When the wind speed decreases below a certain value (1-2 m s À1 ) meandering (low frequency horizontal wind oscillations) starts to prevail. In these conditions it becomes difficult to define a precise mean wind direction and to estimate the airborne dispersion. To study the wind and turbulence characteristics during meandering, two sonic anemometer datasets, containing hourly wind observations, were analysed: the first one, lasting 1 year, was recorded in complex terrain (Graz, Austria) and the second one, lasting about 1 month, was recorded in a rather flat area (Tisby, Sweden). It was found that meandering seems to exist under all meteorological conditions regardless of the stability or wind speed and it was confirmed that meandering sets a lower limit for the horizontal wind component variances. Further, it was found that the autocorrelation functions of the horizontal wind components, computed for the low wind cases, show an oscillating behaviour with the presence of large negative lobes. Two different relationships from the literature, and relevant to these oscillatory aspects, were fitted to the data. They contain two parameters: one associated and relevant to the classical integral time scale and the second with meandering occurrence. Based on these relationships, expressions for the mean square displacement of particles r 2 y ðtÞ were also derived.

In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration of a non-reactive pollutant in Planetary Boundary Layer. We solve these models and we compare the solutions with a real experiment. We found that the fractional derivative models perform far better than the traditional Gaussian model and even better than models found in the literature where it is considered that the diffusion coefficient is a function of the position in order to deal with the anomalous diffusion.

In the present work, we propose a new parameterization for the concentration flux using fractional derivatives. The fractional order differential equation in the longitudinal and vertical directions is used to obtain the concentration distribution of contaminants in the Planetary Boundary Layer. We solve this model and we compare the solution against both real experiments and traditional integer order derivative models. We show that our fractional model gives very good results in fitting the experimental data, and perform far better than the traditional Gaussian model. In fact, the fractional model, with constant wind speed and a constant eddy diffusivity, performs even better than some models found in the literature where it is considered that the wind speed and eddy diffusivity are functions of the position. The results obtained show that the structure of the fractional order differential equation is more appropriate to calculate the distribution of dispersed contaminants in a turbulent flow than an integer-order differential equation. Furthermore, a very important result we found it is that there should be a relation between the order α of the fractional derivative with the physical structure of the turbulent flow.

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Our focus is the time evolution of the turbulent kinetic energy for decaying turbulence in the convective boundary layer. The theoretical model with buoyancy and inertial transfer terms has been extended by a source term due to mechanical energy and validated against large-eddy simulation data. The mechanical effects in a boundary layer of height z i at a convective surface-layer height z = 0.05z i are significant in the time evolution of the vertical component of the spectrum, i.e. they enhance the decay time scale by more than an order of magnitude. Our findings suggest that shear effects seem to feedback to eddies with smaller wavenumbers, preserving the original shape of the spectrum, and preventing the spectrum from shifting towards shorter wavelengths. This occurs in the case where thermal effects only are considered.