Stokes waves in constant vorticity flows

Abstract: I will discuss recent progress on the numerical computation of Stokes waves in constant vorticity flows. Based on a Babenko-kind equation, our result improves those in the 1980s by Simmen and Saffman, Teles da Silva and Peregrine. Notably, it reveals a plethora of new solutions: Crapper's exact solution (even though there is no surface tension), a fluid disk in rigid body rotation, etc. I will also discuss the effects of vorticity on the extreme wave, particularly, the maximum slope for an almost extreme wave. I will discuss some open problems, both analytical and numerical.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

Online Northeast PDE and Analysis Seminar