Dynamics of inertial particles in a random flow with strong permanent shear

TL;DR

This paper investigates how inertial particles behave in a random flow with strong shear, focusing on clustering and separation dynamics, and provides analytical calculations of growth rates and inertia effects.

Contribution

It introduces a perturbation theory to quantify inertia effects on particle separation in a shear-dominated random flow.

Findings

Exponential growth rates of particle separation are derived.

Small inertia causes measurable corrections to Lyapunov exponents.

Clustering behavior persists despite strong shear and randomness.

Abstract

We consider advection of small inertial particles by a random fluid flow with a strong steady shear component. It is known that inertial particles suspended in a random flow can exhibit clusterization even if the flow is incompressible. We study this phenomenon through statistical characteristics of a separation vector between two particles. As usual in a random flow, moments of distance between particles grow exponentially. We calculate the rates of this growth using the saddle-point approximation in the path-integral formalism. We also calculate correction to the Lyapunov exponent due to small inertia by a perturbation theory expansion.