Miles Wheeler

University of Bath

Overhanging water waves with constant vorticity

We consider steady water waves in two dimensions. Without vorticity or surface tension, it is known that the surface of the fluid must be a graph. On the other hand, with nonzero constant vorticity, numerics have long shown so-called ‘overhanging’ waves. I will present the first rigorous construction of such waves, obtained by perturbing a new family of explicit solutions to the problem in the zero-gravity limit. Interestingly, these explicit solutions have the same surfaces as Crapper’s celebrated irrotational capillary waves, even through the flow beneath the surface is completely differently. In the second part of the talk, I will present existence results for solitary waves obtained by global bifurcation. This is joint work with Vera Hur and with Susanna Haziot.