Numerically simulating non-Gaussian sea surfaces

A technique to simulate non-Gaussian time series with a desired (''target'') power spectrum and bispectrum is applied to ocean waves. The targets were obtained from observed bottom pressure fluctuations of shoaling, nonbreaking waves in 2-9 m water depth. The variance (i.e., frequency integrated spectrum), skewness, and asymmetry (i.e., frequency integrated bispectrum) of the simulated time series compare favorably with the observations, even for highly skewed and asymmetric near-breaking waves. The mean lengths of groups of high waves from non-Gaussian simulated time series are closer to observed values than those from Gaussian simulations. The simulations suggest that quadratic phase coupling between waves (of different frequencies) in shallow water results in longer wave groups than occur with linear, uncoupled waves having the identical power spectrum.