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Linear stability of the flow past a spheroidal bubble

Published online by Cambridge University Press:  14 June 2007

BINZE YANG  and
ANDREA PROSPERETTI
BINZE YANG
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
ANDREA PROSPERETTI*
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA Faculty of Applied Science and Burgerscentrum, University of Twente, AE 7500 Enschede, The Netherlands
*
†Author to whom correspondence should be addressed: prosperetti@jhu.edu
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Abstract

The linear stability of the axisymmetric flow past a fixed-shape spheroid with free-slip boundary conditions is studied numerically to gain some insight into the path instability of bubbles rising in liquids. Qualitatively, the results are similar to those for a solid sphere. The m = 1 mode gives rise to a double-threaded wake and proves to be the most unstable mode, with a first regular bifurcation followed by a Hopf bifurcation. The importance of the base-flow vorticity is highlighted by a stability analysis of the axisymmetric base flow ‘frozen’ before reaching steady state. Setting viscosity to zero in the perturbation equations results in a faster growth of the primary instability, which indicates its root in inertial effects.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 582 , 10 July 2007 , pp. 53 - 78
Copyright
Copyright © Cambridge University Press 2007

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