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Abstract

Probability of freak waves in the ocean is linked to higher statistical moments of wave fields (skewness and kurtosis). For generic open ocean waves, these moments can be obtained from wave spectra, since the dynamical component of the kurtosis can be neglected for a broadband wind wave field. However, higher statistical moments depend not just on integral characteristics of wave spectra (e.g. significant wave height), but also on spectral shapes. While there is a consensus that current wave modelling does capture the main features of wind wave evolution, this mostly applies to integral characteristics. At the same time, there are major discrepancies between modelled and observed spectral shapes. In particular, the current wave modelling, based on the Hasselmann kinetic equation, is unable to reproduce the Pierson–Moskowitz spectrum of mature wind waves, well-established in measurements, or to demonstrate the observed transition towards it during long-term spectral evolution. In this work, we perform simulations of wind wave field evolution by the Hasselmann kinetic equation and direct numerical simulations (DNS) with the Zakharov equation, and compare the results with measurements. We identify the neglect of finite non-Gaussianity effects by the Hasselmann equation as the origin of the discrepancies, and demonstrate that the resulting underestimation of spectral width causes a considerable (roughly, by a factor of 2) underestimation of the wave kurtosis, dramatically affecting the estimates of extreme waves probability. Results can be applied to the prediction of extreme waves (e.g. a "100-year wave") for offshore structures.