A Continuum Theory of Superfluid Turbulence based on Extended Thermodynamics

A thermodynamical model of inhomogeneous superfluid turbulence previously formulated is extended in this paper to nonlinear regimes. The theory chooses as fundamental fields the density, the velocity, the energy density, and two extra variables, in order to include the specific properties of the fluid in consideration: the averaged vortex line length per unit volume and a renormalized expression of the heat flux. The relations which constrain the constitutive quantities are deduced from the second principle of thermodynamics using the Liu method of Lagrange multipliers. Using a Legendre transformation, it is shown that the constitutive theory is determined by the choice of only two scalar functions of the intrinsic Lagrange multipliers. The complete non-equilibrium expressions of the mass chemical potential, of the chemical potential of vortices, and of the entropy flux are determined: these relations are exact, because no approximation is used for their determination, and maintain their validity also for processes far from equilibrium.