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 similar to (lambda/lambda(*))(-4 5+beta), where lambda(*) similar to L0S0-3/4 is the resistive dissipation scale. Here L-0 is the outer scale of the turbulence, S-0 is the corresponding Lundquist number, and 0 <= beta < 4/5 is a parameter. The resulting Fourier energy spectrum is E(k(perpendicular to)) alpha k(perpendicular to)(-11/5+2 beta/3), where k(perpendicular to) is the wavenumber normal to the local mean magnetic field, and the critical scale is lambda(c) similar to S-L(-(4-5 beta)(7-20 beta/3)). The simplest model corresponds to beta = 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 (eta) over bark(2 vertical bar 2s) leads (in the simplest case of beta = 0) to the different transition scale lambda(c) similar to L-0(S) over tilde (-4/(7+9s))(0) and the energy spectrum E(k(perpendicular to)) alpha k(perpendicular to)(-(11+9s)/(5+3s)), where (S) over tilde (0) is the corresponding hyper-resistive Lundquist number.