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The effect of viscosity on the stability of a uniformly rotating liquid column in zero gravity

Published online by Cambridge University Press:  23 January 2007

J. P. KUBITSCHEK  and
P. D. WEIDMAN
J. P. KUBITSCHEK*
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA
P. D. WEIDMAN
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427, USA
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Abstract

An investigation of the linear temporal stability of a uniformly rotating viscous liquid column in the absence of gravity is presented. The governing parameters are the rotational Reynolds number Re and the Hocking parameter L, defined as the ratio of surface tension to centrifugal forces. Though the viscosity-independent condition L≥(k2 + n2-1)−1 for stability to disturbances of axial wavenumber k and azimuthal mode number n has been known for some time, the preferred modes, growth rates and frequencies at onset of instability have not been reported. We compute these results over a wide range of L–Re space and determine certain asymptotic behaviours in the limits of L→0, L→∞ and Re→∞. The computations exhibit a continuous evolution toward known inviscid stability results in the large-Re limit and their ultimate transition to an n = 1 spiral mode at small Re. While viscosity is shown to reduce growth rates for axisymmetric disturbances, it also produces a destabilizing effect for n = 2 planar and n = 1 spiral disturbances in certain regions of parameter space. A special feature is the appearance of a tricritical point in L–Re space at which maximum growth rates of the axisymmetric, n = 1 spiral, and n = 2 planar disturbances are equal.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 261 - 286
Copyright
Copyright © Cambridge University Press 2007

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