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On the radial filling of a rotating cylinder

Published online by Cambridge University Press:  20 April 2006

M. Ungarish  and
H. P. Greenspan
M. Ungarish
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
H. P. Greenspan
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

Some aspects of the radial filling of a finite rotating cylinder are considered in the limit of a small Ekman number E. Three main cases are distinguished by the value of τF, the ratio of filling and spin-up times. When τF [Lt ] 1 the effect of the Ekman layers is unimportant and new fluid accumulates behind that already contained by an essentially radial flux. For τF ∼ 1 the Ekman layers are active and entering fluid is added both ahead and behind the initially contained fluid core. which undergoes a process similar to spin-up with the notable difference that here the Ekman layers are non-divergent. In both cases the Rossby number ε is 0(1). When τF [Gt ] 1, ε is small and the Ekman layers control the (quasi-steady) filling. The new fluid is then transported through boundary layers and spread on the moving front from the inside throughout an E¼ layer imbedded in a weak E1/3 layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 141 , April 1984 , pp. 97 - 107
Copyright
© 1984 Cambridge University Press

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