Abstract
The decay of a passive scalar in a sinusoidal shear flow translating in the cross-stream direction at a constant speeduis 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 whenuis 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.
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