Enhanced diffusivity and intercell transition layers in 2-D models of passive advection

Research output: Contribution to journalArticle

Abstract

A class of two-dimensional, isotropic, divergence-free vector fields is introduced and the effective diffusivity of the corresponding advection-diffusion equations is studied. These examples are very idealized flows, but they can be solved exactly in the limit Pe ≫ 1. Scaling laws D* ∝ D0(Pe)α are obtained, where D 0 = molecular diffusion, Pe = Peclet number, with exponents in the range 0 < α < 1, and examples of "stream functions" with logarithmic singularities for which D* ∝ D0Pe. The exponent α is related by a simple formula to the shape of the stream function along cell boundaries, suggesting that similar scaling laws should hold for more general 2-D closed-cell flows.

Original languageEnglish (US)
Pages (from-to)3209-3212
Number of pages4
JournalJournal of Mathematical Physics
Volume32
Issue number11
DOIs
StatePublished - 1991

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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