  Superfluid flow past a potential barrier is a well studied problem in
ultracold Bose gases, however, fewer studies have considered the case of flow
through a disordered potential. Here we consider the case of a superfluid
flowing through a channel containing multiple point-like barriers, randomly
placed to form a disordered potential. We begin by identifying the relationship
between the relative position of two point-like barriers and the critical
velocity of such an arrangement. We then show that there is a mapping between
the critical velocity of a system with two obstacles, and a system with a large
number of obstacles. By establishing an initial superflow through a point-like
disordered potential, moving faster than the critical velocity, we study how
the superflow is arrested through the nucleation of vortices and the breakdown
of superfluidity, a problem with interesting connections to quantum turbulence
and coarsening. We calculate the vortex decay rate as the width of the barriers
is increased, and show that vortex pinning becomes a more important effect for
these larger barriers.
