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The water particle velocity of the wave peaks is closely related to the wave load borne by offshore structures. It is of great value for marine disaster prevention to study the water particle velocity of nonlinear extreme waves represented by Freak waves. This study applies the High-order Spectral Method (HOS) numerical model to analyze the characteristics and influencing factors of the water particle velocity of Freak wave peak with two different generation mechanisms under the initial condition of a weakly modulated Stokes wave train. Our results show that the water particle velocity of the wave peak increases linearly with wave height and initial wave steepness in the evolution stage of modulation instability. While in the later stage, the relationship becomes exponential. Under the condition of similar wave heights, the deformation degrees of Freak waves with different generation mechanisms are distinct, the deformation degree of modulation instability stage is smaller than that of the later stage. The water particle velocity of the wave peaks increases with the deformation degrees. Furthermore, the correlation between wave peak height and water particle velocity is a quadratic function. This provides a theoretical basis for further understanding of nonlinear waves and the prediction of marine disasters.

We theoretically and experimentally investigate the mechanism underlying the generation of upstream-propagating waves induced by a steady current over a horizontal bottom with a patch of sinusoidal ripples. By considering the triad resonant wave–ripple interactions involving two unsteady wave components (which have the same frequency but different wavenumbers) and one bottom ripple component in the presence of a steady uniform current, we derive the general condition under which unsteady upstream- and/or downstream-propagating waves can be induced. The frequency and wavenumbers of the induced propagating waves are given by the triad resonance condition in terms of current speed, water depth and bottom ripple wavenumber. By means of a multiple-scale perturbation analysis, we obtain the nonlinear amplitude evolution equations governing the spatio-temporal evolution of resonance-generated waves. Based on these equations, we find that the amplitude of the generated upstream-propagating waves is dramatically amplified when the associated triad resonance occurs in the neighbourhood of the critical current speed/frequency (corresponding to zero group velocity of unsteady waves in the presence of a current). A series of laboratory experiments in a long wave flume with wide ranges of current speeds and water depths are conducted to verify the theory. The experiments confirm the observation of the phenomenon of upstream-propagating wave generation in a steady flow over a rippled bottom. In particular, the experimental measurements of the kinematics of upstream-propagating waves as well as the critical flow condition for the observation of such wave generation compare well with the theoretical prediction.

Wave energy has drawn much attention as an achievable way to exploit the renewable energy. At present, in order to enhance the wave energy extraction, most efforts have been concentrated on optimizing the wave energy convertor and the power take-off system mechanically and electrically. However, focusing the wave power in specific wave field could also be an alternative to improve the wave energy extraction. In this experimental study, the Bragg resonance effect is applied to focus the wave energy. Because the Bragg resonance effect of the rippled bottom largely amplifies the wave reflection, leading to a significant increase of wave focusing. Achieved with an energy conversion system consisting of a point absorber and a permanent magnet single phase linear motor, the wave energy extracted in the wave flume with and without Bragg resonance effect was measured and compared quantitatively in experiment. It shows that energy extraction by a point absorber from a standing wave field resulted from Bragg resonance effect can be remarkably increased compared with that from a propagating wave field (without Bragg resonance effect).

In a rectangular harbor with a constant bottom slope, transverse oscillation may occur. This kind of wave has a maximum amplitude at the dead end of the harbor and decays exponentially in the offshore direction. This numerical investigation, using the nonlinear wave transformation model FUNWAVE 2.0, demonstrates the generation of subharmonic and synchronous transverse oscillations within a harbor induced by waves impacting normally on. The subharmonic transverse oscillations are trivial if the bottom slope is small, while the synchronous transverse oscillations are trivial and irrelevant for the bottom slopes. For checking the system responses, transverse oscillations within the harbor that also has a small bottom slope across the harbor were also examined. The generation of subharmonic oscillation seems not to be affected by a small transverse bottom slope; however, the synchronous transverse oscillations are enhanced significantly.

Modulation instability is one of the most ubiquitous types of instabilities in nature. As one of the key characteristics of modulation instability, the most unstable condition attracts lots of attention. The most unstable condition is investigated here with two kinds of initial wave systems via a numerical high-order spectral method (HOS) for surface water wave field. Classically, one carrier wave and a pair of sidebands are implied as the first kind of initial wave system: “seeded” wave system. In the second kind of initial wave system: “un-seeded” wave system, only one carrier wave is implied. Two impressive new results are present. One result shows that the grow rates of lower and upper sideband are different within the “seeded” wave system. It means that, for a given wave steepness, the most unstable lower sideband is not in pair with the most unstable upper sideband. Another result shows the fastest growing sidebands are exactly in pair from “unseeded” wave system. And the most unstable conditions of “unseeded” wave system are more or less the mean value of those derived from the lower sidebands and upper sidebands within the “seeded” wave system.

It is known that the upstream-advancing waves can be excited when a steady current travelling over a wavy bottom. While the generation mechanisms are still inconclusive and the related dynamic and kinematic characteristics of the excited water waves are not clear. Focusing on the dynamics of this kind of upstream-advancing waves, especially the critical generation conditions, a series of experiments were carried out in a wave-current-wind flume (80m*1.0m*1.5m) with fixed sinusoidal bottom corrugations. By varying the current velocity and relative water depth, altogether 137 cases were realized. It is found that there exist a region of the current velocity for the exciting of upstream-advancing waves, based on the whole processes recorded, from the pure current to the present of clear upstream-advancing waves to the disappear of the evident waves again. The most unstable conditions correspond to the largest wave amplitudes were investigated in details. The dynamics of the excited waves were analyzed primarily for understanding of the generation mechanisms.

We investigate the dynamic and kinematic characteristics of freak waves using a direct phase-resolved nonlinear numerical method. The focus is on the understanding of the effects of different nonlinear wave-wave interactions on freak waves development and characteristics in the evolution process of modulated Stokes wave trains. Long time simulations of modulated Stokes wave trains, with different parameters, are obtained. Based on these simulations, we find that there are different kinds of freak waves in different time scales due to two kinds of different nonlinear mechanisms. One is the modulation instability and another related to the wave group interaction. Both the dynamic and kinematic characteristics of the different kinds of freak waves are distinct. Occurrence of freak waves (especially of large height) is usually correlated with broadband wave spectra.