Magnetohydrodynamic Turbulence Mediated by Reconnection

• Published in: The Astrophysical journal Vol. 844; no. 2; pp. 125 - 130
• Main Authors: Boldyrev, Stanislav, Loureiro, Nuno F.
• Format: Journal Article
• Language: English
• Published: Philadelphia The American Astronomical Society 01-08-2017; IOP Publishing; Institute of Physics (IOP)
• Subjects: Alignment; Astronomy & Astrophysics; ASTRONOMY AND ASTROPHYSICS; Astrophysics; Computational fluid dynamics; Current sheets; Energy dissipation; Energy spectra; Fluctuations; Fluid flow; Magnetic fields; magnetic reconnection; Magnetism; Magnetohydrodynamic turbulence; Magnetohydrodynamics; magnetohydrodynamics (MHD); Tearing; Turbulence; Turbulent fluctuations; Turnover rate; Wavelengths
• ISSN: 0004-637X; 1538-4357; 1538-4357
• DOI: 10.3847/1538-4357/aa7d02

Magnetic field fluctuations in magnetohydrodynamic turbulence can be viewed as current sheets that are progressively more anisotropic at smaller scales. As suggested by Loureiro & Boldyrev and Mallet et al., below a certain critical thickness, , such current sheets become tearing-unstable. We propose that the tearing instability changes the effective alignment of the magnetic field lines in such a way as to balance the eddy turnover rate at all scales smaller than . As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as , where is the resistive dissipation scale. Here L0 is the outer scale of the turbulence, S0 is the corresponding Lundquist number, and is a parameter. The resulting Fourier energy spectrum is , where is the wavenumber normal to the local mean magnetic field, and the critical scale is . The simplest model corresponds to β = 0, in which case the predicted scaling formally agrees with one of the solutions obtained in Mallet et al. from a discrete hierarchical model of abruptly collapsing current sheets, an approach different from and complementary to ours. We also show that the reconnection-mediated interval is non-universal with respect to the dissipation mechanism. Hyper-resistivity of the form leads (in the simplest case of β = 0) to the different transition scale and the energy spectrum , where is the corresponding hyper-resistive Lundquist number.