A geometric one-fluid model of superfluid helium-4

Abstract

A standard description of superfluid helium-4 is based on the concept of two components (superfluid and normal), which leads to the so called two-fluid models. However, as there are no two kinds of atoms in helium-4, the two components cannot be separated. Superfluid helium-4 is not a mixture of two components, being rather a single fluid with two motions. Here, we present a geometric one-fluid model of superfluid helium-4, which is based on the Hamiltonian formulation of fluid mechanics. The model is derived from the kinetic theory of excitations (treated as an ideal Bose gas under the temperature $1.3K$) and average particle motions. It can be simplified to the Hall–Vinen–Bekharevich–Khalatnikov (HVBK) two-fluid model, where it removes one fitting parameter from the HVBK model, but it also gives extra terms beyond the HVBK model. Actually, we show that the two-fluid models are problematic in case of higher counter-flow velocities, where the usual splitting of total momentum to the superfluid and normal component becomes impossible. Finally, we show how vortex line density may be added to the state variables. The one-fluid model can be seen as a generalization of the two-fluid models that is geometrically consistent, fully compressible, with non-zero superfluid vorticity, and compatible with classical experiments.