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Modulated Taylor–Couette flow

Published online by Cambridge University Press:  26 April 2006

C. F. Barenghi  and
C. A. Jones
C. F. Barenghi
Affiliation:
School of Mathematics, The University, Newcastle-upon-Tyne, NE1 7RU, UK
C. A. Jones
Affiliation:
School of Mathematics, The University, Newcastle-upon-Tyne, NE1 7RU, UK
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Abstract

The onset of instability in temporally modulated Taylor-Couette flow is considered. Critical Reynolds numbers have been found by computing Floquet exponents. We find that frequency modulation of the inner cylinder introduces a small destabilization, in agreement with the narrow-gap theory of Hall and some recent experiments of Ahlers. We review the previous computational literature on this problem, and find a number of contradictory results: the source of these discrepancies is examined, and a satisfactory resolution is achieved. Nonlinear axisymmetric calculations on the modulated problem have been done with an initial value code using a spectral method with collocation. The results are compared satisfactorily with Ahlers' measurements.

At low modulation frequency, a large destabilization has been observed in past experiments. We show that this cannot be explained on the basis of perfect bifurcation theory: an analysis of the modulated amplitude equation shows that very small imperfections can substantially affect the behaviour at low frequency by giving rise to ‘transient’ vortices at subcritical Reynolds number. We argue that these ‘transient’ vortices are the source of the large destabilization seen in some experiments. Modelling the imperfections in the initial-value code provides additional confirmation of this effect.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 208 , November 1989 , pp. 127 - 160
Copyright
© 1989 Cambridge University Press

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