Helium II thermal counterflow: Temperature- and pressure-difference data and analysis in terms of the Vinen theory

Childers, R. K.; Tough, J. T.

doi:10.1103/physrevb.13.1040

Cited by 84 publications

(41 citation statements)

References 16 publications

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“…Table 1 shows the parameter γ as a function of T . The results quantitatively agree with the typical experimental observations of Childers and Tough [27,38]. Additionally, there is a critical velocity of turbulence, below which vortices disappear.…”

Section: Thermal Counterflow Turbulence By the Full Biot-savart Lawsupporting

confidence: 89%

Quantum hydrodynamics

Tsubota¹,

Kobayashi²,

Takeuchi³

2013

Physics Reports

154

181

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Quantum hydrodynamics in superfluid helium and atomic Bose-Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function (order parameter) appears because of Bose-Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in 4 He, which has no analogue with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), "Quantized vortices in superfluid helium and atomic Bose-Einstein condensates", and other review articles.

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Section: Thermal Counterflow Turbulence By the Full Biot-savart Lawsupporting

confidence: 89%

Quantum hydrodynamics

Tsubota¹,

Kobayashi²,

Takeuchi³

2013

Physics Reports

154

181

View full text Add to dashboard Cite

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“…Table 1. shows the values of γ for the different reconnection algorithms. The experimental value of γ at this temperature is 93 [10,45] ; Adachi et al [40] gave numerical results of γ = 109.6. …”

Section: Resultsmentioning

confidence: 88%

“…The superfluid flows in the opposite direction so that ρ n v n + ρ s v s = 0, where ρ n and ρ s are respectively the normal fluid and superfluid densities. We choose this form of turbulence as there has been a wealth of experimental studies [8,10,45], as well as some recent detailed numerical simulations [40,46]. Counterflow turbulence was also used in a recent numerical study by Kondaurova and Nemirovskii [47], where they reported that the use of a reconnection method, similar to the Type IV algorithm, gave a steady state solution for LIA simulations.…”

Section: Numerical Simulationsmentioning

confidence: 99%

The Sensitivity of the Vortex Filament Method to Different Reconnection Models

Baggaley

2012

J Low Temp Phys

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We present a detailed analysis on the effect of using different algorithms to model the reconnection of vortices in quantum turbulence, using the thin-filament approach. We examine differences between four main algorithms for the case of turbulence driven by a counterflow. In calculating the velocity field we use both the local induction approximation (LIA) and the full Biot-Savart integral. We show that results of Biot-Savart simulations are not sensitive to the particular reconnection method used, but LIA results are.

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“…A comprehensive review of the numerous models to describe the threshold of the T 1 instability is clearly beyond the scope of this paper; however, it is worth referring to a few of them to illustrate the level of controversy and, sometimes, confusion about this transition. For instance, the critical superfluid velocity V c of the T 1 instability is predicted to have either no dependence on the pipe diameter or channel hydraulic diameter d [7][8][9] dependence with or without a logarithmic correction [11,12] or a d −1 dependence with a logarithmic correction [13][14][15][16][17][18][19] or, at last, a pure d −1 dependence [20][21][22]. The models that predict no dependence on the diameter clearly overestimate the critical velocity but all the others reach reasonable degrees of agreement with some subsets of experimental data.…”

Section: A Critical Velocities In Superfluid Counterflowsmentioning

confidence: 99%

“…1 shows the typical setup of a counterflow experiment as used, for instance, in Ref. [21]. In this experimental apparatus, the cooling is achieved by evaporation at the liquid-vapor interface, whereas the counterflow is activated by Joule heating in a thermally insulated bulb at the bottom end of the (insulated) pipe.…”

Section: A the Geometrical Settingmentioning

confidence: 99%

Disproportionate entrance length in superfluid flows and the puzzle of counterflow instabilities

2017

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Systematic simulations of the two-fluid model of superfluid helium (He-II) encompassing the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) mutual coupling have been performed in two-dimensional pipe counterflows between 1.3 and 1.96 K. The numerical scheme relies on the lattice Boltzmann method. A Boussinesq-like hypothesis is introduced to omit temperature variations along the pipe. In return, the thermomechanical forcings of the normal and superfuid components are fueled by a pressure term related to their mass-density variations under an approximation of weak compressibility. This modeling framework reproduces the essential features of a thermally driven counterflow. A generalized definition of the entrance length is introduced to suitably compare entry effects (of different nature) at opposite ends of the pipe. This definition is related to the excess of pressure loss with respect to the developed Poiseuille-flow solution. At the heated end of the pipe, it is found that the entrance length for the normal fluid follows a classical law and increases linearly with the Reynolds number. At the cooled end, the entrance length for the superfluid is enhanced as compared to the normal fluid by up to one order of magnitude. At this end, the normal fluid flows into the cooling bath of He-II and produces large-scale superfluid vortical motions in the bath that partly re-enter the pipe along its sidewalls before being damped by mutual friction. In the superfluid entry region, the resulting frictional coupling in the superfluid boundary layer distorts the velocity profiles toward tail flattening for the normal fluid and tail raising for the superfluid. Eventually, a simple analytical model of entry effects allows us to re-examine the long-debated thresholds of T 1 and T 2 instabilities in superfluid counterflows. Inconsistencies in the T 1 thresholds reported since the 1960s disappear if an aspect-ratio criterion based on our modeling is used to discard data sets with the strongest entry effects. Furthermore, it is observed that entry effects can spuriously reproduce the signature of a T 2 transition with a normal flow remaining laminar.

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Helium II thermal counterflow: Temperature- and pressure-difference data and analysis in terms of the Vinen theory

Cited by 84 publications

References 16 publications

Quantum hydrodynamics

Quantum hydrodynamics

The Sensitivity of the Vortex Filament Method to Different Reconnection Models

Disproportionate entrance length in superfluid flows and the puzzle of counterflow instabilities

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