We consider the turbulent energy dissipation from one-dimensional records in experiments using air and gaseous helium at cryogenic temperatures, and obtain the intermittency exponent via the two-point correlation function of the energy dissipation. The air data are obtained in a number of flows in a wind tunnel and the atmospheric boundary layer at a height of about 35 m above the ground. The helium data correspond to the centerline of a jet exhausting into a container. The air data on the intermittency exponent are consistent with each other and with a trend that increases with the Taylor microscale Reynolds number, R_λ, of up to about 1000 and saturates thereafter. On the other hand, the helium data cluster around a constant value at nearly all R_λ, this being about half of the asymptotic value for the air data. Some possible explanation is offered for this anomaly.
We study the nature of the triadic interactions in Fourier space for three-dimensional Navier-Stokes equations based on the helicity content of the participating modes. Using the tool of helical Fourier decomposition we are able to access the effects of a group of triads on the energy cascade process and on the small-scale intermittency. We show that while triadic interactions involving modes with only one sign of helicity results to an inverse cascade of energy and to a complete depletion of the intermittency, absence of such triadic interactions has no visible effect on the energy cascade an…
Intermittency (externally induced) in the two-dimensional (2D) enstrophy cascade is shown to be able to maintain a finite enstrophy along with a vorticity conservation anomaly. Intermittency mechanisms of three-dimensional (3D) energy cascade and 2D enstrophy cascade in fully-developed turbulence (FDT) seem to have some universal features. The parabolic-profile approximation (PPA) for the singularity spectrum f(a) in multi-fractal model is used and extended to the appropriate microscale regimes to exhibit these features. The PPA is also shown to afford, unlike the generic multi-fractal model, …
Fine scales of turbulent velocity fields, beyond the inertial range and well into the dissipative range, are highly intermittent. It has been hypothesized that complex plane singularities are the principal mechanism behind fine scale intermittency. In this article, we view the velocity field of a turbulent flow as an analytic function of time. Although the function is only available for real values of time, we present a numerical technique to analytically continue the function to complex values of time, and with sufficient fidelity to locate and visualize the singularity closest to the real ax…
The motion of a large, neutrally buoyant, particle, freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a manifestation of intermittency. The orientation of the angular velocity with respect to the trajectory, as well as the translational acceleration conditioned on the spinning velocity provide evidence of a lift force acting on the particle.
In this paper, we analyze the sea surface temperature obtained from the global drifter program. The experimental Fourier power spectrum shows a two-decade power-law behavior as $E_θ(f)\propto f^{-7/3}$ in the frequency domain. Dimensional argument suggests a two-dimensional-like Lagrangian forward cascade, in which the enstrophy dissipation $ε_Ω$ is involved. Using the Hilbert-Huang transform and multi-level segment analysis, the measured high-order statistics and the corresponding singularity spectrum confirm the existence of the intermittency with a measured intermittency parameter $μ_θ\sime…
This investigation presents evidence of the relation between the dynamics of intense events in small-scale turbulence and the energy cascade. We use the generalised (Hölder) means to track the temporal evolution of intense events of the enstrophy and the dissipation in direct numerical simulations of isotropic turbulence. We show that these events are modulated by large-scale fluctuations, and that their evolution is consistent with a local multiplicative cascade, as hypothesised by a broad class of intermittency models of turbulence.
Premixed turbulent flames, encountered in power generation and propulsion engines, are an archetype of a randomly advected, self-propagating surface. While such a flame is known to exhibit large-scale intermittent flapping, the possible intermittency of its small-scale fluctuations has been largely disregarded. Here, we experimentally reveal the inner intermittency of a premixed turbulent V-flame, while clearly distinguishing this small-scale feature from large-scale outer intermittency. From temporal measurements of the fluctuations of the flame, we find a frequency spectrum that has a power-…
Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative noise is an intrinsic feature of the turbulent state. The trajectories are conditioned on their entropy exchange. Such selected trajectories concentrate around an optimal path, called instanton, which is the minimum of an effective action. The action is derived from the Langevin equation, estimated from measured data. In particular instantons with negative en…
We demonstrate that like in the forward cascade of three dimensional turbulence that displays intermittency (lack of self-similarity) due to the concentration of energy dissipation in a small set of fractal dimension less than three, the inverse cascade of two-dimensional turbulence can also display lack of self-similarity and intermittency if the energy injection is constrained in a fractal set of dimension less than two. A series of numerical simulations of two dimensional turbulence are examined, using different forcing functions of the same forcing length-scale but different fractal dimens…
We study intermittency of circulation moments in turbulent superfluid helium by using experimental grid turbulence and numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. More precisely, we compute the velocity circulation $Γ_r$ in loops of size $r$ laying in the inertial range. For both, experimental and numerical data, the circulation variance shows a clear Kolmogorov scaling $\langle Γ_r^2 \rangle \sim r^{8/3}$ in the inertial range, independently of the temperature. Scaling exponents of high-order moments are comparable, within error bars, to previously reported anomalous…
In pipe, channel and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we here argue that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous …
We consider the generation of magnetic field by a turbulent flow. For the linear induction equation (i.e. the kinematic dynamo problem), we show that the statistical moments of the magnetic field display multiscaling and in particular moments of different order turn unstable for different values of the control parameter. On a canonical example, we map the problem onto the calculation of the injected power by a time correlated fluctuating force acting on a Brownian particle. We are then able to calculate analytically the growth rate of the moments of the magnetic field and explain the origin of…
We suggest a new approach to probing intermittency corrections to the Kolmogorov law in turbulent flows based on the Auto-Regressive Moving-Average modeling of turbulent time series. We introduce a new index $Υ$ that measures the distance from a Kolmogorov-Obukhov model in the Auto-Regressive Moving-Average models space. Applying our analysis to Particle Image Velocimetry and Laser Doppler Velocimetry measurements in a von Kármán swirling flow, we show that $Υ$ is proportional to the traditional intermittency correction computed from the structure function. Therefore it provides the same infor…
A relation between intermittency and clustering phenomena in velocity field has been revealed for homogeneous fluid turbulence. It is described how the intermittency exponent can be split into sum of two other exponents. One of these exponents (cluster-exponent) characterizes clustering of the 'zero'-crossing points in nearly Gaussian velocity field and another exponent is related to the tails of the velocity probability distribution. The cluster-exponent is uniquely determined by the energy spectrum of the nearly Gaussian velocity field and entire dependence of the intermittency exponent on R…
We investigate the ability of 4D Particle Tracking Velocimetry measurements at high particle density to explore intermittency and irreversibility in a turbulent swirling flow at various Reynolds numbers. For this, we devise suitable tools to remove the experimental noise, and compute the statistics of both Lagrangian velocity increments and wavelet coefficients of the Lagrangian power (the time derivative of the kinetic energy along a trajectory). We show that the signature of noise is strongest on short trajectories, and results in deviations from the regularity condition at small time scales…
In incompressible and periodic statistically stationary turbulence, exchanges of turbulent energy across scales and space are characterised by very intense and intermittent spatio-temporal fluctuations around zero of the time-derivative term, the spatial turbulent transport of fluctuating energy, and the pressure-velocity term. These fluctuations are correlated with each other and with the intense intermittent fluctuations of the interscale energy transfer rate. These correlations are caused by the sweeping effect, the link between non-linearity and non-locality, and also relate to geometrical…
We derive scaling relations for the thermal dissipation rate in the bulk and in the boundary layers for moderate and large Prandtl number (Pr) convection. Using direct numerical simulations of Rayleigh-Bénard convection, we show that the thermal dissipation in the bulk is suppressed compared to passive scalar dissipation. The suppression is stronger for large Pr. We further show that the dissipation in the boundary layers dominates that in the bulk for both moderate and large Pr. The probability distribution functions of thermal dissipation rate, both in the bulk and in the boundary layers, ar…
We performed high resolution numerical simulations of homogenous and isotropic compressible turbulence, with an average 3D Mach number close to 0.3. We study the statistical properties of intermittency for velocity, density and entropy. For the velocity field, which is the primary quantity that can be compared to the isotropic incompressible case, we find no statistical differences in its behavior in the inertial range due either to the slight compressibility or to the different dissipative mechanism. For the density field, we find evidence of ``front-like'' structures, although no shocks are …
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…
It has long been suspected that flows of incompressible fluids at large or infinite Reynolds number (namely at small or zero viscosity) may present finite time singularities. We review briefly the theoretical situation on this point. We discuss the effect of a small viscosity on the self-similar solution of the Euler equations for inviscid fluids. Then we show that single point records of velocity fluctuations in the Modane wind tunnel display correlations between large velocities and large accelerations in full agreement with scaling laws derived from Leray's equations (1934) for self-similar…
The statistics of velocity differences between very heavy inertial particles suspended in an incompressible turbulent flow is found to be extremely intermittent. When particles are separated by distances within the viscous subrange, the competition between quiet regular regions and multi-valued caustics leads to a quasi bi-fractal behavior of the particle velocity structure functions, with high-order moments bringing the statistical signature of caustics. Contrastingly, for particles separated by inertial-range distances, the velocity-difference statistics is characterized in terms of a local …
We analyze the isotropic component of turbulent flows spanning a broad range of Reynolds numbers. The aim is to identify scaling laws and their Reynolds number dependence in flows under different mechanical forcings. To this end, we applied an SO(3) decomposition to data stemming from direct numerical simulations with spatial resolutions ranging from 64^3 to 1024^3 grid points, and studied the scaling of high order moments of the velocity field. The study was carried out for two different flows obtained forcing the system with a Taylor-Green vortex or the Arn'old-Beltrami-Childress flow. Our r…
Recently, by analyzing the measurement data of Nikuradze, it has been proposed (N. Goldenfeld, Phys. Rev. Lett. {\bf{96}}, 044503, 2006) that the friction factor, $f$, of rough pipe flow obeys a scaling law in the turbulent regime. Here, we provide a phenomenological scaling argument to explain this law and demonstrate how intermittency modifies the scaling form, thereby relating $f$ to the intermittency exponent, $η$. By statistically analyzing the measurement data of $f$, we infer a satisfactory estimate for $η$ ($\approx 0.02$), the inclusion of which is shown to improve the data-collapse c…
Hilbert-Huang transform is a method that has been introduced recently to decompose nonlinear, nonstationary time series into a sum of different modes, each one having a characteristic frequency. Here we show the first successful application of this approach to homogeneous turbulence time series. We associate each mode to dissipation, inertial range and integral scales. We then generalize this approach in order to characterize the scaling intermittency of turbulence in the inertial range, in an amplitude-frequency space. The new method is first validated using fractional Brownian motion simulat…
We study the intermittency properties of the energy and helicity cascades in two 1536^3 direct numerical simulations of helical rotating turbulence. Symmetric and anti-symmetric velocity increments are examined, as well as probability density functions of the velocity field and of the helicity density. It is found that the direct cascade of energy to small scales is scale invariant and non-intermittent, whereas the direct cascade of helicity is highly intermittent. Furthermore, the study of structure functions of different orders allows us to identify a recovery of isotropy of strong events at…
The intermittency of turbulent superfluid helium is explored systematically in a steady wake flow from 1.28 K up to T>2.18K using a local anemometer. This temperature range spans relative densities of superfluid from 96% down to 0%, allowing to test numerical predictions of enhancement or depletion of intermittency at intermediate superfluid fractions. Using the so-called extended self-similarity method, scaling exponents of structure functions have been calculated. No evidence of temperature dependence is found on these scaling exponents in the upper part of the inertial cascade, where turbul…
This study proposes a novel framework based on magnitude cumulant and surrogate analyses to reliably detect and estimate the intermittency coefficient from short-length coarse-resolution turbulent time series. Intermittency coefficients estimated from a large number of neutrally stratified atmospheric surface layer turbulent series from various field campaigns are shown to remarkably concur with well-known laboratory experimental results. In addition, surrogate-based hypothesis testing significantly reduces the likelihood of detecting a spurious non-zero intermittency coefficient from non-inte…
A universal relation between intermittency and dissipation within and beyond homogeneous isotropic turbulence
Univ. Grenoble Alpes, CNRS, Grenoble INP（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院）；Institut für Physik und ForWind, Universität Oldenburg（奥尔登堡大学物理与风电研究所）；Univ. Lille, CNRS, ONERA, Arts et Métiers ParisTech, Centrale Lille（里尔大学、法国国家科学研究中心、法国航空国防技术局、巴黎国立高等工艺学院、中央理工学院）
To explain the observed decay of superfluid turbulence at very low temperature, it has been proposed that a cascade of Kelvin waves (analogous to the classical Kolmogorov cascade) transfers kinetic energy to length scales which are small enough that sound can be radiated away. We report results of numerical simulations of the interaction of quantized vortex filaments. We observe the development of the Kelvin-waves cascade, and compute the statistics of the curvature, the amplitude spectrum (which we compare with competing theories) and the fractal dimension.
We investigate the statistics of turbulence in emulsions of two-immiscible fluids of same density. We compute for the first time velocity increments between points conditioned to be located in the same phase or in different phases and examine their probability density functions (PDF) and the associated structure functions (SF). This enables us to demonstrate that the the presence of the interface reduces the skewness of the PDF at scales below the Kolmogorov-Hinze scale and therefore the magnitude of the energy flux towards the dissipative scales, which is quantified by the third-order SF. The…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution of velocity increments is calculated explicitly and expressed in terms of generalized hypergeometric functions of the type ${_n}F_0$, which exhibit power-law tails. The model predictions are found to be in good agreement with experiments on a low temperature gaseous helium jet. It is argued that distributions based on the functions ${_n}F_0$ might be relevan…
Data from Direct Numerical Simulations of disperse bubbly flows in a vertical channel are used to study the effect of the bubbles on the carrier-phase turbulence. A new method is developed, based on the barycentric map approach, that allows to quantify the anisotropy and componentiality of the flow at any scale. Using this the bubbles are found to significantly enhance flow anisotropy at all scales compared with the unladen case, and for some bubble cases, very strong anisotropy persists down to the smallest flow scales. The strongest anisotropy observed was for the cases involving small bubbl…
Intermittency is a hallmark of turbulence, which exists not only in turbulent flows of classical viscous fluids but also in flows of quantum fluids such as superfluid $^4$He. Despite the established similarity between turbulence in classical fluids and quasi-classical turbulence in superfluid $^4$He, it has been predicted that intermittency in superfluid $^4$He is temperature dependent and enhanced for certain temperatures, which strikingly contrasts the nearly flow-independent intermittency in classical turbulence. Experimental verification of this theoretical prediction is challenging since …
Turbulent systems exhibit a remarkable multi-scale complexity, in which spatial structures induce scale-dependent statistics with strong departures from Gaussianity. In Fourier space, this is reflected by pronounced phase synchronization. A quantitative relation between real-space structure, statistics, and phase synchronization is currently missing. Here, we address this problem in the framework of a minimal phase-coupling model, which enables a detailed investigation by means of dynamical systems theory and multi-scale high-resolution simulations. We identify the spectral power-law steepness…
In recent years several local extrema based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work we study systematically the distribution of the local extrema for both synthesized scaling processes and turbulent velocity data from experiments. The results show that for the fractional Brownian motion (fBm) without intermittency correction the measured extremal point density (EPD) agrees well with a theoretical prediction. For a multifractal random walk (MRW) with the lognormal statistics, the measured EPD…
The Reynolds number dependency of intermittency for 2D turbulence is studied in a flowing soap film. The Reynolds number used here is the Taylor microscale Reynolds number R_λ, which ranges from 20 to 800. Strong intermittency is found for both the inverse energy and direct enstrophy cascades as measured by (a) the pdf of velocity differences P(δu(r)) at inertial scales r, (b) the kurtosis of P(\partial_x u), and (c) the scaling of the so-called intermittency exponent μ, which is zero if intermittency is absent. Measures (b) and (c) are quantitative, while (a) is qualitative. These measurement…
In shear flows turbulence first occurs in the form of localized structures (puffs/spots) surrounded by laminar fluid. We here investigate such spatially intermittent flows in a pipe experiment showing that turbulent puffs have a well defined interaction distance, which sets the minimum spacing of puffs as well as the maximum observable turbulent fraction. Two methodologies are employed here. Starting from a laminar flow puffs can be created by locally injecting a jet of fluid through the pipe wall. When the perturbation is applied periodically at low frequencies, as expected, a regular sequenc…
An efficient approach for extracting 3D local averages in spherical subdomains is proposed and applied to study the intermittency of small-scale velocity and scalar fields in direct numerical simulations of isotropic turbulence. We focus on the inertial-range scaling exponents of locally averaged energy dissipation rate, enstrophy and scalar dissipation rate corresponding to the mixing of a passive scalar $θ$ in the presence of a uniform mean gradient. The Taylor-scale Reynolds number $R_λ$ goes up to $1300$, and the Schmidt number $Sc$ up to $512$ (albeit at smaller $R_λ$). The intermittency …
The multifractal theory of turbulence is used to investigate the energy cascade in the Northwestern Atlantic ocean. The statistics of singularity exponents of velocity gradients computed from in situ measurements are used to show that the anomalous scaling of the velocity structure functions at depths between 50 ad 500 m has a linear dependence on the exponent characterizing the strongest velocity gradient, with a slope that decreases with depth. Since the distribution of exponents is asymmetric about the mode at all depths, we use an infinitely divisible asymmetric model of the energy cascade…
We present Lagrangian one-particle statistics from the Risoe PTV experiment of a turbulent flow. We estimate the Lagrangian Kolmogorov constant $C_0$ and find that it is affected by the large scale inhomogeneities of the flow. The pdf of temporal velocity increments are highly non-Gaussian for small times which we interpret as a consequence of intermittency. Using Extended Self-Similarity we manage to quantify the intermittency and find that the deviations from Kolmogorov 1941 similarity scaling is larger in the Lagrangian framework than in the Eulerian. Through the multifractal model we calcu…
With the aim of determining the statistical properties of relativistic turbulence and unveiling novel and non-classical features, we present the results of direct numerical simulations of driven turbulence in an ultrarelativistic hot plasma using high-order numerical schemes. We study the statistical properties of flows with average Mach number ranging from $\sim 0.4$ to $\sim 1.7$ and with average Lorentz factors up to $\sim 1.7$. We find that flow quantities, such as the energy density or the local Lorentz factor, show large spatial variance even in the subsonic case as compressibility is en…
On the large-scale vertical velocity intermittency of turbulent wall flows
University of California, Irvine（加州大学尔湾分校）；Politecnico di Torino（都灵理工大学）；University of Sydney（悉尼大学）；Italian Institute for Environmental Protection and Research (ISPRA)（意大利环境保护与研究研究所）；University of Pennsylvania（宾夕法尼亚大学）；Princeton University（普林斯顿大学）；Duke University（杜克大学）
We introduce a model for the turbulent energy cascade aimed at studying the effect of dynamical scaling on intermittency. In particular, we show that by slowing down the energy transfer mechanism for fixed energy flux, intermittency decreases and eventually disappears. This result supports the conjecture that intermittency can be observed only if energy is flowing towards faster and faster scales of motion.
We discuss the possibility of dual local and non-local cascades in a 3D turbulent Beltrami flow, with inverse energy cascade and direct helicity cascade, by analogy with 2D turbulence. We discuss the corresponding energy spectrum in both local and non-local case. Comparison with a high Reynolds number turbulent von Karman flow is provided and discussed.
The understanding of turbulent flows is one of the biggest current challenges in physics, as no first-principles theory exists to explain their observed spatio-temporal intermittency. Turbulent flows may be regarded as an intricate collection of mutually-interacting vortices. This picture becomes accurate in quantum turbulence, which is built on tangles of discrete vortex filaments. Here, we study the statistics of velocity circulation in quantum and classical turbulence. We show that, in quantum flows, Kolmogorov turbulence emerges from the correlation of vortex orientations, while deviations…
We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.
Spatial clustering and intermittency in the relative velocity of heavy particles of the same size settling in turbulent flows can be strongly affected by gravity. We present a model for the timescale of the fluid velocity gradient seen by particle pairs and propose an effective Kubo number based on this timescale to explain the mechanism of gravity-enhanced clustering. We explore the mechanisms of the gravity-induced reduction or enhancement of the intermittency in the particle radial relative velocity (RRV) at different Stokes numbers based on backward-in-time relative dispersion and preferen…
