Rotationally Invariant and Partially Invariant Flows of a Viscous Incompressible Fluid anf Viscous Gas.

Abstract

The dynamic stochastic approach to the study of mathematical models of thermohydrodynamic large-scale fields is developed in which the mathematical image of stochasticity is the strange attractor of the real atmosphere. This approach is based on methods of analysing non-linear equations of atmosphere. The approximation of these equations is mostly effected using Galerkin's procedures. This reduction is based on the theorem of invariant manifold, especially on the theorem of central manifold for semi-flow of the Navier-Stokes equation. According to the theorem of the central manifold, all significant phenomena related to dynamic systems of thermohydrodynamic equations of atmosphere occur in a particular finite-dimensional formulation. General circulation could be modelled with the aid of relatively single dynamic systems. We shall continue deal with the finite-dimensional approximations of the dissipative, non-divergent, barotropic flow and the bifurcation analysis of the spectral models with a small number of spectral modes and an external force acting only on fundamental modes.