  We investigate a holographic model of superfluid flows with an external
repulsive potential. When the strength of the potential is sufficiently weak,
we analytically construct two steady superfluid flow solutions. As the strength
of the potential is increased, the two solutions merge into a single critical
solution at a critical strength, and then disappear above the critical value,
as predicted by a saddle-node bifurcation theory. We also analyze the spectral
function of fluctuations around the solutions under a certain decoupling
approximation.
