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arXiv · 1401.2528

Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs

Yuri M. Shtemler·Michael Mond·Edward Liverts
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Abstract

The magneto-rotational decay instability (MRDI) of thin Keplerian discs threaded by poloidal magnetic fields is introduced and studied. The linear magnetohydrodynamic problem decouples into eigenvalue problems for in-plane slow- and fast- Alfv'een-Coriolis (AC), and vertical magnetosonic (MS) eigenmodes. The magnetorotational instability (MRI) is composed of a discrete number of unstable slow AC eigenmodes that is determined for each radius by the local beta. In the vicinity of the first beta threshold a parent MRI eigenmode together with a stable AC eigenmode (either slow or fast) and a stable MS eigenmode form a resonant triad. The three-wave MRDI relies on the nonlinear saturation of the parent MRI mode and the exponential growth of two daughter linearly stable waves, slow-AC and MS modes with an effective growth rate that is comparable to that of the parent MRI. If, however, the role of the AC daughter wave is played by a stable fast mode, all three modes remain bounded.

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Yuri M. Shtemler, Michael Mond, Edward Liverts. 2014-01-11. Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs. https://doi.org/10.1093/mnras%2Fstu062

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