Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD


Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD

Kirillov, O. N.; Stefani, F.

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable rotating shear flows, e.g., in Couette-Taylor cells and in accretion disks. What laws of differential rotation are susceptible to the destabilization by the axial or helical magnetic field? The answer to this vital for astrophysical and experimental applications question inevitably leads to the study of spectral and geometrical singularities on the instability threshold. The singularities provide a connection between seemingly discontinuous stability criteria and thus explain paradoxes in the theory of MRI that were kept poorly understood since 1950s. By using the WKB approximation and methods of singular function theory, we resolve two different paradoxes of magnetorotational instability that appear in the limits of infinite and vanishing magnetic Prandtl number. For the latter case we derive a new strict limit of the critical Rossby number. This new limit of Roc = −0.802, which appears for a finite Lundquist number of Lu = 0.618, extends the formerly known inductionless Liu limit of Roc = −0.828 valid at Lu = 0.

Keywords: Magnetorotaional instability; singularity theory; helical magnetorotational instability; Rayleigh line; Velikhov-Chandrasekhar paradox; inductionless HMRI

  • Invited lecture (Conferences)
    Kolloquium des Instituts für Analysis, Dynamik und Modellierung, 13.-15.07.2011, Universität Stuttgart, Deutschland

Permalink: https://www.hzdr.de/publications/Publ-15987
Publ.-Id: 15987