The transition route from laminar to turbulent flow in a magnetohydrodynamic (MHD) duct with a square cross section is investigated in the limit of low magnetic Reynolds number. In the presence of a transverse magnetic field, Hartmann and Shercliff layers are present on the walls orthogonal and parallel to the field direction, respectively. We assume reflection symmetries in both transverse directions, and investigate the competition between transition mechanisms specific to each boundary layer using direct numerical simulations. Independently of the initial location of a finite perturbation, transition relies exclusively on a tripping of the Shercliff layer by perturbations, while the Hartmann layer plays a passive role. This is explained, using a dynamical systems interpretation, by the spatial localization of the edge states in the Shercliff layer at the expense of the Hartmann layer. The link between these nonlinear coherent structures and the linear optimal modes known from nonmodal stability and energy stability theory is pointed out.

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• Intermittency
• Magnetohydrodynamic turbulence
• Nonlinear dynamics in fluids
• Shear flows
• Three-dimensional turbulence
• Transition to turbulence
• Magnetic fluids
• Viscosity
• Direct numerical simulations
• Navier-Stokes equation