Determination of the Decay Exponent in Mechanically Stirred Isotropic Turbulence

TL;DR

This study uses direct numerical simulation to analyze how the decay exponent of isotropic homogeneous turbulence varies with Reynolds number, confirming theoretical predictions and identifying a transition point around Re=250.

Contribution

It provides detailed numerical evidence on the decay exponent behavior across a range of Reynolds numbers, validating Saffman's theoretical predictions.

Findings

Decay exponent matches Saffman's theory at high and low Re

Transition from high to low Re behavior occurs near Re=250

Turbulence decay characteristics depend on Reynolds number

Abstract

Direct numerical simulation is used to investigate the decay exponent of isotropic homogeneous turbulence over a range of Reynolds numbers sufficient to display both high and low Re number decay behavior. The initial turbulence is generated by the stirring action of the flow past many small randomly placed cubes. Stirring occurs at 1/30th of the simulation domain size so that the low-wavenumber and large scale behavior of the turbulent spectrum is generated by the fluid and is not imposed. It is shown that the decay exponent in the resulting turbulence closely matches the theoretical predictions of Saffman (1967) at both high and low Reynolds numbers. The transition from high Reynolds number behavior to low Reynolds number behavior occurs relatively abruptly at a turbulent Reynolds number of around 250.