dorsal/arxiv
View SchemaVariational description of multi-fluid hydrodynamics: Uncharged fluids
| Authors | Reinhard Prix |
|---|---|
| Categories | |
| ArXiv ID | physics/0209024 |
| URL | https://arxiv.org/abs/physics/0209024 |
| DOI | 10.1103/PhysRevD.69.043001 |
| Journal | Phys.Rev. D69 (2004) 043001 |
Abstract
We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems containing an arbitrary number of interacting fluids and superfluids. In addition to spatial variations we use ``time shifts'' in the variational principle, which allows us to describe dissipative processes with entropy creation, such as chemical reactions, friction or the effects of external non-conservative forces. The resulting framework incorporates the generalization of the entrainment effect originally discussed in the case of the mixture of two superfluids by Andreev and Bashkin. In addition to the conservation of energy and momentum, we derive the generalized conservation laws of vorticity and helicity, and the special case of Ertel's theorem for the single perfect fluid. We explicitly discuss the application of this framework to thermally conducting fluids, superfluids, and superfluid neutron star matter. The equations governing thermally conducting fluids are found to be more general than the standard description, as the effect of entrainment usually seems to be overlooked in this context. In the case of superfluid He4 we recover the Landau--Khalatnikov equations of the two-fluid model via a translation to the ``orthodox'' framework of superfluidity, which is based on a rather awkward choice of variables. Our two-fluid model for superfluid neutron star matter allows for dissipation via mutual friction and also ``transfusion'' via beta-reactions between the neutron fluid and the proton-electron fluid.
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"abstract": "We present a formalism for Newtonian multi-fluid hydrodynamics derived from\nan unconstrained variational principle. This approach provides a natural way of\nobtaining the general equations of motion for a wide range of hydrodynamic\nsystems containing an arbitrary number of interacting fluids and superfluids.\nIn addition to spatial variations we use ``time shifts\u0027\u0027 in the variational\nprinciple, which allows us to describe dissipative processes with entropy\ncreation, such as chemical reactions, friction or the effects of external\nnon-conservative forces. The resulting framework incorporates the\ngeneralization of the entrainment effect originally discussed in the case of\nthe mixture of two superfluids by Andreev and Bashkin. In addition to the\nconservation of energy and momentum, we derive the generalized conservation\nlaws of vorticity and helicity, and the special case of Ertel\u0027s theorem for the\nsingle perfect fluid.\n We explicitly discuss the application of this framework to thermally\nconducting fluids, superfluids, and superfluid neutron star matter. The\nequations governing thermally conducting fluids are found to be more general\nthan the standard description, as the effect of entrainment usually seems to be\noverlooked in this context. In the case of superfluid He4 we recover the\nLandau--Khalatnikov equations of the two-fluid model via a translation to the\n``orthodox\u0027\u0027 framework of superfluidity, which is based on a rather awkward\nchoice of variables. Our two-fluid model for superfluid neutron star matter\nallows for dissipation via mutual friction and also ``transfusion\u0027\u0027 via\nbeta-reactions between the neutron fluid and the proton-electron fluid.",
"arxiv_id": "physics/0209024",
"authors": [
"Reinhard Prix"
],
"categories": [
"physics.flu-dyn",
"astro-ph",
"cond-mat"
],
"doi": "10.1103/PhysRevD.69.043001",
"journal_ref": "Phys.Rev. D69 (2004) 043001",
"title": "Variational description of multi-fluid hydrodynamics: Uncharged fluids",
"url": "https://arxiv.org/abs/physics/0209024"
},
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