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

Spiral-driven accretion in protoplanetary discs - I. 2D models