The decay of turbulence generated by a class of multi-scale grids

TL;DR

This study investigates how turbulence generated by a fractal square grid decays, revealing non-classical scaling laws and detailed energy spectra evolution, challenging traditional turbulence models.

Contribution

It provides new experimental evidence on the decay of turbulence from fractal grids, showing deviations from classical scaling and analyzing energy spectra and flow homogeneity.

Findings

Turbulence does not follow classical dissipation scaling.

L and λ are approximately proportional during decay.

Presence of transverse energy and pressure transport.

Abstract

A new experimental investigation of decaying turbulence generated by a low-blockage space-filling fractal square grid is presented. We find agreement with previous works by Seoud & Vassilicos (2007) and Mazellier & Vassilicos (2010) but also extend the length of the assessed decay region and consolidate the results by repeating the experiments with different probes of increased spatial resolution. It is confirmed that this moderately high Reynolds number Re{\lambda} turbulence (up to Re{\lambda} {\simeq}350 here) does not follow the classical high Reynolds number scaling of the dissipation rate {\epsilon} ~ u'^3/L and does not obey the equivalent proportionality between the Taylor-based Reynolds number Re{\lambda} and the ratio of integral scale L to Taylor micro-scale {\lambda}. Instead we observe an approximate proportionality between L and {\lambda} during decay. This non-classical behaviour is investigated by studying how the energy spectra evolve during decay and examining how well they can be described by self-preserving single-length scale forms. A detailed study of homogeneity and isotropy is also presented which reveals the presence of transverse energy transport and pressure transport in the part of the turbulence decay region where we take data (even though previous studies found mean flow and turbulence intensity profiles to be approximately homogeneous in much of the decay region). The exceptionally fast turbulence decay observed in the part of the decay region where we take data is consistent with the non-classical behaviour of the dissipation rate. Measurements with a regular square mesh grid as well as comparisons with active grid experiments by Mydlarski & Warhaft (1996) and Kang, Chester & Meveneau (2003) are also presented to highlight the similarities and differences between these turbulent flows and the turbulence generated by our fractal square grid.