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The magnetorotational instability (MRI) plays a key role for cosmic structureformation by triggering turbulence in the rotating flows of accretion disksthat would be otherwise hydrodynamically stable. In the limit of small magneticPrandtl number, the helical and the azimuthal version of MRI are known to begoverned by a quite different scaling behaviour than the standard MRI with avertical applied magnetic field. Using the short-wavelength approximation foran incompressible, resistive, and viscous rotating fluid we present a unifieddescription of helical and azimuthal MRI, and we identify the universalcharacter of the Liu limit Ro= -0.8284 for the critical Rossby number. Fromthis universal behaviour we are also lead to the prediction of higher azimuthalwavenumber for rather small ratios of azimuthal to axial applied fields.

A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit