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tokens: magnitude, but also on the stopping time. Fig. 11 Rootmean square of in the midplane as a function of r (lower abscissa) and the dimensionless gas pressure gradient parameter Π in the midplane (upper abscissa). The root mean square is calculated using the mass-weighted mean over 500 yr after an equilibrium value of the dust scale height is reached. In the simulation adi_Z=0.02_Lr=90au_taustop=0.1 (blue line), in which the dimensionless dust stopping time τ stop is fixed at 0.1, the Mach number increases with the pressure gradient parameter if Π ≲ 0.09, but is approximately constant if the pressure gradient is stronger. The Mach number in this one and the simulation adi_Z=0.02_Lr=90au (green line), in which the stopping time increases from 0.046 to 0.46, is comparable at all radii. That is, the turbulent strength does not depend significantly on the stopping time in this stopping time regime. The Mach number is lower overall, but depends more strongly on the radius in the simulation adi_Z=0.02_Lr=90au_a=3mm (orange line) in which the stopping time ranges from 0.0046 to 0.046. In this regime, the turbulent strength increases with both the strength of the pressure gradient and the stopping time. 5.3 Radial gas velocity In Fig. 12 , we show the radial velocity of the gas. The gas moves outward on average as a consequence of the inward radial drift of the dust and, as the total angular momentum is conserved, the transfer of angular momentum from the dust to the gas. Yet, the turbulent motions that are induced by the streaming instability lead to the variance in the gas velocity being greater thanthe speed of this mean outward motion. That is, the streaming instability does not cause a sustained inward transport of gas mass (and outward transport of angular momentum) that contributes to the observed stellar accretion ( Alcalá et al. 2017 ). 6 Discussion 6.1 Implications for turbulence and planetesimal formation in protoplanetary disks We have studied the interaction of two instabilities, the vertical shear instability and the streaming instability. Both instabilities appear to be robust: operation of the vertical shear instability requires a vertical rotation profile and a sufficiently short gas cooling timescale. Lin Youdin (2015) show that in the MMSN model, the instability can grow between r ≈ 5 and 50 au. On the other hand, only dust and a radial gas pressure gradient are necessary for the streaming instability to be active. Fig. 12 Radial gas velocity (solid line) as a function of r in the simulations adi_Z=0.02_Lr=9au and adi_Z=0.02_Lr=90au . (The dashed lines marks the boundary between the domains of the two simulations.) The velocity is computed as the mass-weighted average over the vertical domain extent and a time-span of 50 and 500 yr, respectively,after an equilibrium dust scale height has been attained in each simulation. The average radial velocity at r ≥ 3 au is plotted as a dotted line and amounts to 0.035 m s −1 . This outward