Streaming instability in a global patch simulation of protoplanetary disks

Aims. In recent years, sub-millimeter (mm) observations of protoplanetary disks have revealed an incredible diversity of substructures in the dust emission. An important result was the finding that dust grains of mm size are embedded in very thin dusty disks. This implies that the dust mass fraction in the midplane becomes comparable to that of the gas, increasing the importance of the interaction between the two components there. Methods. We use numerical 2.5D simulations to study the interaction between gas and dust in fully globally stratified disks. To this end, we employ the recently developed dust grain module of the PLUTO code. Our model focuses on a typical T Tauri disk model, simulating a short patch of the disk at 10 au which includes grains of a constant Stokes number of St = 0.01 and St = 0.1, corresponding to grains with sizes of 0.9 cm and 0.9 mm, respectively, for the given disk model. Results. By injecting a constant pebble flux at the outer domain, the system reaches a quasi-steady state of turbulence and dust concentrations driven by the streaming instability. For our given setup, and using resolutions up to 2500 cells per scale height, we resolve the streaming instability that leads to local dust clumping and concentrations. Our results show dust density values of around 10-100 times the gas density with a steady-state pebble flux of between 3.5 × 10-4 and 2.5 × 10-3 MEarth yr-1 for the models with St = 0.01 and St = 0.1. Conclusions. Grain size and pebble flux for model St = 0.01 compare well with dust evolution models of the first million years of disk evolution. For those grains, the scatter opacity dominates the extinction coefficient at mm wavelengths. These types of global dust and gas simulations are a promising tool for studies of the gas and dust evolution at pressure bumps in protoplanetary disks.