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The return to isotropy of homogeneous turbulence

Published online by Cambridge University Press:  12 April 2006

John L. Lumley  and
Gary R. Newman
John L. Lumley
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University, University Park Present address: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853.
Gary R. Newman
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University, University Park Present address: Mechanical Engineering Department, Southeastern Massachusetts University, North Dartmouth, Massachusetts 02747.
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Abstract

The return to isotropy of homogeneous turbulence without mean velocity gradients is attacked by considering changes to be slow relative to turbulence time scales. This single assumption permits the problem to be cast as one of finding the form of three invariant functions. Examination of limiting behaviour for large Reynolds number and small anisotropy, as well as small Reynolds number and arbitrary anisotropy, places restrictions on the form of the functions. Realizability conditions (requiring that energies be non-negative) reduce the problem to two functions subject to further restrictions. A convenient interpolation form is found for the functions, satisfying all the restrictions, and it is shown that predictions based on this are in excellent agreement with all available data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 1 , 19 August 1977 , pp. 161 - 178
Copyright
© 1977 Cambridge University Press

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