  The dispersion and mixing of passive particles in a turbulent channel flow is
investigated by means of a network-based representation of their motion. We
employ direct numerical simulations at five different Reynolds numbers, from
$\mathrm{Re}_{\tau}$ = 180 up to $\mathrm{Re}_{\tau}$ = 950, and obtain sets of
particle trajectories via numerical integration. By dividing the channel domain
into wall-normal levels, the motion of particles across these levels is used to
build a time-varying complex network, which is able to capture the transient
phase of the wall-normal mixing process and its dependence on the Reynolds
number, $\mathrm{Re}_{\tau}$. Using network metrics, we observe that the
dispersion of clouds of tracers depends highly on both their wall-normal
starting position and the time elapsed from their release. We identify two main
mechanisms that contribute to the long lasting inhibition of the dispersion of
particles released near the walls. We also show how the relative importance of
these mechanisms varies with the Reynolds number. In particular, at low
$\mathrm{Re}_{\tau}$ the weaker velocity fluctuations appear dominant in
inhibiting dispersion, while at higher Reynolds numbers a larger role is played
by cyclic patterns of motion. At the higher Reynolds numbers employed in this
work, we find that most network properties are Reynolds-independent when scaled
with outer flow variables. Instead, at lower $\mathrm{Re}_{\tau}$, the
aforementioned scaling is not observed. We explore the meaning of the emergence
of this scaling in relation to the features of dispersion and to the network
definition.
