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Low-dimensional bifurcation phenomena in Taylor–Couette flow with discrete azimuthal symmetry

Published online by Cambridge University Press:  26 April 2006

J. J. Kobine  and
T. Mullin
J. J. Kobine
Affiliation:
Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
T. Mullin
Affiliation:
Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
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Abstract

We report the results of an experimental study of flow in a Taylor–Couette system where the usual circular outer cylinder is replaced by one with a square cross-section. The objective is to determine the validity of low-dimensional dynamical systems as a descriptive framework for flows in a domain without the special continuous symmetry of the original problem. We focus on a restricted version of the flow, where the steady flow consists of a single cell, thereby minimizing the multiplicity of solutions. The steady-state bifurcation structure is found to be qualitatively unchanged from that of the standard system. A complex but self-consistent bifurcation structure is uncovered for time-dependent flows, culminating in observations of dynamics similar to those of the finite-dimensional Sil’nikov mechanism. Such behaviour has been observed in the standard system with continuous azimuthal symmetry. The present results extend the range of closed-flow problems where there is an apparent connection between the infinite-dimensional Navier-Stokes equations and finite-dimensional dynamical systems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 275 , 25 September 1994 , pp. 379 - 405
Copyright
© 1994 Cambridge University Press

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