Scaling in Decaying Turbulence at High Reynolds Numbers

TL;DR

This study investigates the scaling behavior of velocity fluctuations in high Reynolds number decaying turbulence, providing evidence for a universal inertial range shape independent of Reynolds number.

Contribution

It presents experimental data showing the inertial range statistics approach a universal shape at high Reynolds numbers, correcting for energy decay effects.

Findings

Scaling exponent of second-order velocity increments is approximately 0.693.

Inertial range statistics become Reynolds number independent at high values.

Evidence supports the existence of a universal inertial range in turbulence.

Abstract

The way the increment statistics of turbulent velocity fluctuations scale with the increment size is a centerpiece of turbulence theories. We report data on decaying turbulence in the Max Planck Variable Density Turbulence Tunnel (VDTT), which show an approach of the inertial range statistics toward a nontrivial shape at small scales. By correcting for the contributions of energy decay to the large-scale statistics with a model, we find the scaling exponent of the second-order velocity increment statistics to be independent of the Reynolds number and equal to $0.693\pm0.003$ for $2000\lesssim R_{\lambda} \lesssim 6000$. This is evidence of a universal inertial range at high Reynolds numbers.