Modelo espectral de heisenberg aplicado ao decaímento da turbulência na camada residual

Abstract

In the study of the dispersion of contaminants in the atmosphere by computational simulations, the Eulerian approach, based in the diffusionadvection equation, is largely employed. In these simulations, concentration values are calculated at each point of a fixed grid in space and time and for this to be done it is necessary to determine an appropriated eddy diffusivity to the planetary boundary layer under consideration. The aim of this work is to describe the decay of turbulence in the residual layer and to derive the corresponding eddy diffusivity for the case of a homogeneous (in the horizontal plane) and isotropic turbulent flow neglecting mechanical and thermal production effects. The decay of turbulence is described as a process in which eddies of a certain size loss their energy by the effect of an eddy viscosity associated with the smallest eddies through a cascade of interactions of local character in the sense of Heisenberg s model. The eddy diffusivities are calculated by considering the dispersive effects of the energy-containing eddies on the basis of Taylor s statistical diffusion model. Considering the hypothesis that the law of decay of the energy spectral density function associated with the ith axis of the reference system is similar to the law of decay of the tridimensional energy spectral density function, the corresponding variance of the turbulent part of the velocity and the corresponding eddy diffusivity are calculated. These quantities, in particular for the vertical axis, are compared with results of large eddy simulations (LES) showing very good agreement. Finally, incorporating the calculated eddy diffusivity in a Eulerian model, the effect of turbulence in the vertical dispersion of an passive scalar contaminant in the residual layer is described for the special case of a instantaneous bidimensional emission source (area source) at a certain height over land and zero mean wind velocity.