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Physics of Fluids / Volume 7 / Issue 1

Phys. Fluids 7, 80 (1995); doi:10.1063/1.868730 (12 pages)

Asymmetry and Hopf bifurcation in spherical Couette flow

Chowdhury K. Mamun1 and Laurette S. Tuckerman2

1Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712
2Department of Mathematics and Center for Nonlinear Dynamics, University of Texas at Austin, Austin, Texas 78712

(Received 19 April 1994; accepted 8 September 1994)

Spherical Couette flow is studied with a view to elucidating the transitions between various axisymmetric steady‐state flow configurations. A stable, equatorially asymmetric state discovered by Bühler [Acta Mech. 81, 3 (1990)] consists of two Taylor vortices, one slightly larger than the other and straddling the equator. By adapting a pseudospectral time‐stepping formulation to enable stable and unstable steady states to be computed (by Newton’s method) and linear stability analysis to be conducted (by Arnoldi’s method), the bifurcation‐theoretic genesis of the asymmetric state is analyzed. It is found that the asymmetric branch originates from a pitchfork bifurcation; its stabilization, however, occurs via a subsequent subcritical Hopf bifurcation. © 1995 American Institute of Physics.

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KEYWORDS and PACS

Keywords

COUETTE FLOW, BIFURCATION, STEADY FLOW, VORTICES, SYMMETRY BREAKING, VISCOUS FLOW, SPHERICAL CONFIGURATION

PACS

  • 47.20.Ft

    Instability of shear flows (e.g., Kelvin-Helmholtz)

  • 47.20.Ky

    Nonlinearity, bifurcation, and symmetry breaking

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.868730

PUBLICATION DATA

ISSN:

1070-6631 (print)  
1089-7666 (online)

For access to fully linked references, you need to log in.
    T. Mullin, K. A. Cliffe and G. Pfister, “Unusual time-dependent phenomena in Taylor-Couette flow at moderately low Reynolds numbers,” Phys. Rev. Lett. 58, 2212 (1987).

    E. Knobloch and D. R. Moore, “Minimal model of binary fluid convection,” Phys. Rev. A 42, 4693 (1990).


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