The magneto-rotational instability near threshold: spatio-temporal amplitude equation and saturation
arXiv:0801.1637 · doi:10.1051/eas/0938018
Abstract
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 (P_m), to a real Ginzburg-Landau equation for the disturbance amplitude. The saturation amplitude A_s is found to scale in this regime as P^δ, 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 P_m << 1.
To appear in conference proceedings 'European Astronomical Society Publications series', EDP Sciences
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