Dispersion in the large-deviation regime. Part 2: Cellular flow at large Peclet number

P. H. Haynes, J. Vanneste

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A standard model for the study of scalar dispersion through the combined effect of advection and molecular diffusion is a two-dimensional periodic flow with closed streamlines inside periodic cells. Over long time scales, the dispersion of a scalar released in this flow can be characterized by an effective diffusivity that is a factor Pe(1/2) larger than molecular diffusivity when the Peclet number Pe is large. Here we provide a more complete description of dispersion in this regime by applying the large-deviation theory developed in Part 1 of this paper. Specifically, we derive approximations to the rate function governing the scalar concentration at large time t by carrying out an asymptotic analysis of the relevant family of eigenvalue problems. We identify two asymptotic regimes and, for each, make predictions for the rate function and spatial structure of the scalar. Regime I applies to distances vertical bar x vertical bar from the scalar release point that satisfy vertical bar x vertical bar = O(Pe(1/4)t). The concentration in this regime is isotropic at large scales, is uniform along streamlines within each cell, and varies rapidly in boundary layers surrounding the separatrices between adjacent cells. The results of homogenization theory, yielding the O(Pe(1/2)) effective diffusivity, are recovered from our analysis in the limit vertical bar x vertical bar

Original languageEnglish
Pages (from-to)351-377
Number of pages27
JournalJournal of Fluid Mechanics
Publication statusPublished - Apr 2014


  • chaotic advection
  • laminar reacting flows
  • mixing and dispersion

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