The energy dispersion of magnetic Rossby waves in zonally nonuniform basic states

Abstract

Abstract The energy dispersion of magnetic Rossby waves was investigated by applying two-dimensional incompressible magnetohydrodynamic equations in both zonally varying basic flow and basic magnetic field. A derived cubic dispersion relation suggests that there are at most three types of magnetic Rossby wave. Two of them represent waves that gradually tend to Alfvén waves during the energy dispersion process. The energy dispersion trajectories (wave rays) finally move with the zonal group velocity that tends to be equal to the zonal phase speed after being reflected by at least one turning location at which the meridional group velocity equal to zero. Along the marching rays, both the wave action density and wave energy tend to be constant values while the wave amplitude will decrease with increasing total wavenumber. The third one represents a wave that gradually have the constant meridional wavenumber, wave action density, wave energy, and wave amplitude. However, the difference in the zonal group velocity and the zonal phase speed suggests that the wave is still dispersive. This type of wave will disappear if specifying uniform basic magnetic field. The cubic dispersion relation is then reduced to a quadratic one. Correspondingly, the remaining two dispersion relations feature a fast- and a slow-propagating magnetic Rossby wave, respectively. They finally tend to be Alfvén waves with no energy dispersion when the energy dispersion process completes.