  A comparison of turbulent diffusion and pair-dispersion in homogeneous,
macroscopically isotropic Navier-Stokes (NS) and nonhelical magnetohydrodynamic
(MHD) turbulence based on high-resolution direct numerical simulations is
presented. Significant differences between MHD and NS systems are observed in
the pair-dispersion properties, in particular a strong reduction of the
separation velocity in MHD turbulence as compared to the NS case. It is shown
that in MHD turbulence the average pair-dispersion is slowed down for
$\tau_\mathrm{d}\lesssim t\lesssim 10 \tau_\mathrm{d}$, $\tau_\mathrm{d}$ being
the Kolmogorov time, due to the alignment of the relative Lagrangian tracer
velocity with the local magnetic field. Significant differences in turbulent
single-particle diffusion in NS and MHD turbulence are not detected. The fluid
particle trajectories in the vicinity of the smallest dissipative structures
are found to be characterisically different although these comparably rare
events have a negligible influence on the statistics investigated in this work.
