Magnetic instabilities in accretion discs

Magnetic fields can drive turbulence and accretion discs due to are ubiquitous in the Universe; their interaction with shear flows in a star or accretion disc can considerably change its momentum transport and mixing. Such flows can become turbulent due to magnetorotational instability (MRI), arising through the coupling of rotating fluid elements by magnetic tension. An important question is how efficiently this turbulence transports the angular momentum outwards, allowing the disc to accrete at the observed rates. To assess the viability of MRI in different regions of the disc, we need to know how this transport scales with varying flow properties. MRI was extensively studied through numerical modelling in a local model of accretion discs, periodic shearing box; however, the results strongly depend on the box size and aspect ratio. On the other hand, global numerical models of the disc are unable to resolve all the flow scales involved in momentum transfer in the limit of fast rotation. Therefore, I adopted another global model of accretion disc flow, Taylor-Couette flow between two co-rotating cylinders, that allows to observe experimentally the onset of MRI in the form of rotating waves. At the time, little was known about the transition from these waves to MRI turbulence, and whether momentum transport scalings obtained with shearing box model hold in global geometry. Finally, \textbf{MRI turbulence was not studied systematically for highly resistive fluids expected in cold regions of accretion discs}, due to computational difficulties in this regime.

In this work, I addressed these questions using fully resolved direct numerical simulations of quasi-Keplerian flows subject to a magnetic field, supported by numerical linear analysis and comparison to MRI experiments. I improved the initial formulation of Taylor-Couette flow code (Guseva et al., 2015) by implementing numerical derivation routines and a general configuration of magnetic field. The code showed excellent scalability in high performance computing centers, and allowed to model unachievable before low-resistivity fluids. My simulations showed that MRI arises in a supercritical Hopf bifurcation as a non-axisymmetric wave; the route to turbulence depends on the ratio of viscosity to magnetic diffusivity of the fluid. For highly resistive fluids, the MRI wave undergoes a catastrophic transition to chaos through a subcritical Hopf bifurcation (Guseva et al., 2015). When conductivity increases, this transition is gradual and involves a succession of oscillatory states (missing reference). Subsequently, I proposed a predictive model for momentum transport by magnetically triggered inertial waves and by magnetocoriolis waves in fully developed MRI turbulence, based on the conservation of angular momentum current (Guseva et al., 2017). Finally, I demonstrated that a fully nonlinear self-sustained dynamo can develop in this flow, so the momentum transport does not have to rely entirely on the presence of external magnetic fields (Guseva et al., 2017). These results allow to predict MRI-induced transport of momentum in accretion discs and other MRI-unstable shear flows.

This work was supported by the German Research Foundation (DFG) grant AV 120/1-1.