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On the nonlinear interaction of Görtler vortices and Tollmien-Schlichting waves in curved channel flows at finite Reynolds numbers

Published online by Cambridge University Press:  21 April 2006

Q. Isa Daudpota ,
Philip Hall  and
Thomas A. Zang
Q. Isa Daudpota
Affiliation:
Computational Methods, Branch, NASA Langley Research Center, Hampton, VA 23665, USA
Philip Hall
Affiliation:
Department of Mathematics, Exeter University, Exeter, UK and Institute for Computer Applications in Science and Engineering
Thomas A. Zang
Affiliation:
Computational Methods, Branch, NASA Langley Research Center, Hampton, VA 23665, USA
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Abstract

The flow in a two-dimensional curved channel driven by an azimuthal pressure gradient can become linearly unstable owing to axisymmetric perturbations and/or non-axisymmetric perturbations depending on the curvature of the channel and the Reynolds number. For a particular small value of curvature, the critical Reynolds number for both these perturbations becomes identical. In the neighbourhood of this curvature value and critical Reynolds number, non-linear interactions occur between these perturbations. The Stuart-Watson approach is used to derive two coupled Landau equations for the amplitudes of these perturbations. The stability of the various possible states of these perturbations is shown through bifurcation diagrams. Emphasis is given to those cases that have relevance to external flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 193 , August 1988 , pp. 569 - 595
Copyright
© 1988 Cambridge University Press

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