Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems

作     者：Zhen-Su She Zhi-Xiong Zhang State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, 100871 Beijing, China 

作者机构：State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University 100871 Beijing China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2009年第25卷第3期

页      面：279-294页

核心收录：

学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）] 

基　　金：the National Natural Science Foundation(90716008) MOST 973 project (2009CB724100) 

主　　题：Turbulence. Scaling law. She-Leveque modelHierarchical symmetry Self-organization - Turbulenceensemble 

摘      要：Scaling is an important measure of multi-scale fluctuation systems. Turbulence as the most remarkable multi-scale system possesses scaling over a wide range of scales. She-Leveque （SL） hierarchical symmetry, since its publication in 1994, has received wide attention. A number of experimental, numerical and theoretical work have been devoted to its verification, extension, and modification. Application to the understanding of magnetohydrodynamic turbulence, motions of cosmic baryon fluids, cosmological supersonic turbulence, natural image, spiral turbulent patterns, DNA anomalous composition, human heart variability are just a few among the most successful examples. A number of modified scaling laws have been derived in the framework of the hierarchical symmetry, and the SL model parameters are found to reveal both the organizational order of the whole system and the properties of the most significant fluctuation structures. A partial set of work related to these studies are reviewed. Particular emphasis is placed on the nature of the hierarchical symmetry. It is suggested that the SL hierarchical symmetry is a new form of the self-organization principle for multi-scale fluctuation systems, and can be employed as a standard analysis tool in the general multi-scale methodology. It is further suggested that the SL hierarchical symmetry implies the existence of a turbulence ensemble. It is speculated that the search for defining the turbulence ensemble might open a new way for deriving statistical closure equations for turbulence and other multi-scale fluctuation systems.