  The streaming instability is a leading candidate mechanism to explain the
formation of planetesimals. Yet, the role of this instability in the driving of
turbulence in protoplanetary disks, given its fundamental nature as a linear
hydrodynamical instability, has so far not been investigated in detail. We
study the turbulence that is induced by the streaming instability as well as
its interaction with the vertical shear instability. For this purpose, we
employ the FLASH Code to conduct two-dimensional axisymmetric global disk
simulations spanning radii from $1$ au to $100$ au, including the mutual drag
between gas and dust as well as the radial and vertical stellar gravity. If the
streaming instability and the vertical shear instability start their growth at
the same time, we find the turbulence in the dust mid-plane layer to be
primarily driven by the streaming instability. It gives rise to vertical gas
motions with a Mach number of up to ${\sim}10^{-2}$. The dust scale height is
set in a self-regulatory manner to about $1\%$ of the gas scale height. In
contrast, if the vertical shear instability is allowed to saturate before the
dust is introduced into our simulations, then it continues to be the main
source of the turbulence in the dust layer. The vertical shear instability
induces turbulence with a Mach number of ${\sim}10^{-1}$ and thus impedes dust
sedimentation. Nonetheless, we find the vertical shear instability and the
streaming instability in combination to lead to radial dust concentration in
long-lived accumulations which are significantly denser than those formed by
the streaming instability alone. Thus, the vertical shear instability may
promote planetesimal formation by creating weak overdensities that act as seeds
for the streaming instability.
