dorsal/arxiv
View SchemaVortex shedding in a model of superflow
| Authors | C. Josserand, Y. Pomeau, S. Rica |
|---|---|
| Categories | |
| ArXiv ID | physics/9901055 |
| URL | https://arxiv.org/abs/physics/9901055 |
| DOI | 10.1016/S0167-2789(99)00066-4 |
Abstract
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.
{
"annotation_id": "548b73ce-fff7-4536-8955-9cb14e96d1ad",
"date_created": "2026-03-02T18:01:21.420000Z",
"date_modified": "2026-03-02T18:01:21.420000Z",
"file_hash": "74fd7865a6d62c05b18dcc045696c9bdfc4fb1395904e53468f4a55417fc8e8b",
"private": false,
"record": {
"abstract": "The present article represents part of the PhD. dissertation by C. Josserand.\nWe discuss the nucleation of quantized vortices in the nonlinear\nSchr\\\"{o}dinger equation (NLS) for a flow around a disk in two spatial\ndimensions. It appears that the vortices are nucleated when the flow becomes\nlocally (at the edge of the disk) supersonic. A detailed study of the phase\nequation for the complex field $\\psi$ gives an Euler-Tricomi type equation for\nthe stationary solutions below threshold. This equation is closely related to\nthe one known in shock wave dynamics for gas. Then using solvability condition,\nwe extract a time-dependent scenario for the evolution of the amplitude of the\nsolution, which we, finally, relate to a known family solution of NLS which\ngives rise to a vortex nucleation. We also give a first order correction at the\nLandau velocity of nucleation, taking into account the geometry of the flow.",
"arxiv_id": "physics/9901055",
"authors": [
"C. Josserand",
"Y. Pomeau",
"S. Rica"
],
"categories": [
"physics.flu-dyn",
"cond-mat.stat-mech"
],
"doi": "10.1016/S0167-2789(99)00066-4",
"title": "Vortex shedding in a model of superflow",
"url": "https://arxiv.org/abs/physics/9901055"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "f016ff83-57e8-4ca0-b6a7-4026de44e08a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}