Helium II thermal counterflow at large heat currents

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

doi:10.1103/physrevb.13.2918

Cited by 31 publications

(6 citation statements)

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“…Let us point out that this transition into a different flow regime is accompanied with a pronounced increase of fluctuations [17], characteristic of phase transitions. The data [16] also clearly show that on increasing the temperature the difference in counterflow velocity between state I and II transitions decreases and around 2 K they become indistinguishable.…”

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confidence: 81%

“…Now let increase the mean flow (i.e., the counterflow velocity U cf ), assuming the normal fluid velocity profile remains flat, and continue discussion in the reference frame where the normal fluid is at rest. It is an established experimental fact that the transition to state II occurs [1,16,17], with distinctly different features. It has been a long lasting challenge to explain the nature of this transition.…”

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confidence: 99%

“…Various counterflow experiments clearly display the transition from state I (Vinen) into state II (Kolmogorov) -the signature is pronounced on temperature and pressure difference versus heat input dependencies. We use here the data of Ladner, Childers and Tough [16] (their Table I), assuming that in state I the normal fluid profile is flat, again providing the unique frame of reference with the normal fluid at rest. Let us point out that this transition into a different flow regime is accompanied with a pronounced increase of fluctuations [17], characteristic of phase transitions.…”

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A flow phase diagram for helium superfluids

Skrbek

2004

Jetp Lett.

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The flow phase diagram for He II and 3 He-B is established and discussed based on available experimental data and the theory of Volovik [JETP Letters 78 (2003) 553]. The effective temperature -dependent but scale -independent Reynolds number Re ef f = 1/q = (1+α ′ )/α, where α and α ′ are the mutual friction parameters and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram allows identification of experimentally observed turbulent states I and II in counterflowing He II with the turbulent regimes suggested by Volovik.We consider the flow of quantum liquids such as He II or 3 He-B that can be described in the framework of the two fluid model (see, e.g., [1]). The normal fluid and superfluid velocity fields are coupled by two terms -by the Gorter-Mellink term that describes the mutual friction between these two liquids when vortices are present in the superfluid, and by the temperature gradient term, responsible, e.g., for the fountain effect. Circulation in the superfluid component is quantized in units of κ (0.997 × 10 −3 cm 2 /s for He II and 0.662 × 10 −3 cm 2 /s for 3 He-B); we assume singly quantized vortices.Let us consider a flow that can be approximated as isothermal [2]. Then the generally coupled complex flow of both components described by the two two-fluid equations can be simplified and becomes easier to understand, especially for two extreme cases:i) There are no quantized vortices in the flow. This represents a situation when the normal and superfluid velocity fields are fully decoupled. The normal fluid thus obeys the usual Navier-Stokes equation (and standard fluid dynamics) while the superfluid flow stays potential. Thus formally the normal fluid could become turbulent without a single vortex being present in the superfluidin the absence of mutual friction the superfluid simply does not know what is happening in the normal fluid. In practice, however, remnant vortices are almost always present, at least in He II [3], pinned to walls which are always rough on the atomic scale. In 3 He-B a vortex free sample is more likely, but the highly viscous normal fluid can hardly become turbulent in the laboratory sized container.ii) The normal fluid is at rest in some frame of reference. Such a possibility arises, for example, for 3 He-B, whose highly viscous normal component is effectively clamped by the walls in a laboratory size container. Moreover, we assume that the quantized vortices in the flow are arranged in such a way that the coarse-grained hydrodynamic equationobtained from the Euler equation after averaging over vortex lines [4], written in the frame of reference of the normal fluid, provides a sufficiently accurate description of the superflow. We shall return to the applicability of this equation later. The normal fluid thus provides a unique frame of reference and we have to deal only with the superfluid velocity v. By re-scaling the time such thatt =...

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A flow phase diagram for helium superfluids

Skrbek

2004

Jetp Lett.

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“…5.3. In liquid helium this causes a viscosity between the two fluids (normal and superfluid) and is the mechanism responsible for the vortex and turbulence generation [190,186].…”

Section: Turbulencementioning

confidence: 99%

Quantum turbulence in trapped atomic Bose–Einstein condensates

et al. 2016

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Turbulence, the complicated fluid behavior of nonlinear and statistical nature, arises in many physical systems across various disciplines, from tiny laboratory scales to geophysical and astrophysical ones. The notion of turbulence in the quantum world was conceived long ago by Onsager and Feynman, but the occurrence of turbulence in ultracold gases has been studied in the laboratory only very recently. Albeit new as a field, it already offers new paths and perspectives on the problem of turbulence. Herein we review the general properties of quantum gases at ultralow temperatures paying particular attention to vortices, their dynamics and turbulent behavior. We review the recent advances both from theory and experiment. We highlight, moreover, the difficulties of identifying and characterizing turbulence in gaseous Bose-Einstein condensates compared to ordinary turbulence and turbulence in superfluid liquid helium and spotlight future possible directions.

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“…Note that, despite its simple geometrical meaning, D does not depend on T because of the complicated temperature dependence of the terms which enter the definition of b. Figure 2 compares our D to experimental measurements [20] of the transition from the state T -1 to the state T -2 in cylindrical pipes. The quantitative agreement between theory and experiments is very good, more so if one considers the relative simplicity of our model.…”

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confidence: 88%

Transition to Normal Fluid Turbulence in Helium II

Melotte¹,

Barenghi²

1998

Phys. Rev. Lett.

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Turbulence in the heat flow of helium II manifests itself as a tangle of quantized vortex lines. It has been known for some time that there are two different forms of turbulence, called the T -1 and the T-2 turbulent states. Experiments show that when a critical velocity is exceeded there is a large increase of the superfluid vortex line density and a transition occurs from T -1 to T -2. Until now, the nature of the two turbulent states and of the critical velocity has been a mystery. We present a model which solves this problem by addressing for the first time the issue of the stability of the normal fluid. The computed transition is found to be in good agreement with the observations. [S0031-9007(98)06114-6] PACS numbers: 47.37. + q, 47.27.Cn, 67.40.Vs Some of the most interesting problems in the hydrodynamics of helium II involve quantized vortex lines [1]. Vortex lines appear, for example, when a container filled with helium is set into rotation. In this case, the vortex configuration is ordered: The vortices align along the rotation axis and form a uniform array. There are also situations in which the vortex system is disordered, for example, when the flow of helium is turbulent. Such turbulence, which manifests itself as a tangle of quantized vortex lines, is receiving renewed experimental attention: At the University of Lancaster, McClintock and co-workers [2] use intense vortex tangles as models of the early universe, and a superfluid wind tunnel is being built by Donnelly at the University of Oregon [3].Motivated by this experimental interest in hard turbulence, we address the more basic but still open question of what happens to turbulence at relatively low speed in the much-studied configuration called counterflow. Measurements in different apparati and using different techniques clearly show that there exist two separate states of turbulence in a circular pipe, called T-1 and T-2 in the literature [4]. T-1 and T -2 are superfluid vortex tangles characterized by very different vortex line densities, T -2's being much larger. If the flow speed exceeds a critical value, there is a transition from T-1 to T -2. The aim of this Letter is to explain for the first time the nature of the two turbulent states and of the critical velocity, until now an outstanding puzzle in the study of superfluid turbulence.The simplest experimental setup which has been widely used to study the superfluid vortex tangle is a counterflow pipe. One end of the pipe is closed and is provided with a resistor which dissipates a known heat flux W ; the other end of the pipe is open to the helium bath. What happens at small W can be easily understood using Landau's two-fluid model. The model describes helium as the intimate mixture of a superfluid component (which flows without any friction) and a normal fluid component (which carries the entropy and viscosity of the liquid). Using subscripts s and n to indicate the super and normal components, respectively, we call r s and r n the densities, v s and v n the velocities, j r s v s 1 r...

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Helium II thermal counterflow at large heat currents

Cited by 31 publications

References 17 publications

A flow phase diagram for helium superfluids

A flow phase diagram for helium superfluids

Quantum turbulence in trapped atomic Bose–Einstein condensates

Transition to Normal Fluid Turbulence in Helium II

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