Numerical modeling of nonlinear surface waves and its validation

We study numerically the evolution of nonlinear surface gravity waves in infinitely deep water using both the exact evolution equations and an asymptotic model correct to the third order in wave steepness. For one-dimensional Stokes waves subject to perturbations at sideband frequencies, the numerical solutions of the third-order nonlinear model found using a pseudo-spectral method are carefully validated with those of the exact equations, and it is found that the third-order model describes accurately the development of spectral components in time. For two-dimensional waves, we study resonant interactions of two mutually-orthogonal gravity wave trains and compare our numerical solutions with available theory and experimental data. We also simulate the evolution of a realistic surface wave field, characterized initially by the JONSWAP spectrum, and examine the occurrence of a larger wave compared with the background wave field.