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On the precession of a resonant cylinder

Published online by Cambridge University Press:  29 March 2006

Roger F. Gans
Roger F. Gans
Affiliation:
Department of Geology, University of California, Los Angeles
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Abstract

A fluid contained in a rotating cylinder has an inertial mode which is excited by forced precession of the container. Wood's (1965, 1966) early work specifically excluded resonance phenomena. Recently McEwan (1970) has discussed resonance phenomena for strong amplitude of excitation, corresponding to rapid precession in this work.

In this paper the magnitude of the resonant response for small precession rate is precisely calculated by matching the Ekman layer suction to the precessional forces. The procedure is to find the resonant mode v1, compute its boundary layers, $\tilde{{\bf v}}_1$, and the associated Ekman layer suction. The second-order problem has a solvability condition which is satisfied by matching the Ekman layer suction to the precession.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 41 , Issue 4 , 15 May 1970 , pp. 865 - 872
Copyright
© 1970 Cambridge University Press

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References

Busse, F. 1968 J. Fluid Mech. 33, 739.
Erdelyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1953 Higher transcendental functions. New York: McGraw-Hill.
Malkus, W. V. R. 1968 Science, 160, 259.
McEwan, A. D. 1970 J. Fluid Mech. 40, 603.
Wood, W. W. 1965 J. Fluid Mech. 22, 337.
Wood, W. W. 1966 Proc. Roy. Soc. A 293, 181.