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arXiv · 0812.4725

Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence

Chuang Liu·Zhi-Qiang Jiang·Fei Ren·Wei-Xing Zhou
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Abstract

We study the statistical properties of return intervals $r$ between successive energy dissipation rates above a certain threshold $Q$ in three-dimensional fully developed turbulence. We find that the distribution function $P_Q(r)$ scales with the mean return interval $R_Q$ as $P_Q(r)=R_Q^{-1}f(r/R_Q)$ except for $r=1$, where the scaling function $f(x)$ has two power-law regimes. The return intervals are short-term and long-term correlated and possess multifractal nature. The Hurst index of the return intervals decays exponentially against $R_Q$, predicting that rare extreme events with $R_Q\to\infty$ are also long-term correlated with the Hurst index $H_\infty=0.639$.

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Chuang Liu, Zhi-Qiang Jiang, Fei Ren, Wei-Xing Zhou. 2008-12-27. Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence. https://doi.org/10.1103/physreve.80.046304

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