In this paper, wave transformation over a submerged reef has been numerically studied based on the OpenFOAM model. This numerical model solves the Reynolds-Averaged Navier-Stokes equations for two-phase flow and employs the volume of fluids (VOF) method for the free surface. The k-ω SST turbulence model is used to simulate wave breaking, and the wave generation library waves2Foam is adopted to generate waves in the model. The numerical model is first validated against the physical experimental data, and it is shown that the model is capable of simulating the key processes of wave shoaling, breaking and transmission over the submerged reef. Then, a series of numerical tests are conducted considering different incident wave heights, submergences and slopes of the reef. The influences of reef slope and submergence on the wave properties over the reef are discussed, which include the wave reflection and transmission coefficients, breaking wave height, wave-induced setup, and energy dissipation.

From the experiment of Li et al. (2015) it was observed that the generation of freak waves in random wave trains may be attributed to the focusing of double wave groups with different peak frequencies. In order to investigate this generation process, a modified wave focusing experiment is carried out, in which the focused waves are generated by two wave groups with different peak frequency differences, assumed to focus at the same point and time. By analyzing the evolutions of the free surface elevation and wavelet spectra of the experimental data, it can be verified that the focusing of double wave groups can reproduce the generation process of the freak waves in random wave trains well. Phase lags of the double wave groups focusing relative to the linear superposition of the corresponding single wave group and changes in the amplitude spectra during the focusing process are obviously observed. The method for the symmetry-based separation of harmonics illustrates that the phase shifts are mainly caused by the third-order non-linearity due to interactions between the two wave groups, rather than the even-order non-linearity. Third-order non-linearity makes the amplitude of waves small in the high-frequency region, resulting in a shift of the actual focusing location from the target location. Further investigations are conducted with the numerical simulation based on the High Order Spectral (HOS) method. The wavenumber-frequency spectra explain the evolution of the amplitude spectra and changes in the dispersive properties both in time and space, demonstrating that the third-order non-linearity changes the dispersion relationship of the wave components more intuitively. The above phenomena become obvious for the cases with smaller peak frequency differences wave spectra. All these observations will lead to a better understanding of the mechanism of freak wave generation and lay an important foundation for the low-cost and large-scale development and utilization of ocean wave energy resources.