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Bifurcations and instabilities in sliding Couette flow

Published online by Cambridge University Press:  19 April 2011

K. DEGUCHI  and
M. NAGATA
K. DEGUCHI
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
*
†Email address for correspondence: [email protected]
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Abstract

We carry out linear and nonlinear analyses on a flow between two infinitely long concentric cylinders with the radii a and b subject to a sliding motion of the inner cylinder in the axial direction. We confirm the linear stability result of Gittler (Acta Mechanica, vol. 101, 1993, p. 1) for the axisymmetric case, namely the flow is linearly stable against axisymmetric perturbations when the radius ratio η = a/b is greater than 0.1415. We extend his analysis to the non-axisymmetric case and find that the stability of the flow is still determined by axisymmetric perturbations. Our nonlinear analysis exhibits that (i) finite-amplitude axisymmetric solutions exist far below the linear critical Reynolds number for η < 0.1415 and (ii) non-axisymmetric travelling wave solutions appear abruptly at a finite Reynolds number even for η > 0.1415 where the linear critical state is absent.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Instability: Nonlinear instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 156 - 178
Copyright
Copyright © Cambridge University Press 2011

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References

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