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Mean field approximations to Couette flow and its stability
Published online by Cambridge University Press: 24 October 2008
Abstract
The preferred-mode method of Roberts (11) is applied to the stability of liquid contained between coaxial cylinders, the inner of which is rotating. Accordingly the velocity field of a steady Taylor vortex is approximated by a truncated Fourier series and the steady state corresponding to a chosen wave number is obtained. The stability of a steady state so obtained is investigated:
(a) With respect to an axisymmetric perturbation associated with a Taylor vortex of a different axial wave number, so that a stable or ‘ preferred ’ steady state is determined. This is done for a narrow gap, η (the ratio of the radii of the cylinders) = 0·95, for Taylor numbers up to 40%, and for a wide gap, η = 0·5, up to 30% beyond the critical values.
(b) For a narrow gap, η = 0·95, with respect to a non-axisymmetric perturbation of a different axial wave number. The solutions obtained for the steady states are found to be stable to such perturbations for a range of Taylor numbers 40% beyond the critical value.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 3 , May 1970 , pp. 657 - 670
- Copyright
- Copyright © Cambridge Philosophical Society 1970
References
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