Fully Nonlinear Numerical Simulation On Wave-current Interactions

Process of wave propagation is usually accompanied with currents. The existence of the current leads to wave deformation and changes the swell spectrum. Likewise, the nonlinear interaction between current and waves changes the wave-flow field. In other words, the coexistence of wave and current can influence the propagation property of respective holders. And submerged bars are the most common construction in costal engineering, which can prevent coastal erosion. A fully-nonlinear numerical wave tank(NWT) based on time-domain theory is used in this paper. The model is extended to simulate regular wave or bichromatic wave groups propagation over various submerged bars with ambient currents. Then the transmitted waves are separated into the free waves and the locked waves with different harmonic frequencies by so-called "two-point" method.The governing equation of the present numerical model is Laplace equation. And the fully nonlinear kinematic and dynamic boundary conditions are given on the free surface. The mixed Eulerian-Lagrangian scheme is adopted to track the transient free surface with the fourth-order Runga-Kutta method for refreshing wave profile and velocity potential at the next time step.An image Green function is utilized to improve the computing efficiency in present numerical model. In order to simulate problems as long as possible within a finite distance, two damping layers are emplaced in front of the incident and the output boundaries, respectively. We also carried out sets of experiments on evolution of waves over physical submerged breakwaters, the same as the numerical studies. There are three types of submerged bars, including a vertical submerged bar, a submerged bar with weather slope and a submerged bar with leeward slope.The present numerical model was verified by comparison with published numerical results,experimental results and the experimental data obtained by the writer. The effects of currents and submerged bars on wave profile, higher-harmonic waves and reflection coefficient are further studied, respectively. After waves pass the submerged obstacle, higher-order harmonic waves generated by nonlinear wave-wave interactions in the shallow water over the obstacle will leave the bar leeward as free waves. We making use of the Fourier transform and orthogonality of trigonometric function to obtain the amplitudes of the nth order locked and free waves. The effects of incident waves,water depth and the slope angle of the submerged obstacle on first-, second-and third-harmonic free wave amplitudes at the leeside of submerged obstacle also are futher studied, respectively.