Mathematical model for hermitized atmospheric dispersion in low winds with eddy diffusivities as linear functions of down wind distance

Summary In the present paper, an attempt is made for generalized the atmospheric diffusion operator. This can be accomplished by employing the realizability procedure, to identify a surface operator, that ensures self-adjointness’ of the atmospheric diffusion operator. The dispersion modeling in low wind speeds assumes importance because of the high frequency of occurrence and episodic nature of these poor diffusion conditions. A steady-state mathematical model for hermitized model has been calculated for the dispersion of air pollutants in low winds by taking into account the diffusion in the three coordinate directions and advection along the mean wind. The eddy diffusivities have been parameterized in terms of downwind distance for near source dispersion (Arya, 1995). The constants involved in this parameterization are the squares of intensities of turbulence. An analytical solution for resulting advection-diffusion equation with the physically relevant boundary conditions has been obtained. The solution has been used to simulate the field tracer data collected at IIT Delhi in low wind convective conditions.