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Taylor-Görtler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations

Published online by Cambridge University Press:  21 April 2006

Philip Hall  and
James Bennett
Philip Hall
Affiliation:
Mathematics Department, North Park Road, University of Exeter, Exeter, UK
James Bennett
Affiliation:
Mathematics Department, North Park Road, University of Exeter, Exeter, UK
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Abstract

The Taylor-Görtler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Görtler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Görtler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Görtler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith & Daniels (1981). As an example of an unsteady spatially varying basic state we also consider the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first ‘Stokes-layer stage’ of the hierarchy of nonlinear states discussed by Smith & Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 171 , October 1986 , pp. 441 - 457
Copyright
© 1986 Cambridge University Press

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