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Mirror-symmetric exact coherent states in plane Poiseuille flow

Published online by Cambridge University Press:  22 October 2013

M. Nagata  and
K. Deguchi
M. Nagata*
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan
K. Deguchi
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: nagata@kuaero.kyoto-u.ac.jp
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Abstract

Two new families of exact coherent states are found in plane Poiseuille flow. They are obtained from the stationary and the travelling-wave mirror-symmetric solutions in plane Couette flow by a homotopy continuation. They are characterized by the mirror symmetry inherited from those continued solutions in plane Couette flow. The first family arises from a saddle-node bifurcation and the second family bifurcates by breaking the top–bottom symmetry of the first family. We find that both families exist below the minimum saddle-node-point Reynolds number known to date (Waleffe, Phys. Fluids, vol. 15, 2003, pp. 1517–1534).

JFM classification

Nonlinear Dynamical Systems: Bifurcation Instability: Nonlinear instability Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 735 , 25 November 2013 , R4
Copyright
©2013 Cambridge University Press 

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