  In this letter we study the mean sizes of Halpha clumps in turbulent disk
galaxies relative to kinematics, gas fractions, and Toomre Q. We use 100~pc
resolution HST images, IFU kinematics, and gas fractions of a sample of rare,
nearby turbulent disks with properties closely matched to z~1.5-2 main-sequence
galaxies (the DYNAMO sample). We find linear correlations of normalized mean
clump sizes with both the gas fraction and the velocity dispersion-to-rotation
velocity ratio of the host galaxy. We show that these correlations are
consistent with predictions derived from a model of instabilities in a
self-gravitating disk (the so-called "violent disk instability model"). We also
observe, using a two-fluid model for Q, a correlation between the size of
clumps and self-gravity driven unstable regions. These results are most
consistent with the hypothesis that massive star forming clumps in turbulent
disks are the result of instabilities in self-gravitating gas-rich disks, and
therefore provide a direct connection between resolved clump sizes and this in
situ mechanism.
