AUGUST 1997 RACHEV AND STANEV 1593 the corresponding velocities]. It will be shown below large speed). Analysis of the Hovmoeller diagrams for that the model shelf in the WR91VR experiment exerts deeper layers leads to similar conclusions. less friction, and consequently the westward propagat- The major difference between the ¯at-bottom exper- ing oscillations have larger amplitudes in the western iment and the experiments WR91 and WR91VR occurs basin than in the WR91 experiment. in the western basin. The dissipation area shifts west- A more detailed understanding of the time±space ward in the ¯at-bottom experiment, and a strong in- variability can be obtained by analyzing the Hovmoeller crease in the variability and in the intensity of the cir- diagrams (meridional velocity at 43ЊN, the zonal line culation (compare Figs. 10a and 10b) is observed in the in Fig. 1a, plotted as a function of time and longitude), coastal area. The position of the velocity maxima in the Fig. 10. The time-averaged velocity along the section Hovmoeller diagrams indicates that the group velocity line is also given in Fig. 10. The diagrams indicate is toward the east. This correlates with the well-known Rossby waves propagation. Their speed in the eastern mechanism of Rossby wave re¯ection from the western subbasin (the slope of the contours) in the WR91 ex- coast and shows that the western coastal zone is the periment is about 2.1 km dayϪ1 (2.5 cm sϪ1). For the main source of instability in the WR91F experiment. ¯at-bottom sea, WR91F, eddies propagate westward The shelf area in the WR91 experiment exerts more with an average speed of about 2.9 km dayϪ1 (3.4 cm dispersed damping. Thus, the instabilities associated sϪ1). Estimates for the WR91VR experiment almost co- with large shears induced by sudden western boundary incide with those for WR91 one in the eastern Black damping in the ¯at-bottom case are reduced in the Sea; therefore the Hovmoeller diagram for this exper- WR91 and, to a lesser extent, in the WR91VR experiment is not shown. For comparison, the results of Latun iments. As a ®nal analysis we refer to some observa- (1990) indicate the speed of eddy propagation to be 1.5 tional results. Using ®ve years of current meter data cm sϪ1. west of the Caucasian coast, Ovchinnikov et al. (1986) The westward propagation has almost constant mag- found a periodicity of about 6 months superimposed on nitude in the eastern basin, but the eddies slow down the seasonal cycle. Later, Eremeev et al. (1990) found pronounced variability with periods of 4±7 months and in the narrow section (between 32Њ and 34ЊE) and to Ϫ1 the west of it. This is illustrated in the Hovmoeller di- phase speeds of 2±6 km day in monthly mean data. agrams by the changing slope of the contours (Fig. 10a). Model-calculated characteristic periods (160 days) and speeds (2.1 km dayϪ1) are within these ranges, which The constant decrease in the speed of the westward could support resonance between seasonal and synoptic propagation in WR91 is in agreement with the decrease variability in the Black Sea. of the eddy size in the western subbasin (Fig. 6). The orientation of the isolines becomes almost parallel to the ordinate in close proximity to the coast, which in- b. Energetics dicates a very slow propagation. The decrease in eddy size and speed is consistent with assuming intense dis- There is phenomenological evidence for eddy pro- sipation of eddy energy, therefore, the western subbasin cesses in the Black Sea but very few theoretical studies. is recognized as a dissipation basin. Model eddies in Among the topics of major importance we mention the the WR91VR experiment behave in a similar way after following: What drives the eddies; are they topograph- passing the narrow section, but the decrease of eddy ically intensi®ed; what is the role of the baroclinic in- speed and scales is less abrupt, and the eddies penetrate stability for the eddy formation? We try to answer these closer to the western coast at speeds slightly larger than questions in the remaining part of the paper. To this aim in the WR91 experiment. we present an analysis on the model energetics. We Comparison of the results of WR91, WR91F, and denote the kinetic energy per unit volume as WR91VR shows clearly the impact of the bottom to- U ´U pography on the eddy propagation (Fig. 10). This west- hh eϭ␳0 . ward propagation is more regular in the WR91 and 2 WR91VR experiments (the regularity is illustrated by repeating the same pattern in time in Fig. 10a). We According to Holland (1975) the volume-averaged total observe a rather regular westward propagation in the kinetic energy in mechanically closed region E ϭ͗e͘, e Ϫ1 ∫∫∫ e WR91F experiment in the ®rst 200 days, as well. How- ͗ ͘ϭV ( ) d␷, (V is the volume of the sea) may be changed by the work done by wind stress (W), by ever, after day 300 eddies start to stagnate in the basin buoyancy forces (B), by the loss of energy due to dis- interior. (A movie of the streamfunction for several sipation in the ¯uid, and at the lateral boundaries (D) years yields convincing proof of the periodic stagnation in the central Black Sea.) This could be due to the to- E ϭ B ϩ W ϩ D. (9) pographic effects in the narrow section. The Hovmoeller t diagram (Fig. 10b) shows better the subsequent accel- Expressions for the terms in Eq. (9) are given by Holland eration, which can be recognized by the discontinuities (1975). Kinetic energy E can be divided into two com- in the contours (very small slope and correspondingly ponents:

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FIG. 9. Time variability of currents and ␴t in different locations at 260 m. The locations A, B, and C are shown in Fig. 1, and the legend in Fig. 9a gives the correspondence between the model variables and the different curves in all plots. (a)±(c) Locations A, B, and C, experiment WR91. Oscillations of the meridional velocity in location A, simulated in experiment WR91VR are also given in (a). (d)±(f) Hodographs in points A, B, and C, experiment WR91. Lines connecting the ends of current vectors in Fig. 9d are labeled each month. There is no labeling in Figs. 9e and 9f since the current vector is periodic and the labels almost overlap. Therefore, the numbering in these ®gures is done only for the ®rst period.

UÅÅ´UU´Uing value estimated by Stanev (1988). The wind forcing Å hhЈ hhЈ Eϭ␳00and EЈϭ ␳ , effect is larger on the internal mode than on the external Ό΂΃22΍Ό΂΃΍ mode (Fig. 11b) as is typical in many QG and PE wind- forced models (see Holland 1975; Treguier 1992). This corresponding to external UÅ and internalUЈ mode ve- h h result is in a qualitative agreement with the estimates locities, where UÅ ϭ HϪ1 ∫ U dz and UЈ ϭ U Ϫ UÅ . h h h h h of Stanev (1988), W ϭ 1.1 ϫ 10Ϫ6 cm2 sϪ1 and W ϭ For the time rate of change of EÅ and EЈ we have i e 0.4 ϫ 10Ϫ6 cm2 sϪ1; however, the present estimates yield Å Et ϭ Ne ϩ Be ϩ We ϩ De magnitudes more than two times as large. Kinetic energy and EЈϭNi ϩBi ϩWi ϩDi, (10) is dissipated mainly due to the lateral friction, which is where the terms on the right-hand side of Eqs. (10) more pronounced in the external mode. represent the work done on the external/internal mode The negative sign of the buoyancy term means that by the nonlinear terms (N ), the pressure forces (B ), the wind does work to maintain the doming form of the e,i e,i isopycnic surfaces. This is an indication that the the wind stress (We,i), and by the dissipation forces (De,i). In a closed basin N ϭϪN. There is no exchange be- wind-driven velocities are larger than the buoyancy- i e driven ones. A similar result was found earlier by Stanev tween internal and external mode kinetic energy (Be ϭ 0) if either the bottom is ¯at or the ocean is homoge- (1988, 1990) in several numerical experiments, forced neous. The net transfer between the external and internal with different combinations of forcing functions, but with about two times lower resolution in the horizontal modes due to topography is T ϭ B Ϫ Bi. We will analyze below the energetic terms as in the paper by Treguier than in the present study. This speci®c conversion of (1992) (Fig. 11a). energy was explained as due to the reduced penetration We showed in section 2d that kinetic energy oscillates of the buoyancy into the deep layers, limited by the around its mean value of 16 cm2 sϪ2 in WR91 experi- extremely strong strati®cation. In the same study, com- ment with a period of about 160 days (Fig. 4). This parison between the results obtained by using different mean value is several times larger than the correspond- horizontal resolution did not show qualitative differ-

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FIG.9.(Continued)

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FIG. 10. Time evolution of zonal section (x±t plot) of the meridional ¯ow at the sea surface; the contour interval is 5 cm sϪ1. Solid lines correspond to positive values; dash lines correspond to negative values. Time-averaged velocity (upper panel) is subtracted from the actual velocity data: (a) in WR91, (b) in WR91F. ences (energy ¯ows did not change direction). We will rents below the halocline were rather slow, whereas in demonstrate now a qualitatively new model behavior. the present model there is an extremely high and deep Kinetic energy is exchanged between the external and penetrating variability on the continental slope. This ex- internal modes through nonlinear and topographic trans- plains the increase in the topographic transfer, compared fers N and T. An explanation of the nonlinear transfer to the previous estimates (increase in the JEBAR), by the concept of inverse cascade is given by Charney which is due to the stronger interactions between cur- (1971). The sign of this transfer in our experiment in- rents and topography in the present model. dicates that perhaps such an inverse cascade occurs. This The signs of the terms in Eq. (10) do not change in was not the case in the previous experiments with the the WR91F experiment (Fig. 11c) compared to the es- Black Sea model (where the magnitude of the corre- timates in the WR91 experiment. The lack of topo- sponding term was an order of magnitude smaller and graphic transfer results in reduced magnitudes of almost its direction was opposite). Topography is found to all terms by about 40%±50%. The nonlinear transfer transfer energy to the internal mode [in the same di- decreases approximately two times, but the net exchange rection as in the work by Stanev (1988, 1990)], but the between the internal and external modes slightly in- estimated magnitude is several times larger now. Thus, creases in WR91F. the nonlinear conversion and the topographic transfer The time variability of the energy terms, Fig. 12, are almost compensated in the present model. gives a convincing illustration of the quasiperiodic mod- The sign of T shows that the external mode currents el behavior. The work done by wind on the internal

¯ow up the topographic slope. There is experimental mode (Wi, full line in Fig. 12a) shows pronounced 160- evidence that a similar situation usually occurs in the day periodicity. The curve, corresponding to the work western and northern parts of the sea where the current done by wind on the external mode (We, full line in Fig. ``attacks'' the bottom slope. In the previous models cur- 12b) has a more complex shape. It has a main period

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FIG. 11. Energy diagrams showing the magnitude and direction of the work done by the energetic terms in Eq. (10). The numbers (cm2 sϪ3) are multiplied by 106. (a) notations, see also Eq. (10),(b) WR91 experiment, and (c) WR91F experiment.

of 160 days, as well, but is in opposite phase to the Wi curve. Double maxima with changing amplitudes are observed in the W curve each half period. At the time e FIG. 12. Time evolution of the terms doing work in Eq. (10). The when the work done by wind (We) reaches a local min- correspondence between the model terms and different curves is given imum, the nonlinear conversion rate (denoted shortly in the legend: (a) internal mode and (b) external mode. by ``advection'' in the ®gure) reaches a maximum. The time for reaching maximum nonlinearity is about three T times longer than the time for reducing the nonlinearity. 1 qÅ ϭ qdt, Apparently, this indicates rather fast overturning after T͵ 0 the instabilities reach some critical value. can be divided into energy of the time-averaged motion UÅÅ´U c. Eddy versus mean circulation EÅϭ␳hh m 02 We will discuss some more details concerning the mesoscale processes by analyzing model simulated and eddy kinetic energy mean and eddy energy. The time-averaged kinetic en- UЈ ´ UЈ ergy EÅϭ␳hh. e 02 U ´ U Å hh Eϭ␳0 , Kinetic energy of the mean motion (MKE), Fig. 13, 2 correlates with the time-averaged velocity ®eld. The where MKE has maxima in narrow regions localized along the

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FIG. 13. (a) Kinetic energy (cm2 sϪ2) of the mean ¯ow in WR91 experiment; (b) eddy kinetic energy (cm2 sϪ2) in the same experiment. eastern Turkish coast and along the Caucasian coast. In mean circulation. Therefore, we will make some com- the second region, currents show very high stability, parisons with previous model studies. There is a simi- resulting in large MKE. A pronounced low energy re- larity of the patterns in Fig. 13 with the ones of Stanev gion is observed in the central part of the sea. The (1988) but the energy is much higher in the present pattern of the mean energy in the main halocline is very study. Like in the quoted study, the MKE maxima ap- similar to the one at the sea surface, but the magnitudes proximately coincide with the position of the mean gyre decrease considerably. (along the coast), but in contrast, the maxima in the Eddy kinetic energy (EKE) is higher than the MKE EKE are in the basin interior (in the area of the narrow in most of the sea (Fig. 13b). Exceptions could be found section). We ®nd increased rms variability in ␴t at the close to the Caucasian and Crimean coasts and in the main pycnocline depth, which indicates that most of the western part of the sea. The energy analyses of the sim- variability is related to the change in the halocline depth. ulations for the North Atlantic, carried out by Beckmann There are important differences between our esti- et al. (1994) as a part of the Community Modeling Effort mates and some estimates for the Gulf Stream region (CME, see Bryan and Holland 1989), demonstrated that (BoÈning and Budich 1992; Treguier 1992; Beckmann et EKE at sea surface is about four times larger than MKE, al. 1994) where the areas with MKE and EKE maxima which is in agreement with the Black Sea simulations. almost coincide. One of the possible reasons for the As shown by the comparison with some previous results nonconformity in the locations of MKE and EKE max- (Stanev 1988, 1989b, 1990), the high EKE in the present ima in the WR91 experiment could be due to the speci®c estimates is mainly due to the improved horizontal res- wind forcing. In the WNMC experiment, which is rel- olution. atively weakly forced, the EKE does not exceed the At present, no observational data are available to ver- MKE, and the area of the absolute maximum in the EKE ify model results on the relative weight of eddy versus is to the west of the Caucasian coast (not in the central

Unauthenticated | Downloaded 09/26/21 06:08 AM UTC AUGUST 1997 RACHEV AND STANEV 1599 basin). In the WR91 experiment, the circulation is more intense, and the energetic regime is strongly dominated by basin oscillations and nonlinearities. The displace- ment between areas where the EKE and MKE reach maxima could also be due to the stabilizing effect that the bottom slope exerts on the currents. This effect is small in the interior of the sea, and the variability is very strong. Another illustration on the impact of the topography could be found in the simulations resulting from the WR91VR experiment, where the maximum of the MKE encompasses the entire basin (no splitting, like in Fig. 13a, is observed in the western basin). We point out again that the discussion above concerns the results simulated using annual-mean forcing. Sea- sonality in the wind forcing tends to displace the EKE maximum along the main gyre, as was shown by Stanev (1988, 1989b, 1990). This feature in the Black Sea circulation will be discussed in more detail in future studies.

FIG. 14. Wavenumber spectra along the section line in Fig. 1 aver- d. Analysis of model evidence for geostrophic aged in time. turbulence What makes the Black Sea interesting from the point of view of eddy dynamics is the fact that eddy scales where spectra are calculated (the overlapping over about are comparable to the basin scales (e.g., the scales of 1Њ is a compromise, resulting from the requirement to the narrow section; the scales of the areas of input or increase the number of data points in order to produce dissipation of energy; the scales of the main topographic reliable estimate of the spectra). The intense eddy pro- features, such as the western Black Sea topographic cesses in the eastern basin are illustrated in the ®gure slope). It is well known that Rossby wave±baroclinic by the higher spectral maximum. instability is related to the interaction with the bottom Evidence for geostrophic turbulence in the Black Sea relief. Topography generally whitens the wavenumber is ambiguous, and the intercomparison of the model spectrum. In the western parts of the oceans Rossby simulations with observational data is dif®cult. Present wave re¯ection results in increasing enstrophy and in results could be compared to the ones of BoÈning and stronger dissipation. In such areas barotropy is a nec- Budich (1992), where the same model is applied to the essary consequence of a red horizontal cascade, related Atlantic Ocean. As in the quoted work, the following to the transfer of enstrophy to larger wave numbers important spectral ranges could be identi®ed: 1) energy- (Rhines 1977). These processes take place, of course, containing range with rather a ¯at spectrum at lower also in the Black Sea. The shelf in the western basin wavenumbers; 2) inertial range, where the spectral slope and the continental slope create very important differ- is close to kϪ3; and 3) dissipation range at higher wave- ences in the circulation in WR91, WR91F,and WR91VR numbers, where the spectral slope is large. The curves related to the eddy dissipation. The Black Sea narrow in Fig. 14 are most similar to the BoÈning and Budich section also affects the eddy regime, as could be seen (1992) polar spectra due to the similarity of the Rossby by the comparison between results in WR91 and WR91F radius of deformation in polar areas and that in the Black (Figs. 10a,b). Sea. We see from Fig. 14 a decrease in the cutoff wave- Further understanding of the eddy dynamics can be length in the western basin, consistent with the results achieved by examination of the power spectra, Fig. 14. of the previous sections, showing smaller eddies in this Since there are obvious differences between the physical part of the sea. The shorter inertial range, compared to balances in the western and eastern Black Sea (see pre- the one in the Tropics, could be due to the effect of vious sections), we calculated the velocity spectra for model friction on the shorter wavelengths. One plausible each subbasin separately. The spectra shown in Fig. 14 explanation of the relatively narrow inertial subrange were calculated by averaging spectra from 50 individual might follow from the result that eddies in our model realizations during the last four years of integration. No rapidly reach scales comparable with the width of the spectral smoothing was applied. The spectral maxima narrow section. The oscillations are rather monochro- are attributed to the longer waves. The cutoff wave- matic (there is a strong preference for particular space length is about 250 km in the eastern basin and about scales, and in the model eddies smaller than those of 190 km in the western basin. The scales are not very the dominate scale are missing); thus the Kolmogorov different since there is some overlapping of the areas cascade is not well developed.

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5. Conclusions and discussion cyclonic (experiment WNMC), we have cyclonic currents, thus indicating the important role of nonlinear Two major focuses in this paper related to eddy vari- processes and, perhaps, coastal-trapped waves. These ability will be emphasized in the discussion: 1) the phe- waves are demonstrated by Sur et al. (1994), using sat- nomenology of the Black Sea circulation inferred from ellite images of the sea surface. Model results, to be the numerical model and 2) the physical mechanisms analyzed in detail in forthcoming paper, exhibit eastward of the circulation. propagating, or sometimes stagnating, undulating fea- The time-averaged circulation, shown in Fig. 5, has tures east of Sakarya Canyon, which correspond with much in common with the well-known annual-mean cir- observations. Waves are periodically excited by the vari- culation features, resulting from dynamic and diagnostic ability with larger scales, and they become very unstable calculations (Bogatko et al. 1979). It is dominated by after reaching the zonal part of the coast. This is ex- a general cyclonic gyre with several quasi-permanent plained by Sur et al. (1994) as a consequence of chang- subbasin-scale eddies. Model snapshots show repeating ing slope and of the direction of the current. This process cycles (about 6 months) illustrating eddy formation (in could be additionally ampli®ed by the interaction of the eastern Black Sea), propagation to the west, and westward propagating Rossby waves with coastal- dissipation (in the western basin). Eddy scales grow trapped waves. These interesting physical processes until they become comparable with the basin's width, could stimulate future studies. The Black Sea, with its which is the scale that contains most of the energy in closed boundaries, seems to be a good candidate for a the spectra. Twelve months after their formation, eddies test basin. enter the western Black Sea, where their propagation is In this paper we used some simpli®cations related to slowed. Eddy paths are strongly affected by the topog- the model forcing, model topography, and model phys- raphy, as well. The major topographic effect is mani- ics. This was done as a ®rst step toward understanding fested in the model by the eddy dissipation in the west- some of the free oscillations of the sea. Much remains ern basin. to be done to determine how realistic are the physical The circulation is characterized by pronounced me- balances discussed in the present paper and to achieve andering of the main gyre. The southern part of the gyre more adequate model simulations of the Black Sea vari- (¯ow to the east) is more unstable than the northern part ability: model intercomparisons and validations against of the gyre along the Caucasian coast. The time vari- observations, improving the resolution, taking into ac- ability is related to westward propagation with peri- count both temperature and salinity and such important odicity of 160 days, which dominates the spectra for forcing functions as strait exchange, precipitation, evap- velocity and density in surface and deep layers. The oration, heat ¯uxes (Stanev 1988, 1990). Free surface speed of the westward propagating waves in the eastern dynamics could result in further improvements in the subbasin is about 3 cm sϪ1, close to the estimates re- model estimates (Oguz et al. 1995). Forced oscillations sulting from observations. After the eddies pass the could also have a signi®cant impact on the model cir- Black Sea narrow section, their speeds decrease with culation, as shown by Stanev (1988). Analysis on the about a factor of 2 in the WR91 experiment. As shown seasonal variability based on experimental data shows by the comparison of WR91, WR91F, and WR91VR half-year periodicity and phase speeds of 2±6 km dayϪ1 experiments, basin wave propagation is very sensitive (Ovchinnikov et al. 1986 and Eremeev et al. 1990), to the bottom topography. which is close to our model estimates. This periodicity The model circulation is far from the Sverdrup bal- could favor resonance between seasonal (forced) and ance. The negative sign of the buoyancy term indicates synoptic (free) variability in the Black Sea, a topic to that the wind does work to maintain the doming form be addressed in a subsequent paper. of the isopycnic surfaces. The exchange between the external and internal modes through nonlinear and to- Acknowledgments. The authors would like to thank pographic transfers N and T is a very important indi- K. BoÈning and H. Friedrich for the very useful com- cation that an inverse cascade probably occurs. EKE ments. The discussion on the mesoscale processes in the and MKE reach maxima in different areas, which is an Black Sea with P. Malanotte-Rizzoli, S. Meacham, G. important difference from the CME estimates for the Korotaev, and T. Oguz, during the Workshop on the Gulf Stream region (BoÈning and Budich 1992; Treguier Black Sea Modeling in So®a, Bulgaria, March 1994, 1992; Beckmann et al. 1994), where the areas of MKE was very stimulating in the ®nal part of this work. We and EKE maxima almost coincide. This is explained as are very grateful to the anonymous reviewers for many a consequence of the speci®c forcing and topography helpful suggestions and comments. in the Black Sea. 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