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Extended Self-Similarity and Hierarchical Structure in Turbulence

Emily S. C. Ching·Zhen-Su She·Weidong Su·Zhengping Zou
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Abstract

It is shown that the two remarkable properties of turbulence, the Extended Self-Similarity (ESS) [R. Benzi {\it et al.}, Phy. Rev. E {\bf 48}, R29, (1993)] and the She-Leveque Hierarchical Structure (SLHS) [Z.S. She and E. Leveque, Phy. Rev. Lett. {\bf 72}, 336, (1994)] are related to each other. In particular, we have shown that a generalized hierarchical structure together with the most intense structures being shock-like give rise to ESS. Our analysis thus suggests that the ESS measured in turbulent flows is an indication of the shock-like intense structures. Results of analysis of velocity measurements in a pipe-flow turbulence support our conjecture.

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Emily S. C. Ching, Zhen-Su She, Weidong Su, Zhengping Zou. 2001-12-11. Extended Self-Similarity and Hierarchical Structure in Turbulence. https://doi.org/10.1103/physreve.65.066303

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