Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Exchange of stabilities in Couette flow between cylinders with Navier-slip conditions


Authors: Isom H. Herron and Pablo U. Suárez
Journal: Quart. Appl. Math. 70 (2012), 743-758
MSC (2010): Primary 76E07; Secondary 76U05, 76A02
DOI: https://doi.org/10.1090/S0033-569X-2012-01274-4
Published electronically: June 22, 2012
MathSciNet review: 3052088
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Abstract: Viscous Couette flow is derived for flow between two infinitely long concentric rotating cylinders with Navier slip on both. Its axisymmetric linear stability is studied within a regime that would be hydrodynamically stable according to Rayleigh's criterion: opposing gradients of angular velocity and specific angular momentum, based on the rotation rates and radii of the cylinders. Stability conditions are analyzed, by methods based on those of Synge and Chandrasekhar. For sufficiently small slip length on the outer cylinder no instability occurs with arbitrary slip length on the inner cylinder. As a corollary, slip on the inner cylinder is shown to be stabilizing, with no slip on the outer cylinder. Two slip configurations are investigated numerically, first with slip only on the outer cylinder, then second with equal slip on both cylinders. It is found that instability does occur (for large outer slip length), and the principle of exchange of stabilities emerges. The instability disappears for sufficiently large slip length in the second case; Rayleigh's criterion provides an explanation for these phenomena.


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Additional Information

Isom H. Herron
Affiliation: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York
Email: herroi@rpi.edu

Pablo U. Suárez
Affiliation: Department of Mathematical Sciences, Delaware State University, Dover, Delaware
Email: psuarez@dsu.edu

DOI: https://doi.org/10.1090/S0033-569X-2012-01274-4
Received by editor(s): December 22, 2010
Published electronically: June 22, 2012
Additional Notes: This paper is in final form and no version of it will be submitted for publication elsewhere.
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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