In this paper we extend to nonlinear regimes a thermodynamical model of inhomogeneous superfluid turbulence previously formulated. 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 relations which constrain the constitutive quantities are deduced from the entropy principle, using the Liu method of Lagrange multipliers. Using a Legendre transformation, in the paper it is shown that the constitutive theory is determined by the choice of only two scalar functions of the intrinsic Lagrange multipliers.
Ardizzone, L.V., Gaeta, G. (2008). Extended Thermodynamics of Turbolent Superfluids:Nonlinear Costitutive Theory. In T. Brugarino, M. Mongiovi' (a cura di), Bollettino di Matematica pura e applicata (pp. 63-71). Roma.