Numerical Simulation Of Nonlinear Wave-wave Interaction

We have done extensive research about a variety of phenomena in the process of wave propagation in the estuary and coastal zone, in comparison, the research about nonlinear wave-wave interaction is not enough. Stokes wave theory is suitable for investigating wave propagation in water with constant depth and large relative depth. Research of nonlinear wave-wave interaction in water with variable depth is rare. It is tremendously significant for studying nonlinear wave-wave interaction in the estuary and coastal zone. For example, the sum-frequency effect and difference-frequency effect caused by wave train formed by two waves with different frequencies play an important role in the stabilization of the breakwater, sediment transport on the beach and the movement of mooring ships. On the topography with a slope, two free waves with closing wave numbers and different directions can trigger edge waves. On the other hand, bound waves transfer energy to free waves, and resonant triad interaction will take place. And the phenomenon is important for the designing of structures in coastal zone and anchor chains of ships. Boussinesq-type equations are nonlinear equations, and they are powerful tools to investigate the wave propagation in the near-shore water zone. So, the text makes use of new type Boussinesq-type equations wave model to investigate the problem of nonlinear wave-wave interaction.Firstly, in the paper, we improve the numerical model of nonlinear wave propagation based on new type Boussinesq-type equations; so, the calculation program can run for long time. Therefore, the model can simulate wave trains propagation effectively, including monochromatic wave, then, we simulate the propagation of bichromatic waves in water zone with constant depth, and compare numerical solutions with theoretical solutions of surface elevation, and we find that, both are in good agreement. So, it proves that the model can simulate the propagation process of bichromatic waves in water zone with constant depth correctly. Then, we discuss the nonlinear wave-wave interaction. Again, in water zone with variable depth, we verify the improved numerical model by the physical model experiment, comparing with physical model experimental data, and we find that, the model can simulate the propagation of monochromatic wave and bichromatic wave correctly in water zone with variable depth. At last, we simulate interactions between bichromatic waves and strong opposing current. Results show that the wave with high frequency is blocked at the blocking point and the wave with low frequency can propagate through it.