Near-field Atmospheric Dispersion Modeling: A New Approach for the Two-dimensional Steady-state Advection-Diffusion Equation Using Fractal Derivative

Abstract

This work presents a method for the analytical solution of the fractal advection-diffusion equation, considering the Hausdorff derivative to maintain dimensional consistency, so that is possible to simulate the atmospheric pollutant dispersion in the Planetary Boundary Layer (PBL). The results show that the fractal parameter is a function of atmospheric stability, explicitly depending on the relationship between friction velocity and convective velocity (\({{u_{*} } \mathord{\left/ {\vphantom {{u_{*} } {w_{*} }}} \right. \kern-0pt} {w_{*} }}\)), and the inclusion of fractal derivative in the atmospheric dispersion equation improves the description of the turbulent transport process in the near-field region.