Thermospheric neutral wind acceleration via ion drag in the conducting E-region of the ionosphere is greatly increased by electron precipitation associated with auroras. This increased acceleration can lead to the development of significant horizontal wind shears, which we find are unstable to the Kelvin-Helmholtz shear instability. Numerical simulation of the neutral response to an intense, postmidnight, diffuse aurora shows the formation of an E-region ''jet stream'' within the aurora, with peak winds speeds >700 m/s after one hour. We propose that this jet stream produces unstable Kelvin-Helmholtz waves, which can drive waves of discrete aurora along the poleward boundary of the preexisting diffuse aurora. We suggest that such auroral waves, driven by the neutral winds, form eastward propagating waves (omega bands) occasionally observed along the poleward boundary of postmidnight diffuse auroras. We also find neutral wind shears that develop in response to discrete auroral arcs to be unstable; however we do not expect the resulting wind waves to drive significant auroral waves along discrete arcs.