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The linear stability of a Stokes layer subjected to high frequency perturbations

Thomas, Christian, Blennerhassett, P. J., Bassom, Andrew P. and Davies, Christopher 2015. The linear stability of a Stokes layer subjected to high frequency perturbations. Journal of Fluid Mechanics 764 , pp. 193-218. 10.1017/jfm.2014.710

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Abstract

Quantitative results for the linear stability of planar Stokes layers subject to small, high-frequency perturbations are obtained for both a narrow channel and a flow approximating the classical semi-infinite Stokes layer. Previous theoretical and experimental predictions of the critical Reynolds number for the classical flat Stokes layer have differed widely with the former exceeding the latter by a factor of two or three. Here it is demonstrated that only a 1 % perturbation, at an appropriate frequency, to the nominal sinusoidal wall motion is enough to result in a reduction of the theoretical critical Reynolds number of as much as 60 %, bringing the theoretical conditions much more in line with the experimentally reported values. Furthermore, within the various experimental observations there is a wide variation in reported critical conditions and the results presented here may provide a new explanation for this behaviour.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Boundary layers; Boundary layer stability
Additional Information: Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/0022-1120/ (accessed 16/03/2015)
Publisher: Cambridge University Press
ISSN: 0022-1120
Date of First Compliant Deposit: 30 March 2016
Date of Acceptance: 4 December 2014
Last Modified: 14 Mar 2019 11:00
URI: http://orca.cf.ac.uk/id/eprint/67932

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