Anomalous diffusion in a randomly modulated velocity field

TL;DR

This paper introduces a simple model of anomalous diffusion driven by a randomly modulated dipole velocity field, aiming to mimic fluid particle behavior in turbulence, and analyzes the fractal dimension of trajectories.

Contribution

It presents a novel toy model for anomalous diffusion using a randomly modulated dipole velocity field and investigates its fractal properties through numerical simulations.

Findings

Fractal dimension in 2D ranges from 1.5 to 1.9.

Fractal dimension in 3D ranges from 1.6 to 2.7.

Model may serve as a simplified analogy for turbulence-related diffusion.

Abstract

This paper proposes a simple model of anomalous diffusion, in which a particle moves with the velocity field induced by a single "dipole" (a doublet or a pair of source and sink), whose moment is modulated randomly at each time step. A motivation to introduce such a model is that it may serve as a toy model to investigate an anomalous diffusion of fluid particles in turbulence. We perform a numerical simulation of the fractal dimension of the trajectory using periodic boundary conditions in two and three dimensions. For a wide range of the dipole moment, we estimate the fractal dimension of the trajectory to be 1.5--1.9 (2D) and 1.6--2.7 (3D).