  Using Lagrangian formalism we consider evolution of the ensemble of
interacting magnetohydrodynamic cyclones governed with Langevin type equations
in the rotating medium. This problem is relevant to the planetary cores where
the Rossby numbers are small and geostrophic balance takes place. We show that
variations of the heat flux at the outer boundary of the spherical shell
modulates frequency of the reversals of the mean magnetic field that is in
accordance with the 3D dynamo simulations. Two scenarios of reversals were
bserved. Either the axial dipole decreases in favour of quadrupole and then
grows in opposite direction or the mean dipole tilts and reverses without
decrease of its amplitude.
