Lagrangian modeling of dispersion in the convective boundary layer over a range of stability

Results are presented from Lagrangian statistical modeling of the mean crosswind-integrated concentration (CWIC) field 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 time-dependent Eulerian velocity fields, which are generated by large-eddy simulation (LES). The CWIC 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 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. In all cases, h and the surface heat flux were approximately the same but the surface shear or friction velocity differed as a result of different mean winds.

For the most unstable case (h/|L|=110), the modeled CWIC 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 h/|L|=16 and 5, the modeled CWIC fields were qualitatively similar to those above, but the dispersion was noticeably reduced---the rate of ascent and descent of plume centerlines and the particle dispersion were all smaller. The slower dispersion was due to the greater surface shear and turbulence dissipation rate in the CBL surface layer and immediately above it, which led to smaller turbulence time and length scales. These 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|.