Free-surface capillary–gravity azimuthal equatorial flows

We dedicate this paper to the investigation of certain special types of geophysical water flows arising in the equatorial ocean which are driven by gravity and surface tension. To be more specific, we consider steady flows–written in cylindrical coordinates–which are moving in the azimuthal direction, with no variation in this direction, and which exhibit a vertical structure and allow for a surface distortion. Using a functional analytic approach we prove that any small deviation of the pressure function from the pressure required to maintain the free surface flat and undisturbed gives rise to a genuine wave solution.