Stuart-type polar vortices on a rotating sphere

Stuart vortices are among the few known smooth explicit solutions of the planar Euler equations with a nonlinear vorticity, and they can be adapted to model inviscid flow on the surface of a fixed sphere. By means of a perturbative approach we show that the method used to investigate Stuart vortices on a fixed sphere provides insight into the dynamics of the large-scale zonal flows on a rotating sphere that model the background flow of polar vortices. Our approach takes advantage of the fact that while a sphere is spinning around its polar axis, every point on the sphere has the same angular velocity but its tangential velocity is proportional to the distance from the polar axis of rotation, so that points move fastest at the Equator and slower as we go towards the poles, both of which remain fixed.