Scaling and memory in the return intervals of energy dissipation rate in three-dimensional fully developed turbulence
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 PQ(r) scales with the mean return interval RQ as PQ(r)=RQ-1f(r/RQ) 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 RQ, predicting that rare extreme events with RQ∞ are also long-term correlated with the Hurst index H∞=0.639.
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