The Use of Large-Eddy Simulations in Lagrangian Particle Dispersion Models

A Lagrangian dispersion model driven by velocity fields from large-eddy simulations (LESs) is presented for passive particle dispersion in the planetary boundary layer (PBL). In this combined LES–Lagrangian stochastic model (LSM), the total velocity is divided into resolved or filtered and unresolved or subfilter-scale (SFS) velocities. The random SFS velocity is modeled using an adaptation of Thomson's LSM in which the ensemble-mean velocity and velocity variances are replaced by the resolved velocity and SFS variances, respectively. The random SFS velocity forcing has an amplitude determined by the SFS fraction of the total turbulent kinetic energy (TKE); the fraction is about 0.15 in the bulk of the simulated convective boundary layer (CBL) used here and reaches values as large as 0.31 and 0.37 in the surface layer and entrainment layer, respectively. For the proposed LES–LSM, the modeled crosswind-integrated concentration (CWIC) fields are in good agreement with the 1) surface-layer similarity (SLS) theory for a surface source in the CBL and 2) convection tank measurements of the CWIC for an elevated release in the CBL surface layer. The second comparison includes the modeled evolution of the vertical profile shape with downstream distance, which shows the attainment of an elevated CWIC maximum and a vertically well-mixed CWIC far downstream, in agreement with the tank data. For the proposed model, the agreement with the tank data and SLS theory is better than that obtained with an earlier model in which the SFS fraction of the TKE is assumed to be 1, and significantly better than a model that neglects the SFS velocities altogether.