Universality in Decaying Turbulence at High Reynolds Numbers

TL;DR

This paper demonstrates that in high Reynolds number decaying turbulence, velocity difference statistics do not follow a power law but instead have a universal form, challenging traditional turbulence theories.

Contribution

It reveals that at high Reynolds numbers, turbulence exhibits a universal velocity difference distribution distinct from the expected power law scaling.

Findings

Velocity difference statistics are universal at high Reynolds numbers.

No evidence of power law scaling in the inertial range.

Implications for turbulence modeling and theory.

Abstract

A hallmark of fluid turbulence theory is the universal power law scaling of the velocity difference statistics between two points in space in the inertial range between the large energy injection scale and the small energy dissipation scale. Even at the highest Reynolds numbers available, laboratory and natural flows such universal power laws have not been convincingly demonstrated. Here we show for the decaying active grid turbulence of the Max Planck Variable Density Turbulence Tunnel that the velocity difference statistics at high Reynolds numbers do not exhibit a power law, but have a universal functional form independent of the Reynolds number. We separate this functional form from the power law exponent and discuss potential consequences for turbulence modelling.