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Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis

Published online by Cambridge University Press:  26 April 2006

G. I. Barenblatt
G. I. Barenblatt
Affiliation:
P. P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, 117218, Russia Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK.
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Abstract

The present work consists of two parts. Here in Part 1, a scaling law (incomplete similarity with respect to local Reynolds number based on distance from the wall) is proposed for the mean velocity distribution in developed turbulent shear flow. The proposed scaling law involves a special dependence of the power exponent and multiplicative factor on the flow Reynolds number. It emerges that the universal logarithmic law is closely related to the envelope of a family of power-type curves, each corresponding to a fixed Reynolds number. A skin-friction law, corresponding to the proposed scaling law for the mean velocity distribution, is derived.

In Part 2 (Barenblatt & Prostokishin 1993), both the scaling law for the velocity distribution and the corresponding friction law are compared with experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 248 , March 1993 , pp. 513 - 520
Copyright
© 1993 Cambridge University Press

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References

Amit, D. 1978 Field theory, the Renormalization Group and Critical Phenomena. McGraw Hill.
Barenblatt, G. I. 1979 Similarty, Self-Similarity, and Intermediate Asymptotics. Plenum.
Barenblatt, G. I. & Monin, A. S. 1979 Similarity laws for turbulent stratified flows. Arch. Rat. Mech. Anal. 70, 307– 317.Google Scholar
Barenblatt, G. I. & Prostokishin, V. M. 1993 Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data. J. Fluid Mech. 248, 521– 529.Google Scholar
Castaing, B., Gagne, Y. & Hopfinger, E. J. 1990 Velocity probability density functions of high Reynolds number turbulence. Physica D 46, 177– 200.Google Scholar
Fisher, R. A. 1937 The wave of advance of advantageous genes. Annls Eugenics 7, 355– 369.Google Scholar
Guderley, K. G. 1942 Starke kugelige und zylindrische Verdichtungstösse in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung. 19 (9), 302– 312.Google Scholar
Kolmogorov, A. N., Petrovsky, I. G. & Piskunov, N. S. 1937 The investigation of a diffusion equation taking into account the growth of matter quantity and its application to a biological problem. Bull. Moscow Univ. A, vol. 1, no. 6.
Landau, L. D. & Lifshitz, E. M. 1987 Hydrodynamics (2nd edn.) Pergamon.
Ma, S.-K. 1976 Modern Theory of Critical Phenomena. Benjamin/Cummings.
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, Vol. 1. MIT Press.
Nikuradze, J. 1932 Gesetzmässigkeiten der turbulenten Strömung in glatten Röhren. VDI Forschungsheft, No. 356.
Schlichting, H. 1968 Grenzschicht-Theorie. G. Braun.
Zeldovich, Ya. B. & Frank-Kamenetsky, D. A. 1938 Theory of uniform flame propagation. J. Phys. Chem. 12, 189– 192.Google Scholar