dorsal/arxiv
View SchemaAlternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of "patches" and "points"
| Authors | Z. Yin, D. C. Montgomery, H. J. H. Clercx |
|---|---|
| Categories | |
| ArXiv ID | physics/0211024 |
| URL | https://arxiv.org/abs/physics/0211024 |
| DOI | 10.1063/1.1578078 |
Abstract
Numerical and analytical studies of decaying, two-dimensional (2D) Navier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort is to determine computable distinctions between two different formulations of maximum entropy predictions for the decayed, late-time state. Both formulations define an entropy through a somewhat ad hoc discretization of vorticity to the "particles" of which statistical mechanical methods are employed to define an entropy, before passing to a mean-field limit. In one case, the particles are delta-function parallel "line" vortices ("points" in two dimensions), and in the other, they are finite-area, mutually-exclusive convected "patches" of vorticity which in the limit of zero area become "points." We use time-dependent, spectral-method direct numerical simulation of the Navier-Stokes equations to see if initial conditions which should relax to different late-time states under the two formulations actually do so.
{
"annotation_id": "73f7ad9b-a1e4-4441-85b3-756e0e7f709d",
"date_created": "2026-03-02T18:00:42.466000Z",
"date_modified": "2026-03-02T18:00:42.466000Z",
"file_hash": "b5acb8d1aad1bd8be3e333630077c1482149a49b74b9fefa7d4c8ac2ebad1c42",
"private": false,
"record": {
"abstract": "Numerical and analytical studies of decaying, two-dimensional (2D)\nNavier-Stokes (NS) turbulence at high Reynolds numbers are reported. The effort\nis to determine computable distinctions between two different formulations of\nmaximum entropy predictions for the decayed, late-time state. Both formulations\ndefine an entropy through a somewhat ad hoc discretization of vorticity to the\n\"particles\" of which statistical mechanical methods are employed to define an\nentropy, before passing to a mean-field limit. In one case, the particles are\ndelta-function parallel \"line\" vortices (\"points\" in two dimensions), and in\nthe other, they are finite-area, mutually-exclusive convected \"patches\" of\nvorticity which in the limit of zero area become \"points.\" We use\ntime-dependent, spectral-method direct numerical simulation of the\nNavier-Stokes equations to see if initial conditions which should relax to\ndifferent late-time states under the two formulations actually do so.",
"arxiv_id": "physics/0211024",
"authors": [
"Z. Yin",
"D. C. Montgomery",
"H. J. H. Clercx"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1063/1.1578078",
"title": "Alternative statistical-mechanical descriptions of decaying two-dimensional turbulence in terms of \"patches\" and \"points\"",
"url": "https://arxiv.org/abs/physics/0211024"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "1844226c-52b9-47d4-bde1-2476bec55157",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}