dorsal/arxiv
View SchemaMatrix Fluid Dynamics
| Authors | E. I. Yakubovich, D. A. Zenkovich |
|---|---|
| Categories | |
| ArXiv ID | physics/0110004 |
| URL | https://arxiv.org/abs/physics/0110004 |
Abstract
The paper reports the recent results on application and extension of the matrix formulation of lagrangian hydrodynamic equations. The matrix approach is based on the notion of continuous deformation of infinitesimal material elements and treats the Jacobi matrix of their derivatives with respect to lagrangian variables as the fundamental quantity completely describing fluid motion. We begin with brief review of the governing matrix equation (for the detailed discussion see Yakubovich, E.I. & Zenkovich, D.A. 2001 Matrix approach to Lagrangian fluid dynamics. J. Fluid Mech. vol. 443, 167-196). The new general relationship between two- and three-dimensional solutions of the matrix equations is then found and applied to 3-D generalization of plane 'Ptolemaic' vortices. As a result, families of non-stationary swirling vortices and of stretched vortices in an axisymmetric strain are constructed and studied. The set of matrix equations is extended to include the effect of viscosity by incorporating an evolution equation for the Cauchy invariants, which represents a lagrangian analogue of the Helmholtz equation for a viscous fluid.
{
"annotation_id": "cbfc7d8b-9e69-42bb-8193-f51020a14562",
"date_created": "2026-03-02T18:00:36.238000Z",
"date_modified": "2026-03-02T18:00:36.238000Z",
"file_hash": "881cc877509edc03d4774678d290dca39c1e3616e055b527626e6efa01160710",
"private": false,
"record": {
"abstract": "The paper reports the recent results on application and extension of the\nmatrix formulation of lagrangian hydrodynamic equations. The matrix approach is\nbased on the notion of continuous deformation of infinitesimal material\nelements and treats the Jacobi matrix of their derivatives with respect to\nlagrangian variables as the fundamental quantity completely describing fluid\nmotion. We begin with brief review of the governing matrix equation (for the\ndetailed discussion see Yakubovich, E.I. \u0026 Zenkovich, D.A. 2001 Matrix approach\nto Lagrangian fluid dynamics. J. Fluid Mech. vol. 443, 167-196). The new\ngeneral relationship between two- and three-dimensional solutions of the matrix\nequations is then found and applied to 3-D generalization of plane \u0027Ptolemaic\u0027\nvortices. As a result, families of non-stationary swirling vortices and of\nstretched vortices in an axisymmetric strain are constructed and studied. The\nset of matrix equations is extended to include the effect of viscosity by\nincorporating an evolution equation for the Cauchy invariants, which represents\na lagrangian analogue of the Helmholtz equation for a viscous fluid.",
"arxiv_id": "physics/0110004",
"authors": [
"E. I. Yakubovich",
"D. A. Zenkovich"
],
"categories": [
"physics.flu-dyn"
],
"title": "Matrix Fluid Dynamics",
"url": "https://arxiv.org/abs/physics/0110004"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "3e260d57-72c4-4ead-9930-5cdae0384312",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}