An Analytical Air Pollution Model with Time Dependent Eddy Diffusivity

Tiziano Tirabassi, Marco Túllio Vilhena, Daniela Buske, Gervásio Annes Degrazia

Department of Mathematics and Statistics (IFM/DME), Federal University of Pelotas (UFPel), Pelotas, Brazil.
epartment of Physics, Federal University of Santa Maria (UFSM), Santa Maria, Brazil.
Graduate Program in Mechanical Engineering, Federal University of Rio Grande do Sul (UFRGS), Porto Alegre, Brazil.
Institute of Atmospheric Sciences and Climate (ISAC), National Research Council (CNR), Bologna, Italy.

DOI: 10.4236/jep.2013.48A1003                

Abstract

Air pollution transport and dispersion in the atmospheric boundary layer are modeled by the advection-diffusion equation, that is, essentially, a statement of conservation of the suspended material in an incompressible flow. Many models simulating air pollution dispersion are based upon the solution (numerical or analytical) of the advection-diffusion equation assuming turbulence parameterization for realistic physical scenarios. We present the general time dependent three-dimensional solution of the advection-diffusion equation considering a vertically inhomogeneous atmospheric boundary layer for arbitrary vertical profiles of wind and eddy-diffusion coefficients. Numerical results and comparison with experimental data are shown.

Keywords

Analytical Solution; Advection-Diffusion Equation; Air Pollution Modeling; Integral Transform; Decomposition Method

Conflicts of Interest

The authors declare no conflicts of interest.

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