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Recycling flow over bottom topography in a rotating annulus

Published online by Cambridge University Press:  12 April 2006

M. K. Davey
M. K. Davey
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge Present address: National Centre for Atmospheric Research, Boulder, Colorado 80303.
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Abstract

Steady flow of an incompressible homogeneous fluid over shallow topography in a rotating annulus is considered. The flow is driven by a differentially rotating lid. The recycling nature of the system means that prescribed upstream conditions are not available to close the problem. Consideration of the balance of transport across streamlines for the geostrophic flow leads to a general circulation condition; namely $\Gamma(\psi) = \frac{1}{2}\Gamma_T(\psi)$, where ϕ is the stream function for the geostrophic flow, Λ is the circulation around a streamline and ΛT is the circulation around the same path calculated using the prescribed upper surface velocity. Using this condition, stream functions for the linear viscous and nonlinear quasi-inviscid flow can be found. Solutions for these two limits, and linearized perturbation solutions for the transition regime between them, are presented for flow over ridges in the annulus.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 3 , 15 August 1978 , pp. 497 - 520
Copyright
© 1978 Cambridge University Press

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