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

Abstract

We study the magnetorotational instability (MRI) using nonmodal stability techniques. Despite the spectral instability of many forms of the 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 to 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 time-scales using these methods. The strong growth over a wide range of wave-numbers suggests that nonmodal linear physics could be of fundamental importance in MRI turbulence.

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Cited by in corpus (10)

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• Energy partition between Alfvénic and compressive fluctuations in magnetorotational turbulence with near-azimuthal mean magnetic field
• A nonlinear approach to transition in subcritical plasmas with sheared flow
• MRI turbulence in vertically stratified accretion discs at large magnetic Prandtl numbers
• Transient growth of perturbations on scales beyond the accretion disc thickness
• Revisiting Kinematic Fast Dynamo in 3-dimensional magnetohydrodynamic plasmas: Dynamo transition from non-Helical to Helical flows
• Impact of magnetic field gradients on the development of the MRI: Applications to binary neutron star mergers and proto-planetary disks
• Radial Stresses and Energy Transport in Accretion Disks