= Solution
The <Shakura--Sunyaev thin disk> model replaces poorly resolved turbulent angular-momentum transport by a stress proportional to pressure,
$$
|T_{R\phi}|=\alpha p,
\qquad 0<\alpha\lesssim1.
$$
Equivalently, an eddy viscosity has $\nu\sim v_{\rm eddy}\ell_{\rm eddy}$. Turbulent motions much faster than the <sound speed> $c_s$ would shock, while eddies much larger than the <disk scale height> $H$ would not fit within the disk. Writing $v_{\rm eddy}\ell_{\rm eddy}=\alpha c_sH$ therefore gives the <alpha disk> prescription
$$
\boxed{
\nu=\alpha c_sH
\simeq\alpha\frac{c_s^2}{\Omega_K}
},
$$
where vertical hydrostatic balance gives $H\simeq c_s/\Omega_K$. The parameter $\alpha$ summarizes the correlation and efficiency of turbulent or magnetic stresses; it is not a molecular viscosity.
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