Publikationsrepositorium - Helmholtz-Zentrum Dresden-Rossendorf

Magnetorotational instability (MRI) is the most likely mechanism for efficient transport of angular momentum in accretion disks. However, despite numerous efforts, the quest for an unambiguous realization of MRI in experiments is still ongoing. To conclusively identify MRI in the laboratory, a large Taylor-Couette experiment with liquid sodium is under construction at the Helmholtz-Zentrum Dresden-Rossendorf within the DRESDYN project. Recently, we have determined the optimal range of parameters for the onset of an axisymmetric mode of the standard MRI (SMRI) with a purely axial background magnetic field and analyzed its nonlinear evolution, saturation and scaling properties in the context of the DRESDYN-MRI experiment. In this sequel paper, we continue SMRI studies and investigate the linear and nonlinear dynamics of non-axisymmetric modes of the instability in a similar magnetized Taylor-Couette setup. For the linear stability analysis, we use $Pm=\nu/\eta \sim 10^{-5}$ typical of liquid sodium used in the experiment. We show that the achievable magnetic Reynolds $Rm\sim 40$ and Lundquist $Lu\sim10$ numbers in this experiment are large enough for the growth of non-axisymmetric $|m|=1$ SMRI modes. For fixed $\mu$, the critical $Rm_c$ for the onset of non-axisymmetric SMRI is about 2-3 time higher than that of axisymmetric SMRI. We follow the evolution of these modes from their exponential growth in the linear regime all over to nonlinear saturation. The structure of the saturated state and its scaling properties with respect to Reynolds number $Re$ are analyzed, which is relevant and important for the DRESDYN-MRI experiment having very high Reynolds numbers ($\sim 10^6$). We show that for $Re \lesssim 10^4$, the magnetic energy of non-axisymmetric SMRI modes does not saturate and eventually decays due to the modification of the radial shear profile of the mean azimuthal velocity by the nonlinear axisymmetric SMRI, that is, the modified shear profile appears to be stable against non-axisymmetric modes. By contrast, for large $Re \gtrsim 10^4$, a sudden rapid growth and saturation of the magnetic energy of non-axisymmetric modes occur, which are radially localized in the turbulent boundary layer near the inner cylinder wall. The saturation amplitude of the non-axisymmetric modes is always a few orders smaller than that of the axisymmetric SMRI mode. We further show that the scaling relations for magnetic energy and torque in the saturated state of SMRI derived for axisymmetric modes in our previous study well carry over to $|m|\geq 1$ non-axisymmetric ones.