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Symmetry-breaking bifurcations in spherical Couette flow

Published online by Cambridge University Press:  26 April 2006

Oleg Yu. Zikanov
Oleg Yu. Zikanov
Affiliation:
Institute for Problems in Mechanics, Russian Academy of Science, 101 Vernadskii Ave., Moscow 117526, Russia Present address: Institut für Strömungsmechanik, Technische Universität Dresden, 01062 Dresden, Germany.
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Abstract

The solutions of the nonlinear and linearized Navier-Stokes equations are computed to investigate the instabilities and the secondary two- and three-dimensional regimes in the flow of an incompressible viscous fluid in a thin gap between two concentric differentially rotating spheres. The numerical technique is finite difference in the radial direction, spectral in the azimuthal direction, and pseudo-spectral in the meridional direction. The study follows the experiments by Yavorskaya, Belyaev and co-workers in which a variety of steady axisymmetric and three-dimensional travelling wave secondary regimes was observed in the case of a thin layer and both boundary spheres rotating. In agreement with the experimental results three different types of symmetry-breaking primary bifurcations of the basic equilibrium are detected in the parameter range under consideration.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 310 , 10 March 1996 , pp. 293 - 324
Copyright
© 1996 Cambridge University Press

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