Propagation of fourth sound in turbulent superfluids via extended thermodynamics

The work deals with further developments of a study previously initiated, in which a macroscopic one-fluid model of inhomogeneous turbulent superfluids, based on extended thermodynamics, had been formulated. In this work the study is carried on. First the influence of the remnant vortices on the propagation of the first and second sound is studied. Then a boundary condition able to explain the reversible flow of superfluid flowing through a thin capillary is postulated and two vector fields, which have the dimensions of velocity and can be interpreted as the velocities of normal and superfluid components, are introduced. By using these new fields, a comparison between this model and the Hall–Vinen–Bekarevich–Khalatnikov model, which uses a two-fluid framework, is performed. The propagation of the fourth sound inside a porous medium is investigated: it is shown that, when the fourth sound is propagated, in addition to the thermodynamic fields (density, velocity, temperature, and heat flux), also the vortex line density vibrates.