Thermodynamical derivation of a hydrodynamical model of inhomogeneous superfluid turbulence

In this paper, we build up a thermodynamical model of inhomogeneous superfluid turbulence to describe vortex diffusion in inhomogeneous turbulent tangles, and a coupling between second sound and vortex-density waves. The theory chooses as fundamental fields the density, the velocity, the energy density, the heat flux, and the averaged vortex line length per unit volume. The restrictions on the constitutive quantities are deduced from the entropy principle, using the Liu method of Lagrange multipliers. Field equations are written and the wave propagation is studied with the aim to describe the mutual interactions between the second sound and the vortex tangle. © 2007 The American Physical Society.