Thermal Counterflow in a Periodic Channel with Solid Boundaries

Baggaley, Andrew W.; Laurie, Jason

doi:10.1007/s10909-014-1226-1

Cited by 31 publications

(43 citation statements)

References 40 publications

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“…3a,c. The VLD is higher near the walls, similar to the steady-state tangles with the parabolic profile of the driving normal-fluid velocity, obtained under periodic streamwise conditions [25][26][27]29,36 . Two edges of the tangle are different: a narrow and sharp edge is formed in the direction of V n and a wide and less steep edge in the direction of V s .…”

Section: Evolution Of Vldsupporting

confidence: 77%

“…Recent advances in the experimental techniques, including flow visualization [22][23][24] , as well as increasing computing power, renewed the interest to the spatial inhomogeneity due to presence of channel walls 19,[25][26][27][28][29][30][31] and spatially-resolved investigations of the transient behavior in the thermal counterflow 32 . The latter work showed that the vortex tangle that eventually fills the whole channel, grows starting from a number of remnant vortex rings.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of turbulent plugs in a superfluid He4 channel counterflow

Pomyalov

2020

Phys. Rev. B

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Quantum turbulence in superfluid He-4 in narrow channels often takes the form of moving localized vortex tangles. Such tangles, called turbulent plugs, also serve as building blocks of quantum turbulence in wider channels. We report on a numerical study of various aspects of the dynamics and structure of turbulent plugs in a wide range of governing parameters. The unrestricted growth of the tangle in a long channel provides a unique view on a natural tangle structure including superfluid motion at many scales. We argue that the edges of the plugs propagate as turbulent fronts, following the advection-diffusion-reaction dynamics. This analysis shows that the dynamics of the two edges of the tangle have distinctly different nature. We provide an analytic solution of the equation of motion for the fronts that define their shape, velocities and effective diffusivity, and analyze these parameters for various flow conditions. arXiv:2002.05002v2 [cond-mat.other]

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Section: Evolution Of Vldsupporting

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Dynamics of turbulent plugs in a superfluid He4 channel counterflow

Pomyalov

2020

Phys. Rev. B

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“…The vortex tangle reaches the statistically steady state even if the counterflow is spatially inhomogeneous. The fluctuations are much larger than those in uniform counterflow [31] or those between two parallel plates [74,75]. The period of the oscillation is about 0.7 s, and the oscillation consists of four stages (a)-(d).…”

Section: Poiseuille and Tail-flattened Normal Flow In A Ductmentioning

confidence: 95%

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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“…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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Thermal Counterflow in a Periodic Channel with Solid Boundaries

Cited by 31 publications

References 40 publications

Dynamics of turbulent plugs in a superfluid He4 channel counterflow

Dynamics of turbulent plugs in a superfluid He4 channel counterflow

Numerical Studies of Quantum Turbulence

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

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