On the Rapid Spectral Evolution of Steep Wave Groups: Directional Spreading and the Spectral Tail

Several studies have shown that wave fields which are ‘out of equilibrium’ can give rise to exaggerated nonlinearity due to enhanced wave-wave interactions [1–3]. Previous studies have also shown that nonlinear wave-wave interactions can alter the characteristics of an extreme wave event in the context of a random sea [4–6] as well as an isolated wave group [7–8].

In this study, we have performed numerical simulations of steep three-dimensional wave groups, formed by the dispersive focusing, using the fully-nonlinear potential flow solver OceanWave3D. We consider the influence of directional spreading and the high-wavenumber tail of the spectrum on the nonlinear wave-wave interactions.

We perform simulations based on Gaussian as well as JONSWAP omnidirectional spectra, combined with both frequency dependent and independent spreading functions. Our simulations indicate that the localised nonlinear features of an individual steep wave event, including group shape and kinematics, may also depend on the spectral equilibrium of the initial sea-state.

We conclude that focused wave events in sea-states with low directional spreading or sea-states without a fully-developed spectral tail are more likely to exhibit attributes of nonlinearity.