Motion of inertial particles in Gaussian fields driven by an infinite-dimensional fractional Brownian motion

TL;DR

This paper investigates the dynamics of inertial particles in fractional Gaussian velocity fields, establishing existence, uniqueness, and attractor properties, with implications for simulating realistic turbulent flows.

Contribution

It introduces a novel model of particle motion driven by infinite-dimensional fractional Brownian motion, proving key properties and visualizing the system's attractor.

Findings

Existence and uniqueness of particle paths

Conditions for a global random attractor

Numerical visualization of the attractor

Abstract

We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the particle velocity. The fluid velocity satisfies a linear stochastic partial differential equation driven by an infinite-dimensional fractional Brownian motion with arbitrary Hurst parameter H in (0,1). The usefulness of such random velocity fields in simulations is that we can create random velocity fields with desired statistical properties, thus generating artificial images of realistic turbulent flows. This model captures also the clustering phenomenon of preferential concentration, observed in real world and numerical experiments, i.e. particles cluster in regions of low vorticity and high strain rate. We prove almost sure existence and uniqueness of particle paths and give sufficient conditions to rewrite this system as a random dynamical system with a global random pullback attractor. Finally, we visualize the random attractor through a numerical experiment.