On the Relaxation of Turbulence at High Reynolds Numbers

TL;DR

This study investigates how turbulence in fluids relaxes at high Reynolds numbers, finding that the relaxation rate remains constant regardless of Reynolds number, challenging some existing models.

Contribution

The paper provides high-precision measurements of turbulence relaxation rates at unprecedentedly high Reynolds numbers, revealing Reynolds-number independence.

Findings

Relaxation rate is Reynolds-number independent at high Re.

Contradicts models predicting Reynolds-number dependence.

Supports models assuming Reynolds-number independence.

Abstract

Turbulent motions in a fluid relax at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the relaxation rate is not generally known. This paper concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reached higher Reynolds numbers than ever before and covered a wide range of them ($10^4 < Re = UM/\nu < 5\times10^6$), we measured the relaxation rate with the unprecedented precision of about 2\%. Here $U$ is the mean speed of the flow, $M$ the forcing scale, and $\nu$ the kinematic viscosity of the fluid. We observed that the relaxation rate was Reynolds-number independent, which contradicts some models and supports others.