The effect of a stable layer at the core-mantle boundary on thermal convection

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Abstract
As a model for convection in the Earth's core we study the linear stability of a rapidly rotating electrically conducting spherical fluid shell, permeated by a toroidal magnetic field B. We look at the effect of introducing a stably stratified layer into the fluid adjacent to the core-mantle boundary (CMB). For values of the Elsasser number (a non-dimensional measure of the magnetic field strength), Λ ≪ 0(1), convection can penetrate significantly into the stable layer. In this weak field case, the constraints of the Taylor-Proudman theorem cause convection to become columnar in structure. As Λ is decreased the azimuthal wave number m, corresponding to the most unstable mode, increases. For Λ = O(1), convection is still unaffected by the introduction of a stable layer, but is no longer columnar. For Λ ≫ O(1), we find that convection becomes concentrated in the unstably stratified region. Except in the low magnetic field strength regime, our findings agree with previous work of Boda (1988) and Ševčík (1989), who studied a similar problem with plane-layer geometry, and with Fearn and Richardson (1991) who considered the cylindrical case.