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Asymmetry and Hopf bifurcation in spherical Couette flow. (English) Zbl 0836.76033
Summary: 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 recently 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 birucation-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.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76U05 General theory of rotating fluids
Software:
NSPCG
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