  We numerically investigate the dynamics of a 2D non-magnetised protoplanetary
disc surrounded by an inflow coming from an external envelope. We find that the
accretion shock between the disc and the inflow is unstable, leading to the
generation of large-amplitude spiral density waves. These spiral waves
propagate over long distances, down to radii at least ten times smaller than
the accretion shock radius. We measure spiral-driven outward angular momentum
transport with 1e-4 < alpha < 1e-2 for an inflow accretion rate Mout>1e-8
Msun/yr. We conclude that the interaction of the disc with its envelope leads
to long-lived spiral density waves and radial angular momentum transport with
rates that cannot be neglected in young non-magnetised protostellar discs.
