Nonlinear Effects on Wave Groups in Random Seas

Abstract

Laboratory simulations of extreme random seas reveal that high wave crests occur more frequently than predicted by the Rayleigh distribution. In this paper, a theory is presented to account for nonlinearities in the sea state to second order resulting in a non-Rayleigh distribution of wave crest and trough amplitudes based on the narrow-band assumption. The resulting probability density functions are then used to predict average wave group characteristics through a modification of linear wave envelope theory which accounts, for example, for a significant decrease in the time intervals between successive runs of high crests compared to linear theory. The nonlinear theory is then verified based on a laboratory data set on deep water wave group statistics for severe seas described by Bretschneider and JONSWAP spectra.