Scientific Research

An Academic Publisher

An Analytical Formulation for Pollutant Dispersion Simulation in the Atmospheric Boundary Layer

In this work we present the solution of the two-dimensional advection-diffusion equation by the GILTT method. The GILTT approach uses, in the series expansion, eigenfunctions given in terms of cosine functions. Here, a different expansion for the solution of the advection-diffusion equation will be explored. In other words, a Sturm-Liouville problem carrying more information of the original problem is considered, given by Bessel functions. Numerical simulations and comparisons with experimental data are presented.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

*Journal of Environmental Protection*, Vol. 4 No. 8A, 2013, pp. 57-64. doi: 10.4236/jep.2013.48A1008.

[1] | J. H. Seinfeld and S. N. Pandis, “Atmospheric chemistry and physics,” John Wiley & Sons, New York, 1998. |

[2] | D. M. Moreira, M. T. Vilhena, D. Buske and T. Tirabassi, “The State-of-Art of the GILTT Method to Simulate Pollutant Dispersion in the Atmosphere,” Atmospheric Research, Vol. 92, No. 1, 2009, pp. 1-17. doi:10.1016/j.atmosres.2008.07.004 |

[3] | D. Buske, M. T. Vilhena, T. Tirabassi and B. Bodmann, “Air Pollution Steady-State Advection Diffusion Equation: The General Three-Dimensional Solution,” Journal of Environmental Protection, Vol. 3, No. 2, 2012, pp. 1124-1134. doi:10.4236/jep.2012.329131 |

[4] | W. Rounds, “Solutions of the Two-Dimensional Diffusion Equation,” Transactions of American Geophysical Union, Vol. 36, 1955, pp. 395-405. doi:10.1029/TR036i003p00395 |

[5] | F. B. Smith, “The Diffusion of Smoke from a Continuous Elevated Point Source into a Turbulent Atmosphere,” Journal of Fluid Mechanics, Vol. 2, No. 1, 1957, pp. 49-76. doi:10.1017/S0022112057000737 |

[6] | R. A. Scriven and B. A. Fisher, “The Long Range Transport of Airborne Material and Its Removal by Deposition and Washout-II. The Effect of Turbulent Diffusion,” Atmospheric Environment, Vol. 9, No. 1, 1975, pp. 59-69. doi:10.1016/0004-6981(75)90054-2 |

[7] | C. Demuth, “A Contribution to the Analytical Steady Solution of the Diffusion Equation for Line Sources,” Atmospheric Environment, Vol. 12, No. 5, 1978, pp. 1255-1258. doi:10.1016/0004-6981(78)90399-2 |

[8] | A. P. van Ulden, “Simple Estimates for Vertical Diffusion from Sources near the Ground,” Atmospheric Environment, Vol. 12, No. 11, 1978, pp. 2125-2129. doi:10.1016/0004-6981(78)90167-1 |

[9] | F. T. M. Nieuwstadt, “An Analytical Solution of the Time-Dependent, One-Dimensional Diffusion Equation in the Atmospheric Boundary Layer,” Atmospheric Environment, Vol. 14, No. 12, 1980, pp. 1361-1364. doi:10.1016/0004-6981(80)90154-7 |

[10] | F. T. M. Nieuwstadt and B. J. de Haan, “An Analytical Solution of One-Dimensional Diffusion Equation in a Non-Stationary Boundary Layer with an Application to Inversion Rise Fumigation,” Atmospheric Environment, Vol. 15, No. 5, 1981, pp. 845-851. doi:10.1016/0004-6981(81)90289-4 |

[11] | M. Tagliazucca, T. Nanni and T. Tirabassi, “An Analytical Dispersion Model for Sources in the Surface Layer,” Novembre-Dicembre, Vol. 8, No. 6, 1985, pp. 771-781. |

[12] | T. Tirabassi, “Analytical Air Pollution and Diffusion Models,” Water, Air and Soil Pollution, Vol. 47, No. 1-2, 1989, pp. 19-24. doi:10.1007/BF00468993 |

[13] | W. Koch, “A Solution of the Two-Dimensional Atmospheric Diffusion Equation with Height-Dependent Diffusion-Coefficient Including Ground-Level Absorption,” Atmospheric Environment, Vol. 23, No. 8, 1989, pp. 1729-1732. doi:10.1016/0004-6981(89)90057-7 |

[14] | T. Tirabassi and U. Rizza, “Applied Dispersion Modelling for Ground-Level Concentrations from Elevated Sources,” Atmospheric Environment, Vol. 28, No. 4, 1994, pp. 611-615. doi:10.1016/1352-2310(94)90037-X |

[15] | M. Sharan, M. P. Singh and A. K. Yadav, “A Mathematical Model for the Atmospheric Dispersion in Low Winds with Eddy Diffusivities as Linear Function of Downwind Distance,” Atmospheric Environment, Vol. 30, No. 7, 1996, pp. 1137-1145. doi:10.1016/1352-2310(95)00368-1 |

[16] | J. S. Lin and L. M. Hildemann, “A Generalised Mathematical Scheme to Analytically Solve the Atmospheric Diffusion Equation with Dry Deposition,” Atmospheric Environment, Vol. 31, No. 1, 1997, pp. 59-71. doi:10.1016/S1352-2310(96)00148-3 |

[17] | M. Sharan and M. Modani, “An Analytical Study for the Dispersion of Pollutants in a Finite Layer under Low Wind Conditions,” Pure and Applied Geophysics, Vol. 162, No. 10, 2005, pp. 1861-1892. doi:10.1007/s00024-005-2696-5 |

[18] | M. Sharan and M. Modani, “A Two-Dimensional Analytical Model for the Dispersion of Air-Pollutants in the Atmosphere with a Capping Inversion,” Atmospheric Environment, Vol. 40, No. 19, 2006, pp. 3469-3489. doi:10.1016/j.atmosenv.2006.01.051 |

[19] | D. M. Moreira, M. T. Vilhena, T. Tirabassi, C. Costa and B. Bodmann, “Simulation of Pollutant Dispersion in Atmosphere by the Laplace Transform: The ADMM Approach,” Water, Air and Soil Pollution, Vol. 177, No. 1-4, 2006, pp. 411-439. doi:10.1007/s11270-006-9182-2 |

[20] | C. P. Costa, M. T. Vilhena, D. M. Moreira and T. Tirabassi, “Semi-Analytical Solution of the Steady Three-Dimensional Advection-Diffusion Equation in the Planetary Boundary Layer,” Atmospheric Environment, Vol. 40, No. 29, 2006, pp. 5659-5669. doi:10.1016/j.atmosenv.2006.04.054 |

[21] | D. Buske, M. T. Vilhena, C. F. Segatto and R. S. Quadros, “A General Analytical Solution of the Advection-Diffusion Equation for Fickian Closure,” In: Integral Methods in Science and Engineering: Computational and Analytic Aspects, Birkhauser, Boston, 2011, pp. 25-34. doi:10.1007/978-0-8176-8238-5_4 |

[22] | P. Kumar and M. Sharan, “An Analytical Model for Dispersion of Pollutants from a Continuous Source in the Atmospheric Boundary Layer,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 466, No. 2144, 2010, pp. 383-406. doi:10.1098/rspa.2009.0394 |

[23] | J. S. Perez Guerrero, L. C. G. Pimentel, J. F. Oliveira Jr., P. F. L. Heilbron Filho and A. G. Ulke, “A Unified Analytical Solution of the Steady-State Atmospheric Diffusion Equation,” Atmospheric Environment, Vol. 55, 2012, pp. 201-212. doi:10.1016/j.atmosenv.2012.03.015 |

[24] | A. K. Blackadar, “Turbulence and Diffusion in the Atmosphere: Lectures in Environmental Sciences,” Springer-Verlag, Berlin, 1997, 185p. doi:10.1007/978-3-642-60481-2 |

[25] | M. T. Vilhena, D. Buske, G. A. Degrazia and R. S. Quadros, “An Analytical Model with Temporal Variable Eddy Diffusivity Applied to Contaminant Dispersion in the Atmospheric Boundary Layer,” Physica A: Statistical Mechanics and Its Applications, Vol. 391, No. 8, 2012, pp. 2576-2584. doi:10.1016/j.physa.2011.11.001 |

[26] | S. E. Gryning and E. Lyck, “Atmospheric Dispersion from Elevated Source in an Urban Area: Comparison between Tracer Experiments and Model Calculations,” Journal of Climate and Applied Meteorology, Vol. 23, No. 4, 1984, pp. 651-654. |

[27] | M. L. Barad, “Project Prairie Grass: A Field Program in Diffusion,” Geophysical Research Paper No. 59, Vols. I and II, AFCRL-TR-58-235 (ASTIA Document No. AF-152572), Air Force Cambridge Research Laboratories, Bedford, 1958. |

[28] | F. T. M. Nieuwstadt, “An Analytical Solution of the Time-Dependent, One-Dimensional Diffusion Equation in the Atmospheric Boundary Layer,” Atmospheric Environment, Vol. 14, No. 12, 1980, pp. 1361-1364. doi:10.1016/0004-6981(80)90154-7 |

[29] | J. C. Doran and T. W. Horst, “An Evaluation of Gaussian Plume-Depletion Models with Dual-Tracer Field Measurements,” Atmospheric Environment, Vol. 19, No. 6, 1985, pp. 939-951. doi:10.1016/0004-6981(85)90239-2 |

[30] | G. A. Degrazia, H. F. Campos Velho and J. C. Carvalho, “Nonlocal Exchange Coefficients for the Convective Boundary Layer Derived from Spectral Properties,” Contributions to Atmospheric Physics, Vol. 70, No. 1, 1997, pp. 57-64. |

[31] | G. A. Degrazia, D. Anfossi, J. C. Carvalho, C. Mangia, T. Tirabassi and H. F. Campos Velho, “Turbulence Parameterization for PBL Dispersion Models in All Stability Conditions,” Atmospheric Environment, Vol. 34, No. 21, 2000, pp. 3575-3583. doi:10.1016/S1352-2310(00)00116-3 |

[32] | H. A. Panofsky and J. A. Dutton, “Atmospheric Turbulence,” John Wiley & Sons, New York, 1984. |

[33] | J. S. Irwin, “A Theoretical Variation of the Wind Profile Power-Low Exponent as a Function of Surface Roughness and Stability,” Atmospheric Environment, Vol. 13, No. 1, 1979, pp. 191-194. doi:10.1016/0004-6981(79)90260-9 |

[34] | S. R. Hanna, “Confidence Limit for Air Quality Models as Estimated by Bootstrap and Jacknife Resampling Methods,” Atmospheric Environment, Vol. 23, No. 6, 1989, pp. 1385-1395. doi:10.1016/0004-6981(89)90161-3 |

Copyright © 2018 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.