Statistical distributions of nonlinear waves from random laboratory wave fields

Abstract

The research focuses on the probabilistic structure of individual wave parameters from deep water laboratory experiments. The studied sea states are characterized by the JONSWAP frequency spectra with different energy content and steepness which offer favourable conditions for intense quasi-resonant modulations resulting in enhanced probability for unusually large wave events. Analysis of the results at different stages of the instability process, as the waves propagate along the tank, confirms the increasing influence of third-order nonlinearity on the extreme wave statistics. In particular, the tails of the empirical distributions over the last gauges consist of a growing number of waves fulfilling the common criteria for abnormality. Moreover, non-skewed surface profiles corresponding to initially large coefficients of kurtosis continue to show substantial deviations from the Rayleigh distribution as a result of the nonlinear exchange of energy between free wave modes. The uncertainty when predicting the empirical tails supports the use of statistical models for the wave amplitudes and heights based on the Gram-Charlier series expansions which demonstrate a generally good agreement, particularly with the crest-to-trough wave heights from the moderately steep sea states.