  The streaming instability is a promising mechanism to overcome the barriers
in direct dust growth and lead to the formation of planetesimals. Most previous
studies of the streaming instability, however, were focused on a local region
of a protoplanetary disk with a limited simulation domain such that only one
filamentary concentration of solids has been observed. The characteristic
separation between filaments is therefore not known. To address this, we
conduct the largest-scale simulations of the streaming instability to date,
with computational domains up to 1.6 gas scale heights both horizontally and
vertically. The large dynamical range allows the effect of vertical gas
stratification to become prominent. We observe more frequent merging and
splitting of filaments in simulation boxes of high vertical extent. We find
multiple filamentary concentrations of solids with an average separation of
about 0.2 local gas scale heights, much higher than the most unstable
wavelength from linear stability analysis. This measures the characteristic
separation of planetesimal forming events driven by the streaming instability
and thus the initial feeding zone of planetesimals.
