dorsal/arxiv
View SchemaCanonical description of ideal magnetohydrodynamic flows and integrals of motion
| Authors | A. V. Kats |
|---|---|
| Categories | |
| ArXiv ID | physics/0406059 |
| URL | https://arxiv.org/abs/physics/0406059 |
| DOI | 10.1103/PhysRevE.69.046303 |
| Journal | Phys. Rev. E, v. 69, April 2004 |
Abstract
In the framework of the variational principle the canonical variables describing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with spatially varying entropy and nonzero values of all topological invariants) are introduced. The corresponding complete velocity representation enables us not only to describe the general type flows in terms of single-valued functions, but also to solve the intriguing problem of the ``missing'' MHD integrals of motion. The set of hitherto known MHD local invariants and integrals of motion appears to be incomplete: for the vanishing magnetic field it does not reduce to the set of the conventional hydrodynamic invariants. And if the MHD analogs of the vorticity and helicity were discussed earlier for the particular cases, the analog of Ertel invariant has been so far unknown. It is found that on the basis of the new invariants introduced a wide set of high-order invariants can be constructed. The new invariants are relevant both for the deeper insight into the problem of the topological structure of the MHD flows as a whole and for the examination of the stability problems. The additional advantage of the proposed approach is that it enables one to deal with discontinuous flows, including all types of possible breaks.
{
"annotation_id": "5c48cbed-ba03-41d3-9359-a0713ef90bbd",
"date_created": "2026-03-02T18:00:49.777000Z",
"date_modified": "2026-03-02T18:00:49.777000Z",
"file_hash": "7232bf4cf152189a1c577fa9a794af8f05ab8d77b00148d5396072921cc2f624",
"private": false,
"record": {
"abstract": "In the framework of the variational principle the canonical variables\ndescribing ideal magnetohydrodynamic (MHD) flows of general type (i.e., with\nspatially varying entropy and nonzero values of all topological invariants) are\nintroduced. The corresponding complete velocity representation enables us not\nonly to describe the general type flows in terms of single-valued functions,\nbut also to solve the intriguing problem of the ``missing\u0027\u0027 MHD integrals of\nmotion. The set of hitherto known MHD local invariants and integrals of motion\nappears to be incomplete: for the vanishing magnetic field it does not reduce\nto the set of the conventional hydrodynamic invariants. And if the MHD analogs\nof the vorticity and helicity were discussed earlier for the particular cases,\nthe analog of Ertel invariant has been so far unknown. It is found that on the\nbasis of the new invariants introduced a wide set of high-order invariants can\nbe constructed. The new invariants are relevant both for the deeper insight\ninto the problem of the topological structure of the MHD flows as a whole and\nfor the examination of the stability problems. The additional advantage of the\nproposed approach is that it enables one to deal with discontinuous flows,\nincluding all types of possible breaks.",
"arxiv_id": "physics/0406059",
"authors": [
"A. V. Kats"
],
"categories": [
"physics.flu-dyn",
"physics.plasm-ph"
],
"doi": "10.1103/PhysRevE.69.046303",
"journal_ref": "Phys. Rev. E, v. 69, April 2004",
"title": "Canonical description of ideal magnetohydrodynamic flows and integrals of motion",
"url": "https://arxiv.org/abs/physics/0406059"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "9ef52fa3-8c11-4ba6-8523-415560f939cc",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}