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The first instability in spherical Taylor-Couette flow

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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Abstract

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.


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http://dx.doi.org/10.1017/S0022112086000150DOIUNSPECIFIED
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=391878&fulltextType=RA&fileId=S0022112086000150PublisherUNSPECIFIED
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.
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Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft Schr271/1-2
Department of Energy (DOE)DE-AM03-76SF00761
Record Number:CaltechAUTHORS:20120627-112149667
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120627-112149667
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.
ID Code:32142
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:27 Jun 2012 18:43
Last Modified:26 Dec 2012 15:25

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