EAS Publications Series
Volume 38, 2009Nonlinear Pulsations and Hydrodynamics of Cepheids
|Page(s)||165 - 173|
|Published online||15 August 2009|
M. Goupil, Z. Kolláth, N. Nardetto and P. Kervella (eds)
EAS Publications Series, 38 (2009) 165-173
The Magneto-Rotational Instability Near Threshold: Spatio-Temporal Amplitude Equation and Saturation
Department of Physics, Technion – Israel Institute of Technology, Israël
2 Department of Astronomy, Columbia University, USA
Corresponding author: firstname.lastname@example.org
We show, by means of a perturbative weakly nonlinear analysis, that the axisymmetric magneto-rotational instability (MRI) in a magnetic Taylor-Couette (mTC) flow in a thin-gap gives rise, for very small magnetic Prandtl numbers , to a real Ginzburg-Landau equation for the disturbance amplitude. The saturation amplitude As is found to scale in this regime as , with 1/2 < δ < 2/3 (depending on the boundary conditions adopted). The asymptotic results are shown to comply with numerical calculations performed by using a spectral code. They suggest that the transport due to the nonlinearly developed MRI may be vanishingly small for 1.
© EAS, EDP Sciences, 2009
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