Shoaling of solitary waves on a uniform plane beach connected to a constant-depth wave tank is investigated numerically using the smoothed particle hydrodynamics (SPH) method. The characteristics of water surface elevations have been analyzed for wave shoaling. To test the validity of the numerical model, the relative wave heights, the time histories of the free surface profiles are measured at several locations along the slope. In addition, the breaking points, breaking index and different breaking types have also been analyzed. Compared with laboratory data, and theory solutions, the calculated results from the present model are acceptable, indicating that the numerical model is reasonable.
Solitary waves are often utilized to investigate the characteristics of tsunami behaviors because of their hydrodynamic similarities. Tsunamis are long water waves of small steepness generated by impulsive geophysical events on the ocean floor or at the coastline. As tsunamis propagate into nearshore beach, shoaling and breaking have a direct relevance to the calamity caused by the run up and run down motion. Consequently the apprehension of wave motion near shoreline is of great importance to many applications in tsunami hazard. Since the work of Boussinesq (1872), there have been numerous attempts at modeling the solitary waves from analytical approach, experiment and numerical methods. For example, based on the nonlinear shallow water (NSW) equations, analytic solutions to the maximum run up of non breaking solitary wave were obtained by Synolakis (1987). Kânoĝlu and Synolakis (1998) used linear shallow water equations to study the propagation and run up of solitary waves. Carrier et al (2003) also presented the run up and run down process of solitary waves on a uniform slope using NSW equations. Experimental results for solitary waves present more useful information to explore the real physical mechanisms of shoaling and breaking.
