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Topology of vortex breakdown bubbles in a cylinder with a rotating bottom and a free surface

Published online by Cambridge University Press:  13 February 2001

MORTEN BRØNS ,
LARS K. VOIGT  and
JENS N. SØRENSEN
MORTEN BRØNS
Affiliation:
Department of Mathematics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
LARS K. VOIGT
Affiliation:
Department of Energy Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
JENS N. SØRENSEN
Affiliation:
Department of Energy Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark
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Abstract

The flow patterns in the steady, viscous flow in a cylinder with a rotating bottom and a free surface are investigated by a combination of topological and numerical methods. Assuming the flow is axisymmetric, we derive a list of possible bifurcations of streamline structures on varying two parameters, the Reynolds number and the aspect ratio of the cylinder. Using this theory we systematically perform numerical simulations to obtain the bifurcation diagram. The stability limit for steady flow is found and established as a Hopf bifurcation. We compare with the experiments by Spohn, Mory & Hopfinger (1993) and find both similarities and differences.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 428 , 10 February 2001 , pp. 133 - 148
Copyright
© 2001 Cambridge University Press

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