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Second-class motions of a shallow liquid

Published online by Cambridge University Press:  28 March 2006

F. K. Ball
F. K. Ball
Affiliation:
C.S.I.R.O. Division of meteorological Physics, Aspendale S. 13, Victoria, Australia[dagger]
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Abstract

When a basin containing a shallow liquid is rotating with angular velocity Ω and the dimensionless number $\varepsilon = 4 \Omega ^2 L^2 | gM$ is small (L and M are typical horizontal and vertical dimensions), then, to a first approximation, the second-class motions behave as if the free surface of the liquid were fixed in its equilibrium position. The lower second-class modes of such a liquid, contained in a paraboloid, are relatively easy to describe on the basis of this approximation. When the liquid is rotating within an elliptical paraboloid and the sense of rotation is opposite to that of the container itself, the motion is unstable for a range of small angular velocities. Such unstable motions always exert a couple tending to oppose the rotation of the container.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 3 , November 1965 , pp. 545 - 561
Copyright
© 1965 Cambridge University Press

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References

Arons, A. B. & Stommel, H. M. 1956 A-plane analysis of the free periods of the second class in meridional and zonal oceans. Deep-sea Res. 4, 23.Google Scholar
Ball, F. K. 1965 The effect of rotation on the simpler modes of motion of a liquid in an elliptic paraboloid. J. Fluid Mech. 22, 529.Google Scholar
Burger, A. 1958 Scale considerations of planetary motions of the atmosphere. Tellus, 10, 195.Google Scholar
Goldsbrough, G. R. 1933 The tides in oceans in a rotating globe, Part IV. Proc. Roy. Soc. A, 140, 241.Google Scholar
Lamb, H. 1932 Hydrodynamics (6th ed.). Cambridge University Press.
Longuet-Higgins, M. S. 1964 Planetary waves on a rotating sphere. Proc. Roy. Soc. A. 279, 446.Google Scholar
Longuet-Higgins, M. S. 1965 Planetary waves on a rotating sphere, Part II. Proc. Roy. Soc. A, 284, 40.Google Scholar
Miles, J. F. & Ball, F. K. 1963 On free surface oscillations in a rotating paraboloid. J. Fluid Mech. 17, 257.Google Scholar
Phillips, N. A. 1963 Geostrophic motion. Rev. Geophys. 1, 123.Google Scholar
Phillips, N. A. 1965 Elementary Rossby waves. Tellus, 17, 295.Google Scholar
Rossby, C. G. 1939 Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centres of action. J. Mar. Res. 2, 38.Google Scholar