Diffusivity dependence of ozone depletion over the midnorthern latitudes

The mixing and reaction properties of advected chemicals (and passive scalars) are determined by the fractal dimension D of the interface between the chemicals. We show that the scaling of the amount m of reacted chemicals with diffusivity $\kappa$ is $m\left(0\right)\mathrm{}-m\left(\kappa \right)\propto {\kappa }^{1-D/2\mathrm{}}$ in the two-dimensional case. This relation is valid in a range of times and diffusivities where the diffusive length scales of the chemicals are within the range of scales where the chemical interface has a well-defined fractal dimension. We apply the relation to the problems of chlorine deactivation and ozone depletion over the midnorthern latitudes. We determine numerically the fractal dimension of an interface advected by stratospheric winds. This allows us, first, to explain the diffusivity dependence of chlorine deactivation and ozone depletion that was previously observed in numerical simulations (Tan et al., J. Geophys. Res., [Atmos.] 103, 1585 (1998)) and, second, to extrapolate the results of such simulations down to realistically low diffusivities.