The formation mechanism of extreme waves in the coastal areas is still an open contemporary problem in fluid mechanics and ocean engineering. Previous studies have shown that the transition of water depth from a deeper to a shallower zone increases the occurrence probability of large waves. Indeed, more efforts are required to improve the understanding of extreme wave statistics variations in such conditions. To achieve this goal, large scale experiments of unidirectional irregular waves propagating over a variable bottom profile considering different transition water depths were performed. The validation of two highly nonlinear numerical models was performed for one representative case. The collected data were examined and interpreted by using spectral or bispectral analysis as well as statistical analysis. The higher probability of occurrence of large waves was confirmed by the statistical distributions built from the measured free surface elevation time series as well as by the local maximum values of skewness and kurtosis around the end of the slope. Strong second-order nonlinear effects were highlighted as waves propagate into the shallower region. A significant amount of wave energy was transmitted to low-frequency modes. Based on the experimental data, we conclude that the formation of extreme waves is mainly related to the second-order effect, which is also responsible for the generation of long waves. It is shown that higher-order nonlinearities are negligible in these sets of experiments. Several existing models for wave height distributions were compared and analysed. It appears that the generalised Boccotti’s distribution can predict the exceedance of large wave heights with good confidence.

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.

We present experimental results of irregular long-crested waves propagating over a submerged trapezoidal bar with the presence of a background current in a wave flume. We investigate the non-equilibrium phenomenon (NEP) induced by significant changes of water depth and mean horizontal flow velocity as wave trains pass over the bar. Using skewness and kurtosis as proxies, we show evidence that an accelerating following current could increase the sea-state non-Gaussianity and enhance both the magnitude and spatial extent of the NEP. We also find that below a ‘saturation relative water depth’ $k_p h_2 \approx 0.5$ ( $k_p$ being the peak wavenumber in the shallow area of depth $h_2$ ), although the NEP manifests, the decrease of the relative water depth does not further enhance the maximum skewness and kurtosis over the bar crest. This work highlights the nonlinear physics according to which a following current could provoke higher freak wave risk in coastal areas where modulation instability plays an insignificant role.

Tsunami surges are frequently simulated by dam-break flows over dry beds. The purpose of this study is to quantitatively investigate the flow kinematics and turbulent characteristics of a surge impacting onto a vertical wall. To quantify the flow kinematics, the particle image velocimetry technique was used in the non-aerated region, while the bubble image velocimetry technique was employed to measure the impact-induced turbulent flow with air entrainment. The measured velocity fields of the impact-induced splash confirmed the feasibility of Ko and Yeh's [Coastal Eng. 131, 1–11 (2018)] model employing a solid-body motion assumption of splash that estimates the impact force by bores and surges at the initial impact stage. Velocity fields and streamlines revealed that the main water body overturned backward and formed a large two-phase vortex, while a small counter rotating vortex was also formed at the corner of the wall-bed junction. The mean velocity magnitude of the small corner vortex is about two-thirds that of the main water body. The mean turbulent intensity of these aerated regions is about 3.4 times that of the non-aerated regions. Based on a wavelet transform-based method, the result reveals that the mean turbulence length scale of the aerated region is about two-thirds that of the non-aerated region. This study reveals for the first time the quantitative flow field results of the surge impact process, which deepen insight of tsunami risk in coastal engineering, thus improving the accuracy of post-damage prediction in coastal areas.