Global stability of MHD disk equilibria with sheared flows: a unified perspective

The velocity shear-driven magneto-rotational instability (MRI) is believed to contribute to turbulence and momentum transport in accretion disks. It is one of a broader class of velocity shear-driven instabilities, in which the stable continuum is generically converted into a sequence of overstable discrete modes. Such instabilities were treated mathematically and numerically by Bondeson et al. [PoP 30, 2167 1987], who focused on fusion applications and considered primarily the effect of sheared axial flows. In order to develop a unified perspective, we first extend the plasma column equilibria studied by Bondeson et al. to include a sheared azimuthal flow. In addition to Suydam modes destabilized by the flow in the vicinity of $\mathbf{k}\cdot\mathbf{B}=0$ surfaces, we find an MRI-like instability driven by the azimuthal flow. Second, we consider a Couette flow with a sheared equilibrium magnetic field as well as a small axial velocity added to the azimuthal flow. Such a generic equilibrium can have different stability properties than predicted by standard analyses, with non-axisymmetric modes linearly growing faster than axisymmetric ones. These general classes of instabilities are potentially important for MRI-generated turbulence in accretion disks and laboratory experiments.