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

## TL;DR

This study uses a string in turbulent flow to measure scale-specific fluctuations and dissipation, exploring the fluctuation-dissipation relation and the concept of an effective temperature in turbulence.

## Contribution

It introduces a mechanical probe for scale-resolved measurements in turbulence and compares experimental results with Kolmogorov theory, linking fluctuation spectra to dissipation and effective temperature concepts.

## Key findings

- Measured fluctuation spectra match Kolmogorov -11/3 law.
- Validated the fluctuation-dissipation relation in turbulent flow.
- Provided insights into the effective temperature in turbulence.

## 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 {\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 ($74000 \leq Re \leq 170000$).