Anomalous diffusion for inertial particles under gravity in parallel flows

TL;DR

This paper explores how inertial particles under gravity exhibit normal or anomalous diffusion in parallel flows, depending on the fluid's energy spectrum, extending known tracer results to particles with inertia and gravity effects.

Contribution

It introduces a model linking the infrared behavior of the energy spectrum to particle diffusion, applicable to particles of any density, including effects of gravity and Brownian motion.

Findings

Diffusion behavior depends on the power-law parameters of the energy spectrum.

Results extend classical tracer diffusion to inertial particles with gravity.

Applicable to steady and time-dependent flows with various sedimentation conditions.

Abstract

We investigate the bounds between normal or anomalous effective diffusion for inertial particles transported by parallel flows. The infrared behavior of the fluid kinetic-energy spectrum, i.e. the possible presence of long-range spatio-temporal correlations, is modeled as a power law by means of two parameters, and the problem is studied as a function of these latter. Our results, obtained in the limit of weak relative inertia, extend well-known results for tracers and apply to particles of any mass density, subject to gravity and Brownian diffusion. We consider both steady and time-dependent flows, and cases of both vanishing and finite particle sedimentation.