We will consider the nonlinear problem of steady gravity-driven waves on the free surface of a three-dimensional flow of an incompressible fluid. In the talk we will discuss a recent progress on three-dimensional waves with vorticity, which is a relatively new subject. The rotational nature of the flow is modeled by the assumption on the velocity field, that is proportional to its curl. Such vector fields are known in magnetohydrodynamics as Beltrami fields. We plan to provide a necessary background on the topic and prove the existence of  three-dimensional doubly periodic waves with vorticity.

The talke is based on a joint work with Erik Wahlén and Douglas Svensson Seth from Lund University.