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.

A NEW VIEW OF NONLINEAR WATER WAVES: The Hilbert Spectrum

“…In numerous controlled experiments (Lake et al 1977;Lake & Yuen 1978;Melville 1982;Su et al 1982;Chereskin & Mollo-Christensen 1985;and Huang et al 1996) the main frequency is seen to shift to a lower frequency, a downshift. This innocent phenomenon presents a serious conflict with wave theory.…”

Three-Dimensional Wave Focusing in Fully Nonlinear Wave Models

“…McLean (1982) theoretically predicted a type of wave instability (called type II), which is predominantly 3D, while BF (called type I) is only 2D. Su et al (1982) experimentally con rmed this prediction by showing how a steep 2D wave train can evolve i n to 3D spilling breakers.…”

On hexagonal gravity water waves

“…In conclusion we note that these wave shapes are only a few among a large number of interesting configurations that can be computed using our approach. In fact, it is the goal of a forthcoming publication [25] to generate and analyze traveling wave solutions in three dimensions that have unsymmetric hexagonal, unsymmetric crescent, and symmetric crescent shapes (please see [16,30,35]). We will present studies of hexagonal wave patterns, crescent-shaped wave patterns in resonant regimes, and model calculations of the skew wave patterns observed by Su [35].…”

“…In the present paper we study genuinely three-dimensional waves which progress steadily without change of form (traveling waves). In particular, our goal has been to model and explain the traveling patterns noticed in the experimental work of Su [35], Su et al [30], and Hammack et al [19,20]. Bryant [9,10], Saffman and Yuen [36,37], and Meiron et al [24] have all calculated waves using a Fourier approach.…”