The statistical properties of turbulence differ in an essential way from those of systems in or near thermal equilibrium because of the flux of energy between vastly different scales at which energy is supplied and at which it is dissipated. We elucidate this difference by studying experimentally and numerically the fluctuations of the energy of a small fluid particle moving in a turbulent fluid. We demonstrate how the fundamental property of detailed balance is broken, so that the probabilities of forward and backward transitions are not equal for turbulence. In physical terms, we found that in a large set of flow configurations, fluid elements decelerate faster than accelerate, a feature known all too well from driving in dense traffic. The statistical signature of rare "flight-crash" events, associated with fast particle deceleration, provides a way to quantify irreversibility in a turbulent flow. Namely, we find that the third moment of the power fluctuations along a trajectory, nondimensionalized by the energy flux, displays a remarkable power law as a function of the Reynolds number, both in two and in three spatial dimensions. This establishes a relation between the irreversibility of the system and the range of active scales. We speculate that the breakdown of the detailed balance characterized here is a general feature of other systems very far from equilibrium, displaying a wide range of spatial scales. I n systems at thermal equilibrium, the probabilities of forward and backward transitions between any two states are equal, a property known as "detailed balance." This fundamental property expresses time reversibility of equilibrium statistics (1). In the important class of nonequilibrium problems, where the dynamics of the system is coupled with a heat bath, the notion of detailed balance can be extended and fluctuation theorems successfully describe the behavior (2, 3). This class contains many experimental situations (4) where quantitative information on irreversibility was obtained (3). When a system driven by thermal noise is characterized by a probability current, the fluctuationdissipation theorem and detailed balance was found to apply in a comoving reference frame (5).In comparison, very little is known concerning the statistical properties of a small part embedded in a fluctuating, turbulent background. The fundamental notion of detailed balance is not expected to apply in such systems. Here we ask, what does the time irreversibility inherent to the large system imply for the statistical properties of small parts in the system and how do we measure the degree of irreversibility (6, 7) (or equivalently, how far is the system away from equilibrium) by monitoring a small part in the system? We focus here on fluid turbulence, a paradigm for ultimate far-from-equilibrium states, where irreversibility of fluctuations is a fundamental property (8, 9). We show that the simplest and most fundamental scalar quantity, namely, the kinetic energy of a fluid particle, enables a clear identification and qua...

Popular summary:Parametrically excited waves are a ubiquitous phenomenon observed in a variety of physical contexts. They span from Faraday waves on the water surface to spin waves in magnetics, electrostatic waves in plasma and second sound waves in liquid helium. Parametrically excited Faraday waves on the surface of vertically vibrated liquids quickly become nonlinear. In dissipative liquids, or in granular media, these nonlinear waves form regular lattices of oscillating solitons (oscillons), resembling in some aspects 2D crystals. If the vertical acceleration is increased, the oscillons do not solely grow in amplitude, their horizontal mobility is also greatly enhanced, and ultimately the lattice melts and becomes disordered. Until recently, the physics of these self-organized waves and their transition to disorder have been studied almost exclusively based on the analysis of the wave motion rather than the motion of their constitutive components, whether they are solid grains or fluid particles.It has recently been discovered that the fluid motion on a liquid surface perturbed by Faraday waves reproduces in detail the statistics of two-dimensional turbulence. This unexpected discovery shifts the current paradigm of order to disorder transition in this system: instead of considering complex wave fields, or wave turbulence, it is conceivable that the 2D Navier-Stokes turbulence, generated by Faraday waves, feedbacks on the wave crystal and disorders it in a statistically predictable fashion. To date, the very mechanism behind the turbulence generation in such waves remains unknown. A better understanding of this phenomenon is important for a wide spectrum of physics applications involving parametric waves.In this paper, we visualize 3D trajectories of floating tracers and reveal that the fluid particles motion injects 2D vortices into the horizontal flow. This is an unexpected and new paradigm for vorticity creation in a 2D flow. The horizontal energy is then spread over the broad range of scales by the turbulent inverse energy cascade. Two-dimensional turbulence destroys the geometrical order of the underlying lattice. The crystal order, however, can be restored by increasing * Nicolas.Francois@anu.edu.au viscous dissipation in the fluid which hinders vorticity creation and thus the development of turbulence. Abstract:We study the generation of 2D turbulence in Faraday waves by investigating the creation of spatially periodic vortices in this system. Measurements which couple a diffusing light imaging technique and particle tracking algorithms allow the simultaneous observation of the threedimensional fluid motion and of the temporal changes in the wave field topography.Quasi-standing waves are found to coexist with a spatially extended fluid transport. More specifically, the destruction of regular patterns of oscillons coincides with the emergence of a complex fluid motion whose statistics are similar to that of two-dimensional turbulence. We reveal that a lattice of oscillons generates vorticity at the osc...

We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional, but its horizontal velocity fluctuations show unexpected similarity with two-dimensional turbulence. The inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity, and it is confirmed by computing the third moment of the horizontal velocity fluctuations. This is observed in deep water in a broad range of wavelengths and vertical accelerations. The results broaden the scope of recent findings on Faraday waves in thin layers [A. von Kameke et al., Phys. Rev. Lett. 107, 074502 (2011)].

Transport of mass, heat and momentum in turbulent flows by far exceeds that in stable laminar fluid motions. As turbulence is a state of a flow dominated by a hierarchy of scales, it is not clear which of these scales mostly affects particle dispersion. Also, it is not uncommon that turbulence coexists with coherent vortices. Here we report on Lagrangian statistics in laboratory two-dimensional turbulence. Our results provide direct experimental evidence that fluid particle dispersion is determined by a single measurable Lagrangian scale related to the forcing scale. These experiments offer a new way of predicting dispersion in turbulent flows in which one of the low energy scales possesses temporal coherency. The results are applicable to oceanographic and atmospheric data, such as those obtained from trajectories of freedrifting instruments in the ocean.

The control of matter motion at liquid–gas interfaces opens an opportunity to create two-dimensional materials with remotely tunable properties. In analogy with optical lattices used in ultra-cold atom physics, such materials can be created by a wave field capable of dynamically guiding matter into periodic spatial structures. Here we show experimentally that such structures can be realized at the macroscopic scale on a liquid surface by using rotating waves. The wave angular momentum is transferred to floating micro-particles, guiding them along closed trajectories. These orbits form stable spatially periodic patterns, the unit cells of a two-dimensional wave-based material. Such dynamic patterns, a mirror image of the concept of metamaterials, are scalable and biocompatible. They can be used in assembly applications, conversion of wave energy into mean two-dimensional flows and for organising motion of active swimmers.