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Structural instability of the bifurcation diagram for two-dimensional flow in a channel with a sudden expansion

Published online by Cambridge University Press:  17 October 2000

J. MIZUSHIMA  and
Y. SHIOTANI
J. MIZUSHIMA
Affiliation:
Department of Mechanical Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan
Y. SHIOTANI
Affiliation:
Department of Mechanical Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan
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Abstract

Flow in a symmetric channel with a sudden expansion makes a transition from a symmetric flow to an asymmetric one due to a symmetry-breaking pitchfork bifurcation on a gradual increase of the Reynolds number if the system is perfectly symmetric. However, an unavoidable infinitesimal imperfection of the system may render the pitchfork bifurcation imperfect. A weakly nonlinear stability analysis is proposed to investigate the structural instability of the bifurcation for such a flow. As a result, an amplitude equation for a disturbance is derived by including the effect of the imperfection of the system, and its coefficients are evaluated numerically. The equilibrium amplitude of the disturbance is calculated from the amplitude equation and compared with the experimental results for the flow in a channel that is presumed symmetric and also with the numerical solution of the full nonlinear equations for the flow in a slightly asymmetric channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 420 , 10 October 2000 , pp. 131 - 145
Copyright
© 2000 Cambridge University Press

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