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Long wavelength vortices in time-periodic flows

Published online by Cambridge University Press:  17 February 2009

Andrew P. Bassom
Affiliation:
Department of Mathematics, University of Exeter, North Park Road, Exeter, Devon, EX4 4QE, UK
P. J. Blennerhassett
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
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Abstract

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The linear stability properties are examined of long wavelength vortex modes in two time-periodic flows. These flows are the motion which is induced by a torsionally oscillating cylinder within a viscous fluid and, second, the flow which results from the sinusoidal heating of an infinite layer of fluid. Previous studies concerning these particular configurations have shown that they are susceptible to vortex motions and linear neutral curves have been computed for wavenumbers near their critical value. These computations become increasingly difficult for long wavelength motions and here we consider such modes using asymptotic methods. These yield simple results which are formally valid for small wavenumbers and we show that the agreement between these asymptotes and numerical solutions is good for surprisingly large wavenumbers. The two problems studied share a number of common features but also have important differences and, between them, our methods and results provide a basis which can be extended for use with other time-periodic flows.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Blennerhassett, P. J., Denier, J. P. and Bassom, A. P., “High wavenumber vortices in time-periodic flows”, submitted to Proc. R. Soc. Lond. A.Google Scholar
[2]Hall, P., “Instability of time-periodic flows”, in: Stability of time dependent and spatially varying flows (eds. Dwoyer, D. L. and Hussaini, M. Y.), (Springer, Berlin, 1987) 206224.CrossRefGoogle Scholar
[3]Lentini, M. and Keller, H. B., “Boundary value problems on semi-infinite intervals and their numerical solution”, SIAM J. Numer. Anal 17 (1980) 577604.CrossRefGoogle Scholar
[4]Seminara, G. and Hall, P., “Centrifugal instability of a Stokes layer: linear theory”, Proc. R. Soc. Lond. A 350 (1976) 299316.Google Scholar