  We study the dynamics of $N$ point vortices on a rotating sphere. The
Hamiltonian system becomes infinite dimensional due to the non-uniform
background vorticity coming from the Coriolis force. We prove that a relative
equilibrium formed of latitudinal rings of identical vortices for the
non-rotating sphere persists to be a relative equilibrium when the sphere
rotates. We study the nonlinear stability of a polygon of planar point vortices
on a rotating plane in order to approximate the corresponding relative
equilibrium on the rotating sphere when the ring is close to the pole. We then
perform the same study for geostrophic vortices. To end, we compare our results
to the observations on the southern hemisphere atmospheric circulation.

Dynamical Systems