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On the onset of three-dimensionality and time-dependence in Görtler vortices

Published online by Cambridge University Press:  26 April 2006

Philip Hall  and
Sharon Seddougui
Philip Hall
Affiliation:
Mathematics Department, Exeter University, North Park Road, Exeter EX4 4QE, UK
Sharon Seddougui
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665, USA
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Abstract

The secondary instability of large-amplitude Görtler vortices in a growing boundary layer is discussed in the fully nonlinear regime. It is shown that the three-dimensional breakdown to a flow with wavy vortex boundaries, similar to that which occurs in the Taylor vortex problem takes place. However, the instability is confined to the thin shear layers which were shown by Hall & Lakin (1988) to trap the region of vortex activity. The disturbance eigenfunctions decay exponentially away from the centre of these layers, so that the upper and lower shear layers can support independent modes of instability. The structure of the instability, in particular its location and speed of downstream propagation, is found to be entirely consistent with recent experimental results. Furthermore, it is shown that the upper and lower layers support wavy vortex instabilities with quite different frequencies. This result is again consistent with the available experimental observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 204 , July 1989 , pp. 405 - 420
Copyright
© 1989 Cambridge University Press

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