Direct numerical simulation of quasi-two-dimensional MHD turbulent shear flows

Direct numerical simulations (DNS) are performed to study the turbulent shear flow of an electrically conducting fluid in a cylindrical container. The flow is driven by the interaction between the radial electric currents ($I$) injected through a large number of small electrodes at the bottom wall and an axial magnetic field. All the numerical parameters, including the geometry of the container, the total injcected currents and the magnetic field, are in line with the experiment performed in J. Fluid Mech. 456, 137-159. First, witth laminar Hartmann layers, three dimensional simulations recover experimentally measured quantities (global angular momentum, velocity profiles). The variation laws for the wall shear stresses, the energy spectra and visualizations of flow structures near the side wall highlight separation and turbulence within the side wall layers. Furthermore, a parametric analysis of the flow reveals that Ekman recirculations have significant influence on the vortex size, the free shear layer, and the global dissipation. Second, we recover the scaling laws of the cutoff scale that separate the large quasi-two-dimensional scales from the small three-dimensional ones (J. Fluid Mech. 118, 507-518), and thus establish their validity in sheared MHD turbulence. Furthermore, we find that three-componentality are and the three-dimensionality appear concurrently and that both the two-dimensional cutoff frequency and the mean energy associated to the axial component of velocity scale with $N_t$, respectively as $0.063N_t^{0.37}$ and $0.126 N_t^{-0.92}$.