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Turbulent velocity profiles from stability criteria

Published online by Cambridge University Press:  19 April 2006

Willem V. R. Malkus
Willem V. R. Malkus
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge
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Abstract

A velocity-defect law for channel flow is shown to result from the single requirement of Reynolds-stress spectral ‘smoothness’ for any mean profile maintained free of inflexions by transient instabilities. The deduced velocity is a logarithmic function of position near boundaries and parabolic in mid-regions of the flow, independent of the detailed mechanisms of momentum transport by the fluid. However, if the ‘smoothness’ of the spectral tail is decreased, a second logarithmic layer of steeper slope emerges inside the first layer. Profile data from drag-reduction experiments gathered by Virk (1975) exhibit the deduced inner log layer and its transition region to the usual outer flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 3 , 13 February 1979 , pp. 401 - 414
Copyright
© 1979 Cambridge University Press

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