Discontinuously stratified equatorial flows with surface tension in spherical coordinates

We provide some exact solutions for the governing equations of geophysical fluid dynamics representing azimuthal equatorial flows with discontinuous density and surface tension. The fluid domain is bounded above by the free surface-which is an unknown of the problem and below by the ocean bottom. The fluid consists of two layers, each having a continuous density and are separated by an interface along which the densities do not match. After deriving formulas for the velocity and for the pressure the existence of functions describing the free surface and the interface is shown by a functional analytic approach.