Route to turbulence in magnetohydrodynamic square duct flow

The transition route from laminar to turbulent flow in a magnetohydrodynamic 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. Independently of the initial location of a finite perturbation in either Shercliff or Hartmann layers, transition relies 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.