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On the stability of the similarity solutions for swirling flow above an infinite rotating disk

Published online by Cambridge University Press:  20 April 2006

R. J. Bodonyi  and
B. S. Ng
R. J. Bodonyi
Affiliation:
Department of Mathematical Sciences, Indiana University - Purdue University, Indianapolis, Indiana 46223
B. S. Ng
Affiliation:
Department of Mathematical Sciences, Indiana University - Purdue University, Indianapolis, Indiana 46223
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Abstract

A stability theory for the steady swirling flow above an infinite rotating disk immersed in an otherwise unbounded rigidly rotating fluid is developed in order to corroborate the various numerical computations considered for this problem. An analysis of the initial-value problem for linearized time-dependent perturbations on the steady-state similarity solutions shows that the disturbance equations have a stable continuum spectrum which, under certain conditions, exhibits only algebraic decay in time. In addition, a numerical analysis on the discrete spectrum shows that there are unstable eigenvalues for certain rotational rates of the disk relative to the fluid at infinity. The results obtained are in good agreement with the large-time behaviour of the corresponding solutions of the unsteady similarity equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 144 , July 1984 , pp. 311 - 328
Copyright
© 1984 Cambridge University Press

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