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). © Europhysics Letters Association.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). © Europhysics Letters Association.

Dec 31, 20080 citations

Vortex-Density Fluctuations, Energy Spectra, and Vortical Regions in Superfluid Turbulence

Andrew William Baggaley, Jason Laurie, Carlo F. Barenghi

Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.

arXiv:1207.7296Physical Review LettersNov 14, 201294 citations

Vortex-Density Fluctuations, Energy Spectra, and Vortical Regions in Superfluid Turbulence

Andrew William Baggaley, Jason Laurie, Carlo Barenghi

Nov 1, 20120 citations

SUPERFLUID TURBULENCE AND DYNAMICS OF QUANTIZED VORTICES

Makoto Tsubota

Superfluid turbulence has been one of the most important problems of superfluid hydrodynamics, in which quantized vortices play a significant role. The recent research on superfluid turbulence enters a new stage rather different from the old ones chiefly devoted to thermal counterflow. After describing the current motivation on these topics, we discuss our research which studies the energy spectrum both by the vortex filament model and the Gross-Pitaevskii model. Both energy spectra are consistent with the Kolmogorov law, which shows a close similarity between superfluid (quantum) and classical turbulence.Superfluid turbulence has been one of the most important problems of superfluid hydrodynamics, in which quantized vortices play a significant role. The recent research on superfluid turbulence enters a new stage rather different from the old ones chiefly devoted to thermal counterflow. After describing the current motivation on these topics, we discuss our research which studies the energy spectrum both by the vortex filament model and the Gross-Pitaevskii model. Both energy spectra are consistent with the Kolmogorov law, which shows a close similarity between superfluid (quantum) and classical turbulence.

Kluwer Academic Publishers eBooksMay 4, 20060 citations

Vortex waves in a rotating superfluid

Karen L. Henderson, Carlo F. Barenghi

In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in 3 He-B, that q = α/(1 − α') < 1.3, where α and α' are mutual friction parameters. The authors put forward a qualitative argument that q is the ratio of dissipative and inertial forces on the superfluid, so for q < 1 inertial forces should overcome the dissipative forces and cause turbulence. Thus 1/ q would play, for a quantum fluid, the same role played in classical fluid dynamics by the Reynolds number (the ratio of inertial forces and dissipative forces in the Navier-Stokes equation). The aim of this work is to supplement this qualitative condition q = 1 with a quantitative calculation. By analysing both axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid, we find that in the long axial wavelength limit the condition q = 1 is the crossover between damped and propagating Kelvin waves; thus, for q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. Besides the relevance to the experiment of Finne et al. , the spectrum of oscillations which we find is relevant to the study of torsional oscillations of a rotating superfluid and generalises to three dimensions the spectrum of Kelvin waves on an isolated vortex line.In a recent experiment, Finne et al. discovered an intrinsic condition for the onset of quantum turbulence in 3 He-B, that q = α/(1 − α') < 1.3, where α and α' are mutual friction parameters. The authors put forward a qualitative argument that q is the ratio of dissipative and inertial forces on the superfluid, so for q < 1 inertial forces should overcome the dissipative forces and cause turbulence. Thus 1/ q would play, for a quantum fluid, the same role played in classical fluid dynamics by the Reynolds number (the ratio of inertial forces and dissipative forces in the Navier-Stokes equation). The aim of this work is to supplement this qualitative condition q = 1 with a quantitative calculation. By analysing both axisymmetric and non-axisymmetric modes of a continuum of vortices in a rotating superfluid, we find that in the long axial wavelength limit the condition q = 1 is the crossover between damped and propagating Kelvin waves; thus, for q > 1, perturbations on the vortices are unlikely to cause vortex reconnections and turbulence. Besides the relevance to the experiment of Finne et al. , the spectrum of oscillations which we find is relevant to the study of torsional oscillations of a rotating superfluid and generalises to three dimensions the spectrum of Kelvin waves on an isolated vortex line.

Europhysics Letters (EPL)Jul 1, 200411 citations

Bottleneck crossover between classical and quantum superfluid turbulence

Victor S. L’vov, Sergey Nazarenko, Oleksii Rudenko

We consider superfluid turbulence near absolute zero of temperature generated by classical means, e.g., towed grid or rotation but not by counterflow. We argue that such turbulence consists of a polarized tangle of mutually interacting vortex filaments with quantized vorticity. For this system, we predict and describe a bottleneck accumulation of the energy spectrum at the classical-quantum crossover scale $\ensuremath{\ell}$. Demanding the same energy flux through scales, the value of the energy at the crossover scale should exceed the Kolmogorov-41 (K41) spectrum by a large factor ${\mathrm{ln}}^{10∕3}(\ensuremath{\ell}∕{a}_{0})$ ($\ensuremath{\ell}$ is the mean intervortex distance and ${a}_{0}$ is the vortex core radius) for the classical and quantum spectra to be matched in value. One of the important consequences of the bottleneck is that it causes the mean vortex line density to be considerably higher than that based on K41 alone, and this should be taken into account in (re)interpretation of new (and old) experiments as well as in further theoretical studies.We consider superfluid turbulence near absolute zero of temperature generated by classical means, e.g., towed grid or rotation but not by counterflow. We argue that such turbulence consists of a polarized tangle of mutually interacting vortex filaments with quantized vorticity. For this system, we predict and describe a bottleneck accumulation of the energy spectrum at the classical-quantum crossover scale $\ensuremath{\ell}$. Demanding the same energy flux through scales, the value of the energy at the crossover scale should exceed the Kolmogorov-41 (K41) spectrum by a large factor ${\mathrm{ln}}^{10∕3}(\ensuremath{\ell}∕{a}_{0})$ ($\ensuremath{\ell}$ is the mean intervortex distance and ${a}_{0}$ is the vortex core radius) for the classical and quantum spectra to be matched in value. One of the important consequences of the bottleneck is that it causes the mean vortex line density to be considerably higher than that based on K41 alone, and this should be taken into account in (re)interpretation of new (and old) experiments as well as in further theoretical studies.

arXiv:nlin/0612018Physical Review BJul 26, 2007154 citations

{a}_{0}

is the vortex core radius) for the classical and quantum spectra to be matched in value. One of the important consequences of the bottleneck is that it causes the mean vortex line density to be considerably higher than that based on K41 alone, and this should be taken into account in (re)interpretation of new (and old) experiments as well as in further theoretical studies.