An experimental study of steep solitary wave reflection at a vertical wall

Abstract

Until now very few experimental investigations have been conducted to study the reflection of steep solitary waves at a vertical wall whereas many theoretical analyses and numerical simulations have been developed in the past. The use of experimental techniques to capture the waveform and associated phenomena during the short-time head-on collision of two solitary waves (or the reflection of a solitary wave by a vertical wall) is not an easy task. Solitary waves with amplitude a/h≤0.556 are experimentally generated by a piston type wavemaker. We have used a high speed camera and our experimental results were compared with previous studies, including both theoretical investigations and numerical simulations.Experimental values of attachment and detachment times, wall residence time, maximum run-up time and phase shift due to reflection at the wall as a function of solitary wave amplitude are new results. In addition, we found that previous theoretical results underestimate wave run-up characteristics (maximal run-up amplitude, attachment and detachment times, wall residence time), except the third-order result of Su and Mirie (1980) who calculated maximal run-up which is in good agreement with experiments. Within the range of solitary wave amplitude considered experimentally, present measurements are in excellent agreement with numerical results of Cooker et al. (1997) and Chambarel et al. (2009).For very steep solitary waves we found numerically the occurrence of a Rayleigh–Taylor instability on the top of the jet due to the head-on collision. A theoretical proof of the existence of this instability is given. Furthermore, the occurrence of this instability is corroborated by numerical computations of the vertical gradient of underwater pressure during the collision of the solitary waves.