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A new nonlinear vortex state in square-duct flow

Published online by Cambridge University Press:  01 July 2010

S. OKINO,
M. NAGATA,
H. WEDIN and
A. BOTTARO
S. OKINO
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
M. NAGATA*
Affiliation:
Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
H. WEDIN
Affiliation:
Dipartimento di Ingegneria, delle Costruzioni, dell'Ambiente e del Territorio, University of Genova, Via Montallegro 1, 16145 Genoa, Italy
A. BOTTARO
Affiliation:
Dipartimento di Ingegneria, delle Costruzioni, dell'Ambiente e del Territorio, University of Genova, Via Montallegro 1, 16145 Genoa, Italy
*
†Email address for correspondence: nagata@kuaero.kyoto-u.ac.jp
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Abstract

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A new nonlinear travelling-wave solution for a flow through an isothermal square duct is discovered. The solution is found by a continuation approach in parameter space, starting from a case where the fluid is heated internally. The Reynolds number for which the travelling wave emerges is much lower than that of the solutions discovered recently by an analysis based on the self-sustaining process (Wedin et al., Phys. Rev. E, vol. 79, 2009, p. 065305; Uhlmann et al., Advances in Turbulence XII, 2009, pp. 585–588). Furthermore, the new travelling-wave solution is shown to be unstable from the onset.

JFM classification

Nonlinear Dynamical Systems: BifurcationInstability: Nonlinear instabilityInstability: Transition to turbulence

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 657 , 25 August 2010, pp. 413 - 429
Copyright
Copyright © Cambridge University Press 2010

References

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