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.

Wave modelling – The state of the art

“…Another example: at WISE-12 mentioned above, Donelan and Meza in two separate papers presented dissipation functions responsible for the spectral peak downshift. Such a feature does not appear in dissipation functions presently in use, but is consistent with laboratory experiments of Tulin and Waseda (1999).…”

Freak Waves in Random Oceanic Sea States

“…The instability causes a local exponential growth in the amplitude of the wave train. This result is established from a linear stability analysis of the NLS equation [8] and has been confirmed, for small values of the steepness, by numerical simulations of the fully nonlinear water wave equations [5,6] (for high values of steepness wave breaking, which is clearly not included in the NLS model, can occur). Moreover, it is known that small-amplitude instabilities are but a particular case of the much more complicated and general analytical solutions of the NLS equation obtained by exploiting its integrability properties via Inverse Scattering theory in the θ-function representation [11,12].…”

“…Furthermore, the focus herein is not to attempt to model ocean waves but instead to study leading order effects using the nonlinear Schroedinger equation, as suggested by [3][4][5]. Research at higher order suggests that the results given herein are indicative of many physical phenomena in the primitive equations [5,6].In this Letter our attention is focused on freak wave generation in numerical simulations of the NLS equation where we assume initial conditions typical of oceanic sea states described by the JONSWAP power spectrum (see, e.g. [13]):…”

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

“…Higher side band modes have also prevailed energy loss during wave breaking (Tulin and Waseda, 1999). That is why we hope that our simplified model still has potentiality to adequately describe some prominent features of wave dynamics on the adverse current.…”

“…This is the temporary frequency downshift phenomenon. In systematic well-controlled experiments, Tulin and Waseda (1999) analyzed the effect of wave breaking on downshifting, highfrequency discretized energy, and the generation of continuous spectra. Experimental data clearly show that the active breaking process increases the permanent frequency downshift in the latter stages of wave propagation.…”