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Ageostrophic effects in rotating stratified flow

Published online by Cambridge University Press:  29 March 2006

Herbert E. Huppert  and
Melvin E. Stern
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Melvin E. Stern
Affiliation:
Graduate School of Oceanography, University of Rhode Island, Kingston, Rhode Island 02881
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Abstract

We consider the low Rossby number (R) flow of a stratified fluid in a long rotating channel, for which the bottom elevation varies in the downstream direction. The quasi-geostrophic response is shown to be singular at the side walls of the channel, and thus an ageostrophic analysis is necessary even for vanishingly small R. Part of the ageostrophic steady-state response is a modified quasi-geostrophic perturbation trapped near the bottom. A second component which is present even as R approaches zero is an internal Kelvin wave whose vertical wavelength adjusts so that the wave remains stationary with respect to the channel bottom and which propagates energy and momentum to infinite heights in an unbounded channel. The case of a bounded layer of fluid is also considered, and the resonance conditions are given. We also calculate the flow field when the bottom elevation varies in the cross-stream direction. We conclude that stagnation or flow reversal can be caused either by the modified quasi-geostrophic component or by the Kelvin wave and estimate the critical condition by an extrapolation of the perturbation velocity computed from linear theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 2 , 23 January 1974 , pp. 369 - 385
Copyright
© 1974 Cambridge University Press

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