  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. We also
show that the global attractor reduces to a single stable steady state when the
rotation is fast enough.
