Modelling Fractal Turbulent Velocity Spectra: Application to a Dispersion Model of Contaminants in Particular Cases of the Planetary Boundary Layer

The present work develops a model for the turbulent velocity spectra that considers the anomalous behaviour of the turbulent flow. The β -model assumes that the standard Kolmogorov phenomenology is valid only in active turbulence regions, and it proposes an expression for the turbulent velocity spectra in the inertial subrange that is a function of the Hausdorff fractal dimension. From this idea, expressions are obtained for the components of the turbulent velocity spectra that describe the turbulence that exists in geophysical turbulence above the ocean and in very stable situations in the planetary boundary layer where intermittent turbulence occurs. With these spectra, the main parameters used in dispersion models are obtained, that is, the eddy diffusivity and the Lagrangian time scale. The eddy diffusivity is used in an Eulerian dispersion model to estimate the concentration of contaminants in the stable boundary layer. The results obtained are compared with experimental data and other models in the literature.