skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow

Abstract

We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor–Couette flow. This is a multiscale, perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor–Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg–Landau equation (GLE), whereas the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.

Authors:
 [1];  [2]
  1. Department of Astronomy, Columbia University, New York, NY 10027 (United States)
  2. Department of Physics and Astronomy, Bates College, Lewiston, ME 04240 (United States)
Publication Date:
OSTI Identifier:
22663599
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 841; 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; AMPLITUDES; AXIAL SYMMETRY; BOUNDARY CONDITIONS; COUETTE FLOW; CYLINDRICAL CONFIGURATION; EVOLUTION; GINZBURG-LANDAU THEORY; INSTABILITY; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NMR IMAGING; NONLINEAR PROBLEMS; PLASMA; SIMULATION

Citation Formats

Clark, S. E., and Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu. The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow. United States: N. p., 2017. Web. doi:10.3847/1538-4357/AA6FF6.
Clark, S. E., & Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu. The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow. United States. doi:10.3847/1538-4357/AA6FF6.
Clark, S. E., and Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu. Sat . "The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow". United States. doi:10.3847/1538-4357/AA6FF6.
@article{osti_22663599,
title = {The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow},
author = {Clark, S. E. and Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu},
abstractNote = {We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor–Couette flow. This is a multiscale, perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor–Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg–Landau equation (GLE), whereas the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.},
doi = {10.3847/1538-4357/AA6FF6},
journal = {Astrophysical Journal},
number = 1,
volume = 841,
place = {United States},
year = {Sat May 20 00:00:00 EDT 2017},
month = {Sat May 20 00:00:00 EDT 2017}
}