Magnetoconvection in a rapidly rotating sphere

Abstract

We investigate numerically magnetoconvection in a rapidly rotating sphere. The model consists of a fluid filled sphere, internally heated, and rapidly rotating in the presence of both a mean toroidal magnetic field and a mean poloidal field. Motivated by the geodynamo problem, we take the magnetostrophic approximation, that is to say we neglect terms proportional to the Ekman number and the Rossby number in the momentum equation. All variables are approximated spectrally in both the radial and meridional directions. A modal dependence is assumed azimuthally. The induction and temperature equations are time stepped pseudospectrally in the angular coordinate, and by collocation in the radial coordinate, while the momentum equation, now diagnostic, is solved at each time step to give the nonaxisymmetric velocity field. Critical Rayleigh numbers and corresponding frequencies are obtained at given azimuthal wavenumber, Roberts number and strengths of the imposed toroidal and poloidal magnetic fields. The results, which include purely magnetic instabilities, are discussed and compared with related studies of magnetoconvection, with and without the presence of an inner core, carried out at small but finite Ekman number or with stress-free boundary conditions.