Ergodic properties of a model for turbulent dispersion of inertial particles

TL;DR

This paper investigates the ergodic behavior of a stochastic model for turbulent dispersion of inertial particles, linking it to Schrödinger equations and employing control theory to analyze its properties.

Contribution

It introduces a stochastic differential equation model for inertial particle dispersion and analyzes its ergodic properties using hypoellipticity and control theory techniques.

Findings

The model's generator is hypoelliptic, ensuring smoothness of solutions.

Ergodic properties are established through control-theoretic methods.

The model relates to the stationary Schrödinger equation in random potentials.

Abstract

We study a simple stochastic differential equation that models the dispersion of close heavy particles moving in a turbulent flow. In one and two dimensions, the model is closely related to the one-dimensional stationary Schroedinger equation in a random delta-correlated potential. The ergodic properties of the dispersion process are investigated by proving that its generator is hypoelliptic and using control theory.