Turbulence of capillary waves forced by steep gravity waves

Abstract

We study experimentally the dynamics and statistics of capillary waves forced by random steep gravity waves mechanically generated in laboratory. Capillary waves are produced here by gravity waves from nonlinear wave interactions. Using a spatio-temporal measurement of the free-surface, we characterize statistically the random regimes of capillary waves in the spatial and temporal Fourier spaces. For a significant wave steepness (0.2 − 0.3), power-law spectra are observed both in space and time, defining a turbulent regime of capillary waves transferring energy from large scale to small scale. Analysis of temporal fluctuations of spatial spectrum demonstrates that the capillary powerlaw spectra result from the temporal averaging over intermittent and strong nonlinear events transferring energy to small scale in a fast time scale, when capillary wave trains are generated in a way similar to the parasitic capillary wave generation mechanism. The frequency and wavenumber power-law exponents of wave spectrum are found to be in agreement with those of the weakly nonlinear Wave Turbulence Theory. However, the energy flux is not constant through the scales and the wave spectrum scaling with this flux is not in good agreement with Wave Turbulence Theory. These results suggest that theoretical developments beyond the classic Wave Turbulence Theory are necessary to describe the dynamics and statistics of capillary waves in natural environment. In particular, in presence of broad scale viscous dissipation and strong nonlinearity, the role of non-local and non-resonant interactions could be reconsidered. † An example of the free-surface reconstruction is depicted in Fig. 2 (a) for the highest forcing amplitude σ h = 3.6 mm at t = 1.51 s. In this example, a large gravity wave

Capillary wave turbulence experiments in microgravity

“…8 shows that this effective energy flux increases with the wave steepness. The values of ef f are comparable with the estimations from the dissipated power by viscosity, which were obtained in a previous capillary wave turbulence experiment in a non weakly nonlinear regime [9]. From the scaling of the three-wave interaction collision integral, for a given value of the energy flux a critical wave-number can be defined k N L ≈ 2/3 (γ/ρ) −1 [30,31].…”

Confinement effects on gravity-capillary wave turbulence

“…clearest) correspond most likely to the strong regime identified by Cobelli et al [36] in which coherent structures are present as discussed by Berhanu et al [37]. Here we keep the steepness of the waves very low and, as previously reported in [10], no power law decay is observed.…”

Experiments in Surface Gravity–Capillary Wave Turbulence

“…, near the gravity-capillary transition) where the dynamics is expected to be dominated by strongly nonlinear structures (white caps, sharp-crested waves) (Newell & Zakharov 1992, Connaughton et al 2003 or by nonlocal interactions, such as parasitic capillary wave generation (Fedorov et al 1998), as evidenced experimentally by the occurence of stochastic energy bursts transferring wave energy nonlocally from gravity waves to all capillary spatial scales quasi-instantaneously (Berhanu & Falcon 2013, Berhanu et al 2018). However, no such transition from a weak turbulence spectrum to a strong turbulence spectrum (Phillips' spectrum) at high wave numbers has been reported experimentally so far.…”

“…Experimentally, the cascading energy flux P can be indirectly measured (see Section 7.2) and is found to be more than one order of magnitude smaller than the critical flux P b (Deike et al 2015, Cazaubiel et al 2019b). The value of τ nl can be measured with a local probe by decaying wave turbulence experiments either in the gravity regime (Bedard et al 2013, Deike et al 2015 or in the gravity-capillary regime (Cazaubiel et al 2019b), and by the broadening of the dispersion relation in stationary experiments using space-time measurements (Herbert et al 2010, Berhanu et al 2018). In the latter case, the width of the energy concentration around the dispersion relation can be quantified either in frequency space by δω ∝ 1/τ nl or in wavenumber space by δk ∝ ∂k ∂ω δω.…”