The inverse structure functions of exit distances have been introduced as a novel diagnostic of turbulence which emphasizes the more laminar regions [1-4]. Using Taylor's frozen field hypothesis, we investigate the statistical properties of the exit distances of empirical 3D fully developed turbulence. We find that the probability density functions of exit distances at different velocity thresholds can be approximated by stretched exponentials with exponents varying with the velocity thresholds below a critical threshold. We show that the inverse structure functions exhibit clear extended self-similarity (ESS). The ESS exponents ξ(p,2) for small p (p<3.5) are well captured by the prediction of ξ(p,2)= p/2 obtained by assuming a universal distribution of the exit distances, while the observed deviations for large p's characterize the dependence of these distributions on the velocity thresholds. By applying a box-counting multifractal analysis of the natural measure constructed on the time series of exit distances, we demonstrate the existence of a genuine multifractality, endowed in addition with negative dimensions. Performing the same analysis of reshuffled time series with otherwise identical statistical properties for which multifractality is absent, we show that multifractality can be traced back to non-trivial dependence in the time series of exit times, suggesting a non-trivial organization of weakly-turbulent regions.
The irreversible turbulent energy cascade epitomizes strongly non-equilibrium systems. At the level of single fluid particles, time irreversibility is revealed by the asymmetry of the rate of kinetic energy change, the Lagrangian power, whose moments display a power-law dependence on the Reynolds number, as recently shown by Xu et al. [H. Xu et al, Proc. Natl. Acad. Sci. U.S.A. 111, 7558 (2014)]. Here Lagrangian power statistics are rationalized within the multifractal model of turbulence, whose predictions are shown to agree with numerical and empirical data. Multifractal predictions are also…
Recent numerical explorations of extremely intense circulation fluctuations at high Reynolds number flows have brought to light novel aspects of turbulent intermittency. Vortex gas modeling ideas, introduced alongside such developments, have led to accurate descriptions of the core and the intermediate tails of circulation probability distribution functions (cPDFs), as well as the scaling exponents associated to statistical moments of circulation. We extend the predictive reach of the vortex gas picture of turbulence, by emphasizing that multifractality breaking, one of its salient phenomenolo…
Disentangling intermittent flow structure contributions to anomalous scaling and multifractality in turbulence
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；Department of Mechanical Engineering, Indian Institute of Technology, Kanpur（坎普尔印度理工学院机械工程系）
The active interaction between the bacteria and fluid generates turbulent structures even at zero Reynolds number. Velocity of such a flow obtained experimentally has been quantitatively investigated based on streamline segment analysis. There is a clear transition at about $16$ times of the organism body length separating two different scale regimes, which may be attributed to the different influence of the viscous effect. Surprisingly the scaling extracted from the streamline segment indicates the existence of scale similarity even at the zero Reynolds number limit. Moreover the multifractal…
We study the statistics of fluid (gas) density and concentration of passive tracer particles (dust) in compressible turbulence. We raise the question of whether the fluid density which is an active field that reacts back on the transporting flow and the passive concentration of tracers must coincide in the steady state, which we demonstrate to be crucial both theoretically and experimentally. The fields' coincidence is provable at small Mach numbers, however at finite Mach numbers the assumption of mixing is needed, not evident due to the possibility of self-organization. Irrespective of wheth…
For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the deformation of a probability density function from Gaussian at large scales to non-Gaussian at smaller scales. Our framework is based on information theory, and uses Shannon entropy and Kullback-Leibler divergence. We propose an extensive application to three-dimensional fully developed turbulence, seen here as a paradigmatic complex system where intermittency wa…
Anisotropy and multifractality in velocity and temperature time series sampled at multiple heights in the roughness sublayer (RSL) over a boreal mixed-coniferous forest are reported. In particular, a turbulent-stress invariant analysis along with a scalewise version of it are conducted to elucidate the nature of relaxation of large-scale anisotropy to quasi-isotropic states at small scales. As the return to isotropy is linked to nonlinear interactions and correlations between different fluctuating velocity components across scales, we study the velocity and temperature time series by using mul…
Drift towards isotropization during the 3D hydrodynamic turbulence onset
Shirshov Institute of Oceanology of RAS（俄罗斯科学院谢尔肖夫海洋学研究所）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；P.N. Lebedev Physical Institute of RAS（俄罗斯科学院列别杰夫物理研究所）；National Research University Higher School of Economics（国立高等经济大学）
Single particle Lagrangian dispersion in Bolgiano turbulence
本文研究了二维湍流对流中Bolgiano-Obukhov区的单颗粒弥散。与显示经典K41现象的流中的色散不同，这里，对拉格朗日速度波动的主要贡献由最大的涡给出。这意味着对于时间间隔$t$中的典型速度波动，时间上的线性行为。局部涡（即具有$t$阶的特征时间）对拉格朗日速度波动的贡献，其空间/时间标度由Bolgiano-Obukhov理论决定，因此标准拉格朗日统计观测量无法检测到。为了解开的贡献所产生的大涡从本地涡，一个策略的基础上退出时间统计已成功地利用。因此，博尔基亚对流中的拉格朗日速度增量提供了一个与\emph{more than smooth}波动信号相关的物理示例。
Key flow regions linked to jet noise sources are investigated through comparison of convection velocity and turbulence measurements in high speed three-stream nozzles. A time-resolved Doppler global velocimetry (DGV) instrument was applied in the Nozzle Acoustic Test Rig (NATR) at NASA's Aero-Acoustic Propulsion Lab to measure 250 kHz repetition laser scattering signals arising from seeding particles at 32 points in high speed flow. Particle image velocimetry (PIV) measurements previously reported by NASA provided mean velocity and turbulence intensity. Results for convection velocity of the p…
The effects of mechanical generation of turbulent kinetic energy and buoyancy forces on the statistics of air temperature and velocity increments are experimentally investigated at the cross over from production to inertial range scales. The ratio of an approximated mechanical to buoyant production (or destruction) of turbulent kinetic energy can be used to form a dimensionless stability parameter $ζ$ that classifies the state of the atmosphere as common in many atmospheric surface layer studies. Here, we assess how $ζ$ affects the scale-wise evolution of the probability of extreme air tempera…
Reynolds proposed that after sufficiently long times, the flow in a pipe should settle to a steady condition: below a critical Reynolds number, flows should (regardless of initial conditions) always return to laminar, while above, eddying motion should persist. As shown, even in pipes several thousand diameters long, the spatio-temporal intermittent flow patterns observed at the end of the pipe strongly depend on the initial conditions, with no indication of an approach to a (statistical) steady state. Exploiting the fact that turbulent puffs do not age, we continuously recreate the puff seque…
