The role of inertia in the evolution of spherical dynamos

Abstract

A numerical parametric study of 3-D spherical dynamos is performed in order to understand the role of inertial effects in the evolution of the simulated dynamo. We vary the Prandtl (Pr) and magnetic Prandtl (Pm) numbers together, maintaining a constant ratio of thermal to magnetic diffusivities and leaving other parameters fixed. For Pr=Pm≥ 1, we find that the solution is only weakly dependent on Pr=Pm, and the principal force balance is between the magnetic, buoyancy and Coriolis forces (MAC balance). At lower values of Pr and Pm, the inertial forces begin to gain importance, and the MAC balance is disturbed. The field becomes less dipolar and weaker, with the effect that a balance between the buoyancy, Coriolis and inertial forces ensues. The low inertia, large Pr=Pm solutions resemble the geomagnetic field more closely, but there are still a few systematic differences between these solutions and the Earth's magnetic field.