Thermal and magnetically driven instabilities in a non-constantly stratified rapidly rotating fluid layer with azimuthal magnetic field

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Abstract
The linear hydromagnetic stability problem for a horizontal non-constantly stratified fluid layer rapidly rotating about the z-axis and permeated by an azimuthal non-homogeneous magnetic field is investigated. A non-linear (parabolic) temperature profile Tequals;T(z) is used to simulate the lower part of the fluid core being unstably stratified and the upper part stably stratified. The problem is solved on the magnetic diffusion timescale and for q<1 (q is the ratio of the thermal and magnetic diffusivities). The model is investigated for various widths of the stably stratified part of the layer and for a wide range of values of the azimuthal magnetic field strength. Three kinds of instability have been found: thermally-driven propagating westward, magnetically-driven propagating westward and magnetically-driven propagating eastward. The most complicated case is with azimuthal wave number mequals;1 for which all three kinds of instabilities occur. For m≧2 only thermally-driven instabilities occur. From the shape of the eigenfunctions it is found that convection develops in the whole layer for all values of the magnetic field strength investigated, regardless of the ratio of the widths of the sublayers.