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

The dispersion modelling 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 has been proposed 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 apparent eddy diffusivities have been parameterized in terms of downwind distance for near-source dispersion (Arya, 1995, J. appl. Met.34, 1112–1122). The constants involved in the parameterization are essentially the squares of intensities of turbulence. An analytical solution for the 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. Various particular cases of the present study have been discussed and the results have been compared with the Gaussian plume solution and Aryaʹs (1995, J. appl. Met.34, 1112–1122) solution.