A new shoreline boundary condition for a highly nonlinear 1DH Boussinesq model for breaking waves

Abstract

In order to model the wave motion and, in turn, the flow, within the nearshore region, in the last decades the derivation and the application of Boussinesq type of models have been extensively investigated. Nevertheless, in the framework of such depth integrated numerical models, the problems of modeling wave breaking and moving onshore boundary at the shoreline are not trivial and several approaches have been proposed to overcome these limits. In the present work an effort toward a more physical based model of the surf and the swash zone has been accomplished. In particular, starting from the work of Musumeci et al. (2005), a new model of the shoreline boundary condition has been implemented. The shoreline boundary condition is developed with a fixed grid method with a wet-dry interface and with a linear extrapolation (Lynett et al. 2002) near the wet-dry boundary has been used and coupled with the shoreline equations (Prasad and Svendsen, 2003). To validate the model a classical test which adopts a monochromatic wave train over a plane beach has been performed. In particular the analytical solution derived by Carrier and Greenspan (1958) has been used for comparison. The comparison between the analytical and numerical horizontal shoreline movements, gives a fairly good agreement. Other tests on breaking of solitary waves have been performed. The solitary wave shoreline oscillation is investigated by comparison with the experimental tests by Synolakis (1986). The results are in fairly good agreement with the experimental data.