We study, by direct numerical simulations in two and three dimensions, the instability caused by the settling and evaporation of water droplets out of a cloudy layer saturated with vapor into a dry subcloud ambient under conditions where mammatus clouds were shown to form but with the addition of background shear. We show that shear changes the type of cloud formation qualitatively from mammatus-like to a newly identified cloud type called asperitas. Intermediate levels of shear are shown to be needed. Shear suppresses the growth of small-scale perturbations, giving rise to smooth, long-lasting structures and smaller rates of mixing. Three-dimensionality is shown to make a qualitative difference, unlike in mammatus clouds. We also show that under non-cloud-like conditions, the instability can be very different.