  We analyse the velocity dispersion properties of 472 z~0.9 star-forming
galaxies observed as part of the KMOS Redshift One Spectroscopic Survey
(KROSS). The majority of this sample is rotationally dominated (83 +/- 5% with
v_C/sigma_0 > 1) but also dynamically hot and highly turbulent. After
correcting for beam smearing effects, the median intrinsic velocity dispersion
for the final sample is sigma_0 = 43.2 +/- 0.8 km/s with a rotational velocity
to dispersion ratio of v_C/sigma_0 = 2.6 +/- 0.1. To explore the relationship
between velocity dispersion, stellar mass, star formation rate and redshift we
combine KROSS with data from the SAMI survey (z~0.05) and an intermediate
redshift MUSE sample (z~0.5). While there is, at most, a weak trend between
velocity dispersion and stellar mass, at fixed mass there is a strong increase
with redshift. At all redshifts, galaxies appear to follow the same weak trend
of increasing velocity dispersion with star formation rate. Our results are
consistent with an evolution of galaxy dynamics driven by disks that are more
gas rich, and increasingly gravitationally unstable, as a function of
increasing redshift. Finally, we test two analytic models that predict
turbulence is driven by either gravitational instabilities or stellar feedback.
Both provide an adequate description of the data, and further observations are
required to rule out either model.
