Magnetohydrodynamic turbulence mediated by reconnection

Stanislav Boldyrev; Nuno F. Loureiro

doi:10.3847/1538-4357/aa7d02

paper

Magnetohydrodynamic turbulence mediated by reconnection

arXiv:1706.07139 · doi:10.3847/1538-4357/aa7d02

Abstract

Magnetic field fluctuations in MHD turbulence can be viewed as current sheets that are progressively more anisotropic at smaller scales. As suggested by Loureiro & Boldyrev (2017) and Mallet et al (2017), below a certain critical thickness $λ_{c}$ 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 $λ_{c}$ . As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as $θ \sim (λ / λ_{*})^{- 4/5 + β}$ , where $λ_{*} \sim L_{0} S_{0}^{- 3/4}$ is the resistive dissipation scale. Here $L_{0}$ is the outer scale of the turbulence, $S_{0}$ is the corresponding Lundquist number, and { $0 \leq β < 4/5$ } is a parameter. The resulting Fourier energy spectrum is $E (k_{⊥}) \propto k_{⊥}^{- 11/5 + 2 β /3}$ , where $k_{⊥}$ is the wavenumber normal to the local mean magnetic field, and the critical scale is $λ_{c} \sim S_{L}^{- (4 - 5 β) / (7 - 20 β /3)}$ . 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 2017) from a discrete hierarchical model of abruptly collapsing current sheets, an approach different 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 $η ~ k^{2 + 2 s}$ leads (in the simplest case of $β = 0$ ) to the different transition scale $λ_{c} \sim L_{0} S ~_{0}^{- 4/ (7 + 9 s)}$ and the energy spectrum $E (k_{⊥}) \propto k_{⊥}^{- (11 + 9 s) / (5 + 3 s)}$ , where $S ~_{0}$ is the corresponding hyper-resistive Lundquist number.

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Magnetohydrodynamic turbulence mediated by reconnection

Abstract

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