Statistics of surface gravity wave turbulence in the space and time domains

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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.
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