New formulations of eddy diffusivity for solution of diffusion equation in a convective boundary layer

In this paper, new formulations of eddy diffusivity have been derived in order to be used in atmospheric dispersion models. The obtained formulae depend on source distance for inhomogeneous turbulence. To evaluate these parameters, the classical statistical diffusion theory, the observed spectral properties, and observed characteristics of energy-containing eddies have been considered. A vertical eddy diffusivity was used in air pollution model validated with data of Copenhagen experiments, and compared with an improved Gaussian model. The results obtained are shown to agree with the measurements of Copenhagen and also with those of the Gaussian model. The current study suggests the inclusion of the memory effect is important in regions near an elevated continuous point source and improves the description of the turbulent transport process of atmospheric contaminants. The major advance shown in this paper is the necessity of including the downwind distance-dependent eddy diffusivity in air quality modeling, and it is demonstrated that such theory would suggest that it should yield better results than the asymptotic solution alone. It, in fact, does yield better results in the near and intermediate fields.