Inverse statistics and multifractality of exit distances in 3D fully developed turbulence

被引:37
作者
Zhou, WX
Sornette, D [1 ]
Yuan, WK
机构
[1] Univ Calif Los Angeles, Dept Earth & Space Sci, Los Angeles, CA 90095 USA
[2] Univ Calif Los Angeles, Inst Geophys & Planetary Phys, Los Angeles, CA 90095 USA
[3] E China Univ Sci & Technol, State Key Lab Chem Engn, Shanghai 200237, Peoples R China
[4] Univ Nice Sophia Antipolis, F-06108 Nice 2, France
[5] CNRS, UMR 6622, Phys Mat Condensee Lab, F-06108 Nice 2, France
基金
中国国家自然科学基金;
关键词
turbulence; inverse statistics; exit distance; extended self-similarity; multifractal analysis;
D O I
10.1016/j.physd.2005.12.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The inverse structure functions of exit distances have been introduced as a novel diagnostic of turbulence which emphasizes the more laminar regions [1-4]. Using Taylor's frozen field hypothesis, we investigate the statistical properties of the exit distances of empirical 3D fully developed turbulence. We find that the probability density functions of exit distances at different velocity thresholds delta v can be approximated by stretched exponentials with exponents varying with the velocity thresholds below a critical threshold. We show that the inverse structure functions exhibit clear extended self-similarity (ESS). The ESS exponents (p, 2) for small p (p < 3.5) are well described by xi(p, 2) = p/2, which derives from the observed approximate universality of the distributions of the exit distances for different velocity thresholds delta v. The data is not sufficient to reject the hypothesis that monofractal ESS is sufficient to explain the data. In contrast, a measure taking into account the dependence between successive exit distances at a given velocity threshold exhibits clear multifractality with negative dimensions, suggesting the existence of a nontrivial dependence in the time series of exit times. (c) 2006 Published by Elsevier B.V.
引用
收藏
页码:55 / 62
页数:8
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