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Fractal derivative multi-scale model of fluid particle transverse accelerations in fully developed turbulence. (English) Zbl 05648287
Summary: The Tsallis distribution and the stretched exponential distribution were successfully used to fit the experimental data of turbulence particle acceleration published in Nature (2001), which manifested a clear departure from the normal distribution. These studies, however, fall short of a clear physical mechanism behind the statistical phenomenological description. In this study, we propose a multiscale diffusion model which considers both normal diffusion in molecular-scale and anomalous diffusion in vortex-scale, and the latter is described by a novel fractal derivative modeling approach. This multi-scale model gives rise to a new probability density function which fits experimental data very well.

76Fluid mechanics
Full Text: DOI
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