Statistical distributions of free surface elevation and wave height for out-of-equilibrium sea-states provoked by strong depth variations

Abstract

As unidirectional irregular wave trains propagate over a steep shoal, the sea-state becomes out-of-equilibrium and is continuously affected by the non-equilibrium dynamics (NED) over dozens of characteristic wavelengths. Using the set of accurate numerical simulations of Zhang et al. (2022), the NED effects on the probability distributions of free surface elevation and wave height, the statistical moments and maximum wave statistics are investigated, in both near-field and far-field regions after the water depth transition. The primary contribution of this work is to assess the applicability and limitations of several popular statistical distribution models in describing non-equilibrium statistics. In addition, a new distribution of the free surface elevation in a lognormal shape is proposed, which predicts the non-equilibrium free surface statistics with satisfactory performance and characterizes well the skewness–kurtosis relationship in the short scale. It is shown that the statistics in the far-field region are significantly influenced by the near-field wave-wave interaction, and beyond the capability of all statistical models considered here. Despite this complexity, the sea-state in the far-field region exhibits lower freak wave probability than a Gaussian sea-state. Implications of these findings for engineering practices are discussed.