A numerical simulation of dispersion from an elevated point source in the convective planetary boundary layer

Abstract

Data from the numerical model developed by Deardorff (1974a) of turbulence in the convective planetary boundary layer are used in conjunction with the Lagrangian diffusion equation to simulate the dispersion of nonbuoyant particles released from an elevated point source. The results show that for a source of height z s = 0.26h , where h is the depth of the mixed layer, the locus of maximum concentration in the cross-wind integrated plume descends to ground-level at a downstream distance x ∼- 0.6hU/w ∗ , where U is the mean wind speed and w ∗ is the convective velocity scale. From this point the maximum remains at ground-level until a distance x ∼- 1.2hU/w ∗ where it appears to ascend. The overall effect of this phenomenon is to make the ground-level cross-wind integrated concentrations larger than those predicted by the Gaussian plume formula at all distances from the source. Calculations are also made of the mean particle height and the root-mean-square vertical and lateral spread of the plume as a function of travel time. These results and the plume concentration profile described above are in excellent agreement with the results of the laboratory simulation performed by Willis and Deardorff (1978) in a companion study. The agreement supports the premise that the dispersive characteristics of the convective mixed layer can be expressed in universal form through the use of the free convection scaling parameters w ∗ and h. The numerical simulation also provides support for the criterion proposed by Deardorff and Willis (1976) for the neglect of streamwise diffusion effects in point and line source plumes.