Particle and particle pair dispersion in turbulence modeled with spatially and temporally correlated stochastic processes

TL;DR

This paper introduces a novel stochastic model for particle dispersion in turbulence that captures key regimes of particle motion, including ballistic, diffusive, and Richardson-like behaviors, and examines the effect of particle inertia.

Contribution

The paper presents a new turbulence dispersion model using correlated stochastic processes and an Heisenberg-like Hamiltonian, capturing multiple dispersion regimes and particle inertia effects.

Findings

Reproduces ballistic regime in mean squared displacement

Shows transition to normal diffusion at long times

Indicates possible Richardson $t^{3}$ law in certain conditions

Abstract

In this paper we present a new model for modeling the diffusion and relative dispersion of particles in homogeneous isotropic turbulence. We use an Heisenberg-like Hamiltonian to incorporate spatial correlations between fluid particles, which are modeled by stochastic processes correlated in time. We are able to reproduce the ballistic regime in the mean squared displacement of single particles and the transition to a normal diffusion regime for long times. For the dispersion of particle pairs we find a $t^{2}$-dependence of the mean squared separation at short times and a $t$-dependence for long ones. For intermediate times indications for a Richardson $t^{3}$ law are observed in certain situations. Finally the influence of inertia of real particles on the dispersion is investigated.