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Asymptotic descriptions of oblique coherent structures in shear flows

Published online by Cambridge University Press:  08 October 2015

Kengo Deguchi*
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Philip Hall*
School of Mathematics, Monash University, Melbourne, VIC 3800, Australia
Email addresses for correspondence:,
Email addresses for correspondence:,


Exact coherent states in plane Couette flow are extended to an oblique parallelogram computational domain and the large-Reynolds-number asymptotic descriptions of the states are derived. When the tilt angle of the domain is increased, the states first obey vortex–wave interaction theory and then develop a new asymptotic structure. The latter asymptotic structure is characterized by a self-similar nonlinear interaction localized in the fluid layer. For the largest scale of the self-similar nonlinear structure, the theory predicts an inverse Reynolds number dependence for the tilt angle of the oblique pattern. That result is consistent with the numerical and experimental observations of the laminar–turbulent banded pattern in shear flows.

© 2015 Cambridge University Press 

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