Thermodynamical derivation of a hydrodynamical model of inhomogeneous superfluid turbulence

Inhomogeneous vortex tangles in counterflow superfluid turbulence: flow in convergent channels

“…We concentrate our attention on dynamical effects, whereas in [22,23] we considered this problem from a thermodynamic point of view, but with less diversity of dynamical equations than in the present paper. In this section we consider the following evolution equation instead of (2):…”

“…with the local counterflow velocity V (x) dependent on x as in (22). Local perturbations, due to the presence of these terms, with respect to Vinen's prediction shall be analyzed in detail.…”

“…As it is known, in Schwarz derivation of Vinen equation, the first term in the right hand size of equation (3) is substituted with γq · IL . The diffusion term in D and the term in α were considered by us in [22,23,25] from a thermodynamic point of view. The original proposal of this section is the term in α , that describes the role of the heat gradient as vortex source.…”

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

“…(6), but with different parameters, and one has the phononhydrodynamic regime, leading to an effective thermal conductivity proportional to the square of the radius of the channel. At temperatures lower than 1K, the phonon mean-free path in liquid helium is of the order of 0.5mm; in this case, and in absence of vortex lines (L = 0), the flux becomes increasingly ballistic and a slip heat flow along the wall must be incorporated [90], in such a way that the effective thermal conductivity becomes proportional to the radius, instead than to the square of the radius.…”

“…In steady states, the heat transfer in turbulent liquid helium [85,[89][90][91][92] may be described by an equation analogous to Eq. (6), taking the form…”