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

Published online by Cambridge University Press:  23 December 2014

Christian Thomas ,
P. J. Blennerhassett ,
Andrew P. Bassom  and
Christopher Davies
Christian Thomas
Affiliation:
Department of Mathematics, South Kensington Campus, Imperial College London, London SW7 2AZ, UK
P. J. Blennerhassett
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Andrew P. Bassom*
Affiliation:
School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia
Christopher Davies
Affiliation:
Department of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Boundary layer stability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 193 - 218
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Copyright
© 2014 Cambridge University Press 

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