Michele Sciacca

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, is 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 l 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 R2 (Landau regime) to another one proportional to Rl (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates.

Integrability of an inhomogeneous nonlinear Schrödinger equation in Bose–Einstein condensates and fiber optics

In this paper, we investigate the integrability of an inhomogeneous nonlinear Schrodinger equation, which has several applications in many branches of physics, as in Bose–Einstein condensates and fiber optics. The main issue deals with Painleve property (PP) and Liouville integrability for a nonlinear Schrodinger-type equation. Solutions of the integrable equation are obtained by means of the Darboux transformation. Finally, some applications on fiber optics and Bose–Einstein condensates are proposed (including Bose–Einstein condensates in three-dimensional in cylindrical symmetry).

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.

Vortex length, vortex energy and fractal dimension of superfluid turbulence at very low temperature

By assuming a self-similar structure for Kelvin waves along vortex loops with successive smaller scale features, we model the fractal dimension of a superfluid vortex tangle in the zero temperature limit. Our model assumes that at each step the total energy of the vortices is conserved, but the total length can change. We obtain a relation between the fractal dimension and the exponent describing how the vortex energy per unit length changes with the length scale. This relation does not depend on the specific model, and shows that if smaller length scales make a decreasing relative contribution to the energy per unit length of vortex lines, the fractal dimension will be higher than unity. Finally, for the sake of more concrete illustration, we relate the fractal dimension of the tangle to the scaling exponents of amplitude and wavelength of a cascade of Kelvin waves.

Vortex dynamics in rotating counterflow and plane Couette and Poiseuille turbulence in superfluid helium

An equation previously proposed to describe the evolution of vortex-line density in rotating counterflow turbulent tangles in superfluid helium [Phys. Rev B 69, 094513 (2004)] is generalized to incorporate nonvanishing barycentric velocity and velocity gradients. Our generalization is compared with an analogous approach proposed by Lipniacki [Eur. J. Mech. B Fluids 25, 435 (2006)], and with experimental results by Swanson et al. [Phys. Rev. Lett. 50, 190 (1983)] in rotating counterflow, and it is used to evaluate the vortex density in plane Couette and Poiseuille flows of superfluid helium.

A mathematical model of counterflow superfluid turbulence describing heat waves and vortex-density waves

The interaction between vortex-density waves and high-frequency second sound in counterflow superfluid turbulence is examined, incorporating diffusive and elastic contributions of the vortex tangle. The analysis is based on a set of evolution equations for the energy density, the heat flux, the vortex line density, and the vortex flux, the latter being considered here as an independent variable, in contrast to previous works. The latter feature is crucial in the transition from diffusive to propagative behavior of vortex-density perturbations, which is necessary to interpret the details of high-frequency second sound.

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 Vinens equation yields the temporal scaling of vortex line density Lt −1 . Schwarz and Rozen (Phys. Rev. Lett. 66, 1898 (1991); Phys. Rev. B 44, 7563 (1991)) observed a faster decay followed by a slower decay. More recently, Skrbek and collaborators (Phys. Rev. E 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

Alternative Vinen Equation and its Extension to Rotating Counterflow Superfluid Turbulence

Abstract Two alternative Vinens evolution equations for the vortex line density L in counterflow superfluid turbulence are physically admissible and lead to analogous results in steady states. In Jou and Mongiovi` [Phys. Rev. B 69 (2004) 094513] the most used of them was generalized to counterflow superfluid turbulence in rotating containers. Here, the analogous generalization for the alternative Vinen equation is proposed. Both generalized Vinens equations are compared with the experimental results, not only in steady states but also in some unsteady situations. From this analysis follows that the stationary solutions of the alternative Vinen equation fit better the experimental data and that its unsteady solutions tend faster to the corresponding final steady-state values than the solutions of the usual Vinens equation.

Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics

In this Letter we show that a recent hydrodynamical model of superfluid turbulence describes vortex density waves and their effects on the speed of high-frequency second sound. In this frequency regime, the vortex dynamics is not purely diffusive, as for low frequencies, but exhibits ondulatory features, whose influence on the second sound is here explored.

Explicit Equations for Uniform Flow Depth

AbstractThe conventional approach in uniform open channel flow is to express the resistance coefficient in the Manning, Darcy-Weisbach, or Chezy form. However, for practical cross sections, includi...