The geometry of inertial particle mixing in urban flows, from deterministic and random displacement models

We use Lagrangian measures, depicted by finite-time Lyapunov exponents, to characterize transport patterns of inertial pollutant particles formed in urban flows. Motivated by actual events we focus on flows in realistic urban geometry. Both deterministic and stochastic particle transport patterns have been identified, as inertial Lagrangian coherent structures. For the deterministic case, the organizing structures are well-defined and we extract them at different hours of a day to reveal the variability of coherent patterns. For the stochastic case, we use a random displacement model for fluid particles and derive the governing equation for inertial particles to examine the change in organizing structures due to "zeroth-order" random noise. We find that, (1) the Langevin equation for inertial particles can be reduced to a random displacement model; (2) using random noise based on inhomogeneous turbulence, whose diffusivity is derived from k - ε models, major coherent structures survive to organize local flow patterns and weaker structures are smoothed out due to random motion.