2016/10/31 by S. E. Clark, Susan E. Clark, Jeffrey S. Oishi · 18 citations
Engineering · Physics and Astronomy · #Advanced Thermodynamic Systems and Engines #Amplitude #Astrophysics and Star Formation Studies #Atomic and Molecular Physics #Boundary value problem #Classical mechanics #Instability #Magnetic field #Magnetohydrodynamics #Magnetorotational instability #Mechanics #Nonlinear system #Physics #Quantum mechanics #Statistical physics #astro-ph.HE #physics.flu-dyn
paper · pdf · doi:10.3847/1538-4357/aa6ff1
published in The Astrophysical Journal 841(1), 1 (IOP Publishing) · 17 pages, 10 figures, accepted to ApJ
arxiv created 2017/04/28 · openalex publication_date 2017/05/16 · arxiv updated 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.