Abstract
We present experimental results on simultaneous space–time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that the both wavenumber and frequency spectra are not universal and dependent on the wave strength, with some evidence in favour of the WTT at larger wave intensities when the finite-flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (p.d.f.) and the structure functions (SFs). Analysing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-Gaussian p.d.f. core and the low-order SFs and the latter in the p.d.f. tails and the high-order SFs. It appears that the x-space signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than the t-space SFs do. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.
Highlights
Understanding statistics of random water surface waves and their mutual nonlinear interaction mechanisms is important for wave forecasting and weather and climate modelling
The random waves are captured by the p.d.f. cores and the low-order structure functions (SFs), whereas the coherent wave crests leave their imprints on the p.d.f. tails and on the high-order SFs
The singular wave crests themselves consist of structures of different shapes, namely numerous non-propagating spikes/splashes and propagating Kuznetsov-type breaks
Summary
Understanding statistics of random water surface waves and their mutual nonlinear interaction mechanisms is important for wave forecasting and weather and climate modelling (see for example Janssen 2004). Since the seldom breaking events are strongly nonlinear, one cannot use the linear dispersion relation for understanding their statistics, and a direct x-space measurement is desirable With these motivations in mind, in the present work we have implemented a new technique for direct one-dimensional measuring of instantaneous surface profiles (see the details below). We are able to measure the k-spectra directly, as well as the higher-order x-space statistics averaged over a discrete set of instants of time, the probability density functions (p.d.f.s) and structure functions (SFs) of the height increments in space This can be done at different levels of wave forcing, but we have excluded the range of very weak forcing for which the finite-flume-size effects were shown to be significant.
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