Evolution of initially localized perturbations in stratified ionized disks

Abstract

A detailed solution of an initial value problem of a vertically localized initial perturbation in rotating magnetized vertically stratified disk is presented. The appropriate linearized MHD equations are solved by employing the WKB approximation and the results are verified numerically. The eigenfrequencies as well as eigenfunctions are explicitly obtained. It is demonstrated that the initial perturbation remains confined within the disk. It is further shown that thin enough disks are stable but as their thickness grows increasing number of unstable modes participate in the solution of the initial value problem. However it is demonstrated that due to the localization of the initial perturbation the growth time of the instability is significantly longer than the calculated inverse growth rate of the individual unstable eigenfunctions.

10 pages, 5 figures. Accepted for publication in MNRAS

References in corpus (6)

• The Formation and Structure of a Strongly Magnetized Corona above Weakly Magnetized Accretion Disks
• Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks
• Magnetorotational Instability in Liquid Metal Couette Flow
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• Evolution of initially localized perturbations in stratified ionized disks

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• Low magnetic-Prandtl number flow configurations for cold astrophysical disk models: speculation and analysis
• Thermomagnetic instability in hot discs
• Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs
• Study of MRI in stratified viscous plasma configuration
• Regimes of the non-exponential temporal growth in thin Keplerian discs under toroidally-dominated magnetic fields