MOMENTUM, VORTICITY, AND HELICITY IN COVARIANT SUPERFLUID DYNAMICS

The convective and potential variational principles that can be used for alternative derivations of the same natural relativistic generalisation of the standard Landau theory of perfect superfluid dynamics are both characterised by the feature that, instead of attributing special importance to a partition in terms of certain non-conserved "superfluid" and "normal" current vectors jSν and jNν they accord a much more prominent role to certain "particle" and "thermal" momentum covectors μν and Θν of which the latter in particular has been unduly neglected in traditional discussions. The present article discusses the interdependence and the dynamic evolution of these quantities, drawing attention to consequences such as the conservation of the flux associated with the "thermal vorticity" form Wμν, and the conservation of the related "thermal helicity" current Hν. The comparison of this theory with some other conducting fluid theories is briefly discussed, and more particularly it is shown explicitly how this generalisation of the fully non-linear Landau theory relates to an analogous generalisation of the more restricted type of theory previously developed by Tisza and London, in which the quantities jSν and jNν had a more fundamental role. © 1992.