The influence of toroidal magnetic field on thermal convection in the core

We present numerical calculations of nonlinear magnetoconvection in a rotating spherical shell. We derive equations for thermal convection in a rotating spherical shell in the presence of a uniform azimuthal magnetic field, assuming the convection is organized along columns parallel to the rotation axis. Solutions obtained for Rayleigh numbers up to 50 times critical indicate that the structure of convection in the outer core and the process of poloidal field generation depend on the toroidal field intensity through the Elsasser numberΛ =σB2/ϱΩ. In calculations with Λ ≪ 1, corresponding to magnetic fields of a few Gauss in the core, the pattern of convection consists of small-scale columnar vortices embedded in a large-scale zonal flow. The induced magnetic field is also small scale. In calculations with Λ ⋍ 1, corresponding to a toroidal field near 20 Gauss in the core, the convection consists of large-scale vortices driven by one or two large-scale spiral plumes. Radial advection by the plumes bends the azimuthal field into loops, creating patches of concentrated magnetic field on the outer boundary where the loops emerge from the sphere. The strong field models are generally more compatible with inferences about the core derived from geomagnetic field observations than the weak field models.