A nonlinear rotational, quasi-2DH, numerical model for spilling wave propagation

The propagation of spilling waves interacting with complex bathymetries was studied by means of a new two-dimensional weakly dispersive, fully nonlinear Boussinesq-type of model. In particular, the governing equations were derived assuming the flow as rotational, and the effects of vorticity due to breaking were included through the surface roller concept, which was defined and implemented on the basis of a new algorithm developed for the purpose. The propagation of vorticity, due to wave breaking, is estimated under the assumption that the effect of convection is leading order with respect to the effect of vorticity-stretching and that the breaking phenomenon does not show high curvature on the horizontal plane. In particular, the dynamic problem is decoupled in a lateral direction considering a series of separated sections in which vorticity is solved. In this way it is possible to obtain rotational information along the domain to a reasonable computational cost. The numerical model was validated in a simple one-dimensional case and then applied to the study of breaking-generated vorticity due to wave motion over a submerged shoal.