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Modeling particulate pollutants dispersed in the atmosphere using fractional turbulent diffusion

Author

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  • Troparevsky, M.I.
  • Muszkats, J.P.
  • Seminara, S.A.
  • Zitto, M.E.
  • Piotrkowski, R.

Abstract

Dispersion of particulate matter from natural or anthropogenic sources into the atmosphere, such as that produced by volcanoes, fires, or industries, often causes severe damages. In particular, fine-sized particles are a serious threat to human health. Therefore, it is important to identify them and evaluate their concentration. This paper aims to quantify the finest-grained ash concentration of a volcanic eruption using a turbulent diffusion model. A stationary regime at some distance from the eruption is considered and axial symmetry is assumed, with the axis in the direction of the wind, neglecting gravitational effects. To account for anomalous diffusion phenomena due to heterogeneities and/or turbulence in the medium where fine particles are dispersed, one of the derivatives in the radial direction is replaced by a fractional derivative of Caputo type. We find approximate analytical solutions in cylindrical coordinates by the Adomian Decomposition Method and compare them with solutions obtained using a numerical scheme. The analytical concentration profiles obtained are successfully compared with satellite images of a real plume originating in an explosive volcanic eruption. We have found that the concentration components depend on a parameter that seems to be directly related to particle size.

Suggested Citation

  • Troparevsky, M.I. & Muszkats, J.P. & Seminara, S.A. & Zitto, M.E. & Piotrkowski, R., 2022. "Modeling particulate pollutants dispersed in the atmosphere using fractional turbulent diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    • Handle: RePEc:eee:phsmap:v:599:y:2022:i:c:s0378437122003478
    DOI: 10.1016/j.physa.2022.127478
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    References listed on IDEAS

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    1. Goulart, A.G.O. & Lazo, M.J. & Suarez, J.M.S. & Moreira, D.M., 2017. "Fractional derivative models for atmospheric dispersion of pollutants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 9-19.
    2. Owolabi, Kolade M. & Pindza, Edson & Atangana, Abdon, 2021. "Analysis and pattern formation scenarios in the superdiffusive system of predation described with Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
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