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The spin down of rotating stratified fluids

Published online by Cambridge University Press:  29 March 2006

W. L. Siegmann
W. L. Siegmann
Affiliation:
Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York
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Abstract

The transient process by which an incompressible dissipative rotating stratified fluid adjusts to a small change in the rotation rate of its container is examined theoretically. The aim is to clarify the effects of the imposed density stratification and of the boundary condition specified for the density perturbation on the behaviour of the fluid, particularly during the time span when the adjustment is performed in a homogeneous fluid. For a weakly stratified fluid in a cylinder, it is shown how these two factors govern the nature and intensity of boundary layers on the vertical wall which close the secondary meridional circulation generated by Ekman layers along the horizontal boundaries. For a more strongly stratified fluid, the usefulness and importance of potential vorticity conservation in determining the quasi-steady motion is verified, and a calculation for a spherical container demonstrates some new features that arise only when the container boundaries are not normal or parallel to the rotation axis. It is shown that experimental results of Holton (1965) are in less good agreement with predictions of the linear theory than had been previously indicated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 47 , Issue 4 , 29 June 1971 , pp. 689 - 711
Copyright
© 1971 Cambridge University Press

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References

Barcilon, V. 1968 Stewartson layers in transient rotating fluid flows J. Fluid Mech. 33, 815.Google Scholar
Barcilon, V. & Pedlosky, J. 1967a On the steady motions produced by a stable stratification in a rapidly rotating fluid J. Fluid Mech. 29, 673.Google Scholar
Barcilon, V. & Pedlosky, J. 1967b A unified linear theory of homogeneous and stratified rotating fluids J. Fluid Mech. 29, 609.Google Scholar
Bretherton, F. P. & Spiegel, E. A. 1968 The effect of the convection zone on solar spin-down. Astrophys. J. 153, L 77.Google Scholar
Campbell, G. A. & Foster, R. M. 1948 Fourier Integrals. Van Nostrand.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P. & Howard, L. N. 1963 On a time-dependent motion of a rotating fluid J. Fluid Mech. 17, 385.Google Scholar
Holton, J. R. 1965 The influence of viscous boundary layers on transient motions in a stratified rotating fluid, part I J. Atmos. Sci. 22, 402.Google Scholar
Holton, J. R. & Stone, P. H. 1968 A note on the spin-up of a stratified fluid J. Fluid Mech. 33, 127.Google Scholar
Howard, L. N. & Siegmann, W. L. 1969 On the initial value problem for rotating stratified flow Studies Appl. Math. 48, 153.Google Scholar
Kroll, J. & Veronis, G. 1970 The spin-up of a homogeneous fluid bounded below by a permeable medium J. Fluid Mech. 40, 225.Google Scholar
Lineykin, P. C. 1955 On the determination of the thickness of the baroclinic layer in the sea Dokl. Akad. Nauk SSSR 101, 461.Google Scholar
Mcdonald, B. E. & Dicke, R. H. 1967 Solar oblateness and fluid spin-down Science, N.Y. 158, 1562.Google Scholar
Pedlosky, J. 1967 The spin up of a stratified fluid J. Fluid Mech. 28, 463.Google Scholar
Pedlosky, J. 1969 Axially symmetric motion of a stratified, rotating fluid in a spherical annulus of narrow gap J. Fluid Mech. 36, 401.Google Scholar
Phillips, O. M. 1970 On flows induced by diffusion in a stably stratified fluid Deep Sea Res. 17, 435.Google Scholar
Sakurai, T. 1969a Spin down of Boussinesq fluid in a circular container J. Phys. Soc. Japan 26, 840.Google Scholar
Sakurai, T. 1969b Spin-down problem of rotating stratified fluid in thermally insulated circular containers J. Fluid Mech. 37, 689.Google Scholar
Walin, G. 1969 Some aspects of time-dependent motion of a stratified rotating fluid J. Fluid Mech. 36, 289.Google Scholar