Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 347 / 2 / b / Solution

In a Keplerian accretion disk, $u_{\varphi }=R\Omega =(GM/R{)}^{1/2}$. Substitution into the steady azimuthal Navier--Stokes equation and cancellation of the common Keplerian factors givesSince $R^2\Omega \propto R^{1/2}$ and $d\Omega /dR=-3\Omega /(2R)$, this reduces to the standard viscous drift formulaThe minus sign describes inward drift when $\nu \Sigma R^{1/2}$ increases outward.