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Universal hierarchical symmetry for turbulence and general multi-scale fluctuation systems 被引量:5
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作者 Zhen-Su She Zhi-Xiong Zhang State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, 100871 Beijing, China 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2009年第3期279-294,共16页
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 i... 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. 展开更多
关键词 Turbulence. Scaling law. She-Leveque modelHierarchical symmetry Self-organization - Turbulenceensemble
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Corrections to the scaling of the second-order structure function in isotropic turbulence 被引量:6
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作者 Le Fang Wouter J. T. Bos +2 位作者 Xiaozhou Zhou Liang Shao Jean-Pierre Bertoglio 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2010年第2期151-157,共7页
The approach of Obukhov assuming a constant skewness was used to obtain analytical corrections to the scaling of the second order structure function, starting from Kolmogorov's 4/5 law. These corrections can be used ... The approach of Obukhov assuming a constant skewness was used to obtain analytical corrections to the scaling of the second order structure function, starting from Kolmogorov's 4/5 law. These corrections can be used in model applications in which explicit expressions, rather than numerical solutions are needed. The comparison with an interpolation formula proposed by Batchelor, showed that the latter gives surprisingly precise results. The modification of the same method to obtain analytical corrections to the scaling law, taking into account the possible corrections induced by intermittency, is also proposed. 展开更多
关键词 Scaling law · Structure function ·Isotropic turbulence
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