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Detailed Reference Information |
Wonhas, A. and Vassilicos, J.C. (2003). Mixing and geometry of advected, chemically reactive scalar fields: Application to chlorine deactivation over the midnorthern latitudes. Journal of Geophysical Research 108: doi: 10.1029/2002JD002333. issn: 0148-0227. |
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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 $m left( 0 right) - m left( kappa right) propto sqrt {kappa}^{1-D^{prime}},$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 $frac {partial}{partial t} left< m left( 0 right) - m left( t right) right> propto sqrt {t}^{1-3D^{prime}}$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. |
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Abstract |
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Keywords
Mathematical Geophysics, Chaos, Mathematical Geophysics, Fractals and multifractals, Mathematical Geophysics, General or miscellaneous |
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Publisher
American Geophysical Union 2000 Florida Avenue N.W. Washington, D.C. 20009-1277 USA 1-202-462-6900 1-202-328-0566 service@agu.org |
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