Non-Equilibrium Thermodynamics of Unsteady Superfluid Turbulence in Counterflow and Rotating Situations

The methods of nonequilibrium thermodynamics are used in this paper to relate an evolution equation for the vortex line density L, describing superfluid turbulence in the simultaneous presence of counterflow and rotation, to an evolution equation for the superfluid velocity vs, in order to be able to describe the full evolution of vs and L, instead of only L. Two alternative possibilities are analyzed, related to two possible alternative interpretations of a term coupling the effects of the counterflow and rotation on the vortex tangle, and which imply some differences between situations where counterflow and rotation vectors are parallel or orthogonal to each other. One arrives to a modified Gorter-Mellink equation with new terms dependent on the angular speed. Finally, two proposals to describe the effects of anisotropy of the vortex tangle on the dynamical equations for vs and L are examined.