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Free-stream turbulence near plane boundaries

Published online by Cambridge University Press:  12 April 2006

J. C. R. Hunt  and
J. M. R. Graham
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics and Department of Engineering, University of Cambridge
J. M. R. Graham
Affiliation:
Department of Aeronautics, Imperial College, London
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Abstract

Grid turbulence convected by a free stream past a rigid surface moving at the same speed as the free stream is analysed by boundary-layer theory and spectral methods. The turbulence is assumed to be weak, i.e. $u^{\prime}_{\infty}/\overline{u}_{\infty}\ll 1$ and its Reynolds number to be large, i.e. $u^{\prime}_{\infty}/\overline{u}_{\infty}\gg 1$ where u′∞ is the r.m.s. turbulent velocity. Two regions are found to exist. The outer, source region B(s) has a thickness of the order of the integral scale L∞. Here the normal component of turbulence decreases and the lateral and streamwise components are amplified. The inner, viscous region B(v) has thickness $[x\nu/\overline{u}_{\infty}]^{\frac{1}{2}} $, where x, v and $\overline{u}_{\infty} $ are the streamwise co-ordinate, kinematic viscosity and mean velocity respectively. Here the turbulent velocity decays to zero at the surface. Spectra variances and cross-correlations are calculated and found to compare well with measurements of turbulence near moving walls by Uzkan & Reynolds (1967) and Thomas & Hancock (1977).

The results of this theory are shown to have a number of applications including the prediction of turbulence near wind-tunnel walls and near flat plates placed parallel to the flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 2 , 30 January 1978 , pp. 209 - 235
Copyright
© 1978 Cambridge University Press

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Footnotes

Main conclusions of this work were presented by J. C. R. Hunt at the University of Southampton Colloquium on Coherent Structures in Turbulence in March 1974.

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