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Upwelling of a stratified fluid in a rotating annulus: steady state. Part 1. Linear theory

Published online by Cambridge University Press:  29 March 2006

J. S. Allen
J. S. Allen
Affiliation:
Department of Aerospace Engineering, The Pennsylvania State University
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Abstract

The linear theory of rotating stratified fluids is applied to describe the steady axisymmetric motion of a stratified fluid in a rotating annulus for values of the stratification parameter $\overline{S} = \sigma N^2/(2\Omega)^2$ that are order one or larger: $\overline{S} \geqslant O(1)$. The motion is mechanically driven by either an applied velocity or by an applied stress at the top surface. The side walls are thermally insulated. Primary attention is given to a study of the meridional, or upwelling circulation. Simple analytical solutions are obtained with the aid of the narrow-gap approximation and a justifiable assumption of an infinite depth. In that case the meridional circulation is confined to a surface Ekman layer and to a Lineykin layer of thick-ness of $O(\overline{S}^{-\frac{1}{2}})$. It is shown how the solutions for the stress-driven upwelling flow in the annulus apply to a two-dimensional linear model of coastal upwelling in a stratified ocean.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 3 , 12 December 1972 , pp. 429 - 445
Copyright
© 1972 Cambridge University Press

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References

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