Lagrangian Modeling of Mean and Fluctuating Concentrations from Sources in the Convective Boundary Layer

Results are presented from Lagrangian statistical modeling of the mean and root-mean-square (rms) concentration fields due to a scalar point source in the convective boundary layer (CBL). In this approach, one follows ``passive particles" in a turbulent flow given the Eulerian velocity fields, which are generated by large-eddy simulation (LES). The mean concentration is found from a ``one-particle" Lagrangian model using the computed probability density function of particle position, i.e., from a large ensemble of particle trajectories. The rms concentration is obtained from a ``two-particle" model in which one tracks the simultaneous motion of two particles that start from a small initial separation and arrive at the ``same" place at the ``same" time. The LESs covered a 5 km x 5 km x 2 km domain and were generated for highly-, moderately-, and weakly-convective CBLs corresponding to the stability index h/|L|=110, 16, and 5, respectively; here, h is the CBL height and L is the Monin-Obukhov length.

For the most unstable case, the mean fields agreed well with the Willis and Deardorff laboratory experiments and reproduced the descent and ascent of plume centerlines from elevated and surface sources, respectively. For moderate and weak convection, the mean fields were qualitatively similar to those above, but the dispersion was noticeably reduced due to the greater surface shear and turbulence dissipation rate in the CBL surface layer and immediately above it; this led to smaller turbulence time and length scales. This is one of the first reports of Lagrangian-modeled rms concentrations for a real boundary layer flow. The results are important because there are currently no experiments, simulations, or observations showing the variation in the plume dispersive properties over a broad range of h/|L|.