  The superflow in a superfluid is bounded from above by Landau's critical
velocity. Within a microscopic bosonic model, I show that below this critical
velocity there is a dynamical instability that manifests itself in an imaginary
sound velocity and that is reminiscent of the two-stream instability in
electromagnetic plasmas. I compute the onset of this instability and its full
angular structure in a relativistic, uniform superfluid for all temperatures.
At weak coupling, the instability only operates in a very small region in the
phase diagram of temperature and superflow. Varying the coupling of the model
suggests that the effect is more prominent at strong coupling and thus could be
important for superfluids in compact stars and in the laboratory.
