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The instability of the steady flow past spheres and disks

Published online by Cambridge University Press:  26 April 2006

Ramesh Natarajan  and
Andreas Acrivos
Ramesh Natarajan
Affiliation:
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA
Andreas Acrivos
Affiliation:
IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, USA
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Abstract

We consider the instability of the steady, axisymmetric base flow past a sphere, and a circular disk (oriented broadside-on to the incoming flow). Finite-element methods are used to compute the steady axisymmetric base flows, and to examine their linear instability to three-dimensional modal perturbations. The numerical results show that for the sphere and the circular disk, the first instability of the base flow is through a regular bifurcation, and the critical Reynolds number (based on the body radius) is 105 for the sphere, and 58.25 for the circular disk. In both cases, the unstable mode is non-axisymmetric with azimuthal wavenumber m = 1. These computational results are consistent with previous experimental observations (Magarvey & Bishop 1961 a, b; Nakamura 1976; Willmarth, Hawk & Harvey 1964).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 254 , September 1993 , pp. 323 - 344
Copyright
© 1993 Cambridge University Press

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