How long do particles spend in vortical regions in turbulent flows?

TL;DR

This study uses DNS to analyze how long particles stay in vortical versus strain-dominated regions in turbulent flows, revealing exponential decay in their residence time distributions and quantifying these durations.

Contribution

It introduces a method to measure and compare the residence times of particles in different flow topologies using the $Q$-$R$ plane analysis in DNS data.

Findings

Residence time PDFs decay exponentially in all regions.

Characteristic times quantify particle durations in flow regions.

Particles spend varying times in vortical and strain-dominated zones.

Abstract

We obtain the probability distribution functions (PDFs) of the time that a Lagrangian tracer or a heavy inertial particle spends in vortical or strain-dominated regions of a turbulent flow, by carrying out direct numerical simulation (DNS) of such particles advected by statistically steady, homogeneous and isotropic turbulence in the forced, three-dimensional, incompressible Navier-Stokes equation. We use the two invariants, $Q$ and $R$, of the velocity-gradient tensor to distinguish between vortical and strain-dominated regions of the flow and partition the $Q-R$ plane into four different regions depending on the topology of the flow; out of these four regions two correspond to vorticity-dominated regions of the flow and two correspond to strain-dominated ones. We obtain $Q$ and $R$ along the trajectories of tracers and heavy inertial particles and find out the time $\mathrm{t_{pers}}$ for which they remain in one of the four regions of the $Q-R$ plane. We find that the PDFs of $\mathrm{t_{pers}}$ display exponentially decaying tails for all four regions for tracers and heavy inertial particles. From these PDFs we extract characteristic times scales, which help us to quantify the time that such particles spend in vortical or strain-dominated regions of the flow.