Critical dispersion of advecting-diffusing tracers in periodic landscapes of hard-wall symmetric potentials

Large-scale, time-asymptotic dispersion properties of diffusing tracers dragged by a uniform drive through a two-dimensional periodic lattice of hard-wall symmetric potentials are investigated. Dispersion is quantified by a typically anisotropic effective diffusivity tensor D, whose eigenvalues and eigenvectors depend on the dimensionless bare diffusivity 1/Pe for each given lattice geometry. Attention is focused on critical lattice geometries yielding sustained macroscale dispersion D-perpendicular to along the direction orthogonal to the uniform drive in the limit where Pe -> infinity. A simple one-dimensional model is proposed, which predicts the anomalous scaling D-perpendicular to similar to 1/[A(1) + A(2) log(Pe)].