The flow beneath a periodic travelling surface water wave

Abstract

We discuss some recent results on the behaviour of the velocity field, pressure and particle trajectories beneath a periodic travelling wave propagating at the surface of water with a flat bed, in a flow without underlying currents. By analysing the governing equations we avoid approximations, thus ensuring the validity of the results without restrictions on the wave amplitude. In particular, the presented approach applies to waves of large amplitude. We also formulate some open problems, venturing into the relatively unexplored field of wave-current interactions.