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Streamwise vortices in heated boundary layers

Published online by Cambridge University Press:  26 April 2006

Philip Hall
Philip Hall
Affiliation:
Department of Mathematics, Manchester University, Manchester M13 9PL, UK
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Abstract

The nonlinear instability of the boundary layer on a heated flat plate placed in an oncoming flow is investigated. Such flows are unstable to stationary vortex instabilities and inviscid travelling wave disturbances governed by the Taylor-Goldstein equation. For small temperature differences the Taylor-Goldstein equation reduces to Rayleigh's equation. When the temperature difference between the wall and free stream is small the preferred mode of instability is a streamwise vortex. It is shown in this case that the vortex, assumed to be of small wavelength, restructures the underlying mean flow to produce a profile which can be massively unstable to inviscid travelling waves. The mean state is shown to be destabilized if the Prandtl number is less than unity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 252 , July 1993 , pp. 301 - 324
Copyright
© 1993 Cambridge University Press

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