= Constant-opacity gas-pressure disk viscosity law
{title2=$\bar\nu\propto\alpha^{4/3}\Sigma^{2/3}\Omega^{-2/3}$}
The <density-weighted mean kinematic viscosity> of the universal vertical profile is $\bar\nu=\alpha\Omega h^2\int_{-\zeta_s}^{\zeta_s}P\,d\zeta$. Substitution of the height scale gives $\bar\nu=C\alpha^{4/3}(\kappa/\sigma)^{1/3}\mathcal R^{4/3}\Sigma^{2/3}\Omega^{-2/3}$. For <Keplerian rotation>, $\Omega^{-2/3}=(GM)^{-1/3}r$. The positive numerical constant depends only on the dimensionless vertical profile and the convention for $\alpha$.
// Target: astrophysics.bigb
Back to article page
