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A spatial analogue of transient growth in plane Couette flow

Published online by Cambridge University Press:  25 October 1999

JACQUES VANNESTE
JACQUES VANNESTE
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK
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Abstract

The linear response of an inviscid two-dimensional Couette flow disturbed by a time-periodic forcing is studied under the assumption that the forcing is distributed along a straight line. When the forcing is tilted against the shear, the disturbance streamfunction and energy are shown to be locally amplified downstream of the source before decaying at large distance. This spatially localized amplification is interpreted as an analogue of the transient growth phenomenon studied in the context of unforced intial-value problems. The self-consistency of the linear approximation and the instability of the disturbance are also examined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 397 , 25 October 1999 , pp. 317 - 330
Copyright
© 1999 Cambridge University Press

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