Marginal turbulent magnetohydrodynamic flow in a square duct

Direct numerical simulations using a high-order finite-difference method were performed of the turbulent flow in a straight square duct in a transverse magnetic field. Without magnetic field the turbulence can be maintained for values of the bulk Reynolds number above approximately Re = 1077 [M. Uhlmann et al., Marginally turbulent flow in a square duct, J. Fluid Mech. 588, 153 (2007)]. In the magnetohydrodynamic case this minimal value of the bulk Reynolds number increases with the Hartmann number. The flow is laminar at Re = 3000 when the Hartmann number is larger than Ha = 12.5 and the flow is turbulent for Ha <= 12.0. The secondary mean flow structure at Re = 3000 consists of eight vortices located mainly at the Hartmann walls. (c) 2010 American Institute of Physics. [doi:10.1063/1.3478877]