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Lubricated pipelining: stability of core–annular flow. Part 4. Ginzburg–Landau equations

Published online by Cambridge University Press:  26 April 2006

Kangping Chen  and
Daniel D. Joseph
Kangping Chen
Affiliation:
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13676, USA
Daniel D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

Nonlinear stability of core-annular flow near points of the neutral curves at which perfect core-annular flow loses stability is studied using Ginzburg-Landau equations. Most of the core-annular flows are always unstable. Therefore the set of core-annular flows having critical Reynolds numbers is small, so that the set of flows for which our analysis applies is small. An efficient and accurate algorithm for computing all the coefficients of the Ginzburg-Landau equation is implemented. The nonlinear flows seen in the experiments do not appear to be modulations of monochromatic waves, and we see no evidence for soliton-like structures. We explore the bifurcation structure of finite-amplitude monochromatic waves at criticality. The bifurcation theory is consistent with observations in some of the flow cases to which it applies and is not inconsistent in the other cases.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 587 - 615
Copyright
© 1991 Cambridge University Press

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