Model of convection in a rotating spherical layer

The model of convection in a rotating spherical layer of a viscous liquid (an external Earth's Core) in Boussinesq approximation is constructed. In equation producing, the field of temperature is expanded on eigen functions of Laplas operator in the layer. The field of speeds is presented by decomposition of toroidal and poloidal components, for which as producing the same functions were used. The selection of modes that can describe the large-scale convection structure comparing with data of the Earth Core is realized. The system of the equations for amplitudes of components of temperature and speed is obtained.