Suppression of infrared instability in transsonic flows by condensation of zero-frequency short wave length phonons

Abstract

We analyze the peculiar infrared instability that characterizes stationary inhomogeneous flows when their velocity crosses the sound speed by decreasing values. For definiteness, we work in the context of one dimensional atomic Bose condensates. These flows are unstable under ultra low real frequency perturbations because of the unbounded mode amplification near the sonic horizon. This results in a condensation of low frequency phonons which produces a spatially structured flow in the supersonic domain. Numerical simulations reveal that this zero-frequency undulation suppresses the instability when its spatial extension is infinite, and when its phase is near that of a "shadow soliton" solution attached to the sonic horizon. These phenomena are akin to the condensation of rotons in flowing superfluid helium-4 when exceeding the Landau velocity. They also pertain to shallow water waves propagating on transcritical flows.