On the origin of intermittency in wave turbulence

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)Corresponding author: [email protected] also occur in plasma waves, internal waves, and Rossby waves in geophysics. It has been suggested that intermittency in wave turbulence may be connected to wave structures (such as cusps, whitecaps or wave breakings) thus motivating theoretical [12] and numerical [13] works. Here, we show experimentally that intermittency does not come from wave breakings and capillary bursts on gravity waves. Using standard signal processing tools, one finds criteria to detect such structures that allow us to study their statistics and their possible role in the origin of intermittency. We also show that intermittency depends on the power injected into the waves. The frequency-power law of the gravity-wave spectrum is known to depend on the forcing parameters [14]. We show that this dependence is not related to these coherent structures. The experimental setup has been described previously [14]. It consists of a square vessel, 20 × 20 cm filled with mercury up to a height of 2.6 cm. Similar results are found with water. Surface waves are generated by the horizontal motion of a rectangular plunging plastic wave maker driven by an electromagnetic exciter. This vibration exciter is driven with a random forcing within a narrow low-frequency range (typically 0.1 to 5 Hz), and a rms voltage amplitude σU from 0.1 to 0.8 V leading to wave mean steepnesses (ratio of crest-to-trough amplitude to its duration) from 1 up to 4 cm/s. The rms value σV of the velocity fluctuations of the wave maker is proportional to σU . The mean power injected 〈I〉 into the fluid scales