Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence

TL;DR

This study experimentally demonstrates that large-scale dynamics in 3D hydrodynamic turbulence reach a statistical equilibrium, allowing for an effective temperature description despite ongoing turbulent cascades.

Contribution

It provides experimental evidence that large scales in 3D turbulence can be described by equilibrium statistical mechanics, bridging turbulence and thermodynamics.

Findings

Large-scale dynamics are in statistical equilibrium.

Energy flux at large scales averages to zero but fluctuates intensely.

Large-scale properties can be characterized by an effective temperature.

Abstract

We investigate experimentally three-dimensional (3D) hydrodynamic turbulence at scales larger than the forcing scale. We manage to perform a scale separation between the forcing scale and the container size by injecting energy into the fluid using centimetric magnetic particles. We measure the statistics of the fluid velocity field at scales larger than the forcing scale (energy spectra, velocity distributions, and energy flux spectrum). In particular, we show that the large-scale dynamics are in statistical equilibrium and can be described with an effective temperature, although not isolated from the turbulent Kolmogorov cascade. In the large-scale domain, the energy flux is zero on average but exhibits intense temporal fluctuations. Our work paves the way to use equilibrium statistical mechanics to describe the large-scale properties of 3D turbulent flows.