
In Fig.~\ref{mlum_r}, we plotted the radii of GMAs against their velocity dispersions, $\sigma$, which represent the root mean squared internal velocity of each cloud caused by the increased difference in velocity for more spatially separated gas parcels. Here, the fit for the Milky Way scales with Eq.~\ref{eqn2} from \citet{Solomon_1987}, which they attribute to virial equilibrium rather than Kolmogorov turbulence as suggested by \citet{Larson_1981}. We see basic correlation with that fit, despite large spread in velocity dispersion.

\begin{equation}
\sigma^2 = \frac{\sqrt{\mathrm{\pi}}} {3.4} R.
\label{eqn2}
\end{equation}

Fig.~\ref{mlum_r} shows that turbulence increases with radius and that the nuclear GMAs are more turbulent than disk GMAs of similar radii. There are no differences between the turbulent properties of the arm and inter-arm GMAs at any radius. 