Numerical investigation on spectral geometries and their relation to non-Gaussianity in sea states with occurrence of rogue waves: wind-sea dominated events

Abstract. The occurrence of rogue waves is closely related to the non-Gaussianity of sea states, and the non-Gaussianity is sensitive to the combination of three spectral geometries: wave steepness, bandwidth, and directional spreading. This paper presents a set of non-Gaussianity references that allow quantitative comparison of the non-Gaussianity of sea states with various combinations of the three geometries. In addition, an approach to introduce arbitrary 2D wave spectra into the references is presented, which allows quantitative investigation of the non-Gaussianity and the corresponding geometries in given sea states. Application in relation to certain rogue waves that occurred in wind-sea dominated sea states showed that the non-Gaussianity of skewness presented high values when those events occurred. However, abnormal values of kurtosis could not be found within the same period, indicating that third-order modulational instabilities were inactive in those events. Quantitative analyses based on the newly presented references revealed that the rogue waves that occurred in wind-sea dominated sea states, and presented extreme height and extreme destructive power, could hardly be formed from the modulational instabilities. This was because of not only the broad energy distribution in terms of direction, but also the broad bandwidth attributable to the developed wind-sea state.