Magnetic field amplification and saturation in two-dimensional magnetohydrodynamic turbulence

Abstract

Two-dimensional (2-D) magnetohydrodynamic turbulence is investigated for weak initial magnetic fields using numerical simulation. It is found that the magnetic field is amplified owing to the formation of flux sheets with saturation due either to resistive diffusion (kinematic regime) or to nonlinear effects (dynamic regime). In the kinematic regime, which corresponds to the problem of passive scalar convection by 2-D Navier–Stokes turbulence, the saturation value of the magnetic energy is observed to scale as EMmax∝η−0.8 in approximate agreement with a simple theoretical estimate, EMmax/EM(0)≂Rm, where Rm is the magnetic Reynolds number. Because of the strongly disparate kinetic and magnetic energy spectra in the kinematic regime, roughly EVk∼k−3, EMk∼k, dynamic interaction on small scales already occurs at very small global energy ratios EM/EV, giving rise to strongly enhanced kinetic energy dissipation. In the fully dynamic regime (reached for EM/EV‖t=0>R−1m) global magnetic and kinetic energies become tightly coupled, with EM/EV being approximately constant in time and the energy dissipation rates being independent of the collisional diffusion coefficients. Finally, the effect of the magnetic Prandtl number Pr=μ/η is discussed.