LAGRANGIAN MODELING OF RELATIVE AND ABSOLUTE DISPERSION IN THE CONVECTIVE BOUNDARY LAYER

Dispersion in the planetary boundary layer (PBL) is a stochastic phenomena caused by PBL turbulence with the fluctuating concentration field usually as important as the mean field. To determine concentration fluctuations due to a point source, one needs estimates of the absolute (or total) and relative dispersion of a scalar plume. This paper presents results of relative and absolute dispersion calculations for passive scalar releases from point sources in the convective boundary layer (CBL). The calculations are obtained using a Lagrangian statistical model in which one follows ``particles" in a turbulent flow given the time-dependent Eulerian velocity fields, which are generated by large-eddy simulation (LES). The absolute dispersion and mean concentration field are found from a ``one-particle" model whereas the relative dispersion is obtained from a two-particle model. For the CBL, this is one of the first calculations of relative dispersion using a Lagrangian two-particle model. The LESs covered a 5 km x 5 km x 2 km domain and were generated for highly- and moderately-convective boundary layers corresponfding to h/|L| = 110 and 16; h is the CBL height and L is the Monin-Obukhov length.

For h/|L| = 110, calculations were made for five source heights ranging from 0.01h to 0.75h. For heights exceeding 0.01h, the absolute dispersion followed the expected linear dependence on time for short times (less than an eddy ``turnover" time), consistent with Taylor's theory. The vertical dispersion tended to a constant of about 0.3h after about 3 turnover times due to plume trapping in the CBL, whereas the lateral width continued to grow but at a reduced rate. The most unique feature occurred for the near-surface source (0.01h) where the vertical spread initially followed a 3/4 power-law time dependence and then accelerated to a growth rate greater than linear with time. The latter was due to the vertical inhomogeneity in the surface layer turbulence and was qualitatively consistent with Yaglom's theory. For all source heights, the relative dispersion exhibited a nearly 3/2 power-law time dependence for short times as expected from Batchelor's theory, but in some cases (near the surface), there was a suggestion of a 5/3 dependence; this could be due to the inhomogenity in the turbulence dissipation rate. These and other results including those for h/|L| = 16 will be presented and discussed in light of the CBL turbulence properties.