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The effect of stable thermal stratification on the stability of viscous parallel flows

Published online by Cambridge University Press:  29 March 2006

K. S. Gage
K. S. Gage
Affiliation:
Institute for Fluid Dynamics and Applied Mathematics, University of Maryland
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Abstract

A unified linear viscous stability theory is developed for a certain class of stratified parallel channel and boundary-layer flows with Prandtl number equal to unity. Results are presented for plane Poiseuille flow and the asymptotic suction boundary-layer profile, which show that the asymptotic behaviour of both branches of the curve of neutral stability has a universal character. For velocity profiles without inflexion points it is found that a mode of instability disappears as η, the local Richardson number evaluated at the critical point, approaches 0.0554 from below. Calculations for Grohne's inflexion-point profile show both major and minor curves of neutral stability for 0 < η [les ] 0.0554; for \[ 0.0554 < \eta < 0.0773 \] there is only a single curve of neutral stability; and, for η > 0.0773, the curves of neutral stability become closed, with complete stabilization being achieved for a value of η of about 0·107.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 1 , 14 May 1971 , pp. 1 - 20
Copyright
© 1971 Cambridge University Press

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