Diffusion properties of small-scale fractional transport models

Abstract

Stochastic transport due to a velocity field modeled by the superposition of small-scale divergence free vector fields activated by Fractional Gaussian Noises (FGN) is numerically investigated. We present two non-trivial contributions: the first one is the definition of a model where different space-time structures can be compared on the same ground: this is achieved by imposing the same average kinetic energy to a standard Ornstein-Uhlenbeck approximation, then taking the limit to the idealized white noise structure. The second contribution, based on the previous one, is the discover that a mixing spatial structure with persistent FGN in the Fourier components induces a classical Brownian diffusion of passive particles, with suitable diffusion coefficient; namely, the memory of FGN is lost in the space complexity of the velocity field.