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A Unified View of the Law of the Wall Using Mixing-Length Theory

Published online by Cambridge University Press:  07 June 2016

V C Patel
V C Patel*
Affiliation:
Institute of Hydraulic Research, University of Iowa
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Summary

It is shown that, if the well-known mixing-length formula is regarded simply as a relationship between the velocity and the stress distributions in the wall region of a turbulent flow, then a truly universal distribution of mixing length is sufficient to describe the experimentally observed departures of the velocity distribution from the usual law of the wall as a result of severe pressure gradients and transverse surface curvature. Comparisons have been made with a wide variety of experimental data to demonstrate the general validity of the mixing-length model in describing the flow close to a smooth wall.

An extension of the re-laminarisation criterion of Patel and Head, and some experimental evidence, suggest that the thick axisymmetric boundary layer on a slender cylinder placed axially in a uniform stream cannot be maintained in a fully turbulent state for values of the Reynolds number, based on friction velocity and cylinder radius, below a certain critical value.

Information

Type
Research Article
Information
Aeronautical Quarterly , Volume 24 , Issue 1 , February 1973 , pp. 55 - 70
Copyright
Copyright © Royal Aeronautical Society. 1973

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