  We study 2D Euler equations on a rotating surface, subject to the effect of
the Coriolis force, with an emphasis on surfaces of revolution. We bring in
conservation laws that yield long time estimates on solutions to the Euler
equation, and examine ways in which the solutions behave like zonal fields,
building on work of B.~Cheng and A.~Mahalov, examining how such 2D Euler
equations can account for the observed band structure of rapidly rotating
planets. Specific results include both an analysis of time averages of
solutions and a study of stability of stationary zonal fields. The latter study
includes both analytical and numerical work.
