Schrauf, Géza (1986) The first instability in spherical Taylor-Couette flow. Journal of Fluid Mechanics, 166 . pp. 287-303. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120627-112149667
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In this paper continuation methods are applied to the axisymmetric Navier-Stokes equations in order to investigate how the stability of spherical Couette flow depends on the gap size σ. We find that the flow loses its stability due to symmetry-breaking bifurcations and exhibits a transition with hysteresis into a flow with one pair of Taylor vortices if the gap size is sufficiently small, i.e. if σ ≤σ_B. In wider gaps, i.e. for σ_B < σ ≤ σ_F, both flows, the spherical Couette flow and the flow with one pair of Taylor vortices, are stable. We predict that the latter exists in much wider gaps than previous experiments and calculations showed. Taylor vortices do not exist if σ > σ_F. The numbers σ_B and σ_F are computed by calculating the instability region of the spherical Couette flow and the region of existence of the flow with one pair of Taylor vortices.
|Additional Information:||© 1986 Cambridge University Press. Received 24 June 1985 and in revised form 24 September 1985. Published online: 21 April 2006. I thank John Bolstadt and Herb Keller for many fruitful discussions. This work was supported by the Deutsche Forschungsgemeinschaft (research scholarship no. Schr271/1-2) and by the U.S. Department of Energy (contract no. DE-AM03-76SF00761.|
|Official Citation:||Géza Schrauf (1986). The first instability in spherical Taylor-Couette flow. Journal of Fluid Mechanics, 166 , pp 287-303 doi:10.1017/S0022112086000150|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||27 Jun 2012 18:43|
|Last Modified:||26 Dec 2012 15:25|
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