Wave-bottom interaction and extreme wave statistics due to shoaling and de-shoaling of irregular long-crested wave trains over steep seabed changes

The formation of abnormal (extreme) waves in coastal areas can be triggered by wave-seabed interaction, in particular by steep bottom changes. As an incident equilibrium sea state passes over a submerged step or bar, non-equilibrium dynamics appears locally and forces the sea state to a new, finite-depth equilibrium along with strong non-Gaussian statistics and an intensified occurrence probability of large waves. In this study, the experimental case Run 3 reported by Trulsen et al. (J. Fluid Mech., vol. 882, 2020, R2) has been investigated numerically with a fully nonlinear model. Furthermore, as both shoaling and de-shoaling effects exist in the set-up with a bar-profile bottom, an additional simulation with a step-profile bottom is performed to isolate the de-shoaling effects. The model is proven excellent by the confrontation of the measurements and simulated results in both time and spectral domains. Strong non-Gaussian behaviour of the sea state is highlighted after the up-slope transition by combining spectral and bi-spectral analyses, and characteristic parameters. With a harmonic extraction approach, we show evidence that both second- and third-order effects triggered by the non-equilibrium dynamics significantly enhance the local kurtosis and occurrence of extreme waves. The statistics of kinematics shows the asymmetry of the wave field evolves somewhat independently in the horizontal and vertical directions. By comparing the simulations of bar- and step-profile cases, we find the de-shoaling process is responsible for the upstream modulation of nonlinear and dispersive parameters, and the enhancement of kurtosis of both horizontal and vertical velocities and horizontal acceleration over the down-slope area.

Automated summary

This study investigates the formation of abnormal waves in coastal areas through numerical analysis, highlighting the significant impact of non-equilibrium dynamics on extreme wave occurrence and the role of the de-shoaling process in modulating parameters and enhancing wave kurtosis.