ABSTRACT

This review is an abridged and updated version of Falkovich et al.[1]. The subject is the combined effect of molecular diffusion and random flow on scalar and vector fields transported by a fluid. We want to understand first when there is mixing and when, on the contrary, inhomogeneities are created and enhanced. We want to distinguish between cases when flow creates small-scale inhomogeneities of the transported fields, which are then killed by molecular diffusion, and cases when large-scale structures of the fields appear. Our goal is to describe temporal and spatial statistical properties of transported fields.