Mixing and geometry of advected, chemically reactive scalar fields: Application to chlorine deactivation over the midnorthern latitudes

Abstract

The mixing and reaction properties of advected chemicals are determined by the fractal dimension (or Kolmogorov capacity) D′ of a cut through the interface between the chemicals. We show that the amount m of reacted chemicals scales like where κ is diffusivity of the chemicals. If interscale transfer produced by the advecting flow has a linear time dependence, then the reaction rate of chemicals scales like with time t. Both relations are valid in a range of times and diffusivities where the diffusive length scales of the chemicals are within the range of scales where the interface between the chemicals has a well‐defined fractal dimension. We apply both relations to the problem of chlorine deactivation, ClO + NO2 → ClONO2, over the midnorthern latitudes. We determine numerically the Kolmogorov capacity of the interface between polar air which is comparatively rich in ClO and midlatitude air which is comparatively rich in NO2. Additionally, we show empirically that interscale transfer by the advecting flow can be well interpreted as having predominantly linear interscale transfer in the range of times under consideration. We can therefore explain diffusivity and time dependencies previously observed in numerical simulations. Furthermore we can extrapolate the results of such simulations down to realistically low diffusivities.