Layered patterns of active scalar fields in a two-dimensional magnetohydrodynamic system

We observe the formation of staircase patterns in the magnetic potential (A) in a weakly magnetized two-dimensional magnetohydrodynamic system driven by a forced, fluctuating vortex array. Layering occurs due to inhomogeneous mixing of A by vortex cells. Magnetic Reynolds number (R_{m})-dependent quenching of the turbulent diffusion of A by weak magnetic fields increases the disparity between the (short) cell circulation time and the (long) time for intercell transport of magnetic potential. Thus, magnetic fields strengthen transport barriers between cells and reinforce the staircase, relative to its passive scalar counterpart. The analysis reveals a feedback mechanism, which promotes staircase formation. Magnetic staircases persist in both the flux expulsion (R_{m}v_{A}^{2}/U_{0}^{2}<1) and vortex disruption (R_{m}v_{A}^{2}/U_{0}^{2}≥1) limits. In the latter case, residual vortex cells homogenize A. Global layering morphology is shown to be well characterized by staircase curvature. Stochastic forcing of magnetic potential can support magnetic staircases against resistive decay.