Eulerian and Lagrangian Analysis of Dispersion in an Idealized Urban Geometry*

Understanding and modeling atmospheric dispersion in urban settings is important for air quality management and emergency response to harmful releases. In addition to prevailing winds and turbulent mixing, building-induced mean flow deflections play a significant role in the fate of dispersing plumes. In this study, Large-Eddy Simulations (LES) of scalar dispersion around an idealized cubical building demonstrate that the overturning motion of the horseshoe vortex inverts the crosswind position of the plume, so that fluid particles reaching the wake region directly behind the cube are more likely to come from upstream locations farther from the center plane of the cube. In addition to the Eulerian analysis of a continuous release, a Lagrangian analysis approach is implemented for efficient numerical access to two-point, two-time, and backward-in-time statistics that are difficult to compute via Eulerian methods. Formally, the probability distribution of Lagrangian particle positions, which is equivalent to the Green's function of the advection diffusion equation, is computed from particle trajectories and used to characterize the spatio-temporal characteristics of the plume. The simulations provide a detailed characterization of scalar dispersion and its relation to flow structures for both continuous and time-dependent releases.