Constant vorticity water flows with full Coriolis term

Abstract

We consider here three-dimensional water flows governed by the geophysical water wave equations exhibiting full Coriolis term. More precisely, under mild assumptions we determine all possible flow solutions to the governing equations that exhibit constant vorticity vector. That is, we show that the vertical component of the velocity vanishes, the horizontal components are constant and the free surface is necessarily flat. Our investigation features three-dimensionality, nonlinearity, Coriolis effects and vorticity, the last aspect being one of relevance in relation to the issue of turbulence.