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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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References

Benjamin, T. BROOKE 1959 Shearing flow over a wavy boundary J. Fluid Mech. 6, 161.Google Scholar
Benjamin, T. BROOKE 1960 Effects of a flexible boundary on hydrodynamic stability J. Fluid Mech. 9, 513.Google Scholar
Bradbury, L. J. S. 1965 The structure of a self-preserving turbulent plane jet J. Fluid Mech. 23, 31.Google Scholar
Corcos, G. M. 1964 The structure of the turbulent pressure field in boundary layer flows J. Fluid Mech. 18, 353.Google Scholar
Corrsin, S. 1949 An experimental verification of local isotropy J. Aero. Sci. 16, 757.Google Scholar
Davies, P. A. O. L., Fisher, M. J. & Barratt, M. J. 1963 The characteristics of the turbulence in the mixing region of a round jet J. Fluid Mech. 15, 337.Google Scholar
Deissler, R. G. 1961 Effects of inhomogeneity and of shear flow in weak homogeneous turbulence Phys. Fluids 4, 1187.Google Scholar
Favre, A. J., Gaviglio, J. J. & Dumas, R. J. 1957 Space-time double correlations in a turbulent boundary layer J. Fluid Mech. 2, 313.Google Scholar
Favre, A. J., Gaviglio, J. J. & Dumas, R. J. 1958 Further space-time double correlations in a turbulent boundary layer J. Fluid Mech. 3, 344.Google Scholar
Lighthill, M. J. 1958 Fourier Analysis and Generalized Functions. Cambridge University Press.
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind J. Fluid Mech. 14, 385.Google Scholar
Malkus, W. V. R. 1956 Outline of a theory of turbulent shear flow J. Fluid Mech. 1, 521.Google Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flow J. Fluid Mech. 3, 185.Google Scholar
Miles, J. W. 1962 On the generation of surface waves by shear flows. Part 4 J. Fluid Mech. 13, 433.Google Scholar
Moffatt, H. K. 1965 The interaction of turbulence with rapid uniform shear. Stanford University research report, Sudaer 242.Google Scholar
Pearson, J. R. A. 1959 The effect of uniform distortion of weak homogeneous turbulence J. Fluid Mech. 5, 274.Google Scholar
Robertson, J. M. 1959 On turbulent plane Couette flow. Proc. 6th Ann. Conf. Fluid Mech., Univ. Texas, Austin, Texas, pp. 169–82.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. Cambridge University Press.
Willmarth, W. W. & Wooldridge, C. E. 1962 Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer J. Fluid Mech. 14, 187.Google Scholar