Analytical Model Study for the Pollutants Dispersion with Coherent Structures Presence

Abstract

Since the beginning of the industrial revolution there has been an effort by the scientific community to understand and describe the phenomenon of dispersion of pollutants in order to develop tools to monitor the impact caused by emissions.

The present work is an analysis of the behavior of the distributions generated by an analytical solution of the advection diffusion equation [1] for pollutants dispersion. This model is unique in that it realistically describes aspects of turbulent phenomena neglected by other analytic models. Previous studies have defined as coherent structures some turbulent characteristics such as vortices, fluctuations in pollutant density, and swirls. Formally, coherent structures are defined through a phase difference property that does not exist in the advection diffusion equation [2]. Modifications were applied in the Fick closure of the equation where a phase difference was included through the insertion of a complex diffusive coefficient.

The parameters linked to the inclusion of the phase need to be analyzed and understood so new possibilities can be aggregated enabling a proper parameterization of the deterministic model with stochastic effects.