Local analysis of thermal and magnetic instabilities in a rapidly rotating fluid

摘要

We examine by means of a local analysis the effects of an azimuthal magnetic fieldB(r) on the stability of a rapidly-rotating fluid subject to a radial temperature gradient, taking the ratio #x3BA;/#x3B7; of thermal to magnetic diffusivities to be small, as in the Earth's core. According to this theory, previous results for the caseB#x221D;rare typical of a certain range of magnetic field profiles, but ifBdecreases withrfaster thanr#x2212;#xBD;we find instead that (i) the critical Rayleigh number increases sharply as the magnetic field strength increases beyond #x201C;magnetostrophic#x201D; values and (ii) the recently-discovered magnetic instabilities triggered bybottom-heavydensity gradients do not occur. IfBincreases withrfaster thanr3/2, on the other hand, the major change to theB#x221D;rpicture of events is that the system becomes unstable to comparatively fast magnetic instabilities as soon as the field passes magnetostrophic values.