Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1504.06691 · Physical Review B

Dynamics of the density of quantized vortex lines in superfluid turbulence

Dmytro Khomenko, Л. П. Кондаурова, Victor S. L’vov, Pankaj Kumar Mishra, Anna Pomyalov, Itamar Procaccia

Published May 22, 2015• 34 citations
arXivHTMLPDF

Abstract

The quantization of vortex lines in superfluids requires the introduction of their density $\mathcal{L}(\mathbit{r},t)$ in the description of quantum turbulence. The space homogeneous balance equation for $\mathcal{L}(t)$, proposed by Vinen on the basis of dimensional and physical considerations, allows a number of competing forms for the production term $\mathcal{P}$. Attempts to choose the correct one on the basis of time-dependent homogeneous experiments ended inconclusively. To overcome this difficulty we announce here an approach that employs an inhomogeneous channel flow which is very suitable to distinguish the implications of the various possible forms of the desired equation. We demonstrate that the originally selected form which was extensively used in the literature is in strong contradiction with our data. We therefore present a new form of an inhomogeneous equation for $\mathcal{L}(\mathbit{r},t)$ that is in agreement with our data and propose that it should be considered for further studies of superfluid turbulence.

DOI
10.1103/physrevb.91.180504

Related papers

Dynamics of the vortex line density in superfluid counterflow turbulence

Dmytro Khomenko, Victor S. L’vov, Anna Pomyalov +1 more

Describing superfluid turbulence at intermediate scales between the intervortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines $\mathcal{L}$. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides $\mathcal{L}$ and the normal and superfluid velocity fields. In this paper, we offer a minimal closure using one additional anisotropy parameter ${I}_{l0}$. Using the example of counterflow superfluid turbulence, we derive two coupled closure equations for the vortex line density and the anisotropy parameter ${I}_{l0}$ with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.

arXiv:1709.00671•Physical review. B./Physical review. B•Jan 16, 2018•5 citations

Generation of Superfluid Turbulence Deduced from Simple Dynamical Rules

Klaus W. Schwarz

It is postulated that a quantized-vortex tangle obeys classical vortex dynamics, and that internal line-line crossings can result in topology-changing reconnections. Implementation of these rules leads to a quantitatively successful description of homogeneous superfluid turbulence.

Physical Review Letters•Jul 26, 1982•146 citations

Modeling quantum fluid dynamics at nonzero temperatures

Natalia G. Berloff, Marc Brächet, Nick P. Proukakis

The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures.

Proceedings of the National Academy of Sciences•Mar 24, 2014•80 citations

Classical and quantum regimes of superfluid turbulence

Григорий Ефимович Воловик

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q −1 playing the same role as the Reynolds number Re= UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re≫1 in classical hydrodynamics, and q ≪1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re s = UR/κ , which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.

arXiv:cond-mat/0310021•Journal of Experimental and Theoretical Physics Letters•Nov 1, 2003•71 citations

Vortex spectrum in superfluid turbulence: Interpretation of a recent experiment

P.-E. Roche, C. F. Barenghi

We discuss a recent experiment in which the spectrum of the vortex line density fluctuations has been measured in superfluid turbulence. The observed frequency dependence of the spectrum, f − 5/3 , disagrees with classical vorticity spectra if, following the literature, the vortex line density is interpreted as a measure of the vorticity or enstrophy. We argue that the disagrement is solved if the vortex line density field is decomposed into a polarised field (which carries most of the energy) and an isotropic field (which is responsible for the spectrum).

arXiv:0709.0368•Europhysics Letters (EPL)•Jan 3, 2008•43 citations

Diffusive Decay of the Vortex Tangle and Kolmogorov turbulence in quantum fluids

Sergey K. Nemirovskii, Л. П. Кондаурова

The idea that chaotic set of quantum vortices can mimic classical turbulence, or at least reproduce many main features, is currently actively being developed. Appreciating significance of the challenging problem of the classical turbulence it can be expressed that the idea to study it in terms of quantized line is indeed very important and may be regarded as a breakthrough. For this reason, this theory should be carefully scrutinized. One of the basic arguments supporting this point of view is the fact that vortex tangle decays at zero temperature, when the apparent mechanism of dissipation (mutual friction) is absent. Since the all possible mechanisms of dissipation of the vortex energy, discussed in the literature, are related to the small scales, it is natural to suggest that the Kolmogorov cascade takes the place with the flow of the energy, just as in the classical turbulence. In a series of recent experiment attenuation of vortex line density was observed and authors attribute this decay to the properties of the Kolmogorov turbulence. In the present work we discuss alternative possibility of decay of the vortex tangle, which is not related to dissipation at small scales. This mechanism is just the diffusive like spreading of the vortex tangle. We discuss a number of the key experiments, considering them both from the point of view of alternative explanation and of the theory of Kolmogorov turbulence in quantum fluids.

arXiv:1007.0480•Jul 3, 2010•0 citations
The quantization of vortex lines in superfluids requires the introduction of their density L(\mathbitr,t)\mathcal{L}(\mathbit{r},t)L(\mathbitr,t) in the description of quantum turbulence. The space homogeneous balance equation for L(t)\mathcal{L}(t)L(t), proposed by Vinen on the basis of dimensional and physical considerations, allows a number of competing forms for the production term P\mathcal{P}P. Attempts to choose the correct one on the basis of time-dependent homogeneous experiments ended inconclusively. To overcome this difficulty we announce here an approach that employs an inhomogeneous channel flow which is very suitable to distinguish the implications of the various possible forms of the desired equation. We demonstrate that the originally selected form which was extensively used in the literature is in strong contradiction with our data. We therefore present a new form of an inhomogeneous equation for L(\mathbitr,t)\mathcal{L}(\mathbit{r},t)L(\mathbitr,t) that is in agreement with our data and propose that it should be considered for further studies of superfluid turbulence.
Describing superfluid turbulence at intermediate scales between the intervortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines L\mathcal{L}L. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides L\mathcal{L}L and the normal and superfluid velocity fields. In this paper, we offer a minimal closure using one additional anisotropy parameter Il0{I}_{l0}Il0​. Using the example of counterflow superfluid turbulence, we derive two coupled closure equations for the vortex line density and the anisotropy parameter Il0{I}_{l0}Il0​ with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.
The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures.
We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q −1 playing the same role as the Reynolds number Re= UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re≫1 in classical hydrodynamics, and q ≪1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re s = UR/κ , which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.
We discuss a recent experiment in which the spectrum of the vortex line density fluctuations has been measured in superfluid turbulence. The observed frequency dependence of the spectrum, f − 5/3 , disagrees with classical vorticity spectra if, following the literature, the vortex line density is interpreted as a measure of the vorticity or enstrophy. We argue that the disagrement is solved if the vortex line density field is decomposed into a polarised field (which carries most of the energy) and an isotropic field (which is responsible for the spectrum).
The idea that chaotic set of quantum vortices can mimic classical turbulence, or at least reproduce many main features, is currently actively being developed. Appreciating significance of the challenging problem of the classical turbulence it can be expressed that the idea to study it in terms of quantized line is indeed very important and may be regarded as a breakthrough. For this reason, this theory should be carefully scrutinized. One of the basic arguments supporting this point of view is the fact that vortex tangle decays at zero temperature, when the apparent mechanism of dissipation (mutual friction) is absent. Since the all possible mechanisms of dissipation of the vortex energy, discussed in the literature, are related to the small scales, it is natural to suggest that the Kolmogorov cascade takes the place with the flow of the energy, just as in the classical turbulence. In a series of recent experiment attenuation of vortex line density was observed and authors attribute this decay to the properties of the Kolmogorov turbulence. In the present work we discuss alternative possibility of decay of the vortex tangle, which is not related to dissipation at small scales. This mechanism is just the diffusive like spreading of the vortex tangle. We discuss a number of the key experiments, considering them both from the point of view of alternative explanation and of the theory of Kolmogorov turbulence in quantum fluids.