Numerical modeling of magnetohydrodynamic convection in a rapidly rotating spherical shell: Weak and strong field dynamo action

In this paper we describe a numerical model for investigating magnetohydrodynamic (MHD) convective flow of a Boussinesq fluid in a rapidly rotating spherical shell, driven by the buoyancy forces arising from incoming buoyant flux at the inner core boundary. The model is designed to investigate the generation of magnetic field in the Earth's fluid outer core. Our model differs from that of G. A. Glatzmaier and P. H. Roberts, who have recently investigated this problem, in several aspects. We apply a different physical approximation in the force balance of the system: instead of viscous stress, we use an axisymmetric inertial force to balance the axial magnetic torque arising from the Lorentz force; we use a mixed spectral-finite difference algorithm for better parallelization of the code; and apply different boundary conditions. We describe our numerical model in detail, and we test it by examining purely thermal convection in a rapidly relating fluid shell and by examining Kumar-Roberts kinematic dynamos (modified for the spherical shell). Our results agree well with those of the previous studies. We also present a weak-field dynamo solution in a very simplified system and strong-field dynamo solutions in a more realistic system. (C) 1999 Academic Press.