The Eddy Flux Transport of the Magnetohydrodynamic Quasi-Geostrophic Disturbances

The classic Eliassen-Palm (E-P) flux in the geophysical fluid dynamics is a vector to qualify the eddy momentum and heat flux transport by Rossby waves in the latitude-height plane. In this investigation, we derive two magnetic E-P fluxes to quantify the eddy energy transport by magnetic Rossby waves by using magnetohydrodynamic quasi-geostrophic theory. The first extends the classic E-P relation; the second arises from the magnetic and motion coupling. In wave-like dynamics, the cross-component flux vanishes, allowing the first flux to fully describe energy propagation. We further show magnetic Rossby waves can grow where Rossby waves cannot. When they develop, the increasing perturbation energy is fed by the zonal flow through Reynolds and Maxwell stresses transport. Our findings, bridging the geophysical fluid dynamics and magnetohydrodynamics, advance understanding of large-scale dynamics in magnetized environments and enhance predictions of planetary magnetic field evolution, space weather, and solar dynamics.