A Mathematical Model for Atmospheric Pollutant Dispersion Incorporating Variable Wind Fields and Deposition Processes
DOI:
https://doi.org/10.31305/rrijm.2025.v10.n12.024Keywords:
Atmospheric dispersion, Advection–diffusion model, Variable wind speed, Mesoscale vertical motionAbstract
Atmospheric pollutant dispersion arises from the combined effects of advection, turbulent diffusion, and removal mechanisms such as dry and wet deposition, all of which interact within the complex structure of the atmospheric boundary layer. While classical advection–diffusion formulations typically assume constant wind fields, empirical observations indicate that wind speed varies significantly with height and distance, particularly within the planetary boundary layer. In this work, a comprehensive mathematical model grounded in gradient transport theory is developed to examine pollutant dispersion from an elevated point source under distance-dependent horizontal wind velocity and vertically varying mesoscale airflow. The formulation incorporates anisotropic turbulent diffusion, natural removal processes, and deposition at both the ground surface and the mixing height. Through nondimensionalization, Fourier transform techniques, and separation of variables, a closed-form analytical solution is derived in terms of generalized series functions. The resulting model offers a physically realistic and flexible analytical framework that enhances the accuracy of pollutant concentration predictions and supports applications in environmental planning, air-quality forecasting, and health-risk assessment across diverse atmospheric settings.
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