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Mean field approximations to Couette flow and its stability

Published online by Cambridge University Press:  24 October 2008

Roy Bradley
Roy Bradley
Affiliation:
Department of Mathematics, Rutherford College of Technology, Ellison Place, Newcastle upon Tyne
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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

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References

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