Navier--Stokes equations on a rapidly rotating sphere
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 sphererotating with angular velocity $1/\epsilon$ becomes zonal in the long timelimit, in the sense that the non-zonal component of the energy becomesbounded by $\epsilon M$.Central …