Eddy diffusivities of inertial particles in random Gaussian flows

TL;DR

This paper derives explicit formulas for eddy diffusivities of inertial particles in Gaussian flows, revealing how inertia influences large-scale transport and connecting it to tracer particle behavior.

Contribution

It provides the first explicit analytic expressions for inertial particle diffusivities in Gaussian flows, applicable to shear and random flow geometries.

Findings

Explicit formulas for eddy diffusivities derived

Inertia effects on transport quantified

Connections made between inertial and tracer particle transport

Abstract

We investigate the large-scale transport of inertial particles. We derive explicit analytic expressions for the eddy diffusivities for generic Stokes times. These latter expressions are exact for any shear flow while they correspond to the leading contribution either in the deviation from the shear flow geometry or in the P\'eclet number of general random Gaussian velocity fields. Our explicit expressions allow us to investigate the role of inertia for such a class of flows and to make exact links with the analogous transport problem for tracer particles.