  The present article represents part of the PhD. dissertation by C. Josserand.
We discuss the nucleation of quantized vortices in the nonlinear
Schr\"{o}dinger equation (NLS) for a flow around a disk in two spatial
dimensions. It appears that the vortices are nucleated when the flow becomes
locally (at the edge of the disk) supersonic. A detailed study of the phase
equation for the complex field $\psi$ gives an Euler-Tricomi type equation for
the stationary solutions below threshold. This equation is closely related to
the one known in shock wave dynamics for gas. Then using solvability condition,
we extract a time-dependent scenario for the evolution of the amplitude of the
solution, which we, finally, relate to a known family solution of NLS which
gives rise to a vortex nucleation. We also give a first order correction at the
Landau velocity of nucleation, taking into account the geometry of the flow.
