Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media

Astrophysical fluids have very large Reynolds numbers and therefore turbulence is their natural state. Magnetic reconnection is an important process in many astrophysical plasmas, which allows restructuring of magnetic fields and conversion of stored magnetic energy into heat and kinetic energy. Turbulence is known to dramatically change different transport processes and therefore it is not unexpected that turbulence can alter the dynamics of magnetic field lines within the reconnection process. We shall review the interaction between turbulence and reconnection at different scales, showing how a state of turbulent reconnection is natural in astrophysical plasmas, with implications for a range of phenomena across astrophysics. We consider the process of magnetic reconnection that is fast in magnetohydrodynamic (MHD) limit and discuss how turbulence—both externally driven and generated in the reconnecting system—can make reconnection independent on the microphysical properties of plasmas. We will also show how relaxation theory can be used to calculate the energy dissipated in turbulent reconnecting fields. As well as heating the plasma, the energy dissipated by turbulent reconnection may cause acceleration of non-thermal particles, which is briefly discussed here.     

Acceleration of particles by shocks in a cosmic plasma

The theory and observational evidence pertaining to particle acceleration by shock waves in astrophysical objects and in space are systematized. Recent works showing observational and theoretical aspects of the problem dealing with shocks in turbulent media are emphasized. The acceleration of particles by shocks in turbulent media is observed in interplanetary space. This acceleration mechanism is of particular interest from the point of view of the origin of cosmic rays, providing the degree form of the spectrum. The index of the spectrum is close to the observable one for galactic cosmic rays. It depends slightly on specific conditions in the acceleration region. Electron and nucleus acceleration in supernova remnants and in radiogalaxies is discussed, and theory and observational data are compared. The theory of particle acceleration by supersonic turbulence is outlined.     

非线性 k-ε 紊流模型在平面叶栅紊流计算中的应用

 采用Speziale的非线性k-ε模型计算了平面叶栅内的紊流流动,并且与标准的k-ε模型的计算结果作了对比,表明非线性模型同样可以应用于具有周期性边界条件的复杂流动,在紊流量的计算结果上表现出了明显的各向异性。     

Topics in Microphysics of Relativistic Plasmas

Astrophysical plasmas can have parameters vastly different from the more studied laboratory and space plasmas. In particular, the magnetic fields can be the dominant component of the plasma, with energy-density exceeding the particle rest-mass energy density. Magnetic fields then determine the plasma dynamical evolution, energy dissipation and acceleration of non-thermal particles. Recent data coming from astrophysical high energy missions, like magnetar bursts and Crab nebula flares, point to the importance of magnetic reconnection in these objects. In this review we outline a broad spectrum of problems related to the astrophysical relevant processes in magnetically dominated relativistic plasmas. We discuss the problems of large scale dynamics of relativistic plasmas, relativistic reconnection and particle acceleration at reconnecting layers, turbulent cascade in force-fee plasmas. A number of astrophysical applications are also discussed.     

GAO-YONG湍流模型对湍流传热的数值模拟

将GAO-YONG湍流模型应用于湍流传热的研究,分别计算了平板剪切湍流和二维平面冲击射流的湍流传热问题.边界层剪切湍流流动与换热的计算表明:与传统的湍流模型不同,GAO-YONG湍流模型不需要对近壁区域做任何特殊处理(比如壁面函数、低Reynolds数修正等)即可模拟出从壁面到主流区的全部流动与传热情况;另外,对于冲击射流Nusselt数的模拟也得到了与实验符合较好的计算结果,准确地捕捉到了2种冲击高度下流场换热的不同特征,表明了GAO-YONG湍流模型能够较高精度地计算湍流换热.      

Turbulence, Magnetic Reconnection in Turbulent Fluids and Energetic Particle Acceleration

Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show how fast and slow modes accelerate energetic particles through the second order Fermi acceleration, while density fluctuations generate magnetic fields in pre-shock regions enabling the first order Fermi acceleration of high energy cosmic rays. Very importantly, however, the first order Fermi cosmic ray acceleration is also possible in sites of magnetic reconnection. In the presence of turbulence this reconnection gets fast and we present numerical evidence supporting the predictions of the Lazarian and Vishniac (Astrophys. J. 517:700–718, 1999) model of fast reconnection. The efficiency of this process suggests that magnetic reconnection can release substantial amounts of energy in short periods of time. As the particle tracing numerical simulations show that the particles can be efficiently accelerated during the reconnection, we argue that the process of magnetic reconnection may be much more important for particle acceleration than it is currently accepted. In particular, we discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers as well as the origin cosmic ray excess in the direction of Heliotail.     

Navier–Stokes analysis methods for turbulent jet flows with application to aircraft exhaust nozzles

This article presents the current status of computational fluid dynamics (CFD) methods as applied to the simulation of turbulent jet flowfields issuing from aircraft engine exhaust nozzles. For many years, Reynolds-averaged Navier–Stokes (RANS) methods have been used routinely to calculate such flows, including very complex nozzle configurations. RANS methods replace all turbulent fluid dynamic effects with a turbulence model. Such turbulence models have limitations for jets with significant three-dimensionality, compressibility, and high temperature streams. In contrast to the RANS approach, direct numerical simulation (DNS) methods calculate the entire turbulent energy spectrum by resolving all turbulent motion down to the Kolmogorov scale. Although this avoids the limitations associated with turbulence modeling, DNS methods will remain computationally impractical in the foreseeable future for all but the simplest configurations. Large-Eddy simulation (LES) methods, which directly calculate the large-scale turbulent structures and reserve modeling only for the smallest scales, have been pursued in recent years and may offer the best prospects for improving the fidelity of turbulent jet flow simulations. A related approach is the group of hybrid RANS/LES methods, where RANS is used to model the small-scale turbulence in wall boundary layers and LES is utilized in regions dominated by the large-scale jet mixing. The advantages, limitations, and applicability of each approach are discussed and recommendations for further research are presented.     

Physical processes in the protoplanetary disk

Protoplanetary evolution is discussed in both its global and local aspects. The global turbulent evolution implies large scale average chemical fractionation and chondrule-sized grains as the building blocks of planetary and possibly also cometary material. Local processes such as electric discharges and associated flash heating of grains allow for chemical, mineralogical, and morphological alterations of the disk material. Large scale turbulence keeps the disk well stirred, however, time dependent (or intermittent) turbulence, associated with e.g. optical depth variations, could lead to dust sedimentation within the disk and subsequent planetesimal formation. Recent relevant astronomical observations of young T Tauri stars are briefly reviewed.     

网格湍流CAARC模型风洞实验

对大气湍流边界层的真实模拟是风工程风洞模拟实验所要满足的基本条件之一，平均速度剖面，湍流度剖面，积分尺度和风谱是反映大气湍流边界层流动的四个最基本的因素。本文首先研究了不同孔隙率的均匀网格湍流场的流动特性，得到湍流度，积分尺度以及风谱的变化规律，然后在变化基中某一个因素而保持另外三个因素不变的条件下，研究了处于均匀网格湍流场中的CAARC模型风荷载响应的变化，从而确定每个因素的独立变化对模型所受风荷的影响。实验结果表明湍流度和积分尺度对结构物所受风载都有很重要的影响，在风洞大气湍流边界层模拟中应该予以充分的考虑，否则将会引起风荷载实验结果的偏差。     

Who Needs Turbulence?

The significant influences of turbulence in neutral fluid hydrodynamics are well accepted but the potential for analogous effects in space and astrophysical plasmas is less widely recognized. This situation sometimes gives rise to the question posed in the title; ??Who need turbulence??? After a brief overview of turbulence effects in hydrodynamics, some likely effects of turbulence in solar and heliospheric plasma physics are reviewed here, with the goal of providing at least a partial answer to the posed question.     

Solar Nebula Magnetohydrodynamics

The dynamical state of the solar nebula depends critically upon whether or not the gas is magnetically coupled. The presence of a subthermal field will cause laminar flow to break down into turbulence. Magnetic coupling, in turn, depends upon the ionization fraction of the gas. The inner most region of the nebula (≲0.1 AU) is magnetically well-coupled, as is the outermost region (≳10 AU). The magnetic status of intermediate scales (∼1 AU) is less certain. It is plausible that there is a zone adjacent to the inner disk in which turbulent heating self-consistently maintains the requisite ionization levels. But the region adjacent to the active outer disk is likely to be magnetically ``dead.' Hall currents play a significant role in nebular magnetohydrodynamics. Though still occasionally argued in the literature, there is simply no evidence to support the once standard claim that differential rotation in a Keplerian disk is prone to break down into shear turbulence by nonlinear instabilities. There is abundant evidence—numerical, experimental, and analytic—in support of the stabilizing role of Coriolis forces. Hydrodynamical turbulence is almost certainly not a source of enhanced turbulence in the solar nebula, or in any other astrophysical accretion disk. This revised version was published online in June 2006 with corrections to the Cover Date.     

湍流输运的张量系数模型

实验表明,除均匀各向同性湍流之外,由湍流脉动引起的标量的输运都是各向异性的,且平均量梯度与湍流输运通量之间有一夹角。因此,在用梯度准则模拟湍流输运时,其输运系数应是一个二阶张量。本文推出一个张量形式的输运系数计算公式,并用它分析均匀各向同性湍流、有应变率的均匀剪切流、管内流动和二维平面射流中的热通量问题,均获得了满意的结果。     

气固两相湍流场纳米颗粒演变特性综述

含纳米颗粒的气固两相湍流场在包括航空等众多领域中很常见,以单体、聚集体和团聚体不同形式存在的纳米颗粒在流场中经过生成、对流、扩散、凝并、破碎等过程,其数密度、尺度、尺度分散度等将发生变化。本文就以上相关研究状况进行了回顾,说明颗粒生成是气相化学反应产生的可冷凝蒸汽物质因表面冷却、绝热膨胀或混合、湍流混合或化学过程产生的过饱和所导致;导致颗粒凝并的原因包括布朗运动、湍流剪切、速度梯度、差异沉降;颗粒的凝并取决于颗粒的尺度和流场的特性,并受初始颗粒分布及湍流扩散控制;湍流场对颗粒凝并的影响除了湍流强度的因素外,还体现在由湍流脉动所引发的颗粒数密度的脉动;颗粒凝并后形成尺度较大的团聚体容易在流场剪切和其他因素作用下发生破碎;剪切破碎是导致颗粒破碎的主要因素,有效破碎系数取决于剪切率和颗粒的体积分数;颗粒的沉降取决于颗粒尺度、形状和流体性质等因素;导致颗粒沉降的因素有重力、扩散、惯性撞击、电场和热迁移等;当存在温度梯度时,热泳力对颗粒沉降也起到重要作用。本文最后提出了有待进一步研究的若干问题。     

Reconnection Diffusion in Turbulent Fluids and Its Implications for Star Formation

Astrophysical fluids are turbulent a fact which changes the dynamics of many key processes, including magnetic reconnection. Fast reconnection of magnetic field in turbulent fluids allows the field to change its topology and connections. As a result, the traditional concept of magnetic fields being frozen into the plasma is no longer applicable. Plasma associated with a given magnetic field line at one instant is distributed along a different set of magnetic field lines at the next instant. This diffusion of plasmas and magnetic field is enabled by reconnection and therefore is termed “reconnection diffusion”. The astrophysical implications of this concept include heat transfer in plasmas, advection of heavy elements in interstellar medium, magnetic field generation etc. However, the most dramatic implications of the concept are related to the star formation process. The reason is that magnetic fields are dynamically important for most of the stages of star formation. The existing theory of star formation has been developed ignoring the possibility of reconnection diffusion. Instead, it appeals to the decoupling of mass and magnetic field arising from neutrals drifting in respect to ions entrained on magnetic field lines, i.e. through the process that is termed “ambipolar diffusion”. The predictions of ambipolar diffusion and reconnection diffusion are very different. For instance, if the ionization of media is high, ambipolar diffusion predicts that the coupling of mass and magnetic field is nearly perfect. At the same time, reconnection diffusion is independent of the ionization but depends on the scale of the turbulent eddies and on the turbulent velocities. In the paper we explain the physics of reconnection diffusion both from macroscopic and microscopic points of view, i.e. appealing to the reconnection of flux tubes and to the diffusion of magnetic field lines. We make use of the Lazarian and Vishniac (Astrophys. J. 517:700, 1999) theory of magnetic reconnection and show that this theory is applicable to the partially ionized gas. We quantify the reconnection diffusion rate both for weak and strong MHD turbulence and address the problem of reconnection diffusion acting together with ambipolar diffusion. In addition, we provide a criterion for correctly representing the magnetic diffusivity in simulations of star formation. We discuss the intimate relation between the processes of reconnection diffusion, field wandering and turbulent mixing of a magnetized media and show that the role of the plasma effects is limited to “breaking up lines” on small scales and does not affect the rate of reconnection diffusion. We address the existing observational results and demonstrate how reconnection diffusion can explain the puzzles presented by observations, in particular, the observed higher magnetization of cloud cores in comparison with the magnetization of envelopes. We also outline a possible set of observational tests of the reconnection diffusion concept and discuss how the application of the new concept changes our understanding of star formation and its numerical modeling. Finally, we outline the differences of the process of reconnection diffusion and the process of accumulation of matter along magnetic field lines that is frequently invoked to explain the results of numerical simulations.     

Microphysics in Astrophysical Plasmas

Although macroscale features dominate astrophysical images and energetics, the physics is controlled through microscale transport processes (conduction, diffusion) that mediate the flow of mass, momentum, energy, and charge. These microphysical processes manifest themselves in key (all) boundary layers and also operate within the body of the plasma. Crucially, most plasmas of interest are rarefied to the extent that classical particle collision length- and time-scales are long. Collective plasma kinetic phenomena then serve to scatter or otherwise modify the particle distribution functions and in so-doing govern the transport at the microscale level. Thus collisionless plasmas are capable of supporting thin shocks, current sheets which may be prone to magnetic reconnection, and the dissipation of turbulence cascades at kinetic scales. This paper lays the foundation for the accompanying collection that explores the current state of knowledge in this subject. The richness of plasma kinetic phenomena brings with it a rich diversity of microphysics that does not always, if ever, simply mimic classical collision-dominated transport. This can couple the macro- and microscale physics in profound ways, and in ways which thus depend on the astrophysical context.     

离心叶轮内稀释固液两相流动的数值模拟

 对固液两相流动进行了数值模拟。液相和固相分别采用 k- ε湍流模型和代数颗粒流( AP)湍流模型并考虑了液固两相间的相互作用。用此模型结合 SIMPLE- C算法对离心叶轮内的稀释固液两相流动进行了计算并研究了颗粒对流场的影响。计算结果同试验结果基本一致     

Stochastic Acceleration by Turbulence

The subject of this paper is stochastic acceleration by plasma turbulence, a process akin to the original model proposed by Fermi. We review the relative merits of different acceleration models, in particular the so called first order Fermi acceleration by shocks and second order Fermi by stochastic processes, and point out that plasma waves or turbulence play an important role in all mechanisms of acceleration. Thus, stochastic acceleration by turbulence is active in most situations. We also show that it is the most efficient mechanism of acceleration of relatively cool non relativistic thermal background magnetized plasma particles. In addition, it can preferentially accelerate electrons relative to protons as is needed in many astrophysical radiating sources, where usually there are no indications of presence of shocks. We also point out that a hybrid acceleration mechanism consisting of initial acceleration by turbulence of background particles followed by a second stage acceleration by a shock has many attractive features. It is demonstrated that the above scenarios can account for many signatures of the accelerated electrons, protons and other ions, in particular ³He and ⁴He, seen directly as Solar Energetic Particles and through the radiation they produce in solar flares.     

Statistical Analysis of Velocity Measuring Systems Employing the Photon Correlation Technique

Velocities of fluid flows and solid objects can be measured by performing photon count correlations on laser light scattered from the measuring region, the most common optical configuration being the laser Doppler system. A statistical analysis for the counting process is presented for both the constant velocity case and for turbulent fluid flows with formulations for specific laser Doppler configurations. For turbulent flow, relationships are derived for the shape of the count correlation in terms of the mean velocity and rms turbulent intensity, taking into account the shape of the turbulence correlation curve. Experimental results recorded for both a constant velocity solid object and for an unseeded turbulent air flow in a wind tunnel are presented, and, in the latter case, comparisons are made with hot-wire measurements.     

壁面湍流模型对湍流分离流动数值模拟的影响

本文用三种近壁湍流模型计算了二个二维的湍流分离流动：单包流动和多包流动。结果表明：二层模型和低Reynolds数模型具有类似的特性。它们基本上给出合理的分离流动结构。壁函数的方法由于对数律的假定基本上不适合于计算湍流的分离流动。