The Impact of Stable Modes on Saturation of Magnetorotational Turbulence

The magnetorotational instability (MRI) plays a pivotal role in the dynamics of protoplanetary disks and the accretion processes near black holes in galactic nuclei. MRI drives turbulence that transports density, heat, and angular momentum in the accretion disk. In ideal MRI, each unstable mode has a corresponding conjugate stable mode with the same absolute value of the growth rate. This project investigates the effects of these conjugate stable modes on local magnetorotational turbulence in a rotating plane Couette flow with a uniform magnetic field. Utilizing the Dedalus framework's eigenvalue problem function, we can find the fastest-growing mode and its conjugate stable mode along with their eigenfunction structures. Additionally, using Dedalus's initial value problem function, we simulated the time evolution of the state vectors of weakly nonlinear MRI until the total energy of the MRI was saturated. We studied the eigenmode amplitude of the fastest-growing mode and its conjugate stable mode with eigenmode projection. We will present results that combine numerical eigenvalue solutions with 3D simulations of MRI-driven turbulence to assess the relevance of conjugate stable modes in the saturation process.