Astronomy and Astrophysics – Astrophysics
Scientific paper
2006-08-17
Phys.Rev.Lett.98:034501,2007
Astronomy and Astrophysics
Astrophysics
Accepted to Physical Review Letters - Nov. 30, 2006. In final form
Scientific paper
10.1103/PhysRevLett.98.034501
We 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 ${\cal P}_{\rm m} \ll 1$.
Menou Kristen
Regev Oded
Umurhan Orkan Mehmet
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