Stuart vortices are among the few known smooth explicit solu-tions of the planar Euler equations with a nonlinear vorticity, and they can beadapted to model inviscid flow on the surface of a fixed sphere. By means ofaperturbativeapproachweshowthatthemethodusedtoinvestigateStuartvortices on a fixed sphere provides insight into the dynamics of the large-scalezonal flows on a rotating sphere that model the background flow of polar vor-tices. Our approach takes advantage of the fact that while a sphere is spinningaround its polar axis, every point on the sphere has the same angular velocitybut its tangential velocity is proportional to the distance from the polar axisof rotation, so that points move fastest at the Equator and slower as we gotowards the poles, both of which remain fixed.