On the evolution and runup of a train of solitary waves on a uniform beach

In this paper the runup of a train of successive solitary waves is studied. Using a wavemaker with 5-m stroke, a series of evenly-spaced solitary waves, up to nine, is generated in a wave flume. These solitary waves shoal and run up on a 1 on 10 slope. The nonlinearity parameter, i.e., the wave height to water depth ratio, ranges between 0.11 and 0.39. The experimental data show that the runup heights of successive solitary waves reach an asymptotic value after the fourth wave in all cases studied. Depending on the nonlinearity, the runup characteristics can be categorized as either weakly or strongly interacting cases. For the former the runup heights of the successive waves are almost identical to that of a single solitary wave. For the latter, the asymptotic runup value is always lower than that of the first wave. Using the experimental data, two- and three-dimensional Reynolds-Averaged Navier-Stokes equations models are first validated with a high degree of accordance. Additional numerical simulations are performed to extend the experimental database and investigate effects of beach slopes and higher wave nonlinearity values. Finally, using both numerical results and the laboratory data, the unified empirical runup formula for single breaking solitary waves and breaking periodic waves is found applicable to obtain the maximum runup height of successive solitary waves.