  Under the right conditions, the streaming instability between imperfectly
coupled dust and gas is a powerful mechanism for planetesimal formation as it
can concentrate dust grains to the point of gravitational collapse. In its
simplest form, the streaming instability can be captured by analyzing the
linear stability of unstratified disk models, which represent the midplane of
protoplanetary disks. We extend such studies by carrying out vertically-global
linear stability analyses of dust layers in protoplanetary disks. We find the
dominant form of instability in stratified dust layers is one driven by the
vertical gradient in the rotation velocity of the dust-gas mixture, but also
requires partial dust-gas coupling. These vertically-shearing streaming
instabilities grow on orbital timescales and occur on radial length scales
$\sim10^{-3}H_\mathrm{g}$, where $H_\mathrm{g}$ is the local pressure scale
height. The classic streaming instability, associated with the relative radial
drift between dust and gas, occur on radial length scales
$\sim10^{-2}H_\mathrm{g}$, but have much smaller growth rates than
vertically-shearing streaming instabilities. Including gas viscosity is
strongly stabilizing and leads to vertically-elongated disturbances. We briefly
discuss the potential effects of vertically-shearing streaming instabilities on
planetesimal formation.
