Artículo

Pérez Guerrero, J.S.; Pimentel, L.C.G.; Oliveira-Júnior, J.F.; Heilbron Filho, P.F.L.; Ulke, A.G. "A unified analytical solution of the steady-state atmospheric diffusion equation" (2012) Atmospheric Environment. 55:201-212
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

A unified analytical solution of the steady-state atmospheric diffusion equation for a finite and semi-infinite/infinite media was developed using the classic integral transform technique (CITT) which is based on a systematized method of separation of variable.The solution was obtained considering an arbitrary mean wind velocity depending on the vertical coordinate (. z) and a generalized separable functional form for the eddy diffusivities in terms of the longitudinal (. x) and vertical coordinates (. z).The examples described in this article show that the well known closed-form analytical solutions, available in the literature, for both finite and semi-infinite/infinite media are special cases of the present unified analytical solution. As an example of the strength of the developed methodology, the Copenhagen and Prairie Grass experiments were simulated (finite media with the mean wind speed and the turbulent diffusion coefficient described by different functional forms). The results indicate that the present solutions are in good agreement with those obtained using other analytical procedures, previously published in the literature. It is important to note that the eigenvalue problem is associated directly to the atmospheric diffusion equation making possible the development of the unified analytical solution and also resulting in the improvement of the convergence behavior in the series of the eigenfunction-expansion. © 2012 Elsevier Ltd.

Registro:

Documento: Artículo
Título:A unified analytical solution of the steady-state atmospheric diffusion equation
Autor:Pérez Guerrero, J.S.; Pimentel, L.C.G.; Oliveira-Júnior, J.F.; Heilbron Filho, P.F.L.; Ulke, A.G.
Filiación:Brazilian Nuclear Energy Commission (CNEN), Rua General Severiano 90, CEP 22290-901, RJ-Rio de Janeiro, Brazil
Department of Meteorology, IGEO, Federal University of Rio de Janeiro, CCMN, Bloco H, 21941-916, RJ-Rio de Janeiro, Brazil
Department of Mechanical Engineering, COPPE, Federal University of Rio de Janeiro, Centro de Tecnologia, Bloco G, 21945-970, RJ-Rio de Janeiro, Brazil
Departamento de Cs. de la Atmósfera y los Océanos, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, 1428 Ciudad Universitaria, Pabellón II, Piso 2, Buenos Aires, Argentina
Unidad Mixta Internacional (UMI), Instituto Franco Argentino sobre Estudios de Clima y sus Impactos (IFAECI), CNRS, Argentina
Palabras clave:Analytical solution; Associated eigenvalue problem; Atmospheric diffusion equation; Integral transform; Analytical procedure; Atmospheric diffusion equations; Closed-form analytical solutions; Convergence behaviors; Copenhagen; Eddy Diffusivities; Eigenvalue problem; Finite media; Functional forms; Integral transform; Integral transform technique; Mean wind speed; Mean-winds; Prairie Grass; Turbulent diffusion coefficients; Vertical coordinates; Eigenvalues and eigenfunctions; Integral equations; Partial differential equations; Diffusion; diffusion; eigenvalue; numerical model; prairie; steady-state equilibrium; wind velocity; article; atmospheric diffusion; controlled study; diffusion coefficient; literature; methodology; prairie; priority journal; steady state; velocity; wind; Copenhagen [(CTY) Hovedstaden]; Denmark; Hovedstaden
Año:2012
Volumen:55
Página de inicio:201
Página de fin:212
DOI: http://dx.doi.org/10.1016/j.atmosenv.2012.03.015
Título revista:Atmospheric Environment
Título revista abreviado:Atmos. Environ.
ISSN:13522310
CODEN:AENVE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_13522310_v55_n_p201_PerezGuerrero

Referencias:

  • Almeida, G.L., Pimentel, L.C.G., Cotta, R.M., Integral transform solutions for atmospheric pollutant dispersion (2008) Environmental Modeling & Assessment, 13, pp. 53-65
  • Bailey, P.B., Gordon, M.K., Shampine, L.F., Automatic solution of the Sturm-Liouville problem (1978) ACM Transactions on Mathematical Software (TOMS), 4, pp. 193-208
  • Barad, M.L., (1958), 1-2. , (Ed.). Project Prairie Grass, A Field Program in Diffusion, Geophysical Research Papers No. 59. Air Force Cambridge Research Centre, Bedford, Mass; Berkowicz, R.R., Olesen, H.R., Torp, U., The Danish Gaussian air pollution model (OML). Description, test and sensitivity analysis in view of regulatory applications (1986) Air Pollution Modeling and Its Application, pp. 453-480. , Plenum Publishing Corporation, C. De Wispeleare, F.A. Schiermeirier, N.V. Gillani (Eds.)
  • Berlyand, M.Y., (1975) Contemporary Problems of Atmospheric Diffusion and Pollution of the Atmosphere, p. 448. , (NERC, Trans.), USEPA, Raleigh, NC, USA
  • Bessagnet, B., Menut, L., Curci, G., Hodzic, A., Guillaume, B., Liousse, C., Moukhtar, S., Schulz, M., Regional modeling of carbonaceous aerosols over Europe - focus on secondary organic aerosols (2008) Journal of Atmospheric Chemistry, 61, pp. 175-202
  • Bosanquet, C.H., Pearson, J.L., The spread of smoke and gases from chimneys (1936) Transactions of the Faraday Society, 32, pp. 1249-1263
  • Businger, J.A., Wyngaard, J.C., Izumi, Y., Bradley, E.F., Flux-profile relationships in the atmospheric surface layer (1971) Journal of the Atmospheric Sciences, 28, pp. 181-189
  • Buske, D., Vilhena, M.T., Moreira, D.M., Tirabassi, T., Simulation of pollutant dispersion for low wind conditions in stable and convective planetary boundary layer (2007) Atmospheric Environment, 41, pp. 5496-5501
  • Byun, D.W., Ching, J.K.S., (1999) Science Algorithms of the EPA Models-3 Community Multiscale Air Quality (CMAQ) Modelling System, , U.S. EPA/600/R-99/030
  • Byun, D.W., Lacser, A., Yamartino, R., Zannetti, P., Eulerian dispersion models (2003) Fundamentals, 1, pp. 213-292. , Published by The EnviroComp Institute and the Air & Waste Management Association, P. Zannetti (Ed.) Chapter 10 of Air Quality Modeling- Theories, Methodologies, Computational Techniques, and Available Databases and Software
  • Carruthers, D.J., McKeown, A.M., Hall, D.J., Porter, S., Validation of ADMS against wind tunnel data of dispersion from chemical warehouse fires (1999) Atmospheric Environment, 33, pp. 1937-1953
  • Cassol, M., Wortmann, S., Rizza, U., Analytic modeling of two-dimensional transient atmospheric pollutant dispersion by double GITT and Laplace transform techniques (2009) Environmental Modelling & Software, 24, pp. 144-151
  • Cotta, R.M., (1993) Integral Transforms in Computational Heat and Fluid Flow, p. 340. , CRC Press, Boca Raton, FL
  • Davies, D.R., Turbulence and diffusion in the lower atmosphere with particular reference to the lateral effect (1947) Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 190, pp. 232-244
  • Degrazia, G.A., Campos Velho, H.F., Carvalho, J.C., Non-local exchange coefficients for the convective boundary layer derived from spectral properties (1997) Contributions to Atmospheric Physics, pp. 57-64
  • Demuth, C., A contribution to the analytical steady solution of the diffusion equation for line sources (1978) Atmospheric Environment, 12, pp. 1255-1258
  • Duffy, D.G., (2001) Green's Functions with Applications, , Chapman & Hall/CRC
  • (2005) Revision to the Guideline on Air Quality Models: Adoption of a Preferred General Purpose (Flat and Complex Terrain) Dispersion Model and Other Revisions, p. 45. , Environmental Protection Agency, North Carolina, U.S, Federal Register/vol. 70, No. 216/Rules and Regulations. Appendix W of 40 CRF Part 51, EPA (Environmental Protection Agency)
  • Frost, R., Turbulence and diffusion in the lower atmosphere (1946) Proceedings of the Royal Society of London. Series A, 186, pp. 20-35
  • Gradshteyn, I.S., Ryshik, I.M., (1980) Tables of Integrals, Series, Products, , Academic Press
  • Grell, G.A., Peckham, S.E., Schmitz, R., McKeen, S.A., Wilczak, J., Eder, B., Fully coupled " online" chemistry within the WRF model (2005) Atmospheric Environment, 39, pp. 6957-6975
  • Gryning, S.E., Lyck, E., Atmospheric dispersion from elevated sources in an urban area: comparison between tracer experiments and model calculations (1984) Journal of Climate and Applied Meteorology, 23, pp. 651-660
  • Gryning, S.E., Batchvarova, E., Brümmer, B., Jørgensen, H., Larsen, S., On the extension of the wind profile over homogeneous terrain beyond the surface boundary layer (2007) Boundary-Layer Meteorology, 124, pp. 251-268
  • Hanna, S.R., Briggs, G.A., Hosker, R.P., (1982) Handbook on Atmospheric Diffusion, p. 107. , U.S. Dept. of Energy Report COE/TIC-11223, Washington, DC
  • Hanna, S.R., Strimaitis, D.G., Chang, J.C., Hazard Response Modeling Uncertainty (A Quantitative Method) (1991) In User's Guide for Software for Evaluation of Hazardous Gas Dispersion Models (Sigma Research Corp., , Westford, USA
  • Huang, C.H., A theory of dispersion in turbulent shear flow (1979) Atmospheric Environment, 13, pp. 453-463
  • Kumar, P., Sharan, M., An analytical model for dispersion of pollutants from a continuous source in the atmospheric boundary layer (2010) Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466, pp. 383-406
  • Lebedeff, S.A., Hameed, S., Steady-state solution of the semi-empirical diffusion equation for area sources (1975) Journal of Applied Meteorology, 14, pp. 546-549
  • Lin, J.S., Hildemann, L.M., Analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities (1996) Atmospheric Environment, 30, pp. 239-254
  • Llewelyn, R.P., An analytical model for the transport, dispersion and elimination of air pollutants emitted from a point source (1983) Atmospheric Environment, 17, pp. 249-256
  • Ma, J., Daggupaty, S.M., A generalized analytical solution for turbulent dispersion with inhomogeneous wind and diffusion coefficient (1998) Environmental Modeling & Assessment, 3, pp. 239-248
  • Marletta, M., Pryce, J.D., Automatic solution of Sturm-Liouville problems using the Pruess method (1992) Journal of Computational and Applied Mathematics, 39, pp. 57-78
  • Mikhailov, M.D., Cotta, R.M., Integral transform solution of eigenvalue problems (1994) Communications Numerical Methods Engineering, 10, pp. 827-835
  • Mikhailov, M.D., Ozisik, M.N., (1984) Unified Analysis and Solutions of Heat and Mass Diffusion, p. 524. , John Wiley & Sons
  • Mikhailov, M.D., Vulchanov, N.L., A computational procedure for Sturm-Liouville problems (1983) Journal of Computational Physics, 50, pp. 323-336
  • Moreira, D.M., Villena, M.T., Tirabassi, T., Buske, D., Cotta, R., Near-source atmospheric pollutant dispersion using the new GILTT method (2005) Atmospheric Environment, 39, pp. 6289-6294
  • Moreira, D.M., Villena, M.T., Buske, D., Tirabassi, T., The state-of-art of the GILTT method to simulate pollutant dispersion in the atmosphere (2009) Atmospheric Research, 92, pp. 1-17
  • Naveira-Cotta, C.P., Cotta, R.M., Orlande, H.R.B., Fudym, O., Eigenfunction expansions for transient diffusion in heterogeneous media (2009) International Journal of Heat and Mass Transfer, 52, pp. 5029-5039
  • Ozisik, M.N., (1980) Heat Conduction, p. 704. , John Wiley & Sons, New York
  • Park, Y.S., Baik, J.J., Analytical solution of the advection-diffusion equation for a ground-level finite area source (2008) Atmospheric Environment, 42, pp. 9063-9069
  • Pasquill, F., Smith, F.B., (1983) Atmospheric Diffusion, p. 437. , John Wiley& Sons, New York
  • Pérez Guerrero, J.S., Skaggs, T.H., Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients (2010) Journal of Hydrology, 390, pp. 57-65
  • Pérez Guerrero, J.S., Pimentel, L.C.G., Skaggs, T.H., Van Genuchten, M.T., Analytical solution of advection-diffusion transport equation using change-of-variable and integral transform (2009) International Journal of Heat and Mass Transfer, 52, pp. 3297-3304
  • Pérez Guerrero, J.S., Skaggs, T.H., Van Genuchten, M.T., Analytical solution for multi-species contaminant transport subject to sequential first-order decay reactions in finite media (2009) Transport in Porous Media, 80, pp. 373-387
  • Pérez Guerrero, J.S., Skaggs, T.H., Van Genuchten, M.T., Analytical solution for multi-species contaminant transport in finite media with time-varying boundary conditions (2010) Transport in Porous Media, 85, pp. 171-188
  • Roberts, O.F.T., The theoretical scattering of smoke in a turbulent atmosphere (1923) Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical, 104, pp. 640-654
  • Rounds, W., Solutions of the two-dimensional diffusion equation (1955) Transactions - American Geophysical Union, 36, pp. 395-405
  • Russell, A., Dennis, R., NARSTO critical review of photochemical models and modeling (2000) Atmospheric Environment, 34, pp. 2283-2324
  • Seinfeld, J.H., Pandis, S.N., (1998) Atmospheric Chemistry and Physics, p. 1326. , John Wiley and Sons, New York
  • Sharan, M., Gupta, S., Two-dimensional analytical model for estimating crosswind-integrated concentration in a capping inversion: eddy diffusivity as a function of downwind distance from the source (2002) Atmospheric Environment, 36, pp. 97-105
  • Sharan, M., Kumar, P., An analytical model for crosswind integrated concentrations released from a continuous source in a finite atmospheric boundary layer (2009) Atmospheric Environment, 43, pp. 2268-2277
  • Sharan, M., Modani, M., An analytical study for the dispersion of pollutants in a finite layer under low wind conditions (2005) Pure and Applied Geophysics, 162, pp. 1861-1892
  • Sharan, M., Modani, M., A two-dimensional analytical model for the dispersion of air-pollutants in the atmosphere with a capping inversion (2006) Atmospheric Environment, 40, pp. 3469-3489
  • Sharan, M., Singh, M.P., Yadav, A.K., A mathematical model for the atmospheric dispersion in low winds with eddy diffusivities as linear functions of downwind distance (1996) Atmospheric Environment, 30, pp. 1137-1145
  • Smith, F.B., The diffusion of smoke from a continuous elevated point-source into a turbulent atmosphere (1957) Journal of Fluid Mechanics, 2, pp. 49-76
  • Storch, R.B., Pimentel, L.C.G., Orlande, H.R.B., Fudym, O., Identification of micro-meteorological parameters for the characterization of atmospheric boundary layers by inverse problem and integral transform technique (2007) Atmospheric Environment, 3, pp. 1-10
  • Sutton, O.G., A theory of eddy diffusion in the atmosphere (1932) Proceedings of the Royal Society of London. Series A, 135, pp. 143-165
  • Sutton, W.G.L., On the equation of diffusion in a turbulent medium (1943) Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 182, pp. 48-75
  • Sutton, O.G., The application to micrometeorology of the theory of turbulent flow over rough surfaces (1949) Quarterly Journal of the Royal Meteorological Society, 75, pp. 335-350
  • Sutton, O.G., (1953) Micrometeorology, p. 320. , McGraw-Hill Book Comp., New York
  • Tirabassi, T., Buske, D., Moreira, D.M., Vilhena, M.T., A two-dimensional solution of the advection-diffusion equation with dry deposition to the ground (2008) Journal of Applied Meteorology and Climatology, 47, pp. 2096-2104
  • Ulke, A.G., New turbulent parameterization for a dispersion model in the atmospheric boundary layer (2000) Atmospheric Environment, 34, pp. 1029-1042
  • Vaughan, L.V., The prediction of atmospheric diffusion by using an eddy diffusivity based on the vertical transfer of heat (1961) Journal of Meteorology, 18, pp. 43-49
  • Vilhena, M.T., Rizza, U., Degrazia, G.A., Mangia, C., Moreira, D.M., Tirabassi, T., An analytical air pollution model: development and evaluation (1998) Contributions to Atmospheric Physics, 71, pp. 315-320
  • Wieringa, J., A revaluation of the Kansas mast influence on measurements of stress and cup-anemometer over speeding (1980) Boundary-Layer Meteorology, 18, pp. 411-430
  • (2009) Mathematica, , Version 7.0, Champaign, IL, Wolfram Research, Inc
  • Wortmann, S., Vilhena, M.T., Moreira, D.M., Buske, D., A new analytical approach to simulate the pollutant dispersion in the PBL (2005) Atmospheric Environment, 39, pp. 2171-2178
  • Yeh, G.T., Green's function of a diffusion equation (1975) Geophysical Research Letters, 2, pp. 293-296
  • Yih, C.S., Similarity solution of a specialized diffusion equation (1952) Transactions - American Geophysical Union, 33, pp. 356-360

Citas:

---------- APA ----------
Pérez Guerrero, J.S., Pimentel, L.C.G., Oliveira-Júnior, J.F., Heilbron Filho, P.F.L. & Ulke, A.G. (2012) . A unified analytical solution of the steady-state atmospheric diffusion equation. Atmospheric Environment, 55, 201-212.
http://dx.doi.org/10.1016/j.atmosenv.2012.03.015
---------- CHICAGO ----------
Pérez Guerrero, J.S., Pimentel, L.C.G., Oliveira-Júnior, J.F., Heilbron Filho, P.F.L., Ulke, A.G. "A unified analytical solution of the steady-state atmospheric diffusion equation" . Atmospheric Environment 55 (2012) : 201-212.
http://dx.doi.org/10.1016/j.atmosenv.2012.03.015
---------- MLA ----------
Pérez Guerrero, J.S., Pimentel, L.C.G., Oliveira-Júnior, J.F., Heilbron Filho, P.F.L., Ulke, A.G. "A unified analytical solution of the steady-state atmospheric diffusion equation" . Atmospheric Environment, vol. 55, 2012, pp. 201-212.
http://dx.doi.org/10.1016/j.atmosenv.2012.03.015
---------- VANCOUVER ----------
Pérez Guerrero, J.S., Pimentel, L.C.G., Oliveira-Júnior, J.F., Heilbron Filho, P.F.L., Ulke, A.G. A unified analytical solution of the steady-state atmospheric diffusion equation. Atmos. Environ. 2012;55:201-212.
http://dx.doi.org/10.1016/j.atmosenv.2012.03.015