**Workshop ISTROF 2014**

Instabilities and Turbulence in Stratified Rotational Flow

Le Havre, June 23-25

**Authors:** Kirillov, Oleg and Stefani, Frank

**Title:** Inductionless instabilities in rotational MHD flows: A comprehensive short-wavelength analysis

**Abstract:** 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, 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 current-free profile.

**References:**

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2. Friedlander, S. & Vishik, M. M. 1995 On stability and instability criteria for magnetohydrodynamics. Chaos 5, 416-423.

3. Eckhardt, B. & Yao, D. 1995 Local stability analysis along Lagrangian paths. Chaos, Solitons & Fractals, 5(11), 2073-2088.

4. Kirillov, O. N. & Stefani, F. 2010 On the relation of standard and helical magnetorotational instability. Astrophys. J., 712, 52-68.

5. Kirillov, O. N., Stefani, F., & Fukumoto, Y. 2012 A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit. Astrophys. J., 756, 83 (6pp).

6. Kirillov, O. N. & Stefani, F. 2013 Extending the range of the inductionless magnetorotational instability. Phys. Rev. Lett., 111, 061103 (5pp).

7. Kirillov, O.N., Stefani, F., Fukumoto, Y. 2014 Instabilities in magnetized rotational flows: A comprehensive short-wavelength approach. Journal of Fluid Mechanics, subm. (arXiv:1401.8276v1)

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