Analytical solutions methods of atmospheric dispersion problems

Atmospheric dispersion of pollutant is a complex problem involving complex terrain, meteorological conditions and release pattern. Here analytical solution procedures have been explored under some restricted condition. Mathematically, the governing equation for atmospheric dispersion equation is a multidimensional advection diffusion equation. Here, the advection-diffusion pollutant dispersion equation has been solved analytically using Clader's and Sutton's models. The boundary condition considered are reflection/dry-deposition at the ground and far-field concentration asymptotically diminishing to zero. The ground absorption has been analytically modeled by Chaberlein's source depletion model and Lin and Hildeman surface depletion model. The power-law variation has been considered for horizontal unidirectional wind velocity and vertical turbulent mass diffusivity. The cross-wind expansion of the plume has been implemented through downwind-distance dependent Sigma model. The calculation for dispersion of Cesium 137 in the atmosphere has been completed. The release is at a rate of 1010 Bq/s for 24 hrs. duration, from an elevated stack of 145 m height in the domain of 150 Km by 150 km horizontal expanse. (author)