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

Galantucci, Luca; Sciacca, Michele; Barenghi, Carlo F.

doi:10.1103/physrevb.92.174530

Cited by 18 publications

(18 citation statements)

References 59 publications

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“…Therefore, it does not require any empirical assumption on the flow. Let us mention that such requirement is more difficult to fulfill [55] in vortex line (or vortex point) simulations of counterflows [18,[56][57][58][59][60][61][62]. Finally, the HVBK model has already served as a mathematical basis for a number of previous numerical counterflow studies, e.g., see Refs.…”

Section: B the Governing Equations Under A Boussinesq-like Hypothesismentioning

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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Section: B the Governing Equations Under A Boussinesq-like Hypothesismentioning

confidence: 99%

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

2017

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“…Galantucci et al studied the two-fluid coupled dynamics in counterflow quantum turbulence of 4 He in channels [82]. They used a 2D simulation of quantized vortices with the Navier-Stokes equation for the normal fluid component, and they investigated the velocity profiles realized by the two-fluid coupled dynamics.…”

Section: Two-dimensional Simulationmentioning

confidence: 99%

Numerical Studies of Quantum Turbulence

2017

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We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose-Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross-Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equilibrium. Hence, numerical studies have been indispensable for studying quantum turbulence. In fact, numerical studies have contributed in revealing the various problems of quantum turbulence. This article reviews the recent developments in numerical studies of quantum turbulence. We start with the motivation and the basics of quantum turbulence and invite readers to the frontier of this research. Though there are many important topics in the quantum turbulence of superfluid helium, this article focuses on inhomogeneous quantum turbulence in a channel, which has been motivated by recent visualization experiments. Atomic Bose-Einstein condensates are a modern issue in quantum turbulence, and this article reviews a variety of topics in the quantum turbulence of condensates e.g. two-dimensional quantum turbulence, weak wave turbulence, turbulence in a spinor condensate, etc., some of which has not been addressed in superfluid helium and paves the novel way for quantum turbulence researches. Finally we discuss open problems.

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“…1 (middle) and (right). By numerically simulating the two-fluid flow in a dynamically self-consistent way 24 (which allows the normal fluid to affect the vortex lines motion and viceversa, unlike the traditional approach of Schwarz [25][26][27][28][29] ), here we show that the normal fluid's circulation pattern coincides with the one schematically shown in Fig. 1 (right).…”

Section: Introductionmentioning

confidence: 72%

“…(refer to Ref. [24] and Supplementary Material for further insight on this numerical reconnection model).…”

Section: Modelmentioning

confidence: 99%

“…At this level of averaging, information about individual vortex lines is lost, hence it is possible to define continuous macroscopic superfluid velocity and vorticity fields, v s and ω s respectively. When computing coarse-grained quantities, we smooth the vortex distribution using a Gaussian kernel to prevent rapid fluctuations of the mutual friction force 24 (cfr. Supplementary Material for a detailed description of the coarse-graining procedure and its smearing effects).…”

Section: Modelmentioning

confidence: 99%

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Large-scale normal fluid circulation in helium superflows

2017

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We perform fully coupled numerical simulations of helium II pure superflows in a channel, with vortex-line\ud density typical of experiments. Peculiar to our model is the computation of the back-reaction of the superfluid\ud vortex motion on the normal fluid and the presence of solid boundaries.We recover the uniform vortex-line density\ud experimentally measured employing second sound resonators and we show that pure superflow in helium II is\ud associated with a large-scale circulation of the normal fluid which can be detected using existing particle-tracking\ud visualization techniques

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

Cited by 18 publications

References 59 publications

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

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

Numerical Studies of Quantum Turbulence

Large-scale normal fluid circulation in helium superflows

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