On the nonlinear saturation of the magnetorotational instability near threshold in a thin-gap Taylor-Couette setup

Abstract

We study the saturation near threshold of the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible fluid in a thin-gap Taylor-Couette configuration. A vertical magnetic field, Keplerian shear and no-slip, conducting radial boundary conditions are adopted. The weakly non-linear theory leads to a real Ginzburg-Landau equation for the disturbance amplitude, like in our previous idealized analysis. For small magnetic Prandtl number (P \ll 1), the saturation amplitude scales as P^{2/3} while the magnitude of angular momentum transport scales as P^{4/3}. The difference with the previous scalings (~P^{1/2} and P respectively) is attributed to the emergence of radial boundary layers. Away from those, steady-state non-linear saturation is achieved through a modest reduction in the destabilizing shear. These results will be useful to understand MRI laboratory experiments and associated numerical simulations.

Accepted with minor changes to Physical Review E

References in corpus (6)

• Experimental observation and characterization of the magnetorotational instability
• On magnetic field generation in Kolmogorov turbulence
• Experimental evidence for magnetorotational instability in a helical magnetic field
• The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs
• A Local Model for Angular Momentum Transport in Accretion Disks Driven by the Magnetorotational Instability
• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow

Cited by in corpus (7)

• Aspect ratio dependence in magnetorotational instability shearing box simulations
• On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks
• Taylor-Couette flow for astrophysical purposes
• Numerical Study of the Magnetorotational Instability in Princeton MRI Experiment
• Microphysical dissipation, turbulence and magnetic fields in hyper-accreting discs
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Hydrodynamical activity in thin accretion disks