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On the relative importance of Taylor-vortex and non-axisymmetric modes in flow between rotating cylinders

Published online by Cambridge University Press:  28 March 2006

E. R. Krueger ,
A. Gross  and
R. C. Di Prima
E. R. Krueger
Affiliation:
Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York Present address: Department of Applied Mathematics, University of Colorado, Boulder, Colorado.
A. Gross
Affiliation:
Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York Present address: Bell Telephone Laboratories, Murray Hill, New Jersey.
R. C. Di Prima
Affiliation:
Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York
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Abstract

The small-gap equations for the stability of Couette flow with respect to non-axisymmetric disturbances are derived. The eigenvalue problem is solved by a direct numerical procedure. It is found that there is a critical value of Ω2/Ω1(Ω1, Ω2 and R1, R2 are the angular velocities and radii of the inner and outer cylinders respectively) of approximately −0·78, above which the critical disturbance is axisymmetric and below which it is non-axisymmetric. In particular for R1/R2 = 0·95, Ω2/Ω1 = −1, the wave-number in the azimuthal direction of the critical disturbance is m = 4. This result is confirmed when the full linear disturbance equations are considered, i.e. the small-gap approximation is not made.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 24 , Issue 3 , March 1966 , pp. 521 - 538
Copyright
© 1966 Cambridge University Press

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