Computation of solitary waves during propagation and runup on a slope

Abstract A numerical time-simulation algorithm for analysing highly nonlinear solitary waves interacting with plane gentle and steep slopes is described by employing a mixed Eulerian–Lagrangian method. The full nonlinear free surface conditions are considered here in a Lagrangian frame of reference without any analytical approximations, and thus the method is valid for very steep waves including overturning. It is found that the runup height is crucially dependent on the wave steepness and the slope of the plane. Pressures and forces exerted on impermeable walls of different inclinations (slopes) by progressive shallow water solitary waves are studied. Strong nonlinear features in the form of pronounced double peaks are visible in the time history of pressure and force signals with increasing heights of the oncoming solitary waves. The effect of nonlinearity is less pronounced as the inclination of the wall decreases with respect to the bottom surface.