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On the stability of viscous free-surface flow supported by a rotating cylinder

Peterson, R.C., Jimack, P.K. and Kelmanson, M.A. (2001) On the stability of viscous free-surface flow supported by a rotating cylinder. Proceedings of the Royal Society Series A: Mathematical, Physical and Engineering Sciences, 457 (2010). pp. 1427-1445. ISSN 1471-2946

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Abstract

Using an adaptive finite-element (FE) scheme developed recently by the authors, we shed new light on the long-standing fundamental problem of the unsteady free-surface Stokes flow exterior to a circular cylinder rotating about its horizontal axis in a vertical gravitational field. For supportable loads, we observe that the steady-state is more readily attained for near-maximal fluid loads on the cylinder than for significantly sub-maximal loads. For the latter, we investigate large-time dynamics by means of a finite-difference approximation to the thin-film equations, which is also used to validate the adaptive FE simulations (applied to the full Stokes equations) for these significantly sub-maximal loads.

Conversely, by comparing results of the two methods, we assess the validity of the thin-film approximation as either the load is increased or the rotation rate of the cylinder is decreased. Results are presented on the independent effects of gravity, surface tension and initial film thickness on the decay to steady-state. Finally, new numerical simulations of load shedding are presented.

Item Type: Article
Copyright, Publisher and Additional Information: © 2001 The Royal Society. This is an author produced version of a paper published in 'Proceedings of the Royal Society Series A: Mathematical, Physical and Engineering Sciences'
Keywords: viscous fluid mechanics, free-surface flow, Stokes approximation, finite-element methods, adaptive meshing
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Repository Assistant
Date Deposited: 16 Nov 2006
Last Modified: 06 Jun 2014 04:09
Published Version: http://dx.doi.org/10.1098/rspa.2000.0780
Status: Published
Publisher: The Royal Society of London
Refereed: Yes
Identification Number: 10.1098/rspa.2000.0780
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1713

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