This paper presents a computational model for coast wave motions with multiple wave breakings. In the Boussinesq model, the wave breaking judgment method is combined with the wave recovery judgment condition, which stops the wave breaking process when triggered. The energy dissipation of wave breaking is corrected, and the dissipation of wave energy is maintained at about 10% during the wave recovery stage, so that the dissipation caused by the residual turbulent motion of wave breaking and the increase in wave height caused by the shallowing of waves due to the water bottom slope are offset. By comparing the calculation results with the experimental results, it is proved that this model can be used to calculate multiple wave breakings. This model is applied to discuss the influence of wave incident angle and wave period on wave height and longshore current and gives the distribution characteristics of wave height and longshore current under multiple wave breakings.

In this study, a set of accurate dispersive nonlinear wave equations is established, using the wave velocity and free surface elevation as variables. These equations improve upon previous equations in which the velocity potential is used as a variable by considering the rotational wave motion and by adding a second-order bottom slope term that applies to general situations, allowing the equations to consider the influence of rapidly changing, horizontal, two-dimensional bottom topographies. The problem of the inaccuracy of the integral calculations used in previous equations in nearshore areas is solved by approximating the integral calculations into differential calculations, and a set of coupled wave equations is established by keeping the free surface elevation and the horizontal velocity constant, thus allowing the calculation of nearshore wave-generated currents. The benefits of the current model are confirmed through comparisons with corresponding laboratory experimental findings and are illustrated through a comparison with the numerical outcomes of other pertinent models.