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The dynamics of driven rotating flow in stadium-shaped domains

Published online by Cambridge University Press:  26 April 2006

J. J. Kobine ,
T. Mullin  and
T. J. Price
J. J. Kobine
Affiliation:
Atmospheric Physics, Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
T. Mullin
Affiliation:
Atmospheric Physics, Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK
T. J. Price
Affiliation:
Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
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Abstract

Results are presented from an experimental investigation of the dynamics of driven rotating flows in stadium-shaped domains. The work was motivated by questions concerning the typicality of low-dimensional dynamical phenomena which are found in Taylor-Couette flow between rotating circular cylinders. In such a system, there is continuous azimuthal symmetry and travelling-wave solutions are found. In the present study, this symmetry is broken by replacing the stationary outer circular cylinder with one which has a stadium-shaped cross-section. Thus there is now only discrete symmetry in the azimuthal direction, and travelling waves are no longer observed. To begin with, the two-dimensional flow field was investigated using numerical techniques. This was followed by an experimental study of the dynamics of flow in systems with finite vertical extent. Configurations involving both right-circular and tapered inner cylinders were considered. Dynamics were observed which correspond to known mechanisms from the theory of finite-dimensional dynamical systems. However, flow behaviour was also observed which cannot be classified in this way. Thus it is concluded that while certain low-dimensional dynamical phenomena do persist with breaking of the continuous azimuthal symmetry embodied in the Taylor-Couette system, sufficient reduction of symmetry admits behaviour at moderately low Reynolds number which is without any low-dimensional characteristics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 294 , 10 July 1995 , pp. 47 - 69
Copyright
© 1995 Cambridge University Press

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