On the magnetorotational instability and elastic buckling

Vasil, Geoffrey M.

doi:10.1098/rspa.2014.0699

Cited by 16 publications

(25 citation statements)

References 42 publications

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“…The most salient feature of this equation is its non-local character. Unlike the present work, which focuses on Keplerian rotation profiles with q = 3/2 with a critical background magnetic field strength, Vasil (2015) focuses on a fixed field strength and a weakly destabilized shear profile. These differences are minor, however: the destabilizing parameter enters the analysis in the same quadratic proportion.…”

Section: Discussionmentioning

confidence: 99%

“…These differences are minor, however: the destabilizing parameter enters the analysis in the same quadratic proportion. Whether and how Vasil (2015)'s amplitude equation is equivalent to our own in the limit of dynamically important resistive and viscous effects is beyond the scope of this work. Nevertheless, the author identifies the nonlinear term responsible for saturation as consisting of flux and field transport and notes these are the only mechanisms able to produce saturation.…”

Section: Discussionmentioning

confidence: 99%

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The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Clark

Oishi

2017

ApJ

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The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple scales analysis of the non-ideal MRI in the weakly nonlinear regime -that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by that the perturbation amplitude follows a Ginzburg-Landau equation. We further find that the Ginzburg-Landau equation will arise for the local MRI system with shear-periodic boundary conditions when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system and demonstrate the pattern formation our model predicts on long length and time scales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Clark

Oishi

2017

ApJ

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“…† Interestingly, a similar saturation mechanism also arises for the standard (MHD) MRI in a non-periodic system when it is near the marginal-stability condition(Vasil 2015).‡ Specifically, the relative magnitude of the rate of heat-flux smoothing of ∆p compared to its rate of creation (via d ln B/dt) varies between β 1/2 (as in the collisionless case), when νc β 1/2 , and 1, when νc ∼ β 1/2 .…”

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confidence: 81%

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

2017

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In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the "parasitic instabilities" that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in MHD). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

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“…This is the first weakly nonlinear analysis of the MRI in a cylindrical geometry, and is thus the global analogue of similar analyses in local approximations (Umurhan et al 2007b;Vasil 2015). Understanding the connection between local and global MRI modes is crucial for interpreting simulation results across domain geometries.…”

Section: Discussionmentioning

confidence: 99%

The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow

Clark

Oishi

2017

ApJ

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We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor-Couette flow. This is a multiscale perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor-Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg-Landau equation (GLE), while the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.

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On the magnetorotational instability and elastic buckling

Cited by 16 publications

References 42 publications

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow

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