Energy spectra of quantum turbulence: Large-scale simulation and modeling

Sasa, Narimasa; Kano, Takuma; Machida, Masahiko; L’vov, Victor S.; Rudenko, Oleksii; Tsubota, Makoto

doi:10.1103/physrevb.84.054525

Cited by 58 publications

(60 citation statements)

References 36 publications

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“…Because the GPE allows sound waves, to analyze turbulent vortex lines, it is necessary to extract from the total energy of the system (which is conserved during the evolution) the incompressible kinetic energy part whose spectrum is relevant to our discussion. To reach a steady-state, large-scale external forcing and small-scale damping was added to the GPE (43). The resulting turbulent energy spectrum agrees with KO-41 scaling in homogeneous (Fig.…”

Section: Numerical Experiments: Gpe Vfm and Hvbkmentioning

confidence: 75%

“…Numerical simulations of the GPE in a 3D periodic box have been performed for decaying turbulence (41) following an imposed arbitrary initial condition, and for forced turbulence (42,43). Because the GPE allows sound waves, to analyze turbulent vortex lines, it is necessary to extract from the total energy of the system (which is conserved during the evolution) the incompressible kinetic energy part whose spectrum is relevant to our discussion.…”

Section: Numerical Experiments: Gpe Vfm and Hvbkmentioning

confidence: 99%

See 1 more Smart Citation

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Barenghi

L’vov

Roche

2014

Proc. Natl. Acad. Sci. U.S.A.

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109

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Turbulence in superfluid helium is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, interpenetrating turbulent fluids: the first is inviscid with quantized vorticity, and the second is viscous with continuous vorticity. Despite this double nature, the observed spectra of the superfluid turbulent velocity at sufficiently large length scales are similar to those of ordinary turbulence. We present experimental, numerical, and theoretical results that explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller scales. He.) Besides the lack of viscosity, another major difference from ordinary (classical) fluids such as water or air is that, in helium, vorticity is constrained to vortex line singularities of fixed circulation κ = h=M, where h is Planck's constant, and M is the mass of the relevant boson (M = m 4 , the mass of He, the vortex core radius ξ ≈ 10 −10 m is comparable to the interatomic distance. Thus, quantization of circulation results in the appearance of another characteristic length scale: the mean separation between vortex lines, ℓ. In typical experiments (both in 4 He and 3 He), ℓ is orders of magnitude smaller than the scale D of the largest eddies but is also orders of magnitudes larger than ξ.There is a growing consensus (2) that superfluid turbulence at large scales R ℓ is similar to classical turbulence if excited similarly, for example by a moving grid. The idea is that motions at scales R ℓ should involve at least a partial polarization (3-5) of vortex lines and their organization into vortex bundles that, at such large scales, should mimic continuous hydrodynamic eddies. Therefore, one expects a classical Richardson-Kolmogorov energy cascade, with larger "eddies" breaking into smaller ones. The spectral signature of this classical cascade is indeed observed experimentally in superfluid helium. In the absence of viscosity, in superfluid turbulence the kinetic energy should cascade downscale without loss, until it reaches scales R ∼ ℓ, where the discreteness becomes important. It is also believed that the energy is further transferred downscales by the interacting Kelvin waves (helical perturbation of the individual vortex lines) where it is radiated away by thermal quasiparticles (phonons and rotons in 4 He). Although this scenario seems reasonable, crucial details are yet to be established. Our understanding of superfluid turbulence at scales of the order of ℓ is still at infancy stage, and what happens at scales below ℓ is a question of intensive debates. The "quasiclassical" region of scales, R ℓ, is better understood, but still less than classical hydrodynamic turbulence. The main reason is that at nonzero temperatures (but still below the critical temperature), superfluid helium is a two-fluid system. According to the theory of Landau and Tisza (6), it consists of two interpenetrating components: the inviscid superfluid, of density ρ s and velocity u s (associated to the quantum ground stat...

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Section: Numerical Experiments: Gpe Vfm and Hvbkmentioning

confidence: 75%

Section: Numerical Experiments: Gpe Vfm and Hvbkmentioning

confidence: 99%

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Barenghi

L’vov

Roche

2014

Proc. Natl. Acad. Sci. U.S.A.

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109

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“…On the hand, a quantized vortex is a stable and definite topological defect, so investigating QT may connect the cascade process in the real and wavenumber spaces. Actually, some numerical works of the VF [171,172] and GP [173] models found the bundle-like structure of quantized vortices, which is thought to be indispensable for the cascade process in CT.…”

Section: Energy Spectrum and Cascadementioning

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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“…Details of this activity can be read in a series of papers by L'vov, Nazarenko and coauthors 19 . 18,20,21 Let us consider this problem on the basis of general formula (1) (see 16 ). We take s(ξ ,t) = (x(z,t), y(z,t), z) and denote the two-dimensional vector (x(z,t), y(z,t)) as aρ(z,t) (where the dimensionless amplitude a ≪ 1).…”

Section: D Kelvin Waves Spectrum and 3d Velocity Spectrummentioning

confidence: 99%

Energy Spectrum of the 3D Velocity Field, Induced by Vortex Tangle

Nemirovskii

2012

J Low Temp Phys

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A review of various exactly solvable models on the determination of the energy spectra E(k) of 3D-velocity field, induced by chaotic vortex lines is proposed. This problem is closely related to the sacramental question whether a chaotic set of vortex filaments can mimic the real hydrodynamic turbulence. The quantity < v(k)v(−k) > can be exactly calculated, provided that we know the probability distribution functional P({s(ξ ,t)}) of vortex loops configurations. The knowledge of P({s(ξ ,t)}) is identical to the full solution of the problem of quantum turbulence and, in general, P is unknown. In the paper we discuss several models allowing to evaluate spectra in the explicit form. This cases include standard vortex configurations such as a straight line, vortex array and ring. Independent chaotic loops of various fractal dimension as well as interacting loops in the thermodynamic equilibrium also permit an analytical solution. We also describe the method of an obtaining the 3D velocity spectrum induced by the straight line perturbed with chaotic 1D Kelvin waves on it. PACS number(s): 67.25.dk, 47.37.+q, 03.75.Kk

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Energy spectra of quantum turbulence: Large-scale simulation and modeling

Cited by 58 publications

References 36 publications

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Numerical Studies of Quantum Turbulence

Energy Spectrum of the 3D Velocity Field, Induced by Vortex Tangle

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