Singularities on the boundaries of magnetorotational instabilities and scaling laws
Singularities on the boundaries of magnetorotational instabilities and scaling laws
Kirillov, O.; Stefani, F.
In the theory of magnetorotational instability and its modern extensions such as the helical MRI, nontrivial scaling laws between the critical parameters are observed. In case of the standard MRI it is well known that the Reynolds and Hartmann numbers are scaled as Re ∼ Ha^{2} while for the helical MRI Re ∼ Ha^{3}. What is less known is that the thresholds of SMRI and HMRI plotted as surfaces in the space of parameters, possess singularities that determine the scaling laws. Moreover, the two paradoxes of SMRI and HMRI in the limits of infinite and zero magnetic Prandtl number (Pm), respectively, sharply correspond to the singularities on the instability thresholds. In either case, it is the local Plücker conoid structure that explains the nonuniqueness of the critical Rossby number, and its crucial dependence on the Lundquist number. For HMRI, we have found an extension of the former Liu limit Roc ≃ −0.828 (valid for Lu = 0) to a somewhat higher value Ro ≃ −0.802 at Lu = 0.618 which is, however, still below the Kepler value.
Keywords: Standard Magnetorotational instability; Helical magnetorotational instability; interaction parameter; scaling law

Proceedings in Applied Mathematics and Mechanics (PAMM) 11(2011), 655656
DOI: 10.1002/pamm.201110317
Permalink: https://www.hzdr.de/publications/Publ16413
Publ.Id: 16413