  In this work, we explore the diversity of ionised gas kinematics (rotational
velocity $v_{\phi}$ and velocity dispersion $\sigma_g$) 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 $\sigma_g$ have preferentially flat
metallicity gradients, whereas those with intermediate values of $\sigma_g$
show a large scatter in the metallicity gradients. Additionally, steep negative
gradients appear almost only in rotation-dominated galaxies ($v_{\phi}/\sigma_g
> 1$), whereas most dispersion-dominated galaxies show flat gradients. We use
our recently developed analytic model of metallicity gradients to provide a
physical explanation for these observed trends. In the case of high $\sigma_g$,
the inward radial advection of gas dominates over metal production and causes
efficient metal mixing, thus giving rise to flat gradients. For low $\sigma_g$,
it is the cosmic accretion of metal-poor gas diluting the metallicity that
gives rise to flat gradients. Finally, the reason for intermediate $\sigma_g$
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
$\sigma_g$ 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 that gas kinematics plays a critical role in setting metallicity
gradients in high-redshift galaxies.
