We studied the anisotropization of homogeneous magnetohydrodynamic turbulence at low magnetic Reynolds numbers. Flows of this type are not only important for different engineering applications, but also provide an appealing framework for studies of quasi–two-dimensional turbulence with strongly modified transport properties. The results of large-scale forced, direct numerical simulations are presented and compared with those obtained with the quasi–normal scale elimination theory. For a weak magnetic field, the simulations validated the theoretical predictions, including the generation of the $k^{-7/3}$ range of the energy spectra and its propagation toward higher wave numbers with increasing magnetic field strength. In a strong magnetic field, the turbulence attains a quasi–two-dimensional state with an enstrophy cascade inertial range of the normal flow components in the normal plane and a passive scalar inertial-convective range of the parallel component. The corresponding energy spectra are in a good agreement with logarithmically corrected $k^{-3}$ and $k^{-1}$ theoretical predictions. With increasing Reynolds number at constant magnetic field the enstrophy cascade becomes unstable and is replaced by helicity cascade with $k^{-7/3}$ energy spectrum. The enstrophy cascade is restored with an increasing magnetic field. An investigation of the mechanism of energy injection into the parallel component in a strong magnetic field revealed that the energy is supplied directly by an external force. The spectrum of the parallel component depends on the isotropy of external forcing and is, thus, not universal.

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• Magnetohydrodynamic turbulence
• Magnetohydrodynamics