A Simple Analytic Approximation of the Ground-Level Concentration for Elevated Line Sources

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  • a Mathematical Department, Facolt´ di Ingegneria, Ancona University, Bologna, Italy
  • | b Laboratorio Fisbat-CNR, Bologna, Italy
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Abstract

By an analytical treatment of the advection-diffusion equation, the upper and lower bounds of the ground-level concentration (glc) have been found for a continuous, elevated line source. These two bounds have been used to construct a Fickian-type formula where the source height and the inversion height are expressed by simple functions of the vertical profiles of wind velocity and turbulent diffusivity. This simple formula is found to give a good estimate of the glc predicted by the K-equation for a diverse class of vertical profiles, in a reasonably wide range of downwind distances.

Abstract

By an analytical treatment of the advection-diffusion equation, the upper and lower bounds of the ground-level concentration (glc) have been found for a continuous, elevated line source. These two bounds have been used to construct a Fickian-type formula where the source height and the inversion height are expressed by simple functions of the vertical profiles of wind velocity and turbulent diffusivity. This simple formula is found to give a good estimate of the glc predicted by the K-equation for a diverse class of vertical profiles, in a reasonably wide range of downwind distances.

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