Scaling laws for vortical nucleation solutions in a model of superflow

The bifurcation diagram corresponding to stationary solutions of the nonlin ear Schrodinger equation describing a superflow around a disc is numericall y computed using continuation techniques. When the Mach number is varied, i t is found that the stable and unstable (nucleation) branches are connected through a primary saddle-node and a secondary pitchfork bifurcation. Compu tations are carried out for values of the ratio xi/d of the coherence lengt h to the diameter of the disc in the range 1/5-1/80. It is found that the c ritical velocity converges for xi/d --> 0 to an Eulerian value, with a scal ing compatible with previous investigations, The energy barrier for nucleat ion solutions is found to scale as xi(2). Dynamical solutions are studied a nd the frequency of supercritical vortex shedding is found to scale as the square root of the bifurcation parameter. (C) 2000 Elsevier Science B.V. Al l rights reserved.