We use a high-resolution cosmological zoom simulation of a Milky Way-sized halo to study the observable features in velocity and metallicity space associated with the dynamical influence of spiral arms. For the first time, we demonstrate that spiral arms, that form in a disc in a fully cosmological environment with realistic galaxy formation physics, drive large-scale systematic streaming motions. In particular, on the trailing edge of the spiral arms the peculiar galactocentric radial and azimuthal velocity field is directed radially outward and azimuthally backward, whereas it is radially inward and azimuthally forward on the leading edge. Owing to the negative radial metallicity gradient, this systematic motion drives, at a given radius,...