My talk at the Fluid Mechanics and Meteorology Seminar at the University of Surrey, United Kingdom.
I will present recent theoretical results obtained in collaboration with Frank Stefani and Yasuhide Fukumoto. We perform a local stability analysis of rotational flows in the presence of a constant vertical magnetic field and an azimuthal magnetic field with a general radial dependence characterized by an appropriate magnetic Rossby number. Employing the short-wavelength approximation we develop a unified framework for the investigation of the standard, the helical, and the azimuthal version of the magnetorotational instability (MRI), as well as of current-driven kink-type instabilities. Considering the viscous and resistive setup, our main focus is on the case of small magnetic Prandtl numbers which applies, e.g., to liquid metal experiments but also to the colder parts of accretion disks. We show in particular that the inductionless versions of MRI that were previously thought to be restricted to comparably steep rotation profiles extend well to the Keplerian case if only the azimuthal field slightly deviates from its field-free profile. We also find an explicit criterion for the critical magnetic field at the onset of the Tayler instability (TI) and demonstrate the details of transition between TI and azimuthal MRI in support of the planned MRI-TI experiment.