3D MHD Turbulence Research Articles

Statistical properties of three-dimensional Hall magnetohydrodynamics turbulence

The three-dimensional (3D) Hall magnetohydrodynamics (HMHD) equations are often used to study turbulence in the solar wind. Some earlier studies have investigated the statistical properties of 3D HMHD turbulence by using simple shell models or pseudospectral direct numerical simulations (DNSs) of the 3D HMHD equations; these DNSs have been restricted to modest spatial resolutions and have covered a limited parameter range. To explore the dependence of 3D HMHD turbulence on the Reynolds number Re and the ion-inertial scale di, we have carried out detailed pseudospectral DNSs of the 3D HMHD equations and their counterparts for 3D MHD (di = 0). We present several statistical properties of 3D HMHD turbulence, which we compare with 3D MHD turbulence by calculating (a) the temporal evolution of the energy-dissipation rates and the energy; (b) the wave-number dependence of fluid and magnetic spectra; (c) the probability distribution functions of the cosines of the angles between various pairs of vectors, such as the velocity and the magnetic field; and (d) various measures of the intermittency in 3D HMHD and 3D MHD turbulence.

The Littlewood-Paley $ pth $-order moments in three-dimensional MHD turbulence

In this paper, we consider the Littlewood-Paley \begin{document}$ p $\end{document} th-order ( \begin{document}$ 1\le p ) moments of the three-dimensional MHD periodic equations, which are defined by the infinite-time and space average of \begin{document}$ L^p $\end{document} -norm of velocity and magnetic fields involved in the spectral cut-off operator \begin{document}$ \dot\Delta_m $\end{document} . Our results imply that in some cases, \begin{document}$ k^{-\frac{1}{3}} $\end{document} is an upper bound at length scale \begin{document}$ 1/k $\end{document} . This coincides with the scaling law of many observations on astrophysical systems and simulations in terms of 3D MHD turbulence.

FARADAY DISPERSION FUNCTIONS OF GALAXIES

The Faraday dispersion function (FDF), which can be derived from an observed polarization spec- trum by Faraday rotation measure synthesis, is a profile of polarized emissions as a function of Faraday depth. We study intrinsic FDFs along sight lines through face-on, Milky-Way-like galaxies by means of a sophisticated galactic model incorporating 3D MHD turbulence, and investigate how much the FDF contains information intrinsically. Since the FDF reflects distributions of thermal and cosmic- ray electrons as well as magnetic fields, it has been expected that the FDF could be a new probe to examine internal structures of galaxies. We, however, find that an intrinsic FDF along a sight line through a galaxy is very complicated, depending significantly on actual configurations of turbulence. We perform 800 realizations of turbulence, and find no universal shape of the FDF even if we fix the global parameters of the model. We calculate the probability distribution functions of the standard deviation, skewness, and kurtosis of FDFs and compare them for models with different global pa- rameters. Our models predict that the presence of vertical magnetic fields and large scale-height of cosmic-ray electrons tend to make the standard deviation relatively large. Contrastingly, differences in skewness and kurtosis are relatively less significant.

LARGE-SCALE MAGNETIC STRUCTURE FORMATION IN THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC TURBULENCE

The inverse cascade of magnetic helicity in 3D-MHD turbulence is believed to be one of the processes responsible for large scale magnetic structure formation in astrophysical systems. In this work we present an exhaustive set of high resolution direct numerical simulations (DNS) of both forced and decaying 3D-MHD turbulence, to understand this structure formation process. It is first shown that an inverse cascade of magnetic helicity in small-scale driven turbulence does not necessarily generate coherent large-scale magnetic structures. The observed large-scale magnetic field, in this case, is severely perturbed by magnetic fluctuations generated by the small-scale forcing. In the decaying case, coherent large-scale structure form similar to those observed astronomically. Based on the numerical results the formation of large-scale magnetic structures in some astrophysical systems, is suggested to be the consequence of an initial forcing which imparts the necessary turbulent energy into the system, which, after the forcing shuts off, decays to form the large-scale structures. This idea is supported by representative examples e.g. cluster of galaxies.

MODELING STATISTICAL PROPERTIES OF SOLAR ACTIVE REGIONS THROUGH DIRECT NUMERICAL SIMULATIONS OF 3D-MHD TURBULENCE

Statistical properties of the Sun's photospheric turbulent magnetic field, especially those of the active regions (ARs), have been studied using the line-of-sight data from magnetograms taken by the Solar and Heliospheric Observatory and several other instruments. This includes structure functions and their exponents, flatness curves, and correlation functions. In these works, the dependence of structure function exponents ({zeta}{sub p}) of the order of the structure functions (p) was modeled using a non-intermittent K41 model. It is now well known that the ARs are highly turbulent and are associated with strong intermittent events. In this paper, we compare some of the observations from Abramenko et al. with the log-Poisson model used for modeling intermittent MHD turbulent flows. Next, we analyze the structure function data obtained from the direct numerical simulations (DNS) of homogeneous, incompressible 3D-MHD turbulence in three cases: sustained by forcing, freely decaying, and a flow initially driven and later allowed to decay (case 3). The respective DNS replicate the properties seen in the plots of {zeta}{sub p} against p of ARs. We also reproduce the trends and changes observed in intermittency in flatness and correlation functions of ARs. It is suggested from this analysis that an AR in themore » onset phase of a flare can be treated as a forced 3D-MHD turbulent system in its simplest form and that the flaring stage is representative of decaying 3D-MHD turbulence. It is also inferred that significant changes in intermittency from the initial onset phase of a flare to its final peak flaring phase are related to the time taken by the system to reach the initial onset phase.« less

Universal properties of three-dimensional magnetohydrodynamic turbulence: do Alfvénwaves matter?

We analyse the effects of the propagating Alfvén waves, arising due to non-zero meanmagnetic fields, on the nonequilibrium steady states of three-dimensional (3D)homogeneous magnetohydrodynamic (MHD) turbulence. In particular, theeffects of Alfvén waves on the universal properties of 3DMHD turbulence arestudied in a one-loop self-consistent mode-coupling approach. We calculate thekinetic- and magnetic-energy spectra. We find that even in the presence of amean magnetic field the energy spectra are Kolmogorov-like, i.e., scale ask−5/3 in the inertialrange where k is a Fourier wavevector belonging to the inertial range. We also elucidate the multiscalingof the structure functions in a log-normal model by evaluating the relevant intermittencyexponents, and our results suggest that the multiscaling deviations from the simpleKolmogorov scaling of the structure functions decrease with increasing strength of themean magnetic field. Our results compare favourably with many existing numerical andobservational results.

Scaling laws in decaying helical hydromagnetic turbulence

AbstractWe study the evolution of growth and decay laws for the magnetic field coherence length ξ, energy EM and magnetic helicity H in freely decaying 3D MHD turbulence. We show that with certain assumptions, self‐similarity of the magnetic power spectrum alone implies that ξ ∼ t1/2. This in turn implies that magnetic helicity decays as H ∼ t–2s, where s = (ξdiff/ξH)2, in terms of ξdiff, the diffusion length scale, and ξH, a length scale defined from the helicity power spectrum. The relative magnetic helicity remains constant, implying that the magnetic energy decays as EM ∼ t–1/2–2s. The parameter s is inversely proportional to the magnetic Reynolds number ReM, which is constant in the self‐similar regime. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Kolmogorov-Style Argument for the Decaying Homogeneous MHD Turbulence

Similarity solutions for 2D MHD and 3D MHD turbulence are obtained assuming the invariance of the mean square magnetic potential and the magnetic helicity respectively in the limit of infinite Reynolds number. The temporal decay laws of the energy, the cross-helicity and the magnetic helicity are derived from these similarity solutions. The present conjecture concerning the decay process is discussed in comparison with the one employed by J. B. Taylor (1974).