Computation of solitary waves during propagation and runup on a slope

A numerical time-simulation algorithm for analysing highly nonlinear solita ry waves interacting with plane gentle and steep slopes is described by emp loying a mixed Eulerian-Lagrangian method. The full nonlinear free surface conditions are considered here in a Lagrangian frame of reference without a ny analytical approximations, and thus the method is valid for very steep w aves including overturning. It is found that the runup height is crucially dependent on the wave steepness and the slope of the plane. Pressures and f orces exerted on impermeable walls of different inclinations (slopes) by pr ogressive shallow water solitary waves are studied. Strong nonlinear featur es in the form of pronounced double peaks are visible in the time history o f pressure and force signals with increasing heights of the oncoming solita ry waves. The effect of nonlinearity is less pronounced as the inclination of the wall decreases with respect to the bottom surface. (C) 1999 Elsevier Science Ltd. All rights reserved.