Modeling Particulate Pollutants Dispersed in the Atmosphere Using Fractional Turbulent Diffusion

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 fine-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. To account for anomalous diffusion phenomena due to heterogeneities and/or turbulence in the medium where fine particles are dispersed, the second spatial derivative 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 plumeoriginating 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