  In an equilibrium axisymmetric galactic disc, the mean galactocentric radial
and vertical velocities are expected to be zero everywhere. In recent years,
various large spectroscopic surveys have however shown that stars of the Milky
Way disc exhibit non-zero mean velocities outside of the Galactic plane in both
the Galactocentric radial and vertical velocity components. While radial
velocity structures are commonly assumed to be associated with non-axisymmetric
components of the potential such as spiral arms or bars, non-zero vertical
velocity structures are usually attributed to excitations by external sources
such as a passing satellite galaxy or a small dark matter substructure crossing
the Galactic disc. Here, we use a three-dimensional test-particle simulation to
show that the global stellar response to a spiral perturbation induces both a
radial velocity flow and non-zero vertical motions. The resulting structure of
the mean velocity field is qualitatively similar to what is observed across the
Milky Way disc. We show that such a pattern also naturally emerges from an
analytic toy model based on linearized Euler equations. We conclude that an
external perturbation of the disc might not be a requirement to explain all of
the observed structures in the vertical velocity of stars across the Galactic
disc. Non-axisymmetric internal perturbations can also be the source of the
observed mean velocity patterns.
