Abstract
Accurate representations of the surface potential and the orbital velocity of nonlinear water waves are obtained, given the spatial wave-elevation field and its time derivative along two-dimensional sections of the ocean surface. The effect of a horizontal current is accounted for. The method is three-dimensional. The kernel of an integral equation and its right-hand side, both nonlinear functions of the elevation, are obtained in series expansions, and expressed explicitly by Fourier transform (FFT). Calculations for a periodic sine-wave and non-periodic model directional irregular wave field over swaths (wave slope in the range ±0.3 in both cases) illustrate the formulas. The Gibbs phenomenon along the boundaries affects the very high-order contributions in the non-periodic case.
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