Scaling laws of wave-cascading superfluid turbulence

Narita, Yasuhito

doi:10.1063/1.4985725

Cited by 3 publications

(1 citation statement)

References 60 publications

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“…We note that the present study is not the first to claim that the spectral index of the energy cascade at scales smaller than the mean intervortex distance is −3. For example, Narita theoretically estimated the value by constructing the phenomenological model and using the method for magneto-fluid turbulence theory [68]. Regarding numerical simulation, Yepez et al simulated quantum turbulence described by the GP equation using a unitary quantum lattice gas algorithm, and obtained the value −3 [69].…”

Section: On the Spectral Index Of Quantum Stress Cascadementioning

confidence: 99%

Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory

Tanogami

2020

Preprint

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To understand the effect of quantum stress on energy transfer across scales, we study threedimensional quantum turbulence as described by the Gross-Pitaevskii equation by using the analytical method exploited in the Onsager "ideal turbulence" theory. It is shown that two types of scale-to-scale energy flux exist that contribute to the energy cascade: the energy flux that is the same as in classical turbulence, and that induced by quantum stress. We then propose a definition of the inertial range for quantum turbulence small large , where large is determined through pressure-dilatation and small through quantum-stress-strain. Under assumptions on the regularity of the velocity and density fields, we show that, in the steady state in which the total mean kinetic energy is constant, the classical-type energy flux becomes dominant in i large , while the quantum-type flux becomes dominant in small i, where i is the mean intervortex distance. Correspondingly, the velocity power spectrum exhibits a power-law behavior:

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Section: On the Spectral Index Of Quantum Stress Cascadementioning

confidence: 99%

Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory

Tanogami

2020

Preprint

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A Mathematical Analysis of the Intermediate Behaviour of the Energy Cascades of Quantum Turbulence

Jou

Sciacca

2023

Acta Appl Math

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We propose a mathematical interpolation between several regimes of energy cascade in quantum turbulence in He II. On the basis of a physical interpretation of such mathematical expression we discuss in which conditions it is expected to appear an intermediate $k^{2}$ k 2 regime (equipartition regime) in the transition region between the hydrodynamic regime and the Kelvin wave regime (namely, between the $k^{-5/3}$ k − 5 / 3 and $k^{-1}$ k − 1 regions in coflow situations and between the $k^{-3}$ k − 3 and $k^{-1}$ k − 1 regions in counterflow situations). It is seen that if the energy rate transfer from the hydrodynamic region to the Kelvin wave region is sufficiently slow, such equipartition region will be present, but for higher values of such energy rate transfer it will disappear. For high rates of the energy rate transfer, the transition regime between the hydrodynamic and the Kelvin wave regimes will be monotonous, characterized by a negative exponent of $k$ k between $-5/3$ − 5 / 3 and −1 (or between −3 and −1), instead of the positive 2 exponent of the equipartition regime.

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Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory

Tanogami

2021

Phys. Rev. E

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We refute the criticism expressed in a Comment by Krstulovic, L'vov, and Nazarenko [arXiv:2107.10598] on our paper [Phys. Rev. E 103, 023106 (2021)]. We first show that quantization of circulation is not ignored in our analysis. Then, we propose a more sophisticated analysis to avoid a subtle problem with the regularity of the velocity field. We thus defend the main results of our paper, which predicts the double-cascade scenario where the quantum stress cascade follows the Richardson cascade. We also provide a conjecture on the relation between the Kelvin-wave cascade and the quantum stress cascade.

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Scaling laws of wave-cascading superfluid turbulence

Cited by 3 publications

References 60 publications

Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory

Theoretical analysis of quantum turbulence using the Onsager "ideal turbulence" theory

A Mathematical Analysis of the Intermediate Behaviour of the Energy Cascades of Quantum Turbulence

Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory

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