Alternative Vinen equation and its extension to rotating counterflow superfluid turbulence

Abstract

Two alternative Vinen's evolution equations for the vortex line density L in counterflow superfluid turbulence, are physically admissible and lead to analogous results in steady states. In Phys. Rev. B, 69, 094513 (2004) the most used of them was generalized to counterflow superfluid turbulence in rotating containers. Here, the analogous generalization for the alternative Vinen's equation is proposed. Both generalized Vinen's equations are compared with the experimental results, not only in steady-states but also in some unsteady situations. From this analysis follows that the solutions of the alternative Vinen's equation tend significantly faster to the corresponding final steady state values than the solutions of the usual Vinen's equation, and that the latter seems more suitable for the description of the experimental available data.

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

“…We have commented this aspect with detail in [23] and we summarize it in Figure 2, where we have plotted the dimensionless quantity Lr 2 in terms of the dimensionless heat flux α 0 Γ, with α 0 ≡ [30] for γ , and from [31] for the ratio γ /γ .…”

Non-equilibrium thermodynamics analysis of rotating counterflow superfluid turbulence

“…In Ref. [18], the extension of Vinen equation (2) to the case of V parallel to Ω was considered in order to explore whether these further arguments are enough to establish which of both equations, (1) or (2), is more suitable to describe actual experimental results. Of course, to have a satisfactory version of the macroscopic alternative Vinen equation (the same arguments are also valid for the extension of Vinen equation), the respective coefficients of all terms will have to be microscopically calculated and found to coincide with macroscopic observations.…”

“…The main aims of this paper is to extend the modified alternative Vinen equation, already proposed in [18], to include situations where the angle between V and Ω is not assigned (Section 2). Furthermore, the compatibility between the generalization of the alternative Vinen equation and the evolution equation for the velocity V s is studied from the non-equilibrium thermodynamics viewpoint (Section 3).…”

“…Since experimental results in pure counterflow are also described by the alternative Vinen equation, in [18] a generalization of it to rotating counterflow was proposed following the main lines of Ref. [15].…”

“…In Ref. [18], the dimensionless quantities appearing in the evolution equation (5) are determined by comparison with the experimental data in the steady state, obtaining…”