Dimension Density: An Intensive Measure of Chaos in Spatially Extended Turbulent Systems

摘要

The determination of correlation dimensions by the Grassberger-Procaccia algorithm from an experimental time series has become a standard tool in the analysis of low dimensional chaotic systems. Here we want to carry over this method to spatially extended systems which have a decaying spatial correlation. In these cases the total number of degrees of freedom or overall ''dimension'' grows with the size of the system. Then in a finite size system the dimension of the overall dynamics can be recovered already from a single point measurement, if the resolution is greater than some size dependent threshold. Therefore we expect that the measured dimension values will increase when smaller and smaller spatial structures are resolved. This feature is also observed in turbulence experiments (U. Frisch). Thus the objective is to get an intensive (i.e. size independent) measure which locally characterizes turbulent systems. 5 refs., 2 figs. (ERA citation 12:012992)