On the relation of standard and helical magnetorotational instability

Abstract

The magnetorotational instability (MRI) plays a crucial role for cosmic structure formation by enabling turbulence in Keplerian disks which would be otherwise hydrodynamically stable. With particular focus on MRI experiments with liquid metals, which have small magnetic Prandtl numbers, it has been shown that the helical version of this instability (HMRI) has a scaling behaviour that is quite different from that of the standard MRI (SMRI). We discuss the relation of HMRI to SMRI by exploring various parameter dependencies. We identify the mechanism of transfer of instability between modes through a spectral exceptional point that explains both the transition from a stationary instability (SMRI) to an unstable travelling wave (HMRI) and the excitation of HMRI in the inductionless limit. For certain parameter regions we find new islands of the HMRI.

48 pages, 13 figures

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Cited by in corpus (22)

• Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella?
• Instabilities in magnetized spherical Couette flow
• Local instabilities in magnetized rotational flows: A short-wavelength approach
• Extending the range of the inductionless magnetorotational instability
• Transition to magnetorotational turbulence in Taylor--Couette flow with imposed azimuthal magnetic field
• The role of boundaries in the MagnetoRotational Instability
• A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit
• Inviscid helical magnetorotational instability in cylindrical Taylor-Couette flow
• Paradoxes of magnetorotational instability and their geometrical resolution
• Generalised quasi-linear approximation of the HMRI
• Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
• Two types of axisymmetric helical magnetorotational instability in rotating flows with positive shear
• Linking dissipation-induced instabilities with nonmodal growth: the case of helical magnetorotational instability
• Transport properties of the Azimuthal Magnetorotational Instability
• Interplay between tidal flows and magnetic fields in nonlinear simulations of stellar and planetary convective envelopes
• Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor flows
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow
• Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence
• Magnetic field dynamos and magnetically triggered flow instabilities
• Analysis of azimuthal magnetorotational instability of rotating MHD flows and Tayler instability via an extended Hain-Lust equation
• Absolute versus convective helical magnetorotational instabilities in Taylor-Couette flows
• Laboratory modeling of MHD accretion disks