The overtaking interaction of the double solitary waves over a plane slope is studied experimentally. The slope of the plane beach is 1:20. For the cases of the double solitary waves of different amplitude ratios and different relative wave crest distances, the time series of the surface elevation and waterline movement are measured by wave gauges and recorded by high speed cameras respectively. Three categories of overtaking solitary wave interactions are reproduced in the wave flume. It is found that the maximum runup amplification coefficient of the double solitary waves is dependent of the relative distance between two initial peaks of the double solitary waves. Breaking of solitary waves plays an important role in damping the wave energy and then changing the maximum runup of the double solitary waves.
It has been a traditional subject to understand the runup of the long wave propagating over a constant depth region and then climbing up a sloping beach of constant slope because of importance of predicting tsunami runup on beaches. Based on the assumption that solitary waves can be used to model some characteristics of the propagation of tsunamis from offshore to beach, much work on physical and mathematical models of propagation and runup of a single solitary wave on the beach has been done, particularly at the W.M. Keck Lab of Hydraulic and Water Resources, California Institute of Technology. Hammack (1972) implemented experimentally the generation of tsunamis in a flume of uniform depth by an impulsively raised or lowered portion of the bottom. Goring (1978) proposed the solitary wave generation method for a wave flume with a piston type wavemaker and presented the experimental and numerical studies on the solitary wave propagating from a water layer of constant depth to the continental shelf. Synolakis (1987) proposed an analytical solution of the solitary wave propagation and runup to the shallow water equations and presented the characteristics of runup of breaking and non-breaking solitary waves. Li & Raichlen (2001) proposed a nonlinear solution to the nonlinear shallow water equations by using a hodograph transformation and reported an experimental study on runup of nonbreaking and breaking solitary wave. Madsen et al (2008) discussed, considering the effects of geophysical scales on wave propagations, the possibility of solitary wave generation in an ocean and presented the numerical results of disintegration of a long wave into an undular bore. Using the Boussinesq model, Baba et al.(2015) presented numerical simulations of the undular bore generation for 2011 Tohoku tsunami event, which shows that there are several solitary waves riding on a long leading wave front in Sendai shallow coastal region. Zhao et al (2016) studied numerically the generation of undular bores and soliton fission for the long waves propagating on the gentle continental shelves in both the East China Sea and the South China Sea.
