## Abstract

The bifurcation diagram corresponding to stationary solutions of the nonlinear Schrödinger equation describing a superflow around a disc is numerically computed using continuation techniques. When the Mach number is varied, it is found that the stable and unstable (nucleation) branches are connected through a primary saddle-node and a secondary pitchfork bifurcation. Computations are carried out for values of the ratio ξ/d of the coherence length to the diameter of the disc in the range 1/5-1/80. It is found that the critical velocity converges for ξ/d → 0 to an Eulerian value, with a scaling compatible with previous investigations. The energy barrier for nucleation solutions is found to scale as ξ^{2}. Dynamical solutions are studied and the frequency of supercritical vortex shedding is found to scale as the square root of the bifurcation parameter.

Original language | English (US) |
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Pages (from-to) | 126-140 |

Number of pages | 15 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 140 |

Issue number | 1-2 |

DOIs | |

State | Published - Jun 1 2000 |

## Keywords

- Bifurcation diagram
- Superfluid
- Vortex nucleation

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics