HYDROMAGNETIC-WAVES IN RAPIDLY ROTATING SPHERICAL-SHELLS GENERATED BYPOLOIDAL DECAY MODES

This paper presents the first attempt to examine the stability of a po loidal magnetic field in a rapidly rotating spherical shell of electri cally conducting fluid. We find that a steady axisymmetric poloidal ma gnetic field loses its stability to a non-axisymmetric perturbation wh en the Elsasser number A based on the maximum strength of the field ex ceeds a value about 20. Comparing this with observed fields, we find t hat, for any reasonable estimates of the appropriate parameters in pla netary interiors, our theory predicts that all planetary poloidal fiel ds are stable, with the possible exception of Jupiter. The present stu dy therefore provides strong support for the physical relevance of mag netic stability analysis to planetary dynamos. We find that the fluid motions driven by magnetic instabilities are characterized by a nearly two-dimensional columnar structure attempting to satisfy the Proudman -Taylor theorm. This suggests that the most rapidly growing perturbati on arranges itself in such a way that the geostrophic condition is sat isfied to leading order. A particularly interesting feature is that, f or the most unstable mode, contours of the non-axisymmetric azimuthal flow are closely aligned with the basic axisymmetric poloidal magnetic field lines. As a result, the amplitude of the azimuthal component of the instability is smaller than or comparable with that of the poloid al component, in contrast with the instabilities generated by toroidal decay modes (Zhang and Fearn, 1994). It is shown, by examining the sa me system with and without fluid inertia, that fluid inertia plays a s econdary role when the magnetic Taylor number Tm greater than or simil ar to 10(5). We find that the direction of propagation of hydromagneti c waves driven by the instability is influenced strongly by the size o f the inner core.