Vortex shedding in a model of superflow

The present paper represents part of the Ph.D. dissertation by C. Josserand [Dynamique des superfluides: Nucleation de vortex et transition de premier , Thesis Universite Paris VI, 1997]. We discuss the nucleation of quantized vortices in the nonlinear Schrodinger equation (NLS) for a flow around a d isk in two spatial dimensions. It appears that the vortices are nucleated w hen the flow becomes locally (at the edge of the disk) supersonic. A detail ed study of the phase equation for the complex field psi gives an Euler-Tri comi type equation for the stationary solutions below threshold. This equat ion is closely related to the one known in shock wave dynamics for gas. The n using the 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. (C) 1999 Elsevier Science B. V. All rights reserved.