Three-dimensional domino model in geodynamo

The Lagrangian formalism is applied to consider temporal evolution of the ensemble of interacting magnetohydrodynamical cyclones governed by Langevin-type equations in a rotating medium. This problem is relevant for fast-rotating convective objects such as the cores of planets and a number of stars, where the Rossby numbers are far below unity and the geostrophic balance of the forces takes place. The paper presents the results of modeling for both the two-dimensional (2D) case when the cyclones can rotate relative to the rotation axis of the whole system in the vertical plane, and for the case of spatial rotation by two angles. It is shown that variations in the heat flux on the outer boundary of the spherical shell modulate the frequency of the reversals of the mean dipole magnetic field, which agrees with the three-dimensional (3D) modeling of the planetary dynamo. Applications of the model for giant planets are discussed, and an explanation for some episodes in the history of the geomagnetic field in the past is suggested.