Analytical Solution Of The Advection-diffusion Equation For A Ground-level Finite Area Source

摘要

An advection-diffusion equation for a ground-level finite area source is solved analytically in a closed form using the superposition method. Power laws are assumed for height-dependent wind speed and vertical eddy diffusivity and for the downwind distance-dependent standard deviation of concentration distribution in the lateral direction. Results of the analysis show that the ground-level concentration increases with increasing downwind distance inside the source region and then decreases rapidly beyond the downwind edge of the source region. The ground-level concentration inside the source region is sensitive to exponents in the power laws for wind speed and vertical eddy diffusivity, while the ground-level concentration outside the source region is sensitive to the standard deviation of concentration distribution in the lateral direction. The solution for the ground-level finite area source is compared with solutions for a laterally infinite area source and a point source. The ratio of the ground-level concentration for the finite area source to that for the laterally infinite area source is highly dependent on lateral eddy diffusivity but almost independent of exponents in the power laws for wind speed and vertical eddy diffusivity. This is also true for the ratio of the ground-level concentration for the finite area source to that for the point source.