Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence

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

“…This situation is found in radial flows, flows in convergent channel, or flows in entrance regions. In the previous paper [22,23,25] we studied some aspects of this problem from a thermodynamic perspective, to examine the restrictions on the sign of some coefficients imposed by the second law of thermodynamics. Essentially, the terms in D and α in equation (3), plus other terms depending on temperature gradient that we have not considered here.…”

“…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.…”

K-ϵ-L model in turbulent superfluid helium

“…In the equations (2.1) a "dot" over the main fields stands for ∂ ∂t + v • ∇ and ∇ standing for the gradient operator. The term −D L ∇ 2 in the last equation of the system (2.1) takes vortex diffusion into account [18,28,29,30,31]. Let's assume that the mass density is constant, namely ρ = 0, which yields ∇ • v = 0 and assume an isothermal situation, in which the energy balance equation is not necessary.…”

Heat rectification in He II counterflow in radial geometries

“…, with S the entropy per unit volume and T the absolute temperature, ζ = λ 1 /τ 1 , with λ 1 the intrinsic thermal conductivity of the superfluid, and τ 1 the relaxation time of the heat flux, χ a coupling parameter between q and ∇L, and K the mutual friction coefficient between the vortex lines and the heat carriers, mainly phonons and rotons, through their corresponding collisions. Equations like (2) may be analyzed in general by using extended thermodynamics [26][27][28] and have been applied to the description of heat transport in several concrete situations [21,29,30]. A detailed discussion on the sign of coefficient χ was made in [22].…”

“…However, we have also focused a part of our analyses in inhomogeneous situations where L changes with position [37]. An especially, relevant and simple situation is that of cylindrical radial flows [29,30,37], which is relevant, for instance, in the cooling of cylindrical systems through superfluid helium.…”