A Stochastic Single-Particle Lagrangian Model for the Concentration Fluctuations in a Plume Dispersing Inside an Urban Canopy

Abstract

A new approach for estimating concentration fluctuations intensity in dense built-up environments using a Lagrangian stochastic (LS) particle model is described. Following past success in modelling the dynamics of concentration variance as a diffusion-advection process, the ensemble-averaged concentration variance is represented by particles that advect and diffuse throughout the computational domain. The calculation of the concentration variance is addressed by assuming an appropriate distribution of effective variance sources for a given mean concentration field. Dissipation is treated by allowing the variance carried by every particle to decay exponentially with a locally-estimated decay time. The approach has the benefit of easily handling complex boundary conditions. It can also be easily and naturally implemented as an extension to an existing LS model, which is used for mean concentration estimations. The method differs from existing two-particle methods that demand knowledge of the structure function of the flow. It is also more computationally efficient than micro-mixing approaches that involve maintaining high population levels of particles in every grid volume. The model is compared with high frequency concentration measurements, taken as part of the JU2003 (Joint Urban 2003) experiment that was carried out in Oklahoma City. Good agreement is observed.