Two hydrological surveys carried out in the northern Black Sea in summer 2016 and 2017 are processed with a hydrodynamic model that also assimilates observational data, which made it possible to more accurately describe the meso- and submesoscale features of hydrophysical fields and determine their possible formation mechanisms. High spatial resolution (horizontal grid of similar to 1.6 x 1.6 km and 27 vertical horizons) and ERA5 atmospheric forcing is used in calculations. The energy terms in the equations of the kinetic and potential energy budget for each year were analyzed to consider possible physical eddy formation mechanisms (baroclinic instability, current flow around coastline irregularities). Such specific features of circulation as the Rim Current along the coast, anticyclonic eddies near the southeastern coast of Crimea, and the area of cyclonic vorticity in the eastern deep-water part of the sea are observed for both years. Along the coast, under the action of weak winds, small-scale eddies were generated when the current was flowing around irregularities in the coastline and bottom topography. A large anticyclonic eddy was formed between 33 degrees and 34 degrees E in 2016 and between 31 degrees and 32 degrees E in 2017. With increased wind action in 2017, more intense currents developed and eddy formations in the upper layer of water were less pronounced than in 2016.

In this work, based on the results of predictive calculations, the accuracy of reproducing the Black Sea circulation is analyzed using new approximations of nonlinear terms in the transport equations, ensuring the conservation of temperature and salinity to a power greater than two. Numerical experiments have been carried out that differ in schemes for calculating temperature and salinity. In the first experiment, traditional schemes were used to ensure the conservation of temperature and salinity in the first and second degrees; in the second one, the temperature was maintained in the first and fifth degrees and salinity in the first and third; in the third experiment, the temperature was maintained in the first and third and salinity in the first and fifth degrees. Calculations were performed on the basis of MHI model with a resolution of 1.6 km and accounting a realistic atmospheric forcing for 2016. The validation of results was carried out based on comparison of model fields with data from contact and satellite measurements of temperature and salinity in 2016. An analysis of average and root mean square errors showed that, compared to the traditional approximation, the new difference schemes for the advection–diffusion equations of heat and salt, ensuring the preservation of predictive parameters to a power greater than two, improve the accuracy of reproducing of the Black Sea salinity in the upper 100-m layer throughout the year. Root mean square errors in the salinity field decrease by 15–20

Purpose. The study is purposed at deriving a finite-difference equation of potential vorticity for a threedimensional baroclinic fluid with regard for diffusion and viscosity in a quasi-static approximation. Its terms are calculated and analyzed in numerical modeling of the Black Sea circulation for two periods - winter and summer 2011. Methods and Results. A finite-difference equation for the potential vorticity of a stratified incompressible fluid is obtained for a system of discrete equations of sea dynamics in the hydrostatic approximation allowing for viscosity, diffusion, river inflow, water exchange through the straits and atmospheric forcing. It is shown that the main contribution to the potential vorticity is made by its vertical component. The horizontal components are predominant in the areas of river inflow and water exchange through the straits. The vertical component of potential vorticity, except for the river inflow zones, is conditioned by the value and structure of an absolute eddy. The main contribution in the sea upper layer of the coastal region, its northwestern part and along the Anatolian coast is made by the advection of potential vorticity. At the lower horizons, its highest values are observed in the coastal strip, at that its character is more pronounced near the southern coast of the sea. Conclusions. Analysis of the potential vorticity equation has shown that the value of the advective terms is conditioned by the divergence of the product of nonlinear terms in the motion equations and density gradient. The main conclusion consists in the following: locally, the sum of vertical and horizontal advection of potential vorticity is two orders of magnitude less than each of them separately.

Purpose. The study is purposed at deriving the discrete equations of absolute and potential vorticity for a three-dimensional stratified incompressible fluid as an exact consequence of the finite-difference equations of sea dynamics in the field of a potential mass force in the adiabatic approximation provided that viscosity and diffusion are absent. The properties of two-dimensional projections of the absolute vorticity equation onto coordinate planes and the three-dimensional potential vorticity equation are analyzed. Methods and results. In order to determine the discrete analogues of absolute and potential vorticity, an additional grid is introduced, where the finite-difference equations for the components both of absolute and potential vorticity are written down. Two-dimensional analogues of the three-dimensional equation of absolute vorticity on the planes (x, y), (y, z) and (x, z) are obtained; they possess the feature of preserving vorticity, energy and enstrophy (square of vorticity). A discrete equation for potential vorticity of a stratified incompressible fluid is derived from the finite-difference system of three-dimensional equations of sea dynamics in the adiabatic approximation at the absence of viscosity and diffusion. Conclusions. In the case of a linear equation of state, the discrete equations of absolute vorticity and potential vorticity which are the exact consequence of finite-difference formulation are obtained. The equation of potential vorticity is of a divergent form, and two-dimensional analogues of the absolute vorticity equation on the planes (x, y), (y, z) and (x, z) have two quadratic invariants that provide preservation of the average wave number.

Purpose. The study is purposed at obtaining the approximations providing the presence of discrete non-linear invariants for the difference system of the sea dynamics equations in the absence of external forces, friction and diffusion, and at analyzing the features of the resulting schemes at the example of calculating the Black Sea circulation for 2011. Methods and Results. The method of undetermined coefficients at which the new unknowns are introduced is applied, that makes it possible to satisfy the additional conditions. The schemes providing simultaneous preservation of temperature in the first and the K-th (K > 1) degrees and salinity in the first and the L-th (L > 1) degrees, were obtained. The approximations of temperature and salinity found on the box faces with a polynomial dependence of density on temperature and salinity lead to a divergent form of the density advection equation. This form provides fulfilling the law of conservation both of the total energy and the sum of kinetic and dynamic potential energy in a discrete formulation. Based on the analysis of circulation in the Black Sea in 2011, it is shown that at increase of the degree of invariants, the following effects take place: the gradients in the temperature field in the frontal zones as well as the processes of the saltier water upwelling in the sea center and the fresher water downwelling along its periphery are intensified, and the intensity of small-scale features in the vertical velocity field decreases. Conclusions. A discrete dynamical model in a quasi-static approximation was obtained. It has a number of nonlinear invariants corresponding to the continuous problem. The results of calculating the Black Sea circulation for real conditions in 2011 showed that presence of the degree invariants exceeding two made it possible to specify the circulation features on small scales.

Three experiments were performed to reconstruct the fields of currents during the periods of hydrological cruises at the R/V “Professor Vodyanitsky” in 2016: June - July (summer season), September - October (autumn season) and November - December (autumn-winter season) on the basis of the z-coordinate hydrodynamic model of the Black sea and a procedure of assimilation of contact measurements of temperature and salinity. The components, that made the most significant contribution in the equations of dencity of kinetic and potential energy, were analyzed in order to study the possible mechanisms of formation of the reconstructed features of water dynamics.

An analysis of the dynamic and energy characteristics of water circulation in the northern part of the Black Sea has been performed on the basis of assimilation in the numerical model of the data of three hydrological surveys in 2016, carried out on expeditions of 87, 89, and 91 cruises of the R/V Professor Vodyanitsky (summer, autumn, and autumn–winter seasons). Numerical experiments are implemented on a horizontal grid ( 1.6 × 1.6 km) with 27 vertical horizons and an atmospheric effect close to the real one was used. A procedure of assimilation of the observational data is based on the Kalman filter, taking into account the heterogeneity and nonisotropy of the errors of the estimates of the temperature and salinity fields. The integral energy terms in the kinetic and potential energy budget equations for three seasons are estimated. In the summer season, there is a slight weakening of the main Black Sea current—the Rim Current (RC)—and the main mechanism for the formation of anticyclonic eddies near Sevastopol and near the southeastern shores of Crimea is baroclinic instability of the current (as evidenced by the increase in the slope of isopycnical surfaces and negative values of the work of the buoyancy force). An anticyclonic eddy near Yalta with a radius of about 25 km was generated due to the development of shear instability of the current. In the autumn season, the RC jet is pressed to the shore and there is a decrease in the number of eddies in comparison with the summer season. The formation of anticyclonic eddies with a radius of about 35–40 km in the western part of the region is caused by barotropic instability of the current and the formation of eddies along the Crimean coast is caused by baroclinic instability. In the autumn–winter season, the RC has a pronounced jet character and there is an increase in the processes of baroclinic instability with the generation of eddies of different scales between the coast and the RC, as well as in the area located between 31.5 and 33° E, with the weakening of the wind effect. During all seasons, small-scale anticyclonic and cyclonic eddies could be generated along the western and eastern coast of Crimea in the upper layer when the current flows around the coastline and inhomogeneities of the bottom topography under the action of weak winds.

Оценки бюджета доступной потенциальной энергии в черном море при использовании новых схем аппроксимации уравнений адвекции-диффузии тепла и соли 1Демышев С.Г.,

A four-dimensional and energy analysis of hydrophysical fields in the limited area of the Black Sea was carried out on the basis of assimilation of hydrological data in the numerical model (autumn–winter season of 2016). The Rim Current was clearly reconstructed. Multi-scale eddies could be generated between the shore and the Rim Current during some weakening of the wind forcing. Cyclonic and anticyclonic eddies were noticed in the western area, they could merge into larger one during the further calculation. The most energetically significant components in the kinetic and potential energy budget equations were found and analyzed from 15th of November to 5th of December, 2016. Possible mechanisms of circulation features of the Black Sea were determined, analyzing of energy fields (for example, baroclinic and/or barotropic instability). The obtained results were compared with all available data of instrumental measurements.

Purpose. The study is aimed at identifying possible physical mechanisms for the variability of available potential energy density and buoyancy fluxes in the upper active layer of the Black Sea. Methods and Results. Spatial distribution of the available potential energy density and buoyancy fluxes was studied based on analyzing the thermohaline characteristics of the Black Sea circulation in 2011 and 2016 resulted from the numerical experiments performed using the Black Sea dynamics model developed in the Marine Hydrophysical Institute. The model included the EMODNet bathymetry and the SKIRON system data on wind velocity, heat fluxes, precipitation, evaporation, and sea surface temperature. The numerical experiments provided the daily fields of current velocities, temperature and salinity based on which the density of available potential energy and the buoyancy work were calculated. It is shown that the spatial-temporal variability of the available potential energy density in the Black Sea was formed by the mechanisms different for the upper 30-m layer and for the main halocline layer. The buoyancy work was revealed to be of seasonal variability.Conclusions. In the upper layer, the variability of the available potential energy density is related primarily to the propagation of freshened river waters, whereas in the main halocline layer (75-150 m), the field structure is conditioned by mesoscale dynamics. In the first case, the increased values of the available potential energy density are observed during a year on the northwestern shelf and on the basin periphery; in the central part of the sea, the distribution of available potential energy density is determined by the atmospheric conditions. In the layer below 75 m, the maximum values of the available potential energy density correspond to the anticyclonic eddies. In consequence of the intensive water mixing in the upper active layer during the cold period of a year, the buoyancy work is conditioned by vertical velocity. In a spring-summer period, a two-layer structure of the field is observed which governed by the sign of density anomalies. The upper layer thickness constitutes 20- 30 m and corresponds to the depth of seasonal thermocline. In the main halocline, the highest absolute values of the buoyancy work are observed in the zones of intense mesoscale anticyclones.

Purpose. The study is purposed at analyzing the physical mechanisms of formation of the Black and Marmara seas circulation structures based on the numerical experiments with climatic boundary conditions. Methods and Results. To investigate the reasons for the formation of circulation features, the energetic approach was applied that permitted to calculate the work of the forces affecting the marine environment. Location in the same geographical region determines similarity of atmospheric conditions for the Black and Marmara seas, and a clearly pronounced two -layer water stratification in both basins is related to a significant difference in salinity of the Black Sea and Mediterranean waters. To analyze the mechanisms of circulation variability, the mean and eddy fields formed under the impact of climatic atmospheric forcing and calculated using a numerical model of sea dynamics were considered. Wind influence, thermohaline fluxes on the sea surface, buoyancy work, friction, and diffusion were quantitatively assessed based on calculation of the Lorenz energy cycle components. The common features were found in the mechanisms of mesoscale variability, and the differences - in the mechanisms of large-scale circulation variability. Conclusions. It is shown that the main source of energy for the Black Sea mean circulation is wind stress work, and as for the Marmara Sea, the dominant factor is buoyancy work. For both basins, variability of the eddy kinetic energy characterizing the mesoscale dynamics is conditioned by baroclinic instability. At that, about a quarter of the available potential energy in the Black Sea, and about a half of it in the Marmara Sea is transformed into the eddy kinetic energy.

The purpose of this work is to determine the initial Cs137 concentration field in the Black Sea immediately after the Chernobyl accident using spatially and time-distributed measurement data based on the adjoint equation method. The calculation of the flow velocities was carried out using a three-dimensional model of the Black Sea circulation MGI with a horizontal grid step of 1.6 km. When calculating the currents, the wind effect was set according to SKIRON data. The method of adjoint equations is used to determine the location of a possible radioactive fallout according to measurements that were carried out on the 33rd flight of the NIS “Akademik Vernadsky” in June-July 1986. The National Centers for Environmental Prediction (NCEP) data on the wind situation and precipitation intensity are analyzed. The information of the IRSN (Institute of Nuclear and Radiation Safety of France) on the processes of transfer of radioactive contamination from the Chernobyl nuclear power plant towards the Black Sea is considered. Based on the solution of the adjoint problem, a possible area of radioactive fallout was determined, the location of which coincides with IRSN data on areas of increased isotope concentration in the atmosphere over the Black Sea region in late April–early May 1986.

The purpose of this work is to study the behavior of the Black Sea deep-water currents below the permanent pycnocline under regular (climatic) and anomalous atmospheric forcing. The annual variability of Black Sea current fields at horizons deeper than 300 m and the response of deep-water currents to the atmospheric anomalous quasitropical cyclone in September 2005 in the southwestern Black Sea are analyzed. Thus, the variability of deep-water currents is assessed both when the climatic fluxes of heat, moisture and wind at the sea surface change quite smoothly throughout the year and when the circulation is forced by an extreme atmospheric cyclone during its 5-day passage over the sea surface and one month after the cyclone leaves the sea basin. It is shown that the velocities of Black Sea currents during anomalous cyclone forcing can increase several times compared to their typical values, and the relaxation of the current field after the quasitropical cyclone crosses the sea edge can take up to 4–5 weeks in the deep sea layer.

This work presents an analysis of the Lorenz energy cycles derived from the simulation results of the Black Sea circulation. Three numerical experiments are carried out based on an eddy-resolving z-model with a horizontal resolution of 1.6 km and taking into account different atmospheric forcing: climatic data, 2011, and 2016. The annual mean circulation for these time intervals reflects the climatic basin-scale, basin-scale (2011) and eddy (2016) regimes. Main differences between experiments are (1) the intensity of atmospheric fluxes and (2) SST assimilation and direct consideration of shortwave radiation in the realistic forcing simulations. The Lorenz energy cycles components are considered in detail. Some common features between climatic and realistic energetics are detected. The annual mean energy conversion from mean motion to the eddy is observed for all circulation regimes. Also, it is obtained that the annual mean buoyancy work enhances the mean current for all experiments, which evidences about maintaining of isopycnal surfaces slope such that a condition for converting available potential energy into kinetic energy is realized. Qualitative difference in the energy transfers for the climatic calculation, basin-scale and eddy regimes is revealed. Conversion from the eddy kinetic energy to eddy available potential energy is observed only for climatic circulation. For the basin-scale circulation the eddy kinetic energy is increasing mainly due to the transfer from the mean current kinetic energy through barotropic instability. The growth of the eddy kinetic energy for the eddy regime is provided by conversion of the available potential energy due to baroclinic instability.

This paper presents an assessment of the seasonal variability of the velocity fields, mean and eddy kinetics, and available potential energies, and the energy conversion rates for the eddy and basin-scale circulation regimes. The data were obtained through the numerical modeling of the Black Sea circulation for 2011 and 2016. It revealed significant differences in the current structure in the southern and central sea parts for 2011 and 2016. In 2011, the Rim Current was an almost continuous cyclonic basin-scale gyre, while in 2016 a system of mesoscale anticyclones was observed in the southern part. The variability of the mean kinetic energy depends more on the circulation regime than on the season of the year, while the distribution of the mean available potential energy is predominantly seasonal. The eddy kinetic energy depends on both the circulation regime and the season. In winter, the energy transport from the mean current via a barotropic instability mechanism sustains the mesoscale eddy generation. In summer, the mesoscale variability in the basin-scale regime is provided by commensurate contributions of barotropic and baroclinic instability, and, in the eddy regime, mainly by the energy transport from the available potential energy through the baroclinic instability.

Hydrophysical fields and arrays of kinetic and potential energy budget components, continuous in time and space, were reconstructed on the basis of a thermohydrodynamic model and observational measurements of temperature and salinity in 2007 and 2009 in the region of western Crimea. To implement the procedure of assimilation of data observations, we used a four-dimensional analysis, based on a Kalman filter, taking into account the heterogeneity and non-isotropy of error estimates of temperature and salinity. We used a real atmospheric forcing and a high resolution (a horizontal grid ~1.6 × 1.6 km and 30 vertical layers from 1 to 1200 m). The change of kinetic energy was determined mainly by wind action, vertical friction and the work of pressure forces; change in potential energy—by advection of potential energy. The calculated fields of currents were characterized by mesoscale eddy formations and jet currents. A horizontal velocity shear (resulting from the negative work of the wind force) and current flow around the coastline under the action of weak winds could be possible mechanisms of the generation of coastal mesoscale and submesoscale eddies in the coastal zone.

Purpose. The work is aimed at obtaining a discrete equation for the rate of the available potential energy change in strict accordance with the finite-difference formulation that ensures adequate reproduction of discrete energy, and at analyzing its terms based on the results of a numerical experiment with realistic atmospheric forcing. Methods and Results. On the basis of the well-known methods of computational mathematics (method of indeterminate coefficients and imitation modeling), a finite-difference equation for the available potential energy, which corresponded to its differential form, was obtained. In the equation structure, an additional term, which was conditioned by transition to a discrete problem and had a diffusion form, appeared. Energy analysis for the hydrological winter of 2011 in the Black Sea showed that the highest values of available potential energy in the upper layer were observed in the central region of the sea. Below 100 m, the available potential energy increased towards the coast where intense mesoscale variability was observed. At the depths exceeding 200 meters, the largest stock of this energy was concentrated in the Sevastopol and Batumi anticyclones. Action of the main forces, namely the forces of buoyancy, advection and horizontal diffusion, takes place in the coastal areas of the sea. Conclusions. The resulting difference equation for the rate of the available potential energy change exactly corresponds to the discrete formulation and, therefore, accurately reflects the energy of the discrete problem. Analysis of the equation permitted to show that in winter, the rate of the available potential energy change is influenced predominantly by eddy activity at the depth slope.

The aim of this work is to study the seasonal variability of the mean current kinetic energy MKE, the eddy kinetic energy EKE, the mean available potential energy MPE, the eddy available potential energy EPE, and the rates of energy conversion for basin-scale and eddy circulation regimes in the Black Sea. The basin-scale circulation is a regime when the entire basin is covered by the cyclonic Main Black Sea Current (the Rim Current), which spread over the continental slope. The eddy circulation is a regime when the Rim Current is partially or completely destroyed and intense mesoscale eddies evolve in the abyssal part of the sea. Monthly energy characteristics are calculated based on eddy-resolving simulation data derived under atmospheric forcing SKIRON. Analysis of the reconstructed current fields showed that the basin-scale and the eddy circulation regime are realized in 2011 and in 2016, respectively. Seasonal signal is weakly manifested in the variability of the MKE; its value depends on the wind forcing and current velocities, which are higher in the basin-scale circulation regime. The distribution of the MPE is predominantly seasonal; temporal variability is qualitatively similar for both regimes and is caused by increase in the density anomaly due to warming up of seawater. The energy transport MPE→MKE due to the buoyancy work is provided in the subsurface layer for all seasons and the Cold Intermediate Layer for the warm seasons in both regimes. Seasonal variability of the EKE and the mechanisms of its intensification are different for two circulation regimes. The EKE is maximal in spring and summer in the basin-scale circulation regime, and in the cold season in the eddy circulation regime. In winter, when the Rim Current or its elements are most intense, irrespective of the circulation regime, the mesoscale eddies develop mainly due to energy transport MKE→EKE via barotropic instability mechanism. In summer, the mesoscale variability in the basin-scale circulation regime is due to commensurate contributions of barotropic and baroclinic instability, and in the eddy circulation regime only by the energy transport MPE→EKE due to baroclinic instability. The reported study was funded by the Marine Hydrophysical Institute state task No. 0555-2021-0004.

Fields of currents and arrays of energy budget components were investigated with the help of the numerical model of dynamics using hydrological data from 89th cruise of the R/V Professor Vodyanitsky. To implement the procedure of data assimilation, we used a four-dimensional analysis procedure, based on a Kalman filtering, taking into account the heterogeneity and non-isotropy of error estimates of thermohaline characteristics. Wind action and vertical friction made a significant contribution in the change of kinetic energy, vertical turbulent diffusion and advection of potential energy—in the change of potential energy. The following features of circulation were obtained in the numerical experiment for the autumn season of 2016: anticyclonic eddies near Sevastopol, cyclonic and anticyclonic eddies at the south-eastern coasts of Crimea and other parts of area under consideration, a flow of the Rim Current along the Crimean coast. High values of work of the wind force and vertical dissipation were observed in the zones of formation of mesoscale eddies. Negative values of the buoyancy work were noticed to the west of the region and along the eastern coast of Crimea.