Solitary Wave Runup on Plane Slopes

Abstract

This study deals with the runup of solitary waves on a uniform plane beach connected to an open ocean of constant depth. The waves are nonbreaking during the runup process. A nonlinear solution to the classical shallow water equation, that describes the wave characteristics on the beach, is obtained analytically by using a hodograph transformation. It was found that the nonlinear theory agreed well with experimental results. The maximum runup predicted by the nonlinear theory is larger than that predicted earlier and the correction is on the order of the offshore relative wave height for a given slope. This correction for nonbreaking waves on beaches decreases as the beach slope steepens.