Constant vorticity water flows in the equatorial β-plane approximation with centripetal forces

Abstract

In this paper, we consider three-dimensional equatorial flows with constant vorticity beneath a wave train and above a flat bed in the β-plane approximation with centripetal forces. As a striking upshot, we show that the equatorial flow is necessarily irrotational and the free surface is necessarily flat if it exhibits a constant vorticity, owing to the presence of centripetal forces. For the case exhibiting the surface tension, we prove that there are no equatorial flows exhibiting a constant vorticity.