The fluctuation–dissipation relation on a Melde string in a turbulent flow; considerations on a ‘dynamical temperature’

Abstract

We 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 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 ≤ Re ≤ 170000).

Susceptibility divergence, phase transition and multistability of a highly turbulent closed flow

“…Turbulent flows being intrinsically out-of-equilibrium systems, there is a priori no reason to describe them using tools borrowed from thermodynamics. However, in recent years, developments of out-of-equilibrium thermodynamics led, in particular, to a number of interesting applications to turbulence [18,19,20]. In this context, one may wonder whether the observed turbulent transitions can be interpreted in terms of phase transitions with a symmetry-breaking or susceptibility divergence signature.…”

Dependence of the Fluctuation-Dissipation Temperature on the Choice of Observable

“…In contrast, if ∆S > 0, the system can be described by two parameters, a reference temperature (e.g., T p=0 ) and ∆S. It would be interesting to try to measure ∆S experimentally or numerically through the use of the FDR, in real out-of-equilibrium systems like granular gases [23] or turbulent flows [34].…”

Effective temperatures for single particle system under dichotomous noise

“…Besides, on systems described by the generalised Langevin Equation (1) we have aforementioned, similar surveys can be carried out on non-equilibrium systems to which proxies for the temperature were or can be considered, namely granular-matter systems [15], fluid activated dynamics [35], turbulence [36], simple fluids with preferred spatial direction (shear flow) [37], interacting vortices in disordered superconductors [38], gene network models [39], biological self-assembly processes [40] and ratchets [41] or even in finance, where the volatility of a financial instrument can be reinterpreted as an effective temperature as well [42].…”