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A finite-element method for inertial waves in a frustum

Published online by Cambridge University Press:  26 April 2006

Gary A. Henderson  and
Keith D. Aldridge
Gary A. Henderson
Affiliation:
Centre for Research in Earth and Space Science, York University, 4700 Keele Street, North York, Ontario M3J 1P3, Canada
Keith D. Aldridge
Affiliation:
Centre for Research in Earth and Space Science, York University, 4700 Keele Street, North York, Ontario M3J 1P3, Canada
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Abstract

A finite-element method has been developed to model inertial waves in a frustum of a cone, since analytical methods have proved inadequate. The governing Poincaré problem is posed as a variational principle and approximate eigensolutions are computed. The numerical results are used to complete the interpretation of the experimental results of Beardsley (1970) for a frustum of a cone. The significant role played by characteristic surfaces partly explains the enigmatic nature of the ill-posed boundary-value problem that describes inertial wave resonances.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 234 , January 1992 , pp. 317 - 327
Copyright
© 1992 Cambridge University Press

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References

Aldridge, K. D. 1967 An experimental study of axisymmetric inertial oscillations of a rotating liquid sphere. PhD dissertation, M.I.T.
Aldridge, K. D. 1972 Axisymmetric inertial oscillations of a fluid in a rotating spherical shell. Mathematika 19, 163–168.Google Scholar
Aldridge, K. D., Lumb, L. I. & Henderson, G. A. 1989 A Poincaré model for the Earth's fluid core. Geophys. Astrophys. Fluid Dyn. 48, 5–23.Google Scholar
Beardsley, R. C. 1970 An experimental study of inertial waves in a closed cone. Stud. Appl. Maths. 49, 187–196.Google Scholar
Bryan, G. H. 1889 The waves on a rotating liquid spheroid of finite ellipticity. Phil. Trans. R. Soc. Lond. A 180, 187–219.Google Scholar
Davies, A. J. 1980 Finite Element Method: A First Approach. Clarendon.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P. 1969 On the inviscid theory of rotating fluids. Stud. Appl. Maths 48, 19–28.Google Scholar
Høiland, E. 1962 Discussion of a hyperbolic equation relating to inertia and gravitational fluid oscillations. Geofys. Publ. 24, 211–227.Google Scholar
Kelvin, Lord 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.Google Scholar
McIntyre, J. E. & Tanner, T. M. 1987 Fuel slosh in a spinning on-axis propellant tank: an eigenmode approach. Space Commun. Broad. 5, 229–251.Google Scholar
Murphy, C. 1986 Stability of liquid-filled projectiles with unusual coning frequencies. Report BRL-MR-3530, Ballistic Research Laboratories.
Pohl, A. 1984 Dynamic effects of liquid on spinning spacecraft. Proc. First INTELSAT/ESA Symp. on the Dynamic Effects of Liquids on Spacecraft Attitude Control.
Poincaré, H. 1910 Sur le précession des corps déformables. Bull. Astronomique 27, 321–356.Google Scholar
Smylie, D. E. & Rochester, M. G. 1986 A variational principle for the subseismic wave equation. Geophys. J. R. Astr. Soc. 86, 553–561.Google Scholar
Stewartson, K. 1959 On the stability of a spinning top containing liquid. J. Fluid Mech. 5, 577–592.Google Scholar
Stewartson, K. & Rickard, J. A. 1969 Pathological oscillations of a rotating fluid. J. Fluid Mech. 35, 759–773.Google Scholar