Journal of Fluid Mechanics

Free-stream turbulence near plane boundaries 1

J. C. R.  Hunt a1 and J. M. R.  Graham a2
a1 Department of Applied Mathematics and Theoretical Physics and Department of Engineering, University of Cambridge
a2 Department of Aeronautics, Imperial College, London

Article author query
hunt jc   [Google Scholar] 
graham jm   [Google Scholar] 


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[infty infinity] 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[infty infinity]. 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.

(Received September 22 1976)
(Revised March 12 1977)


1 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.