General results on zonation in rotating systems with a β-effect and the electromagnetic force

Abstract

Time averages are common observables in analysis of experimental data and numerical simulations of physical systems. We \nwill investigate, from the angle of partial differential equation \nanalysis, some oscillatory geophysical fluid dynamics in three \ndimensions: Navier–Stokes equations in a fast-rotating, spherical shell, and magnetohydrodynamics subject to strong Coriolis \nand Lorentz forces. Upon averaging their oscillatory solutions \nin time, interesting patterns such as zonal flows can emerge. \nMore rigorously, we will prove that, when the restoring forces \nare strong enough, time-averaged solutions stay close to the null \nspaces of the wave operators, whereas the solutions themselves \ncan be arbitrarily far away from these subspaces.