Том 52, № 4 (2016)

A brief analysis of the oceanographic papers printed in this issue is presented. For convenience of the reader, the paper by K. Bryan, a prominent scientist and expert in modeling the physical characteristics of the ocean, is discussed in detail. The remaining studies are described briefly in several sections: direct prognostic modeling, diagnosis–adaptation, four-dimensional analysis, and operational oceanography. At the end of the study, we separately discuss the problem of the reproduction of coastal intensification of temperature, salinity, density, and currents. We believe that the quality of the simulation results can be best assessed in terms of the intensity of coastal currents. In conclusion, this opinion is justified in detail.

Problems are considered in which the role of Casimirs in forming dynamics of the two-dimensional ideal incompressible fluid is basically studied; in particular, the conditions are formulated which arise in the stability problem of two-dimensional flows in the presence of Casimirs. Some general approaches to the construction of difference schemes for solving equations of two-dimensional fluid which possess the given Casimirs are considered.

A numerical experiment on the reproduction of the variability in the state of North Atlantic water in 1948–2007 with a spatial resolution of 0.25° has been performed using the global ocean model developed at Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), and the Shirshov Institute of Oceanology (IO RAS) (the INM–IO model). The data on the state of the atmosphere, radiation fluxes, and bulk formulas of the CORE-II protocol are used as boundary conditions. Five successive 60-year calculation cycles have been performed in order to obtain the quasi-equilibrium state of a model ocean. For the last 20 years, the main elements of large-scale ocean circulation have been analyzed and compared with the WOA09 atlas data and the results of other models.

The energy characteristics of circulation in the Black Sea have been numerically analyzed for 2006. The annually and seasonally averaged integral components of the budget of both kinetic and potential energies are considered. It is shown that, over the period under study, wind forcing, buoyancy force, and friction are the main factors determining variations in the mechanical energy of the Black Sea. During the cold months, wind forcing maximally contributes to the kinetic energy. In spring, the contribution made by buoyancy force is dominant. The values of buoyancy force are maximum within the upper quasi-homogeneous layer during the warm season and on horizons, where the waters of the cold intermediate layer are concentrated, during the fall–winter season.

Calculation results are presented for long-term mean annual surface currents in the North Atlantic based on direct drifter measurements and numerical experiments with the ocean general circulation model using both climatic arrays of hydrological data World Ocean Atlas 2009 and Argo profiling data. The calculations show that the technique suggested for model calculations of oceanographic characteristics of the World Ocean with the use of Argo data significantly improves the climatic fields of the temperature and salinity even on a coarse grid. The comparison of the model calculation results with drifter data showed that the temperature and salinity fields found from Argo data with the use of data variational interpolation on a regular grid allow the calculation of realistic currents and can be successfully used as initial conditions in hydrodynamic models of the ocean dynamics.

Models and methods of the numerical modeling of ocean hydrodynamics dating back to the pioneering works of A.S. Sarkisyan are considered, with emphasis on the formulation of problems and algorithms of mathematical modeling and the four-dimensional variational assimilation of observational data. An algorithm is proposed for studying the sensitivity of the optimal solution to observational data errors in a seasurface temperature assimilation problem in order to retrieve heat fluxes on the surface. An example of a solution of the optimal problem of the World Ocean hydrodynamics with the assimilation of climatic temperature and salinity observations is offered.

The formulation and the algorithm of solving an ocean model for the prediction and assimilation of the observed data which makes it possible to reconstruct the circulation in the deep-water parts of the sea and at a shallow water shelf, as well as to describe the large time–space variability in the surface level, are considered. The model uses a vertical hybrid σ–z coordinate system: the several upper tens of meters of the ocean are described in the σ-coordinate system and the rest of the water column is described in the z coordinates. Such hybridization extends the possibilities of models for reconstructing thermo-hydrodynamic processes in different sea basins and the World Ocean. The differential formulation of the model in the σ–z coordinate system is presented; the simplified records of several operators that are allowable in the case of a small thickness of the ocean σ-layer are described. The construction of a computational grid, approximation of the bottom topography on it, and discretization of equations and boundary conditions of the models are considered; an approach to describing the bottom friction at shallow waters is offered. The results of the comparative experiments in the z and σ–z coordinate models are analyzed.