Relative dispersion of particle pairs in turbulent channel flow

TL;DR

This study investigates how pairs of particles disperse in turbulent channel flow using DNS, revealing short-time ballistic behavior, turbulence irreversibility, and the influence of shear, with an adapted cascade model for wall-bounded turbulence.

Contribution

It extends the understanding of particle pair dispersion from isotropic turbulence to wall-bounded flows, introducing a normalisation method and adapting a cascade model for channel flows.

Findings

Ballistic regime observed at short times across all wall distances.

Short-time dispersion linked to turbulence irreversibility.

Mean shear influences early-stage dispersion near walls and channel center.

Abstract

Lagrangian tracking of particle pairs is of fundamental interest in a large number of environmental applications dealing with contaminant dispersion and passive scalar mixing. The aim of the present study is to extend the observations available in the literature on relative dispersion of fluid particle pairs to wall-bounded turbulent flows, by means of particle pair tracking in direct numerical simulations (DNS) of a turbulent channel flow. The mean-square change of separation between particle pairs follows a clear ballistic regime at short times for all wall distances. The Eulerian structure functions governing this short-time separation are characterised in the channel, and allow to define a characteristic time scale for the ballistic regime, as well as a suitable normalisation of the mean-square separation leading to an overall collapse for different wall distances. Through fluid particle pair tracking backwards and forwards in time, the temporal asymmetry of relative dispersion is illustrated. At short times, this asymmetry is linked to the irreversibility of turbulence, as in previous studies on homogeneous isotropic flows. The influence of the initial separation (distance and orientation) as well as the influence of mean shear are addressed. By decomposing the mean-square separation into the dispersion by the fluctuating velocity field and by the average velocity, it is shown that the influence of mean shear becomes important at early stages of dispersion close to the wall but also near the channel centre. The relative dispersion tensor $\Delta_{ij}$ is also presented and particularly the sign and time evolution of the cross-term $\Delta_{xy}$ are discussed. Finally, a ballistic cascade model previously proposed for homogeneous isotropic turbulence is adapted here to turbulent channel flows. Preliminary results are given and compared to the DNS.