A geodynamo model incorporating a finitely conducting inner core

Abstract

A direct spectral solution is presented for the mean-field geodynamo equations. The momentum equation, with inertia neglected but viscosity retained, is solved in a spherical shell. The induction equation is solved in a similar fashion, and includes Ohmic dissipation in the finitely conducting inner core. The existence of a second Taylor's constraint is pointed out, requiring the integrated Lorentz torque on the inner core to vanish in the limit of vanishing viscosity. In the slightly supercritical regime this constraint is shown to be violated, resulting in a differential rotation of the inner core actively driving a portion of the outer core flow. In the more strongly supercritical regime this constraint is shown to be satisfied, the process of adjustment involving a minimization of the Ohmic dissipation in the inner core.