The energy dispersion of magnetic Rossby waves in the quasi-geostrophic shallow water magnetohydrodynamic theory

Abstract This research firstly comprehensively investigates the energy dispersion of magnetic Rossby waves in zonally non-uniform basic states by applying the quasi-geostrophic (QG) shallow water magnetohydrodynamic (SWMHD) equations. The eddy momentum and heat flux transported by magnetic Rossby waves, which can be described by the group velocity vector, have significant impacts on the large-scale dynamics of various celestial bodies. The findings suggest that the energy dispersion paths, also called rays, are curves and restricted in limited regions in the non-uniform basic states, in contrast with straight lines in the uniform basic states. Furthermore, the limited propagative regions are influenced by three important meridional locations, which are defined as the symmetric turning location, the asymmetric turning location, and the critical location. The first two reflect rays and the third one acts as an asymptote. The propagative region that is enclosed by a turning location and a critical location is more general. Besides, the occurrence of the asymmetric turning location, which is mainly depended on the distribution of the zonal basic flow, is a quite new feature of the energy dispersion for magnetic Rossby waves since there is no asymmetric turning location for Rossby waves on the Earth’s atmosphere and ocean. The results have important applications in illustrating interactions between magnetic Rossby waves and zonally basic states and in explaining the maintenance of the zonal flow and meridional circulation of various celestial bodies.