  The gas-phase velocity dispersions in disk galaxies, which trace turbulence
in the interstellar medium, are observed to increase with lookback time.
However, the mechanisms that set this rise in turbulence are observationally
poorly constrained. To address this, we combine kiloparsec-scale ALMA
observations of CO(3-2) and CO(4-3) with HST observations of H$\alpha$ to
characterize the molecular gas and star formation properties of seven local
analogues of main sequence galaxies at $z \sim 1-2$, drawn from the DYNAMO
sample. Investigating the ''molecular gas main sequence'' on kpc-scales, we
find that galaxies in our sample are more gas-rich than local star-forming
galaxies at all disk positions. We measure beam smearing corrected molecular
gas velocity dispersions and relate them to the molecular gas and star
formation rate surface densities. Despite being relatively nearby ($z \sim
0.1$), DYNAMO galaxies exhibit high velocity dispersions and gas and star
formation rate surface densities throughout their disks, when compared to local
star forming samples. Comparing these measurements to predictions from star
formation theory, we find very good agreements with the latest
feedback-regulated star formation models. However, we find that theories which
combine gravitational energy dissipation from radial gas transport with
feedback over-estimate the observed molecular gas velocity dispersions.
