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Streamline topology in the near wake of a circular cylinder at moderate Reynolds numbers

Published online by Cambridge University Press:  25 July 2007

MORTEN BRØNS ,
BO JAKOBSEN ,
KRISTINE NISS ,
ANDERS V. BISGAARD  and
LARS K. VOIGT
MORTEN BRØNS*
Affiliation:
Department of Mathematics, Technical University of Denmark, Building 303S, DK-2800 Kongens Lyngby, Denmark
BO JAKOBSEN
Affiliation:
Department of Mathematics, Technical University of Denmark, Building 303S, DK-2800 Kongens Lyngby, Denmark Department of Mathematics and Physics, Roskilde University, PO Box 260, DK-4000 Roskilde, Denmark
KRISTINE NISS
Affiliation:
Department of Mathematics, Technical University of Denmark, Building 303S, DK-2800 Kongens Lyngby, Denmark Department of Mathematics and Physics, Roskilde University, PO Box 260, DK-4000 Roskilde, Denmark
ANDERS V. BISGAARD
Affiliation:
Department of Mathematics, Technical University of Denmark, Building 303S, DK-2800 Kongens Lyngby, Denmark
LARS K. VOIGT
Affiliation:
Department of Mechanics, Technical University of Denmark, Building 403, DK-2800 Kongens Lyngby, Denmark
*
† Author to whom correspondence should be addressed: [email protected].
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Abstract

For the flow around a circular cylinder, the steady flow changes its topology at a Reynolds number around 6 where the flow separates and a symmetric double separation zone is created. At the bifurcation point, the flow topology is locally degenerate, and by a bifurcation analysis we find all possible streamline patterns which can occur as perturbations of this flow. We show that there is no a priori topological limitation from further assuming that the flow fulfils the steady Navier–Stokes equations or from assuming that a Hopf bifurcation occurs close to the degenerate flow.

The steady flow around a circular cylinder experiences a Hopf bifurcation for a Reynolds number about 45–49. Assuming that this Reynolds number is so close to the value where the steady separation occurs that the flow here can be considered a perturbation of the degenerate flow, the topological bifurcation diagram will contain all possible instantaneous streamline patterns in the periodic regime right after the Hopf bifurcation. On the basis of the spatial and temporal symmetry associated with the circular cylinder and the structure of the topological bifurcation diagram, two periodic scenarios of instantaneous streamline patterns are conjectured. We confirm numerically the existence of these scenarios, and find that the first scenario exists only in a narrow range after the Hopf bifurcation whereas the second one persists through the entire range of Re where the flow can be considered two-dimensional. Our results corroborate previous experimental and computational results.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 584 , 10 August 2007 , pp. 23 - 43
Copyright
Copyright © Cambridge University Press 2007

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Footnotes

‡

Present address: NKT Flexibles I/S, Priorparken 510, DK-2605 Brøndby, Denmark.

‖

Present address: ANSYS Europe Ltd, West Central 127, Milton Park, Abingdon, Oxfordshire, OX14 4SA, UK.

References

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