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 $P_Q(r)$ 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 $H_{\infty }=0.639$.

5 pages, 5 figures

References in corpus (5)

• Recurrence time analysis, long-term correlations, and extreme events
• Return interval distribution of extreme events and long term memory
• Indication of multiscaling in the volatility return intervals of stock markets
• Statistical properties of volatility return intervals of Chinese stocks
• Multiscaling behavior in the volatility return intervals of Chinese indices