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A note on the mirror-symmetric coherent structure in plane Couette flow

Published online by Cambridge University Press:  14 June 2013

M. Nagata
M. Nagata*
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
*
†Email address for correspondence: nagata@kuaero.kyoto-u.ac.jp
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Abstract

We note that the mirror-symmetric solution in plane Couette flow, found recently by Gibson, Halcrow & Cvitanović (J. Fluid Mech., vol. 611, 2009, pp. 107–130) and Itano & Generalis (Phys. Rev. Lett., vol. 102, 2009, p. 114501), belongs to the solution group classified as ‘ribbon’ in rotating-plane Couette flow (RPCF). It represents a subcritical (in terms of the system rotation) solution at zero rotation rate on the three-dimensional tertiary flow branch which bifurcates from the second streamwise-independent flow in RPCF. The way of its appearance is similar to that of the Nagata solution (J. Fluid Mech., vol. 217, 1990, pp. 519–527), which lies on the subcritical three-dimensional tertiary flow branch bifurcating from the first streamwise-independent flow in RPCF.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Instability: Nonlinear instability Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , R1
Copyright
©2013 Cambridge University Press 

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