High-order Structure Functions Research Articles

Small-scale turbulent characteristics in transcritical wall-bounded flows

Considerable efforts have been devoted to the understanding of the small-scale characteristics in turbulent flows. While the universality of small-scale quantities has been established for incompressible flows, their extension to high-pressure transcritical flows remains an open area of research. To address this question, we investigate the real-fluid thermodynamic effects on small-scale velocity statistics of high-pressure transcritical wall-bounded turbulence. We show that in the locally isotropic region for transcritical flows, low-order moments of small-scale statistics collapse for all cases and Kolmogorov's (1941) theory holds. However, real-fluid thermodynamic effects introduce deviations in the tails of the probability density function for the velocity derivative and, consequently, high-order moments of velocity gradients and dissipation rate in transcritical flows cannot collapse in the locally isotropic region. Analysis of the intermittency shows that the low-order structure functions in transcritical flows follow extended self-similarity, while the dependence of the intermittency factor on real-fluid effects is observed for high-order structure functions. The real-fluid effects on intermittency are explained by turbulent structures related to rare events. Additionally, the dissipation rate moments for transcritical flows follow a universal scaling with Reynolds number, and the scaling exponents are different from those of incompressible flows. These results extend the small-scale universality in incompressible flows (Schumacher et al., Proc. Natl Acad. Sci. USA, vol. 111, 2014, pp. 10961–10965) to realistic flows with significant changes in thermodynamic properties, and provide a physical underpinning of the scaling laws of small-scale statistics at transcritical conditions.

An analysis of the turbulence in the central region of the Orion Nebula (M42) – II. Homogeneity and power-spectrum analyses

ABSTRACT In this second paper, we continue our analysis of the turbulence in the Huygens region of the Orion Nebula (M42). We calculate the associated transverse structure functions up to eighth order and find that the higher-order transverse structure functions are almost proportional to the second-order transverse structure function. We find that, after proper normalization, the higher-order transverse structure functions only differ by very small deviations from the second-order transverse structure function in a subinterval of the inertial range. We demonstrate that this implies that the turbulence in the Huygens region is quasi-log–homogeneous or, to a better degree of approximation, binomially weighted log–homogeneous in the statistical sense. This implies that there is some type of invariant statistical structure in the velocity field of the Huygens region. We also obtain and analyse the power spectrum of the turbulent field. We find that it displays a large tail that follows, very approximately, two power laws: one of the form E(k) ∝ k−2.7 for the initial side of the tail, and one of the form E(k) ∝ k−1 for the end of the tail. We find that the power law with exponent β ∼ −2.7 corresponds to spatial scales of 0.0301–0.6450 pc. We find that the exponent of the first power law β ∼ −2.7 is related to the exponent α2 of the second-order structure function in the inertial range. We interpret the second power law with exponent β ∼ −1 as an indicator of viscous-dissipative processes occurring at scales of δr = 1–5 pixels, which correspond to spatial scales of 0.00043–0.00215 pc.

Asymmetry of velocity increments in turbulence

We use well-resolved direct numerical simulations of high-Reynolds-number turbulence to study a fundamental statistical property of turbulence -- the asymmetry of velocity increments -- with likely implications on important dynamics. This property, ignored by existing small-scale phenomenological models, manifests most prominently in the non-monotonic trend of velocity increment moments (or structure functions) with the moment order, and in differences between ordinary and absolute structure functions for a given separation distance. We show that high-order structure functions arise nearly entirely from the negative side of the probability density of velocity increments, essentially removing the ambiguity between ordinary and absolute moments, and provide a plausible dynamical interpretation of this result.

Bolgiano–Obukhov scaling in two-dimensional isotropic convection

The existence of Bolgiano–Obukhov (BO) scaling in Rayleigh–Bénard convection (RBC) has long been speculated. However, due to the inhomogeneity and anisotropy of the flow, and the lack of clear scale separation, no conclusive evidence has been found. To avoid these non-ideal factors, we construct an idealized isotropic convection system by introducing an additional horizontal buoyancy field to RBC in a doubly periodic domain. We focus on the two-dimensional case so that its upscale kinetic energy flux can enable a long inertial range for detecting the BO scaling. Through direct numerical simulations of this system, we justify the existence of BO scaling using second- and third-order structure functions, which are in good agreement with our theoretically obtained scaling relations from the Kármán–Howarth–Monin equations. These theoretical and numerical results provide direct support for the conjecture that the existence of the BO scaling in RBC is associated with the inverse kinetic energy cascade. For higher-order structure functions, we found strong intermittent effects in the buoyancy field, but not in the velocity. By comparing the present system with the canonical anisotropic RBC in a periodic domain, the effects of anisotropy on the scaling properties are elucidated.

Global expressions for high-order structure functions in Burgers turbulence

Since the famous work by Kolmogorov on incompressible turbulence, the structure-function theory has been a key foundation of modern turbulence study. Due to the simplicity of Burgers turbulence, structure functions are calculated to arbitrary orders, which provides numerous implications for other compressible turbulent systems. We present the derivation of exact forcing-scale resolving expressions for high-order structure functions of the burgers turbulence. Compared with the previous theories, where the structure functions are calculated in the inertial range based on the statistics of shocks, our expressions link high-order structure functions in different orders without extra information on the flow structure and are valid beyond the inertial range, therefore they are easily checked by numerical simulations.

Complexity of Magnetic-field Turbulence at Reconnection Exhausts in the Solar Wind at 1 au

Abstract Magnetic reconnection is a complex mechanism that converts magnetic energy into particle kinetic energy and plasma thermal energy in space and astrophysical plasmas. In addition, magnetic reconnection and turbulence appear to be intimately related in plasmas. We analyze the magnetic-field turbulence at the exhaust of four reconnection events detected in the solar wind using the Jensen–Shannon complexity-entropy index. The interplanetary magnetic field is decomposed into the LMN coordinates using the hybrid minimum variance technique. The first event is characterized by an extended exhaust period that allows us to obtain the scaling exponents of higher-order structure functions of magnetic-field fluctuations. By computing the complexity-entropy index we demonstrate that a higher degree of intermittency is related to lower entropy and higher complexity in the inertial subrange. We also compute the complexity-entropy index of three other reconnection exhaust events. For all four events, the B L component of the magnetic field displays a lower degree of entropy and higher degree of complexity than the B M and B N components. Our results show that coherent structures can be responsible for decreasing entropy and increasing complexity within reconnection exhausts in magnetic-field turbulence.

Response of Reynolds stresses and scaling behavior of high-order structure functions to a water-worked gravel-bed surface and its implication on sediment transport

The aim of this experimental study is to investigate the interaction between turbulent flow and a gravel-bed that mimics the actual roughness structures of a natural bed and its implication on sediment transport. In particular, the response of the Reynolds stresses and the role of intermittency to the bed roughness is the primary focus of the current study. To this end, the flow field, measured with an Acoustic–Doppler Velocimeter (ADV), is thoroughly examined, considering the conditional Reynolds shear stresses and the high-order structure functions of velocity. The study results show that the features and the roughness structure of the water-worked gravel-bed (WWGB) have a strong impact on bursting events. The reason for this is attributed to the flow layer above the crest in the WWGBs being primarily affected by sweep events rather than ejection events, although the latter events are prevalent in this flow layer in an immobile, man-made, gravel-bed. These coherent structures, which are primarily responsible for sediment transport, also are the key cause of the presence of an intermittency excess that breaks the Kolmogorov self-similarity hypothesis, leading to multi-fractal behavior of the velocity structure functions.

On the combined effect of internal and external intermittency in turbulent non-premixed jet flames

This paper analyzes the combined effect of internal intermittency and external intermittency on the dynamics of small-scale turbulent mixing in a turbulent non-premixed jet flame. The phenomenon of external intermittency in turbulent jet flames originates from a very thin layer, known as turbulent/non-turbulent interface, that separates the inner turbulent core from the outer irrotational surrounding fluid. The impact of external intermittency on turbulence is evaluated across the jet flame by the self-similarity scaling of higher-order structure functions of the mixture fraction. It is shown that the scaling of structure functions exhibits a growing departure from the prediction of classical scaling laws toward the edge of the flame. Empirical evidence is provided that this departure is primarily due to external intermittency and the associated break down of self-similarity. External intermittency creates local gradients that are significantly more intense compared to those created by internal intermittency alone. As chemical reactions usually take place in thin layers in the vicinity of the turbulent/non-turbulent interface, an accurate statistical description of these intense events is necessary to predict the turbulence-chemistry interaction. The study is based on data from a highly-resolved direct numerical simulation of a temporally evolving planar jet flame.

Turbulence anisotropy and intermittency in open-channel flows on rough beds

An experimental campaign, based on Particle Image Velocimetry measurements in a laboratory flume with different median sediment sizes in the no-motion condition, has been carried out aiming at investigating the effects of bed roughness on turbulence anisotropy in two different vertical zones of the turbulent open-channel flow. An analysis of turbulence anisotropy, which relies on second-order structure functions and anisotropy angle, has been performed. The scale-dependent anisotropy level has been quantified, verifying the tendency of the system to span from large-scale anisotropy, due to the main shear of the boundary layer, to small-scale isotropy. Isotropy is well-established for the largest sediment sizes. High-order structure function analysis reveals that intermittency is more pronounced in the near-bed layers, where the flow is more populated by coherent vortices. Spectral anisotropy and intermittency strongly characterize the transport properties of turbulence and are, therefore, important phenomena for natural bed rivers.

Modelling Lagrangian velocity and acceleration in turbulent flows as infinitely differentiable stochastic processes

Abstract

Stirring anisotropic turbulence with an active grid

We study spectra and high-order structure functions in anisotropic wind tunnel turbulence, which is generated using an active grid. In the first experiment, we impose homogeneous shear turbulence with a constant gradient of the mean flow and (approximately) homogeneous turbulent fluctuations. We measure mixed structure functions of order 2, 3, 4, 6, and 10 using an array of two-component hotwires. These structure functions, which vanish for isotropic turbulence, display scaling with scaling exponents that highlight intermittency: the return to isotropy at small scales of large fluctuations is much slower than expected on the basis of a simple Kolmogorov-like scaling argument [J. L. Lumley, “Similarity and the turbulent energy spectrum,” Phys. Fluids 10, 855 (1967)]. In the second experiment, we impose anisotropy in otherwise homogeneous turbulence through the time modulation of the active grid. This is done by driving the grid using signals from a turbulence (shell) model, which acts as a convenient turbulent random signal generator. In this way, different statistical properties of different velocity components could be imposed. Similar to the first experiment, our interest is in the return to isotropy of the small-scale turbulent fluctuations, which is quantified using second-order quantities such as spectra and correlation functions. Also, in this case, the strongly anisotropic correlations induced by the forcing at large scales tend to return to isotropy at small, inertial-range scales, but with the imprint of large-scale anisotropy retained.

Large-Eddy Simulation of Conditionally Neutral Boundary Layers: A Mesh Resolution Sensitivity Study

Abstract Large-eddy simulation (LES) is used to model turbulent winds in a nominally neutral atmospheric boundary layer at varying mesh resolutions. The boundary layer is driven by wind shear with zero surface heat flux and is capped by a stable inversion. Because of entrainment the boundary layer is in a weakly stably stratified regime. The simulations use meshes varying from 1282 × 64 to 10242 × 512 grid points in a fixed computational domain of size (2560, 2560, 896) m. The subgrid-scale (SGS) parameterizations used in the LES vary with the mesh spacing. Low-order statistics, spectra, and structure functions are compared on the different meshes and are used to assess grid convergence in the simulations. As expected, grid convergence is primarily achieved in the middle of the boundary layer where there is scale separation between the energy-containing and dissipative eddies. Near the surface second-order statistics do not converge on the meshes studied. The analysis also highlights differences between one-dimensional and two-dimensional velocity spectra; differences are attributed to sampling errors associated with aligning the horizontal coordinates with the vertically veering mean wind direction. Higher-order structure functions reveal non-Gaussian statistics on all scales, but are highly dependent on the mesh resolution. A generalized logarithmic law and a k−1 spectral scaling regime are identified with mesh-dependent parameters in agreement with previously published results.

Unified Quantitative Description of Solar Wind Turbulence Intermittency in Both Inertial and Kinetic Ranges

Abstract There are various ways of describing intermittent features in space plasma turbulence, but we lack a unified paradigm to connect the results from these different approaches. In this work, we aim to construct a unified paradigm to describe various intermittency-related quantities with the same set of parameters. The Castaing function, which describes the scale-dependent turbulence amplitude as a logarithmic normal distribution, is adopted as a fitting function to describe the probability distribution of magnetic field difference at various timescales τ. Two fitting parameters (μ, λ) as a function of τ are obtained and regarded as the fundamental information, based on which various characteristics related to intermittency can be derived at one time, e.g., the high-order structure functions, their scaling exponent as a function of the order, or the flatness as a function of τ. We find it is the derivative ratio, DR = , that determines the order trend of the scaling exponent ζ(m). A negative DR of a small absolute is responsible for a curved ζ(m) in the inertial range, and a large positive DR leads to a straight ζ(m) in the kinetic range. Therefore, it is suggested that the probability distribution function of the magnetic increments spreads in width (λ(τ)) with decreasing τ in the inertial range, while it is saturated and even slightly reduced in the kinetic range. Moreover, it is found that the turnings between the inertial and kinetic scales for the two Castaing fitting parameters μ(τ) and λ 2(τ) occur at different scales: lnτ ∼ 0 and lnτ ∼ 2, respectively. The reason for this different behavior is still unclear.

Statistics of turbulence and intermittency enhancement in superfluid He4 counterflow

We report a detailed analysis of the energy spectra, second- and high-order structure functions of velocity differences in superfluid $^4$He counterflow turbulence, measured in a wide range of temperatures and heat fluxes. We show that the one-dimensional energy spectrum $E_{xz} (k_y)$ (averaged over the $xz$-plane, parallel to the channel wall), directly measured as a function of the wall-normal wave-vector $k_y$, gives more detailed information on the energy distribution over scales than the corresponding second-order structure function $S_{2}(\delta_y)$. In particular, we discover two intervals of $k_y$ with different apparent exponents: $E_{xz} (k_y)\propto k_y^{-m_C}$ for $k\lesssim k_\times$ and $E_{xz} (k_y)\propto k_y^{-m_F}$ for $k\gtrsim k_\times$. Here $k_\times$ denotes wavenumber that separate scales with relatively strong (for $k\lesssim k_\times$) and relatively weak (for $k\gtrsim k_\times$) coupling between the normal-fluid and superfluid velocity components. We interpret these $k$-ranges as cascade-dominated and mutual friction-dominated intervals, respectively. General behavior of the experimental spectra $E_{xz}(k_y)$ agree well with the predicted spectra [Phys. Rev. B 97, 214513 (2018)]. Analysis of the $n$-th order structure functions statistics shows that in the energy-containing interval the statistics of counterflow turbulence is close to Gaussian, similar to the classical hydrodynamic turbulence. In the cascade- and mutual friction-dominated intervals we found some modest enhancement of intermittency with respect of its level in classical turbulence. However, at small scales, the intermittency becomes much stronger than in the classical turbulence.

Extremes, intermittency, and time directionality of atmospheric turbulence at the crossover from production to inertial scales

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 $\zeta$ that classifies the state of the atmosphere as common in many atmospheric surface layer studies. Here, we assess how $\zeta$ affects the scale-wise evolution of the probability of extreme air temperature excursions, their asymmetry and time reversibility. The analysis makes use of high frequency velocity and air temperature time series measurements collected at $z$=5 m above a grass surface at very large Reynolds numbers $Re=u_* z/\nu > 1\times 10^5$ ($u_*$ is the friction velocity and $\nu$ is the kinematic viscosity of air). Using conventional higher-order structure functions, temperature exhibits larger intermittency and wider multifractality when compared to the longitudinal velocity component, consistent with laboratory studies and simulations conducted at lower $Re$. Moreover, deviations from the classical Kolmogorov scaling for the longitudinal velocity are shown to be reasonably described by the She-Leveque vortex filament model that has no 'tunable' parameters and is independent of $\zeta$. The work demonstrates that external boundary conditions, and in particular the magnitude and sign of the sensible heat flux, have a significant impact on temperature advection-diffusion dynamics within the inertial range. In particular, atmospheric stability affects both the buildup of intermittency and the persistent asymmetry and time irreversibility observed in the first two decades of inertial sub-range scales.

Intermittency spectra of current helicity in solar active regions

We analyse the spatial distribution of current helicity in solar active regions. A comparison of current helicity maps derived from three different instruments (Helioseismic and Magnetc Imager on board the Solar Dynamics Observatory, SDO/HMI, Spectro-Polarimeter on board the Hinode, and Solar Magnetic Field Telescope at the Huairou Solar Observing Station, China, HSOS/SMFT) is carried out. The comparison showed an excellent correlation between the maps derived from the spaceborne instruments and moderate correlation between the maps derived from SDO/HMI and HSOS/SMFT vector magnetograms. The results suggest that the obtained maps characterize real spatial distribution of current helicity over an active region. To analyse intermittency of current helicity, we traditionally use the high-order structure functions and flatness function approach. The slope of a flatness function within some range of scales - the flatness exponent - is a measure of the degree of intermittency. SDO/HMI vector magnetograms for 3 ARs (NOAA 11158, 12494, and 12673) were used to calculate the flatness exponent time variations. All three ARs exhibited emergence of a new magnetic flux during the observational interval. The flatness exponent indicated the increase of intermittency 12-20 hours before the emergence of a new flux. We suppose that this behaviour can indicate subphotospheric fragmentation or distortion of the pre-existed electric current system by emerging magnetic flux.

Design and Construction of Hybrid Microcapsules with Higher-Order Structure and Multiple Functions.

The construction of inorganic‐protein hybrid microcapsules by using bovine serum albumin, metal ion clusters, and poly (N‐isopropylacrylamide) nanoconjugates as building blocks is presented. These microcapsules have robust membranes, which can keep their spherical morphology. They support interfacial catalytic activity by the ion clusters on their surface, and can be used as a platform to immobilize enzyme on the interface of oil/water to increase the diversity and efficiency of catalysis. These microcapsules also act as a container to make materials away from bacteria when existing silver clusters on the membrane. The obtained results highlight the construction of these microcompartments. These novel microcompartments can provide some new opportunities in bottom‐up synthetic biology, bioinspired microstorage/ microreactor, and drug/gene delivery in the future.

The collisionality dependence of intermittency level in drift-wave turbulence in the stellarator TJ-K

The link between plasma collisionality and the intermittency of edge drift-wave turbulence is investigated experimentally in the stellarator TJ-K and compared to results obtained from slab Hasegawa-Wakatani (HW) simulations. The kurtosis of experimental time series of density and potential fluctuations was analysed at different frequency scales. Using this method on data from a range of discharges, it was found that the intermittency level increases with increasing collisionality for density fluctuations, whereas potential fluctuations are generally self-similar. In addition, a high-order structure function analysis of density time-series data also shows a trend towards higher intermittency levels as collisionality is increased. HW simulations are found to produce a qualitatively similar trend in the intermittency level compared to experimental analyses. The transition to intermittent fluctuations at higher collisionalities can be understood in the framework of the HW model as the decoupling of the density field from the self-similar potential field when moving from the adiabatic to the hydrodynamic limit, where the density behaves like a passive scalar, resulting in the intermittency levels observed in the vorticity.

Escherichia coli FtsA forms lipid-bound minirings that antagonize lateral interactions between FtsZ protofilaments

Most bacteria divide using a protein machine called the divisome that spans the cytoplasmic membrane. Key divisome proteins on the membrane’s cytoplasmic side include tubulin-like FtsZ, which forms GTP-dependent protofilaments, and actin-like FtsA, which tethers FtsZ to the membrane. Here we present genetic evidence that in Escherichia coli, FtsA antagonizes FtsZ protofilament bundling in vivo. We then show that purified FtsA does not form straight polymers on lipid monolayers as expected, but instead assembles into dodecameric minirings, often in hexameric arrays. When coassembled with FtsZ on lipid monolayers, these FtsA minirings appear to guide FtsZ to form long, often parallel, but unbundled protofilaments, whereas a mutant of FtsZ (FtsZ*) with stronger lateral interactions remains bundled. In contrast, a hypermorphic mutant of FtsA (FtsA*) forms mainly arcs instead of minirings and enhances lateral interactions between FtsZ protofilaments. Based on these results, we propose that FtsA antagonizes lateral interactions between FtsZ protofilaments, and that the oligomeric state of FtsA may influence FtsZ higher-order structure and divisome function.

High-order structure functions for passive scalar fed by a mean gradient

Transport equations for even-order structure functions are written for a passive scalar mixing fed by a mean scalar gradient, with a Schmidt number Sc=1. Direct numerical simulations (DNS), in a range of Reynolds numbers Rλ ∈ [88, 529] are used to assess the validity of these equations, for the particular cases of second-and fourth-order moments. The involved terms pertain to molecular diffusion, transport, production, and dissipative-fluxes. The latter term, present at all scales, is equal to: i) the mean scalar variance dissipation rate, ⟨χ⟩, for the second-order moments transport equation; ii) non-linear correlations between χ and second-order moments of the scalar increment, for the fourth-order moments transport equation.The equations are further analysed to show that the similarity scales (i.e., variables which allow for perfect collapse of the normalised terms in the equations) are, for second-order moments, fully consistent with Kolmogorov–Obukhov–Corrsin (KOC) theory. However, for higher-order moments, adequate similarity scales are built from ⟨χn⟩. The similarity is tenable for the dissipative range, and the beginning of the scaling range.