Non-equilibrium thermodynamics analysis of rotating counterflow superfluid turbulence

In two previous papers two evolution equations for the vortex line density $L$, proposed by Vinen, were generalized to rotating superfluid turbulence and compared with each other. Here, the already generalized alternative Vinen equation is extended to the case in which counterflow and rotation are not collinear. Then, the obtained equation is considered from the viewpoint of non-equilibrium thermodynamics. According with this formalism, the compatibility between this evolution equation for $L$ and that one for the velocity of the superfluid component is studied. The compatibility condition requires the presence of a new term dependent on the anisotropy of the tangle, which indicates how the friction force depends on the rotation rate.Comment: 18 pages, 3 figure

Waves propagation in turbulent superfluid helium in presence of combined rotation and counterflow

A complete study of the propagation of waves (namely longitudinal density and temperature waves, longitudinal and transversal velocity waves and heat waves) in turbulent superfluid helium is made in three situations: a rotating frame, a thermal counterflow, and the simultaneous combination of thermal counterflow and rotation. Our analysis aims to obtain as much as possible information on the tangle of quantized vortices from the wave speed and attenuation factor of these different waves, depending on their relative direction of propagation with respect to the rotation vector.Comment: 17 pages, 2 figure

Transition to ballistic regime for heat transport in helium II

The size-dependent and flux-dependent effective thermal conductivity of narrow capillaries filled with superfluid helium is analyzed from a thermodynamic continuum perspective. The classical Landau evaluation of the effective thermal conductivity of quiescent superfluid, or the Gorter-Mellinck regime of turbulent superfluids, are extended to describe the transition to ballistic regime in narrow channels wherein the radius $R$ is comparable to (or smaller than) the phonon mean-free path $\ell$ in superfluid helium. To do so we start from an extended equation for the heat flux incorporating non-local terms, and take into consideration a heat slip flow along the walls of the tube. This leads from an effective thermal conductivity proportional to $R^2$ (Landau regime) to another one proportional to $R\ell$ (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates.Comment: 16 page

Coupled normal fluid and superfluid profiles of turbulent helium II in channels

We perform fully coupled two--dimensional numerical simulations of plane channel helium II counterflows with vortex--line density typical of experiments. The main features of our approach are the inclusion of the back reaction of the superfluid vortices on the normal fluid and the presence of solid boundaries. Despite the reduced dimensionality, our model is realistic enough to reproduce vortex density distributions across the channel recently calculated in three--dimensions. We focus on the coarse--grained superfluid and normal fluid velocity profiles, recovering the normal fluid profile recently observed employing a technique based on laser--induced fluorescence of metastable helium molecules.Comment: 26 pages, 8 Figures, accepted for publication in Phys. Rev.

Effective thermal conductivity of helium II: from Landau to Gorter-Mellink regimes

The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter-Mellink regime). To do so we use an expression for the quantum vortex line density $L$ in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity

Effective thermal conductivity of superuid helium: Laminar, turbulent and ballistic regimes

In this paper we extend previous results on the effective thermal conductivity of liquid helium II in cylindrical channels to rectangular channels with high aspect ratio. The aim is to compare the results in the laminar regime, the turbulent regime and the ballistic regime, all of them obtained within a single mesoscopic formalism of heat transport, with heat flux as an independent variable

The saturation of decaying counterflow turbulence in helium II

We are concerned with the problem of the decay of a tangle of quantized vortices in He II generated by a heat current. Direct application of Vinen's equation yields the temporal scaling of vortex line density $L \sim t^{-1}$. Schwarz and Rozen [Phys. Rev. Lett. {\bf 66}, 1898 (1991); Phys. Rev. B {\bf 44}, 7563 (1991)] observed a faster decay followed by a slower decay. More recently, Skrbek and collaborators [Phys. Rev. E {\bf 67}, 047302 (2003)] found an initial transient followed by the same classical $t^{-3/2}$ scaling observed in the decay of grid-generated turbulence. We present a simple theoretical model which, we argue, contains the essential physical ingredients, and accounts for these apparently contradictory results.Comment: 19 pages, 5 figure

Waves propagation in superfluid helium in presence of combined rotation and counterflow

Using the linear macroscopic mono-fluid model of liquid helium II, in which the fundamental fields are the density ?, the velocity v, the temperature T and heat flux q and taking into account the expression of an additional pressure tensor Pw, introduced to describe phenomena linked to vortices, a complete study of wave propagation is made in the complex situation involving thermal counterflow in a rotating cylinde