dorsal/arxiv
View SchemaMotion Equation of Vorticity for Newton Fluid
| Authors | Xiao Jianhua |
|---|---|
| Categories | |
| ArXiv ID | physics/0512051 |
| URL | https://arxiv.org/abs/physics/0512051 |
Abstract
The vorticity plays an important role in aerodynamics and rotational flow. Usually, they are studied with modified Navier-Stokes equation. This research will deduce the motion equation of vorticity from Navier-Stokes equation. To this propose, the velocity gradient field is decomposed as the stack of non-rotation field and pure-rotation field. By introducing the Chen S+R decomposition, the rotational flow is redefined. For elastic fluid, the research shows that for Newton fluid, the local average rotation always produces an additional pressure on the rotation plane. This item is deterministic rather than stochastic (as Reynolds stress) or adjustable. For non-elastic fluid, such as air, the research shows that the rotation will produce an additional stress along the rotation axis direction, that is on the normal direction of rotation plane. This result can be used to explain the lift force connected with vortex. The main purpose of this research is to supply a solvable mathematical model for the calculation of vorticity and pressure when suitable boundary condition is adapted. Based on this understanding, some way to control the movement of vortices may be produced.
{
"annotation_id": "04287c3d-8375-4260-9a2c-ae1ce5162e44",
"date_created": "2026-03-02T18:01:03.605000Z",
"date_modified": "2026-03-02T18:01:03.605000Z",
"file_hash": "821dc5bc30057f9e1e344d728a2b002c656f323bfb78e6ce3d6ce3ceb128ba4a",
"private": false,
"record": {
"abstract": "The vorticity plays an important role in aerodynamics and rotational flow.\nUsually, they are studied with modified Navier-Stokes equation. This research\nwill deduce the motion equation of vorticity from Navier-Stokes equation. To\nthis propose, the velocity gradient field is decomposed as the stack of\nnon-rotation field and pure-rotation field. By introducing the Chen S+R\ndecomposition, the rotational flow is redefined. For elastic fluid, the\nresearch shows that for Newton fluid, the local average rotation always\nproduces an additional pressure on the rotation plane. This item is\ndeterministic rather than stochastic (as Reynolds stress) or adjustable. For\nnon-elastic fluid, such as air, the research shows that the rotation will\nproduce an additional stress along the rotation axis direction, that is on the\nnormal direction of rotation plane. This result can be used to explain the lift\nforce connected with vortex. The main purpose of this research is to supply a\nsolvable mathematical model for the calculation of vorticity and pressure when\nsuitable boundary condition is adapted. Based on this understanding, some way\nto control the movement of vortices may be produced.",
"arxiv_id": "physics/0512051",
"authors": [
"Xiao Jianhua"
],
"categories": [
"physics.flu-dyn"
],
"title": "Motion Equation of Vorticity for Newton Fluid",
"url": "https://arxiv.org/abs/physics/0512051"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b2e81ce9-9f71-4eb9-b0f9-09fe430231a6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}