On damping source in model of the shallow water on rotating sphere

We investigate exact shallow water on a rotating sphere. This model is used in oceanoiogy and physics of atmosphere for describing large-scale motions of gas and fluid. We construct and study solution, which describes the damped ring source on the sphere. The motion takes place in a spherical belt. System of equations of shallow water on the sphere has solutions of two types: supercritical (supersonic) and subcritical (subsonic).