Evaluation of Fluid Mixing States Based on Statistical Thermodynamic Formalism—Spectra of Degree of Mixedness—

Abstract

The previous measures used to evaluate quantitatively fluid mixing states have defined mixedness with only a few parameters. However, these measures can not to express the characteristics of a mixing pattern that shows complicated changes throughout the mixing process. In this study, statistical thermodynamic formalism based on escort probability measure is applied to analyze fluid mixing patterns, and the mixing indices are defined as spectra. These spectra enable us to describe comprehensively the characteristics of mixing patterns from the viewpoints of information, theory multifractal theory and thermodynamics. Many of the indices previously proposed to express the degree of mixedness are included as special cases of these spectra. The spectra proposed in this study represent an improvement of the traditional concepts of degree of mixedness.