Suppression of the large-scale Lorentz force by turbulence

Abstract

The components of the total stress tensor (Reynolds stress plus Maxwell stress) are computed within the quasilinear approximation for a driven turbulence influenced by a large-scale magnetic background field. The conducting fluid has an arbitrary magnetic Prandtl number and the turbulence without the background field is assumed as homogeneous and isotropic with a free Strouhal number St. The total large-scale magnetic tension is always reduced by the turbulence with the possibility of a `catastrophic quenching' for large magnetic Reynolds number Rm so that even its sign is reversed. The total magnetic pressure is enhanced by turbulence with short correlation time (`white noise') but it is reduced by turbulence with long correlation time. Also in this case the sign of the total pressure may reverse but only for special turbulences with sufficiently large St> 1. The turbulence-induced terms of the stress tensor are suppressed by strong magnetic fields. For the tension term this quenching grows with the square of the Hartmann number of the magnetic field. For microscopic (i.e. small) diffusivity values the magnetic tension term becomes thus highly quenched even for field amplitudes much smaller than their equipartition value. In the opposite case of large-eddy simulations the magnetic quenching is only mild but then also the turbulence-induced Maxwell tensor components for weak fields remain rather small.