Role of the zonal flow in multi-scale multi-mode turbulence with small-scale shear flow in tokamak plasmas

The structural characteristics of zonal flows and their roles in the nonlinear interaction of multi-scale multi-mode turbulence are investigated numerically via a self-consistent Landau-fluid model. The multi-mode turbulence here is composed of a shorter wavelength electromagnetic (EM) ion temperature gradient (ITG) mode and a Kelvin-Helmholtz (KH) instability with long wavelengths excited by externally imposed small-scale shear flows. For strong shear flow, a prominent periodic intermittency of fluctuation intensity except for dominant ITG component is revealed in turbulence evolution, which onset time depends on the ion temperature gradient and the shear flow amplitudes corresponding to different KH instabilities. It is identified that the intermittency phenomenon results from the zonal flow dynamics, which is mainly generated by the KH mode and back-reacts on it. It is demonstrated that the odd symmetric components of zonal flow (same symmetry as the external flow) make the radial parity of the KH mode alteration through adjusting the drift velocities at two sides of the resonant surface so that the KH mode becomes bursty first. Afterwards, the ITG intermittency follows due to nonlinear mode coupling. Parametric dependences of the features of the intermittency are elaborated. Finally, associated turbulent heat transport is evaluated.     

不可微不可逆映象中的V型阵发

一个既不可微(或不连续)又不可逆的一维映象可以展示一种新型的阵发。它的机制是稳定不动点与映象不可微或不连续点碰撞而消失。这种阵发可以在该不动点附近的线性化映象本征值绝对值在阵发前为小于1的任何值的情况发生,因而可能突然出现在倍周期分岔序列中途任一部分,使序列中断进入混沌。在稳定不动点消失后映象产生的阵发时间序列中,层流相长度呈现与外控参数距临界值距离的对数依赖关系。这种新型标度规律不依赖于映象的细节。作者认为这种阵发应广泛存在于许多实际系统之中。 关键词：     

Intermittent nature of acceleration in near wall turbulence

Using direct numerical simulation of a fully developed turbulent channel flow, we investigate the behavior of acceleration near a solid wall. We find that acceleration near the wall is highly intermittent and the intermittency is in large part associated with the near wall organized coherent turbulence structures. We also find that acceleration of large magnitude is mostly directed towards the rotation axis of the coherent vortical structures, indicating that the source of the intermittent acceleration is the rotational motion associated with the vortices that causes centripetal acceleration.     

Nonlinear dispersion relation of geodesic acoustic modes

The energy input and frequency shift of geodesic acoustic modes (GAMs) due to turbulence in tokamak edge plasmas are investigated in numerical two-fluid turbulence studies. Surprisingly, the turbulent GAM dispersion relation is qualitatively equivalent to the linear GAM dispersion but can have drastically enhanced group velocities. In up-down asymmetric geometry the energy input due to turbulent transport may favor the excitation of GAMs with one particular sign of the radial phase velocity relative to the magnetic drifts and may lead to pulsed GAM activity.     

Magnetosheath plasma turbulence and its spatiotemporal evolution as observed by the cluster spacecraft

We study the plasma turbulence, at scales larger than the ion inertial length scale, downstream of a quasiparallel bow shock using Cluster multispacecraft measurements. We show that turbulence is intermittent and well described by the extended structure function model, which takes into account the spatial inhomogeneity of the cascade rate. For the first time we use multispacecraft observations to characterize the evolution of magnetosheath turbulence, particularly its intermittency, as a function of the distance from the bow shock. The intermittency significantly changes over the distance of the order of 100 ion inertial lengths, being increasingly stronger and anisotropic away from the bow shock.     

Mixing of a passive scalar across a thin shearless layer: concentration of intermittency on the sides of the turbulent interface

The advection of a passive scalar through an initial flat interface separating two different isotropic decaying turbulent fields is investigated in two and three dimensions. Simulations have been performed for a range of Taylor’s microscale Reynolds numbers from 45 to 250 and for a Schmidt number equal to 1. Different to the case where the transport involves the momentum and kinetic energy only and one intermittency layer is formed in the low-turbulent energy side of the system, in the passive scalar concentration field two intermittent layers are observed to develop at the sides of the interface. The layers move normally to the interface in opposite directions. The dimensionality produces different time scaling of the passive scalar diffusion, which is much faster in the two-dimensional case. In two dimensions, the propagation of the intermittent layers exhibits a significant asymmetry with respect to the initial position of the interface and is deeper for the layer which moves towards the high kinetic energy side of the system. In three dimensions, the two intermittent layers propagate nearly symmetrically with respect the centre of the mixing region. During the temporal decay, inside the mixing, which is both inhomogeneous and anisotropic but devoid of a mean velocity shear, the passive scalar spectra are computed. In three dimensions, the exponent in the scaling range gets in time a value close to that of the kinetic energy spectrum of isotropic turbulence (?5/3). In two dimensions, instead the exponent settles down to a value that is about one-half of the corresponding isotropic case. By means of an analysis based on simple wavy perturbations of the interface we show that the formation of the double layer of intermittency is a dynamic general feature not specific to the turbulent transport. These results of our numerical study are discussed in the context of experimental results and numerical simulations.     

Observation of intermittency in wave turbulence

We report the observation of intermittency in gravity-capillary wave turbulence on the surface of mercury. We measure the temporal fluctuations of surface wave amplitude at a given location. We show that the shape of the probability density function of the local slope increments of the surface waves strongly changes across the time scales. The related structure functions and the flatness are found to be power laws of the time scale on more than one decade. The exponents of these power laws increase nonlinearly with the order of the structure function. All these observations show the intermittent nature of the increments of the local slope in wave turbulence. We discuss the possible origin of this intermittency.     

Lagrangian dynamics of drift-wave turbulence

The statistical properties of Lagrangian particle transport are investigated in dissipative drift-wave turbulence modelled by the Hasegawa-Wakatani system. By varying the adiabaticity parameter c, the flow regime can be modified from a hydrodynamic limit for c=0 to a geostrophic limit for c→∞. For c of order unity the quasi-adiabatic regime is obtained, which might be relevant to describe the edge turbulence of fusion plasmas in tokamaks. This particularity of the model allows one to study the change in dynamics when varying from one turbulent flow regime to another. By means of direct numerical simulation we consider four values for c and show that the Lagrangian dynamics is most intermittent in the hydrodynamic regime, while the other regimes are not or only weakly intermittent. In both quasi-adiabatic and quasi-geostrophic regimes the PDFs of acceleration exhibit exponential tails. This behaviour is due to the pressure term in the acceleration and not a signature of intermittency.     

大气湍流间歇性及其对光波传播的影响

当光波在大气中传播时,由于大气湍流的作用,其光束质量将会极大地恶化。对于这类问题的处理,长期以来都是以Tartask ii等人的理论为指导,而他们的理论是根据Kolmogrov于1941年建立的局地均匀各向同性湍流理论(K41)建立的,所以K41理论是这一领域奠基的基石。然而,随着湍流研究的深入,人们已经逐渐意识到K41湍流理论的各方面的缺点,其中尤其明显的是,K41理论忽略了湍流的间歇特征。在湍流现代理论中,湍流间歇性的研究一直是处于中心位置。经过数十年的不懈的努力,目前人们已经对湍流间歇性有了一些初步的成果和认识。本文综述了试图将湍流间歇性引入随机介质中光传播问题的考虑之中的各种尝试。我们首先结合光学问题的需要对湍流及其间歇性研究现状及重要成果进行了概要的回顾和说明。在此基础上,我们以两种方式对间歇性大气湍流中光传播问题进行分析:首先,我们以一种简单的非Gauss场模型为基础分析间歇性大气湍流中的光场统计性质;然后,我们将统计矩方程展开到四阶累积函数,分析了近Gauss场附近的光场统计性质。我们还以层次结构模型为基础对二阶统计矩进行了进一步的研究。     

大气湍流间歇性及其对光波传播的影响

当光波在大气中传播时，由于大气湍流的作用，其光束质量将会极大地恶化。对于这类问题的处理，长期以来都是以Tartaskii等人的理论为指导，而他们的理论是根据Kolmogrov于1941年建立的局地均匀各向同性湍流理论（K41）建立的，所以K41理论是这一领域奠基的基石。然而，随着湍流研究的深入，人们已经逐渐意识到K41湍流理论的各方面的缺点，其中尤其明显的是，K41理论忽略了湍流的间歇特征。在湍流现代理论中，湍流间歇性的研究一直是处于中心位置。经过数十年的不懈的努力，目前人们已经对湍流间歇性有了一些初步的成果和认识。本文综述了试图将湍流间歇性引入随机介质中光传播问题的考虑之中的各种尝试。我们首先结合光学问题的需要对湍流及其间歇性研究现状及重要成果进行了概要的回顾和说明。在此基础上，我们以两种方式对间歇性大气湍流中光传播问题进行分析：首先，我们以一种简单的非Gauss场模型为基础分析间歇性大气湍流中的光场统计性质；然后，我们将统计矩方程展开到四阶累积函数，分析了近Gauss场附近的光场统计性质。我们还以层次结构模型为基础对二阶统计矩进行了进一步的研究。     

Intermittency near the phase boundary of chaotic synchronization in spatially extended systems

The intermittent behavior of spatially extended systems is investigated using the example of unidirectionally coupled Pierce diodes. It isshown that the same type of intermittency as in finite-scaled systems is characteristic of this system near the boundary of the chaotic phase synchronization regime, i.e., needle-eye type intermittency, which is in fact also equivalent to type I intermittency with noise in the supercritical region.     

Clarifying the concepts of wave propagation through intermittent media

A unified exposition of the concepts of wave propagation through an intermittent atmosphere is set forth. By use of the simple example of the mutual coherence function, consistent definitions with experimental ramifications are introduced. I show that (a) the long-range limit of propagation through intermittency involves an effective medium that is distinct from the nonintermittent propagation case, (b) there is no evidence that coherence always improves in the presence of intermittency, and (c) the estimation procedures of the parameters of turbulence by the current algorithms should be changed.     

Observation of intermittency in edge plasma of SUNIST tokamak

The temporal intermittency of the fluctuation-driven particle transport fluxes is analysed by using data obtained from Langmuir probe array in the edge of the Sino-United Spherical Tokamak (SUNIST). The conditional statistics analysis indicates that the intermittent structures have a characteristic time width of about 30μs, which is the typical fluctuation time scaling. It is also found that the transport fluxes have a multifractal character over the fluctuation time scales, and exhibit a long-time-range correlation character with self-similar parameter H>0.5 in the plasma confinement time scales. Furthermore, the analyses show that the level of the intermittency and the long-range correlation of the fluxes vary with increasing plasma density. These observations are consistent with the prediction of the avalanche-like model.     

Chaotic transition in a three-coupled phase-locked loop system

The chaotic transition is observed in a three-coupled phase-locked loop (PLL) system in both experiments and numerical simulations. In this system, three PLL oscillators are connected with the periodic boundary condition. Intermittency is found in partially synchronized phase, in which two of three oscillators synchronize with each other and form a pair, and the chaotic transition occurs due to the recombination of synchronized pairs so that different pair is re-formed. In this phase, on-off intermittency is also observed and statistical analyses are carried out for on-off intermittent time series. This intermittency is considered as a hybrid type of intermittency with both on-off intermittency and intermittency due to the recombination of synchronized pairs present in the same time series. We also show the chaotic transition phenomena in a three-coupled logistic map system. (c) 2001 American Institute of Physics.     

Laser Doppler velocimetry analysis of transitional pipe flow

The objective of this study has been to experimentally analyze the correlation structure of the strong temporal intermittency which characterizes pipe flow close to the transition to turbulence. In doing so transitional pipe flow has been analyzed by Laser Doppler velocimetry and the Reynolds number dependence of the covariance function has been studied. The range which has been analyzed covers the transition to turbulence and moderately developed turbulence (Reynolds number from 1 500 to 5 000). The correlation structure which has been evidenced is generally in agreement with the deterministic, dynamical, interpretation of temporal intermittency which explains the intermittent behavior as a result of a saddle node bifurcation. However, the analysis has evidenced fluctuations even before the onset of turbulence. The structure of these fluctuations is perfectly autoregressive which leads us to conclude that the transition to turbulence can be viewed as a transition from linear randomness to (non-linear) homogeneity. Received 29 March 1999 and Received in final form 6 September 1999     

Intermittency in dissipative dynamical systems

We show that the intermittency displayed by a differential system proposed by Yamada and Fujisaka can be interpreted in the general framework of intermittent transitions to turbulence studied by Pomeau and the author.     

Intermittency of the density fluctuations and its influence on the radial transport in the boundary of J-TEXT

To improve the understanding of the turbulence intermittency,a detailed investigation of the intermittency of the density fluctuations has been performed in the boundary of J-TEXT.The intermittency of the density fluctuations and its influence on the radial transport are reported.The probability distribution functions of the density fluctuations are not scale-invariant,being inconsistent with the self-organized criticality hypothesis.The underlying dynamics of the intermittency are detected using the quiet-time statistical method.The probability distribution function of the quiet times shows double-power-law regions,indicating the existence of correlations between the successive burst events.     

On the superdiffusive scalings of transport in plasma

It is proposed to consider the scalings of anomalous transport (superdiffusion), determined experimentally in turbulent plasma of the Earth’s magnetosphere and laboratory plasma of thermonuclear facilities and processed using modern statistical cascade models of strong turbulence with intermittency, also within the approach of physical kinetics to the theory of plasma turbulence.     

Laminar–Turbulent Intermittency in Annular Couette–Poiseuille Flow: Whether a Puff Splits or Not

Direct numerical simulations were carried out with an emphasis on the intermittency and localized turbulence structure occurring within the subcritical transitional regime of a concentric annular Couette–Poiseuille flow. In the annular system, the ratio of the inner to outer cylinder radius is an important geometrical parameter affecting the large-scale nature of the intermittency. We chose a low radius ratio of 0.1 and imposed a constant pressure gradient providing practically zero shear on the inner cylinder such that the base flow was approximated to that of a circular pipe flow. Localized turbulent puffs, that is, axial uni-directional intermittencies similar to those observed in the transitional circular pipe flow, were observed in the annular Couette–Poiseuille flow. Puff splitting events were clearly observed rather far from the global critical Reynolds number, near which given puffs survived without a splitting event throughout the observation period, which was as long as 104 outer time units. The characterization as a directed-percolation universal class was also discussed.     

Sound-wave coherence in atmospheric turbulence with intrinsic and global intermittency

The coherence function of sound waves propagating through an intermittently turbulent atmosphere is calculated theoretically. Intermittency mechanisms due to both the turbulent energy cascade (intrinsic intermittency) and spatially uneven production (global intermittency) are modeled using ensembles of quasiwavelets (QWs), which are analogous to turbulent eddies. The intrinsic intermittency is associated with decreasing spatial density (packing fraction) of the QWs with decreasing size. Global intermittency is introduced by allowing the local strength of the turbulence, as manifested by the amplitudes of the QWs, to vary in space according to superimposed Markov processes. The resulting turbulence spectrum is then used to evaluate the coherence function of a plane sound wave undergoing line-of-sight propagation. Predictions are made by a general simulation method and by an analytical derivation valid in the limit of Gaussian fluctuations in signal phase. It is shown that the average coherence function increases as a result of both intrinsic and global intermittency. When global intermittency is very strong, signal phase fluctuations become highly non-Gaussian and the average coherence is dominated by episodes with weak turbulence.