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

In this paper we describe a numerical model for investigating magnetohydrod ynamic (MHD) convective flow of a Boussinesq fluid in a rapidly rotating sp herical shell, driven by the buoyancy forces arising from incoming buoyant flux at the inner core boundary. The model is designed to investigate the g eneration of magnetic field in the Earth's fluid outer core. Our model diff ers from that of G. A. Glatzmaier and P. H. Roberts, who have recently inve stigated this problem, in several aspects. We apply a different physical ap proximation 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 a lgorithm for better parallelization of the code; and apply different bounda ry 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 sh ell). Our results agree well with those of the previous studies. We also pr esent a weak-field dynamo solution in a very simplified system and strong-f ield dynamo solutions in a more realistic system. (C) 1999 Academic Press.