Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence

In this paper, we use a non-equilibrium thermodynamic framework to generalize a previous nonlocal model of counterflow superfluid turbulence to incorporate some new coupled terms which may be relevant in the evolution of inhomogeneous vortex tangles. The theory chooses as fundamental fields the energy density, the heat flux, and the averaged vortex line length per unit volume. The constitutive quantities are assumed to depend on the fundamental fields and on their first spatial derivatives, allowing us to describe thermal dissipation, vortex diffusion and a new contribution to vortex formation. The restrictions on the constitutive relations are deduced from the entropy principle, using the Liu method of Lagrange multipliers. The form of the entropy and the entropy flux are compared with those obtained in the maximum-entropy formalism. The several non-local terms are discussed in detail to clarify their physical meaning, and an experiment is proposed to check their actual existence and measure their values.