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Dean vortices in finite-aspect-ratio ducts

Published online by Cambridge University Press:  31 January 2013

Philip E. Haines ,
James P. Denier  and
Andrew P. Bassom
Philip E. Haines
Affiliation:
School of Mathematical Sciences, The University of Adelaide, South Australia 5005, Australia
James P. Denier*
Affiliation:
Department of Engineering Science, The University of Auckland, Auckland 1142, New Zealand
Andrew P. Bassom
Affiliation:
School of Mathematics & Statistics, The University of Western Australia, Crawley 6009, Australia
*
†Email address for correspondence: j.denier@auckland.ac.nz
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Abstract

We consider the development of Dean vortices in a curved channel of finite aspect ratio. Solutions to the axisymmetric Navier–Stokes equations are obtained through a finite-element analysis, allowing us to explore the complex and rich bifurcation pattern of the flow as the aspect ratio and Dean number vary. We demonstrate a new class of finite-amplitude vortices and discuss their relationship to similar structures seen in finite-length Taylor–Couette flow.

JFM classification

Instability: Instability Instability: Nonlinear instability
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , R8
Copyright
©2013 Cambridge University Press

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Footnotes

‡

Current address: Department of Mathematics, University College London.

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