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In the present work, we propose a new parameterization for the concentrationflux using fractional derivatives. The fractional order differential equationin the longitudinal and vertical directions is used to obtain the concentrationdistribution of contaminants in the Planetary Boundary Layer. We solve thismodel and we compare the solution against both real experiments and traditionalinteger order derivative models. We show that our fractional model gives verygood results in fitting the experimental data, and perform far better than thetraditional Gaussian model. In fact, the fractional model, with constant windspeed and a constant eddy diffusivity, performs even better than some modelsfound in the literature where it is considered that the wind speed and eddydiffusivity are functions of the position. The results obtained show that thestructure of the fractional order differential equation is more appropriate tocalculate the distribution of dispersed contaminants in a turbulent flow thanan integer-order differential equation. Furthermore, a very important result wefound it is that there should be a relation between the order $\alpha$ of thefractional derivative with the physical structure of the turbulent flow.

physica a statistical mechanics and its applications

A new parameterization for the concentration flux using the fractional  calculus to model the dispersion of contaminants in the Planetary Boundary  Layer