| Issue |
EAS Publications Series
Volume 38, 2009
Nonlinear Pulsations and Hydrodynamics of Cepheids
|
|
|---|---|---|
| Page(s) | 165 - 173 | |
| DOI | https://doi.org/10.1051/eas/0938018 | |
| 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
1
Department of Physics, Technion – Israel Institute of Technology, Israël
2
Department of Astronomy, Columbia University, USA
Corresponding author: regev@physics.technion.ac.il
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