Evolution of anisotropy in direct numerical simulations of MHD turbulence in a strong magnetic field on elongated periodic domains

The response of initially isotropic turbulence to a strong magnetic field in the low magnetic Reynolds number regime has been studied using direct numerical simulations on elongated solution domains that are necessary for reliable results at long evolution times. Most results are obtained using a 16 384 x 2048(2) periodic domain of aspect ratio 8, without numerical forcing, after a presimulation that creates the desired initial conditions before the magnetic field is applied. At early times, velocity fluctuations parallel to the magnetic field becomes dominant as a result of Joule dissipation being weaker in this direction. However, this anisotropy is reversed after several large-eddy timescales. Statistics of the velocity gradients indicate a strong trend toward local axisymmetry and quasi-two-dimensionality, with reduced intermittency. Scale-dependent anisotropy is studied in spectral space in terms of a wave number (k(1)) along the magnetic field and a radial wave number (k(r)) in the orthogonal plane. Axisymmetric spectra show that the Joule dissipation plays a dominant role in causing kinetic energy to be concentrated in a narrow spectral region at very low values of k(1), which would not be captured if the domain were cubic. Simulations spanning over two orders of magnitude variation in the magnetic interaction parameter (N) show that Reynolds stress anisotropy scales with the Joule time only for a short initial period. At large N, accelerated development of anisotropy leads to an even greater need for elongated domains which have not been employed frequently in the literature. Overall the results in this work provide both a confirmation of trends seen in simulations on cubic domains at earlier times and new observations at later times where the benefits of an elongated domain are clearly evident. A clear parametnzation of Reynolds number effects still awaits larger simulations at inevitably higher cost.