  The dispersion of a passive scalar by wall turbulence, in the limit of
infinite Peclet number, is analyzed using frozen velocity fields from the DNS
by our group. The Lagrangian trajectories of fluid particles in those fields
are integrated and used to compute the first and second-order moments of the
distribution of fluid-particle displacements. It is shown that the largest
scales in the flow dominate turbulent diffusion, and the computed dispersions
are in good agreement with measurements in the atmospheric boundary layer. This
agreement can be understood noting that the life times of the large strucutures
are much longer than the time scale of the transition from linear to Gaussian
particle spreading in the cross-stream plane. Numerical experiments performed
computing the Lagrangian trajectories in reference frames moving at different
velocities suggest that this transition is controlled by the difference between
the mean streamwise velocity and the phase speed of the large-scale structures
of the cross-stream velocities. In the streamwise direction, the effect of the
mean shear dominates and produces elongated scalar patches, with dispersion
exponents which are different from the transverse ones.
