By Vlad Vicol
Appears in collection : Physics and Mathematics of hydrodynamic and wave turbulence / Physique et Mathématiques de la turbulence hydrodynamique et de la turbulence d'ondes
Anomalous diffusion is the fundamental ansatz of phenomenological theories of passive scalar turbulence. In this talk 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. We also propose an analytical framework to study anomalous diffusion, via a backward cascade of renormalized eddy viscosities. Our proof is by “fractal” homogenization, that is, we perform a cascade of homogenizations across arbitrarily many length scales.
By Anne-Laure Dalibard
By Anne-Laure Dalibard
