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 of del ´Alamo & Jim´enez(2001). The Lagrangian trajectories of fluid particles in these 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 dispersion is in good agreement with measurements in the atmospheric boundary layer. This agreement can be understood by noting that the lifetimes of the large structures are much longer than the time scale of the transition from linear to Gaussian particle spreading in the cross-stream plane. Numerical experiments on 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 andthe phase speed of the large-scale structures of the cross-stream velocity field. In the streamwise direction, the effect of the mean shear dominates and produces elongatedscalar patches, with dispersion exponents which are different from the transverse ones.
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 of del ´Alamo & Jim´enez(2001). The Lagrangian trajectories of fluid particles in these 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 dispersion is in good agreement with measurements in the atmospheric boundary layer. This agreement can be understood by noting that the lifetimes of the large structures are much longer than the time scale of the transition from linear to Gaussian particle spreading in the cross-stream plane. Numerical experiments on 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 andthe phase speed of the large-scale structures of the cross-stream velocity field. In the streamwise direction, the effect of the mean shear dominates and produces elongatedscalar patches, with dispersion exponents which are different from the transverse ones. Read More
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