Numerical study of edge waves using extended Boussinesq equations

An edge wave numerical model was developed based on extended Boussinesq equations with the internal wave-generation method. The form of edge waves near a seawall was chosen as the input signal in order to avoid treatment of the moving shoreline on a sloping beach. As there was an energy transfer between different edge wave modes, not only the target mode but also other modes appeared in the simulations. Due to the nonlinear effect, the simulation results for mode-0 edge waves were slightly modulated by mode-1 and mode-2 waves. As the magnitudes of these higher-mode waves are not significantly related to those of the target mode, the internal wave-generation method in Boussinesq equations can produce high-quality edge waves. The numerical model was used to investigate the nonlinear properties of standing edge waves, and the numerical results were in strong agreement with theory.

Numerical study of nonlinear interactions of bi-chromatic progressive deep-water waves

This paper proposes a 3-D non-hydrostatic free surface flow model with a newly proposed general boundary-fitted grid system to simulate the nonlinear interactions of the bi-chromatic deep-water gravity waves.First,the monochromatic bidirectional and bi-chromatic bidirectional waves of small wave steepness are successively simulated to verify the abilities of the numerical model.Then,a series of bi-chromatic progressive waves of moderate wave steepness and different crossing angles are simulated and analyzed in detail.It is found that if the crossing angle is close to or smaller than the resonant angle,apparent discrepancies are observed among the numerical results,the linear wave theory,and the steady third-order theory.Otherwise,the three solutions coincide well.Through analysis,it is concluded that the discrepancies are caused by the third-order quasi-resonant interactions between the bi-chromatic progressive waves.Such interactions not only could modify the wave spectrum,but could also change the wave shape patterns.

A numerical investigation of interactions between extreme waves and a vertical cylinder

In this paper,the interactions between extreme waves and a vertical cylinder are investigated through a 3-D two-phase flow model.The numerical model is verified and validated by experimental data.Then,two factors are considered,the global wave steepness and the frequency bandwidth of the wave groups,in the studies of the in-line wave forces and the wave run-up around a cylinder.It is found that both the in-line wave forces and the wave run-up are remarkably increased with the increase of the global wave steepness,whereas the effect of the frequency bandwidth on the in-line wave forces is relatively weak in comparison with its effect on the wave run-up.The minimum and maximum wave run-ups are located in the directions of 22.5°and 180°with respect to the direction of the incident waves,respectively.Additionally,a new empirical formula is proposed for predicting the in-line wave forces by using only the free surface elevations around the cylinder.The results of the formula agree well with the simulation results.