Friction on quantized vortices in helium II. A review

Barenghi, Carlo F.; Donnelly, Russell J.; Vinen, W. F.

doi:10.1007/bf00682247

Cited by 283 publications

(260 citation statements)

References 40 publications

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“…While these results are indeed simple, they have the same order of magnitude than the coefficients B and B ′ of the previous theory 45 and also of the experiments 44 . The agreement is better for B than for B ′ .…”

Section: Vortices and Mutual Frictionsupporting

confidence: 72%

Liquid4Henear the superfluid transition in the presence of a heat current and gravity

Haussmann¹

1999

Phys. Rev. B

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The effects of a heat current and gravity in liquid 4 He near the superfluid transition are investigated for temperatures above and below T λ . We present a renormalization-group calculation based on model F for the Green's function in a self-consistent approximation which in quantum manyparticle theory is known as the Hartree approximation. The approach can handle the average order parameter ψ = 0 above and below T λ and includes effects of vortices. We calculate the thermal conductivity λT(∆T, Q) and the specific heat C(∆T, Q) for all temperature differences ∆T = T −T λ and heat currents Q in the critical regime. Furthermore, we calculate the temperature profile T (z). Below T λ we find a second correlation length ξ1 ∼ Q −1 (T λ − T ) +ν which describes the dephasing of the order-parameter field due to vortices. We find dissipation and mutual friction of the superfluidnormal fluid counterflow and calculate the Gorter-Mellink coefficient A. We compare our theoretical results with recent experiments.

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Section: Vortices and Mutual Frictionsupporting

confidence: 72%

Liquid4Henear the superfluid transition in the presence of a heat current and gravity

Haussmann¹

1999

Phys. Rev. B

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“…The normal fluid affects the superfluid through these terms. On the other hand, the dynamics of the normal fluid component are described by the forced Navier-Stokes equation [67,70,71,72] …”

Section: Coupled Dynamics Of the Two-fluid Modelmentioning

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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“…The first three are temperature dependent material properties, and κ = h/m (where h is Planck's constant and m is the mass of the molecules of the thermal superfluid). As shown by Barenghi, Donnelly & Vinen (1983), the microscopic mutual friction coefficients d and d t can be expressed in terms of the macroscopic experimentally measured mutual friction coefficients of Hall & Vinen (1956). By specifying appropriate initial and boundary conditions, we evolve V n (x, t) and X s (x, t) according to nonlinear integro-differential laws that we discuss next.…”

Section: Model Of Thermal Superfluid Dynamicsmentioning

confidence: 99%

Spreading of superfluid vorticity clouds in normal-fluid turbulence

Kivotides

2010

J. Fluid Mech.

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In this paper, we formulate a self-consistent model of thermal superfluid dynamics. By solving it, we analyse the problem of superfluid vorticity cloud propagation in normal-fluid turbulence. We show that superfluid cloud expansion is driven by pattern-forming superfluid vortex instabilities taking place in the interface layer between the cloud's bulk and the outer undisturbed normal-fluid turbulence. The radius of the cloud increases linearly with time. Mutual friction transfers energy from the normal-fluid turbulence to the superfluid cloud, whilst damping the smallest normal-fluid turbulence motions. This damping action is much weaker than viscous dissipation effects in a corresponding pure normal-fluid turbulence. The energy spectrum of superfluid turbulence presents the k −3 scaling that characterizes the spiral superfluid vorticity patterns of normal vortex tube-superfluid vortex interactions. The corresponding k −2 pressure spectrum signifies the singular nature of superfluid vorticity. These two scalings coincide in wavenumber space with the Kolmogorov regime in the normal-fluid turbulence. We compute a fractal dimension d f ≈ 1.652 for superfluid vorticity. Due to simpler underlying superfluid vortex dynamics in relation to the strongly nonlinear classical vortex dynamics, this fractal dimension is smaller than the corresponding dimension of vortex tube centrelines in classical turbulence.

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Friction on quantized vortices in helium II. A review

Cited by 283 publications

References 40 publications

Liquid4Henear the superfluid transition in the presence of a heat current and gravity

Liquid4Henear the superfluid transition in the presence of a heat current and gravity

Numerical Studies of Quantum Turbulence

Spreading of superfluid vorticity clouds in normal-fluid turbulence

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