Stability Rayleigh criteria

While a purely hydrodynamic source for turbulence has not yet been demonstrated, the situation is much different when MHD effects are considered in a shearing, Keplerian disk. In this case, the Rayleigh criterion for stability can be shown to be irrelevant provided only that the angular velocity of the disk decreases with radius, even an infinitesimal magnetic field will grow at the expense of the shear motions. 

If 22 = 0, for example, the Rayleigh criterion indicates that Couette flow is unstable for any 12]. On the other hand, the approximate stability criterion (12-158) for a viscous fluid says that the system will remain stable for... 

The first condition will be recognized as Rayleigh s criterion, which is easy to satisfy, for example if the liner is initially in rigid rotation. If satisfied initially it will be satisfied throughout the cycle. The second condition is that the effective gravity at the inner surface should always be directed radially outwards this condition is most severe at turnaround. The third condition is necessary because the outer gas-liquid interface cannot be stabilized by rotation. 

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