| Numerical and theoretical techniques are presented for the study of traveling wave solutions to the gravity water wave problem. The gravity water wave problem is reformulated in terms of surface variables giving rise to the Zakharov-Craig-Sulem formulation, and traveling waves are studied by introducing a phase velocity vector as a parameter. Our numerical methods are concerned with a Fourier spectral collocation discretization of these equations, and the implementation of an Euler-Newton predictor-corrector numerical continuation method. We then study various traveling waves in two and three dimensions, and observe such phenomena as the wave with Stokes singularity (a wave with corner shaped crest with angle of 120... |
