A numerical model employing the residual Eulerian formulation and small eddy diffusivity coefficients is used to calculate the distributions of chemical tracers and chlorine species. The predicted densities of nitrous oxide, methane, and chlorocarbons are shown to be in good agreement with available observations and to exhibit strong latitude gradients. Computed spatial variations in methane produce large variations in the HCl and ClO densities. In particular, a pronounced local minimum in HCl is obtained near 40 km for certain latitudes and seasons, with a corresponding maximum in ClO, primarily as a result of transport of atmospheric methane. It is suggested that spatial and short-term temporal variability in methane has potentially important consequences for the HCl and ClO distributions in the atmosphere, and their variability, and for the chlorine-catalyzed destruction of stratospheric ozone.