A weakly nonlinear analysis of the magnetorotational instability in a model channel flow

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dc.creatorUmurhan, O. M.
dc.creatorMenou, K.
dc.creatorRegev, O.
dc.date2006-08-17
dc.date2007-01-09
dc.date.accessioned2026-07-07T10:23:26Z
dc.date.available2026-07-07T10:23:26Z
dc.descriptionWe show by means of a perturbative weakly nonlinear analysis that the axisymmetric magnetorotational instability (MRI) of a viscous, resistive, incompressible rotating shear flow in a thin channel gives rise to a real Ginzburg-Landau equation for the disturbance amplitude. For small magnetic Prandtl number (${\cal P}_{\rm m}$), the saturation amplitude is $\propto \sqrt{{\cal P}_{\rm m}}$ and the resulting momentum transport scales as ${\cal R}^{-1}$, where $\cal R$ is the {\em hydrodynamic} Reynolds number. Simplifying assumptions, such as linear shear base flow, mathematically expedient boundary conditions and continuous spectrum of the vertical linear modes, are used to facilitate this analysis. The asymptotic results are shown to comply with numerical calculations using a spectral code. They suggest that the transport due to the nonlinearly developed MRI may be very small in experimental setups with ${\cal P}_{\rm m} \ll 1$.
dc.descriptionAccepted to Physical Review Letters - Nov. 30, 2006. In final form
dc.identifierhttps://arxiv.org/abs/astro-ph/0608374
dc.identifierhttp://arxiv.org/abs/astro-ph/0608374
dc.identifierPhys.Rev.Lett.98:034501,2007
dc.identifierdoi:10.1103/PhysRevLett.98.034501
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/175831
dc.subjectAstrophysics
dc.subjectPattern Formation and Solitons
dc.titleA weakly nonlinear analysis of the magnetorotational instability in a model channel flow
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