A QUANTITATIVE MEASURE OF THE CHAOTIC BEH AVIOR IN CONSERVATIVE-SYSTEMS - A STUDY OF TRANSPORT PHENOMENA IN OPEN SYSTEMS

Assessment of such a measure has been revealed to be especially diffic ult due to the lake of mathematical criteria applicable to conservativ e systems. Existing tools are mainly based on the characterization of the 'strangeness' of the attractors. These asymptotic measures are thu s limited to dissipative systems. We have adapted some of these tools in order to apply them to conservative systems, based on short time ob servations of the system instead of asymptotic observations. In this s tudy we have used the alternating Dean flow as a benchmark and on the basis of which the mathematical tools have been constructed. Instead o f observing an attractor, we suggest observing the image formed by the cross section of a tracer filament injected upstream of the flow. Suc h an image is simulated by using a numerical model for the flow. With the image, we evaluate the 'information dimension' as well as the 'int egral correlation dimension'. Since we use short time observations, th e dimensions depend on the initial position of the injected filament. However, their evolution follows the apparent disorder observed on the images. As a global measure of the chaotic behavior, we suggest calcu lating the mean value of the dimensions for all injection positions de fined as 'mean integral correlation dimensions'. (C) Elsevier, Paris.