Magnetohydrodynamic Turbulence Mediated by Reconnection
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, $${\lambda }_{c}$$, 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 $${\lambda }_{c}$$. As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as $$\theta \sim {(\lambda /{\lambda }_{* })}^{-4/5+\beta }$$, where $${\lambda }_{* }\sim {L}_{0}{S}_{0}^{-3/4}$$ is the resistive dissipation scale. Here L 0 is the outer scale of the turbulence, S 0 is the corresponding Lundquist number, and $$0\leqslant \beta \lt 4/5$$ is a parameter. The resulting Fourier energy spectrum is $$E({k}_{\perp })\propto {k}_{\perp }^{-11/5+2\beta /3}$$, where $${k}_{\perp }$$ is the wavenumber normal to the local mean magnetic field, and the critical scale is $${\lambda }_{c}\sim {S}_{L}^{-(4-5\beta )/(7-20\beta /3)}$$. 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. 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 $$\tilde{\eta }{k}^{2+2s}$$ leads (in the simplest case of β = 0) to the different transition scale $${\lambda }_{c}\sim {L}_{0}{\tilde{S}}_{0}^{-4/(7+9s)}$$ and the energy spectrum $$E({k}_{\perp })\propto {k}_{\perp }^{-(11+9s)/(5+3s)}$$, where $${\tilde{S}}_{0}$$ is the corresponding hyper-resistive Lundquist number.
- Research Organization:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0016215
- OSTI ID:
- 1537190
- Journal Information:
- The Astrophysical Journal (Online), Vol. 844, Issue 2; ISSN 1538-4357
- Publisher:
- Institute of Physics (IOP)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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