A new numerical method for surface hydrodynamics

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Abstract
We present a new numerical method for studying the evolution of free and bound waves on the nonlinear ocean surface. The technique, based on a representation due to Watson and West (1975), uses a slope expansion of the velocity potential at the free surface and not an expansion about a reference surface. The numerical scheme is applied to a number of wave and wave train configurations including longwave‐shortwave interactions and the three‐dimensional instability of waves with finite slope. The results are consistent with those obtained in other studies. One strength of the technique is that it can be applied to a variety of wave train and spectral configurations without modifying the code.