Generation of magnetic fields by convection in a rotating sphere, I

Abstract

The magnetohydrodynamic dynamo problem is solved for an electrically conducting spherical fluid shell with spherically symmetric distributions of gravity and heat sources. The dynamics of motions generated by thermal buoyancy are dominated by the effects of rotation of the fluid shell. Dynamos are found for low and intermediate values of the Taylor number, T ≲ 10 5, if the scale of the nonaxisymmetric component of the velocity field is sufficiently small. The generation of magnetic fields of quadrupolar symmetry is preferred at Rayleigh numbers close to the critical value R c for onset of convection. As the Rayleigh number increases, the generation of dipolar magnetic fields becomes preferred.