On the origin of intermittency in wave turbulence

Abstract

Abstract. -Using standard signal processing tools, we experimentally report that intermittency of wave turbulence on the surface of a fluid occurs even when two typical large-scale coherent structures (gravity wave breakings and bursts of capillary waves on steep gravity waves) are not taken into account. We also show that intermittency depends on the power injected into the waves. The dependence of the power-law exponent of the gravity-wave spectrum on the forcing amplitude cannot be also ascribed to these coherent structures. Statistics of these both events are studied.Understanding the origin of intermittency is a challenging problem in varied domains involving turbulent flows. Intermittency is the occurrence of bursts of intense motion within more quiescent fluid flow [1,2]. This leads to strong deviations from Gaussian statistics that become larger and larger when considering fluctuations at smaller and smaller scales. In three-dimensional hydrodynamic turbulence, the origin of these deviations has been ascribed to the formation of coherent structures (strong vortices) since the 50's [1]. However, the physical mechanism of intermittency is still an open question [3]. Intermittency has also been observed in granular systems [4], in magnetohydrodynamic turbulence in geophysics [5] or in the solar wind [6], and in systems involving transport by a turbulent flow [7]. A recent observation of intermittency has been reported in wave turbulence [8], a system that strongly differs from high Reynolds number hydrodynamic turbulence. It could thus motivate explanations of intermittency different than the ones considering the dynamics of the Navier-Stokes equation.The aim of this Letter is to investigate if some coherent structures are responsible of intermittency in wave turbulence. In the case of wave turbulence on a surface of a fluid, coherent structures such as bursts of capillary waves on steep gravity waves [9] and wave breakings [10] are wellknown phenomena, these latters being recently taken into account in numerical simulations [11]. Wave breakings (a)

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.…”

“…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].…”

Role of the basin boundary conditions in gravity wave turbulence

“…However, this does not explain the spectrum exponent dependence on the forcing in both cases (see figure 7). It has been shown previously that removing such coherent structures from the wave amplitude signal leads to a gravity spectrum exponent that still depends on the forcing but with less variation, of the order of 25 % (Falcon et al 2010b). Using a similar criterion to define the occurrence of wave breaking events (time intervals where the wave acceleration is greater than six times its standard deviation), we compute the spectrum of the wave signal not including wave breakings.…”

“…In the same way, when these wave slope divergences are assumed to be isolated peaks or cusps (D = 0) distributed isotropically and propagating as ω = √ gk, the f −5 Phillips' spectrum is found again. Experimentally, it has been shown that intermittency occurs in gravity wave turbulence (Falcon, Fauve & Laroche 2007a;Nazarenko et al 2010), and is enhanced by coherent structures such as breaking waves (Falcon, Roux & Laroche 2010b). Third, strongly nonlinear waves involved in laboratory experiments may lead to non-local interactions in k-space, dissipation at all scales of the cascade (energy flux not conserved), and no scale separation between linear, nonlinear and dissipating time scales, unlike weak turbulence hypotheses.…”