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The maintenance of Reynolds stress in turbulent shear flow

Published online by Cambridge University Press:  28 March 2006

O. M. Phillips
O. M. Phillips
Affiliation:
Mechanics Department, The Johns Hopkins University, Baltimore and Hydronautics Incorporated, Laurel, Md.
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Abstract

A mechanism is proposed for the manner in which the turbulent components support Reynolds stress in turbulent shear flow. This involves a generalization of Miles's mechanism in which each of the turbulent components interacts with the mean flow to produce an increment of Reynolds stress at the ‘matched layer’ of that particular component. The summation over all the turbulent components leads to an expression for the gradient of the Reynolds stress τ(z) in the turbulence \[ \frac{d\tau}{dz} = {\cal A}\Theta\overline{w^2}\frac{d^2U}{dz^2}, \]where ${\cal A}$ is a number, Θ the convected integral time scale of the w-velocity fluctuations and U(z) the mean velocity profile. This is consistent with a number of experimental results, and measurements on the mixing layer of a jet indicate that A = 0·24 in this case. In other flows, it would be expected to be of the same order, though its precise value may vary somewhat from one to another.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 27 , Issue 1 , 11 January 1967 , pp. 131 - 144
Copyright
© 1967 Cambridge University Press

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