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We present a three dimensional velocity analysis of Milky Way disk kinematicsusing LAMOST K giant stars and the GPS1 proper motion catalogue. We find thatGalactic disk stars near the anticenter direction (in the range ofGalactocentric distance between $R=8$ and $13$ kpc and vertical positionbetween $Z=-2$ and $2$ kpc) exhibit asymmetrical motions in the Galactocentricradial, azimuthal, and vertical components. Radial motions are not zero, thusdeparting from circularity in the orbits; they increase outwards within$R\lesssim 12$ kpc, show some oscillation in the northern ($0 < Z < 2$ kpc)stars, and have north-south asymmetry in the region corresponding to awell-known nearby northern structure in the velocity field. There is a clearvertical gradient in azimuthal velocity, and also an asymmetry that shifts froma larger azimuthal velocity above the plane near the solar radius to fasterrotation below the plane at radii of 11-12 kpc. Stars both above and below theplane at $R\gtrsim 9$ kpc exhibit net upward vertical motions. We discuss somepossible mechanisms that might create the asymmetrical motions, such asexternal perturbations due to dwarf galaxy minor mergers or dark mattersub-halos, warp dynamics, internal processes due to spiral arms or the Galacticbar, and (most likely) a combination of some or all of these components.

3D Asymmetrical motions of the Galactic outer disk with LAMOST K giant stars