Point vortices dynamics on a rotating sphere and modeling of global atmospheric vortices interaction

Abstract

It is shown that the hydrodynamics equations for a thin spherical liquid layer are satisfied by the stream function of a pair of antipodal point vortices (APVs), in contrast to the stream function of a single point vortex on a sphere with a background of a uniform opposite sign vorticity. A simple zero solution of the equation of the absolute vorticity conservation is used for bypassing the well-known nonlinear problem of a point vortices interaction with a regular vorticity field, and an exact solution for the APV dynamics problem on a rotating sphere is obtained. Due to this, a new stable stationary solution for the dynamics of APV is obtained, which can model the dynamics of the global vortex structures, such as atmospheric centers of action.