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Crossflow effects on the growth rate of inviscid Görtler vortices in a hypersonic boundary layer

Published online by Cambridge University Press:  26 April 2006

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

The effects of crossflow on the growth rate of inviscid Görtler vortices in a hypersonic boundary layer with pressure gradient are studied in this paper. Attention is focused on the inviscid mode trapped in the temperature adjustment layer; this mode has greater growth rate than any other mode at the minimum order of the Görtler number at which Görtler vortices may exist. The eigenvalue problem which governs the relationship between the growth rate, the crossflow amplitude and the wavenumber is solved numerically, and the results are then used to clarify the effects of crossflow on the growth rate of inviscid Görtler vortices. It is shown that crossflow effects stabilize Görtler vortices in different manners for incompressible and hypersonic flows. The neutral mode eigenvalue problem is found to have an exact solution, and as a byproduct, we have also found the exact solution to a neutral mode eigenvalue problem which was formulated, but unsolved before, by Bassom & Hall (1991).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 276 , 10 October 1994 , pp. 343 - 367
Copyright
© 1994 Cambridge University Press

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