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 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. 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 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 Δφ = 1/6° and Δλ = 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.
2. Description of the model
a. The numerical model and boundary conditions
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 Δz 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 Ah = −0.1 × 1019 cm4 s−1 and Kh = −0.4 × 1019 cm4 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, Av = 1.5 cm2 s−1, and the vertical diffusion coefficient, Kv = 0.1 cm2 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 102–103 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 Center1 (NMC) twice daily (at 0000 and 1200 UTC) meteorological analysis of the sea surface wind components Wx, Wy 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 (τλ, τφ) = ραCD|W|(Wx, Wy), where CD = 1.3 × 103, we calculate the wind stress components τλ and τφ 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 ρ*, Fig. 3c, which enters in the restoring term in Eq. (8). The relaxation time 1/η is chosen as 10 days. Sensitivity analyses on the model response to changing η 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 two experiments: The first is forced with the annual-mean 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.
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 discretization. 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 ≡ 106 m3 s−1). There are several quasi-permanent 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 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 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 flat-bottom 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. However, 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 circulation 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 quasi-permanent 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 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 circulation: 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 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
We showed in section 2d that kinetic energy oscillates around its mean value of 16 cm2 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 wind-forced models (see Holland 1975; Treguier 1992). This result is in a qualitative agreement with the estimates of Stanev (1988), Wi = 1.1 × 10−6 cm2 s−1 and We = 0.4 × 10−6 cm2 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 buoyancy-driven 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 differences (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 (Wi, full line in Fig. 12a) shows pronounced 160-day periodicity. The curve, corresponding to the work done by wind on the external mode (We, full line in Fig. 12b) has a more complex shape. It has a main period of 160 days, as well, but is in opposite phase to the Wi curve. Double maxima with changing amplitudes are observed in the We curve each half period. At the time when the work done by wind (We) reaches a local minimum, the nonlinear conversion rate (denoted shortly by “advection” in the figure) reaches a maximum. The time for reaching maximum nonlinearity is about three times longer than the time for reducing the nonlinearity. Apparently, this indicates rather fast overturning after the instabilities reach some critical value.
c. Eddy versus mean circulation
Eddy kinetic energy (EKE) is higher than the MKE in most of the sea (Fig. 13b). Exceptions could be found close to the Caucasian and Crimean coasts and in the western part of the sea. The energy analyses of the simulations for the North Atlantic, carried out by Beckmann et al. (1994) as a part of the Community Modeling Effort (CME, see Bryan and Holland 1989), demonstrated that EKE at sea surface is about four times larger than MKE, which is in agreement with the Black Sea simulations. As shown by the comparison with some previous results (Stanev 1988, 1989b, 1990), the high EKE in the present estimates is mainly due to the improved horizontal resolution.
At present, no observational data are available to verify model results on the relative weight of eddy versus mean circulation. Therefore, we will make some comparisons with previous model studies. There is a similarity of the patterns in Fig. 13 with the ones of Stanev (1988) but the energy is much higher in the present study. Like in the quoted study, the MKE maxima approximately coincide with the position of the mean gyre (along the coast), but in contrast, the maxima in the EKE are in the basin interior (in the area of the narrow section). We find increased rms variability in σt at the main pycnocline depth, which indicates that most of the variability is related to the change in the halocline depth.
There are important differences between our estimates and some estimates for the Gulf Stream region (Böning and Budich 1992; Treguier 1992; Beckmann et al. 1994) where the areas with MKE and EKE maxima almost coincide. One of the possible reasons for the nonconformity in the locations of MKE and EKE maxima in the WR91 experiment could be due to the specific wind forcing. In the WNMC experiment, which is relatively weakly forced, the EKE does not exceed the MKE, and the area of the absolute maximum in the EKE is to the west of the Caucasian coast (not in the central basin). In the WR91 experiment, the circulation is more intense, and the energetic regime is strongly dominated by basin oscillations and nonlinearities. The displacement 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. Seasonality 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.
d. Analysis of model evidence for geostrophic turbulence
What makes the Black Sea interesting from the point of view of eddy dynamics is the fact that eddy scales are comparable to the basin scales (e.g., the scales of the narrow section; the scales of the areas of input or dissipation of energy; the scales of the main topographic features, such as the western Black Sea topographic slope). It is well known that Rossby wave–baroclinic instability is related to the interaction with the bottom relief. Topography generally whitens the wavenumber spectrum. In the western parts of the oceans Rossby wave reflection results in increasing enstrophy and in stronger dissipation. In such areas barotropy is a necessary consequence of a red horizontal cascade, related to the transfer of enstrophy to larger wave numbers (Rhines 1977). These processes take place, of course, also in the Black Sea. The shelf in the western basin and the continental slope create very important differences in the circulation in WR91, WR91F, and WR91VR related to the eddy dissipation. The Black Sea narrow section also affects the eddy regime, as could be seen by the comparison between results in WR91 and WR91F (Figs. 10a,b).
Further understanding of the eddy dynamics can be achieved by examination of the power spectra, Fig. 14. Since there are obvious differences between the physical balances in the western and eastern Black Sea (see previous sections), we calculated the velocity spectra for each subbasin separately. The spectra shown in Fig. 14 were calculated by averaging spectra from 50 individual realizations during the last four years of integration. No spectral smoothing was applied. The spectral maxima are attributed to the longer waves. The cutoff wavelength is about 250 km in the eastern basin and about 190 km in the western basin. The scales are not very different since there is some overlapping of the areas where spectra are calculated (the overlapping over about 1° is a compromise, resulting from the requirement to increase the number of data points in order to produce reliable estimate of the spectra). The intense eddy processes in the eastern basin are illustrated in the figure by the higher spectral maximum.
Evidence for geostrophic turbulence in the Black Sea is ambiguous, and the intercomparison of the model simulations with observational data is difficult. Present results could be compared to the ones of Böning and Budich (1992), where the same model is applied to the Atlantic Ocean. As in the quoted work, the following important spectral ranges could be identified: 1) energy-containing range with rather a flat spectrum at lower wavenumbers; 2) inertial range, where the spectral slope is close to k−3; and 3) dissipation range at higher wavenumbers, where the spectral slope is large. The curves in Fig. 14 are most similar to the Böning and Budich (1992) polar spectra due to the similarity of the Rossby radius of deformation in polar areas and that in the Black Sea. We see from Fig. 14 a decrease in the cutoff wavelength in the western basin, consistent with the results of the previous sections, showing smaller eddies in this part of the sea. The shorter inertial range, compared to the one in the Tropics, could be due to the effect of model friction on the shorter wavelengths. One plausible explanation of the relatively narrow inertial subrange might follow from the result that eddies in our model rapidly reach scales comparable with the width of the narrow section. The oscillations are rather monochromatic (there is a strong preference for particular space scales, and in the model eddies smaller than those of the dominate scale are missing); thus the Kolmogorov cascade is not well developed.
5. Conclusions and discussion
Two major focuses in this paper related to eddy variability will be emphasized in the discussion: 1) the phenomenology of the Black Sea circulation inferred from the numerical model and 2) the physical mechanisms of the circulation.
The time-averaged circulation, shown in Fig. 5, has much in common with the well-known annual-mean circulation features, resulting from dynamic and diagnostic calculations (Bogatko et al. 1979). It is dominated by a general cyclonic gyre with several quasi-permanent subbasin-scale eddies. Model snapshots show repeating cycles (about 6 months) illustrating eddy formation (in the eastern Black Sea), propagation to the west, and dissipation (in the western basin). Eddy scales grow until they become comparable with the basin’s width, which is the scale that contains most of the energy in the spectra. Twelve months after their formation, eddies enter the western Black Sea, where their propagation is slowed. Eddy paths are strongly affected by the topography, as well. The major topographic effect is manifested in the model by the eddy dissipation in the western basin.
The circulation is characterized by pronounced meandering of the main gyre. The southern part of the gyre (flow to the east) is more unstable than the northern part of the gyre along the Caucasian coast. The time variability is related to westward propagation with periodicity of 160 days, which dominates the spectra for velocity and density in surface and deep layers. The speed of the westward propagating waves in the eastern subbasin is about 3 cm s−1, close to the estimates resulting from observations. After the eddies pass the Black Sea narrow section, their speeds decrease with about a factor of 2 in the WR91 experiment. As shown by the comparison of WR91, WR91F, and WR91VR experiments, basin wave propagation is very sensitive to the bottom topography.
The model circulation is far from the Sverdrup balance. The negative sign of the buoyancy term indicates that the wind does work to maintain the doming form of the isopycnic surfaces. The exchange between the external and internal modes through nonlinear and topographic transfers N and T is a very important indication that an inverse cascade probably occurs. EKE and MKE reach maxima in different areas, which is an important difference from the CME estimates for the Gulf Stream region (Böning and Budich 1992; Treguier 1992; Beckmann et al. 1994), where the areas of MKE and EKE maxima almost coincide. This is explained as a consequence of the specific forcing and topography in the Black Sea.
With approximately the same model and forcing functions as in Stanev et al. (1995), but with much finer horizontal resolution, we succeeded in simulating in the present study a quite different circulation regime. Even when forcing the model with winds whose curl is weakly cyclonic (experiment WNMC), we have cyclonic currents, thus indicating the important role of nonlinear processes and, perhaps, coastal-trapped waves. These waves are demonstrated by Sur et al. (1994), using satellite images of the sea surface. Model results, to be analyzed in detail in forthcoming paper, exhibit eastward propagating, or sometimes stagnating, undulating features east of Sakarya Canyon, which correspond with observations. Waves are periodically excited by the variability with larger scales, and they become very unstable after reaching the zonal part of the coast. This is explained by Sur et al. (1994) as a consequence of changing slope and of the direction of the current. This process could be additionally amplified by the interaction of westward propagating Rossby waves with coastal-trapped waves. These interesting physical processes could stimulate future studies. The Black Sea, with its closed boundaries, seems to be a good candidate for a test basin.
In this paper we used some simplifications related to the model forcing, model topography, and model physics. This was done as a first step toward understanding some of the free oscillations of the sea. Much remains to be done to determine how realistic are the physical balances discussed in the present paper and to achieve more adequate model simulations of the Black Sea variability: model intercomparisons and validations against observations, improving the resolution, taking into account both temperature and salinity and such important forcing functions as strait exchange, precipitation, evaporation, heat fluxes (Stanev 1988, 1990). Free surface dynamics could result in further improvements in the model estimates (Oguz et al. 1995). Forced oscillations could also have a significant impact on the model circulation, as shown by Stanev (1988). Analysis on the seasonal variability based on experimental data shows half-year periodicity and phase speeds of 2–6 km day−1 (Ovchinnikov et al. 1986 and Eremeev et al. 1990), which is close to our model estimates. This periodicity could favor resonance between seasonal (forced) and synoptic (free) variability in the Black Sea, a topic to be addressed in a subsequent paper.
Acknowledgments
The authors would like to thank K. Böning and H. Friedrich for the very useful comments. The discussion on the mesoscale processes in the Black Sea with P. Malanotte-Rizzoli, S. Meacham, G. Korotaev, and T. Oguz, during the Workshop on the Black Sea Modeling in Sofia, Bulgaria, March 1994, was very stimulating in the final part of this work. We are very grateful to the anonymous reviewers for many helpful suggestions and comments.
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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 profiles are shown in Fig. 1b.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
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).
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
Mean vertical density profile (σt units) for the Black Sea; solid line corresponds to initial density, dash line corresponds to density at the end of the integration.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
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 σt. The contour interval is 0.1 σt units.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
Kinetic energy (cm2 s−2) during the integration. The legend in the figure refers to the experiment nomenclature; see Table 1.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
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 η from Eq. (8) is set to 1/300 days, (d) WR91D experiment, (e) WR91F experiment, and (f) WR91VR experiment.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
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.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
Snapshots of the horizontal velocities at the sea surface, corresponding to the first three streamfunction snapshots in Fig. 6.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
Density (σt 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 σt units. The shallow part of the sea is shaded.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
Time variability of currents and σt 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.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
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.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
Energy diagrams showing the magnitude and direction of the work done by the energetic terms in Eq. (10). The numbers (cm2 s−3) are multiplied by 106. (a) notations, see also Eq. (10),(b) WR91 experiment, and (c) WR91F experiment.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
Time evolution of the terms doing work in Eq. (10). The correspondence between the model terms and different curves is given in the legend: (a) internal mode and (b) external mode.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
(a) Kinetic energy (cm2 s−2) of the mean flow in WR91 experiment; (b) eddy kinetic energy (cm2 s−2) in the same experiment.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
Wavenumber spectra along the section line in Fig. 1 averaged in time.
Citation: Journal of Physical Oceanography 27, 8; 10.1175/1520-0485(1997)027<1581:EPISSA>2.0.CO;2
List of the numerical experiments.
National Centers for Environmental Prediction.
