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The linear stability of high-frequency flow in a torsionally oscillating cylinder

Published online by Cambridge University Press:  28 March 2007

P. J. BLENNERHASSETT  and
ANDREW P. BASSOM
P. J. BLENNERHASSETT
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia
ANDREW P. BASSOM
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Crawley 6009, Australia
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Abstract

The linear stability of the Stokes layer induced in a fluid contained within a long cylinder oscillating at high frequency about its longitudinal axis is investigated. The disturbance equations are derived using Floquet theory and the resulting system solved using pseudo-spectral methods. Both shear modes and axially periodic centripetal disturbance modes are examined and neutral stability curves and corresponding critical conditions for instability identified. For sufficiently small cylinder radius it is verified that the centripetal perturbations limit the stability of the motion but that in larger-radius configurations the shear modes associated with the Stokes layer take over this role. These results suggest a possible design, free of entry-length effects, for experiments intended to examine the breakdown of oscillatory boundary layers.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 576 , 10 April 2007 , pp. 491 - 505
Copyright
Copyright © Cambridge University Press 2007

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