Pure and Applied Geophysics

, Volume 176, Issue 4, pp 1797–1806 | Cite as

A Model Using Fractional Derivatives with Vertical Eddy Diffusivity Depending on the Source Distance Applied to the Dispersion of Atmospheric Pollutants

  • Paulo Henrique Farias Xavier
  • Erick Giovani Sperandio Nascimento
  • Davidson Martins MoreiraEmail author


This work presents an analytical solution of the two-dimensional advection–diffusion equation of fractional order, in the sense of Caputo and applied it to the dispersion of atmospheric pollutants. The solution is obtained using Laplace decomposition and homotopy perturbation methods, and it considers the vertical eddy diffusivity dependency on the longitudinal distance of the source with fractional exponents of the same order of the fractional derivative (K\(\propto\)xα). For validation of the model, simulations were compared with data from Copenhagen experiments considering moderately unstable conditions. The best results were obtained with α = 0.98, considering wind measured at 10 m, and α = 0.94 with wind measured at a height of 115 m.


Decomposition method advection–diffusion equation planetary boundary layer pollutant dispersion 



We thank the financial support of CNPq and FAPESB.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Paulo Henrique Farias Xavier
    • 1
  • Erick Giovani Sperandio Nascimento
    • 1
  • Davidson Martins Moreira
    • 1
    Email author
  1. 1.SENAI CIMATECSalvadorBrazil

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