Simulations of Magnetohydrodynamic Turbulence in a Strongly Magnetized Medium

By Jungyeon Cho, A. Lazarian, Ethan Vishniac. 2001

364 citations recorded by the source corpus.

We analyze three-dimensional numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic field. We sum over nonlinear interactions within Fourier wave bands and find that the timescale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions, we show that the turbulent motions in the plane perpendicular to the local mean magnetic field are similar to ordinary hydrodynamic turbulence, while motions parallel to the field are consistent with a scaling correction that arises from the eddy anisotropy. We present the structure tensor describing velocity statistics of Alfvénic and pseudo-Alfvénic turbulence. Finally, we confirm that an imbalance of energy moving up and down magnetic field lines leads to a slow decay of turbulent motions, and speculate that this imbalance is common in the interstellar medium, where injection of energy is intermittent both in time and space.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/f632bf2510f9fe2584b15953e6c4ae0fb842c62c

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Citations in the corpus

Cosmic-Ray Propagation: Nonlinear Diffusion Parallel and Perpendicular to Mean Magnetic Field (2007, methodology): “Strong MHD turbulence In strong MHD turbulence, we assume that the Alfvén and the pseudo-Alfvén modes follow the scaling obtained in Cho et al. (2002), which is consistent with the GS95 model: IA(k) = IS(k) = L−1/3M 4/3 A 6π exp ( − L 1/3|k‖| M 4/3 A k 2/3 ⊥ ) , (7) The pitch angle scattering…”
Evaluation of the turbulent energy cascade rates from the upper inertial range in the solar wind at 1 AU (2007, background): “... Analysis and simulations based on MHD equations also show that the turbulent cascades are mostly in the direction perpendicular to the background magnetic field and produce smaller perpendicular scales [e.g., Shebalin et al.,, 1983; Oughton et al., 1994; Matthaeus et al., 1996; Ghosh et al., 199”
Simulations of the Small-Scale Turbulent Dynamo (2003, background): “In fact, this theory only appears to work for anisotropic MHD turbulence with an externally imposed strong mean field (Maron & Goldreich 2001; Cho et al. 2002; Müller et al. 2003).”
HEATING OF THE SOLAR CHROMOSPHERE AND CORONA BY ALFVÉN WAVE TURBULENCE (2011, background): “Such counter- propagating waves with different spatial patterns and multiple modes are subject to strong nonlinear interactions (e.g., Shebalin et al. 1983; Higdon 1984; Oughton & Matthaeus 1995; Goldreich & Sridhar 1995, 1997; Bhattacharjee & Ng 2001; Cho et al. 2002; Oughton et al. 2004).”
Alfvénic Turbulence in the Extended Solar Corona: Kinetic Effects and Proton Heating (2003, background): “This spectral anisotropy is discussed in more detail by, e.g., Goldreich & Sridhar (1995), Maron & Goldreich (2001), and Cho et al. (2002), and possible observational evidence of such elongated inhomogeneities was presented by Grall et al. (1997).”
NUMERICAL TESTS OF FAST RECONNECTION IN WEAKLY STOCHASTIC MAGNETIC FIELDS (2009, background): “…expected to have only marginal impact on the nature of field line stochasticity (see also Cho & Vishniac 2000; Maron & Goldreich 2001; Lithwick & Goldreich 2001; Cho et al. 2002; Cho & Lazarian 2002, 2003), provided that the GS95 scalings are generalized to include the case of weak MHD turbulence.”
Self-consistent Coronal Heating and Solar Wind Acceleration from Anisotropic Magnetohydrodynamic Turbulence (2007, background): “…numberMA = u/VA and the numerical factor of √ 3π comes from the normalization of an assumed shape of the turbulence spectrum (see Appendix C of Cranmer & van Ballegooijen 2005; see also Higdon 1984; Shebalin et al. 1983; Goldreich & Sridhar 1995, 1997; Bhattacharjee & Ng 2001; Cho et al. 2002).”
ASTROPHYSICAL GYROKINETICS: KINETIC AND FLUID TURBULENT CASCADES IN MAGNETIZED WEAKLY COLLISIONAL PLASMAS (2007, background): “Numerical simulations of 3D MHD turbulence do not support the possibility of a parallel Alfvén-wave cascade (Shebalin et al. 1983; Oughton et al. 1994; Cho & Vishniac 2000; Maron & Goldreich 2001; Cho et al. 2002; Müller et al. 2003).”
Density Fluctuations in MHD Turbulence: Spectra, Intermittency, and Topology (2006, methodology): “This is an extension of the procedures employed in Cho & Vishniac (2000) and Cho et al. (2002).”
Turbulent molecular clouds (2012, background): “More recently, this issue has been investigated further in various analytical and numerical studies (e.g. Cho et al. 2002, Boldyrev 2005, Lee et al. 2010, Beresnyak 2011, Mason et al. 2012, Wan et al. 2012) and still appears to be a matter of debate.”
Imbalanced Strong MHD Turbulence (2006, neutral): “…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. 2005; Boldyrev 2005; Müller & Grappin 2005; Beresnyak & Lazarian…”
FAST MAGNETIC RECONNECTION AND SPONTANEOUS STOCHASTICITY (2011, methodology): “The importance of the local system of reference was implicit in Kraichnan (1965) but was first discussed within the GS95 model in subsequent publications (LV99, Cho & Vishniac (2000); Maron & Goldreich (2001); Cho et al. (2002); Cho & Lazarian (2002)). al.”
On the Generation, Propagation, and Reflection of Alfvén Waves from the Solar Photosphere to the Distant Heliosphere (2004, background): “(C7) Cho et al. (2002) analyzed numerical simulations of MHD turbulence and found that g(y) can be fit reasonably well by decaying exponential or Castaing functions.”