108 research outputs found
Variational description of multi-fluid hydrodynamics: Uncharged fluids
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.Comment: uses RevTeX 4; 20 pages. To appear in PRD. v2: removed discussion of
charged fluids and coupling to electromagnetic fields, which are submitted as
a separate paper for a clearer presentation v3: fixed typo in Eq.(9), updated
some reference
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