BooksStandalone TitlesCollected Volumepp. 125–167

Anomalous diffusion via iterative quantitative homogenization: An overview of the main ideas

  • Scott Armstrong

    Courant Institute of Mathematical Sciences, New York University, USA; Sorbonne Université, Paris, France

  • Vlad Vicol

    Courant Institute of Mathematical Sciences, New York University, USA
Anomalous diffusion via iterative quantitative homogenization: An overview of the main ideas cover
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Abstract

Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence and has been confirmed numerically and experimentally to an extraordinary extent. The purpose of this survey is to discuss our recent result, in which we construct a class of incompressible vector fields that have many of the properties observed in a fully turbulent velocity field, and for which the associated scalar advection-diffusion equation generically displays anomalous diffusion. Our main contribution is to propose an analytical framework in which to study anomalous diffusion via a backward cascade of renormalized eddy viscosities.