Shell Model Of The Turbulence In The Fast Rotating Sphere

The consequent analysis of convection in the Earth and some other astrophysical bodies reveals that the Reynolds number Re can be 10⁷ and larger, what means that turbulent flow exists. Even most recent and sophysticated 3D models of dynamo can resolve scales of order l ~ 10^-2, what is very far from the scale of diffusion l_{d ~} Re^-3/4. From the other point of view there are models of the turbulence which under some conditions can reproduce basic physical properties, e.g., the spectrum, structural functions. Such models do not require large computer capacity. We present the combined model of thermal convection in the sphere with the free rotating inner core. The large scales are resolved using control volume approximation of the original Navier-Stokes and heat flux equations. To find solution on the small scales we apply the shell model technique. The interaction between large-scale motions and turbulence is taken into account. We consider the first runs of the full MHD problem also.