Abstract
Traveling gravity-capillary water waves on the interface of a three-dimensional fluid of infinite depth are computed. The vortex sheet formulation with the small scale approximation is used as the mathematical model for the fluid motion. The fluid interface is parameterized isothermally. The traveling wave ansatz for parameterized surfaces is described. Waves are computed using Fourier collocation and quasi-Newton iteration; large amplitude overturned traveling waves are computed via a dimension-breaking based numerical continuation method.
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