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Quasi-steady flow of a rotating stratified fluid in a sphere

Published online by Cambridge University Press:  11 April 2006

Susan Friedlander
Susan Friedlander
Affiliation:
Department of Mathematics, University of Illinois at Chicago Circle
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Abstract

The steady and quasi-steady motion achieved in a rotating stratified sphere of fluid is studied in the context of a linearized Boussinesq model. In certain parameter ranges an explicit expression is obtained for the flow field as a functional of the surface stress. The non-singular interior solution is used to examine the behaviour of the boundary layer close to the equator. The results agree with previous conclusions about the behaviour of a rotating stratified fluid in simpler geometries. Viewing the problem as a simple model for the interior core of the sun, this work indicates a solar spin-down time that is within the lifetime of the sun.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 2 , 28 July 1976 , pp. 209 - 228
Copyright
© 1976 Cambridge University Press

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References

Barcilon, V. & Pedlosky, J. 1967 A unified linear theory of homogeneous and stratified rotating fluids. J. Fluid Mech. 29, 609.Google Scholar
Buzyna, G. & Veronis, G. 1971 Spin-up of a stratified fluid: theory and experiment. J. Fluid Mech. 50, 579.Google Scholar
Dicke, R. H. 1964 The sun's rotation and relativity. Nature. 202, 432.Google Scholar
Dicke, R. H. 1967 The solar spin-down problem. Astrophys. J. 149, L121.Google Scholar
Dowden, J. M. 1972 An equatorial boundary layer. J. Fluid Mech. 56, 193.Google Scholar
Friedlander, S. 1972 Spin-down in a stratified rotating fluid. Ph.D. thesis, Princeton University.
Friedlander, S. 1974 Spin-down in a rotating stratified fluid: part I. Studies in Appl. Math. 53, 111.Google Scholar
Holton, J. R. 1965 The influence of viscous boundary layers on transient motion in a stratified rotating fluid. J. Atmos. Sci. 22, 402.Google Scholar
Howard, L. N., Moore, D. W. & Spiegel, E. A. 1967 Solar spin-down problem. Nature. 214, 1297.Google Scholar
Howard, L. N. & Siegmann, W. L. 1969 On the initial value problem for rotating stratified flow. Studies in Appl. Math. 48, 153.Google Scholar
Moore, D. & Weir, A. D. 1976 Spin-up in a rotating sphere. In preparation.
Pedlosky, J. 1967 The spin-up of a stratified fluid. J. Fluid Mech. 28, 463.Google Scholar
Sakurai, T. 1969 Spin-down of a rotating stratified fluid in thermally insulated circular cylinders. J. Fluid Mech. 37, 689.Google Scholar
Sakurai, T., Clark, A. & Clark, P. 1971 Spin-down of a Boussinesq fluid of small Prandtl number in a circular cylinder. J. Fluid Mech. 49, 753.Google Scholar
Stewartson, K. 1966 On almost rigid rotations. Part 2. J. Fluid Mech. 26, 131.Google Scholar