A Langevin equation for the energy cascade in fully-developed turbulence

Experimental data from a turbulent jet flow is analysed in terms of an additive, continuous stochastic process where the usual time variable is replaced by the scale. We show that the energy transfer through scales is well described by a linear Langevin equation, and discuss the statistical properties of the corresponding random force in detail. We find that the autocorrelation function of the random force decays rapidly: the process is therefore Markov for scales larger than Kolmogorov's dissipation scale $\eta$. The corresponding autocorrelation scale is identified as the elementary step of the energy cascade. However, the probability distribution function of the random force is both non-Gaussian and weakly scale-dependent.Comment: 25 pages, 10 figures, elsart.sty, to be published in Physica

Experimental study of energy transport between two granular gas thermostats

We report on the energy transport between two coupled probes in contact with granular thermostats at different temperatures. In our experiment, two identical blades, which are electromechanically coupled, are immersed in two granular gases maintained in different non-equilibrium stationary states, characterized by different temperatures. First, we show that the energy flux from one probe to another is, in temporal average, proportional to the temperature difference, as in the case of equilibrium thermostats. Second, we observe that the instantaneous flux is highly intermittent and that fluctuations exhibit an asymmetry which increases with the temperature difference. Interestingly, this asymmetry, related to irreversibility, is correctly accounted for by a relation strongly evoking the Fluctuation Theorem. As is, our experiment is a simple macroscopic realisation, suitable for the study of energy exchanges between systems in non-equilibrium steady states

The Hatano-Sasa equality: transitions between steady states in a granular gas

An experimental study is presented, about transitions between Non-Equilibrium Steady States (NESS) in a dissipative medium. The core device is a small rotating blade that imposes cycles of increasing and decreasing forcings to a granular gas, shaken independently. The velocity of this blade is measured, subject to the transitions imposed by the periodic torque variation. The Hatano-Sasa equality, that generalises the second principle of thermodynamics to NESS, is verified with a high accuracy (a few $10^{-3}$), at different variation rates. Besides, it is observed that the fluctuating velocity at fixed forcing follows a generalised Gumbel distribution. A rough evaluation of the mean free path in the granular gas suggests that it might be a correlated system, at least partially

On the heat flux and entropy produced by thermal fluctuations

We report an experimental and theoretical analysis of the energy exchanged between two conductors kept at different temperature and coupled by the electric thermal noise. Experimentally we determine, as functions of the temperature difference, the heat flux, the out-of- equilibrium variance and a conservation law for the fluctuating entropy, which we justify theoretically. The system is ruled by the same equations of two Brownian particles kept at different temperatures and coupled by an elastic force. Our results set strong constrains on the energy exchanged between coupled nano-systems kept at different temperature.

Statistical properties of the energy exchanged between two heat baths coupled by thermal fluctuations

We study both experimentally and theoretically the statistical properties of the energy exchanged between two electrical conductors, kept at different temperature by two different heat reservoirs, and coupled by the electric thermal noise. Such a system is ruled by the same equations as two Brownian particles kept at different temperatures and coupled by an elastic force. We measure the heat flowing between the two reservoirs, the thermodynamic work done by one part of the system on the other, and we show that these quantities exhibit a long time fluctuation theorem. Furthermore, we evaluate the fluctuating entropy, which satisfies a conservation law. These experimental results are fully justified by the theoretically analysis. Our results give more insight into the energy transfer in the famous Feymann ratchet widely studied theoretically but never in an experiment.Comment: arXiv admin note: substantial text overlap with arXiv:1301.431

Fluctuation-dissipation relation on a Melde string in a turbulent flow, considerations on a "dynamical temperature"

3,5 new printed pagesWe report on measurements of the transverse fluctuations of a string in a turbulent air jet flow. Harmonic modes are excited by the fluctuating drag force, at different wave-numbers. This simple mechanical probe makes it possible to measure excitations of the flow at specific scales, averaged over space and time: it is a scale-resolved, global measurement. We also measure the dissipation associated to the string motion, and we consider the ratio of the fluctuations over dissipation (FDR). In an exploratory approach, we investigate the concept of {\it effective temperature} defined through the FDR. We compare our observations with other definitions of temperature in turbulence. From the theory of Kolmogorov ($1941$), we derive the exponent $-11/3$ expected for the spectrum of the fluctuations. This simple model and our experimental results are in good agreement, over the range of wave-numbers, and Reynolds number accessible ($74000 \leq Re \leq 170000$)

Low frequency spectra of bending wave turbulence

We study experimentally the dynamics of long waves among turbulent bending waves in a thin elastic plate set into vibration by a monochromatic forcing at a frequency $f_0$. This frequency is chosen large compared with the characteristic frequencies of bending waves. As a consequence, a range of conservative scales, without energy flux in average, exists for frequencies $f<f_0$. Within this range, we report a flat power density spectrum for the orthogonal velocity, corresponding to energy equipartition between modes. Thus, the average energy per mode $\beta^{-1}$ -- analogous to a temperature -- fully characterizes the large-scale turbulent wave field. We present an expression for $\beta$ as a function of the forcing frequency and amplitude, and of the plate characteristics

Simultaneous and accurate measurement of the dielectric constant at many frequencies spanning a wide range

We present an innovative technique which allows the simultaneous measurement of the dielectric constant of a material at many frequencies, spanning a four orders of magnitude range chosen between 10 --2 Hz and 10 4 Hz. The sensitivity and accuracy are comparable to those obtained using standard single frequency techniques. The technique is based on three new and simple features: a) the precise real time correction of the amplication of a current amplier; b) the specic shape of the excitation signal and its frequency spectrum; and c) the precise synchronization between the generation of the excitation signal and the acquisition of the dielectric response signal. This technique is useful in the case of relatively fast dynamical measurements when the knowledge of the time evolution of the dielectric constant is needed