Resumo: A numerical simulation of the pollutant dispersion in the stable boundary layer (SBL) is performed. The goal is to study the pollutant dispersion close to its source under weak winds. The closure of the advection-diffusion eqaution is carried out by turbulence models that are dependent or not on the distance of the pollutant source. These models were derived from the local similarity theory and Taylor statistical theory. The results of the simulation show that both models present differences of concentrations near the source. However, the agreement between the models is good at large distances from the source. As the wind velocity increases these differences on the concentrations tend to propagate to larger distances from the source.