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

TL;DR

This paper derives eddy diffusivity from energy spectra considering turbulence anomalies in the planetary boundary layer, and evaluates its performance in classical and fractional dispersion models against experimental data.

Contribution

It introduces a new eddy diffusivity model based on energy spectra and fractal dimensions, accounting for turbulence anomalies in the planetary boundary layer.

Findings

Fractional dispersion models with the new diffusivity match experimental data well.

The model captures anomalous turbulence behavior in stable and convective regimes.

Results improve understanding of pollutant dispersion in complex turbulent flows.

Abstract

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.