Hydromagnetic waves in rapidly rotating spherical shells generated by magnetic toroidal decay modes

Abstract

Abstract Instabilities in the form of slow azimuthally travelling hydrodynamic waves in a rapidly rotating, stress-free, electrically conducting spherical fluid shell are investigated. The instabilities are generated by the toroidal decay mode of the lowest order or a combination of toroidal decay modes. It is found that the Elsasser number Λc at the onset of instability is always Λc = O(10) for various profiles of the basic magnetic field. It is also found that the hydromagnetic waves of the preferred instability propagate eastward [i.e. for solutions proportional to exp i(mφ + ωt), ω < 0] and are characterized by nearly two-dimensional columnar fluid motions attempting to satisfy the Proudman-Taylor theorem, indicating that the most rapidly growing magnetic disturbance arranges itself in such a way that the corresponding magnetic forces balance only the ageostrophic component of the Coriolis force. Except for the Stewartson-type velocity boundary layer at the equator of the inner core, the velocity and ...