A Study on Nonlinear Wave-Current Interactions by the Extended Boussinesq Equations

A set of Boussinesq-type equations derived by Lin et al. (2004) is applied to study the wave transformations with the presence of currents. A sponge layer is used to suppress the reflection of waves from the boundary and a source function is employed to generate the incident waves and increase numerical stability. Compared with the Stokes-type third order solutions, the numerical model proposed by Lin et al. (2004) simulates the nonlinear waveform well around the critical limitations of the shallow water depth. The harmonic wave heights increased as the wave passed over the obstacle in the following current cases by numerical experiments. Finally, the effect of the number of the ripples and currents on the reflected coefficients is elucidated. The results demonstrate that the reflected coefficients do not increase with the number of ripples between four and six, for a given following flow.