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Nonaxisymmetric modes of magnetorotational and possible hydrodynamical instabilities in the upcoming DRESDYN-MRI experiments: Linear and nonlinear dynamics

Mishra, A.; Mamatsashvili, G.; Stefani, F.


The quest for an unambiguous detection of magnetorotational instability (MRI) in experiments is still ongoing despite recent promising results. To conclusively identify MRI in the laboratory, a large cylindrical Taylor-Couette experiment with liquid sodium is under construction within the DRESDYN project. Recently, we have analyzed the nonlinear dynamics and scaling properties of axisymmetric standard MRI with an axial background magnetic field in the context of the DRESDYN-MRI experiment. In this sequel paper, we investigate the linear and nonlinear dynamics of nonaxisymmetric MRI in the same magnetized Taylor-Couette flow of liquid sodium. We show that the achievable highest Lundquist Lu=10 and magnetic Reynolds Rm=40 numbers in this experiment are large enough for the linear instability of nonaxisymmetric modes with azimuthal wave number |m|=1, although the corresponding critical values of these numbers are usually higher than those for the axisymmetric mode. The structure of the ensuing nonlinear saturated state and its scaling properties with respect to Reynolds number Re are analyzed, which are important for the DRESDYN-MRI experiment having very high Re≳106. It is shown that for Re≲4×104, the nonaxisymmetric MRI modes eventually decay, since the modified shear profile of the mean azimuthal velocity due to the nonlinear axisymmetric MRI appears to be stable against nonaxisymmetric instabilities. By contrast, for larger Re≳4×104, a rapid growth and saturation of the nonaxisymmetric modes of nonmagnetic origin occurs, which are radially localized near the inner cylinder wall, forming a turbulent boundary layer. However, for all the parameters considered, the saturation amplitude of these nonaxisymmetric modes is always a few orders smaller than that of the axisymmetric MRI mode. Therefore, the results of our previous axisymmetric study on the scaling properties of nonlinear MRI states also hold when nonaxisymmetric modes are included.

Keywords: MHD; Taylor-Couette flow; Magnetorotational Instability; Turbulence

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