dorsal/arxiv
View SchemaGeneral vorticity conservation
| Authors | Hasan Gumral |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9801007 |
| URL | https://arxiv.org/abs/solv-int/9801007 |
Abstract
The motion of an incompressible fluid in Lagrangian coordinates involves infinitely many symmetries generated by the left Lie algebra of group of volume preserving diffeomorphisms of the three dimensional domain occupied by the fluid. Utilizing a 1+3-dimensional Hamiltonian setting an explicit realization of this symmetry algebra and the related Lagrangian and Eulerian conservation laws are constructed recursively. Their Lie algebraic structures are inherited from the same construction. The laws of general vorticity and helicity conservations are formulated globally in terms of invariant differential forms of the velocity field.
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"abstract": "The motion of an incompressible fluid in Lagrangian coordinates involves\ninfinitely many symmetries generated by the left Lie algebra of group of volume\npreserving diffeomorphisms of the three dimensional domain occupied by the\nfluid. Utilizing a 1+3-dimensional Hamiltonian setting an explicit realization\nof this symmetry algebra and the related Lagrangian and Eulerian conservation\nlaws are constructed recursively. Their Lie algebraic structures are inherited\nfrom the same construction. The laws of general vorticity and helicity\nconservations are formulated globally in terms of invariant differential forms\nof the velocity field.",
"arxiv_id": "solv-int/9801007",
"authors": [
"Hasan Gumral"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "General vorticity conservation",
"url": "https://arxiv.org/abs/solv-int/9801007"
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