Fast scalar decay in a shear flow: modes and pseudomodes

J. Vanneste, J. G. Byatt-Smith

Research output: Contribution to journalArticlepeer-review

Abstract

The decay of a passive scalar in a sinusoidal shear flow translating in the cross-stream direction at a constant speed a is studied in the limit of small diffusivity K. The decay rate, obtained by solving an eigenvalue problem, is found to tend to a non-zero constant as kappa -> 0 when u is of order kappa(1/2). 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 kappa as kappa(2/5).

Original languageEnglish
Pages (from-to)219-229
Number of pages11
JournalJournal of Fluid Mechanics
Volume572
DOIs
Publication statusPublished - 10 Feb 2007

Keywords

  • DIFFERENTIAL-OPERATORS
  • PASSIVE SCALARS
  • PSEUDOSPECTRA
  • DIFFUSION

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