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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

Allen, J. S. 1972 Upwelling of a stratified fluid in a rotating annulus. Part 2. Numerical Submitted to J. Fluid Mech.Google Scholar
Barcilon, V. & Pedlosky, J. 1967a Linear theory of rotating stratified fluid motions. J. Fluid Mech. 29, 1–16.Google Scholar
Barcilon, V. & Pedlosky, J. 1967b A unified linear theory of homogeneous and stratified rotating fluids. J. Fluid Mech. 29, 609–621.Google Scholar
Blumsacp, S. L. 1972 The transverse circulationnear a coast. J. Phys. Ocealzogr. 2, 34–40.Google Scholar
Collins, C. A., Mooers, C. N. K., Stevenson, M. R., Smith, R. L. & Pattullo, J. G. 1968 Direct current measurements in the frontal zone of a coastal upwelling region. J. Oceanogr. Soc. Japan, 24, 295–306.Google Scholar
Durance, J. A. & Johnson, J. A. 1970 East coast ocean currents. J. Fluid Mech. 44, 161–172.Google Scholar
Garvine, R. W. 1971 A simple model of coastal upwelling dynamics. J. Phys. Oceanogr. 1, 169–179.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hsueh, Y. & Kenney, R. N. 1972 Steady coastal upwelling in a continuously stratified ocean. J. Phys. Oceanogr. 2, 27–33.Google Scholar
Leetma, A. 1969 On the theory of coastal upwelling. Ph.D. thesis, M.I.T.
Leetma, A. 1971 Some effects of stratification on rotating fluids. J. Atmos. Sci. 28, 65–71.Google Scholar
Lineykin, P. S. 1955 On the determination of the thickness of the baroclinic layer in the oeean. Dokl. Akad. Nauk Sssr, 101, 461–464.Google Scholar
Pedlosky, J. 1968 An overlooked aspect of the wind-driven oceanic circulation. J. Fluid Mech. 32, 809–821.Google Scholar
Pedlosky, J. 1970 Notes on the 1970 Summer Program in Geophysical Fluid Dynamics, The Woods Hole Oceanographic Institution, no. 70-50, vol. 1, 1–67.