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The nonlinear evolution of the magnetic interchange or buoyancy instability of a differentially rotating disk threaded by an ordered vertical magnetic field is investigated. A 2D ideal fluid in the equatorial plane of a central mass in the corotating frame of reference is considered as a model for the disk. If the rotation rate of the disk is Keplerian, the disk is found to be stable. If the vertical magnetic field is sufficiently strong, and the field strength decreases with distance from the central object, and thus the rotation of the disk deviates from Keplerian, if is found that an instability develops. The magnetic flux and disk matter expand outward in certain ranges of azimuth, while disk matter with less magnetic flux moves inward over the remaining range of azimuth, showing a characteristic development of an interchange instability.
Kaisig et al. (Sat,) studied this question.