Derivação de coeficientes de difusão turbulenta em condições de vento norte: aplicação em um modelo analítico euleriano de dispersão de poluentes

Abstract

The advection-diffusion equation has been extensively used in air pollution models to simulate mean contaminant concentrations in the planetary boundary layer (PBL). Therefore, in a Eulerian framework, it is possible to theoretically model the dispersion from a continuous point source, given adequate boundary and initial conditions and the knowledge of the mean wind velocity and turbulent concentration fluxes. The choice of an appropriate parameterization for such fluxes plays an important role in the performance of air quality dispersion models based on the advection-diffusion equation. As a consequence, much of the turbulent dispersion research is associated with the specification of these fluxes. The most commonly used approximation for closing the advection-diffusion equation is to relate the turbulent concentration fluxes to mean concentration gradients through the use of eddy diffusivities, which carry within them the physical structure of the turbulent transport phenomenon. For a continuous point source the eddy diffusivities may vary spatially and temporally along the contaminant travel time. Taylor s statistical diffusion theory (1921) determines that the turbulent dispersion depends on the distance from a continuous point source. In the proximity of the source, the fluid particles tend to preserve the memory from their initial turbulent environment. For long travel times, this memory is lost, and the motion of the particles depends only on the local turbulence properties (BATCHELOR, 1949).The aim of the present study is to present a new formulation for the eddy diffusivities in terms of the distance from the source in an inhomogeneous, shear-generated turbulence. The proposition is based on expressions for the turbulent velocity spectra and the statistical diffusion theory. These eddy diffusivities, derived for neutral conditions are described by a complex integral formulation that must be numerically solved. An additional aim of this work is to obtain a simple algebraic expression for the eddy diffusivities in a neutral PBL as a function of the turbulence properties (inhomogeneous turbulence) and the distance from the source. Therefore, the hypothesis to be tested in this study is whether the complex integral formulation for eddy diffusivities can be expressed (substituted) by a simpler algebraic expression. Finally, to investigate the influence of the memory effect in the turbulent dispersion process, a vertical eddy diffusivity is evaluated as a function of the distance from the source against its asymptotic limit employing an Eulerian air pollution model and atmospheric dispersion experiments that were carried out in strong wind conditions.