Abstract
A special attention has been given to the issue of searching analytical solutions for the advection-diffusion equation in order to simulate the pollutant dispersion in the Atmospheric Boundary Layer (ABL). In this work we take a step forward assuming a transient three-dimensional problem with nonlocal closure of the turbulent diffusion. The problem of closing the turbulence in the advection-diffusion equation is modified considering a generic equation for the turbulent diffusion. The countergradient term in the turbulence closure made additional terms to appear in the advection-diffusion equation and these terms are related to the asymmetrical transport in the convective boundary layer. This new equation is solved by the 3D-GILTT method. Numerical results and statistical comparisons with experimental data are presented.
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References
Blackadar, A.K.: Turbulence and diffusion in the atmosphere: lectures in Environmental Sciences. Springer-Verlag, 185pp. (1997).
Buske, D., Vilhena, M.T., Moreira, D.M., and Tirabassi, T.: An analytical solution of the advection-diffusion equation considering non-local turbulence closure. Environ. Fluid Mechanics 7, 43–54 (2007).
Buske, D., Vilhena, M.T., Moreira, D.M. and Tirabassi, T.: An Analytical Solution for the Transient Two-Dimensional Advection-Diffusion Equation with Non-Fickian Closure in Cartesian Geometry by Integral Transform Technique. Integral Methods in Science and Engineering: Computational methods, Boston: Birkhauser, 33–40 (2010).
Buske, D., Vilhena, M.T., Segatto, C.F. and Quadros, R.S.: A General Analytical Solution of the Advection-Diffusion Equation for Fickian Closure. Integral Methods in Science and Engineering: Computational and Analytic Aspects, Boston: Birkhauser, 25–34 (2011).
Caughey, S.J.: Observed characteristics of the atmospheric boundary layer. In: Atmospheric turbulence and air pollution modeling, Boston, 1982.
Costa, C.P., Vilhena, M.T., Moreira, D.M. and Tirabassi, T.: Semi-analytical solution of the steady three-dimensional advection-diffusion equation in the planetary boundary layer. Atmos. Environ. 40, n. 29, 5659–5669 (2006).
Costa, C.P.; Tirabassi, T.; Vilhena, M.T. & Moreira, D.M. (2011). A general formulation for pollutant dispersion in the atmosphere. J. Eng. Math., Published online. Doi 10.1007/s10665-011-9495-z.
Deardorff, J.W.: The countergradient heat flux in the lower atmosphere and in the laboratory. J. Atmo. Sci. 23, 503–506 (1966).
Deardorff, J.W.: Numerical investigation of neutral and unstable planetary boundary layers. J. Atmo. Sci. 29, 91–115 (1972).
Deardorff, J.W. and Willis, G.E.: A parameterization of diffusion into the mixed layer. J. Appl. Meteor. 14, 1451–1458 (1975).
Degrazia, G.A., Campos Velho, H.F., Carvalho, J.C.: Nonlocal exchange coefficients for the convective boundary layer derived from spectral properties. Cont. Atm. Phys., 57–64 (1997).
Demuth, C.: A contribution to the analytical steady solution of the diffusion equation for line sources. Atm. Env. 12, 1255–1258 (1978).
Degrazia, G.A., Moreira, D.M. and Vilhena, M.T.: Derivation of an eddy diffusivity depending on source distance for vertically inhomogeneous turbulence in a convective boundary layer. J. Appl. Meteor. 40, 1233–1240 (2001).
Druilhet, A., Frangi, J.P, Guedalia, D. and Fontan, J.: Experimental studies of the turbulence structure parameters of the convective boundary layer. J. Clim. Appl. Meteorol. 22, 594–608 (1983).
Ertel, H.: Der vertikale turbulenz-wärmestrom in der atmosphäre. Meteor. Z. 59, 250–253 (1942).
Gryning, S.E. and Lyck, E.: Atmospheric dispersion from elevated source in an urban area: comparison between tracer experiments and model calculations. J. Appl. Meteor. 23, 651–654 (1984).
Hanna, S.R.: Confidence limit for air quality models as estimated by bootstrap and jacknife resampling methods. Atm. Env. 23, 1385–1395 (1989).
Irwin, J.S.: A theoretical variation of the wind profile power-low exponent as a function of surface roughness and stability. Atm. Env. 13, 191–194(1979).
Kaimal, J.C., Wyngaard, J.C., Haugen, D.A., Cot, O.R., Izumi, Y., Caughey, S.J. and Readings, C.J.: Turbulence structure in the convective boundary layer. J. Atmos. Sci. 33, 2152–2169 (1976).
Moreira, D.M., Vilhena, M.T., Tirabassi, T., Costa, C. and Bodmann, B.: Simulation of pollutant dispersion in atmosphere by the Laplace transform: the ADMM approach. Water, Air and Soil Pollution 177, 411–439 (2006a).
Moreira, D.M., Vilhena, M.T., Buske, D. and Tirabassi, T.: The GILTT solution of the advection-diffusion equation for an inhomogeneous and nonstationary PBL. Atm. Env. 40, 3186–3194 (2006b).
Moreira, D. M., Vilhena, M. T., Buske, D. and Tirabassi, T.: The state-of-art of the GILTT method to simulate pollutant dispersion in the atmosphere. Atm. Research 92, 1–17 (2009).
Nieuwstadt F.T.M. and de Haan B.J.: An analytical solution of one-dimensional diffusion equation in a nonstationary boundary layer with an application to inversion rise fumigation. Atmos. Environ. 15, 845–851 (1981).
Panofsky, A.H., Dutton, J.A.: Atmospheric Turbulence. John Wiley & Sons, New York (1988).
Rounds, W.: Solutions of the two-dimensional diffusion equation. Trans. Am. Geophys. Union 36, 395–405 (1955).
Seinfeld, J.H. and Pandis, S.N. (1998). Atmospheric chemistry and physics. John Wiley & Sons, New York, 1326 pp.
Sharan, M., Singh, M.P. and Yadav, A.K.: A mathematical model for the atmospheric dispersion in low winds with eddy diffusivities as linear functions of downwind distance. Atmos. Environ. 30, n.7, 1137–1145 (1996).
Tirabassi, T.: Analytical air pollution and diffusion models. Water, Air and Soil Pollution 47, 19–24 (1989).
Tirabassi T.: Operational advanced air pollution modeling. PAGEOPH 160, n. 1-2, 05–16 (2003).
van Dop, H., Verver, G.S.: Countergradient transport revisited. J. Atm. Sci. 58, 2240–2247 (2001).
Wyngaard, J.C. and Weil, J.C.: Transport asymmetry in skewed turbulence. Phys. Fluids A 3, 155–162 (1991).
Wortmann, S., Vilhena, M.T., Moreira, D.M. and Buske, D.: A new analytical approach to simulate the pollutant dispersion in the PBL. Atm. Env. 39, 2171–2178 (2005).
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The authors thank CNPq and FAPERGS for partial financial support of this work.
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Buske, D., Vilhena, M.T.B., Bodmann, B.E.J., Quadros, R.S., Tirabassi, T. (2015). Pollutant Dispersion in the Atmosphere: A Solution Considering Nonlocal Closure of Turbulent Diffusion. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_9
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DOI: https://doi.org/10.1007/978-3-319-16727-5_9
Publisher Name: Birkhäuser, Cham
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