Seminar

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:

A study of wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed is discussed.

For large-amplitude periodic traveling waves that propagate at the water surface in the same direction as the underlying current (downstream waves), we prove explicit uniform bounds for their amplitude. In particular, our estimates show that the maximum amplitude of the waves becomes vanishingly small as the vorticity increases without limit. We also prove that the downstream waves on a global bifurcating branch are never overhanging, and that their mass flux and Bernoulli constant are uniformly bounded. This is joint work with Walter Strauss (Brown University, USA) and Eugen Varvaruca (University of Iasi, Romania).