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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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