Development of a coupled model for the interaction between internal solitary waves and free surface waves

Internal solitary waves (ISWs) and free surface waves interact dynamically; this is necessary for the safety of offshore structures and underwater vehicles. A coupled model was developed to simulate the interaction between ISWs and free surface waves in continuously stratified ocean waters. The density transport equation was introduced into a two-phase (air-water) model based on the three-dimensional Navier-Stokes equations. The method of initializing the flow field was adopted to generate ISWs based on the fully nonlinear Dubreil-Jacotin-Long (DJL) equation, and the relaxation zone method was employed to generate and absorb the surface waves. Grid sensitivity analysis revealed that the height of the refined grid region beneath the surface should be at least thirty times the surface wave height in the deep ocean applications, which is quite different from that required for simulating surface waves in coastal areas. Validation of the model against laboratory experiments demonstrated that the simulated results agree well with the measured data. The coupled model was applied to simulate the surface displacement induced by an ISW and the modulation of surface waves by the ISW. The simulation results indicate that the coupled model can capture for the interaction between ISWs and surface waves, providing a potential tool for studying the coupled effects between them.