Freely-Decaying, Homogeneous Turbulence Generated by Multi-scale Grids

TL;DR

This study compares turbulence generated by conventional and multi-scale grids in a wind tunnel, finding similar decay behaviors and spectral properties, challenging previous reports of higher decay exponents with multi-scale grids.

Contribution

It demonstrates that multi-scale grids produce turbulence with decay and spectral characteristics nearly identical to conventional grids under controlled conditions.

Findings

Turbulence exhibits a power-law decay with exponent close to 6/5.

Spectra follow classical Kolmogorov scaling.

Results contradict prior studies reporting higher decay exponents.

Abstract

We investigate wind tunnel turbulence generated by both conventional and multi-scale grids. Measurements were made in a tunnel which has a large test-section, so that possible side wall effects are very small and the length assures that the turbulence has time to settle down to a homogeneous shear-free state. The conventional and multi-scale grids were all designed to produce turbulence with the same integral scale, so that a direct comparison could be made between the different flows. Our primary finding is that the behavior of the turbulence behind our multi-scale grids is virtually identical to that behind the equivalent conventional grid. In particular, all flows exhibit a power-law decay of energy, $u^2 \sim t^{-n}$, where $n$ is very close to the classical Saffman exponent of $n = 6/5$. Moreover, all spectra exhibit classical Kolmogorov scaling, with the spectra collapsing on the integral scales at small $k$, and on the Kolmogorov micro-scales at large $k$. Our results are at odds with some other experiments performed on similar multi-scale grids, where significantly higher energy decay exponents and turbulence levels have been reported.