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Asymptotic theory of turbulent shear flows

Published online by Cambridge University Press:  29 March 2006

Kirit S. Yajnik
Kirit S. Yajnik
Affiliation:
Department of Mechanical Engineering Indian Institute of Technology Kanpur
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Abstract

A theory is proposed in this paper to describe the behaviour of a class of turbulent shear flows as the Reynolds number approaches infinity. A detailed analysis is given for simple representative members of this class, such as fully developed channel and pipe flows and two-dimensional turbulent boundary layers. The theory considers an underdetermined system of equations and depends critically on the idea that these flows consist of two rather different types of regions. The method of matched asymptotic expansions is employed together with asymptotic hypotheses describing the order of various terms in the equations of mean motion and turbulent kinetic energy. As these hypotheses are not closure hypotheses, they do not impose any functional relationship between quantities determined by the mean velocity field and those determined by the Reynolds stress field. The theory leads to asymptotic laws corresponding to the law of the wall, the logarithmic law, the velocity defect law, and the law of the wake.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 2 , 22 June 1970 , pp. 411 - 427
Copyright
© 1970 Cambridge University Press

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References

Clauser, F. H. 1956 Adv. Appl. Mech. 4, 1–51.
Cole, J. 1968 Perturbation Methods in Applied Mathematics. New York: Blaisdell.
Coles, D. 1956 J. Fluid Mech. 1, 191–226.
Goldstein, S. 1948 Quart. J. Mech. Appl. Math. 1, 43–69.
Kaplun, S. 1967 Fluid Mechanics and Singular Perturbations. (Ed. P. A. Lagerstrom, L. N. Howard & C-S. Liu) London: Academic.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 J. Fluid Mech. 30, 741–753.
Millikan, C. B. 1938 Proc. Fifth Intern. Congress Appl. Mech. Cambridge, Mass. p. 386–392.
Phillips, O. M. 1969 Ann. Rev. Fluid Mech. 1, 245–264.
Rotta, J. C. 1962 Prog. in Aero. Sci. Vol. 2. Oxford: Pergamon.
Schultz-Grunow 1956 NACATM 986.
Smith, D. W. & Walker, J. H. 1959 NASA Rep. R–26.
Stewartson, K. 1958 Quart. J. Mech. Appl. Math. 11, 399–410.
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow. (1st edn.) Cambridge University Press.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. New York: Academic.