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

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 both wavenumber and the frequency spectra are not universal and dependent on the wave strength, with some evidence in favor of 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 (PDF) and the structure functions (SFs). Analyzing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-gaussian PDF core and in the low-order SFs, and the latter -in the PDF tails and the high-order SF's. It appears that the xspace signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than do the t-space SFs. 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.

Intermittency in integrable turbulence

“…Implementing an optical filtering technique, we also examine the statistics of intensity of light fluctuations on different scales and we observe that the PDFs show heavy tails that strongly depend on the scales. This reveals an unexpected phenomenon of intermittency that is similar to the one reported in several other wave systems, though they are fundamentally far from being described by an integrable wave equation [30,[32][33][34][35].…”

“…We stress here that the deviations from Gaussianity reported in Fig. 3 can be related, in a more general way, to several observations of the intermittency phenomenon previously made in wave turbulence [30,32,33], solar wind [34], or in the Faraday experiment [35]. However, it must be emphasized that all previous works have investigated wave systems that are far from being integrable.…”

“…The intermittency phenomenon is usually evidenced by using spectral filtering methods and by showing the existence of deviations from Gaussianity through the measurement of the kurtosis of fluctuations that are found at the output of some frequency filter. Spectral fluctuations can be examined at the output of an ideal one-mode spectral filter passing only a single Fourier component [12,30]. Time fluctuations at the output of ideal high-pass or bandpass frequency filters can also be considered [29,31].…”

“…PDFs of second-order differences of the wave height have also been measured in wave turbulence [32]. Using this kind of technique, the phenomenon of intermittency has been initially reported in fully developed turbulence [29], but it is also known to occur in wave turbulence [30,32,33], solar wind [34], or in the Faraday experiment [35].…”

Nonlocal Resonances in Weak Turbulence of Gravity-Capillary Waves

“…Laboratory experiments largely fail to reproduce this predictions, in particular for the gravity waves. In large or small waves tanks, the spectral exponent of the gravity waves is seen to vary strongly with the forcing intensity and to be close to the WTT predictions at the highest forcing magnitude, at odds with the weak nonlinearity hypothesis [9,10]. Furthermore the measurement of the exponent of the injected power is also different from that predicted by WTT [10].…”