An Analytical Air Pollution Model with Time Dependent Eddy Diffusivity

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

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.

Highlights

The processes governing the transport and diffusion of pollutants present large variability and distinct forms, the phenomenon is of such complexity that it would be impossible to describe it without the use of mathematical models
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
Applying the idea of Decomposition method [4,5], we reduce the advection-diffusion equation (ADE) with temporal dependence of the eddy diffusivity into a set of recursive ADE’s with eddy diffusivity just depending on the spatial variable z, which is directly solved by the GILTT method

Summary

Introduction

The processes governing the transport and diffusion of pollutants present large variability and distinct forms, the phenomenon is of such complexity that it would be impossible to describe it without the use of mathematical models. In the K approach, diffusion is considered, at a fixed point in space, proportional to the local gradient of the concentration of the diffused material It is fundamentally Eulerian since it considers the motion of fluid within a spatially fixed system of reference. (Generalized Integral Laplace Transform Technique) whose main feature relies on the analytical solution of transformed GITT (Generalized Integral Transform Technique) solutions by the Laplace Transform technique [2,3] This methodology has been largely applied in the topic of simulations of pollutant dispersion in the Atmospheric Boundary Layer (ABL) and is a general steady state solution for any profiles of wind and eddy diffusivity.

The Analytical Solution

Model Evaluation against Experimental Data

Results 1

Conclusions