Euler equation on a fast rotating sphere—Time-averages and zonal flows

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 S2S2. Of particular interest is the incompressible Euler equation. We prove that finite-time-averages of solutions stay close to a subspace of longitude-independent zonal flows. The initial data are unprepared and can be arbitrarily far away from this subspace. Our analytical study justifies the global Coriolis effect in the spherical geometry as the underlying mechanism of this phenomenon. We use Riemannian geometric tools including the Hodge theory in the proofs.