Lagrangian stochastic modeling of a fluctuating plume in the convective boundary layer

A Lagrangian stochastic model of dispersion in the atmospheric convective boundary layer is derived. The turbulence is assumed to be non-homogeneous and non-Gaussian in the vertical direction, homogeneous and Gaussian in the horizontal directions. The model describes the evolution of an airborne contaminant in terms of motion of its centroid and diffusion of particles relative to the centroid. The vertical motion of the centroid is simulated using non-stationary Lagrangian stochastic equations incorporating a time-dependent filter for the turbulent energy. The filtering procedure removes the contribution of turbulent eddies smaller than the cloud instantaneous size to the meandering. The instantaneous dispersion of particles relative to the centroid is parameterized using inertial range similarity formulae. The model is applied to the case of continuous stationary releases and the crosswind dispersion is calculated according to Taylorʹs theory. The model satisfies the well-mixed condition and is capable of calculating all moments of concentration. Mean concentration and concentration fluctuations for several source heights are simulated and compared with laboratory observations.