ABSTRACT
The planetary rotation gives rise to the Coriolis force which acts on the moving masses and could make them rotate in the opposite sense from planetary rotation. Non-uniform heating in the planetary atmospheres produces winds with different structures. The equations for waves on shallow water have been long known and studied. It is enough to note that the Korteweg-de Vries equation was derived from them. The simplest nontrivial solution to the equations for a shallow atmosphere is zonal flow. The zonal flows on Jupiter clearly change direction several times from the equator to the pole and are rather inhomogeneous. The stability theory of zonal flows is based on Rayleigh's theorem. Rayleigh investigates the stability of a plane-parallel flow of incompressible fluid. The similarity between the mathematical descriptions of Rossby waves and drift waves in plasma discovered by Hasegawa and Mima, experiments with shallow rotating water are of obvious interest for modelling convective transport processes in plasmas as well.
