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A swirling spiral wave solution in pipe flow

Published online by Cambridge University Press:  20 November 2013

K. Deguchi  and
A. G. Walton
K. Deguchi*
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
A. G. Walton*
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email addresses for correspondence: k.deguchi@imperial.ac.uk, a.walton@imperial.ac.uk
†Email addresses for correspondence: k.deguchi@imperial.ac.uk, a.walton@imperial.ac.uk
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Abstract

A numerically exact full Navier–Stokes counterpart of the asymptotic nonlinear solution in Hagen–Poiseuille flow proposed by Smith & Bodonyi (Proc. R. Soc. A, vol. 384, 1982, pp. 463–489) is discovered. The solution takes the form of a spiral travelling wave, with a novel feature being a strong induced component of swirl. Our solution shows excellent quantitative agreement with the asymptotic theory at Reynolds numbers of the order of $1{0}^{8} $.

JFM classification

Waves/Free-surface Flows: Critical layers Instability: Nonlinear instability Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 737 , 25 December 2013 , R2
Copyright
©2013 Cambridge University Press 

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