We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop exponential tails. For the first time we present evidence of strong four-wave coupling in nonlinear waves (high tricoherence), which points to modulation instability as the main mechanism in rogue waves. The generation of rogue waves is identified as the onset of a distinct tail in the probability density function of the wave heights. Their probability is higher than expected from the measured wave background.

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We present experimental results on the properties of bounded turbulence in thin fluid layers. In contrast with the theory of two-dimensional ͑2D͒ turbulence, the effects of the bottom friction and of the spectral condensation of the turbulence energy are important in our experiment. Here we investigate how these two factors affect statistical moments of turbulent fluctuations. The inverse energy cascade in a bounded turbulent quasi-2D flow leads to the formation of a large coherent vortex ͑condensate͒ fed by turbulence. This vortex, depending on its strength, can substantially affect the turbulence statistics, even at small scales. Up to the intermediate strength of the condensate, the velocity moments similar to those in isotropic 2D turbulence are recovered by subtracting the coherent component from the velocity fields. A strong condensate leaves a footprint on the underlying turbulence; it generates stronger non-Gaussianity and reduces the efficiency of the inverse energy cascade. Remarkably, the energy flux in the cascade derived from the third-order structure function using the Kolmogorov flux relation gives physically meaningful values in a broad range of experimental parameters regardless of the condensate strength. This result has important implications for the analysis of the atmospheric wind data in upper troposphere and lower stratosphere.

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...

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