 Vertically averaged alpha closure for a mixed-pressure layer

For the constant gas-radiation ratio vertical disc structure, the integrated alpha prescription $\bar{\nu }\Sigma =\int \mu dz=(\alpha /\Omega )\int pdz$ gives the displayed mean kinematic viscosity and $\lambda /(1+\lambda )=\alpha H\Omega \kappa \Sigma /(8c)$. Uniform dynamic viscosity and nonuniform pressure are compatible because this prescription is an integrated equality. Imposing the corresponding pointwise equality would not preserve the exact vertical solution.