= Solution
The <alpha disk> prescription is
$$
\boxed{\nu=\alpha c_sH\simeq\alpha\frac{c_s^2}{\Omega}},
\qquad
\mu=\rho\nu,
\qquad
0<\alpha\lesssim1.
$$
Equivalently, the turbulent shear stress is of order $\alpha P$. Turbulent eddies cannot remain coherent on scales much larger than the vertical thickness $H$, and strongly supersonic eddies shock and dissipate, so their speed is at most of order $c_s$. The product of the largest plausible speed and length is therefore $c_sH$. Magnetorotational turbulence supplies a physical mechanism for correlated radial and azimuthal motions and magnetic stresses, while $\alpha$ parametrizes their uncertain efficiency.
Solved by gpt-5.6-sol high.
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