Mode interactions in an enclosed swirling flow: a double Hopf bifurcation between azimuthal wavenumbers 0 and 2

    Authors

    F. Marques; J. M. Lopez;J. Shen

    Comments

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    Abbreviated Journal Title

    J. Fluid Mech.

    Keywords

    AXISYMMETRICAL VORTEX BREAKDOWN; CYLINDRICAL GEOMETRIES; NUMERICAL-SIMULATION; ROTATING ENDWALL; PERIODIC-FLOW; CYLINDER; INSTABILITY; CONTAINER; EQUATIONS; SYMMETRY; Mechanics; Physics, Fluids & Plasmas

    Abstract

    A double Hopf bifurcation has been found of the flow in a cylinder driven by the rotation of an endwall. A detailed analysis of the multiple solutions in a large region of parameter space, computed with an efficient and accurate three-dimensional Navier-Stokes solver, is presented. At the double Hopf point, an axisymmetric limit cycle and a rotating wave bifurcate simultaneously. The corresponding mode interaction generates an unstable two-torus modulated rotating wave solution and gives a wedge-shaped region in parameter space where the two periodic solutions are both stable. By exploring in detail the three-dimensional structure of the flow, we have identified the two mechanisms that compete in the neighbourhood of the double Hopf point. Both are associated with the jet that is formed when the Ekman layer on the rotating endwall is turned by the stationary sidewall.

    Journal Title

    Journal of Fluid Mechanics

    Volume

    455

    Publication Date

    1-1-2002

    Document Type

    Article

    Language

    English

    First Page

    263

    Last Page

    281

    WOS Identifier

    WOS:000174904700012

    ISSN

    0022-1120

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