Azimuthal magnetorotational instability at low and high magnetic Prandtl numbers

A. Guseva^{1, 2} - R. Hollerbach³ - A. P. Willis⁴ - M. Avila^{1, 2}

¹ Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Am Fallturm, 28359 Bremen, Germany
² Institute of Fluid Mechanics, Friedrich-Alexander University of Erlangen-Nürnberg, Cauerstraße 4, 91058 Erlangen, Germany
³ School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
⁴ School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK

Abstract
Magnetorotational instability is considered to be one of the most powerful sources of turbulence in hydrodynamically stable quasi-Keplerian flows, such as those governing the accretion disk flows. Although the linear stability of these flows with an applied external magnetic field has been studied for decades, the influence of the instability on the outward angular momentum transport, necessary for the accretion of the disk, is still not well known. In this work, we model a Keplerian rotation with Taylor-Couette flow and imposed azimuthal magnetic field using both linear and nonlinear approaches. We present scalings of instability with Hartmann and Reynolds numbers via linear analysis and direct numerical simulations for two magnetic Prandtl numbers of 1.4 ·10⁻⁶ and 1. Inside the instability domains, modes with different axial wavenumbers dominate, resulting in sub-domains of instabilities which appear different for each Pm. Direct numerical simulations show the emergence of 1- and 2-frequency spatio-temporally oscillating structures for Pm = 1 close the onset of instability, as well as the significant enhancement of the angular momentum transport for Pm = 1, if compared to Pm = 1.4 ·10⁻⁶. Figs 7, Refs 11.