The Anisotropy of MHD Alfv\'{e}nic Turbulence

By Jungyeon Cho, Ethan Vishniac. 2000

276 citations recorded by the source corpus.

We perform direct 3-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size $2\pi$ threaded by strong uniform magnetic fields. We use a pseudo-spectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale-{\it independent}. We discuss why this is {\it not} the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along {\it local} magnetic field lines. The results are consistent with the scaling law $\tilde{k}_{\parallel} \sim \tilde{k}_{\perp}^{2/3}$ proposed by Goldreich and Sridhar (1995, 1997). Here $\tilde{k}_{\|}$ (and $\tilde{k}_{\perp}$) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations which may be a sign of limitations to the model, or our inability to fully resolve the inertial range of turbulence in our simulations.

Subfields: Astronomy and Astrophysics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/9963feb70b1df3e70a032721fe070ce2aec91dae

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Citations in the corpus

Simulations of Magnetohydrodynamic Turbulence in a Strongly Magnetized Medium (2001, methodology): “Diagnostics for our code can be found in Cho and Vishniac (2000b).”
Anisotropy of Alfvénic turbulence in the solar wind and numerical simulations (2010, methodology): “2) and previous simulations (Cho & Vishniac 2000), the contours are elongated in the parallel direction.”
THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS (2012, background): “2 because strongly sub-Alfvénic flows become highly anisotropic (e.g., Mac Low 1999; Cho & Vishniac 2000; Cho & Lazarian 2003; Beresnyak et al. 2005; Brunt et al. 2010; Esquivel & Lazarian 2011).”
PERPENDICULAR ION HEATING BY LOW-FREQUENCY ALFVÉN-WAVE TURBULENCE IN THE SOLAR WIND (2010, background): “The valuec3 = 5/3 is suggested by in situ measurements of magnetic-field fluctuations in the solar wind (Matthaeus and Goldstein 1982; Bruno and Carbone 2005), as well as some theoretical and numerical studies of MHD turbulence (Goldreich and Sridhar 1995; Cho and Vishniac 2000).”
A NEW JEANS RESOLUTION CRITERION FOR (M)HD SIMULATIONS OF SELF-GRAVITATING GAS: APPLICATION TO MAGNETIC FIELD AMPLIFICATION BY GRAVITY-DRIVEN TURBULENCE (2011, background): “For MHD turbulence, a similar scal- ing exponent is found (e.g., Cho & Vishniac 2000; Cho et al. 2009).”
A Model of Turbulence in Magnetized Plasmas: Implications for the Dissipation Range in the Solar Wind (2007, methodology): “…MHD turbulence has been spearheaded by forward modeling through detailed numerical simulations [Shebalin et al., 1983; Matthaeus et al., 1996, 1998; Cho and Vishniac, 2000; Müller and Biskamp, 2000; Biskamp and Müller , 2000; Maron and Goldreich, 2001; Cho et al., 2002; Cho and Lazarian, 2003;…”
A prescription for the turbulent heating of astrophysical plasmas (2010, background): “The resulting state of critical balance is supported by numerical simulations (Cho & Vishniac 2000) and observations in the solar wind (Horbury et al. 2008; Podesta 2009).”
EMPIRICAL CONSTRAINTS ON PROTON AND ELECTRON HEATING IN THE FAST SOLAR WIND (2009, background): “This value is also close to the exponent of−10/3 that has been predicted for a purely perpendicular cascade having a one-dimensional power spectrum of k−5/3⊥ (see Kolmogorov 1941; Fyfe et al. 1977; Higdon 1984; Goldreich & Sridhar 1995; Cho & Vishniac 2000; Boldyrev 2005; Horbury et al. 2008).”
Simulations of Incompressible Magnetohydrodynamic Turbulence (2000, methodology): “Our simulations differ from those of Cho & Vishniac (2000) in that they are excited anisotropically so that we can study the deep inertial range of MHD turbulence.”
Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas (2001, unknown): “Those by Cho & Vishniac (2000b) support both equations (1) and (2), and those by & Biskamp (2000) support equationMu ller (1).”
Cosmic-Ray Scattering and Streaming in Compressible Magnetohydrodynamic Turbulence (2004, methodology): “This m odeland the legitim acy ofthe separation into m odes were tested successfully with incom pressibleM HD num ericalsim ulations(Cho & Vishniac2000;M aron & Goldreich 2001,CLV02).”
The Milky Way’s Kiloparsec-Scale Wind: A Hybrid Cosmic-Ray and Thermally Driven Outflow (2007, background): “…in the turbulent cascade seen in both experiments and theoretical studies of MHD turbulence (see, e.g. Shebalin et al. 1983; Goldreich & Sridhar 1995; Cho & Vishniac 2000; Milano et al. 2001), which has also been invoked in studies of turbulence in supernovae as well (Ptuskin & Zirakashvili 2003).”
Anisotropy in Fast and Slow Solar Wind Fluctuations (2005, background): “Also, note that for the slow wind the anisotropy is more pronounced at smaller scales than at larger scales, something expected from numerical simulation studies and phenomenological arguments (see, e.g., Oughton et al. 1994; Cho & Vishniac 2000; Milano et al. 2001).”
Modeling the Pan-Spectral Energy Distribution of Starburst Galaxies. I. The Role of ISM Pressure and the Molecular Cloud Dissipation Timescale (2004, background): “In a m agnetized and turbulentinterstellarm edium ,num ericalsim ulations(e.g.Cho & Vishniac (2000b))have shown thatthe localm agnetic eld willstay in equipartition with thegasturbulentenergy; V B = p 4 : (25) Thisprovides the coupling between the gasdensity and the m agnetic eld which isa…”
Theory of Star Formation (2007, background): “…in the power spectrum, generally consistent with the scaling prediction of Goldreich & Sridhar (1995), for both incompressible and compressible MHD turbulence (Cho & Vishniac, 2000; Maron & Goldreich, 2001; Cho, Lazarian, & Vishniac, 2002a; Vestuto, Ostriker, & Stone, 2003; Cho & Lazarian, 2003).”
Imbalanced Strong MHD Turbulence (2006, background): “…has attracted a sizable literature (Iroshnikov 1963; Kraichnan 1965; Shebalin et al. 1983; Goldreich & Sridhar 1995, 1997; Ng & Bhattacharjee 1996; Cho & Vishniac 2000; Biskamp & Müller 2000; Maron & Goldreich 2001; Cho et al. 2002; Galtier et al. 2000, 2002; Müller et al. 2003; Galtier et al.…”