Hydromagnetic stability of the Kennedy-Higgins model of the Earth's core

The linear stability of a spherical shell of an electrically- and thermally-conducting viscous fluid rotating uniformly in the presence of a co-rotating toroidal magnetic field is studied when the lower part of the fluid is top-heavy and the upper part is bottom-heavy. For small amplitudes of the magnetic field, instability occurs in a thin cylindrical cell whose generators are parallel to the rotation axis. The dependence of the thickness of the cell on the angular velocity, on the magnetic field's strength and on the diffusivities of the fluid is the same as in the case of the already-known problem of the wholly-unstratified shell. Although convection here is buoyancy driven for small values of the magnetic field's amplitude, the distance which convection within the cell can penetrate into the stably-stratified portion of the cell depends on the numerical value of the field amplitude. For moderate and large values of the amplitude of the magnetic field instability occurs in the whole volume of the fluid. In the unstably-stratified portion of the fluid instability is buoyancy driven while magnetic instability prevails in the stably-stratified part of the fluid with stable stratification being an essential ingredient.