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Pseudo-three-timescale approximation of exponentially modulated free-surface waves

Published online by Cambridge University Press:  14 April 2009

MARK A. KELMANSON
MARK A. KELMANSON*
Affiliation:
Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
†Email address for correspondence: mark@maths.leeds.ac.uk
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Abstract

A novel pseudo-three-timescale asymptotic procedure is developed and implemented for obtaining accurate approximations to solutions of an evolution equation arising in thin-film free-surface viscous flow. The new procedure, which employs strained fast and slow timescales, requires considerably fewer calculations than its standard three-timescale counterpart employing fast, slow and slower timescales and may readily be applied to other evolution equations of fluid mechanics possessing wave-like solutions exhibiting exponential decay in amplitude and variations in phase over disparate timescales. The new method is validated on the evolution of free-surface waves on a thin, viscous film coating the exterior of a horizontal rotating cylinder and is shown to yield accurate solutions up to non-dimensional times exceeding by an order of magnitude those of previous related studies. Results of the new method applied to this test problem are demonstrated to be in excellent agreement, over large timescales, with those of corroborative spectrally accurate numerical integrations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 625 , 25 April 2009 , pp. 435 - 443
Copyright
Copyright © Cambridge University Press 2009

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References

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