Simulations of Magnetorotational Instability in a Magnetized Couette Flow

Abstract

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we present non-ideal two-dimensional magnetohydrodynamic simulations of the nonlinear evolution of MRI in the experimental geometry. The simulations adopt initially uniform vertical magnetic fields, conducting radial boundaries, and periodic vertical boundary conditions. No-slip conditions are imposed at the cylinders. Our linear growth rates compare well with existing local and global linear analyses. The MRI saturates nonlinearly with horizontal magnetic fields comparable to the initial axial field. The rate of angular momentum transport increases modestly but significantly over the initial state. For modest fluid and magnetic Reynolds numbers Re, Rm between 100 and 1000, the final state is laminar reduced mean shear except near the radial boundaries, and with poloidal circulation scaling as the square root of resistivity, in partial agreement with the analysis of Knobloch and Julien. A sequence of simulations at Rm=20 and 100 < Re < 25,600 enables extrapolation to the experimental regime (Rm ~ 20, Re ~ 10^7), albeit with unrealistic boundary conditions. MRI should increase the experimentally measured torque substantially over its initial purely hydrodynamic value.

29 pages, 15 figures and 3 tables, accepted by ApJ

References in corpus (5)

• Experimental observation and characterization of the magnetorotational instability
• New type of magneto-rotational instability in cylindrical Taylor-Couette flow
• Local Axisymmetric Diffusive Stability of Weakly-Magnetized, Differentially-Rotating, Stratified Fluids
• Numerical and Experimental Investigation of Circulation in Short Cylinders
• The stability of MHD Taylor-Couette flow with current-free spiral magnetic fields between conducting cylinders

Cited by in corpus (24)

• Helical Magnetorotational Instability in Magnetized Taylor-Couette Flow
• Aspect ratio dependence in magnetorotational instability shearing box simulations
• Angular Momentum Transport in Protoplanetary and Black-Hole Accretion Disks: The Role of Parasitic Modes in the Saturation of MHD Turbulence
• Viscous, Resistive Magnetorotational Modes
• On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks
• Numerical simulations of the Princeton magneto-rotational instability experiment with conducting axial boundaries
• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
• Extending the range of the inductionless magnetorotational instability
• Axisymmetric Magnetorotational Instability in Viscous Accretion Disks
• The role of boundaries in the MagnetoRotational Instability
• Traveling waves in magnetized Taylor-Couette flow
• On the nonlinear saturation of the magnetorotational instability near threshold in a thin-gap Taylor-Couette setup
• Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid
• Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette Flow
• Destabilization of rotating flows with positive shear by azimuthal magnetic fields
• Taylor-Couette flow for astrophysical purposes
• Numerical Study of the Magnetorotational Instability in Princeton MRI Experiment
• Instability in electromagnetically driven flows Part I
• Linking dissipation-induced instabilities with nonmodal growth: the case of helical magnetorotational instability
• Noise-Sustained Convective Instability in a Magnetized Taylor-Couette Flow
• Instability in electromagnetically driven flows Part II
• Onset of Plasmoid Reconnection during Magnetorotational Instability
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Magnetic field dynamos and magnetically triggered flow instabilities