scholarly journals Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence

2019 ◽  
Vol 876 ◽  
pp. 5-18 ◽  
Author(s):  
Riddhi Bandyopadhyay ◽  
William H. Matthaeus ◽  
Sean Oughton ◽  
Minping Wan
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Mhd Turbulence ◽  
Length Scales ◽  
Magnetohydrodynamic Turbulence ◽  
Stringent Constraint ◽  
Transient Period ◽  
Incompressible Mhd

In an earlier paper (Wan et al., J. Fluid Mech., vol. 697, 2012, pp. 296–315), the authors showed that a similarity solution for anisotropic incompressible three-dimensional magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\boldsymbol{B}_{0}$, exists if the ratio of parallel to perpendicular (with respect to $\boldsymbol{B}_{0}$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor–Kármán-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, mean field strength, and cross-helicity, on the nature of similarity decay is discussed.

scholarly journals The influence of a mean magnetic field on three-dimensional magnetohydrodynamic turbulence

1994 ◽  
Vol 280 ◽  
pp. 95-117 ◽  
Author(s):  
Sean Oughton ◽  
Eric R. Priest ◽  
William H. Matthaeus
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
Incompressible Mhd

Building on results from two-dimensional magnetohydrodynamic (MHD) turbulence (Shebalin, Matthaeus & Montgomery 1983), the development of anisotropic states from initially isotropic ones is investigated numerically for fully three-dimensional incompressible MHD turbulence. It is found that when an external d.c. magnetic field (B0) is imposed on viscous and resistive MHD systems, excitations are preferentially transferred to modes with wavevectors perpendicular to B0). The anisotropy increases with increasing mechanical and magnetic Reynolds numbers, and also with increasing wavenumber. The tendency of B0 to inhibit development of turbulence is also examined.

scholarly journals Kinetic helicity and MHD turbulence

2000 ◽  
Vol 64 (2) ◽  
pp. 179-193 ◽  
Author(s):  
SEAN OUGHTON ◽  
ROSSELLA PRANDI
Keyword(s):  
Magnetic Field ◽  
Initial Level ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Turnover Time ◽  
Direct Numerical Simulations ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
Correlation Lengths ◽  
Initial States

The issue of dynamical anisotropy in helical three-dimensional magnetohydrodynamic turbulence with a mean magnetic field B0 is investigated. Using high-resolution direct numerical simulations, we follow the evolution of various isotropic initial states characterized by their different values of the kinetic helicity. The cross helicity and magnetic helicity of the initial conditions are also varied. In agreement with earlier work, we find that such initial states become anisotropic in of order an eddy-turnover time, with correlation lengths parallel to B0 remaining largely unchanged while finer scales are excited in the perpendicular directions. Moreover, it is found that the development of both the anisotropy and the energy are essentially independent of the initial level of kinetic helicity. The physics associated with this latter feature is discussed.

scholarly journals Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

2018 ◽  
Vol 32 (32) ◽  
pp. 1850390
Author(s):  
Minos A. Neto ◽  
J. Roberto Viana ◽  
Octavio D. R. Salmon ◽  
E. Bublitz Filho ◽  
José Ricardo de Sousa
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Three Dimensional ◽  
Effective Field ◽  
The Body ◽  
Bravais Lattice ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic

The critical frontier of the isotropic antiferromagnetic Heisenberg model in a magnetic field along the z-axis has been studied by mean-field and effective-field renormalization group calculations. These methods, abbreviated as MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic a specific Bravais lattice. The frontier line in the plane of temperature versus magnetic field was obtained for the simple cubic and the body-centered cubic lattices. Spin clusters with sizes N = 1, 2, 4 were used so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. For the simple cubic lattice, the MFRG frontier exhibits a notorious re-entrant behavior. This problem is improved by the EFRG technique. However, both methods agree at lower fields. For the body-centered cubic lattice, the MFRG method did not work. As in the cubic lattice, all the EFRG results agree at lower fields. Nevertheless, the EFRG-12 approach gave no solution for very low temperatures. Comparisons with other methods have been discussed.

scholarly journals Oscillatory migratory large-scale fields in mean-field and direct simulations

2009 ◽  
Vol 5 (S264) ◽  
pp. 197-201
Author(s):  
Dhrubaditya Mitra ◽  
Reza Tavakol ◽  
Axel Brandenburg ◽  
Petri J. Käpylä
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Large Scale ◽  
Mean Field ◽  
Direct Numerical Simulations ◽  
Mhd Equations ◽  
Perfect Conductor ◽  
Large Scale Magnetic Field ◽  
Wedge Shape ◽  
Polarity Reversals

AbstractWe summarise recent results form direct numerical simulations of both non-rotating helically forced and rotating convection driven MHD equations in spherical wedge-shape domains. In the former, using perfect-conductor boundary conditions along the latitudinal boundaries we observe oscillations, polarity reversals and equatorward migration of the large-scale magnetic fields. In the latter we obtain angular velocity with cylindrical contours and large-scale magnetic field which shows oscillations, polarity reversals but poleward migration. The occurrence of these behviours in direct numerical simulations is clearly of interest. However the present models as they stand are not directly applicable to the solar dynamo problem. Nevertheless, they provide general insights into the operation of turbulent dynamos.

scholarly journals Properties of Magnetohydrodynamic Turbulence in the Solar Wind

1980 ◽  
Vol 91 ◽  
pp. 143-146
Author(s):  
M. Dobrowolny ◽  
A. Mangeney ◽  
P.L. Veltri
Keyword(s):  
Solar Wind ◽  
General Property ◽  
Magnetized Plasma ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
Non Linear ◽  
Incompressible Mhd ◽  
Linear Interactions

The observations of MHD turbulence in the solar wind indicate that this is in a state characterized, to a good degree by the absence of non linear interactions. It is argued that this is a general property of incompressible MHD turbulence in a magnetized plasma.

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

2008 ◽  
Vol 86 (10) ◽  
pp. 1203-1207
Author(s):  
M Momeni ◽  
M Moslehi-Fard
Keyword(s):  
Three Dimensional ◽  
Qualitative Change ◽  
Mhd Turbulence ◽  
Self Similarity ◽  
Simulation Data ◽  
Magnetohydrodynamic Turbulence ◽  
Exponential Tails ◽  
Turbulent Field ◽  
Field Fluctuations ◽  
52.35 Ra

High-resolution direct numerical simulation data for three-dimensional magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box are used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. The energy PDFs exhibit similarity over all scales of the turbulent system since they show no substantial qualitative change in shape as the scale of the fluctuations varies. This is in sharp and surprising contrast to the well-known behavior of PDFs of turbulent field fluctuations of, for example, velocity, and magnetic and Elsässer fields. The PDFs have exponential tails and satisfy the function P(| δX |) ~ exp(–A | δX | μ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the scale of length varies. The compensated structure functions exhibit self-similarity for the respective fluctuations, and it is a reliable way in turbulence. PACS Nos.: 52.30.–q , 52.30.Cv , 52.35.Ra , 52.65.–y

scholarly journals The Radio–FIR Correlation: Is MHD Turbulence the Cause?

2003 ◽  
Vol 20 (3) ◽  
pp. 252-256 ◽  
Author(s):  
Brent A. Groves ◽  
Jungyeon Cho ◽  
Michael Dopita ◽  
Alex Lazarian
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Magnetic Field Strength ◽  
Far Infrared ◽  
Mhd Turbulence ◽  
Physical Reason ◽  
Magnetohydrodynamic Turbulence ◽  
Gas Density ◽  
Global Magnetic Field

AbstractThe radio–far infrared correlation is one of the tightest correlations found in astronomy. Many of the models explaining this correlation rely on the association of global magnetic field strength with gas density. In this letter we put forward that the physical reason for this association lies within the processes of magnetohydrodynamic turbulence.

scholarly journals Anisotropy in MHD turbulence due to a mean magnetic field

1983 ◽  
Vol 29 (3) ◽  
pp. 525-547 ◽  
Author(s):  
John V. Shebalin ◽  
William H. Matthaeus ◽  
David Montgomery
Keyword(s):  
Magnetic Field ◽  
Reynolds Numbers ◽  
Combined Effects ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
High Wavenumbers

The development of anisotropy in an initially isotropie spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops through the combined effects of an externally imposed d.c. magnetic field and viscous and resistive dissipation at high wavenumbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wavenumbers.

Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number

1998 ◽  
Vol 358 ◽  
pp. 299-333 ◽  
Author(s):  
OLEG ZIKANOV ◽  
ANDRE THESS
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Boundary Conditions ◽  
Interaction Parameter ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetic Interaction Parameter

The transformation of initially isotropic turbulent flow of electrically conducting incompressible viscous fluid under the influence of an imposed homogeneous magnetic field is investigated using direct numerical simulation. Under the assumption of large kinetic and small magnetic Reynolds numbers (magnetic Prandtl number Pm[Lt ]1) the quasi-static approximation is applied for the computation of the magnetic field fluctuations. The flow is assumed to be homogeneous and contained in a three-dimensional cubic box with periodic boundary conditions. Large-scale forcing is applied to maintain a statistically steady level of the flow energy. It is found that the pathway traversed by the flow transformation depends decisively on the magnetic interaction parameter (Stuart number). If the magnetic interaction number is small the flow remains three-dimensional and turbulent and no detectable deviation from isotropy is observed. In the case of a strong magnetic field (large magnetic interaction parameter) a rapid transformation to a purely two-dimensional steady state is obtained in agreement with earlier analytical and numerical results for decaying MHD turbulence. At intermediate values of the magnetic interaction parameter the system exhibits intermittent behaviour, characterized by organized quasi-two-dimensional evolution lasting several eddy-turnover times, which is interrupted by strong three-dimensional turbulent bursts. This result implies that the conventional picture of steady angular energy transfer in MHD turbulence must be refined. The spatial structure of the steady two-dimensional final flow obtained in the case of large magnetic interaction parameter is examined. It is found that due to the type of forcing and boundary conditions applied, this state always occurs in the form of a square periodic lattice of alternating vortices occupying the largest possible scale. The stability of this flow to three-dimensional perturbations is analysed using the energy stability method.

Weak magnetohydrodynamic turbulence and intermittency

2015 ◽  
Vol 770 ◽  
Author(s):  
R. Meyrand ◽  
K. H. Kiyani ◽  
S. Galtier
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Three Dimensional ◽  
Leading Order ◽  
Magnetohydrodynamic Turbulence ◽  
Asymptotic Regime ◽  
Resonant Interactions ◽  
Vector Separation ◽  
Parallel Current

Three-dimensional numerical simulation is used to investigate intermittency in incompressible weak magnetohydrodynamic turbulence with a strong uniform magnetic field $\boldsymbol{b}_{\mathbf{0}}$ and zero cross-helicity. At leading order, this asymptotic regime is achieved via three-wave resonant interactions with the scattering of a wave on a 2D mode for which $k_{\Vert }=0$. When the interactions with the 2D modes are artificially reduced, we show numerically that the system exhibits an energy spectrum with $k_{\bot }^{-3/2}$, whereas the expected exact solution with $k_{\bot }^{-2}$ is recovered with the full nonlinear system. In the latter case, strong intermittency is found when the vector separation of structure functions is taken transverse to $\boldsymbol{b}_{\mathbf{0}}$. This result may be explained by the influence of the 2D modes whose regime belongs to strong turbulence. In addition to shedding light on the origin of this intermittency, we derive a log-Poisson law, ${\it\zeta}_{p}=p/8+1-(1/4)^{p/2}$, which fits the data perfectly and highlights the important role of parallel current sheets.

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