= Thin-accretion-disk truncation error
{title2=$O((H/r)^2)$}
For smooth radial variation on scale $r$, $c_s\sim\Omega H$, $\nu\sim\alpha\Omega H^2$, $u_r\sim\nu/r$ and $u_z\sim Hu_r/r$. The exact point-mass vertical gravity differs from $\Omega_K^2z$ by relative order $(H/r)^2$. Radial <pressure> support changes the rotation and dominant shear heating by the same order. Meridional viscous forces, radial radiative-flux divergence, thermal <advection> and compressional work are at most order $(H/r)^2$ relative to their retained vertical terms for $\alpha\lesssim1$. These estimates require secular disk evolution and exclude sharp radial <boundary layers> or independently rapid vertical motion.
// Target: gravitational-instability-of-an-astrophysical-disk.bigb
Back to article page
