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.

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