@ARTICLE{2016arXiv161001616C,
  author = {{Clark}, S.~E. and {Oishi}, J.~S.},
  title = {{The weakly nonlinear magnetorotational instability in a thin-gap Taylor-Couette flow}},
  journal = {ArXiv e-prints},
  archiveprefix = {arXiv},
  eprint = {1610.01616},
  primaryclass = {astro-ph.HE},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena, Physics - Fluid Dynamics},
  year = {2016},
  month = {oct},
  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 thin-gap, Cartesian channel. Our results confirm the finding by Umurhan et al. (2007) that the perturbation amplitude follows a Ginzburg-Landau equation. We extend these results by performing a detailed force balance for the saturated azimuthal velocity and vertical magnetic field, demonstrating 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 length and time scales. }},
  adsurl = {http://adsabs.harvard.edu/abs/2016arXiv161001616C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System},
}


@ARTICLE{2016arXiv161001603C,
  author = {{Clark}, S.~E. and {Oishi}, J.~S.},
  title = {{The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow}},
  journal = {ArXiv e-prints},
  archiveprefix = {arXiv},
  eprint = {1610.01603},
  primaryclass = {astro-ph.HE},
  keywords = {Astrophysics - High Energy Astrophysical Phenomena, Physics - Fluid Dynamics},
  year = {2016},
  month = {oct},
  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), while 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. }},
  adsurl = {http://adsabs.harvard.edu/abs/2016arXiv161001603C},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System},
}


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