DOI: 10.1017/s0022112067000096. The maintenance of Reynolds stress in turbulent shear flow

The maintenance of Reynolds stress in turbulent shear flow

10.1017/s0022112067000096

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

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 thew-velocity fluctuations andU(z) the mean velocity profile. This is consistent with a number of experimental results, and measurements on the mixing layer of a jet indicate thatA= 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.

Authors 1

O. M. Phillips (first)

References 19 Referenced 34

Favre, A. J. , Gaviglio, J. J. & Dumas, R. J. 1957 Space-time double correlations in a turbulent boundary layer J. Fluid Mech. 2,313. (10.1017/S0022112057000166)
Miles, J. W. 1962 On the generation of surface waves by shear flows. Part 4 J. Fluid Mech. 13,433. (10.1017/S0022112062000828)
Robertson, J. M. 1959 On turbulent plane Couette flow. Proc. 6th Ann. Conf. Fluid Mech .,Univ. Texas,Austin, Texas,pp.169–82.
Malkus, W. V. R. 1956 Outline of a theory of turbulent shear flow J. Fluid Mech. 1,521. (10.1017/S0022112056000342)
Miles, J. W. 1957 On the generation of surface waves by shear flow J. Fluid Mech. 3,185. (10.1017/S0022112057000567)
Bradbury, L. J. S. 1965 The structure of a self-preserving turbulent plane jet J. Fluid Mech. 23,31. (10.1017/S0022112065001222)
Moffatt, H. K. 1965 The interaction of turbulence with rapid uniform shear.Stanford University research report, Sudaer 242.
Benjamin, T. BROOKE 1960 Effects of a flexible boundary on hydrodynamic stability J. Fluid Mech. 9,513. (10.1017/S0022112060001286)
Deissler, R. G. 1961 Effects of inhomogeneity and of shear flow in weak homogeneous turbulence Phys. Fluids 4,1187. (10.1063/1.1706194)
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. (10.1017/S0022112062001160)
Corrsin, S. 1949 An experimental verification of local isotropy J. Aero. Sci. 16,757.
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind J. Fluid Mech. 14,385. (10.1017/S0022112062001305)
Lighthill, M. J. 1958 Fourier Analysis and Generalized Functions .Cambridge University Press. (10.1017/CBO9781139171427)
Pearson, J. R. A. 1959 The effect of uniform distortion of weak homogeneous turbulence J. Fluid Mech. 5,274. (10.1017/S0022112059000192)
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. (10.1017/S0022112058000021)
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. (10.1017/S0022112063000306)
Benjamin, T. BROOKE 1959 Shearing flow over a wavy boundary J. Fluid Mech. 6,161. (10.1017/S0022112059000568)
Corcos, G. M. 1964 The structure of the turbulent pressure field in boundary layer flows J. Fluid Mech. 18,353. (10.1017/S002211206400026X)
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow .Cambridge University Press.

Dates

Type	When
Created	19 years, 5 months ago (March 28, 2006, 2:51 a.m.)
Deposited	6 years, 4 months ago (April 17, 2019, 9:14 a.m.)
Indexed	2 months, 1 week ago (June 21, 2025, 1:02 a.m.)
Issued	58 years, 7 months ago (Jan. 11, 1967)
Published	58 years, 7 months ago (Jan. 11, 1967)
Published Online	19 years, 5 months ago (March 28, 2006)
Published Print	58 years, 7 months ago (Jan. 11, 1967)

Funders 0

None

BibTeX

@article{Phillips_1967, title={The maintenance of Reynolds stress in turbulent shear flow}, volume={27}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112067000096}, DOI={10.1017/s0022112067000096}, number={1}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Phillips, O. M.}, year={1967}, month=jan, pages={131–144} }

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