Decay of magnetohydrodynamic turbulence at low magnetic Reynolds number

Abstract

We report a detailed numerical investigation of homogeneous decaying turbulence in an electrically conducting fluid in the presence of a uniform constant magnetic field. The asymptotic limit of low magnetic Reynolds number is assumed. Large-eddy simulations with the dynamic Smagorinsky model are performed in a computational box sufficiently large to minimize the effect of periodic boundary conditions. The initial microscale Reynolds number is about 170 and the magnetic interaction parameter N varies between 0 and 50. We find that except for a short period of time when N = 50, the flow evolution is strongly influenced by nonlinearity and cannot be adequately described by any of the existing theoretical models. One particularly noteworthy result is the near equipartition between the rates of Joule and viscous dissipations of the kinetic energy observed at all values of N during the late stages of the decay. Further, the velocity components parallel and perpendicular to the magnetic field decay at different rates, whose value depends on the strength of the magnetic field and the stage of the decay. This leads to a complex evolution of the Reynolds stress anisotropy ellipsoid, which goes from being rod-shaped, through spherical to disc-shaped. We also discuss the possibility of the power-law decay, the comparison between computed, experimental and theoretical decay exponents, the anisotropy of small-scale fluctuations, and the evolution of the spectral energy distributions.