PDE Seminar: Water waves solutions of the Euler equations with affine vorticity, Filippo Remonato (NTNU)
I will present several solutions of the Euler equations with affine vorticity.
We start by reviewing the bifurcation theory for the water wave problem, following in the footsteps of Ehrnstrom-Escher-Wahlén, and then turn our attention to the numerical approach, where the combination of standard Finite Elements and B-splines basis functions, recently known as Isogeometric Analysis, is used to solve the Euler equations in their full free-boundary setting, without any reduction to a fixed domain.
Periodic travelling waves solutions are found bifurcating from the line of trivial solutions in accordance with the theory, and we will look at several branches for both small and large amplitude waves with particular attention to the internal critical layers structure.
These preliminary results are part of a joint work with the University of Pavia, Italy.