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On trapped oscillations in a slightly viscous rotating fluid

Published online by Cambridge University Press:  29 March 2006

K. Stewartson
K. Stewartson
Affiliation:
Department of Mathematics, University College London
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Abstract

Some properties of trapped oscillations in an inviscid rotating fluid were studied by Stewartson (1971, 1972). In this paper the modifications necessary to allow for a small viscosity in the fluid are discussed. It is found that concentrated disturbances of the kind used in ray theory are only possible if the rays are thought of as emanating from two sources outside the fluid and at opposite ends of the ray. Otherwise the ray must have a lateral tail, which vitiates the notion of a ray. The double-source character of rays is preserved at reflexions except when at glancing incidence. In this case a substantial part of the ray strength is lost and may give rise to a lateral tail if uncompensated. The focusing of the rays at the limit cycle is also discussed and shown to lead to a catastropic loss of energy, so that a free oscillation if set up rapidly decays. A simple forced oscillation is considered and shown to lead to weak resonances in the bands of trapped oscillations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 54 , Issue 4 , 22 August 1972 , pp. 749 - 761
Copyright
© 1972 Cambridge University Press

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