33 research outputs found
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 . 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 ), 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 (), we derive the exponent 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 ()
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 . 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
. 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 -- analogous to a temperature -- fully
characterizes the large-scale turbulent wave field. We present an expression
for 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