Renormalized transport of inertial particles in surface flows

TL;DR

This paper investigates how recirculations in surface flows affect inertial particle transport, revealing that recirculation can decrease or increase streaming velocity and providing explicit formulas for eddy diffusivity and transport efficiency.

Contribution

It introduces a perturbative approach to quantify the impact of recirculations on inertial particle transport in surface flows, including explicit expressions for eddy diffusivity.

Findings

Recirculation decreases streaming velocity in low recirculation regimes.

Recirculation increases streaming velocity when recirculation is large.

Explicit formulas for eddy diffusivity and transport efficiency are derived.

Abstract

Surface transport of inertial particles is investigated by means of the perturbative approach, introduced by Maxey (J. Fluid Mech. 174, 441 (1987)), which is valid in the case the deflections induced on the particle trajectories by the fluid flow can be considered small. We consider a class of compressible random velocity fields, in which the effect of recirculations is modelled by an oscillatory component in the Eulerian time correlation profile. The main issue we address here is whether fluid velocity fluctuations, in particular the effect of recirculation, may produce nontrivial corrections to the streaming particle velocity. Our result is that a small (large) degree of recirculation is associated with a decrease (increase) of streaming with respect to a quiescent fluid. The presence of this effect is confirmed numerically, away from the perturbative limit. Our approach also allows us to calculate the explicit expression for the eddy diffusivity, and to compare the efficiency of diffusive and ballistic transport.