  In this work, we explore the diversity of ionised gas kinematics (rotational
velocity $v_{\phi}$ and velocity dispersion $\sigma_{\mathrm{g}}$) and
gas-phase metallicity gradients at $0.1 \leq z \leq 2.5$ using a compiled data
set of 74 galaxies resolved with ground-based integral field spectroscopy. We
find that galaxies with the highest and the lowest $\sigma_{\mathrm{g}}$ have
preferentially flat metallicity gradients, whereas those with intermediate
values of $\sigma_{\mathrm{g}}$ show a large scatter in the metallicity
gradients. Additionally, steep negative gradients appear almost only in
rotation-dominated galaxies ($v_{\phi}/\sigma_{\mathrm{g}} > 1$), whereas most
dispersion-dominated galaxies show flat gradients. We use our recently
developed analytic model of metallicity gradients to provide a physical
explanation for the shape and scatter of these observed trends. In the case of
high $\sigma_{\mathrm{g}}$, the inward radial advection of gas dominates over
metal production and causes efficient metal mixing, thus giving rise to flat
gradients. For low $\sigma_{\mathrm{g}}$, it is the cosmic accretion of
metal-poor gas diluting the metallicity that gives rise to flat gradients.
Finally, the reason for intermediate $\sigma_{\mathrm{g}}$ showing the steepest
negative gradients is that both inward radial advection and cosmic accretion
are weak as compared to metal production, which leads to the creation of
steeper gradients. The larger scatter at intermediate $\sigma_{\mathrm{g}}$ may
be due in part to preferential ejection of metals in galactic winds, which can
decrease the strength of the production term. Our analysis shows how gas
kinematics play a critical role in setting metallicity gradients in
high-redshift galaxies.
