Standard and Helical Magnetorotational Instability

Abstract

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable rotating shear flows, e.g., in accretion disks. What laws of differential rotation are susceptible to the destabilization by axial, azimuthal, or helical magnetic field? The answer to this question, which is vital for astrophysical and experimental applications, 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 several paradoxes in the theory of MRI that were poorly understood since the 1950s.

Analysis of azimuthal magnetorotational instability of rotating magnetohydrodynamic flows and Tayler instability via an extended Hain-Lüst equation

“…By performing the WKB analysis of the extended Hain-Lüst equation, we obtain the dispersion relation in the short radial wavelength limit in Section III. Section IV confirms that this approach restores the known results [4,5] for the SMRI and the AMRI, when restricted to axisymmetric disturbances.…”

“…A steady rotating flow with the angular velocity Ω(r)e z , parallel to the z-axis is considered as a base state. The Rossby number is defined [4,5] by Ro = 1/2 (d log Ω/d log r) = rΩ ′ /(2Ω), where the prime designates the derivative with respect to r. Without loss of generality, we assume that Ω > 0. For a non-magnetized flow, Rayleigh's criterion states that the instability with respect to axisymmetric disturbance occurs when the Rossby number, Ro < −1, which fails to include the Keplerian flow (Ro = −3/4).…”

“…The latter is called the azimuthal MRI (AMRI), for which the magnetic field has only the azimuthal component B = B θ (r)e θ . The instability caused by their combination is called the helical MRI (HMRI) [4,5,9].…”

Magneto‐convection in a rotating layer of nanofluid

“…Effect of rotation on a ferromagnetic fluid heated and soluted from below in the presence of dust particle was investigated by Sunil et al . Kirillov and Stefani studied the standard and helical magnetorotational instability.…”

“…Pardeep et al [38] studied the effect of magnetic field on thermal instability of a rotating viscoelastic fluid. Thermal convection in micropolar ferrofluid in the presence of rotation was studied by Sunil et al [39] Effect of rotation on a ferromagnetic fluid heated and soluted from below in the presence of dust particle was investigated by Sunil et al [40] Kirillov and Stefani [41] studied the standard and helical magnetorotational instability.…”