AN APPLICATION OF THE THEORY OF KINEMATICS OF MIXING TO THE STUDY OF TROPOSPHERIC DISPERSION

The most common technique used for numerical simulations of tracer mix ing is that of the numerical solution of the advection-diffusion equat ion with the unresolved fluxes parameterized using the similarity theo ry. Despite correct predictions of the overall directions of transport , models based on a numerical solution of the advection-diffusion equa tion lack sufficient accuracy to correctly reproduce the coupling of m ixing with small scale processes which are sensitive to the microstruc ture of the tracer distribution. The objective of this paper is to rev isit the basic formalism employed in numerical models used to investig ate atmospheric tracers. The main mathematical method proposed here is the theory of kinematics of mixing which could be applied effectively for simulations of atmospheric transport processes. At the beginning of the paper, we introduce simple mathematical transformations in orde r to demonstrate how complex topological structures are created by mix ing processes. These idealistic flow systems are essential to explain transport properties of much more complex three-dimensional geophysica l flows. An example of the application of the kinematics of mixing to the analysis of tracer transport on a planetary scale is presented in the following sections. The complex filamentary structures simulated i n the numerical experiment are evaluated using some commonly applied s tatistical measures in order to compare the results with the data publ ished in the literature. The results of the experiment are also analys ed with the help of simple conceptual models of fluid filaments. The m icrostructure of the tracer distribution introduced in the paper is es sential to increase our understanding of atmospheric transport and to develop more realistic parameterizations of small-scale mixing. The pr esented results could also be used to improve calculations of the coup ling between microphysical processes and tracer mixing. (C) 1998 Elsev ier Science Ltd. All rights reserved.