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Title: Magnetorotational instability: nonmodal growth and the relationship of global modes to the shearing box

We study magnetorotational instability (MRI) using nonmodal stability techniques. Despite the spectral instability of many forms of MRI, this proves to be a natural method of analysis that is well-suited to deal with the non-self-adjoint nature of the linear MRI equations. We find that the fastest growing linear MRI structures on both local and global domains can look very different from the eigenmodes, invariably resembling waves shearing with the background flow (shear waves). In addition, such structures can grow many times faster than the least stable eigenmode over long time periods, and be localized in a completely different region of space. These ideas lead—for both axisymmetric and non-axisymmetric modes—to a natural connection between the global MRI and the local shearing box approximation. By illustrating that the fastest growing global structure is well described by the ordinary differential equations (ODEs) governing a single shear wave, we find that the shearing box is a very sensible approximation for the linear MRI, contrary to many previous claims. Since the shear wave ODEs are most naturally understood using nonmodal analysis techniques, we conclude by analyzing local MRI growth over finite timescales using these methods. The strong growth over a wide range of wave-numbers suggestsmore » that nonmodal linear physics could be of fundamental importance in MRI turbulence.« less
Authors:
;  [1]
  1. Department of Astrophysical Sciences and Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543 (United States)
Publication Date:
OSTI Identifier:
22370039
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 797; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCRETION DISKS; APPROXIMATIONS; AXIAL SYMMETRY; DIFFERENTIAL EQUATIONS; INSTABILITY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NMR IMAGING; SPACE; STABILITY; TURBULENCE