Mesure du chaos dans les systèmes conservatifs en vue de l'étude des transferts dans les systèmes ouverts

Assessment of such a measure has been revealed to be especially difficult due to the lake of mathematical criteria applicable to conservative systems. Existing tools are mainly based on the characterization of the ‘strangeness’ of the attractors. These asymptotic measures are thus limited to dissipative systems. We have adapted some of these tools in order to apply them to conservative systems, based on short time observations of the system instead of asymptotic observations. In this study we have used the alternating Dean flow as a benchmark and on the basis of which the mathematical tools have been constructed. Instead of observing an attractor, we suggest observing the image formed by the cross section of a tracer filament injected upstream of the flow. Such an image is simulated by using a numerical model for the flow. With the image, we evaluate the ‘information dimension’ as well as the ‘integral correlation dimension’. Since we use short time observations, the 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 calculating the mean value of the dimensions for all injection positions defined as ‘mean integral correlation dimensions’.