Paradoxes of magnetorotational instability and their geometrical resolution

Abstract

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable accretion discs. By using the WKB approximation and methods of singular function theory, we resolve two different paradoxes of MRI 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 $\mathrm{R}{\mathrm{o}}_{\mathrm{c}}=-0.802$, which appears for a finite Lundquist number of $\mathrm{Lu}=0.618$, extends the formerly known inductionless Liu limit of $\mathrm{R}{\mathrm{o}}_{\mathrm{c}}=-0.828$ valid at $\mathrm{Lu}=0$.

4 pages, 3 figures, refs added

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Cited by in corpus (13)

• Local instabilities in magnetized rotational flows: A short-wavelength approach
• Extending the range of the inductionless 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
• Standard and helical magnetorotational instability: How singularities create paradoxal phenomena in MHD
• Paradoxical transitions to instabilities in hydromagnetic Couette-Taylor flows
• Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence
• Analysis of azimuthal magnetorotational instability of rotating MHD flows and Tayler instability via an extended Hain-Lust equation
• Unification theory of instabilities of visco-diffusive swirling flows
• High-speed standard magneto-rotational instability
• Instabilities in visco-thermodiffusive swirling flows
• DRESDYN - A new facility for MHD experiments with liquid sodium
• Laboratory experiments and numerical simulations on magnetic instabilities