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.
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http://dx.doi.org/10.1103/PhysRevLett.109.205304 | DOI Listing |
Phys Rev Lett
December 2024
Department of Engineering Science, University of Electro-Communications, Tokyo 182-8585, Japan.
When a two-component mixture of immiscible fluids is stirred, the fluids are split into smaller domains with more vigorous stirring. We numerically investigate the sizes of such domains in a fully developed turbulent state of a two-component superfluid stirred with energy input rate ε. For the strongly immiscible condition, the typical domain size is shown to be proportional to ε^{-2/5}, as predicted by the Kolmogorov-Hinze theory in classical fluids.
View Article and Find Full Text PDFProc Natl Acad Sci U S A
March 2024
Department of Physics, Courant Institute of Mathematical Sciences, Tandon School of Engineering, New York University, New York, NY 11201.
Transition from laminar to turbulent states of classical viscous fluids is complex and incompletely understood. Transition to quantum turbulence (QT), by which we mean the turbulent motion of quantum fluids such as helium II, whose physical properties depend on quantum physics in some crucial respects, is naturally more complex. This increased complexity arises from superfluidity, quantization of circulation, and, at finite temperatures below the critical, the two-fluid behavior.
View Article and Find Full Text PDFPhys Rev E
October 2023
Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India.
We obtain the von Kármán-Howarth relation for the stochastically forced three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model of superfluid turbulence in helium (^{4}He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analytical studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) P(γ), of the ratio γ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as P(γ)∼γ^{3}, for γ≪1, and P(γ)∼γ^{-3}, for γ≫1. Furthermore, we show that the PDF P(θ) of the angle θ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: P(θ)∼θ for θ≪θ_{*} and P(θ)∼θ^{-4} for θ_{*}≪θ≪1, where θ_{*} is a crossover angle that we estimate.
View Article and Find Full Text PDFRev Sci Instrum
October 2023
Univ. Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France.
An analytical model of open-cavity second sound resonators is presented and validated against simulations and experiments in superfluid helium using a new resonator design that achieves unprecedented resolution. The model incorporates diffraction, geometrical misalignments, and flow through the cavity and is validated using cavities operated up to their 20th resonance in superfluid helium. An important finding is that resonators can be optimized to selectively sense either the quantum vortex density carried by the throughflow-as typically done in the literature-or the mean velocity of the throughflow.
View Article and Find Full Text PDFSci Adv
July 2023
Université Grenoble Alpes, Institut Néel, CNRS UPR2940, 25 rue des Martyrs, BP 166, Grenoble Cedex 9 38042, France.
Quantum vortices are a core element of superfluid dynamics and elusively hold the keys to our understanding of energy dissipation in these systems. We show that we are able to visualize these vortices in the canonical and higher-symmetry case of a stationary rotating superfluid bucket. Using direct visualization, we quantitatively verify Feynman's rule linking the resulting quantum vortex density to the imposed rotational speed.
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