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

1581 Eddy Processes in Semienclosed Seas: A Case Study for the Black Sea NICKOLAY H. RACHEV AND EMIL V. STANEV Department of Meteorology and Geophysics, University of Sofia, Sofia, Bulgaria (Manuscript received 14 December 1994, in final form 29 November 1995) ABSTRACT The enclosed boundaries and small scales of some seas lead to the formation of specific physical balances, which motivates the oceanographic interest in studying the dynamics of semienclosed ocean basins. The focus in the paper is on the specific 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 1/10 and 1/6 is forced with annual-mean wind stress data. Buoyancy flux 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 s 1. 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 Experiments and theory have shown remarkable progress in the past two decades, resulting in elucidation of some important physical processes, which govern the mesoscale/synoptic eddies. A large amount of knowledge already exists for the Gulf Stream, Kuroshio, Antarctic Circumpolar, and equatorial currents. However, the impact of large-scale turbulence and baroclinic instability on the circulation in semienclosed seas is not well understood. Regional studies could be of general oceanographic interest, showing specific physical balances in areas where the Rossby radius of deformation is comparable to the basin scales. Decreasing resolution to about 1/10, or less, and integrating models for sufficiently long times, are realistic with present computers for entire (enclosed) basins if their size is small enough. In the present study we use the Black Sea as a test basin. Therefore, a short introduction to the physical oceanography of this sea is given below with a focus on the topics discussed in the paper. The Black Sea (Fig. 1a) is a typical example of an ocean basin where the vertical stratification is dominated by salinity. This is due to the specific water balance and Corresponding author address: Prof. Emil V. Stanev, Department of Meteorology and Geophysics, University of Sofia, 5, J. Bourchier Street, 1126 Sofia, Bulgaria. E-mail: Stanev@phys.uni-sofia.bg to the very small exchange with the Mediterranean Sea. The freshwater input from rivers and the net balance between precipitation and evaporation tend to decrease salinity in surface layers. The input of more saline water through the Strait of Bosphorus compensates the salinity deficit at the sea surface, and an extremely stable stratification is formed down to 200 300 m. It tends to decrease the vertical mixing and favors the unique environment of the Black Sea, which is manifested by the existence of an anoxic layer occupying 90% of its volume. The Black Sea can be regarded as a two-layer basin in which the deep layer is much thicker than the upper one (Fig. 2). Synoptic scales are larger than the corresponding scales in the neighboring Mediterranean Sea [eddy diameters could reach 200 km (Latun 1990)] and may approach the width of the narrow section between the Crimea and Sinop (later in the text we refer to this simply as the Black Sea narrow section). The growth of instabilities in this small basin is sometimes limited by the basin scales, which could give more relative weight to the basin or subbasin mode oscillations. The Black Sea has a relatively simple coastal line in contrast to the Mediterranean Sea. The configuration of the deep sea is geometrically even simpler, and the deep bottom topography is rather smooth. The continental slope is steep in the southern and eastern Black Sea, and rather flat between the Crimea and the Bulgarian coast (Fig. 1b), where depths less than 100 m dominate. 1997 American Meteorological Society

1582 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 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 profiles are shown in Fig. 1b. Thus, regional conditions for the synoptic processes are quite different over large areas in the deep sea than over the continental shelf. This motivates us to address in the paper the penetration of the synoptic eddies from the eastern to the western part of the sea, focusing on the impact that the basin shape and bottom topography have on their mobility. Dynamic computations initiated early this century (Knipovich 1932; Filippov 1968; Bogatko et al. 1979) established the concept of a basinwide circulation gyre (named recently in some studies Rim Current), with two centers in the eastern and western basin, named Knipovich spectacles. Much less is known about the space and time variability of the Black Sea circulation with FIG. 1b. Bottom profiles along the thick section lines in Fig. 1a, plotted with different vertical discretization. The capital letters at each profile 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 significantly 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 fine-resolution (details on the resolution of the topography are given in section 2b).

1583 synoptic scales, though large surveys were carried out recently (Oguz et al. 1994) with a very dense coverage of the entire basin. Numerical modeling has resulted in some progress in the study of the Black Sea eddy field too, but much still remains to be done. The horizontal resolution was first reduced to 20 km for the entire Black Sea in the nonlinear diagnostic model of Bulgakov and Korotaev (1987), which is rather coarse for eddy resolution in this basin. The Bryan and Cox GCM with horizontal resolution 1/6 and 1/3 was later applied by Stanev (1988, 1989b, 1990) to study the variability of the circulation. Forcing functions with seasonal oscillations (wind stress, heat flux, precipitation minus evaporation, river runoff, and exchange through the Strait of Bosphorus) were used in different combinations to study the response of the model sea to external forcing. Some of the topics, addressed in these studies, to be reconsidered in the present paper are 1) the sensitivity of the circulation to horizontal and vertical resolution, 2) mean versus time dependent circulation, and 3) model energetics. In the recent paper of Oguz et al. (1995) the individual impact of the mechanical and thermohaline forcing on the model simulations was studied, using finer resolution (variable in the horizontal, with grid intervals between 5 and 15 km) than in the previous studies. The novelty in this work is the more precise formulation of the effects of buoyancy forcing on the barotropic circulation. This was achieved by using active free surface dynamics. Though some important topics related to the eddy field in the Black Sea were addressed before, there are some principal items requiring systematic model development 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 physics, followed by discussion. FIG. 2. Mean vertical density profile ( t units) for the Black Sea; solid line corresponds to initial density, dash line corresponds to density at the end of the integration. 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 Uh p n L(U h) f Uh A U h h t 0 A U, (1) v h zz p g, (2) z L(1) 0. (3) In the above equations U (u,, w) is the velocity vector, U h its horizontal component, f 2 sin( )k, k (0, 0, 1), p and are the pressure and density, n 1 for Laplacian mixing, and n 2 for biharmonic mixing. The advection operator L( ) and the Laplacian are defined as 1 L( ) {sec( )a [(u ) ( /sec( )) ] (w ) } (4) z 1 1 ( ) sec( )a {sec( ) [ sec ( )] }, (5) where is any scalar quantity, a is the radius of the earth, and subscripts,, and z denote differentiation. Numerical experiments carried out by Stanev (1990) showed that the buoyancy due to temperature has secondary effect on the general circulation of the Black Sea. Therefore, the density is used here as a thermodynamic variable so that the corresponding conservation equation reads n L( ) Kh Kv zz. (6) t The coefficients of turbulent diffusion for momentum and density are A h,v and K h,v, respectively, where h is horizontal and v vertical. Convection is introduced in the model using the convective adjustment procedure of Bryan (1969). As in the standard Cox (1984) code, the lateral boundaries are insulating and nonslip, and the bottom is taken

1584 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 to be insulating and free slip. The model assumes the following boundary conditions at z 0: A U, (7) 0 v h z Kv z ( * ) z, (8) where is the wind stress, * is the climatological density, is an inverse timescale, and z is the thickness of the first model layer. The numerical algorithms are documented in Bryan (1969) and Cox (1984). b. Model geometry and parameters The model resolution is 1/10 in latitude and 1/6 in longitude, giving almost square grid elements in the horizontal with a grid size of about 11 13 km. The present study aims to provide estimates for some important physical processes in the Black Sea rather than a detailed reproduction of large number of circulation features. This is one of the motivations to make some model simplifications, including the minimum necessary resolution. Nonuniform resolution is used in the vertical with z chosen as 40, 60, 80, 160, 320, and 880 m. We remind here that Hecht et al. (1988) showed that for the deeper (and more complicated in stratification) Mediterranean Sea eight levels are sufficient to describe the major features of the vertical stratification. Also, Barnier et al. (1991) conclude that the number of vertical modes that require high resolution tends to be limited. In their six-layer experiments with a resolution of 10 km the dynamical role of the modes 5 and 6 seems to be of secondary importance. Following the idea that the model resolution has to be consistent in the three dimensions, we assume that with our coarse vertical grid we do not neglect more detail (relevant to baroclinic instability) than we do with the fine 11-km horizontal grid. The above arguments do not neglect the need to more precisely resolve the bottom topography, particularly over the shelf and in the shelf open sea transition zone (Fig. 1b). In the present study, the topography is discretized from the bathymetric map of UNESCO with the model resolution. With this rather coarse vertical resolution we capture the most important topographic features (the shelf area, the sharp bottom slope, and the flat interior). The comparison between bottom topography resolved with a limited number of vertical levels and the topography resolved with much finer resolution is shown in Fig. 1b for several sections across the shelf and on the continental slope. In the fine resolution case we use 22 vertical levels. The thickness of each of the first four levels is 5 m, of the following seven levels 10 m, and it constantly increases in the deep layers as follows: 30, 40, 50, 60, 80, 100, 130, 170, 240, 310, and 340 m. No pronounced differences are seen between the two topographies on the steep continental slope. This agrees with the results of Oguz et al. (1995), showing that to accurately resolve the steep continental slope in the Black Sea, the model resolution has to be better than five kilometers. With coarser resolution in the horizontal, the Black Sea continental slope looks like a vertical wall, independent of the vertical resolution, Fig. 1b. However, the profiles for the shelf region differ one from another in the coarse- and fine-resolution case (the meridional profile between the coast and location A, Fig. 1b). It is shown later that this difference, along with the insufficient resolution of the continental slope in the western Black Sea, could have a very strong impact on the eddy dynamics. Mixing and diffusion in the horizontal are parameterized with biharmonic operators, with coefficients A h 0.1 10 19 cm 4 s 1 and K h 0.4 10 19 cm 4 s 1 (see also Cox 1985; Holland 1989; and Böning and Budich 1992), which are just sufficient to prevent noise. For horizontal resolutions of about 10 km, as in the present case, the flow dependency on the biharmonic coefficient is small (Barnier et al. 1991), which is supported by our preliminary sensitivity experiments. The vertical mixing coefficient, A v 1.5 cm 2 s 1, and the vertical diffusion coefficient, K v 0.1 cm 2 s 1, are chosen small enough not to create unrealistically strong mixing in the deep layers. We admit that the parameterizations of the subgrid-scale processes, the model dissipation, or the numerical formulations could affect model estimates; therefore further studies, including model intercomparisons, are needed. In the present study, the Strait of Bosphorus is closed [the impact of the salt balance on the model circulation is discussed by Stanev (1988, 1990) and more recently by Oguz et al. (1995) and Stanev et al. (1997)]. Since the focus in this paper is not on the climatic but rather on the synoptic processes, we carry out the integration for relatively short periods (less than decade), not allowing substantial changes in the vertical baroclinic structure. As it is known from tracer studies (Östlund 1974) and from numerical model experiments (Stanev 1988), the timescale related to the exchange with the Mediterranean Sea is about 10 2 10 3 years. The vertical stratification remains close to the initial during the relatively short integration in the present study (Fig. 2), which shows that the errors resulting from closing the strait are small. c. Model forcing There is a strong uncertainty in the quality of the existing forcing functions for the Black Sea (Staneva and Stanev 1997), but no studies on the response of the model eddies to different mechanical forcing have been carried out before. Therefore, we run several experiments, aimed to illustrate the sensitivity of the model Black Sea to data from different origin: atmospheric analysis data and ship observations. The first dataset is calculated from the U. S. National Meteorological Cen-

1585 ter 1 (NMC) twice daily (at 0000 and 1200 UTC) meteorological analysis of the sea surface wind components W x, W y for the period 1980 89, with resolution of 1. This period corresponds to the period of integration used by Stanev et al. (1995), which enables intercomparisons between the results using similar forcing, but different horizontal resolution. Using the bulk formula (, ) C D W (W x, W y ), where C D 1.3 10 3, we calculate the wind stress components and from the annual-mean wind magnitudes and directions. The computed values are interpolated onto the model grid. The wind stress curl, Fig. 3a, is positive in the eastern and southwestern Black Sea and negative in the rest of the basin, which does not seem to correlate well with other climatic data (see below). Climatic data for the wind stress, originating from ship observations (Sorkina 1974) were compiled and analyzed by Rachev et al. (1991). The corresponding annual-mean wind stress curl pattern, Fig. 3b, is very different from the one corresponding to the NMC climate. Wind stress curl reaches 40 10 8 Pa m 1 in the eastern Black Sea (close to the Caucasian coast), whereas in the NMC climate the maximum is about 5 10 8 Pa m 1, and it is located in the southern Black Sea. The corresponding extrema for the anticyclonic curl are 27 10 8 Pa m 1 in the climatic data of Rachev et al. (1991) and 5 10 8 Pa m 1 in the NMC climate. For more details on the mechanical forcing we refer to the paper by Staneva and Stanev (1997). It is well known that linear Sverdrup dynamics have little effect in a small basin; therefore wind stress is also shown in Figs. 3a,b to better illustrate the mechanical forcing. In both datasets wind stress is higher in the western Black Sea than in the remainder of the basin. Due to the coarse resolution in the NMC analysis data, wind stress patterns are very smooth. Pronounced differences in the wind stress direction are observed in the western Black Sea. These strong differences could result in substantial changes in the circulation and in the physical balances, which will be shown later. Climatological temperature and salinity data for the Black Sea are analyzed in Blatov et al. (1984), Stanev et al. (1988), and Stanev (1989a). From the monthly mean climatic data we calculate annual-mean sea surface density *, Fig. 3c, which enters in the restoring term in Eq. (8). The relaxation time 1/ is chosen as 10 days. Sensitivity analyses on the model response to changing in the range 10 300 days showed that this parameter has small impact on the eddy dynamics (at least for the relatively short integration time). d. Model experiments To study the sensitivity of the model circulation to mechanical forcing by different sources we performed 1 National Centers for Environmental Prediction. two experiments: The first is forced with the annualmean wind stress of Rachev et al. (1991), (Wind Rachev et al. 1991 hereafter WR91) experiment and the second is forced by the NMC annual-mean wind stress, WNMC (Wind NMC) experiment (Table 1). The integration starts from rest in both experiments. The initial density is taken from the annual-mean data. The volume mean kinetic energy reaches a quasiperiodic state after 2 3 years, Fig. 4. The curves, corresponding to the WNMC and WR91 experiments, are very different. The energy is higher in the WR91 experiment, due to the stronger forcing, and the oscillations (160-day period) are very pronounced. The amplitudes in the WNMC experiment are negligibly small. Since both experiments are initialized from the same initial conditions, but the temporal variability is too different, we conclude that the quasiperiodic solution is dominated by the forcing and the resulting internal dynamics, and not (or negligibly) by the initial data. The vertical stratification at the end of the integration is not changed significantly, Fig. 2, which indicates that the mean Rossby radius of deformation remains unchanged throughout the experiments. The next experiment is forced with double the wind stress of Rachev et al. (WR91D experiment), which enables one to better understand the model response to increased winds. The corresponding curve in Fig. 4 has about 2 3 times higher mean value, the amplitude of the oscillations is about 5 times larger, and they are more irregular than in the WR91 experiment. To study the effect that bottom relief has on the circulation we performed two additional experiments forced with the wind stress of Rachev et al. (1991). In the first we set a flat bottom (WR91F experiment) at depth 1540 m equal to the maximum depth in the WR91 experiment. In the second additional experiment we use much finer vertical resolution (WR91VR) with 22 levels. This permits better resolution of the continental slope and the continental shelf. We will analyze the performance of the present model by comparing our results with some estimates of earlier studies. With a horizontal resolution of 1/4 (which does not resolve eddies in the Black Sea), but with essentially the same model, Stanev et al. (1995) and Staneva and Stanev (1997) studied the oceanic response to different types of forcing functions, which included seasonal, as well as short periodic variability. The sensitivity of the model simulations to the horizontal resolution was previously addressed for the Black Sea by Stanev (1988, 1990), who used two different resolutions: 1/2 and 1/6. Since the same numerical model was used in these studies, we will try to revise some of the past results, taking into account the effects resulting from the finer resolution in the present study. When no reference to the experimental nomenclature is given further in the text, we imply the WR91 experiment.

1586 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 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 10 8 Pa m 1, 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 interval is 5 10 8 Pa m 1. (c) Annual-mean sea surface density t. The contour interval is 0.1 t units. 3. Analysis on the model-simulated circulation a. Time-averaged fields The available information from hydrographic surveys is not sufficient to decide whether some of the observed eddies are quasi-permanent or transient features. By analyzing time-averaged simulation results, we will try to answer this question. In the following we will also illustrate the sensitivity of the circulation to different mechanical forcing, bottom relief, and vertical discretiza-

1587 TABLE 1. List of the numerical experiments. Experiment WR91 WNMC WR91D WR91F WR91VR Mechanical forcing Annual-mean wind stress from Rachev et al. (1991) Annual-mean wind stress derived from twice daily NMC analysis data Annual-mean wind stress from Rachev et al. (1991) with double magnitude Annual-mean wind stress from Rachev et al. (1991) Annual-mean wind stress from Rachev et al. (1991) Topography Variable, coarse vertical resolution Variable, coarse vertical resolution Variable, coarse vertical resolution Flat Variable, fine vertical resolution tion. The averaging is carried out over at least five 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 shows that averaging for five eddy periods gives quite 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, reveals rather low correlation (large part of the western subbasin is dominated by anticyclonic wind stress in Fig. 3a and by cyclonic mass transport in Fig. 5a), indicating that the circulation is far from the Sverdrup balance. The physical balance in the 1/4 resolution experiments (Stanev et al. 1995) was rather different, and there was a good correlation between the patterns of the wind stress curl and of the total transport streamfunction. This important difference between the coarse- and fine-resolution simulations is an indication that in the case of nonlinear dynamics the Black Sea circulation depends substantially on the basin shape and topography, which governs the propagation of coastal trapped waves rather than on the wind stress curl. This seems plausible if we have in mind that the relatively small scale of the sea could act as a limiting factor for the magnitude of annual-mean wind stress curl. The basin interior in the WNMC experiment is dominated by cyclonic circulation with mean transport of about 1 Sv (Sv 10 6 m 3 s 1 ). There are several quasipermanent anticyclonic eddies between the coast and the main gyre. The comparison with the observations (Kaz min and Sklyarov 1982; Stanev et al. 1988; Oguz et al. 1992; Oguz et al. 1993) shows an agreement in the positions of the Kaliakra, Bosphorus, Sinop, and Batumi quasi-permanent eddies. However, the circulation in the northern Black Sea seems not to be realistically simulated. There is only qualitative agreement between the circulation patterns simulated in WNMC and WR91 experiments in the basin interior. The circulation in the second experiment intensifies (Fig. 5b), particularly in FIG. 4. Kinetic energy (cm 2 s 2 ) during the integration. The legend in the figure refers to the experiment nomenclature; see Table 1. the eastern subbasin, reaching about 4.5 Sv. Some of the quasi-permanent eddies, which we find in Fig. 5a, disappear; others intensify (e.g., the Sakarya eddy) or their locations become more realistic (e.g., the Batumi eddy). The peculiarity of the mass transport in the northwestern Black Sea simulated in the WNMC experiment, Fig. 5a (but not supported by observations), disappears in the WR91 experiment, Fig. 5b. The circulation in the WR91 experiment has much in common with the diagnostic and prognostic calculations of the annual-mean circulation (Bogatko et al. 1979; Blatov et al. 1984; Bulgakov and Korotaev 1987; Stanev et al. 1988; Oguz et al. 1994). The anticyclonic eddy seaward of the Sakarya canyon (Oguz et al. 1993) is simulated in all experiments, with some differences due to different forcing and topography. It seems that this is one of the most stable subbasin-scale quasi-permanent features of the circulation. Doubling the wind forcing in the WR91D experiment drastically changes the circulation pattern, compared to that in the WR91 experiment, Fig. 5d. The circulation in the eastern basin intensifies, and the transport maximum reaches 7 Sv. The circulation in the western basin weakens (particularly in the westernmost part of the sea). The anticyclone off the Sakarya canyon is shifted farther toward the open sea, and the quasi-permanent Batumi eddy is not simulated. The pronounced difference between the simulations in the WR91D and WR91 experiments shows that the similarity in the patterns of mechanical forcing (double the wind stress) does not result in similar circulation patterns, which indicates that the circulation might be dominated by nonlinear processes. The discrepancy between the simulations in the

1588 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 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 first plot is 0.2 Sv; in the rest of the figures 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 general circulation in this sea shows clearly that using inappropriate mechanical forcing in the eddy-resolving models could lead to severe inconsistencies. This sensitivity is an important modeling problem since existing datasets for the mechanical forcing in the Black Sea show large differences (Staneva and Stanev 1997). We have to admit here that the above results could depend on the friction in the model. The intensity of the circulation in the WR91F experiment (Fig. 5e) is comparable to the one in the WR91D experiment, but the decoupling of the circulation in both parts of the sea disappears (the maximum moves from the eastern Black Sea into its westernmost zone). The anticyclonic circulation is localized in the northern (now deep) area and along the southern coast. The Batumi quasi-permanent eddy disappears in the flatbottom experiment, which shows that this important circulation feature is rather sensitive to changes in the model topography. The comparison between Figs. 5b and 5e indicates that the anticyclonic eddies along the Turkish coast are more pronounced in the flat-bottom experiment, which compares better with observations (Oguz et al. 1993). This could serve as an indication that with a resolution of about 12 km the slope area is not accurately resolved, which could result in underestimation of the coastal/topographic control. We remind here that 5-km resolution in this extremely steep area is also not sufficient for accurate simulations (Oguz et al. 1995). Assuming vertical wall along the southern coast seems to better approximate the real topography with the model resolution. Model sensitivity with respect to the relaxation coefficient in Eq. (8) and with respect to different vertical resolution is illustrated by the comparison of Fig. 5c (relaxation time 300 day) and Fig. 5f (WR91VR experiment) with Fig. 5b (central experiment WR91). Even with unrealistically large relaxation time of 300 days, compared to the one of 10 days in WR91, the streamfunction patterns change insignificantly. How-

1589 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 pronounced impact. It is better observed in the western Black Sea, where the differences between the model topographies are stronger (Fig. 1b). The time-averaged circulation intensifies in WR91VR due to the more accurate resolution of the topography and to the resulting changes in the dissipation. b. Model eddies We will demonstrate the eddy generation, evolution, and dissipation, trying to find the common features between the present estimates and the observations. Differently from the mean circulation patterns in Fig. 5, the streamfunction snapshots, Fig. 6, are dominated by eddies and give quite a different view of the circulation. The systematic analyzes of Blatov et al. (1984) and of Golubev and Tuzhylkin (1990) show that the Black Sea eddies have diameters ranging from 30 to 220 km. With our model resolution of about 11 13 km we capture the medium and large size eddies. Analyses of a large number of snapshots, that is, a movie of the experiments, reveal a regular periodic cycle; thus Fig. 6 is representative for the whole integration in the WR91 experiment. Eddies form in the easternmost Black Sea (once every six months) and constantly grow with time. After about 12 months they enter the western Black Sea and dissipate. There are some regularities in the eddy evolution, which are different for cyclonic and anticyclonic eddies. Anticyclones have almost equal scales zonally and meridionally at the initial phase of their evolution. Five months after they appear (at this time the eddy center reaches about 37 E), anticyclonic eddies start to elongate in the meridional direction and become sandwiched between two cyclonic eddies. The cyclonic eddy to the west is still intense but its westward velocity starts to decrease in the narrow section; the one to the east intensifies, moves rather rapidly to the west, and flattens the anticyclone. The elongated anticyclone moves farther west, but its meridional extension starts to decrease when it enters the narrow section between Sinop and Crimea. Next, its pathway turns to the southwest (towards the Bosphorus Strait). In such a way the anticyclonic cir-

1590 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 culation in this area (the Sakarya eddy) is constantly maintained. The cyclones continue to the west and merge with the weak, but permanent, cyclonic eddy; thus they contribute to maintaining the cyclonic circulation in the western Black Sea. The pathways of the cyclones and anticyclones in the eastern Black Sea coincide in the WR91 experiment, whereas the anticyclones tend to propagate to the south from the cyclones in the WR91F experiment. This explains the higher anticyclonic rotation along the Turkish coast in the WR91F experiment (compare Fig. 5e with Fig. 5b). The comparison of model and survey data reveals some similarities in the dynamics of the anticyclonic eddies in the central Black Sea (Altman et al. 1984; Latun 1990). Observed eddies are less elongated than those in the model simulations before entering the Black Sea narrow section. However, their shape becomes similar to that of the model simulated eddies in the narrow section. Moving farther west these eddies again become symmetric. The vertically integrated transport, estimated for this eddy by Golubev and Tuzhylkin (1990), ranges from 1.2 to 3.3 Sv. The corresponding numbers estimated from the model are between 3 and 5 Sv, when the eddy is within the area of the narrow section. The comparison between the mean patterns and the snapshots could give information on the dominating modes in the simulated circulation. Mean patterns are dominated by one or two gyres, with scales of the order of the basin scales [modes with wavenumbers n 1 and n 2; see Eremeev et al. (1992)]. Snapshots are dominated by 4 5 eddies, with scales on the order of the width of the narrow section (wavenumbers 4, 5, and 6). From the comparison between the magnitudes of the mean and eddy transports we see that the subbasin-scale modes start to dominate the solution. This accumulation of energy in the higher wavenumbers is due to the specific physical mechanisms of the model (see section 4). Sea surface velocities, Fig. 7, reach maxima of about 45 cm s 1, which is in a good agreement with the observations compiled by Blatov et al. (1984). The maxima decrease with increasing depth to about 25 30 cm s 1 at 70 m, and to 5 10 cm s 1 at 1100 m. No strong indications could be found from the model results that the circulation reverses in deep layers. However, the Sakarya and Batumi anticyclones are better pronounced 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 find vertical coherency down to the bottom, particularly in the areas filled with strong eddies. In contrast to the vertically averaged streamfunction patterns, current patterns are dominated not only by eddies but also by pronounced meandering of the main gyre. Some meanders increase in amplitude and form rings, which is the case illustrated in Fig. 7. We see in Fig. 7a an anticyclonic meander south of the Crimea Peninsula. It constantly grows and moves to the west (Fig. 7b). After two months, the circulation in the area of this meander closes, which indicates that a ring is formed (Fig. 7c). The ring formation process and simulated magnitudes of the surface currents compare well with observations (Oguz et al. 1994). There is good correlation between the circulation patterns and the horizontal anomalies in the density field. As seen from the comparison between the time-averaged pattern, Fig. 8a, and the two snapshots, Figs. 8b and 8c (corresponding to Figs. 7b and 7c), these anomalies disappear in the time-averaged pattern. The density anomalies in the cyclonic eddies correlate with the mean upward transport in the basin interior and associated down welling in the coastal areas. The southern part of the main gyre (flow to the east) is more unstable than the part of the gyre along the Caucasian coast (flow to the northwest). This result is in good agreement with the earlier theoretical analyses (Blatov et al. 1984) of the baroclinic instability of the Black Sea currents as a function of their direction. Simulated current patterns indicate that the instabilities (meanders) are created in the area of the Batumi quasipermanent eddy and propagate against the gyre (to the west). The excitation of the Sinop anticyclonic eddy could be regarded as stimulated by the growing instability moving to the west. In about 2 3 months the large anticyclonic meander reaches the narrow section and evolves into a ring (Fig. 7). Though possible conclusions based on the correlation between the transport patterns of suspended matter and plankton derived from satellite observations, and the model simulated patterns are questionable, we refer to the results of Sur et al. (1994). The comparison demonstrates that the horizontal scales and the speed of propagation of the eddies/meanders west of the Caucasian coast are comparable in the model simulations and in the observations. Unlike some theoretical estimates (e.g., Blatov et al. 1984, no dissipation included), the numerical model does not indicate increased baroclinic instability close to the Bulgarian coast. However, the change in the dissipation mechanisms in the WR91F experiment changes completely the results. The decreased dissipation in the western basin (due to the absence of the shelf) enables the eddies to reach the westernmost Black Sea, thus intensifying the variability and the instabilities in this area (see section 4). 4. Physical analyses a. Time variability We begin the analysis on the time variability by examining the velocity components and density at points A, B, and C, marked in Fig. 1a. The oscillations have large amplitudes and are very regular in the eastern and central subbasins; amplitudes are smaller and more chaotic in the western subbasin, Figs. 9a c. Model data show good correlation between the surface values and

1591 FIG. 7. Snapshots of the horizontal velocities at the sea surface, corresponding to the first three streamfunction snapshots in Fig. 6. those at the depth of the halocline (260 m) in the eastern and central subbasins. Statistical analysis of the simulated data in the same regions shows that the main periodicity (160 days) dominates the spectra for velocity and density in surface and deep layers. Velocities at sea surface and at 260 m show maximum coherency at about 145 days and much lower secondary peak at about 20 days. It is difficult to find pronounced regularities in the western subbasin (Fig. 9a) where periods of 145, 160, 205, and 288 days are observed. The coherency between the processes in the surface layer and at 260 m is less pronounced in western subbasin than elsewhere in the sea. The trend of decreasing periodicity in the western basin is even stronger in the WNMC experiment. From the above considerations it follows that there are two very different regimes dominating the circula-

1592 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG.8.Density( t units) at 260 m in the WR91 experiment. (a) Time-averaged field; (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 Sea and a turbulentlike regime in the western basin. The change of the oscillations from monochromatic in the eastern basin to chaotic in the western basin is clearly illustrated by the hodographs (Figs. 9d f). The regularity of the oscillations in the western Black Sea is affected also by the resolution of the shelf. The line labeled by asterisks in Fig. 9a (oscillations of the meridional velocity at location A for the WR91VR experiment) reveals slightly better regularity than the corresponding curve resulting from the WR91 experiment. This sensitivity is very strong [note the similarity of the bottom profiles when the topography is differently resolved (Fig. 1b) and the difference in the amplitudes of

1593 the corresponding velocities]. It will be shown below that the model shelf in the WR91VR experiment exerts less friction, and consequently the westward propagating oscillations have larger amplitudes in the western basin than in the WR91 experiment. A more detailed understanding of the time space variability can be obtained by analyzing the Hovmoeller diagrams (meridional velocity at 43 N, the zonal line in Fig. 1a, plotted as a function of time and longitude), Fig. 10. The time-averaged velocity along the section line is also given in Fig. 10. The diagrams indicate Rossby waves propagation. Their speed in the eastern subbasin (the slope of the contours) in the WR91 experiment is about 2.1 km day 1 (2.5 cm s 1 ). For the flat-bottom sea, WR91F, eddies propagate westward with an average speed of about 2.9 km day 1 (3.4 cm s 1 ). Estimates for the WR91VR experiment almost coincide with those for WR91 one in the eastern Black Sea; therefore the Hovmoeller diagram for this experiment is not shown. For comparison, the results of Latun (1990) indicate the speed of eddy propagation to be 1.5 cm s 1. The westward propagation has almost constant magnitude in the eastern basin, but the eddies slow down in the narrow section (between 32 and 34 E) and to the west of it. This is illustrated in the Hovmoeller diagrams by the changing slope of the contours (Fig. 10a). The constant decrease in the speed of the westward propagation in WR91 is in agreement with the decrease 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 indicates a very slow propagation. The decrease in eddy size and speed is consistent with assuming intense dissipation of eddy energy, therefore, the western subbasin is recognized as a dissipation basin. Model eddies in the WR91VR experiment behave in a similar way after passing the narrow section, but the decrease of eddy speed and scales is less abrupt, and the eddies penetrate closer to the western coast at speeds slightly larger than in the WR91 experiment. Comparison of the results of WR91, WR91F, and WR91VR shows clearly the impact of the bottom topography on the eddy propagation (Fig. 10). This westward propagation is more regular in the WR91 and WR91VR experiments (the regularity is illustrated by repeating the same pattern in time in Fig. 10a). We observe a rather regular westward propagation in the WR91F experiment in the first 200 days, as well. However, after day 300 eddies start to stagnate in the basin interior. (A movie of the streamfunction for several years yields convincing proof of the periodic stagnation in the central Black Sea.) This could be due to the topographic effects in the narrow section. The Hovmoeller diagram (Fig. 10b) shows better the subsequent acceleration, which can be recognized by the discontinuities in the contours (very small slope and correspondingly large speed). Analysis of the Hovmoeller diagrams for deeper layers leads to similar conclusions. The major difference between the flat-bottom experiment and the experiments WR91 and WR91VR occurs in the western basin. The dissipation area shifts westward in the flat-bottom experiment, and a strong increase in the variability and in the intensity of the circulation (compare Figs. 10a and 10b) is observed in the coastal area. The position of the velocity maxima in the Hovmoeller diagrams indicates that the group velocity is toward the east. This correlates with the well-known mechanism of Rossby wave reflection from the western coast and shows that the western coastal zone is the main source of instability in the WR91F experiment. The shelf area in the WR91 experiment exerts more dispersed damping. Thus, the instabilities associated with large shears induced by sudden western boundary damping in the flat-bottom case are reduced in the WR91 and, to a lesser extent, in the WR91VR experiments. As a final analysis we refer to some observational results. Using five years of current meter data west of the Caucasian coast, Ovchinnikov et al. (1986) found a periodicity of about 6 months superimposed on the seasonal cycle. Later, Eremeev et al. (1990) found pronounced variability with periods of 4 7 months and phase speeds of 2 6 km day 1 in monthly mean data. Model-calculated characteristic periods (160 days) and speeds (2.1 km day 1 ) are within these ranges, which could support resonance between seasonal and synoptic variability in the Black Sea. b. Energetics There is phenomenological evidence for eddy processes in the Black Sea but very few theoretical studies. Among the topics of major importance we mention the following: What drives the eddies; are they topographically intensified; what is the role of the baroclinic instability for the eddy formation? We try to answer these questions in the remaining part of the paper. To this aim we present an analysis on the model energetics. We denote the kinetic energy per unit volume as U h Uh e 0. 2 According to Holland (1975) the volume-averaged total kinetic energy in mechanically closed region E e, e V 1 (e) d, (V is the volume of the sea) may be changed by the work done by wind stress (W), by buoyancy forces (B), by the loss of energy due to dissipation in the fluid, and at the lateral boundaries (D) E t B W D. (9) Expressions for the terms in Eq. (9) are given by Holland (1975). Kinetic energy E can be divided into two components:

1594 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 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 figures is done only for the first period. U U h h U U h h Ē 0 and E 0, 2 2 corresponding to external Ū h and internal U h mode velocities, where Ū h H 1 U h dz and U h U h Ū h. For the time rate of change of Ē and E we have Ē t N e B e W e D e and E N i B i W i D i, (10) where the terms on the right-hand side of Eqs. (10) represent the work done on the external/internal mode by the nonlinear terms (N e,i ), the pressure forces (B e,i ), the wind stress (W e,i ), and by the dissipation forces (D e,i ). In a closed basin N i N e. There is no exchange between internal and external mode kinetic energy (B e 0) if either the bottom is flat or the ocean is homogeneous. The net transfer between the external and internal modes due to topography is T B B i. We will analyze below the energetic terms as in the paper by Treguier (1992) (Fig. 11a). We showed in section 2d that kinetic energy oscillates around its mean value of 16 cm 2 s 2 in WR91 experiment with a period of about 160 days (Fig. 4). This mean value is several times larger than the corresponding value estimated by Stanev (1988). The wind forcing effect is larger on the internal mode than on the external mode (Fig. 11b) as is typical in many QG and PE windforced models (see Holland 1975; Treguier 1992). This result is in a qualitative agreement with the estimates of Stanev (1988), W i 1.1 10 6 cm 2 s 1 and W e 0.4 10 6 cm 2 s 1 ; however, the present estimates yield magnitudes more than two times as large. Kinetic energy is dissipated mainly due to the lateral friction, which is more pronounced in the external mode. The negative sign of the buoyancy term means that the wind does work to maintain the doming form of the isopycnic surfaces. This is an indication that the wind-driven velocities are larger than the buoyancydriven ones. A similar result was found earlier by Stanev (1988, 1990) in several numerical experiments, forced with different combinations of forcing functions, but with about two times lower resolution in the horizontal than in the present study. This specific conversion of energy was explained as due to the reduced penetration of the buoyancy into the deep layers, limited by the extremely strong stratification. In the same study, comparison between the results obtained by using different horizontal resolution did not show qualitative differ-

1595 FIG. 9.(Continued)

1596 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG. 10. Time evolution of zonal section (x t plot) of the meridional flow at the sea surface; the contour interval is 5 cm s 1. 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 flows did not change direction). We will demonstrate now a qualitatively new model behavior. Kinetic energy is exchanged between the external and internal modes through nonlinear and topographic transfers N and T. An explanation of the nonlinear transfer by the concept of inverse cascade is given by Charney (1971). The sign of this transfer in our experiment indicates that perhaps such an inverse cascade occurs. This was not the case in the previous experiments with the Black Sea model (where the magnitude of the corresponding term was an order of magnitude smaller and its direction was opposite). Topography is found to transfer energy to the internal mode [in the same direction as in the work by Stanev (1988, 1990)], but the estimated magnitude is several times larger now. Thus, the nonlinear conversion and the topographic transfer are almost compensated in the present model. The sign of T shows that the external mode currents flow up the topographic slope. There is experimental evidence that a similar situation usually occurs in the western and northern parts of the sea where the current attacks the bottom slope. In the previous models currents below the halocline were rather slow, whereas in the present model there is an extremely high and deep penetrating variability on the continental slope. This explains the increase in the topographic transfer, compared to the previous estimates (increase in the JEBAR), which is due to the stronger interactions between currents and topography in the present model. The signs of the terms in Eq. (10) do not change in the WR91F experiment (Fig. 11c) compared to the estimates in the WR91 experiment. The lack of topographic transfer results in reduced magnitudes of almost all terms by about 40% 50%. The nonlinear transfer decreases approximately two times, but the net exchange between the internal and external modes slightly increases in WR91F. The time variability of the energy terms, Fig. 12, gives a convincing illustration of the quasiperiodic model behavior. The work done by wind on the internal mode (W i, full line in Fig. 12a) shows pronounced 160- day periodicity. The curve, corresponding to the work done by wind on the external mode (W e, full line in Fig. 12b) has a more complex shape. It has a main period