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

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.

20 pages, 6 figures, 3 tables

References in corpus (6)

• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
• Hall equilibrium of thin Keplerian disks embedded in mixed poloidal and toroidal magnetic fields
• Evolution of initially localized perturbations in stratified ionized disks
• Non-Dissipative Saturation of the Magnetorotational Instability in Thin Disks
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Cited by in corpus (1)

• Explosive magnetorotational instability in Keplerian disks