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On the gravitationally forced motions of a compressible fluid within a horizontally rotating cylinder

Published online by Cambridge University Press:  29 March 2006

Roger F. Gans
Roger F. Gans
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge
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Abstract

The effect of gravity acting perpendicularly to the stratification induced by rotation in a compressible fluid is investigated. The γ = 1 approximation used by Gans (1974) in an investigation of the free modes of a rotating gas is used to find an inviscid solution. The boundary layers are calculated, and their suctions are shown to lead to a resonance. The amplitude of the resonance mode is calculated and seen to be of the same order as the simple inviscid solution, so that a corrected solution can be obtained.

The stability of the system is discussed in a simple fashion. It seems likely that a turbulent core will form in a cylinder. The interaction of such a core with the remainder of the fluid is beyond the scope of this paper. Finally a procedure by which a zonal flow field can be found is given.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 67 , Issue 3 , 11 February 1975 , pp. 611 - 624
Copyright
© 1975 Cambridge University Press

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References

Gans, R. F. 1970 J. Fluid Mech. 41, 865.
Gans, R. F. 1974 J. Fluid Mech. 62, 657.
Gautschi, W. & Cahill, W. F. 1964 In Handbook of Mathematical Functions (ed. M. Abramowitz & I. A. Stegun), pp. 227–251. Dover.