scholarly journals Anisotropic three-dimensional MHD turbulence

1996 ◽  
Vol 101 (A4) ◽  
pp. 7619-7629 ◽  
Author(s):  
William H. Matthaeus ◽  
Sanjoy Ghosh ◽  
Sean Oughton ◽  
D. Aaron Roberts
Keyword(s):  
Three Dimensional ◽  
Mhd Turbulence

scholarly journals Reflection-driven magnetohydrodynamic turbulence in the solar atmosphere and solar wind

2019 ◽  
Vol 85 (4) ◽  
Author(s):  
Benjamin D. G. Chandran ◽  
Jean C. Perez
Keyword(s):  
Solar Wind ◽  
Heating Rate ◽  
Three Dimensional ◽  
Power Spectra ◽  
Inertial Range ◽  
Magnetic Flux Tube ◽  
Analytic Model ◽  
Mhd Turbulence ◽  
Background Magnetic Field ◽  
Turbulent Heating

We present three-dimensional direct numerical simulations and an analytic model of reflection-driven magnetohydrodynamic (MHD) turbulence in the solar wind. Our simulations describe transverse, non-compressive MHD fluctuations within a narrow magnetic flux tube that extends from the photosphere, through the chromosphere and corona and out to a heliocentric distance  $r$ of 21 solar radii  $(R_{\odot })$ . We launch outward-propagating ‘ $\boldsymbol{z}^{+}$ fluctuations’ into the simulation domain by imposing a randomly evolving photospheric velocity field. As these fluctuations propagate away from the Sun, they undergo partial reflection, producing inward-propagating ‘ $\boldsymbol{z}^{-}$ fluctuations’. Counter-propagating fluctuations subsequently interact, causing fluctuation energy to cascade to small scales and dissipate. Our analytic model incorporates dynamic alignment, allows for strongly or weakly turbulent nonlinear interactions and divides the $\boldsymbol{z}^{+}$ fluctuations into two populations with different characteristic radial correlation lengths. The inertial-range power spectra of $\boldsymbol{z}^{+}$ and $\boldsymbol{z}^{-}$ fluctuations in our simulations evolve toward a $k_{\bot }^{-3/2}$ scaling at $r>10R_{\odot }$ , where $k_{\bot }$ is the wave-vector component perpendicular to the background magnetic field. In two of our simulations, the $\boldsymbol{z}^{+}$ power spectra are much flatter between the coronal base and $r\simeq 4R_{\odot }$ . We argue that these spectral scalings are caused by: (i) high-pass filtering in the upper chromosphere; (ii) the anomalous coherence of inertial-range $\boldsymbol{z}^{-}$ fluctuations in a reference frame propagating outwards with the $\boldsymbol{z}^{+}$ fluctuations; and (iii) the change in the sign of the radial derivative of the Alfvén speed at $r=r_{\text{m}}\simeq 1.7R_{\odot }$ , which disrupts this anomalous coherence between $r=r_{\text{m}}$ and $r\simeq 2r_{\text{m}}$ . At $r>1.3R_{\odot }$ , the turbulent heating rate in our simulations is comparable to the turbulent heating rate in a previously developed solar-wind model that agreed with a number of observational constraints, consistent with the hypothesis that MHD turbulence accounts for much of the heating of the fast solar wind.

scholarly journals Spectral properties of magnetohydrodynamic convection with mean horizontal temperature gradient

2006 ◽  
Vol 2 (S239) ◽  
pp. 513-513
Author(s):  
D. Skandera ◽  
W.-Ch. Müller
Keyword(s):  
Temperature Field ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Numerical Simulations ◽  
Spectral Properties ◽  
Three Dimensional ◽  
Numerical Code ◽  
Dimensional System ◽  
Horizontal Temperature Gradient ◽  
Mhd Turbulence

AbstractSpectral properties of convective magnetohydrodynamic (MHD) turbulence in two and three dimensions are studied by means of direct numerical simulations (Skandera D. & Müller W.-C. 2006). The investigated system is set up with a mean horizontal temperature gradient in order to avoid a development of elevator instabilities in a fully periodic box. All simulations are performed without mean magnetic field. The applied resolution is 5123 and 20482. The MHD equation are solved by a numerical code (Müller & Biskamp 2000) that uses a standard pseudospectral scheme. For removing of aliasing errors a spherical truncation method is employed. Obtained results are compared with predictions of various existing phenomenological theories for magnetohydrodynamic and convective turbulence (Müller & Biskamp 2000). While the three-dimensional system is found to operate in a Kolmogorov-like regime where buoyant forces have a negligible impact on the turbulence dynamics (relatively low Rayleigh number achieved in the simulation; Ra ∼106), the two-dimensional system exhibits interesting irregular quasi-oscillations between a buoyancy dominated Bolgiano-Obukhov-like regime of turbulence and a standard Iroshnikov-Kraichnan-like regime of turbulence (Müller & Biskamp 2000). The most important parameter determining the turbulent regime of 2D magnetoconvection, apart from a high Rayleigh number, seems to be the mutual alignment of velocity and magnetic fields. The non-linear dynamics and the interplay between individual fields are examined with different transfer functions that confirm basic assumptions about directions of energy transfer in spectral space. Kinetic, magnetic and temperature energy are transported by a turbulent cascade from large to smaller scales. The local/nonlocal character of the transport is tested for several individual terms in the governing equations. Moreover, other statistical quantities, e.g. probability density functions, are computed as well. A passive character of the temperature field in the investigated three-dimensional magnetoconvection is supported by computations of intermittency using extended self-similarity. The intermittency of the Elsasser field z+ is in agreement with results from numerical simulations of isotropic MHD turbulence (Müller & Biskamp 2000). The intermittency of the temperature field is found to approximately agree with results of passive scalar measurements in hydrodynamic turbulence (Ruiz-Chavarria, Baudet & Ciliberto 1996).

scholarly journals Magnetohydrodynamic simulation code CANS+: Assessments and applications

2019 ◽  
Vol 71 (4) ◽  
Author(s):  
Yosuke Matsumoto ◽  
Yuta Asahina ◽  
Yuki Kudoh ◽  
Tomohisa Kawashima ◽  
Jin Matsumoto ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Rotational Instability ◽  
Mhd Turbulence ◽  
Simulation Code ◽  
Practical Applications ◽  
High Order Scheme ◽  
Nonlinear Growth ◽  
Numerical Tests ◽  
Fifth Order

Abstract We present a new magnetohydrodynamic (MHD) simulation package with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements the Harten–Lax–van Leer–discontinuitues (HLLD) approximate Riemann solver, the fifth-order-monotonicity-preserving interpolation (MP5) scheme, and the hyperbolic divergence cleaning method for a magnetic field. This choice of schemes has significantly improved numerical accuracy and stability, and saved computational costs in multidimensional problems. Numerical tests of one- and two-dimensional problems show the advantages of using the high-order scheme by comparing with results from a standard second-order total variation diminishing monotonic upwind scheme for conservation laws (MUSCL) scheme. The present code enables us to explore the long-term evolution of a three-dimensional accretion disk around a black hole, in which compressible MHD turbulence causes continuous mass accretion via nonlinear growth of the magneto-rotational instability (MRI). Numerical tests with various computational cell sizes exhibits a convergent picture of the early nonlinear growth of the MRI in a global model, and indicates that the MP5 scheme has more than twice the resolution of the MUSCL scheme in practical applications.

Strong MHD helical turbulence and the nonlinear dynamo effect

1976 ◽  
Vol 77 (2) ◽  
pp. 321-354 ◽  
Author(s):  
A. Pouquet ◽  
U. Frisch ◽  
J. Léorat
Keyword(s):  
Large Scale ◽  
Magnetic Energy ◽  
Three Dimensional ◽  
Power Laws ◽  
Inertial Range ◽  
Small Scale ◽  
Mhd Turbulence ◽  
Inverse Cascade ◽  
Small Scales ◽  
Dynamo Effect

To understand the turbulent generation of large-scale magnetic fields and to advance beyond purely kinematic approaches to the dynamo effect like that introduced by Steenbeck, Krause & Radler (1966)’ a new nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions. For this, techniques introduced for ordinary turbulence in recent years by Kraichnan (1971 a)’ Orszag (1970, 1976) and others are generalized to MHD; in particular we make use of the eddy-damped quasi-normal Markovian approximation. The resulting closed equations for the evolution of the kinetic and magnetic energy and helicity spectra are studied both theoretically and numerically in situations with high Reynolds number and unit magnetic Prandtl number.Interactions between widely separated scales are much more important than for non-magnetic turbulence. Large-scale magnetic energy brings to equipartition small-scale kinetic and magnetic excitation (energy or helicity) by the ‘Alfvén effect’; the small-scale ‘residual’ helicity, which is the difference between a purely kinetic and a purely magnetic helical term, induces growth of large-scale magnetic energy and helicity by the ‘helicity effect’. In the absence of helicity an inertial range occurs with a cascade of energy to small scales; to lowest order it is a −3/2 power law with equipartition of kinetic and magnetic energy spectra as in Kraichnan (1965) but there are −2 corrections (and possibly higher ones) leading to a slight excess of magnetic energy. When kinetic energy is continuously injected, an initial seed of magnetic field will grow to approximate equipartition, at least in the small scales. If in addition kinetic helicity is injected, an inverse cascade of magnetic helicity is obtained leading to the appearance of magnetic energy and helicity in ever-increasing scales (in fact, limited by the size of the system). This inverse cascade, predicted by Frischet al.(1975), results from a competition between the helicity and Alféh effects and yields an inertial range with approximately — 1 and — 2 power laws for magnetic energy and helicity. When kinetic helicity is injected at the scale linjand the rate$\tilde{\epsilon}^V$(per unit mass), the time of build-up of magnetic energy with scaleL[Gt ] linjis$t \approx L(|\tilde{\epsilon}^V|l^2_{\rm inj})^{-1/3}.$

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

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.

scholarly journals MHD turbulence-Star Formation Connection: from pc to kpc scales

2010 ◽  
Vol 6 (S274) ◽  
pp. 333-339 ◽  
Author(s):  
E. M. de Gouveia Dal Pino ◽  
R. Santos-Lima ◽  
A. Lazarian ◽  
M. R. M. Leão ◽  
D. Falceta-Gonçalves ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Star Formation ◽  
Magnetic Flux ◽  
Numerical Simulations ◽  
Magnetic Reconnection ◽  
Turbulent Flows ◽  
Molecular Clouds ◽  
Three Dimensional ◽  
Mhd Turbulence ◽  
Star Forming

AbstractThe transport of magnetic flux to outside of collapsing molecular clouds is a required step to allow the formation of stars. Although ambipolar diffusion is often regarded as a key mechanism for that, it has been recently argued that it may not be efficient enough. In this review, we discuss the role that MHD turbulence plays in the transport of magnetic flux in star forming flows. In particular, based on recent advances in the theory of fast magnetic reconnection in turbulent flows, we will show results of three-dimensional numerical simulations that indicate that the diffusion of magnetic field induced by turbulent reconnection can be a very efficient mechanism, especially in the early stages of cloud collapse and star formation. To conclude, we will also briefly discuss the turbulence-star formation connection and feedback in different astrophysical environments: from galactic to cluster of galaxy scales.

scholarly journals Why, how and when MHD turbulence at low becomes three-dimensional

2014 ◽  
Vol 761 ◽  
pp. 168-205 ◽  
Author(s):  
Alban Pothérat ◽  
Rico Klein
Keyword(s):  
Magnetic Field ◽  
Metal Flow ◽  
Three Dimensional ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Opposite Wall ◽  
Liquid Metal Flow ◽  
Dc Current ◽  
The Magnetic Field

AbstractMagnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number is experimentally investigated by studying a liquid metal flow in a cubic domain. We focus on the mechanisms that determine whether the flow is quasi-two-dimensional, three-dimensional or in any intermediate state. To this end, forcing is applied by injecting a DC current $I$ through one wall of the cube only, to drive vortices spinning along the magnetic field. Depending on the intensity of the externally applied magnetic field, these vortices extend part or all of the way through the cube. Driving the flow in this way allows us to precisely control not only the forcing intensity but also its dimensionality. A comparison with the theoretical analysis of this configuration singles out the influences of the walls and of the forcing on the flow dimensionality. Flow dimensionality is characterised in several ways. First, we show that when inertia drives three-dimensionality, the velocity near the wall where current is injected scales as $U_{b}\sim I^{2/3}$. Second, we show that when the distance $l_{z}$ over which momentum diffuses under the action of the Lorentz force (Sommeria & Moreau, J. Fluid Mech., vol. 118, 1982, pp. 507–518) reaches the channel width $h$, the velocity near the opposite wall $U_{t}$ follows a similar law with a correction factor $(1-h/l_{z})$ that measures three-dimensionality. When $l_{z}<h$, by contrast, the opposite wall has less influence on the flow and $U_{t}\sim I^{1/2}$. The central role played by the ratio $l_{z}/h$ is confirmed by experimentally verifying the scaling $l_{z}\sim N^{1/2}$ put forward by Sommeria & Moreau ($N$ is the interaction parameter) and, finally, the nature of the three-dimensionality involved is further clarified by distinguishing weak and strong three-dimensionalities previously introduced by Klein & Pothérat (Phys. Rev. Lett., vol. 104 (3), 2010, 034502). It is found that both types vanish only asymptotically in the limit $N\rightarrow \infty$. This provides evidence that because of the no-slip walls, (i) the transition between quasi-two-dimensional and three-dimensional turbulence does not result from a global instability of the flow, unlike in domains with non-dissipative boundaries (Boeck et al. Phys. Rev. Lett., vol. 101, 2008, 244501), and (ii) it does not occur simultaneously at all scales.

scholarly journals Three-Dimensional Simulations of Accretion Disks

1997 ◽  
Vol 163 ◽  
pp. 179-189 ◽  
Author(s):  
John F. Hawley ◽  
Steven A. Balbus
Keyword(s):  
Angular Momentum ◽  
Accretion Disk ◽  
Accretion Disks ◽  
Three Dimensional ◽  
Spiral Waves ◽  
Central Issue ◽  
Transport Mechanisms ◽  
Mhd Turbulence ◽  
Mhd Instability ◽  
Three Dimensional Simulations

AbstractThe transport of angular momentum is the central issue in accretion disk dynamics. We review recent three-dimensional simulations that investigate possible transport mechanisms. Purely hydrodynamic local instabilities and turbulence are ruled out; global spiral waves remain a possibility. MHD turbulence, arising from a local MHD instability, has been shown effective in transporting angular momentum at dynamically important rates. These results establish the basic picture of accretion disk transport.

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