  We have searched for in-falling stellar streams on to the local Milky Way
disc in the CORAVEL and RAVE surveys. The CORAVEL survey consists of local
dwarf stars (Nordstrom et al. Geneva-Copenhagen survey) and local Famaey et al.
giant stars. We select RAVE stars with radial velocities that are sensitive to
the Galactic vertical space velocity (Galactic latitude b < -45 deg). Kuiper
statistics have been employed to test the symmetry of the Galactic vertical
velocity distribution functions in these samples for evidence of a net vertical
flow that could be associated with a (tidal?) stream of stars with vertically
coherent kinematics. In contrast to the `Field of Streams' found in the outer
halo, we find that the local volumes of the solar neighbourhood sampled by the
CORAVEL dwarfs (complete within ~3 x 10^-4 kpc^3), CORAVEL giants (complete
within ~5 x 10^-2 kpc^3) and RAVE (5-15% complete within ~8 kpc^3) are devoid
of any vertically coherent streams containing hundreds of stars. This is
sufficiently sensitive to allow our RAVE sample to rule out the passing of the
tidal stream of the disrupting Sagittarius (Sgr) dwarf galaxy through the solar
neighbourhood. This agrees with the most recent determination of its orbit and
dissociates it from the Helmi et al. halo stream. Our constraints on the
absence of the Sgr stream near the Sun could prove a useful tool for
discriminating between Galactic potential models. The lack of a net vertical
flow through the solar neighbourhood in the CORAVEL giants and RAVE samples
argues against the Virgo overdensity crossing the disc near the Sun. There are
no vertical streams in the CORAVEL giants and RAVE samples with stellar
densities >1.6 x 10^4 and 1.5 x 10^3 stars kpc^-3 respectively and therefore no
evidence for locally enhanced dark matter.
