http://arxiv.org/abs/2211.10811
Magnetorotational instability (MRI) is the most likely mechanism driving angular momentum transport in astrophysical disks. However, despite many efforts, a direct experimental evidence of MRI in laboratory is still missing. Recently, performing 1D linear analysis of the standard version of MRI (SMRI) between two rotating coaxial cylinders with an axial magnetic field, we showed that SMRI can be detected in the upcoming DRESDYN-MRI experiment with cylindrical magnetized Taylor-Couette (TC) flow with liquid sodium. In this follow-up study related to 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. We do an analysis over the extensive ranges of magnetic Reynolds number $Rm\in [8.5, 37.1]$, Lundquist number $Lu\in[1.5, 15.5]$ and Reynolds number, $Re\in[10^3, 10^5]$. For fixed $Rm$, we investigate the nonlinear dynamics of SMRI for small magnetic Prandtl numbers down to $Pm\sim O(10^{-4})$, aiming for values typical of liquid sodium. In the saturated state, the magnetic energy of SMRI and associated torque on the cylinders, characterizing 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 as a function of $Re$ and find a power law dependence $Re^{-0.6…-0.5}$ for the magnetic energy and $Re^{0.4…0.5}$ for the torque at all sets of $(Lu,Rm)$ and high $Re\geq 4000$. We also explore the dependence on Lundquist number and angular velocity. The scaling laws derived here will be instrumental in the subsequent analysis and comparison of numerical results with those obtained from the DRESDYN-MRI experiments in order to conclusively and unambiguously identify SMRI in laboratory.
A. Mishra, G. Mamatsashvili and F. Stefani
Tue, 22 Nov 22
26/83
Comments: 21 pages, 15 figures, 2 Tables, submitted to Physical Review Fluids