A Lagrangian Two-Particle Model Driven by LES for Concentration Fluctuations in the Atmospheric Boundary Layer

Dispersion in the atmospheric boundary layer (ABL) is important for many problems including air quality, atmospheric chemistry, and toxic releases. A key feature of dispersion is its large variability, which arises from the stochastic nature of the ABL turbulence. This is especially true in the convective boundary layer (CBL) where a small "instantaneous" plume from an elevated source meanders widely due to the large convective eddies and produces large fluctuations in concentration over short time periods. The root-mean-square (rms) fluctuating concentration found at short downstream distances is often as large as the mean concentration. The plume is carried to the surface intermittently by strong downdrafts, whereas the local plume spread is determined by relative dispersion or inertial-subrange turbulence (Batchelor, 1950).

We present a new Lagrangian two-particle dispersion model (L2PDM) driven by large eddy simulations (LESs) for modeling dispersion and concentration fluctuations in the ABL with focus on the CBL. In this approach, one tracks the simultaneous motion of two particles that start from a small initial separation and spread due to inertial-range turbulence. Thomson (1990) developed a three-dimensional stochastic L2PDM, but it was restricted to homogeneous isotropic turbulence. We extended this model to more complex ABL flows by coupling the model with LES. As with one-particle models (Weil, 2004), we decompose the total particle velocity into "resolved" and "subfilter-scale" (SFS) components. However, in the L2PDM the SFS velocity of each particle depends on the position of both particles since their velocities are correlated; this is expressed through the two-point velocity correlation function, which is explicity included. Their resolved velocities also are correlated, and this is implicitly included in the LES resolved field.

The L2PDM-LES was applied first to an instantaneous source (or "puff") in the CBL and found to give the correct variation of the relative dispersion with time. We also found that the mean concentration versus time or distance from the L2PDM agreed with that from the one-particle LPDM as it should. In addition, the mean concentration fields were compared with the convection tank data of Willis and Deardorff (1976, 1978, 1981) and Hibberd (2000) and matched the variation of the concentration with both downstream distance and source height. Finally, we compared the rms concentration fields with those of Hibberd (2000) and obtained qualitative and quantitative agreement. These and other results will be presented and discussed.