Experiments on nonlinear instabilities and evolution of steep gravity-wave trains

Abstract

A series of experiments on strong nonlinear instabilities of gravity-wave trains of large steepness 0·25 ≤ ak ≤ 0·34 in deep water in a long tow tank and a wide basin were performed. These experiments clarified several phenomena such as subharmonic instabilities, wave breaking, evolution of power spectra and directional energy spreading. It was found that an initial two-dimensional wavetrain of large steepness evolved into a series of three-dimensional spilling breakers, and was followed by a transition to a two-dimensional modulated wave train during which a series of oblique wave groups were radiated. The final stage of evolution was a series of modulated, two-dimensional wave groups with lower steepness and frequency. The three most frequent normal modes of two-dimensional subharmonic instabilities underlying the frequency downshifting, in the order of their relative occurrence, are found to be about 4/3, 5/4 and 3/2 in terms of the ratio of the fundamental to perturbed wave frequencies. The Bimescale for the phenomenon of the frequency downshifting is from 40 to 60 fundamental wave periods. Comparisons of the experimental results with existing theories showed that observed processes have several qualitative similarities with theoretical computations.