Exact, purely azimuthal stratified equatorial flows in cylindrical coordinates

This paper is concerned with the derivation of an exact solution to the governing equations for geophysical fluid dynamics expressed in terms of cylindrical coordinates. It is demonstrated, by way of a functional analytic approach, that there is a well-defined relationship between the imposed pressure at the free-surface and the resulting distortion of the surface, and it is established that this relationship exhibits the expected monotonicity properties. This exact solution for stratified fluid flow is then subjected to a short-wavelength perturbation stability analysis.