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Stability of turbulent channel flow, with application to Malkus's theory

Published online by Cambridge University Press:  28 March 2006

W. C. Reynolds  and
W. G. Tiederman
W. C. Reynolds
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, California
W. G. Tiederman
Affiliation:
Shell Development Company, Emeryville, California
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Abstract

The Orr-Sommerfeld stability problem has been studied for velocity profiles appropriate to turbulent channel flow. The intent was to provide an evaluation of Malkus's theory that the flow assumes a state of maximum dissipation, subject to certain constraints, one of which is that the mean velocity profile is marginally stable. Dissipation rates and neutral stability curves were obtained for a representative two-parameter family of velocity profiles. Those in agreement with experimental profiles were found to be stable; the marginally stable profile of greatest dissipation was not in good agreement with experiments. An explanation for the apparent success of Malkus's theory is offered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 27 , Issue 2 , 2 February 1967 , pp. 253 - 272
Copyright
© 1967 Cambridge University Press

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