Asymmetry and Hopf bifurcation in spherical Couette flow

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  • Chowdhury K. Mamun
    Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712
  • Laurette S. Tuckerman
    Department of Mathematics and Center for Nonlinear Dynamics, University of Texas at Austin, Austin, Texas 78712

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<jats:p>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.</jats:p>

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