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On the linear instability of elliptic pipe flow

Published online by Cambridge University Press:  26 April 2006

R. R. Kerswell  and
A. Davey
R. R. Kerswell
Affiliation:
Department of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, UK Present address: Department of Mathematics, University of Bristol, BS8 1TW, UK.
A. Davey
Affiliation:
Department of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, UK
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Abstract

The linear stability of elliptic pipe flow is considered for finite aspect ratios thereby bridging the gap between the small-aspect-ratio analysis of Davey & Salwen (1994) and the large-aspect-ratio asymptotics of Hocking (1977). The flow is found to become linearly unstable above an aspect ratio of about 10.4 to the spanwise-modulated analogue of the Orr-Sommerfeld mode to which plane Poiseuille flow first loses stability. This disturbance is found to possess a series of intense vortices along its critical layer at lateral stations far removed from the central minor axis. The critical Reynolds number appears to fall from infinity as the aspect ratio increases above 10.4, ultimately approaching Hocking's (1977) asymptotic result at much larger aspect ratios.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 316 , 10 June 1996 , pp. 307 - 324
Copyright
© 1996 Cambridge University Press

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