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

TL;DR

This paper investigates the statistical properties of return intervals between energy dissipation events in 3D turbulence, revealing scaling, multifractality, and long-term correlations, especially for rare extreme events.

Contribution

It uncovers the scaling behavior, multifractal nature, and long-term correlations of return intervals in turbulence, highlighting the persistence of extreme events.

Findings

Return intervals follow a scaled distribution with two power-law regimes.

Return intervals exhibit multifractal and long-term correlated behavior.

Rare extreme events are also long-term correlated with a Hurst index of 0.639.

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 $H_\infty=0.639$.