Statistics of waves with different steepness simulated in a wave basin

Modulational instabilities induced by third-order nonlinear interactions among freely propagating waves can cause the statistics of various surface features to deviate significantly from the predictions based on the linear Gaussian and second-order models. This study analyzes deep-water waves with different initial steepness measured in a wave basin and characterized with such instabilities, and compares the statistics of wave heights, crest and trough amplitudes observed with a variety of theoretical approximations based on Gram–Charlier expansions. The results indicate that the theoretical approximations describe the empirical distributions observed reasonably well, for the most part. Further comparisons also show that the zero-up- and zero-down crossing heights of the largest waves observed in the experimental series do not exceed Miche–Stokes type upper limits.

► This study analyzes deep-water waves with different initial steepness measured in a wave basin.
► It compares the statistics of the waves with a variety of theoretical Gram–Charlier expansions.
► The theoretical approximations describe the empirical distributions observed reasonably well.
► The up-crossing and down-crossing heights of the largest waves do not exceed Miche–Stokes limits.