Solution of the Atmospheric Diffusion Equation with Longitudinal Wind Speed Depending on Source Distance

Davidson Martins Moreira,Taciana Toledo De Almeida Albuquerque

doi:10.1590/0102-778631220150028

Abstract

Abstract An integral semi-analytical solution of the atmospheric diffusion equation considering wind speed as a function of both downwind distance from a pollution source and vertical height is presented. The model accounts for transformation and removal mechanisms via both chemical reaction and dry deposition processes. A hypothetical dispersion of contaminants emitted from an urban pollution source in the presence of mesoscale winds in an unstable atmospheric boundary layer is showed. The results demonstrate that the mesoscale winds generated by urban heat islands advect contaminants upward, which increases the intensity of air pollution in urban areas.

Highlights

The atmospheric dispersion equation has long been used to describe the transport of air contaminants in a turbulent atmosphere
To compare with a solution obtained in this work we use the results obtained by Agarwal and Tandon (2010), that present a numerical solution to the twodimensional advection-diffusion equation considering an idealized situation with wind speed depending on x and z variables
The present study primarily focuses on the concentration distribution of air contaminants in a given region under the influence of large-scale and mesoscale winds

Summary

Introduction

The atmospheric dispersion equation has long been used to describe the transport of air contaminants in a turbulent atmosphere. We mention the works of Rounds (1955), Smith (1957), Scriven and Fisher (1975), Demuth (1978), van Ulden (1978), Nieuwstadt and de Haan (1981), Sharan et al (1996), Lin and Hildemann (1997), Wortmann et al (2005), Sharan and Modani (2006), Sharan and Kumar (2009) In all of these models, the wind speed is either a power law or logarithmic profile of vertical height and, the eddy diffusivity has been assumed either a power law or a parabolic profile of z or a function of downwind distance from the source. To compare with a solution obtained in this work we use the results obtained by Agarwal and Tandon (2010), that present a numerical solution to the twodimensional advection-diffusion equation considering an idealized situation with wind speed depending on x and z variables This idealized study tries to show the effect of urban heat islands on urban air pollution through mathematical modeling.

The Model

Numerical Results

Summary and Conclusion