Volume 16, Issue 4

In this paper we study the adjoint equations method as a tool for finding integral invariants for hydrodynamical equations. Using equations for a two-dimensional incompressible fluid and equations for shallow water as examples, we show the effectiveness of inhomogeneous adjoint equations for original homogeneous problems. It is shown that these methods allow us to find new useful invariants

We consider the numerical scheme of the three-dimensional model of enclosed and semienclosed sea hydrodynamics with variable sea surface topography described by a linear free-surface equation. We derive equations integrated over the upper sea layer and consider the formulation of the finite difference scheme of the model in the spherical coordinate system and the derivation of the sea free-surface equation which is approximated by an implicit time scheme. A peculiarity of the model is that it directly takes into account real water fluxes at the upper boundary in a mass balance equation, in this case we need not specify sources or artificial salt fluxes in a salt balance equation. We give an example of the model efficiency in the problem of modelling the seasonal variability of the Caspian Sea circulation and level.

The aim of this paper is to continue to study the Kuroshio current ‘bimodality’ south of Japan. We analyse a difference in hydrophysical fields for two states of the current. The observational data was obtained in 40 oceanographic cruises organized by the Far East Regional Hydrometeorological Research Institute during a period of 1980-1990. Some periods were characterized by the onshore (shelf) non-large-meander state and during the other periods a typical offshore large-meander path formed. Using this data, we obtain an estimate for the 3D velocity field in a diagnostic calculation by P-vector inverse and dynamic methods. The complete diagnostic calculations of the 3D velocity fields are carried out for the chosen periods by the Novosibirsk Computing Center Ocean Circulation Model (NCCOCM). In addition, we analyse the pressure tendency (PT) equation and the vertical velocity Wand Q-equations by the quasigeostrophic approach.

Using the data of observations of the ice cover in theWeddell Sea near the Antarctic coast in a period of the polar night, we carried out numerical experiments with the one-dimensional model of the atmospheric boundary layer. The processes of background advective heat and moisture transport, the catabatic component of motions and vertical turbulent snow transport under the conditions of blowing snow are parameterized in the model. It is shown that the results on the computation of temperature and specific humidity are in good agreement with the corresponding observational data when we take into account the joint efect of baroclinity and relief. It is also established that the consideration of the snow turbulent diffusion process leads to the higher quality of reproducing the wind velocity and friction stress in the atmospheric surface layer.

- Mathematical models of the general circulation in oceans and seas are reviewed. Basic model equations which in oceanology are traditionally called primitive equations are considered. They follow from the classic hydrodynamical equations of a rotating fluid with the use of Boussinesq, hydrostatic, incompressibility, turbulent viscosity, and diffusivity approximations. Boundary and initial conditions are formulated and discussed together with parameterization of turbulent processes that occur on scales smaller than can be described by model calculations. The assertions concerning the uniqueness and existence of the solutions of ocean and sea dynamics problems (for some simplifications of governing equations) are formulated. Some conceptual, alternative, and generalized models of circulation in seas and oceans are presented: shallow-water equations, an ocean model in bottom-following coordinates, a free-surface generalized model of sea dynamics. The following problems arising in numerical calculations of sea and ocean dynamics are considered: the choice of a differential formulation of the problem; the approximation of the differential problem with respect to spatial coordinates; the implicit methods for integrating the model with respect to time with the use of splitting procedures. Approaches to the solution of observational data assimilation and initialization problems are discussed using adjoint equations and optimal control methods. On the basis of numerical experiments the importance of two oceanic effects to excitation of polar motion is estimated: nonlinearities between circulation and tides and the circulation induced potential due to loading and self-attraction of a baroclinic ocean.