WKB instability thresholds of the magnetized cylindrical Couette-Taylor flow in helical magnetic fields

We consider a cylindrical Couette-Taylor (CT) flow of an electrically conducting viscous and resistive fluid in an external helical magnetic field. Local stability of the flow is studied with respect to three-dimensional perturbations within a short-wavelength approximation. Maximization of the critical Rossby number at the instability threshold is performed with respect to the non-dimensional parameters of the problem characterizing hydrodynamic and magnetic effects. Quite surprisingly, it is found that the critical Rossby number at the threshold of magnetorotational instability in the case of infinitesimally small magnetic Prandtl number is universally bounded from above by a quantity 2 − 2√2 known as the Liu limit, which is below that of Keplerian rotation (−3/4).