scholarly journals Ideal MHD turbulence: the inertial range spectrum with collisionless dissipation

2015 ◽  
Vol 3 ◽  
Author(s):  
Rudolf A. Treumann ◽  
Wolfgang Baumjohann ◽  
Yasuhito Narita
Keyword(s):  
Inertial Range ◽  
Mhd Turbulence ◽  
Ideal Mhd ◽  
Collisionless Dissipation

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 Dust settling and rings in the outer regions of protoplanetary discs subject to ambipolar diffusion

2018 ◽  
Vol 617 ◽  
pp. A117 ◽  
Author(s):  
A. Riols ◽  
G. Lesur
Keyword(s):  
Large Scale ◽  
Diffusion Theory ◽  
Ambipolar Diffusion ◽  
Mhd Turbulence ◽  
Low Velocity ◽  
Zonal Flows ◽  
T Tauri ◽  
Ideal Mhd ◽  
Weakly Ionized ◽  
Protoplanetary Discs

Context. Magnetohydrodynamic (MHD) turbulence plays a crucial role in the dust dynamics of protoplanetary discs. It affects planet formation, vertical settling, and is one possible origin of the large scale axisymmetric structures, such as rings, recently imaged by ALMA and SPHERE. Among the variety of MHD processes in discs, the magnetorotational instability (MRI) has raised particular interest since it provides a source of turbulence and potentially organizes the flow into large scale structures. However, the weak ionization of discs prevents the MRI from being excited beyond 1 AU. Moreover, the low velocity dispersion observed in CO and strong sedimentation of millimetre dust measured in T-Tauri discs are in contradiction with predictions based on ideal MRI turbulence. Aims. In this paper, we study the effects of non-ideal MHD and magnetized winds on the dynamics and sedimentation of dust grains. We consider a weakly ionized plasma subject to ambipolar diffusion characterizing the disc outer regions (≫1 AU). Methods. To compute the dust and gas motions, we performed numerical MHD simulations in the stratified shearing box, using a modified version of the PLUTO code. We explored different grain sizes from micrometre to few centimetres and different disc vertical magnetizations with plasma beta ranging from 103 to 105. Results. Our simulations show that the mm-cm dust is contained vertically in a very thin layer, with typical heightscale ≲0.4 AU at R = 30 AU, compatible with recent ALMA observations. Horizontally, the grains are trapped within the pressure maxima (or zonal flows) induced by ambipolar diffusion, leading to the formation of dust rings. For micrometre grains and strong magnetization, we find that the dust layer has a size comparable to the disc heightscale H. In this regime, dust settling cannot be explained by a simple 1D diffusion theory but results from a large scale 2D circulation induced by both MHD winds and zonal flows. Conclusions. Our results suggest that non-ideal MHD effects and MHD winds associated with zonal flows play a major role in shaping the radial and vertical distribution of dust in protoplanetary discs. Leading to effective accretion efficiency α ≃ 10−3–10−1, non-ideal MHD models are also a promising avenue to reconcile the low turbulent activity measured in discs with their relatively high accretion rates.

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$t \approx L(|\tilde{\epsilon}^V|l^2_{\rm inj})^{-1/3}.$

scholarly journals Rank-Ordered Multifractal Analysis (ROMA) of probability distributions in fluid turbulence

2011 ◽  
Vol 18 (2) ◽  
pp. 261-268 ◽  
Author(s):  
C. C. Wu ◽  
T. Chang
Keyword(s):  
Multifractal Analysis ◽  
Probability Distributions ◽  
Inertial Range ◽  
Space Plasmas ◽  
Mhd Turbulence ◽  
Turbulent Fluid Flow ◽  
Fluid Turbulence ◽  
Natural Connection ◽  
Johns Hopkins University ◽  
Turbulence Data

Abstract. Rank-Ordered Multifractal Analysis (ROMA) was introduced by Chang and Wu (2008) to describe the multifractal characteristic of intermittent events. The procedure provides a natural connection between the rank-ordered spectrum and the idea of one-parameter scaling for monofractals. This technique has successfully been applied to MHD turbulence simulations and turbulence data observed in various space plasmas. In this paper, the technique is applied to the probability distributions in the inertial range of the turbulent fluid flow, as given in the vast Johns Hopkins University (JHU) turbulence database. In addition, a new way of finding the continuous ROMA spectrum and the scaled probability distribution function (PDF) simultaneously is introduced.

scholarly journals The decay of isotropic magnetohydrodynamics turbulence and the effects of cross-helicity

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Antoine Briard ◽  
Thomas Gomez
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Total Energy ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Mhd Turbulence ◽  
Previous Prediction

Decaying homogeneous and isotropic magnetohydrodynamics (MHD) turbulence is investigated numerically at large Reynolds numbers thanks to the eddy-damped quasi-normal Markovian (EDQNM) approximation. Without any background mean magnetic field, the total energy spectrum $E$ scales as $k^{-3/2}$ in the inertial range as a consequence of the modelling. Moreover, the total energy is shown, both analytically and numerically, to decay at the same rate as kinetic energy in hydrodynamic isotropic turbulence: this differs from a previous prediction, and thus physical arguments are proposed to reconcile both results. Afterwards, the MHD turbulence is made imbalanced by an initial non-zero cross-helicity. A spectral modelling is developed for the velocity–magnetic correlation in a general homogeneous framework, which reveals that cross-helicity can contain subtle anisotropic effects. In the inertial range, as the Reynolds number increases, the slope of the cross-helical spectrum becomes closer to $k^{-5/3}$ than $k^{-2}$. Furthermore, the Elsässer spectra deviate from $k^{-3/2}$ with cross-helicity at large Reynolds numbers. Regarding the pressure spectrum $E_{P}$, its kinetic and magnetic parts are found to scale with $k^{-2}$ in the inertial range, whereas the part due to cross-helicity rather scales in $k^{-7/3}$. Finally, the two $4/3$rd laws for the total energy and cross-helicity are assessed numerically at large Reynolds numbers.

scholarly journals Variable Energy Fluxes and Exact Relations in Magnetohydrodynamics Turbulence

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 225
Author(s):  
Mahendra Verma ◽  
Manohar Sharma ◽  
Soumyadeep Chatterjee ◽  
Shadab Alam
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Numerical Simulations ◽  
Inertial Range ◽  
Energy Fluxes ◽  
Mhd Turbulence ◽  
Conservation Of Energy ◽  
Exact Relations ◽  
The Magnetic Field ◽  
Variable Energy

In magnetohydrodynamics (MHD), there is a transfer of energy from the velocity field to the magnetic field in the inertial range itself. As a result, the inertial-range energy fluxes of velocity and magnetic fields exhibit significant variations. Still, these variable energy fluxes satisfy several exact relations due to conservation of energy. In this paper, using numerical simulations, we quantify the variable energy fluxes of MHD turbulence, as well as verify several exact relations. We also study the energy fluxes of Elsässer variables that are constant in the inertial range.

Temperature and Entropy in Ideal Magnetohydrodynamic Turbulence

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
John V. Shebalin
Keyword(s):  
Dynamical System ◽  
Probability Density Function ◽  
Fourier Analysis ◽  
Numerical Experiments ◽  
Magnetic Energy ◽  
Fourier Mode ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
Ideal Mhd ◽  
Ideal Magnetohydrodynamic

Fourier analysis of incompressible, homogeneous magnetohydrodynamic (MHD) turbulence produces a model dynamical system on which to perform numerical experiments. Statistical methods are used to understand the results of ideal (i.e., nondissipative) MHD turbulence simulations, with the goal of finding those aspects that survive the introduction of dissipation. This statistical mechanics is based on a Boltzmannlike probability density function containing three “inverse temperatures,” one associated with each of the three ideal invariants: energy, cross helicity, and magnetic helicity. However, these inverse temperatures are seen to be functions of a single parameter that may defined as the “temperature” in a statistical and thermodynamic sense: the average magnetic energy per Fourier mode. Here, we discuss temperature and entropy in ideal MHD turbulence and their use in understanding numerical experiments and physical observations.

scholarly journals Scaling laws in Hall-inertial range turbulence

2019 ◽  
Author(s):  
Yasuhito Narita ◽  
Wolfgang Baumjohann ◽  
Rudolf A. Treumann
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Spatial Scales ◽  
Electric Energy ◽  
Power Spectra ◽  
Inertial Range ◽  
Energy Spectra ◽  
Mhd Turbulence

Abstract. There is an increasing amount of observational evidence in space plasma for the breakdown of inertial-range spectra of magnetohydrodynamic (MHD) turbulence on spatial scales smaller than the ion inertial length. Magnetic energy spectra often exhibit a steepening, which is reminiscent of dissipation of turbulence energy, for example in wave-particle interactions. Electric energy spectra, on the other hand, tend to be flatter than those of MHD turbulence, which is indicative of a dispersive process converting magnetic into electric energy in electromagnetic wave excitation. Here we develop a model of the scaling laws and the power spectra for the Hall-inertial range in plasma turbulence. A phenomenological approach is taken. The Hall electric field attains an electrostatic component when the wave vectors are perpendicular to the mean magnetic field. The power spectra of Hall-turbulence are steep for the magnetic field with slope of −7/3 for compressible magnetic turbulence, they are flatter for the Hall electric field with slope −1/3. Our model for the Hall-turbulence serves as a likely candidate to explain the steepening of the magnetic energy spectra in the solar wind neither as indication of the dissipation range nor the dispersive range but as the Hall-inertial range. Our model also reproduces the shape of energy spectra in Kelvin-Helmholtz turbulence observed at the Earth magnetopause.

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