Journal of Fluid Mechanics

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

G. I.  Barenblatt a1p1
a1 P. P. Shirshov Institute of Oceanology, Russian Academy of Sciences, Moscow, 117218, Russia

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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.

(Published Online April 26 2006)
(Received May 30 1992)
(Revised October 15 1992)

p1 Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK.