Universal Velocity Statistics in Decaying Turbulence

Abstract

In turbulent flows, kinetic energy is transferred from large spatial scales to small ones, where it is converted to heat by viscosity. For strong turbulence, i.e., high Reynolds numbers, Kolmogorov conjectured in 1941 that this energy transfer is dominated by inertial forces at intermediate spatial scales. Since Kolmogorov's conjecture, the velocity difference statistics in this so-called inertial range have been expected to follow universal power laws for which theoretical predictions have been refined over the years. Here we present experimental results over an unprecedented range of Reynolds numbers in a well-controlled wind tunnel flow produced in the Max Planck Variable Density Turbulence Tunnel. We find that the measured second-order velocity difference statistics become independent of the Reynolds number, suggesting a universal behavior of decaying turbulence. However, we do not observe power laws even at the highest Reynolds number, i.e., at turbulence levels otherwise only attainable in atmospheric flows. Our results point to a Reynolds number-independent logarithmic correction to the classical power law for decaying turbulence that calls for theoretical understanding.