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

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 wavenumbers. 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 with the string motion, and we consider the ratio of the fluctuations to the 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 wavenumbers and Reynolds number accessible (74 000≤Re≤170 000). (letter)