The Dynamics of Magnetic Rossby Waves in the Quasigeostrophic Shallow Water Magnetohydrodynamic Theory

Abstract

The dynamics of magnetic Rossby waves are investigated by applying a quasigeostrophic shallow water magnetohydrodynamic system, which is linearized with respect to both uniform background flow and uniform magnetic field. Due to the influence of the free surface divergence, the phase speed for magnetic Rossby waves can be either a monotonically increasing or a monotonically decreasing function, and the resulting difference between the group velocity and the phase speed can be either positive or negative. This is determined by whether the corresponding Alfvén wave speed is the upper limit or not. Differently, the phase speed is always a monotonically increasing function and the difference between the group velocity and the phase speed is always positive for incompressible magnetic Rossby waves. Multiplying a factor, the wavenumber vector shares the same endpoint with the group velocity vector. The endpoint moves on a cycle that has a center at the k-axis and is tangent to the l-axis in the wavenumber space. The circle is quite similar to the Longuet-Higgins circle for Rossby waves on Earth’s atmosphere and ocean. The fundamental dynamics is the theoretical basis for deeply understanding the meridional energy transport by waves and the interaction between waves and the background states.