Water waves with vorticity and the Schwarz function #

Darren Crowdy

11:10 Monday in 2Q42.

Part of the Advances in water waves and free-surface flows session.

Abstract #

The theory of water waves is centuries old, but it remains a vibrant area of research. Most theoretical work on water waves takes the flow to be irrotational, but there is growing recent interest in the effect of vorticity on the structure of the waves. This talk will present a novel theoretical formulation of the problem of steadily-travelling two-dimensional water waves in the presence of vorticity. The approach is based on the notion of a Schwarz function of a curve. It unifies our understanding of several recent results in the water wave literature and provides a wealth of new exact mathematical solutions to this challenging free boundary problem.