Application of the full reduction technique for solution of equations with vector form non-linearity

Abstract

We consider making use of the full reduction algorithm for solving the equations with a vector non-linearity. The solutions of such the equations describe the planetary scale non-linear vortex structures of the Earth atmosphere, ionosphere and magnetosphere. We present the modification of full reduction technique for Charney-Obukhov equation with periodic boundary conditions. This technique allows to reduce significantly calculation time and to apply much more detailed spatial grid for studying non-linear processes in the near-Earth space.