Global Bifurcation of Water Waves over Constant Vorticity Flows with Critical Layers - Thylefors,Erik (Master's Theses in Mathematical Sciences, 2025)
We consider two-dimensional travelling water waves over flows with constant vorticity and critical layers. We use global analytic bifurcation theory to show the existence of a global curve of solutions which either approaches a solitary wave or forms a critical point along the surface. In contrast to most of the previous studies, we fix the Bernoulli constant and use the wavenumber as a bifurcation parameter. We also derive several new bounds for Stokes waves with critical layers and constant vorticity.
Keywords: Water waves; global analytic bifurcation theory; Euler equations; gravity waves