Diffusion properties of small-scale fractional transport models

TL;DR

This paper investigates how small-scale fractional Gaussian noise influences stochastic transport, revealing that certain spatial structures with persistent FGN lead to classical Brownian diffusion, despite the complex underlying noise.

Contribution

It introduces a model comparing different space-time structures under a unified energy constraint and shows that persistent FGN in Fourier space results in classical diffusion.

Findings

Persistent FGN in Fourier components induces Brownian diffusion.

The model allows comparison of different space-time structures.

Memory of FGN is lost in the spatial velocity field.

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.