Numerical study of magnetohydrodynamic duct flow at high Reynolds and Hartmann numbers

High-resolution direct numerical simulations are conducted to analyse turbulent states of the flow of an electrically conducting fluid in a duct of square cross-section with electrically insulating walls and imposed transverse magnetic field. The Reynolds number of the flow is 10(5) and the Hartmann number varies from 0 to 400. It is found that there is a broad range of Hartmann numbers in which the flow is neither laminar nor fully turbulent, but has laminar core, Hartmann boundary layers and turbulent zones near the walls parallel to the magnetic field. Analysis of turbulent fluctuations shows that each zone consists of two layers: the boundary layer near the wall characterized by small-scale turbulence and the outer layer dominated by large-scale vortical structures strongly elongated in the direction of the magnetic field. We also find a peculiar scaling of the mean velocity, according to which the reciprocal von Karman coefficient grows nearly linearly with the distance to the wall.