NAVIER-STOKES EQUATIONS ON A RAPIDLY ROTATING SPHERE

We extend our earlier beta-plane results [al-Jaboori and Wirosoetisno, 2011, DCDS-B 16:687-701] to a rotating sphere. Specifically, we show that the solution of the Navier-Stokes equations on a sphere rotating with angular velocity 1/epsilon becomes zonal in the long time limit, in the sense that the non-zonal component of the energy becomes bounded by epsilon M. Central to our proof is controlling the behaviour of the nonlinear term near resonances. We also show that the global attractor reduces to a single stable steady state when the rotation is fast enough.