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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access published online on July 28, 2007
The Quarterly Journal of Mechanics and Applied Mathematics, doi:10.1093/qjmam/hbm014
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© The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A NOTE ON THE LINEAR STABILITY OF A TWO-DIMENSIONAL STOKES LAYER

PJ Blennerhassett

( School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia )

Andrew P. Bassom{dagger}

( School of Mathematics and Statistics, University of Western Australia, Crawley 6009, Australia )

{dagger} < bassom{at}maths.uwa.edu.au>

Received 21 March 2007. Revise 18 May 2007.
  Abstract

The fluid motion generated adjacent to an infinite flat plate undergoing orbital motion in its own plane is a generalization of the classical Stokes-layer profile. We show that the stabilities of these flows can be related to each other via two transformations directly analogous to the well-known Squire transformation. The main result obtained is that, in general, the two-dimensional Stokes layer is more stable than the corresponding unidirectional Stokes layer. A further by-product of the analysis is the construction of a shear flow having identical neutral stability conditions when subject to either two- or three-dimensional disturbances.


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