  We present gas and stellar kinematics of a high-resolution zoom-in
cosmological chemodynamical simulation, which fortuitously captures the
formation and evolution of a star-forming barred spiral galaxy, from redshift
$z\sim3$ to $z\sim2$ at the peak of the cosmic star formation rate. The galaxy
disc grows by accreting gas and substructures from the environment. The spiral
pattern becomes fully organised when the gas settles from a thick (with
vertical dispersion $\sigma_{v} >$ 50 km/s) to a thin ($\sigma_{v} \sim 25$
km/s) disc component in less than 1 Gyr. Our simulated disc galaxy also has a
central X-shaped bar, the seed of which formed by the assembly of dense
gas-rich clumps by $z \sim 3$. The star formation activity in the galaxy mainly
happens in the bulge and in several clumps along the spiral arms at all
redshifts, with the clumps increasing in number and size as the simulation
approaches $z=2$. We find that stellar populations with decreasing age are
concentrated towards lower galactic latitudes, being more supported by
rotation, and having also lower velocity dispersion; furthermore, the stellar
populations on the thin disc are the youngest and have the highest average
metallicities. The pattern of the spiral arms rotates like a solid body with a
constant angular velocity as a function of radius, which is much lower than the
angular velocity of the stars and gas on the thin disc; moreover, the angular
velocity of the spiral arms steadily increases as function of time, always
keeping its radial profile constant. The origin of our spiral arms is also
discussed.
