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Velocity-derivative skewness and two-time velocity correlations of isotropic turbulence as predicted by the LET theory

Published online by Cambridge University Press:  26 April 2006

W. D. Mccomb ,
V. Shanmugasundaram  and
P. Hutchinson
W. D. Mccomb
Affiliation:
Department of Physics, Edinburgh University, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK
V. Shanmugasundaram
Affiliation:
Department of Physics, Edinburgh University, The King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK
P. Hutchinson
Affiliation:
Engineering Sciences Division, Harwell Laboratory, Oxfordshire OX11 ORA, UK Present address: School of Mechanical Engineering, Cranfield Institute of Technology, Cranfield, Bedford MK43 OAL, UK.
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Abstract

The local-energy-transfer (LET) theory was used to calculate freely decaying turbulence for arbitrary initial conditions over a range of microscale-based Reynolds numbers 0.5 [les ] Rλ(tf) [les ] 1009, where tf is the final time of computation. The predicted skewness factor S(Rλ) agreed closely with the results of numerical simulations at low-to-moderate Reynolds numbers and followed the same general trend at larger values of Rλ. It was also found that, for Rλ(tf) [les ] 5, the LET calculation was almost indistinguishable from that of the direct-interaction approximation (DIA), with the difference between the two theories tending to zero as Rλ(tf)∞ 0.

Two-time correlation and propagator (or response) functions were also obtained. Tests of their scaling behaviour suggest that, contrary to general belief, the convective sweeping of the energy-containing range is much less important than the Kolmogorov timescale in determining inertial-range behaviour. This result raises questions about the accepted explanation for the failure of the direct-interaction approximation, thus motivating a discussion about the relevance of random Galilean invariance (RGI). It is argued that, for a properly constructed ensemble of transformations to inertial frames, invariance in every realization necessarily implies RGI. It is suggested that the defects of the direct-interaction approximation can be understood in terms of a failure to renormalize the stirring forces.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 91 - 114
Copyright
© 1989 Cambridge University Press

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