Clustering of Rapidly Settling, Low-Inertia Particle Pairs in Isotropic Turbulence. I. Drift and Diffusion Flux Closures

TL;DR

This paper develops a stochastic theory to describe how low-inertia, rapidly settling particle pairs cluster in isotropic turbulence, focusing on drift and diffusion fluxes at small scales.

Contribution

It introduces new closures for drift and diffusion fluxes in the PDF equation for particle pair positions in turbulence, specifically for low-inertia, rapidly settling particles.

Findings

Closures derived for drift and diffusion fluxes in the PDF equation.

Focus on particle pairs at scales smaller than the Kolmogorov length.

Applicable in regimes with small Stokes and Froude numbers.

Abstract

In this two--part study, we present the development and analysis of a stochastic theory for characterizing the relative positions of monodisperse, low-inertia particle pairs that are settling rapidly in homogeneous isotropic turbulence. In the limits of small Stokes number and Froude number such that $Fr \ll St_\eta \ll 1$, closures are developed for the drift and diffusion fluxes in the probability density function (PDF) equation for the pair relative positions. The theory focuses on the relative motion of particle pairs in the dissipation regime of turbulence, i.e., for pair separations smaller than the Kolmogorov length scale. In this regime, the theory approximates the fluid velocity field in a reference frame following the primary particle as locally linear.