and position and temperature of accretion disk walls in T Tauri protoplanetary disks, those indicated in the above equation (e.g. D’Alessio et al. 2005, Espaillat et al. 2007, Hughes et al 2009), one should expect the breakdown of the thin disk approximation (${\mathcal M} >>1$, e.g. Pringle 1981), and consequently, the transition to radial flow.

Taking typical inferred values for $R/H$ at the wall of $\sim 5$ (e.g. D’Alessio et al. 2005, Espaillat et al. 2007, Hughes et al 2009), we can now write the condition for the transition to radial flow, locally at the wall, as:

$$10=6 \pi \alpha (n-1/2).$$

We see that for a standard value of $n\sim1$ the above equation implies a reasonable value of $\alpha \sim 1$ at the thick wall, significantly higher than the values of $\sim 0.01$ and lower, which apply for the body of the thin accretion disk beyond this radius. A substantial increase of $\alpha$ as $R/H$ decreases is expected in any turbulence driven viscosity model for accretion disks, e.g. Firmani, Hernandez & Gallagher (1996), in the context of galactic disks.

In terms of the debate surrounding the inference of inner holes in observed accretion disks, many solutions have been proposed in 