Variational derivation of Newtonian multi-fluid hydrodynamics
Abstract
We present a formalism to derive Newtonian multi-fluid hydrodynamics from a ``convective'' variational principle, which was initially introduced in general relativity by Taub and subsequently largely developed by Carter. This method provides a straightforward way to obtain the general form of the equations of motion for a wide range of hydrodynamic systems containing an arbitrary number of interacting charged and uncharged fluids and superfluids. The use of time shifts in addition to purely spatial variations allows us further to describe even dissipative processes that lead to entropy creation, for example chemical reactions, friction or the presence of external non-conservative forces. In order to illustrate the generality of this framework we explicitly discuss its application to perfect fluids, thermally and electrically conducting fluids, superfluid He4, neutron star matter and superconductors.Keywords
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