Novel similarities in the free-surface profiles and velocities of solitary waves traveling over a very steep beach

This study investigates experimentally similarity and Froude number similitude (FNS) in the dimensionless flow features of three solitary waves traveling on a 1:3 sloping beach. These three waves, designated as cases A, B, and C, respectively, have different heights H0 (=5.8 cm, 2.9 cm, and 1.815 cm) and still water depths h0 (=16.0 cm, 8.0 cm, and 5.0 cm), but identical ratios H0/h0 (=0.363). A high-speed particle image velocimetry system is employed to obtain the free surface profiles (FSPs) and velocity fields/profiles. These features include the free surface elevation (FSE)/FSP time series; velocity fields and profiles, positions, and propagation speeds of flow demarcation curves; times and maximum onshore distances of the maximum run-up heights (MRHs); and times and onshore distances of hydraulic jumps for cases A and B. When the swash tip of a solitary wave reaches the MRH, the contact point becomes almost immobile for a short time interval, with the contact angle changing from obtuse, via right, to acute angle. For cases A and B, the similarities in the dimensionless MRHs and times, at which the run-down motions of the wave tips start, are affirmed. These facts highlight that the swash tips and contact points are subject to complex interactions among gravity force, viscous friction, and surface tension of fluid. Case C, having the smallest length scale, is only focused on the arrival or starting time of the MRH or run-down motion and the MRH and used as a counterexample to demonstrate the absence of similarity or FNS due to the relatively prominent effects of viscous friction and surface tension.