Statistics of nonlinear waves generated in an offshore wave basin

This study analyzes waves generated in a deepwater wave basin and characterized by modulational instabilities induced by third-order nonlinear interactions among freely propagating waves, which can cause the statistics of various surface features to deviate significantly from the predictions based on the linear Gaussian and second-order models. Comparisons are provided between the statistics of wave envelopes and phases, wave heights, and crest and trough amplitudes observed for various theoretical approximations based on Gram-Charlier expansions. The results suggest that the comparisons for the wave envelopes tend to be somewhat poor, particularly in the presence of relatively strong instabilities. In contrast, the comparisons for wave phases, crest-to-trough heights, and crest and trough amplitudes all indicate that the theoretical approximations represent the empirical distributions observed reasonably well, for the most part. Furthermore, the heights and crests of the largest waves do not exceed Miche-Stokes-type upper bounds.