Waves in the Earth's core. II. Magneto–Coriolis modes

Abstract

We investigate the normal modes of a rapidly rotating, electrically conducting, inviscid fluid sphere in the presence of a background magnetic field. Neglecting the fast modes that are essentially slightly modified inertial waves, we focus on the slower branch of modes traditionally called magneto–Coriolis (MC) modes. We focus on the magnetostrophic limit, an approximation that neglects the fluid inertia for these modes by setting the magnetic Rossby number E η equal to zero, converting the momentum equation from a prognostic to a diagnostic equation. In contrast to a local analysis and contrary to previous assertions, this inertialess-inviscid double limit is perfectly well behaved and shows that E η → 0 and E η = 0 are essentially identical. With applied axisymmetric background fields, we find the modes are critically damped, with decay rates greater than or equal to the eigenfrequency, in contrast to the local theory. We find evidence for both eastward and westward propagating columnar modes, in contradiction of commonly perceived wisdom. The results bode well for numerical time integrations based on the magnetostrophic approximation, which is highly suited to the core of the Earth and holds the potential for more realistic solutions of the dynamo equations.