Abstract: In this talk we consider the water wave problem in a two-dimensional domain of infinite depth in the presence of nonzero constant vorticity. I will describe the effects of uniform shear flow on the modulation of weakly nonlinear quasi-monochromatic surface gravity waves. In particular, starting from the Hamiltonian formulation of this problem and using techniques from Hamiltonian transformation theory, we derive a Hamiltonian Dysthe equation for the time evolution of the wave envelope. We also test the model against direct numerical simulations of the full Euler equations. This is a joint work with C. Sulem and P. Guyenne.
univienna.zoom.us/j/64775698490
(Meeting ID: 647 7569 8490; Passcode: 329457)