large fluctuations in concentration over short time periods---from
seconds, to minutes, and longer---which are important in many
problems. The latter include air quality, surface-air exchange, and
atmospheric chemistry among others. The fluctuations are caused by the
stochastic nature of ABL turbulence and are especially large in a
convective boundary layer (CBL) where a small "instantaneous" plume
from an elevated source meanders widely due to the large convective
eddies, producing large fluctuations in surface concentrations. The
root-mean-square (rms) fluctuating concentrations are often larger
than the mean concentration at short downstream distances and depend
on the averaging time.
In this paper, we investiage rms fluctuations, concentration PDFs, and
peak concentrations from sources in convective and stable boundary
layers using a Lagrangian "two-particle" dispersion model (L2PDM)
driven by large-eddy simulations (LES). With this approach, one
follows the simultaneous trajectories of two particles that start from a small localized source, spread due to inertial-subrange turbulence,
and lead to relative dispersion about the local plume centerline. With
the L2PDM, we extended Thomson's (1990) idealized model (for
homogeneous turbulence) to more complex and realistic ABL flows by
coupling his model with LES. The particle velocities are divided into
"resolved" and "subfilter-scale" components as in one-particle models
(Weil et al., 2004). Here, however, the SFS velocity of each particle
depends on the position of both particles due to their velocity
correlation, which is explicity included.
L2PDM-LES results were generated for sources ranging from the surface
to near the ABL top, and for each about 75 realizations were obtained
to yield well-defined statistics. The mean concentration versus
distance agreed with earlier "one-particle" LPDM results and with the
convection tank data of Willis and Deardorff (1976, 1978, 1981) and
Hibberd (2000). In addition, the modeled rms concentrations gave both
qualitative and quantitative agreement with the tank data of Deardorff
and Willis (1984), Hibberd (2000), and Weil et al. (2002). The L2PDM
also predicted the variation of the concentration statistics with
averaging time, which ranged from about 1 - 35 min. Results showed that the rms fluctuation decreased with averaging time in agreement
with theory (Tennekes and Lumley, 1972) for long times and provided
new results for short averaging times. Corresponding results have been
obtained for the concentration cumulative (probability) distribution
function. These and other results will be presented and discussed.
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