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Nonlinear Evolution of Magnetorotational Instability in a Magnetized TaylorCouette Flow: Scaling Properties and Relation to Upcoming DRESDYNMRI Experimen
Mishra, A.; Mamatsashvili, G.; Stefani, F.
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 1D linear analysis
of the standard version of MRI (SMRI) between two rotating coaxial cylinders with an imposed axial
magnetic field, we showed that SMRI can be detected in the upcoming DRESDYNMRI experiment
based on cylindrical magnetized TaylorCouette (TC) flow with liquid sodium. In this followup
study, being also related to the DRESDYNMRI experiments, we focus on the nonlinear evolution
and saturation properties of SMRI and analyze its scaling behavior with respect to various param
eters of the basic TC flow using a pseudospectral code. We conduct a detailed analysis over the
extensive ranges of magnetic Reynolds number Rm ∈ [8.5, 37.1], Lundquist number Lu ∈ [1.5, 15.5]
and Reynolds number, Re ∈ [103, 105]. For fixed Rm, we investigate the nonlinear dynamics of
SMRI for small magnetic Prandtl numbers down to P m ∼ O(10−4), aiming ultimately for those
values typical of liquid sodium used in the experiments. In the saturated state, the magnetic en
ergy of SMRI and associated torque exerted on the cylinders, characterising 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 en
ergy 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. The scaling laws derived here will be instrumental in the subsequent analysis and com
parison of numerical results with those obtained from the DRESDYNMRI experiments in order to
conclusively and unambiguously identify SMRI in laboratory.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 1D linear analysis
of the standard version of MRI (SMRI) between two rotating coaxial cylinders with an imposed axial
magnetic field, we showed that SMRI can be detected in the upcoming DRESDYNMRI experiment
based on cylindrical magnetized TaylorCouette (TC) flow with liquid sodium. In this followup
study, being also related to the DRESDYNMRI experiments, we focus on the nonlinear evolution
and saturation properties of SMRI and analyze its scaling behavior with respect to various param
eters of the basic TC flow using a pseudospectral code. We conduct a detailed analysis over the
extensive ranges of magnetic Reynolds number Rm ∈ [8.5, 37.1], Lundquist number Lu ∈ [1.5, 15.5]
and Reynolds number, Re ∈ [103, 105]. For fixed Rm, we investigate the nonlinear dynamics of
SMRI for small magnetic Prandtl numbers down to P m ∼ O(10−4), aiming ultimately for those
values typical of liquid sodium used in the experiments. In the saturated state, the magnetic en
ergy of SMRI and associated torque exerted on the cylinders, characterising 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 en
ergy 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 Re^(0.4...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. The scaling laws derived here will be instrumental in the subsequent analysis and com
parison of numerical results with those obtained from the DRESDYNMRI experiments in order to
conclusively and unambiguously identify SMRI in laboratory.

Lecture (Conference)
The 12th pamir International Conference on Fundamental and Applied MHD, 04.07.2022, Krakow, Poland 
Lecture (Conference)
9th International Symposium on Bifurcations and Instabilities in Fluid Dynamics, 16.19.08.2022, Groningen, Netherlands 
Contribution to WWW
arXiv:2211.10811 [physics.fludyn]: https://arxiv.org/abs/2211.10811
Permalink: https://www.hzdr.de/publications/Publ35588
Publ.Id: 35588