089 Darren Crowdy

Water waves with vorticity and the Schwarz function // 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 has been growing interest, especially recently, in the effect of vorticity on the structure of the waves. The assumption of irrotationality has the theoretical advantage that complex analysis techniques can be used to analyze the problem in the two-dimensional setting. This talk will present a novel theoretical formulation of the problem of steadily-travelling water waves in the presence of vorticity (where the assumption of irrotationality is dropped) but in the absence of gravity or capillarity. 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.