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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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