Superdiffusion in nearly stratified flows

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.