Laboratory observations of wave group evolution, including breaking effects

Abstract

The nonlinear evolution of deep-water wave groups, which are initiated by unstable three-wave systems, have been observed in a large wave tank (50 m long, 4.2 m wide, 2.1 m deep), equipped with a programmable, high-resolution wave generator. A large number of experiments were conducted (over 80 cases) for waves 1.0–4.0 m long, initial steepness ε=0.10–0.28, and normalized sideband frequency differences, δω=δω, 0.2–1.4. Using an array of eight high-resolution wave wires distributed in range (up to 43 m fetch), spectral evolution was studied in detail including the effect of background disturbances on the evolution. Minimizing those, new observations were made which extend the pioneering work of Lake et al. (1977) and of Melville (1982). Foremost, near recurrence without downshifting was observed without breaking, despite a significant but reversible energy transfer to the lower sideband at peak modulation; complete recurrence was prevented by the spreading of discretized energy to higher frequencies. Strong breaking was found to increase the transfer of energy from the higher to the lower sideband and to render that transfer irreversible. The end state of the evolution following strong breaking is an effective downshifting of the spectral energy, where the lower and the carrier wave amplitudes nearly coincide; the further evolution of this almost two-wave system was not studied here. Breaking during strong modulation was observed not only for the fastest growing initial condition, but over a wide parameter range. An explanation of the sideband behaviour in both the breaking and non-breaking case was given based on wave energy and momentum considerations, including the separate effects of energy and momentum loss due to breaking, and transfer to discretized higher frequencies throughout the spectra. Attention was drawn to the latter, which was almost universally observed.