An understanding of the way mixing affects chemical reactions requires information beyond that contained in the conventional tracer power spectrum. A more complete characterization of the tracer fluctuations is provided by the probability distribution function (PDF) of the tracer, its gradients, and its increments over finite distances. Such PDF's are also useful in diagnosing the nature of mixing at scales that cannot be directly observed, through the effect of the small scale mixing on various aspects of the PDF.
A great deal of theoretical progress has been made on the understanding of the PDF problems for advection/diffusion by idealized flows (generally temporally random and spatially smooth). These results indicate a certain measure of universality in the shape of the PDF's. It is unclear whether the results carry over to the more structured flows characterizing the Stratosphere, particularly in view of the existence of a number of barriers to transport. To address this issue, and to build a base of phenomenology for the interpretation of observed stratospheric PDF's, we have carried out a series of advection/diffusion simulations of a decaying tracer, driven by observed lower stratospheric winds. In this presentation, we will concentrate on our results for the tracer gradients and finite-distance increments.
The primary results are:
1. The PDF of tracer gradients is largely independent of initial conditions and geographical location, and can be fit by a stretched exponential distribution with stretching parameter of about 0.5. This parameter increases with increasing Peclet number.
2. The PDF of tracer increment (difference) also shows stretched exponential behavior. The stretching parameter smoothly evolves from about 0.5 for dissipation-range separations to about 2.0 for integral-scale separations.
These results are very similar to experimental results and theoretical predictions for idealized flows.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics