Magnetohydrodynamic Shallow Water Waves: Linear Analysis

TL;DR

This paper conducts a linear analysis of inviscid, incompressible MHD shallow water systems on a sphere, identifying five wave modes, including newly characterized magnetostrophic modes influenced by magnetic fields and rotation.

Contribution

It introduces the concept of magnetostrophic modes and provides analytical solutions for perturbations in MHD shallow water systems, expanding understanding of wave dynamics in spherical geometries.

Findings

Identification of five wave modes in MHD shallow water systems.

Discovery of magnetostrophic modes with lower frequencies near the poles.

Analytical functions for velocity, height, and magnetic perturbations in certain limits.

Abstract

We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincare modes and one magneto-Rossby mode) are previously known. The other two wave modes are strongly influenced by the magnetic field and rotation, and have substantially lower angular frequencies; as such, we term them "magnetostrophic modes". We obtain analytical functions for the velocity, height and magnetic field perturbations in the limit that the magnitude of the MHD analogue of Lamb's parameter is large. On a sphere, the magnetostrophic modes reside near the poles, while the other modes are equatorially confined. Magnetostrophic modes may be an ingredient in explaining the frequency drifts observed in Type I X-ray bursts from neutron stars.