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Fast scalar decay in a shear flow: modes and pseudomodes

Published online by Cambridge University Press:  23 January 2007

J. VANNESTE  and
J. G. BYATT-SMITH
J. VANNESTE
Affiliation:
School of Mathematics, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, UK
J. G. BYATT-SMITH
Affiliation:
School of Mathematics, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, UK
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Abstract

The decay of a passive scalar in a sinusoidal shear flow translating in the cross-stream direction at a constant speed u is studied in the limit of small diffusivity κ. The decay rate, obtained by solving an eigenvalue problem, is found to tend to a non-zero constant as κ→0 when u is of order κ1/2. This result, establishing that fast decay is possible in shear flows, is fragile however: because of the existence of pseudomodes, the addition of a small noise leads to decay rates that decrease to zero with κ as κ2/5.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 219 - 229
Copyright
Copyright © Cambridge University Press 2007

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