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Asymptotic analysis of plane turbulent Couette-Poiseuille flows

Published online by Cambridge University Press:  19 April 2006

Kurt O. Lund  and
William B. Bush
Kurt O. Lund
Affiliation:
University of California, San Diego, California
William B. Bush
Affiliation:
University of California, San Diego, California
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Abstract

Matched asymptotic expansions, are used to describe turbulent Couette–Poiseuille flow (plane duct flow with a pressure gradient and a moving wall). A special modification of conventional eddy-diffusivity closure accounts for the experimentally observed non-coincidence of the locations of zero shear stress and maximum velocity. An asymptotic solution is presented which is valid as the Reynolds number tends to infinity for the whole family of Couette–Poiseuille flows (adverse, favourable, and zero pressure gradients in combination with a moving wall). It is shown that plane Poiseuille flow is a limiting case of Couette–Poiseuille flow. The solution agrees with experimental data for plane Couette flow, for the limiting plane Poiseuille flow, and for a special case having zero net flow and an adverse pressure gradient. The asymptotic analysis shows that conventional eddy diffusivity closures are inadequate for general Couette–Poiseuille flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 1 , 16 January 1980 , pp. 81 - 104
Copyright
© 1980 Cambridge University Press

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