2012
DOI: 10.1103/physrevlett.109.224501
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Nondissipative Saturation of the Magnetorotational Instability in Thin Disks

Abstract: A new nondissipative mechanism is proposed for the saturation of the axisymmetric magnetorotational (MRI) instability in thin Keplerian disks that are subject to an axial magnetic field. That mechanism relies on the energy transfer from the MRI to stable magnetosonic waves. Such mode interaction is enabled due to the vertical stratification of the disk that results in the discretization of its MRI spectrum, as well as by applying the appropriate boundary conditions. A second order Duffing-like amplitude equati… Show more

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Cited by 15 publications
(35 citation statements)
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“…Nonlinear equilibrium solutions are the local manifestations of the global equilibria calculated by Ogilvie (1997) and connect to the local winds calculated by Ogilvie (2012). They also generalise the weakly nonlinear states calculated by Liverts et al (2012) at the onset of the MRI. But being steady, they must be distinguished from the exponentially growing channel flow solutions of Latter et al (2010).…”
Section: Families Of 1d Nonlinear Mhd Equilibriamentioning
confidence: 57%
“…Nonlinear equilibrium solutions are the local manifestations of the global equilibria calculated by Ogilvie (1997) and connect to the local winds calculated by Ogilvie (2012). They also generalise the weakly nonlinear states calculated by Liverts et al (2012) at the onset of the MRI. But being steady, they must be distinguished from the exponentially growing channel flow solutions of Latter et al (2010).…”
Section: Families Of 1d Nonlinear Mhd Equilibriamentioning
confidence: 57%
“…Other approaches have focused on saturation via diversion of energy into magnetosonic waves, or generation of large-scale magnetic fields via a dynamo process. Liverts et al (2012) suggested that the MRI saturates by driving nonresonant magnetosonic waves in a bursty oscillatory manner. Umurhan et al (2007) perform a weakly non-linear analysis of the MRI and find that it saturates with only a modest reduction in background shear, with an amplitude proportional to the square root of the magnetic Prandtl number, provided this is much smaller than unity.…”
Section: Previous Work On the Saturation Of The Mrimentioning
confidence: 99%
“…Liverts and coworkers [24] derived an ordinary differential Duffing equation for the thin-disk MRI. We see in §5 that (67) represents a possible infinity of coupled Duffing equations.…”
Section: Nonlinear Asymptotic Analysismentioning
confidence: 99%