An experimental study was carried out to investigate the maximum run-up of non-breaking solitary waves on both smooth and rough plane beaches. Artificial beaches with different slopes and bottom roughness were studied. Our experimental results showed that, for waves running up relatively steep (e.g., 20°) slopes, viscosity and roughness have little effect on the maximum run-up. In this case, the inviscid long wave theories are adequate for predicting the run-up height. However, for waves running up over mildly sloped beaches, the viscous and roughness effects were found to be very significant and can reduce the maximum run-up by more than 50 % compared with the inviscid predictions.
Tsunami-induced coastal inundation has always been of great concern to the civil defense agencies in the Pacific Rim countries. In the recent decade alone, more than 4,000 people were killed during tsunami attacks in the Pacific basin (Gonzalez 1999). A better understanding of tsunami run-up and inundation would be helpful in developing better tsunami mitigation plans. Tsunamis are considered as long waves and are usually modeled by the depth-averaged nonlinear and nondispersive shallow water equations. Carrier and Greenspan (1958) solved the shallow water equations analytically and obtained solutions for predicting long wave run-up over smooth plane beaches. Later, Synolakis (1987) extended Carrier and Greenspan's (1958) analytical solution to obtain the following simple power law for predicting solitary wave run-up on a smooth plane beach: Here R is the maximum run-up height, a the initial wave amplitude, h the unperturbed uniform water depth, and fl the inclination angle of the plane beach (see Fig.l).