 Viscous torque in an accretion disk

The viscous torque in an accretion disk is the rate of outward angular momentum transport by an internal shear stress. For an axisymmetric thin disk rotating with angular velocity $\Omega (r)$, a local Newtonian viscous stress has $T_{r\varphi }=\rho \nu rd\Omega /dr$. Integrating that stress over a cylinder and multiplying by the lever arm givesHere $\bar{\nu }$ is the density-weighted mean kinematic viscosity, with units of length squared per time. The vertically integrated quantity is $\bar{\nu }\Sigma$. For decreasing $\Omega$, the sign convention makes $\mathcal{G}>0$, describing outward angular momentum transport. More general internal stresses can be represented by an effective $\bar{\nu }$ through the same integrated torque relation.^[ref]