Interoccurrence time statistics in fully-developed turbulence

Abstract

Emergent extreme events are a key characteristic of complex dynamical systems. The main tool for detailed and deep understanding of their stochastic dynamics is the statistics of time intervals of extreme events. Analyzing extensive experimental data, we demonstrate that for the velocity time series of fully-developed turbulent flows, generated by (i) a regular grid; (ii) a cylinder; (iii) a free jet of helium, and (iv) a free jet of air with the Taylor Reynolds numbers Reλ from 166 to 893, the interoccurrence time distributions P(τ) above a positive threshold Q in the inertial range is described by a universal q- exponential function, P(τ) = β(2 − q)[1 − β(1 − q)τ]1/(1−q), which may be due to the superstatistical nature of the occurrence of extreme events. Our analysis provides a universal description of extreme events in turbulent flows.

The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations

“…The normalization factor (equation (3)) reflects the value th = (2 − q) as found in Manshour et al (2016): for MLO at Q = 1 the values obtained from the q-exponential fit for = 18.7±1, q = 1.55±0.1, and = 40±3, using the relation above, give th = 18 ± 3. The same result is obtained for the other stations: VRS Q = 1.2, = 47 ± 1, q = 1.53 ± 0.07, = 81 ± 6, and th = 38.1 ± 6.1; CVO Q = 1.2, = 17±2, q = 1.54±0.12, = 37 ± 7, and th = 17.02 ± 7.…”

“…Hence, the behavior of the PDF is described by a Tsallis q ‐exponential function (equation ) and possesses asymptotic power laws (Briggs & Beck, ; Manshour et al, ): where α is a normalization factor (Beck, ; Wilk & Włodarczyk, ), q is a measure of the deviation from an exponential distribution, and q > 1 indicates a long‐tailed distribution. A number of authors have shown that the limit of validity for the parameter q lies in the range 1≤ q ≤2.…”

Scaling Properties of Atmospheric Wind Speed in Mesoscale Range

“…Here, the scale-dependent features of the wind speed have been using different methods, and the results compared with the classical values found in the literature. Initially, the Hurst exponent H has been evaluated by using Empirical Mode Decomposition (EMD) [30][31][32], and interoccurrence times (IOT) statistics [33][34][35][36]. The value obtained is in good agreement with the classical estimation of H obtained via the first order structure function for the inertial sub-range [35,37], without the necessity of employing the extended self-similarity (ESS) procedure [38].…”

“…Central panel: power-law fit of the first two order structure function; dashed lines represent the theoretical scaling obtained via least squares fit, S 1 ∼ 0.21±0.01 and S 2 ∼ 0.38±0.01 , respectively. Right panel: comparison of scaling exponents ζ(n) for orders n = 1 → 4 (circles) for all samples, with respect to other experimental values reported in the literature [10,23,35,38].…”

“…A further method used to obtain information on the scaling properties of a stochastic processes, is theIOT τ analysis [33][34][35][36]. IOTs are a measure of the time between the occurrence of two or more subsequent extreme events in the data that exceed a fixed threshold Q (Figure 7, upper panel).…”