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We investigate the stellar kinematics of the Galactic disc in 7 $<$ $R$ $<$13\,kpc using a sample of 118\,945 red giant branch (RGB) stars from LAMOST andGaia. We characterize the median, dispersion and skewness of the distributionsof the 3D stellar velocities, actions and orbital parameters across theage-metallicity and the disc $R$ -- $Z$ plane. Our results reveal abundant butclear stellar kinematic patterns and structures in the age -- metallicity andthe disc $R$ -- $Z$ plane. The most prominent feature is the strong variationsof the velocity, action, and orbital parameter distributions from the young,metal-rich thin disc to the old, metal-poor thick disc, a number ofsmaller-scale structures -- such as velocity streams, north-south asymmetries,and kinematic features of spiral arms -- are clearly revealed. Particularly,the skewness of $V_{\phi}$ and $J_{\phi}$ reveals a new substructure at$R\simeq12$\,kpc and $Z\simeq0$\,kpc, possibly related to dynamical effects ofspiral arms in the outer disc. We further study the stellar migration throughanalysing the stellar orbital parameters and stellar birth radii. The resultssuggest that the thick disc stars near the solar radii and beyond are mostlymigrated from the inner disc of $R\sim4 - 6$\,kpc due to their highlyeccentrical orbits. Stellar migration due to dynamical processes with angularmomentum transfer (churning) are prominent for both the old, metal-rich stars(outward migrators) and the young metal-poor stars (inward migrators). Thespatial distribution in the $R$ -- $Z$ plane for the inward migrators born at aGalactocentric radius of $>$12\,kpc show clear age stratifications, possibly anevidence that these inward migrators are consequences of splashes triggered bymerger events of satellite galaxies that have been lasted in the past few gigayears.

Age-metallicity dependent stellar kinematics of the Milky Way disc from LAMOST and Gaia