Statistical equilibrium of large scales in three-dimensional hydrodynamic turbulence*

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 centimeter-scale magnetic stirrers immersed in a large fluid reservoir. By measuring the statistics of the fluid velocity field, we experimentally evidence that the large scales in 3D turbulence are in statistical equilibrium, a regime predicted seventy years ago, but had not been reported experimentally so far. This equipartition regime of large scales can then be described with an effective temperature, although it is not isolated from the turbulent Kolmogorov cascade that develops towards small scales. In the large-scale domain, the energy flux is zero on average but exhibits intense temporal fluctuations. These findings pave the way to use classical concepts of equilibrium statistical mechanics to describe the large-scale properties of 3D turbulent flows.

J.-B. Gorce and E. Falcon, Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence, in press in Physical Review Letters (2022).