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Viscous incompressible flow between concentric rotating spheres. Part 2. Hydrodynamic stability

Published online by Cambridge University Press:  29 March 2006

B. R. Munson  and
D. D. Joseph
B. R. Munson
Affiliation:
Department of Mechanical Engineering, Duke University, Durham, North Carolina
D. D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota
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Abstract

The energy theory of hydrodynamic stability is applied to the viscous incompressible flow of a fluid contained between two concentric spheres which rotate about a common axis with prescribed angular velocities. The critical Reynolds number is calculated for various radius and angular velocity ratios such that it is certain the basic laminar motion is stable to any disturbances. The stability problem is solved by means of a toroidal–poloidal representation of the disturbance flow and numerical integration of the resulting eigenvalue problem.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 49 , Issue 2 , 29 September 1971 , pp. 305 - 318
Copyright
© 1971 Cambridge University Press

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