Dynamics and transport of magnetorotational instabilities in Taylor--Couette flows

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Turbulent transport of gas is a necessary physical process to explain the rates at which matter accretes and solar systems form in astrophysical disks. However, angular momentum increases radially in such disks and hence gas motion is expected to be laminar according to the Rayleigh criterion for rotating fluids. The solution to this riddle is provided by the magnetorotational instability (MRI), which operates in disks provided that the gas is ionized. In the last two decades there has been a great deal of numerical studies studying the properties of the MRI. Simulations are usually performed using the shearing sheet approximation, which is a local model of an accretion disk. Recently, there has been considerable interest in obtaining the MRI in laboratory experiments. The canonical experiment for the MRI is the swirling flow of a liquid metal between two concentric and independently rotating cylinders with an imposed axial magnetic field. Linear stability studies of this problem have been carried out, and shown to be in reasonable agreement with experiment for helical magnetic fields. However, little is known of the nonlinear saturation, bifurcation scenario, transition to turbulence and transport properties of the MRI, which is crucial for accretion in disks.The main goal of this project is to provide a characterization of magnetorotational instabilities in flows between corotating cylinders in the nonlinear regime. The various flavors of the MRI, corresponding to different magnetic field configurations, will be contrasted with one another, and transport scaling will be computed and used to infer properties in the astrophysical context. The results will be extensively compared with properties of the same instability in the shearing sheet approximation, in which the imposed radially periodic boundary conditions are thought to play a key role in the nonlinear saturation and properties of the turbulent flow. The project will provide a wealth of data for benchmarking and especially for comparison with laboratory experiments that have already been performed or are either under way or planned.