Effects of nonlinearity on the crest shape of extreme irregular sea waves: Nonlinear harmonic separation and analysis.

This article investigates the influence of nonlinearity on the crest shape—height and width—of extreme directional water waves in both infinite (deep) and finite (intermediate) water depths using HOS-ocean, an open-source fully nonlinear High-Order Spectral model. By extending harmonic separation methods up to the sixth order, the study reveals that in deep water, nonlinear interactions broaden the wave spectrum and increase crest elevations, whereas in finite water depths, energy transfers lead to spectral narrowing around the peak and a reduction in maximum crest height despite significant crest widening, forming so-called "walls of water." The research highlights that higher-order nonlinear harmonics, especially third to sixth order, play a crucial role in shaping extreme waves in finite depths, with difference terms (zeroth harmonic) notably reducing crest height due to their out-of-phase contributions. These findings have implications for the design and resilience of offshore and nearshore structures, emphasizing the necessity of incorporating fully nonlinear physics beyond linear or second-order theories to accurately predict extreme wave impacts.