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Free-surface oscillations in a slowly rotating liquid

Published online by Cambridge University Press:  28 March 2006

John W. Miles
John W. Miles
Affiliation:
Department of Mathematics, Institute of Advanced Studies Australian National University, Canberra
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Abstract

Free-surface oscillations of a liquid relative to an equilibrium state of uniform rotation about the vertical of an axisymmetric container are considered for small $\alpha = \omega ^2a|g$, where ω is the angular velocity of rotation and a the cylinder radius. A variational approximation is used to obtain explicit results, with an error of O(α2), for axisymmetric gravity and inertial waves in a flat-bottomed circular cylinder; these results are found to be in agreement with observations reported by Fultz (1962). The first-order (in ω) effects of rotation on asymmetric waves in a circular cylinder also are determined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 2 , February 1964 , pp. 187 - 194
Copyright
© 1964 Cambridge University Press

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References

Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms, vol. II. New York: McGraw-Hill Book Co.
Fultz, D. 1962 Trans. N.Y. Acad. Sci. 24, 321.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Miles, J. W. 1959 Phys. Fluids 2, 297.
Miles, J. W. 1963 J. Fluid Mech. 17, 75.
Miles, J. W. & Ball, F. K. 1963 J. Fluid Mech. 17, 257.
Murty, T. S. 1962 Gravity waves in a rotating paraboloidal dish. M.S. Dissertation, University of Chicago.
Platzman, G. W. 1962 (unpublished; see Fultz, l.c. ante).
Rayleigh, Lord 1903 Phil. Mag. 5, 297; Scientific Papers, 5, 93.