Second-class motions of a shallow liquid
- 1 September 1965
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 23 (03) , 545-561
- https://doi.org/10.1017/s0022112065001532
Abstract
When a basin containing a shallow liquid is rotating with angular velocity Ω and the dimensionless number 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.Keywords
This publication has 7 references indexed in Scilit:
- Elementary Rossby wavesTellus, 1965
- The effect of rotation on the simpler modes of motion of a liquid in an elliptic paraboloidJournal of Fluid Mechanics, 1965
- On free-surface oscillations in a rotating paraboloidJournal of Fluid Mechanics, 1963
- Geostrophic motionReviews of Geophysics, 1963
- Scale Consideration of Planetary Motions of the AtmosphereTellus A: Dynamic Meteorology and Oceanography, 1958
- Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of actionJournal of Marine Research, 1939
- The tides in Oceans on a Rotating Globe.—Part IVProceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1933