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Adjustment under gravity in a rotating channel

Published online by Cambridge University Press:  11 April 2006

A. E. Gill
A. E. Gill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
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Abstract

What transient motions occur as a fluid responds to gravitational forces in a rotating channel, and what equilibrium does the fluid adjust to? This problem is studied to illustrate how boundaries affect the process of adjustment to a geostrophic equilibrium. In particular, linear solutions are found for an infinitely long channel of constant width and constant depth when there is an initial discontinuity in the level of the free surface. The results are summarized in the figures, and can be described in terms of Poinearé waves and Kelvin waves. When the channel is wide compared with the Rossby radius, the final state involves a current of that width which follows the left-hand boundary (for Northern-Hemisphere rotation) to the position of the initial discontinuity, then crosses the channel and continues downstream along the right-hand wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 77 , Issue 3 , 8 October 1976 , pp. 603 - 621
Copyright
© 1976 Cambridge University Press

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References

Blumen, W. 1972 Rev. Geophys. Space Phys. 10, 485.
Cahn, A. 1945 J. Met. 2, 113.
Dickinson, R. E. 1969 Rev. Geophys. 7, 483.
Erdélyi, A., Magnus, W., Oberhettinger, F. & Triconii, F. G. 1954 Tables of Integral Transforms, vol. 1. McGraw-Hill.
Euler, L. 1755 Mem. Acad. Berlin, 11, 279, 316. (See also Opera Omnia Ser. Secunda, vol. XII, pp. 54, 92. Lausanne, 1954.)
Gill, A. E. & Clarke, A. J. 1974 Deep-sea Res. 21, 325.
Hendershott, M. C. & Speranza, A. 1971 Deep-sea Res. 18, 959.
Kelvin, Lord 1879 Proc. Roy. Soc. Edin. 10, 92. (See also Phil. Mag. 10 (1880), 97; Math. Phys. Papers, vol. IV, p. 141, Cambridge University Press 1910.)
Krauss, W. 1966 Interne Wellen, Methoden und Ergebnisse der Theoretischen Ozeano-graphic, vol. 11. Berlin: Gerbriider Borntraeger.
Laplace, P. S. 1778/9 Mém. Acad. Roy. Sciences Paris, 1775 volume, p. 75–182 (publ. 1778), 1776 volume, pp. 177, 525 (publ. 1779). (See also Oeuvres, vol. ix, pp. 71, 187, 283. Paris: Gauthier-Villars, 1893.)
Morse, P. M. & Feshbach, H., 1953 Methods of Theoretical Physics. McGraw-Hill.
Poincaré, S. 1910 Théorie des Marées. Leçons de Mécanique Celeste, vol. 3. Paris: Gauthier-Villars.
Rossby, C. G. 1937 J. Mar. Res. 1, 15.
Rossby, C. G. 1938 J. Mar. Res. 1, 239.
Taylon, G. I. 1921 Proc. Lond. Math. Soc. 20, 148.