Variance anisotropy in compressible 3‐D MHD

Three-dimensional direct numerical simulations are used to study the energy cascade rate in isothermal compressible magnetohydrodynamic turbulence. Our analysis is guided by a two-point exact law derived recently for this problem in which flux, source, hybrid, and mixed terms are present. The relative importance of each term is studied for different initial subsonic Mach numbers MS and different magnetic guide fields B0. The dominant contribution to the energy cascade rate comes from the compressible flux, which depends weakly on the magnetic guide field B0, unlike the other terms whose modulus increase significantly with MS and B0. In particular, for strong B0 the source and hybrid terms are dominant at small scales with almost the same amplitude but with a different sign. A statistical analysis made with an isotropic decomposition based on the SO (3) rotation group is shown to generate spurious results in presence of B0, when compared with an axisymmetric decomposition better suited to the geometry of the problem. Our numerical results are compared with previous analyses made with in-situ measurements in the solar wind and the terrestrial magnetosheath.

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“…2013; Federrath 2016; Meyrand, Galtier & Kiyani 2016; Oughton et al. 2016; Sujovolsky & Mininni 2016; Andrés et al. 2017).…”

Section: Discussionmentioning

confidence: 99%

Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence

et al. 2018

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“…an asymptotic stated of decaying weakly compressible MHD turbulence (see Matthaeus et al 1996;Oughton et al 2016). The function is periodic with period π and its form (eq.…”

Section: Implication Of the Selection Criterionmentioning

confidence: 99%

Three-dimensional local anisotropy of velocity fluctuations in the solar wind

Verdini

Grappin

Alexandrova

et al. 2019

Monthly Notices of the Royal Astronomical Society

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We analyse velocity fluctuations in the solar wind at magneto-fluid scales in two datasets, extracted from Wind data in the period 2005-2015, that are characterised by strong or weak expansion. Expansion affects measurements of anisotropy because it breaks axisymmetry around the mean magnetic field. Indeed, the small-scale threedimensional local anisotropy of magnetic fluctuations (δB) as measured by structure functions (SF B ) is consistent with tube-like structures for strong expansion. When passing to weak expansion, structures become ribbon-like because of the flattening of SF B along one of the two perpendicular directions. The power-law index that is consistent with a spectral slope −5/3 for strong expansion now becomes closer to −3/2. This index is also characteristic of velocity fluctuations in the solar wind. We study velocity fluctuations (δV) to understand if the anisotropy of their structure functions (SF V ) also changes with the strength of expansion and if the difference with the magnetic spectral index is washed out once anisotropy is accounted for. We find that SF V is generally flatter than SF B . When expansion passes from strong to weak, a further flattening of the perpendicular SF V occurs and the small-scale anisotropy switches from tube-like to ribbon-like structures. These two types of anisotropy, common to SF V and SF B , are associated to distinct large-scale variance anisotropies of δB in the strong-and weak-expansion datasets. We conclude that SF V show anisotropic threedimensional scaling similar to SF B , with however systematic flatter scalings, reflecting the difference between global spectral slopes.

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“…This is justifiable since, at the scales of interest (from a few parsecs to about 100 pc), the expected anisotropy is only moderate (see below). However, the anisotropy of magnetic fields is of high physical significance as it reflects the dynamics of MHD turbulence with and without a global mean magnetic field (Goldreich & Sridhar 1997;Brandenburg & Lazarian 2013 and references therein; see also Cho & Vishniac 2000;Cho & Lazarian 2002a, 2003bMallet et al 2016 andOughton et al 2016). It also reflects the effects of galactic differential rotation and compression of the random magnetic field in shocks.…”

Section: Anisotropy Of the Magnetic Fieldmentioning

confidence: 99%

Supernova-regulated ISM. V. Space and Time Correlations

Hollins

Sarson

Shukurov

et al. 2017

ApJ

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We apply correlation analysis to random fields in numerical simulations of the supernova-driven interstellar medium (ISM) with the magnetic field produced by dynamo action. We solve the magnetohydrodynamic (MHD) equations in a shearing Cartesian box representing a local region of the ISM, subject to thermal and kinetic energy injection by supernova explosions, and parameterized, optically thin radiative cooling. We consider the cold, warm, and hot phases of the ISM separately; the analysis mostly considers the warm gas, which occupies the bulk of the domain. Various physical variables have different correlation lengths in the warm phase: 40, 50, and 60 pc for the random magnetic field, density, and velocity, respectively, in the midplane. The correlation time of the random velocity is comparable to the eddy turnover time, about 10 year 7 , although it may be shorter in regions with a higher star formation rate. The random magnetic field is anisotropic, with the standard deviations of its components b b b x y z having approximate ratios 0.5 0.6 0.6 in the midplane. The anisotropy is attributed to the global velocity shear from galactic differential rotation and locally inhomogeneous outflow to the galactic halo. The correlation length of Faraday depth along the z axis, 120 pc, is greater than for electron density, 60 90 pc -, and the vertical magnetic field, 60 pc. Such comparisons may be sensitive to the orientation of the line of sight. Uncertainties of the structure functions of synchrotron intensity rapidly increase with the scale. This feature is hidden in a power spectrum analysis, which can undermine the usefulness of power spectra for detailed studies of interstellar turbulence.

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Variance anisotropy in compressible 3‐D MHD

Cited by 19 publications

References 81 publications

Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence

Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence

Three-dimensional local anisotropy of velocity fluctuations in the solar wind

Supernova-regulated ISM. V. Space and Time Correlations

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