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Inertial modes with large azimuthal wavenumbers in an axisymmetric container

Published online by Cambridge University Press:  20 April 2006

W. W. Wood
W. W. Wood
Affiliation:
Mathematics Department, University of Melbourne, Parkville, Australia, 3052
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Abstract

Free oscillations are considered of a fluid rotating with constant angular velocity $\Omega \hat{\rm z}$ in a rigid axisymmetric container. Modes are sought that vary rapidly in an axial (r, z) plane with a length scale O(n−1) times that of the container, where n [Gt ] 1. The azimuthal wavenumber k > 0 is also taken to be large. The modulated wave modes postulated (represented as in (4.1)) prove to have a quiescent zone near the axis. Elsewhere their pressure is of a uniform order of magnitude. Their velocity however is locally magnified by a factor O(n) near the critical circles. It is argued that for k/n [Lt ] 1 the modulated waves eligible as modes in smooth, convex containers are of two kinds; one, which generally occurs for continuous frequency bands, being singular and indeterminate; the other being like the modes in a sphere. Modes of the second kind are determined for eigenfrequencies ω ≃ √2 Ω for containers whose axia lcross-sections are symmetrical about z = 0 and about r = ±z.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 427 - 449
Copyright
© 1981 Cambridge University Press

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