An experimental investigation focusing on the effect of dissipation on the evolution of the Benjamin–Feir instability is reported. A series of wave trains with added sidebands, and varying initial steepness, perturbed amplitudes and frequencies, are physically generated in a long wave flume. The experimental results directly confirm the stabilization theory of Segur et al. (J. Fluid Mech., vol. 539, 2005, pp. 229–271), i.e. dissipation can stabilize the Benjamin–Feir instability. Furthermore, the experiments reveal that the effect of dissipation on modulational instability depends strongly on the perturbation frequency. It is found that the effect of dissipation on the growth rates of the sidebands for the waves with higher perturbation frequencies is more evident than on those of waves with lower perturbation frequencies. In addition, numerical simulations based on Dysthe’s equation with a linear damping term included, which is estimated from the experimental data, can predict the experimental results well if the momentum integral of the wave trains is conserved during evolution.

A nonlinear Schrödinger equation for the propagation of two-dimensional surface gravity waves on linear shear currents in finite water depth is derived. In the derivation, linear shear currents are assumed to be a linear combination of depth-uniform currents and constant vorticity. Therefore, the equation includes the combined effects of depth-uniform currents and constant vorticity. Next, using the equation, the properties of the modulational instability of gravity waves on linear shear currents are investigated. It is showed that shear currents significantly modify the modulational instability properties of weakly nonlinear waves. Furthermore, the influence of linear shear currents on Peregrine breather which can be seen as a prototype of freak waves is also studied. It is demonstrated that depth-uniform opposing currents can reduce the breather extension in both the time and spatial domain in intermediate water depth, but following currents has the adverse impact, indicating that a wave packets with freak waves formed on following currents contain more hazardous waves in finite water depth. However, the corresponding and coexisting vorticity can counteract the influence of currents. Additionally, if the water depth is deep enough, shear currents have negligible effect on the characteristics of Peregrine breathers.

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.

A typhoon is a restrictive factor in the development of floating wind power in China. However, the influences of multistage typhoon wind and waves on offshore wind turbines have not yet been studied. Based on Typhoon Mangkhut, in this study, the characteristics of the motion response and structural loads of an offshore wind turbine are investigated during the travel process. For this purpose, a framework is established and verified for investigating the typhoon-induced effects of offshore wind turbines, including a multistage typhoon wave field and a coupled dynamic model of offshore wind turbines. On this basis, the motion response and structural loads of different stages are calculated and analyzed systematically. The results show that the maximum response does not exactly correspond to the maximum wave or wind stage. Considering only the maximum wave height or wind speed may underestimate the motion response during the traveling process of the typhoon, which has problems in guiding the anti-typhoon design of offshore wind turbines. In addition, the coupling motion between the floating foundation and turbine should be considered in the safety evaluation of the floating offshore wind turbine under typhoon conditions.

The nonlinear evolution of waves propagating on a spatially varying opposing current has been observed in a wave–current flume. Regular waves with different initial periods and different initial steepness, s (0.05 < s < 0.19), were generated and observed. Frequency downshift, even with very small initial steepness, was identified. As expected, it was found that opposing currents can have significant interactions with wavetrains. The ultimate frequency downshift increases with the increase in initial steepness. The evolution of frequency modulation was observed via the instantaneous frequency extracted by the Morlet-wavelet transform. The instantaneous frequency showed that often the process of frequency downshift can be local in time and gradual, but abrupt changes of local frequency were also detected. The presence of an opposing current can gradually block the primary wave energy and destroy the conservation of the wave action at downwave locations, thus increasing the asymmetric modulation and accelerating the effective frequency downshift.

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.