Nonaxisymmetric standard magnetorotational instability induced by a free-shear layer

The standard magnetorotational instability (SMRI) is a unique MHD instability, offering a promising explanation for the turbulence observed in accretion disks across the Universe. The instability requires a fast differentially rotating conductive flow with a moderate magnetic field parallel to the rotation axis. Recently, using magnetic field measurement, we have observed the axisymmetric version of SMRI at magnetic Reynolds number Rm≥3 in a modified Taylor-Couette experiment using liquid metal (Phys. Rev. Lett. 119, 115001 (2022)). Alongside this, we also unearthed a novel non-axisymmetric linear instability with a dominant m = 1 azimuthal structure, occurring in a parameter space akin to the axisymmetric SMRI (Nat. Commun. 13, 4679 (2022)). Here, using global linear analysis, we confirmed that the observed nonaxisymmetric instability is the nonaxisymmetric SMRI caused by a free shear layer at the mid-radius between the two cylinders, formed by the angular speed jump between two electrically conducting rings at each end cap. The nonaxisymmetric SMRI in our system is a combination of two axially traveling waves in opposite directions. It has an induction branch that occurs at Rm>2, a threshold an order of magnitude smaller than the threshold in an ideal Couette profile without free layers in conventional theoretical and numerical studies. The induction branch scales with the Lehnert number and perturbs the magnetic field more as Rm increases, as observed in the experiment. The inductionless branch, on the other hand, scales with the Hartman number and does not perturb the magnetic field. Both branches lead to a vortex in the bulk region, contributing to outward angular momentum transport therein, consistent with the axisymmetric SMRI. The linear analysis results were independently reproduced by nonlinear simulations of the same parameter space.