The route to turbulence in magnetohydrodynamic square duct flow

TL;DR

This paper investigates how laminar flow transitions to turbulence in a magnetohydrodynamic square duct, highlighting the critical role of Shercliff layers and the passive role of Hartmann layers in the transition process.

Contribution

It reveals that transition to turbulence is driven by Shercliff layer perturbations, with a dynamical systems perspective linking edge states to linear optimal modes.

Findings

Transition relies on Shercliff layer tripling by perturbations.

Hartmann layer remains passive during transition.

Edge states are localized in Shercliff layers.

Abstract

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 which wall turbulence eventually occupies, 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 non-linear coherent structures and the linear optimal modes known from non-modal stability and energy stability theory is pointed out.