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The linear stability of flat Stokes layers

Published online by Cambridge University Press:  21 August 2002

P. J. BLENNERHASSETT  and
ANDREW P. BASSOM
P. J. BLENNERHASSETT
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia; [email protected]
ANDREW P. BASSOM
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia; [email protected] Permanent address: School of Mathematical Sciences, University of Exeter, North Park Road, Exeter, Devon EX4 4QE, UK, [email protected]
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Abstract

The linear stability of the Stokes layer generated by an oscillating flat plate is investigated using Floquet theory. The results obtained include the behaviour of the growth rate of the disturbances, part of the corresponding neutral curve and the structure of neutrally stable disturbances. Previously unknown properties of the growth rate cause the neutral curve to have a complicated geometry: the majority of the marginal curve is defined by waves propagating relative to the basic flow and the curve is smooth in character, but for certain very narrow bands of wavenumbers it was found that stationary modes are the first to become unstable. This phenomenon has the consequence that the underlying smooth neutral curve is punctuated by thin finger-like features. The structure of the eigenfunctions showed that the neutrally stable disturbances tend to grow most rapidly just after the wall velocity passes through zero.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 464 , 10 August 2002 , pp. 393 - 410
Copyright
© 2002 Cambridge University Press

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