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Separation and the Taylor-column problem for a hemisphere

Published online by Cambridge University Press:  29 March 2006

J. D. A. Walker  and
K. Stewartson
J. D. A. Walker
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907
K. Stewartson
Affiliation:
Department of Mathematics, University College, London
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Abstract

A layer of viscous incompressible fluid is confined between two horizontal plates which rotate rapidly in their own plane with a constant angular velocity. A hemisphere has its plane face joined to the lower plate and when a uniform flow is forced past such an obstacle, a Taylor column bounded by thin detached vertical shear layers forms. The linear theory for this problem, wherein the Rossby number ε is set equal to zero on the assumption that the flow is slow, is examined in detail. The nonlinear modifications of the shear layers are then investigated for the case when ε ∼ E½, where E is the Ekman number. In particular, it is shown that provided that the Rossby number is large enough separation occurs in the free shear layers. The extension of the theory to flow past arbitrary spheroids is indicated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 66 , Issue 4 , 11 December 1974 , pp. 767 - 789
Copyright
© 1974 Cambridge University Press

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