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Accretion discs are ubiquitous in the universe and it is a crucial issue tounderstand how angular momentum and mass are being radially transported inthese objects. Here, we study the role played by non-linear spiral patternswithin hydrodynamical and non self-gravitating accretion disc assuming thatexternal disturbances such as infall onto the disc may trigger them. To do so,we computed self-similar solutions that describe discs in which a spiral wavepropagates. Such solutions present both shocks and critical sonic points thatwe carefully analyze. For all allowed temperatures and for several spiralshocks, we calculated the wave structure. In particular we inferred the angleof the spiral patern, the stress it exerts on the disc as well as theassociated flux of mass and angular momentum as a function of temperature. Wequantified the rate of angular momentum transport by means of the dimensionless$\alpha$ parameter. For the thickest disc we considered (corresponding to $h/r$values of about 1/3), we found values of $\alpha$ as high as $0.1$, and scalingwith the temperature $T$ such that $\alpha \propto T^{3/2} \propto (h/r)^3$.The spiral angle scales with the temperature as $\arctan(r/h)$. The existenceof these solutions suggests that perturbations occurring at disc outerboundaries, such as for example perturbations due to infall motions, canpropagate deep inside the disc and therefore should not be ignored, even whenconsidering small radii.

Spiral-driven accretion in protoplanetary discs - II Self-similar solutions