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Vinen, W. F.; Niemela, J. J.

doi:10.1023/a:1019695418590

Cited by 491 publications

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“…As in classical 3D hydrodynamic turbulence [8], a turbulent Kolmogorov cascade is observed at scales in between the energy injection scale and mean inter-vortex distance [9,10]. At scales smaller than the inter-vortex distance, the quantized vortices can not be considered as a continuous field and different mechanisms appear to be relevant to carry the energy to scales small enough to be dissipated by phonon emission [11,12]. Numerical simulations of different models confirm this scenario [13,[15][16][17].…”

Section: Introductionmentioning

confidence: 78%

Grid superfluid turbulence and intermittency at very low temperature

Krstulovic

2016

Phys. Rev. E

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Low-temperature grid generated turbulence is investigated by using numerical simulations of the Gross-Pitaevskii equation. The statistics of regularized velocity increments are studied. Increments of the incompressible velocity are found to be skewed for turbulent states. Results are later confronted with the (quasi) homogeneous and isotropic Taylor-Green flow, revealing the universality of the statistics. For this flow, the statistics are found to be intermittent and a Kolmogorov constant close to the one of classical fluid is found for the second order structure function.

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Section: Introductionmentioning

confidence: 78%

Grid superfluid turbulence and intermittency at very low temperature

Krstulovic

2016

Phys. Rev. E

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“…Though there are several existing review articles on QT [1,2,3,4,5,6], this articles focuses on the numerical studies of QT. The contents of this article are as follows.…”

Section: Introductionmentioning

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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“…Such quantum turbulence (QT) consists of definite topological defects known as quantized vortices and has recently attracted interest as a way to better understand turbulence [3].…”

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confidence: 99%

Quantum turbulence in a trapped Bose-Einstein condensate

2007

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We study quantum turbulence in trapped Bose-Einstein condensates by numerically solving the Gross-Pitaevskii equation. Combining rotations around two axes, we successfully induce quantum turbulent state in which quantized vortices are not crystallized but tangled. The obtained spectrum of the incompressible kinetic energy is consistent with the Kolmogorov law, the most important statistical law in turbulence. The study of turbulence has a very long history, going back at least to Leonardo da Vinci, and understanding and controlling turbulence are great dreams of science and technology. Classical turbulence (CT) exhibits highly complicated configurations of eddies. Many studies have been devoted to the dynamical and statistical properties of CT after Kolmogorov's pioneering work [1,2] on flow at very high Reynolds number, namely, fully developed CT. The characteristic behavior of CT has been believed to be sustained by the Richardson cascade of eddies from large to small scales. However, in CT, there is no universal way to identify each eddy, because they continue to nucleate, diffuse, and disappear. As a result, many aspects of CT are still not perfectly understood.Turbulence is also possible in superfluids, such as the superfluid phases of 4 He and 3 He. Such quantum turbulence (QT) consists of definite topological defects known as quantized vortices and has recently attracted interest as a way to better understand turbulence [3].Superfluid 4 He has been extensively studied, in particular with relation to quantized vortices [4]. Below the lambda temperature T λ = 2.17 K, liquid 4 He enters the superfluid state through Bose-Einstein condensation. The hydrodynamics of superfluid 4 He is strongly influenced by quantum effects; any rotational motion is sustained by quantized vortices with quantized circulation κ = /m, where m is the particle mass. There are two typical cooperative phenomena of quantized vortices. One is a vortex lattice under rotation in which straight quantized vortices form a triangular lattice along the rotation axis [5]. The other is a vortex tangle in QT in which vortices become tangled in a flow [6,7].QT has been studied as a problem in low temperature physics since its discovery some 50 years ago. Its study has recently entered a new stage beyond low temperature physics. One of the main motivations of recent studies is to investigate the relationship between QT and CT. Some similarities between the two types of turbulence have been experimentally observed in superfluid 4 He [8, 9] and 3 He [10,11], and have been theoretically confirmed by numerical simulations of the quantized vortex-filament model [12] and a model using the Gross-Pitaevskii (GP) equation [13,14,15,16]. In particular, we have successfully obtained the Kolmogorov law for QT, which is one of the most important statistical laws in CT [17] by a numerical simulation of the GP equation [14,15].The similarity between QT and CT means that QT is an ideal prototype to study the statistics and vortex dynamics of turbulence, because QT ...

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Cited by 491 publications

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Grid superfluid turbulence and intermittency at very low temperature

Grid superfluid turbulence and intermittency at very low temperature

Numerical Studies of Quantum Turbulence

Quantum turbulence in a trapped Bose-Einstein condensate

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