  Understanding the dynamics and stability of transonic flows in quantum
fluids, especially for those beyond one spatial dimension, is an outstanding
challenge, with applications ranging from nonlinear optics and condensed matter
to analogue gravity. One intriguing possibility is that a system with a
spatially bounded supersonic flow may evolve into a self-oscillating state that
periodically emits solitons, in a process originating from the well-known
Landau instability. Here, we report observation of self-oscillating supersonic
flows in a two-dimensional atomic superfluid. By imposing a local particle sink
with strong loss, we induce a convergent radial flow forming an acoustic
analogue of a black-hole horizon and an inner horizon around the sink. The
observed superflow appears to be modulated by quasi-periodic bursts of
superluminal signals. We measure their frequencies and find agreement with
numerical simulations of soliton oscillation frequencies within the black-hole
horizon. The presented experiment demonstrates a new method for creating
supersonic flows in atomic superfluids, which may find applications in quantum
simulations of curved spacetime, supersonic turbulence, and self-oscillating
dynamics in dissipative many-body systems.
