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

Euler Equation on a Rotating Surface