# Diffusion Properties of Small-Scale Fractional Transport Models

## TL;DR

This paper studies how particles move in complex fluid flows modeled with fractional noise, revealing that certain noise patterns lead to standard diffusion behavior.

## Contribution

The paper introduces a unified model for comparing transport structures and discovers that persistent fractional noise leads to classical Brownian diffusion.

## Key findings

- A model was defined to compare different space-time transport structures with equal kinetic energy.
- Persistent FGN in spatial structures results in classical Brownian diffusion of passive particles.
- The memory of FGN is lost in complex velocity fields, leading to standard diffusion behavior.

## 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 discovery that a mixing spatial structure with persistent FGN in the Fourier components induces a classical Brownian diffusion of passive particles, with a suitable diffusion coefficient; namely, the memory of FGN is lost in the space complexity of the velocity field.