  The stability and dynamics of nonlinear Schrodinger superflows past a
two-dimensional disk are investigated using a specially adapted pseudo-spectral
method based on mapped Chebychev polynomials. This efficient numerical method
allows the imposition of both Dirichlet and Neumann boundary conditions at the
disk border. Small coherence length boundary-layer approximations to stationary
solutions are obtained analytically. Newton branch-following is used to compute
the complete bifurcation diagram of stationary solutions. The dependence of the
critical Mach number on the coherence length is characterized. Above the
critical Mach number, at coherence length larger than fifteen times the
diameter of the disk, rarefaction pulses are dynamically nucleated, replacing
the vortices that are nucleated at small coherence length.
