Two types of axisymmetric helical magnetorotational instability in rotating flows with positive shear

TLDR: In this paper, a double-diffusive helical magnetorotational instability with positive shear was revealed and investigated for a wide range of axial and azimuthal magnetic fields and the magnetic Prandtl number was not too close to unity.

Abstract: We reveal and investigate a type of linear axisymmetric helical magnetorotational instability which is capable of destabilizing viscous and resistive rotational flows with radially increasing angular velocity, or positive shear. This instability is double-diffusive by nature and is different from the more familiar helical magnetorotational instability, operating at positive shear above the Liu limit, in that it works instead for a wide range of the positive shear when (i) a combination of axial and azimuthal magnetic fields is applied and (ii) the magnetic Prandtl number is not too close to unity. We study this instability first with radially local Wentzel-Kramers-Brillouin (WKB) analysis, deriving the scaling properties of its growth rate with respect to Hartmann, Reynolds, and magnetic Prandtl numbers. Then we confirm its existence using a global stability analysis of the magnetized flow confined between two rotating coaxial cylinders with purely conducting or insulating boundaries and compare the results with those of the local analysis. From an experimental point of view, we also demonstrate the presence of this instability in a magnetized viscous and resistive Taylor-Couette flow with positive shear for such values of the flow parameters, which can be realized in upcoming experiments at the DRESDYN facility. Finally, this instability might have implications for the dynamics of the equatorial parts of the solar tachocline and dynamo action there, since the above two necessary conditions for the instability to take place are satisfied in this region. Our global stability calculations for the tachocline-like configuration, representing a thin rotating cylindrical layer with the appropriate boundary conditions—conducting inner and insulating outer cylinders—and the values of the flow parameters, indicate that it can indeed arise in this case with a characteristic growth time comparable to the solar cycle period.