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Experimental and Theoretical Results on Magnetorotational Instability (MRI)
 

The MRI is thought to be one of the primary mechanisms by which angular momentum is transported in astrophysical accretion disks. It may also act as a dynamo, and may play a role in galaxy disks and in stars. An attempt to study its properties in the laboratory is now underway. After successfully transitioning to the liquid metal phase at the Princeton MRI experiment, we began MHD experiments by imposing an axial magnetic field on hydrodynamically unstable flows with the outer cylinder at rest after allowing about one minute for the system to reach a statistically steady state. After about 15 seconds, coherent MHD structures emerge with azimuthal mode number m=1. By spatial Fourier decomposition, we found there are actually two rotating modes: one rotates faster than the other. Both of these speeds increase with the strength of the imposed magnetic field. These two modes exhibit the predicted dependence of rotating speeds on magnetic field by fast and slow magnetocoriolis waves as shown in the figure below. The observation is significant in that the slow magnetocoriolis wave goes to zero frequency and becomes unstable giving rise to the MRI with sufficient rotation and shear. The observation of these driven damped waves gives us a means of diagnosing the stability threshold for the MRI. 

graph

Numerical simulations play a key role in interpreting the results of the experiment. We have conducted a series of preliminary 3D MHD numerical simulations of the nonlinear development of MRI for low magnetic Prandtl numbers relevant to the experiment. The figure below shows a volume rendering of axial magnetic field in the experimental geometry for one of the cases run in Rayleigh-unstable regime at Re=3000 and Rm=1.

 

Volume Rendering of Axial Magnetic Field

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