Turbulent magnetohydrodynamic flow in a square duct: Comparison of zero and finite magnetic Reynolds number cases

Three-dimensional turbulent magnetohydrodynamic flow in a duct with a square cross section and insulating walls is investigated by direct numerical simulations. The flow evolves in the presence of a uniform vertical magnetic field and is driven by an applied mean pressure gradient. A boundary element technique is applied to treat the magnetic field boundary conditions at the walls consistently. Our primary focus is on the large-and small-scale characteristics of turbulence in the regime of moderate magnetic Reynolds numbers up to Rm similar to 10(2) and a comparison of the simulations with the quasistatic limit at Rm = 0. The present simulations demonstrate that differences to the quasistatic case arise for the accessible magnetic Prandtl number Pm similar to 10(-2) and different Hartmann numbers up to Ha = 43.5. Hartmann and Shercliff layers at the duct walls are affected differently when a dynamical coupling to secondary magnetic fields is present. This becomes manifest by the comparison of the mean streamwise velocity profiles as well as the skin friction coefficients. While large-scale properties change only moderately, the impact on small-scale statistics is much stronger as quantified by an analysis of local anisotropy based on velocity derivatives. The small-scale anisotropy is found to increase at moderate Rm. These differences can be attributed to the additional physical phenomena which are present when secondary magnetic fields evolve, such as the expulsion of magnetic flux in the bulk of the duct or the presence of turbulent electromotive forces.