Shell models in rapidly rotating dynamo systems

A typical feature of convection of rapidly rotating planets is a geostrophic state. This state is characterized by the following two different scales: the large one along the axis of rotation and the small transverse one. For the liquid cores of planets, their ratio can be some orders of magnitude already at the onset of convection. This phenomenon complicates simulations of convection and dynamo processes and requires a special analysis, essentially in the nonlinear regime. We consider the main features of the spectra for various intensities of heat sources in the existing spherical models of convection and geodynamo and propose a simple shell model which can mimic some properties of the original dynamo system.