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The Mixing Length Derived from Kármán’s Similarity Hypothesis

Published online by Cambridge University Press:  07 June 2016

Michio Nishioka  and
Shūsuke Iida
Michio Nishioka
Affiliation:
University of Osaka Prefecture, Japan
Shūsuke Iida
Affiliation:
University of Osaka Prefecture, Japan
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Summary

From Kármán’s similarity hypothesis, we derive the equation which describes the mixing length in terms of the turbulent shear stress. For a boundary layer with linear stress distribution, the equation is in reasonable agreement with Bradshaw’s measurements. For a boundary layer with injection, it is shown that injection has an appreciable effect upon the mixing length when (vw/2) /(τ/ρ)1/2 becomes comparable to the Kármán constant. Close similarity is also pointed out between the hypotheses due to Kármán and Townsend. Moreover, the diffusion constant in Townsend’s hypothesis is determined to be 0.25, which is in good agreement with the value 0.2 obtained by Townsend from one experiment.

Type
Research Article
Information
Aeronautical Quarterly , Volume 24 , Issue 1 , February 1973 , pp. 71 - 76
Copyright
Copyright © Royal Aeronautical Society. 1973

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References

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