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Free-stream turbulence near plane boundaries

  • J. C. R. Hunt (a1) and J. M. R. Graham (a2)
  • DOI: http://dx.doi.org/10.1017/S0022112078000130
  • Published online: 01 April 2006
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.

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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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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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