Propagation and reflection of diffusionless torsional waves in a sphere

Abstract

We consider an inviscid and perfectly conducting fluid sphere in rapid rotation and permeated by a background magnetic field. Such a system admits normal modes in the form of torsional oscillations, namely azimuthal motions of cylinders coaxial with the rotation axis.We analyse this system for a particular background magnetic field that provides a new closed form normal mode solution. We derive Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximations to the normal modes, and focus particularly on the reflections that take place on the rotation axis and at the equator. We propose a procedure to calculate the reflection coefficients and we discuss the analogy of our findings with well-known seismological results. Our analytical results are tested against numerical calculations and show good agreement.