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The motion of a rising disk in a rotating axially bounded fluid for large Taylor number

Published online by Cambridge University Press:  26 April 2006

Marius Ungarish  and
Dmitry Vedensky
Marius Ungarish
Affiliation:
Department of Computer Science, Technion, Haifa 32000, Israel
Dmitry Vedensky
Affiliation:
Department of Computer Science, Technion, Haifa 32000, Israel
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Abstract

The motion of a disk rising steadily along the axis in a rotating fluid between two infinite plates is considered. In the limit of zero Rossby number and with the disk in the middle position, the boundary value problem based on the linear, viscous equations of motion is reduced to a system of dual-integral equations which renders ‘exact’ solutions for arbitrary values of the Taylor number, Ta, and disk-to-wall distance, H (scaled by the radius of the disk). The investigation is focused on the drag and on the flow field when Ta is large (but finite) for various H. Comparisons with previous asymptotic results for ‘short’ and ‘long’ containers, and with the preceding unbounded-configuration ‘exact’ solution, provide both confirmation and novel insights.

In particular, it is shown that the ‘free’ Taylor column on the particle appears for H > 0.08 Ta and attains its fully developed features when H > 0.25 Ta (approximately). The present drag calculations improve the compatibility of the linear theory with Maxworthy's (1968) experiments in short containers, but for the long container the claimed discrepancy with experiments remains unexplained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 291 , 25 May 1995 , pp. 1 - 32
Copyright
© 1995 Cambridge University Press

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