Analytical Study of Atmospheric Pollution Dispersion with Distance Dependent Wind and Constant Removal Dynamics

Abstract

This study presents an analytical investigation into the dispersion of atmospheric pollutants under the influence of a spatially varying wind velocity and a constant pollutant removal rate. A one-dimensional, steady-state mathematical model is developed, wherein the wind velocity increases linearly with distance from the pollution source, and pollutant removal is modeled through a constant rate sink term representing scavenging processes such as chemical reactions, dry and wet deposition, and precipitation. The governing advection reaction equation is solved exactly, yielding an explicit expression for the pollutant concentration as a function of distance. Parametric analysis reveals that both increasing wind gradients and higher removal rates significantly reduce pollutant concentrations downwind. Specifically, when wind acceleration is present (i.e., non-zero wind gradient), pollutants disperse more rapidly than under constant wind conditions. Additionally, higher removal rates amplify the decay of concentration profiles, particularly in combination with accelerated wind. These findings emphasize the nonlinear interplay between transport and loss mechanisms, offering practical insights for air quality management, urban planning, and the strategic siting of emission sources.