Turbulent Superfluid Profiles and Vortex Density Waves in a Counterflow Channel
In this paper we study the two-dimensional profiles of the superfluid component velocity and the quantized vortex-points density in a counterflow channel where the influence of the walls cannot be neglected. The numerical results obtained show the presence of vortex density waves in the channel, as shown in a recent paper by means of the one-fluid model.
Non-classical Velocity Statistics in Counterflow Quantum Turbulence
In this work we analyse the statistical distribution of turbulent superfluid velocity components in a He II counterflow channel, via two-dimensional numerical simulations pre- sented in past studies. The Probability Density Functions (PDFs) of the superfluid velocity components are investigated at lengthscales smaller than the average intervortex spacing, for varying vortex densities and different wall-normal distances. The results obtained con- firm the non-classical signature of quantum turbulence already observed in past numerical studies.
Large-scale normal fluid circulation in helium superflows
We perform fully-coupled numerical simulations of helium II pure superflows in a channel, with vortex- line density typical of experiments. Peculiar to our model is the computation of the back-reaction of the superfluid vortex motion on the normal fluid and the presence of solid boundaries. We recover the uniform vortex-line density experimentally measured employing second sound resonators and we show that pure superflow in helium II is associated with a large-scale circulation of the normal fluid which can be detected using existing particle-tracking visualization techniques.
Refrigeration of an array of cylindrical nanosystems by superfluid helium counterflow
Abstract Motivated by the challenge of computer refrigeration, we study the limits set by the transition to quantum turbulence on the cooling of an array of heat-producing cylindrical nanosystems by means of superfluid-helium counterflow. The effective thermal conductivity in laminar counterflow superfluid helium is obtained in channels with rectangular cross section, through arrays of mutually parallel cylinders and in the combined situation of arrays of orthogonal cylinders inside the rectangular channel. The maximum cooling capacity is analyzed on the condition that turbulence is avoided and that the highest temperature does not exceed the lambda temperature.
Effective thermal conductivity of superuid helium: Laminar, turbulent and ballistic regimes
Abstract 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.
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 molec…
Refrigeration of an Array of Cylindrical Nanosystems by Flowing Superfluid Helium
We consider the refrigeration of an array of heat-dissipating cylindrical nanosystems as a simplified model of computer refrigeration. We explore the use of He II as cooling fluid, taking into account forced convection and heat conduction. The main conceptual and practical difficulties arise in the calculation of the effective thermal conductivity. Since He II does not follow Fourier’s law, the effective geometry-dependent conductivity must be extracted from a more general equation for heat transfer. Furthermore, we impose the restrictions that the maximum temperature along the array should be less than (Formula presented.) transition temperature and that quantum turbulence is avoided, in o…
Turbulent Superfluid Profiles in a Counterflow Channel
We have developed a two-dimensional model of quantised vortices in helium II moving under the influence of applied normal fluid and superfluid in a counterflow channel. We predict superfluid and vortex-line density profiles which could be experimentally tested using recently developed visualization techniques.
Classical and quantum vortex leapfrogging in two-dimensional channels
The leapfrogging of coaxial vortex rings is a famous effect which has been noticed since the times of Helmholtz. Recent advances in ultra-cold atomic gases show that the effect can now be studied in quantum fluids. The strong confinement which characterizes these systems motivates the study of leapfrogging of vortices within narrow channels. Using the two-dimensional point vortex model, we show that in the constrained geometry of a two-dimensional channel the dynamics is richer than in an unbounded domain: alongsize the known regimes of standard leapfrogging and the absence of it, we identify new regimes of backward leapfrogging and periodic orbits. Moreover, by solving the Gross-Pitaevskii…
Thermodynamics of computation and linear stability limits of superfluid refrigeration of a model computing array
We analyze the stability of the temperature profile of an array of computing nanodevices refrigerated by flowing superfluid helium, under variations in temperature, computing rate, and barycentric velocity of helium. It turns out that if the variation in dissipated energy per bit with respect to temperature variations is higher than some critical values, proportional to the effective thermal conductivity of the array, then the steady-state temperature profiles become unstable and refrigeration efficiency is lost. Furthermore, a restriction on the maximum rate of variation in the local computation rate is found.