A deformed derivative model for turbulent diffusion of contaminants in the atmosphere

A.G. Goulart, M.J. Lazo and J.M.S. Suarez

Physica A: Statistical Mechanics and its Applications, 2020, vol. 557, issue C

Abstract: In the present work, we propose an advection–diffusion equation with Hausdorff deformed derivatives to stud the turbulent diffusion of contaminants in the atmosphere. We compare the performance of our model to fit experimental data against models with classical and Caputo fractional derivatives. We found that the Hausdorff equation gives better results than the tradition advection–diffusion equation when fitting experimental data. Most importantly, we show that our model and the Caputo fractional derivative model display a very similar performance for all experiments. This last result indicates that regardless of the kind of non-classical derivative we use, an advection–diffusion equation with non-classical derivative displaying power-law mean square displacement is more adequate to describe the diffusion of contaminants in the atmosphere than a model with classical derivatives. Furthermore, since Hausdorff derivatives can be related to several deformed operators, and since differential equations with the Hausdorff derivatives are easier to solve than equations with Caputo and other non-local fractional derivatives, our result highlights the potential of deformed derivative models to describe the diffusion of contaminants in the atmosphere.

Keywords: Dispersion of contaminants; Eulerian model; Hausdorff derivative (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:557:y:2020:i:c:s0378437120304398

DOI: 10.1016/j.physa.2020.124847

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