The aim of the project is to investigate the physical mechanisms and processes governing instabilities in an accretion disc orbiting a massive central object, which may give rise to turbulence. Because pure hydrodynamic models fail to explain astrophysical data, additional phenomena should be considered in order to explain how turbulence drives the transport of angular momentum. A primary candidate is the magnetorotational instability (MRI), which is triggered by the interaction of the accretion disk’s motion with a background magnetic field. The proposed work will combine numerical simulations within an idealized framework known as the ‘Taylor-Couette configuration’ with magnetohydrodynamic theory. The results will enable a comparison with the forthcoming DRESDYN-MRI experiment using liquid sodium, currently under construction at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR, Germany), which aims to detect and study different types of MRI in the laboratory.