An Experimental Study of Runup of Several Successive Solitary Waves of Same Wave Height on Slope

Rong, Yiyi (Shanghai Jiao Tong University) | Wu, Wei (Shanghai Jiao Tong University) | Liu, Hua (Shanghai Jiao Tong University)

OnePetro 

Abstract

Runup of a train of three successive solitary waves on a mild slope is investigated experimentally. The modified Goring’s method and the third order solution of solitary wave are used to generate two or three solitary waves by a piston type wave maker of long stroke. It is first reported that the runup amplification coefficients of the following solitary waves are smaller than that of the leading solitary wave for the triple solitary waves while the runup amplification coefficient of the third wave is greater than that of the second wave. The mechanism of the variations of the runup amplification coefficients of all waves in the successive solitary wave train is that the down rush flows of the leading wave causes breaking of the following wave during runup.

INTRODUCTION

Runup of tsunami on a beach is an important subject to evaluate inundation risk on coastal regions. Due to moving waterline on a beach and breaking of waves, it has been one of most challenging problems in nonlinear water wave dynamics associated with coastal engineering. Much work has been done on theoretical analysis, numerical simulation and experimental measurement on runup of a single solitary wave on beaches. Synolakis (1987) developed an analytical solution for nonbreaking waves on a plane beach based on the nonlinear shallow water equation. Li & Raichlen (2001) proposed a nonlinear solution to the classical shallow water equation by using a hodograph transformation and reported an experimental study on runup process of nonbreaking and breaking solitary wave. Fuhrman and Madsen (2008) proposed the reduced surf similarity parameter for solitary waves, the beach slope divided by the offshore wave height to depth ratio, which provides good coherency with experimental breaking and runup data and analytical nonbreaking runup expressions. The full nonlinear and highly dispersive Boussinesq equations were used by Zhao et al.(2012) to investigate the evolution and run-up of solitary waves and N-waves on plane beaches Zhao et al.(2013) carried out numerical simulation of tsunami waves propagating on the continental shelf with an extremely gentle slope. The numerical results show that the N-shape tsunami wave could evolve into a train of periodic waves, undular bores or solitons when it propagates from deep water to shallow water over a long plane beach of gentle slope. Firstly, experiments on runup of two successive solitary waves with same amplitude on a plane beach were carried out by Lo et al. (2013) and Pujala et al. (2015). Xuan et al. (2013) implemented the generation and runp of two successive solitary waves with different wave amplitudes in a wave flume. Even though much work has been done about the overtaking or head-on collision of two solitary waves theoretically, particularly at the multi-solitary wave solution of the KdV equation, there is little work on runup of three or more solitary waves on a beach.