Shallow water equations on a rotating attracting sphere. 2. Simple stationary waves and sound characteristics

This paper studies a model of shallow water on a rotating attracting sphere that describes large-scale motions of the planetary atmospheric gases and World ocean water. The propagation of sound perturbations on an equilibrium state is studied. The system of equations for bicharacteristics is integrated in elliptic functions. A description of simple stationary waves is given. It is proved that there exist two types of solutions (supercritical and subcritical) describing gas motion in a spherical zone, so that one of the boundary parallels is a source and the other is a sink. The obtained solutions are interpreted as large-scale circulating cells in the atmosphere.