Nonlinear evolution of magnetorotational instability in a magnetized Taylor-Couette flow: Scaling properties and relation to upcoming DRESDYN-MRI experiment

Magnetorotational instability (MRI) is considered as the most likely mechanism driving angular momentum transport in astrophysical disks. However, despite many efforts, a direct and conclusive experimental evidence of MRI in laboratory is still missing. Recently performing one-dimensional linear analysis of the standard version of MRI (SMRI) in a Taylor-Couette (TC) flow between two rotating coaxial cylinders threaded by an axial magnetic field, we showed that SMRI can be detected in the upcoming DRESDYN-MRI experiment based on a cylindrical magnetized TC flow of liquid sodium. In this followup study, also related to the DRESDYN-MRI experiments, we focus on the nonlinear evolution and saturation properties of SMRI and analyze its scaling behavior with respect to various parameters of the basic TC flow using a pseudospectral code. We conduct a detailed analysis over the extensive ranges of magnetic Reynolds number Rm & ISIN; [8.5, 37.1], Lundquist number Lu & ISIN; [1.5, 15.5], and Reynolds number, Re & ISIN; [103, 105]. We focus on the small magnetic Prandtl number, Pm << 1, regime down to Pm & SIM; 10-4, aiming ultimately for those very small values typical of liquid sodium used in the experiments. In the saturated state, the magnetic energy of SMRI and associated normalized torque due to perturbations exerted on the cylinders, which characterizes angular momentum transport, both increase with Rm for fixed (Lu, Re), while for fixed (Lu, Rm), the magnetic energy decreases and torque increases with increasing Re. We also study the scaling of the magnetic energy and torque in the saturated state as a function of Re and find a power-law dependence of the form Re-0.6...-0.5 for the magnetic energy and Re0.4...0.5 for the torque at all sets of (Lu, Rm) and sufficiently high Re 4000. We also explore the dependence on Lundquist number and angular velocity of the cylinders. The scaling laws derived flows and comparison of numerical results with those obtained from the DRESDYN-MRI experiments in order to conclusively and unambiguously identify SMRI in the laboratory.