On Landau’s prediction for large-scale fluctuation of turbulence energy dissipation

Abstract

Kolmogorov’s theory for turbulence, proposed in 1941, is based on a hypothesis that small-scale statistics are uniquely determined by the kinematic viscosity and the mean rate of energy dissipation. Landau remarked that the local rate of energy dissipation should fluctuate in space over large scales and hence should affect small-scale statistics. Experimentally, we confirm the significance of this large-scale fluctuation, which is comparable to the mean rate of energy dissipation at the typical scale for energy-containing eddies. The significance is independent of the Reynolds number and the configuration for turbulence production. With an increase of scale r above the scale of largest energy-containing eddies, the fluctuation comes to have the scaling r−1∕2 and becomes close to Gaussian. We also confirm that the large-scale fluctuation affects small-scale statistics.