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Turbulent Couette flow profiles that maximize the efficiency function

Published online by Cambridge University Press:  26 April 2006

L. M. Smith
L. M. Smith
Affiliation:
Massachusetts Institute of Technology, Department of Mathematics, Cambridge, MA 02139, USA
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Abstract

A previous study revealed that only maximization of the efficiency function, from among a large class of mean field moments, results in both a logarithmic law and a velocity defect law in turbulent Poiseuille channel flow. The efficiency function, [Escr], is the product of a drag coefficient and the ratio of the fluctuation and mean dissipation rate integrals. Here, maximum [Escr] is explored in Couette flow to test its generality as a statistical stability criterion for turbulent shear flows. The optimal flow exhibits a logarithmic law but does not have a velocity defect law. A decreasing velocity defect is predicted for Reynolds numbers up to 30 000. This prediction is shown to be supported by the existing data, which are limited to Reynolds numbers less than 20 000.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991, pp. 509 - 525
Copyright
© 1991 Cambridge University Press

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