Euler equations on a fast rotating sphere — time-averages and zonal flows. published in European Journal of Mechanics B/Fluids

Abstract. Motivated by recent studies in geophysical and planetary sciences, we investigate the PDE-analytical aspects of time-averages for barotropic, inviscid flows on a fast rotating sphere S2. Of particular interests are the incompressible Euler equations. We prove that the finite-time-average of the solution stays close to a subspace of longitude-independent zonal flows. The intial data can be arbitrarily far away from this subspace. Meridional variation of the Coriolis parameter underlies this phenomenon. Our proofs use Riemannian geometric tools, in particular the Hodge Theory. 1