Evaluation of the eddy diffusivity in a pollutant dispersion model in the planetary boundary layer

• Published in: Environmental fluid mechanics (Dordrecht, Netherlands : 2001) Netherlands : 2001), 2024-06, Vol.24 (3), p.489-504
• Main Authors: Goulart, A., Suarez, J. M. S., Lazo, M. J., Marques, J. C.
• Format: Article
• Language: English
• Subjects: Boundary layers; Central limit theorem; Classical Mechanics; Diffusion coefficients; Diffusivity; Dispersion; Dispersion models; Earth and Environmental Science; Earth Sciences; Eddies; Eddy diffusion; Eddy diffusivity; Energy spectra; Environmental Physics; Fluid mechanics; Fractal geometry; Fractals; Hydrogeology; Hydrology/Water Resources; Oceanography; Original Article; Planetary boundary layer; Pollutants; Pollution dispersion; Spectra; Turbulence; Turbulent flow; Velocity; Vortices
• ISSN: 1567-7419; 1573-1510
• DOI: 10.1007/s10652-024-10005-1

In this work, eddy diffusivity is derived from the energy spectra for the stable and convective regimes in the planetary boundary layer. The energy spectra are obtained from a spectral model for the inertial subrange that considers the anomalous behavior of turbulence. This spectrum is expressed as a function of the Hausdorff fractal dimension. The diffusivity eddies are employed in a classical Eulerian dispersion model, where the derivatives are of integer order and in fractional dispersion model, where the derivatives are of fractional order. The eddy diffusivity proposed considers the anomalous nature of geophysical turbulent flow. The results obtained with the fractional and classic dispersion models using the eddy diffusivity proposed is satisfactory when compared with the experimental data of the Prairie Grass and Hanford experiments in a stable regime, and the Copenhagen experiment in a convective regime.