Analytical study of a generalised Dirichlet–Neumann operator and application to three-dimensional water waves on Beltrami flows
We consider three-dimensional doubly periodic steady water waves with vorticity, under the action of gravity and surface tension; in particular we consider so-called Beltrami flows, for which the velocity field and the vorticity are collinear. We adapt a recent formulation of the corresponding problem for localised waves which involves a generalisation of the classical Dirichlet–Neumann operator.