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Fig. 7

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Left panel: average root mean square zd,rms and standard deviation σzd of vertical particle positions. Right panel: radial dust diffusion coefficients Dr for Δrinit = 0.1 au (circles) and Δrinit = 0.01 au (squares). In both panels, blue, orange, and green symbols represent quantities at r = 55 au in our two-dimensional simulation of the vertical shear instability with a dust size of 3 mm as well as at r = 55 au and at r = 30 au for the dust with a size of 1 mm in the three-dimensional simulation conducted by F20. While the vertical diffusion coefficients at r = 55 au in the latter simulation and in ours are comparable, the radial coefficients are larger by almost an order of magnitude in our simulation. Nonetheless, vertical diffusion is similarly dependent on scale while radial diffusion is scale-independent both in the two- and the three-dimensional simulation. At r = 30 au, the Rossby wave instability induces a giant vortex in the simulation by F20, which gives rise to diffusion that is similar in strength in the radial and vertical dimensions as well as on small and large scales.

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