Superdiffusion in nearly stratified flows

Marco Avellaneda, Andrew J. Majda

Research output: Contribution to journalArticlepeer-review


In classical work, Mathéron and the Marsilly showed that superdiffusive scaling of mean-square displacements occurs in transport diffusion for stratified flows with steady simple shear layers and long-range spatial correlations. More recently the authors have calculated a formula for the non-Gaussian large-scale long-time renormalized Green function for these problems. Here the scaling laws and renormalized Green functions for diffusion in "nearly stratified" flows are studied; in such flows the simple shear layer with long-range correlations is perturbed by incompressible flows with short-range correlations. Here it is established that these flows belong to the same universality class as the simple shear layers, with a renormalized Green function with a similar structure but reflecting homogenization by the transverse displacements. The tools in the analysis involve a modification of homogenization theory and also rigorous diagrammatic perturbation theory.

Original languageEnglish (US)
Pages (from-to)689-729
Number of pages41
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Nov 1992


  • Superdiffusion
  • anomalous transport
  • homogenization
  • random flows

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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