Measuring the Streaming motion in the Milky Way disc with Gaia EDR3 +
  We map the 3D kinematics of the Galactic disc out to 3.5 kpc from the Sun,
and within 0.75 kpc from the midplane of the Milky Way. To this end, we combine
high quality astrometry from \gedrthree{}, with the radial velocities from
\gdrtwo{}, and from major spectroscopic surveys including \apogee{}, \galah{},
and \lamost{}. We construct an axisymmetric model for the mean velocity field,
and then subtract this on a star-by-star basis to obtain the peculiar velocity
field in the Galactocentric components, \vphi{}, \vR, \vz, as well as the
heliocentric line-of-sight, \vlos{}. The velocity residuals are quantified
using the power spectrum, and we find that the peak power ($A$) in the midplane
($|z|<0.25$ kpc) is ($A_{\phi},A_{\rm R},A_{\rm Z},A_{\rm
los}$)=($4.2,8.5,2.6,4.6$), at $0.25 < |z|/[{\rm kpc}] < 0.5$, is
($A_{\phi},A_{\rm R},A_{\rm Z},A_{\rm los}$)=($4.0,7.9,3.6,5.3$), and at $0.5 <
|z|/[{\rm kpc}] < 0.75$, is ($A_{\phi},A_{\rm R},A_{\rm Z},A_{\rm
los}$)=($1.9,6.9,5.2,6.4$). Our results provide for the first time, a measure
of the streaming motion in the disc in the individual components. We find that
streaming is most significant in the Galactocentric radial component, and at
all heights ($|Z|$) probed, but is also not negligible in the other components.
Additionally, we find that the patterns in the velocity field overlap spatially
with models for the Spiral arms in the Milky Way. Finally, we demonstrate using
a simulation that phase mixing of disrupting spiral arms can generate such
residuals in the velocity field, where the radial component is dominant, just
as in the real data. The simulation also suggests that with evolution of time
both the amplitude and the physical scale of the peculiar motion decreases.
