Energy Spectra of Developed Turbulence in Helium Superfluids

L’vov, Victor S.; Nazarenko, Sergey; Skrbek, L.

doi:10.1007/s10909-006-9230-8

Cited by 68 publications

(83 citation statements)

References 22 publications

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“…These experiments were also consistent in that they showed similarities between QT and CT. Vinen theoretically considered this similarity and proposed that the superfluid and the normal fluid are likely to be coupled by mutual friction at scales larger than the intervortex spacing l and would thus behave like a classical fluid [91]. This idea was confirmed by Kivotides et al through numerical simulation of coupled dynamics of a vortex filament and a normal fluid [92] and by L'vov et al through theoretical analysis of the two-fluid model [93].…”

Section: Quantum Turbulence At Finite Temperaturesmentioning

confidence: 93%

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Quantum hydrodynamics

Tsubota¹,

Kobayashi²,

Takeuchi³

2013

Physics Reports

154

181

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Quantum hydrodynamics in superfluid helium and atomic Bose-Einstein condensates (BECs) has been recently one of the most important topics in low temperature physics. In these systems, a macroscopic wave function (order parameter) appears because of Bose-Einstein condensation, which creates quantized vortices. Turbulence consisting of quantized vortices is called quantum turbulence (QT). The study of quantized vortices and QT has increased in intensity for two reasons. The first is that recent studies of QT are considerably advanced over older studies, which were chiefly limited to thermal counterflow in 4 He, which has no analogue with classical traditional turbulence, whereas new studies on QT are focused on a comparison between QT and classical turbulence. The second reason is the realization of atomic BECs in 1995, for which modern optical techniques enable the direct control and visualization of the condensate and can even change the interaction; such direct control is impossible in other quantum condensates like superfluid helium and superconductors. Our group has made many important theoretical and numerical contributions to the field of quantum hydrodynamics of both superfluid helium and atomic BECs. In this article, we review some of the important topics in detail. The topics of quantum hydrodynamics are diverse, so we have not attempted to cover all these topics in this article. We also ensure that the scope of this article does not overlap with our recent review article (arXiv:1004.5458), "Quantized vortices in superfluid helium and atomic Bose-Einstein condensates", and other review articles.

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Section: Quantum Turbulence At Finite Temperaturesmentioning

confidence: 93%

“…At t = 0, we turn on the rotation Ω x = Ω z = 0.6ω and elliptical deformation δ z = δ y = 0.025, and numerically calculate the time development of the GP equation (93). In the initial stage, vortices start to enter the BEC making the system quite anisotropic.…”

Section: Quantum Turbulence In Atomic Bose-einstein Condensatesmentioning

confidence: 99%

Quantum hydrodynamics

Tsubota¹,

Kobayashi²,

Takeuchi³

2013

Physics Reports

154

181

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“…What then happens to the energy spectrum? Although theoretical consideration has been given to this problem, 34) the answer remains controversial and has not yet been clarified. While this is an important problem, it is not investigated in the present study.…”

Section: New Experiments On Energy Spectramentioning

confidence: 99%

Quantum Turbulence

Tsubota

2008

J. Phys. Soc. Jpn.

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The present article reviews the recent developments in the physics of quantum turbulence. Quantum turbulence (QT) was discovered in superfluid 4 He in the 1950s, and the research has tended toward a new direction since the mid 90s. The similarities and differences between quantum and classical turbulence have become an important area of research. QT is comprised of quantized vortices that are definite topological defects, being expected to yield a model of turbulence that is much simpler than the classical model. The general introduction of the issue and a brief review on classical turbulence are followed by a description of the dynamics of quantized vortices. Then, we discuss the energy spectrum of QT at very low temperatures. At low wavenumbers, the energy is transferred through the Richardson cascade of quantized vortices, and the spectrum obeys the Kolmogorov law, which is the most important statistical law in turbulence; this classical region shows the similarity to conventional turbulence. At higher wavenumbers, the energy is transferred by the Kelvin-wave cascade on each vortex. This quantum regime depends strongly on the nature of each quantized vortex. The possible dissipation mechanism is discussed. Finally, important new experimental studies, which include investigations into temperaturedependent transition to QT, dissipation at very low temperatures, QT created by vibrating structures, and visualization of QT, are reviewed. The present article concludes with a brief look at QT in atomic BoseEinstein condensates.

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“…The second class of simplified models, Differential Approximation Models (DAMs), use a closure in which the multi-dimensional k-space integral in the wave interaction term (collision integral in the wave kinetic equation) is replaced by a nonlinear differential term that preserve the main properties and scalings of the Kelvin wave dynamics such as the energy and wave action conservations, scaling of the characteristic evolution time with respect to the wave intensity and the wavenumber k. DAMs have proved to be a very useful tool in the analysis of fluid dynamical and wave turbulence in the past [5,15,16,17,18,19,20,21], and here we study them in the context of the Kelvin wave turbulence. DAMs are particularly useful when one would like to understand the temporal evolution of the spectrum, when the physical forcing and dissipation need to be included, or when the Kelvin wave system is subject to more involved boundary conditions leading to simultaneous presence of two cascades in the same range of scales, or a thermalization (bottleneck) spectrum accumulation near a flux-reflecting boundary .…”

Section: Introductionmentioning

confidence: 99%

Modeling Kelvin Wave Cascades in Superfluid Helium

et al. 2009

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We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the latter and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and the closeness of the numerics for the higher-order DAM to the analytical predictions for the lower-order DAM .

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Energy Spectra of Developed Turbulence in Helium Superfluids

Abstract: We suggest a "minimal model" for the 3D turbulent energy spectra in super-

Cited by 68 publications

References 22 publications

Quantum hydrodynamics

Quantum hydrodynamics

Quantum Turbulence

Modeling Kelvin Wave Cascades in Superfluid Helium

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