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Transition in pipe flow: the saddle structure on the boundary of turbulence

Published online by Cambridge University Press:  01 October 2008

Y. DUGUET ,
A. P. WILLIS  and
R. R. KERSWELL
Y. DUGUET
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
A. P. WILLIS
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
R. R. KERSWELL
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
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Abstract

The laminar–turbulent boundary Σ is the set separating initial conditions which relaminarize uneventfully from those which become turbulent. Phase space trajectories on this hypersurface in cylindrical pipe flow appear to be chaotic and show recurring evidence of coherent structures. A general numerical technique is developed for recognizing approaches to these structures and then for identifying the exact coherent solutions themselves. Numerical evidence is presented which suggests that trajectories on Σ are organized around only a few travelling waves and their heteroclinic connections. If the flow is suitably constrained to a subspace with a discrete rotational symmetry, it is possible to find locally attracting travelling waves embedded within Σ. Four new types of travelling waves were found using this approach.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 613 , 25 October 2008 , pp. 255 - 274
Copyright
Copyright © Cambridge University Press 2008

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