Non-Gaussian limit of a tracer motion in an incompressible flow

TL;DR

This paper studies the long-term behavior of a tracer particle in a random incompressible flow, revealing a non-Gaussian limit process of Rosenblatt type under certain conditions.

Contribution

It identifies a class of velocity fields where the scaled tracer trajectories converge to a non-Gaussian Rosenblatt process, expanding understanding of anomalous diffusion in fluid flows.

Findings

Limit process is non-Gaussian Rosenblatt type

Applicable to a specific class of divergence-free velocity fields

Provides new insights into tracer dynamics in complex flows

Abstract

We consider a massless tracer particle moving in a random, stationary, isotropic and divergence free velocity field. We identify a class of fields, for which the limit of the laws of appropriately scaled tracer trajectory processes is non-Gaussian but a Rosenblatt type of process.