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Magnetorotational instability (MRI) is the most likely mechanism for angularmomentum transport in accretion disks. However, despite numerous efforts, thequest for an unambiguous identification of MRI in laboratory is still ongoing.For this purpose, a big Taylor-Couette experiment with liquid sodium iscurrently under construction within DRESDYN project. In preparation for theseexperiments, we have determined optimal parameters for axisymmetric standardMRI (SMRI) with an axial magnetic field and analyzed its nonlinear evolution.In this sequel paper, we investigated the linear and nonlinear dynamics ofnon-axisymmetric SMRI modes in a similar magnetized Taylor-Couette setup atvery small magnetic Prandtl numbers $Pm \sim 10^{-5}$ of liquid sodium. Weshowed that the achievable magnetic Reynolds $Rm\sim 40$ and Lundquist$Lu\sim10$ numbers in this experiment are large enough for the growth ofnon-axisymmetric $|m|=1$ SMRI modes, but the corresponding critical $Rm_c$ isabout 2-3 times higher than that of axisymmetric SMRI. Then we followed thenonlinear evolution of these modes and analyzed the structure of the saturatedstate and its scaling properties with $Re$. For $Re \lesssim 10^4$, thenon-axisymmetric SMRI modes do not saturate and eventually decay due to themodification of the radial profile of the mean azimuthal velocity by thenonlinear saturation of the axisymmetric SMRI. By contrast, for large $Re\gtrsim 10^4$, a rapid growth and saturation of other, nonmagnetic type ofnon-axisymmetric modes occur, which are radially localized in the turbulentboundary layer near the inner cylinder wall. The saturation amplitude of thesenon-axisymmetric modes is always a few orders smaller than that of theaxisymmetric one. We showed that the scaling relations for the magnetic energyand torque derived for axisymmetric SMRI in our previous study well carry overto the present 3D case.

Non-axisymmetric standard magnetorotational instability in the upcoming DRESDYN-MRI experiments -- linear and nonlinear dynamics