Magnetohydrodynamic turbulence: Generalized formulation and extension to compressible cases

A general framework that incorporates the Iroshnikov-Kraichnan (IK) and Goldreich-Sridhar (GS) phenomenalogies of magnetohydrodynamic (MHD) turbulence is developed. This affords a clarification of the regimes of validity of the IK and GS models and hence help resolve some controversies on this aspect. This general formulation appears to have a certain robustness as revealed here by its form invariance with respect to inclusion of compressible effects. Generalizations of the IK and GS spectra to compressible MHD turbulence are given. These two branches are shown to merge with the MHD shockwave spectrum, as to be expected, in the infinite compressibility limit.     

Magnetic discontinuities in magnetohydrodynamic turbulence and in the solar wind

Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, Δθ, across fixed spatial increments Δx in direct numerical simulations of MHD turbulence with an imposed uniform guide field B(0). A large region of the probability density function (pdf) for Δθ is found to follow an exponential decay, proportional to exp(-Δθ/θ(*)), with characteristic angle θ(*)≈(14°)(b(rms)/B(0))(0.65) for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of b(rms)/B(0). We also observe an excess of small angular discontinuities when Δx becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.     

Renormalization group theory for fluid and plasma turbulence

For the last several decades, renormalization group (RG, or RNG) methods have been applied to a wide variety of problems of turbulence in hydrodynamics and plasma physics. A comprehensive review of this work will be presented, covering RG methods in hydrodynamic turbulence and in turbulent systems with coupled fluctuating fields like magnetohydrodynamic (MHD) turbulence. This review will attempt to specifically consider several questions about RG: (1) Does RG provide an improvement over previous analytical theories like the direct interaction approximation, or is RG a useful simplification of those theories? (2) How are nonlocal, or ‘sweeping’ effects treated in RG formalisms, or are they ignored entirely? (3) Can RG theories treat both local and nonlocal interactions in turbulence?     

Anisotropy of imbalanced Alfvénic turbulence in fast solar wind

We present the first measurement of the scale-dependent power anisotropy of Elsasser variables in imbalanced fast solar wind turbulence. The dominant Elsasser mode is isotropic at lower spacecraft frequencies but becomes increasingly anisotropic at higher frequencies. The subdominant mode is anisotropic throughout. There are two distinct subranges exhibiting different scalings within what is normally considered the inertial range. The low Alfvén ratio and the different scaling of the Elsasser modes suggests an interpretation of the observed discrepancy between the velocity and magnetic field scalings, the total energy is dominated by the latter. These results do not appear to be fully explained by any of the current theories of incompressible imbalanced MHD turbulence.     

Saturated state of the nonlinear small-scale dynamo

We consider the problem of incompressible, forced, nonhelical, homogeneous, and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra in remarkable agreement with numerical results at least in the case of a one-scale flow. We conjecture that the statistics seen in numerical simulations could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.     

Weak compressible magnetohydrodynamic turbulence in the solar corona

This Letter presents a calculation of the power spectra of weakly turbulent Alfvén waves and fast magnetosonic waves ("fast waves") in low- plasmas. It is shown that three-wave interactions transfer energy to high-frequency fast waves and, to a lesser extent, high-frequency Alfvén waves. High-frequency waves produced by MHD turbulence are a promising explanation for the anisotropic heating of minor ions in the solar corona.     

Mean velocity profile in a sheared and thermally stratified atmospheric boundary layer

A stability correction function φ(m)(ζ) that accounts for distortions to the logarithmic mean velocity profile (MVP) in the lower atmosphere caused by thermal stratification was proposed by Monin and Obukhov in the 1950s using dimensional analysis. Its universal character was established from many field experiments. However, theories that describe the canonical shape of φ(m)(ζ) are still lacking. A previous link between the spectrum of turbulence and the MVP is expanded here to include the effects of thermal stratification on the turbulent kinetic energy dissipation rate and eddy-size anisotropy. The resulting theory provides a novel explanation for the power-law exponents and coefficients already reported for φ(m)(ζ) from numerous field experiments.     

Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers

Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>1 and small magnetic Prandtl number Pm<1. The dependence of the critical Rmc for dynamo on the hydrodynamic Reynolds number Re is obtained for 1 less than or similar Re less than or similar 6700. In the limit Pm<1, Rmc is about 3 times larger than for the previously well-established dynamo at large and moderate Prandtl numbers: Rmc less than or similar 200 for Re greater than or similar 6000 compared to Rmc approximately 60 for Pm>or=1. It is not yet possible to determine numerically whether the growth rate of the magnetic energy is proportional, Rm1/2 in the limit Rm-->infinity, as it should be if the dynamo is driven by the inertial-range motions at the resistive scale.     

Helical Mode Absolute Statistical Equilibrium of Ideal Three-Dimensional Hall Magnetohydrodynamics

Using the Fourier helical decomposition,we obtain the absolute statistical equilibrium spectra of left-and righthanded helical modes in the incompressible ideal Hall magnetohydrodynamics(MHD). It is shown that the left-handed helical modes play a major role on the spectral transfer properties of turbulence when the generalized helicity and magnetic helicity are both positive. In contrast, the right-handed helical modes will play a major role when both are negative. Furthermore, we also find that if the generalized helicity and magnetic helicity have opposite signs, the tendency of equilibrium spectra to condense at the large or small wave numbers will be presented in different helical sectors. This indicates that the generalized helicity dominates the forward cascade and the magnetic helicity dominates the inverse cascade properties of the Hall MHD turbulence.     

A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability,implementation and tests

The ideal MHD equations are a central model in astrophysics, and their solution relies upon stable numerical schemes. We present an implementation of a new method, which possesses excellent stability properties. Numerical tests demonstrate that the theoretical stability properties are valid in practice with negligible compromises to accuracy. The result is a highly robust scheme with state-of-the-art efficiency. The scheme’s robustness is due to entropy stability, positivity and properly discretised Powell terms. The implementation takes the form of a modification of the MHD module in the FLASH code, an adaptive mesh refinement code. We compare the new scheme with the standard FLASH implementation for MHD. Results show comparable accuracy to standard FLASH with the Roe solver, but highly improved efficiency and stability, particularly for high Mach number flows and low plasma β. The tests include 1D shock tubes, 2D instabilities and highly supersonic, 3D turbulence. We consider turbulent flows with RMS sonic Mach numbers up to 10, typical of gas flows in the interstellar medium. We investigate both strong initial magnetic fields and magnetic field amplification by the turbulent dynamo from extremely high plasma β. The energy spectra show a reasonable decrease in dissipation with grid refinement, and at a resolution of 512³ grid cells we identify a narrow inertial range with the expected power law scaling. The turbulent dynamo exhibits exponential growth of magnetic pressure, with the growth rate higher from solenoidal forcing than from compressive forcing. Two versions of the new scheme are presented, using relaxation-based 3-wave and 5-wave approximate Riemann solvers, respectively. The 5-wave solver is more accurate in some cases, and its computational cost is close to the 3-wave solver.     

Study of Surface and Bulk Instabilities in MHD Duct Flow with Imitation of Insulator Coating Imperfections

1 Introduction To understand the inherent relationship between surface and bulk MHD instabilities in liquid metal self-cooled blanket channels and in liquid-metal free surface devices, differently-scaled copper wires were connected to the electrodes to imitate various insulator coating imperfection conditions, and therefore to recreate surface and bulk MHD instabilities related to micro crack MHD effects observed in previous experiments MHD instability is an important problem, as it will affect heat transfer and possibly divertor and limiter performance. Although many researchers have contributed to the understanding of MHD effects via experiments and theory.     

Closure approach to high-order structure functions of turbulence

Let T(p) be the structure function of order p of turbulence. First T2 is determined, then T3 is derived from T2, and finally T(p) (p>3) are derived from T2 and T3. This closure scheme is realized by a non-Gaussian statistical model. We use it to study the scaling law of T(p), and we find that the available data on scaling exponents favor Kolmogorov's 1941 theory rather than his 1962 theory. We also predict the high-order universal constants of inertial-range scaling.     

Supersonic turbulence and structure of interstellar molecular clouds

The interstellar medium provides a unique laboratory for highly supersonic, driven hydrodynamic turbulence. We propose a theory of such turbulence, test it by numerical simulations, and use the results to explain observational scaling properties of interstellar molecular clouds, the regions where stars are born.     

Decay and growth laws in homogeneous shear turbulence

Homogeneous anisotropic turbulence has been widely studied in the past decades, both numerically and experimentally. Shear flows have received a particular attention because of the numerous physical phenomena they exhibit. In the present paper, both the decay and growth of anisotropy in homogeneous shear flows at high Reynolds numbers are revisited thanks to a recent eddy-damped quasi-normal Markovian closure adapted to homogeneous anisotropic turbulence. The emphasis is put on several aspects: an asymptotic model for the slow part of the pressure–strain tensor is derived for the return to isotropy process when mean velocity gradients are released. Then, a general decay law for purely anisotropic quantities in Batchelor turbulence is proposed. At last, a discussion is proposed to explain the scattering of global quantities obtained in DNS and experiments in sustained shear flows: the emphasis is put on the exponential growth rate of the kinetic energy and on the shear parameter.     

Turbulent cascades

Turbulent cascades at high Reynolds numbers are explained briefly in terms of multipliers and multiplier distributions. Two properties of the multipliers ensure the existence of power laws for locally averaged energy dissipation rate: (a) the existence of a multiplier probability density function that is independent of the level of the cascade, and (b) the statistical independence of multipliers at one level on those at previous levels. Under certain conditions described in the paper, the same two properties of multipliers guarantee that velocity increments over inertial-range separation distances also possess power laws. This work is specifically motivated by the need to understand the influence on scaling of the experimental observations that property (a) is true for turbulence, but property (b) is not; and additional motivation is the need to relate cascade models to intermittent vortex stretching (and folding). This effect has been modeled by allowing the multiplier distribution to depend on the magnitude of the local strain rate, and it is demonstrated that this rate-dependent model accounts for the statistical dependence observed in experiments. It is also shown that this model is consistent with the uncorrelated cascade models except for very weak singularity strengths (or for negative moments below a certain order), leading to the conclusion that, for all practical purposes, the uncorrelated level-independent multipliers abstract the essence of the breakdown process in turbulence.     

基于距离度量的LAMOST光谱中连续谱异常的自动检测

连续谱异常是指恒星光谱在获得和处理过程中由于星际消光和流量定标等原因造成连续谱严重偏离甚至中断的现象,这对光谱的谱线提取以及其他一些后续处理工作带来负面影响。提出了一种基于距离度量的连续谱异常光谱的自动检测方法,相比传统人眼检查在保证正确率的情况下大大地提高了工作效率。该方法首先通过光谱的lick线指数来确定待测光谱的恒星类型,同时对待测光谱进行归一化处理;然后分别提取待测光谱和对应类型模板光谱的连续谱;最后进行连续谱模板匹配,在每个波长点计算待测光谱和其模板光谱的流量差值,分析流量差值的分布,检验有多少差值点分布在在均值(β)附近的±α个标准差(δ)的范围内,进而可确定是否有连续谱异常。实验表明提出方法的可以快速有效的识别出连续谱异常的恒星光谱。     

Irradiance scintillation index for Gaussian beam based on the generalized anisotropic von Karman spectrum

Experiments and theoretical investigations have shown that the atmosphere turbulence exhibits both anisotropic and non-Kolmogorov properties. In this paper, based on the anisotropic generalized von Karman spectrum and the Rytov approximation theory, new expression for the irradiance scintillation index of optical waves is derived for Gaussian beam propagating through weak anisotropic non-Kolmogorov turbulence. Compared with previously published results, it considers simultaneously the asymmetry property of turbulence cells or eddies in the orthogonal xy-plane, the general spectral power law in the range 3–4 instead of constant value of 11/3 for the Kolmogorov turbulence, and the finite turbulence inner and outer scales. Two anisotropic factors are introduced to parameterize the anisotropy of turbulence cells or eddies in horizontal and vertical directions. In the special cases of these two anisotropic factors equaling one and the finite turbulence inner and outer scales equaling separately zero and infinite, the derived expression can reduce correctly to the previously published results. Calculations are performed to analyze the derived results.     

磁流体力学湍流的一些规律

本文从处理湍流场的普遍方法──“任一物理量都可分解成平均值与涨落值之和”出发，利用量纲估计和磁流体力学湍流近似对磁流体力学基本方程进行讨论，得出有关磁流体力学湍流场的一些结论．这些结论对研究目前阶段的磁流体力学湍流理论是很有用的。