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Skrbek L, Schmoranzer D, Midlik Š, Sreenivasan KR. Phenomenology of quantum turbulence in superfluid helium. Proc Natl Acad Sci U S A 2021; 118:e2018406118. [PMID: 33790051 PMCID: PMC8072252 DOI: 10.1073/pnas.2018406118] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Quantum turbulence-the stochastic motion of quantum fluids such as 4He and 3He-B, which display pure superfluidity at zero temperature and two-fluid behavior at finite but low temperatures-has been a subject of intense experimental, theoretical, and numerical studies over the last half a century. Yet, there does not exist a satisfactory phenomenological framework that captures the rich variety of experimental observations, physical properties, and characteristic features, at the same level of detail as incompressible turbulence in conventional viscous fluids. Here we present such a phenomenology that captures in simple terms many known features and regimes of quantum turbulence, in both the limit of zero temperature and the temperature range of two-fluid behavior.
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Affiliation(s)
- Ladislav Skrbek
- Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic;
| | - David Schmoranzer
- Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Šimon Midlik
- Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Katepalli R Sreenivasan
- Department of Physics, Courant Institute of Mathematical Sciences, Tandon School of Engineering, New York University, New York, NY 11201
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2
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Stagg GW, Parker NG, Barenghi CF. Superfluid Boundary Layer. PHYSICAL REVIEW LETTERS 2017; 118:135301. [PMID: 28409989 DOI: 10.1103/physrevlett.118.135301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2016] [Indexed: 06/07/2023]
Abstract
We model the superfluid flow of liquid helium over the rough surface of a wire (used to experimentally generate turbulence) profiled by atomic force microscopy. Numerical simulations of the Gross-Pitaevskii equation reveal that the sharpest features in the surface induce vortex nucleation both intrinsically (due to the raised local fluid velocity) and extrinsically (providing pinning sites to vortex lines aligned with the flow). Vortex interactions and reconnections contribute to form a dense turbulent layer of vortices with a nonclassical average velocity profile which continually sheds small vortex rings into the bulk. We characterize this layer for various imposed flows. As boundary layers conventionally arise from viscous forces, this result opens up new insight into the nature of superflows.
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Affiliation(s)
- G W Stagg
- Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| | - N G Parker
- Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| | - C F Barenghi
- Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
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3
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Krstulovic G. Grid superfluid turbulence and intermittency at very low temperature. Phys Rev E 2016; 93:063104. [PMID: 27415355 DOI: 10.1103/physreve.93.063104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2015] [Indexed: 06/06/2023]
Abstract
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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Affiliation(s)
- Giorgio Krstulovic
- Laboratoire J.L. Lagrange, UMR7293, Université de la Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, B.P. 4229, 06304 Nice Cedex 4, France
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4
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Baggaley AW, Tsepelin V, Barenghi CF, Fisher SN, Pickett GR, Sergeev YA, Suramlishvili N. Visualizing Pure Quantum Turbulence in Superfluid 3He: Andreev Reflection and its Spectral Properties. PHYSICAL REVIEW LETTERS 2015; 115:015302. [PMID: 26182103 DOI: 10.1103/physrevlett.115.015302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2015] [Indexed: 06/04/2023]
Abstract
Superfluid 3He-B in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in 3He-B by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the intervortex separation.
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Affiliation(s)
- A W Baggaley
- Joint Quantum Centre Durham-Newcastle, and School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - V Tsepelin
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - C F Barenghi
- Joint Quantum Centre Durham-Newcastle, and School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - S N Fisher
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - G R Pickett
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Y A Sergeev
- Joint Quantum Centre Durham-Newcastle, and School of Mechanical and Systems Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - N Suramlishvili
- Department of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
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Walmsley PM, Tompsett PA, Zmeev DE, Golov AI. Reconnections of quantized vortex rings in superfluid 4He at very low temperatures. PHYSICAL REVIEW LETTERS 2014; 113:125302. [PMID: 25279635 DOI: 10.1103/physrevlett.113.125302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2014] [Indexed: 06/03/2023]
Abstract
Collisions in a beam of unidirectional quantized vortex rings of nearly identical radii R in superfluid 4He in the limit of zero temperature (0.05 K) were studied using time-of-flight spectroscopy. Reconnections between two primary rings result in secondary vortex loops of both smaller and larger radii. Discrete steps in the distribution of flight times, due to the limits on the earliest possible arrival times of secondary loops created after either one or two consecutive reconnections, are observed. The density of primary rings was found to be capped at the value 500 cm-2R-1 independent of the injected density. This is due to collisions between rings causing the piling up of many other vortex rings. Both observations are in quantitative agreement with our theory.
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Affiliation(s)
- P M Walmsley
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - P A Tompsett
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - D E Zmeev
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom and Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - A I Golov
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
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Fisher SN, Jackson MJ, Sergeev YA, Tsepelin V. Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in 3He-B. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4659-66. [PMID: 24704872 PMCID: PMC3970857 DOI: 10.1073/pnas.1312543110] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Andreev reflection of quasiparticle excitations provides a sensitive and passive probe of flow in superfluid (3)He-B. It is particularly useful for studying complex flows generated by vortex rings and vortex tangles (quantum turbulence). We describe the reflection process and discuss the results of numerical simulations of Andreev reflection from vortex rings and from quantum turbulence. We present measurements of vortices generated by a vibrating grid resonator at very low temperatures. The Andreev reflection is measured using an array of vibrating wire sensors. At low grid velocities, ballistic vortex rings are produced. At higher grid velocities, the rings collide and reconnect to produce quantum turbulence. We discuss spatial correlations of the fluctuating vortex signals measured by the different sensor wires. These reveal detailed information about the formation of quantum turbulence and about the underlying vortex dynamics.
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Affiliation(s)
- Shaun Neil Fisher
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Martin James Jackson
- Faculty of Mathematics and Physics, Charles University in Prague, 121 16 Prague, Czech Republic
| | - Yuri A. Sergeev
- School of Mechanical and Systems Engineering, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom; and
- Joint Quantum Centre Durham–Newcastle, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Viktor Tsepelin
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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7
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Vinen WF, Skrbek L. Quantum turbulence generated by oscillating structures. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4699-706. [PMID: 24704877 PMCID: PMC3970854 DOI: 10.1073/pnas.1312551111] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The paper summarizes important aspects of quantum turbulence that have been studied successfully with oscillating structures. It describes why some aspects are proving hard to interpret, and it outlines the need for new types of experiment and new developments in theoretical and computational work.
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Affiliation(s)
- William F. Vinen
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom; and
| | - Ladislav Skrbek
- Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
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Baggaley AW, Barenghi CF, Sergeev YA. Three-dimensional inverse energy transfer induced by vortex reconnections. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:013002. [PMID: 24580315 DOI: 10.1103/physreve.89.013002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2013] [Indexed: 06/03/2023]
Abstract
In low-temperature superfluid helium, viscosity is zero and vorticity takes the form of discrete vortex filaments of fixed circulation and atomic thickness. We present numerical evidence of three-dimensional inverse energy transfer from small length scales to large length scales in superfluid turbulence generated by a flow of vortex rings. We argue that the effect arises from the anisotropy of the flow, which favors vortex reconnections of vortex loops of the same polarity, and that it has been indirectly observed in the laboratory. The effect opens questions about analogies with related processes in ordinary turbulence.
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Affiliation(s)
- Andrew W Baggaley
- School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, United Kingdom
| | - Carlo F Barenghi
- Joint Quantum Centre Durham-Newcastle and School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
| | - Yuri A Sergeev
- Joint Quantum Centre Durham-Newcastle and School of Mechanical and Systems Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom
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9
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Bradley DI, Fisher SN, Guénault AM, Haley RP, O'Sullivan S, Pickett GR, Tsepelin V. Fluctuations and Correlations of Pure Quantum Turbulence in Superfluid 3He-B. PHYSICAL REVIEW LETTERS 2008; 101:065302. [PMID: 18764468 DOI: 10.1103/physrevlett.101.065302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2008] [Revised: 07/01/2008] [Indexed: 05/26/2023]
Abstract
We describe the first measurements of line-density fluctuations and spatial correlations of quantum turbulence in superfluid 3He-B. All of the measurements are performed in the low-temperature regime, where the normal-fluid density is negligible. The quantum turbulence is generated by a vibrating grid. The vortex-line density is found to have large length-scale correlations, indicating large-scale collective motion of vortices. Furthermore, we find that the power spectrum of fluctuations versus frequency obeys a -5/3 power law which verifies recent speculations that this behavior is a generic feature of fully developed quantum turbulence, reminiscent of the Kolmogorov spectrum for velocity fluctuations in classical turbulence.
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Affiliation(s)
- D I Bradley
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
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Goto R, Fujiyama S, Yano H, Nago Y, Hashimoto N, Obara K, Ishikawa O, Tsubota M, Hata T. Turbulence in boundary flow of superfluid 4He triggered by free vortex rings. PHYSICAL REVIEW LETTERS 2008; 100:045301. [PMID: 18352293 DOI: 10.1103/physrevlett.100.045301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2007] [Indexed: 05/26/2023]
Abstract
The transition to turbulence in the boundary flow of superfluid 4He is investigated using a vortex-free vibrating wire. At high wire vibration velocities, we found that stable alternating flow around the wire enters a turbulent phase triggered by free vortex rings. Numerical simulations of vortex dynamics demonstrate that vortex rings can attach to the surface of an oscillating obstacle and expand unstably due to the boundary flow of the superfluid, forming turbulence. Experimental investigations indicate that the turbulent phase continues even after stopping the injection of vortex rings, which is also confirmed by the simulations.
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Affiliation(s)
- R Goto
- Graduate School of Science, Osaka City University, Osaka 558-8585, Japan
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12
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Charalambous D, Skrbek L, Hendry PC, McClintock PVE, Vinen WF. Experimental investigation of the dynamics of a vibrating grid in superfluid 4He over a range of temperatures and pressures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:036307. [PMID: 17025743 DOI: 10.1103/physreve.74.036307] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2006] [Indexed: 05/12/2023]
Abstract
In an earlier paper [Nichol, Phys. Rev. E, 70, 056307 (2004)] some of the present authors presented the results of an experimental study of the dynamics of a stretched grid driven into vibration at or near its resonant frequency in isotopically pure superfluid 4He over a range of pressures at a very low temperature, where the density of normal fluid is negligible. In this paper we present the results of a similar study, based on a different grid, but now including the temperature range where the normal fluid density is no longer insignificant. The new grid is very similar to the old one except for a small difference in the character of its surface roughness. In many respects the results at low temperature are similar to those for the old grid. At low amplitudes the results are somewhat history dependent, but in essence there is no damping greater than that in vacuo. At a critical amplitude corresponding to a velocity of about 50 mms(-1) there is a sudden and large increase in damping, which can be attributed to the generation of new vortex lines. Strange shifts in the resonant frequency at intermediate amplitudes observed with the old grid are no longer seen, however they must therefore have been associated with the different surface roughness, or perhaps were due simply to some artifact of the old grid, the details of which we are currently unable to determine. With the new grid we have studied both the damping at low amplitudes due to excitations of the normal fluid, and the dependence of the supercritical damping on temperature. We present evidence that in helium at low amplitudes there may be some enhancement in the effective mass of the grid in addition to that associated with potential flow of the helium. In some circumstances small satellite resonances are seen near the main fundamental grid resonance, which are attributed to coupling to some other oscillatory system within the experimental cell.
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Affiliation(s)
- D Charalambous
- Department of Physics, University of Lancaster, Lancaster LA1 4YB, United Kingdom.
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Finne AP, Eltsov VB, Eska G, Hänninen R, Kopu J, Krusius M, Thuneberg EV, Tsubota M. Vortex multiplication in applied flow: A precursor to superfluid turbulence. PHYSICAL REVIEW LETTERS 2006; 96:085301. [PMID: 16606194 DOI: 10.1103/physrevlett.96.085301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2005] [Revised: 10/27/2005] [Indexed: 05/08/2023]
Abstract
A surface-mediated process is identified in 3He-B which generates vortices at a roughly constant rate. It precedes a faster form of turbulence where intervortex interactions dominate. This precursor becomes observable when vortex loops are introduced in low-velocity rotating flow at sufficiently low mutual friction dissipation at temperatures below 0.5Tc. Our measurements indicate that the formation of new loops is associated with a single vortex interacting in the applied flow with the sample boundary. Numerical calculations show that the single-vortex instability arises when a helical Kelvin wave expands from a reconnection kink at the wall and then intersects again with the wall.
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Affiliation(s)
- A P Finne
- Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 2200, FIN-02015 HUT, Finland
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Bradley DI, Clubb DO, Fisher SN, Guénault AM, Haley RP, Matthews CJ, Pickett GR, Tsepelin V, Zaki K. Decay of pure quantum turbulence in superfluid 3He-B. PHYSICAL REVIEW LETTERS 2006; 96:035301. [PMID: 16486721 DOI: 10.1103/physrevlett.96.035301] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2005] [Indexed: 05/06/2023]
Abstract
We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.
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Affiliation(s)
- D I Bradley
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
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