as $\Delta v$ is increased [J07, @BaiStone2010c]. Estimates of the radial pressure support in discs can be extracted from models of column density and temperature structure. A gas parcel orbiting at a radial distance $r$ from the star, where the disc aspect ratio is $H/r$ and the mid-plane radial pressure gradient is ${\mathrm{d}}\ln P/{\mathrm{d}}\ln r$, orbits at a sub-Keplerian speed $v=v_{\rm K}-\Delta v$. The speed reduction $\Delta v$ is given by $$\frac{\Delta v}{c_{\rm s}} = -\frac{1}{2} \frac{H}{r} \frac{{\mathrm{d}}\ln P}{{\mathrm{d}}\ln r} \, .$$ In the Minimum Mass Solar Nebula of [@Hayashi1981] ${\mathrm{d}}\ln P/{\mathrm{d}}\ln
r=-3.25$ in the mid-plane [e.g. @Youdin2008]. The resulting scaling of the sub-Keplerian speed with the orbital distance is $$\frac{\Delta v}{c_{\rm s}} \approx 0.05 \left( \frac{r}{\rm AU} \right)^{1/4}
  \, .$$ The slightly colder disc model used by [@Brauer+etal2008a] yields instead $$\frac{\Delta v}{c_{\rm s}} \approx 0.04 \left( \frac{r}{\rm AU} \right)^{1/4}
  \, .$$ In more complex disc models the pressure profile is changed e.g. in interfaces between regions of weak and strong turbulence [@Lyra+etal2008b]. We use throughout this paper a fixed value of $\Delta v/c_{\rm s}=0.05$.

Another difference from the simulations of J07 is that the turbulent viscosity of the gas flow is around 2-3 times higher, because of the increased 