抄録
Fractal dimension is utilized for characterization of geometrical patterns that have self-similar structure. In order to evaluate the complex pattern whose fractal dimension depends on position, we have to use multifractal analysis. Application of the multifractal analysis makes it possible to analyze the more detail characteristics about the mixing pattern than utilization of an ordinary scalar index such as degree of mixing. The multifractal analysis of mixing pattern is expressed by a spectrum consisting of local fractal dimension and global ones. In this study, the multifractal analysis has been extended to be able to treat the mixing fluid systems that contain multi-components. In order to get the discrete expression of the mixing pattern, we divide the whole system into coarse-grained cells with the same area, and further divide the every coarse-grained cell to sub-cells with the same area. We restricted the sub-cells to have a single-component fluid. For each coarse-grained cell, we calculated the probability density finding the cell boundaries between the reference component sub-cell and the other component sub-cell. With these joint probabilities for each reference component, we defined the new probability measure representing the local mixing information. Our multifractal analysis of multi-components mixing pattern has been performed based on these probability measures. From the obtained multifractal spectrum, we can get the temporal and spatial details about the degree of the mutual dispersion between the components.
