The Kelvin-Helmholtz instability in an expanding universe and its effect on dark matter

We extend the Kelvin-Helmholtz instability to an expanding background. We study the evolution of a non-viscous irrotational fluid and find that for wavelengths much smaller than the Rubble scale small perturbations of the fluid are unstable for wavenumbers larger than a critical value. We then apply this result in the early universe, treating cold dark matter as a classical fluid with vanishing background pressure.