Flow structure beneath rotational water waves with stagnation points

Abstract

The purpose of this work is to explore in detail the structure of the interior flow generated by periodic surface waves on a fluid with constant vorticity. The problem is mapped conformally to a strip and solved numerically using spectral methods. Once the solution is known, the streamlines, pressure and particle paths can be found and mapped back to the physical domain. We find that the flow beneath the waves contains zero, one, two or three stagnation points in a frame moving with the wave speed, and describe the bifurcations between these flows. When the vorticity is sufficiently strong, the pressure in the flow and on the bottom boundary also has very different features from the usual irrotational wave case.