1
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Verma AK, Shukla S, Shukla V, Basu A, Pandit R. Statistical properties of superfluid turbulence in ^{4}He from the Hall-Vinen-Bekharevich-Khalatnikov model. Phys Rev E 2023; 108:045103. [PMID: 37978641 DOI: 10.1103/physreve.108.045103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/19/2023] [Accepted: 09/08/2023] [Indexed: 11/19/2023]
Abstract
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. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, as well as the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature T, by using the experimentally determined mutual-friction coefficients for superfluid helium ^{4}He, so our results are of direct relevance to superfluid turbulence in this system.
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Affiliation(s)
- Akhilesh Kumar Verma
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Sanjay Shukla
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Vishwanath Shukla
- Department of Physics, Indian Institute of Technology, Kharagpur, Kharagpur 721302, India
| | - Abhik Basu
- Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700064, West Bengal, India
| | - Rahul Pandit
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
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2
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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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3
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Tanogami T. Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory. Phys Rev E 2021; 103:023106. [PMID: 33736002 DOI: 10.1103/physreve.103.023106] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 01/27/2021] [Indexed: 11/07/2022]
Abstract
We investigate three-dimensional quantum turbulence as described by the Gross-Pitaevskii model using the analytical method exploited in the Onsager "ideal turbulence" theory. We derive the scale independence of the scale-to-scale kinetic energy flux and establish a double-cascade scenario: At scales much larger than the mean intervortex ℓ_{i}, the Richardson cascade becomes dominant, whereas at scales much smaller than ℓ_{i}, another type of cascade is induced by quantum stress. We then evaluate the corresponding velocity power spectrum using a phenomenological argument. The relation between this cascade, which we call quantum stress cascade, and the Kelvin-wave cascade is also discussed.
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4
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Dutta K. Mutual-friction-driven turbulent statistics in the hydrodynamic regime of superfluid ^{3}He-B. Phys Rev E 2019; 99:033111. [PMID: 30999398 DOI: 10.1103/physreve.99.033111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2018] [Indexed: 06/09/2023]
Abstract
It is well known that the turbulence that evolves from the tangles of vortices in quantum fluids at scales larger than the typical quantized vortex spacing ℓ has a close resemblance with classical turbulence. The temperature-dependent mutual friction parameter α(T) drives the turbulent statistics in the hydrodynamic regime of quantum fluids that involves a self-similar cascade of energy. From a simple theoretical analysis, here we show that superfluid ^{3}He-B in the presence of mutual damping exhibits a k^{-5/3} Kolmogorov energy spectrum in the entire inertial range ℓ<r<L at temperature T≲0.2T_{c}, while at T≳0.2T_{c} dissipation begins to dominate larger eddies exhibiting a k^{-3} spectrum toward the energy pumping scale L. At T≈0.35T_{c}, eddies of all size, being highly affected by damping, exhibit a k^{-3} spectrum in the entire inertial range. The consistency of this result with the predictions of recent direct numerical simulations indicates that the present theoretical framework is applicable in quantifying the hydrodynamic regime of quantum turbulence.
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Affiliation(s)
- Kishore Dutta
- Department of Physics, Handique Girls' College, Guwahati 781 001, India
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5
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Kobayashi M, Cugliandolo LF. Quench dynamics of the three-dimensional U(1) complex field theory: Geometric and scaling characterizations of the vortex tangle. Phys Rev E 2017; 94:062146. [PMID: 28085364 DOI: 10.1103/physreve.94.062146] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2016] [Indexed: 11/07/2022]
Abstract
We present a detailed study of the equilibrium properties and stochastic dynamic evolution of the U(1)-invariant relativistic complex field theory in three dimensions. This model has been used to describe, in various limits, properties of relativistic bosons at finite chemical potential, type II superconductors, magnetic materials, and aspects of cosmology. We characterize the thermodynamic second-order phase transition in different ways. We study the equilibrium vortex configurations and their statistical and geometrical properties in equilibrium at all temperatures. We show that at very high temperature the statistics of the filaments is the one of fully packed loop models. We identify the temperature, within the ordered phase, at which the number density of vortex lengths falls off algebraically and we associate it to a geometric percolation transition that we characterize in various ways. We measure the fractal properties of the vortex tangle at this threshold. Next, we perform infinite rate quenches from equilibrium in the disordered phase, across the thermodynamic critical point, and deep into the ordered phase. We show that three time regimes can be distinguished: a first approach toward a state that, within numerical accuracy, shares many features with the one at the percolation threshold; a later coarsening process that does not alter, at sufficiently low temperature, the fractal properties of the long vortex loops; and a final approach to equilibrium. These features are independent of the reconnection rule used to build the vortex lines. In each of these regimes we identify the various length scales of the vortices in the system. We also study the scaling properties of the ordering process and the progressive annihilation of topological defects and we prove that the time-dependence of the time-evolving vortex tangle can be described within the dynamic scaling framework.
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Affiliation(s)
- Michikazu Kobayashi
- Department of Physics, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan
| | - Leticia F Cugliandolo
- Sorbonne Universités, Université Pierre et Marie Curie-Paris 6, Laboratoire de Physique Théorique et Hautes Energies UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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6
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Barenghi CF, Sergeev YA, Baggaley AW. Regimes of turbulence without an energy cascade. Sci Rep 2016; 6:35701. [PMID: 27761005 PMCID: PMC5071764 DOI: 10.1038/srep35701] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2016] [Accepted: 09/30/2016] [Indexed: 11/17/2022] Open
Abstract
Experiments and numerical simulations of turbulent 4He and 3He-B have established that, at hydrodynamic length scales larger than the average distance between quantum vortices, the energy spectrum obeys the same 5/3 Kolmogorov law which is observed in the homogeneous isotropic turbulence of ordinary fluids. The importance of the 5/3 law is that it points to the existence of a Richardson energy cascade from large eddies to small eddies. However, there is also evidence of quantum turbulent regimes without Kolmogorov scaling. This raises the important questions of why, in such regimes, the Kolmogorov spectrum fails to form, what is the physical nature of turbulence without energy cascade, and whether hydrodynamical models can account for the unusual behaviour of turbulent superfluid helium. In this work we describe simple physical mechanisms which prevent the formation of Kolmogorov scaling in the thermal counterflow, and analyze the conditions necessary for emergence of quasiclassical regime in quantum turbulence generated by injection of vortex rings at low temperatures. Our models justify the hydrodynamical description of quantum turbulence and shed light into an unexpected regime of vortex dynamics.
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Affiliation(s)
- C. F. Barenghi
- Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
| | - Y. A. Sergeev
- Joint Quantum Centre (JQC) Durham-Newcastle, School of Mechanical and Systems Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
| | - A. W. Baggaley
- Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
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7
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Zmeev DE, Walmsley PM, Golov AI, McClintock PVE, Fisher SN, Vinen WF. Dissipation of Quasiclassical Turbulence in Superfluid ^{4}He. PHYSICAL REVIEW LETTERS 2015; 115:155303. [PMID: 26550733 DOI: 10.1103/physrevlett.115.155303] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2015] [Indexed: 06/05/2023]
Abstract
We compare the decay of turbulence in superfluid ^{4}He produced by a moving grid to the decay of turbulence created by either impulsive spin-down to rest or by intense ion injection. In all cases, the vortex line density L decays at late time t as L∝t^{-3/2}. At temperatures above 0.8 K, all methods result in the same rate of decay. Below 0.8 K, the spin-down turbulence maintains initial rotation and decays slower than grid turbulence and ion-jet turbulence. This may be due to a decoupling of the large-scale superfluid flow from the normal component at low temperatures, which changes its effective boundary condition from no-slip to slip.
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Affiliation(s)
- D E Zmeev
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - P M Walmsley
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - A I Golov
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - S N Fisher
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - W F Vinen
- School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
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8
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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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9
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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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10
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Berloff NG, Brachet M, Proukakis NP. Modeling quantum fluid dynamics at nonzero temperatures. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4675-82. [PMID: 24704874 PMCID: PMC3970864 DOI: 10.1073/pnas.1312549111] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The detailed understanding of the intricate dynamics of quantum fluids, in particular in the rapidly growing subfield of quantum turbulence which elucidates the evolution of a vortex tangle in a superfluid, requires an in-depth understanding of the role of finite temperature in such systems. The Landau two-fluid model is the most successful hydrodynamical theory of superfluid helium, but by the nature of the scale separations it cannot give an adequate description of the processes involving vortex dynamics and interactions. In our contribution we introduce a framework based on a nonlinear classical-field equation that is mathematically identical to the Landau model and provides a mechanism for severing and coalescence of vortex lines, so that the questions related to the behavior of quantized vortices can be addressed self-consistently. The correct equation of state as well as nonlocality of interactions that leads to the existence of the roton minimum can also be introduced in such description. We review and apply the ideas developed for finite-temperature description of weakly interacting Bose gases as possible extensions and numerical refinements of the proposed method. We apply this method to elucidate the behavior of the vortices during expansion and contraction following the change in applied pressure. We show that at low temperatures, during the contraction of the vortex core as the negative pressure grows back to positive values, the vortex line density grows through a mechanism of vortex multiplication. This mechanism is suppressed at high temperatures.
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Affiliation(s)
- Natalia G. Berloff
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
- Cambridge-Skoltech Quantum Fluids Laboratory, Skolkovo Institute of Science and Technology ul. Novaya, Skolkovo 143025, Russian Federation
| | - Marc Brachet
- Centre National de la Recherche Scientifique, Laboratoire de Physique Statistique, Université Pierre-et-Marie-Curie Paris 06, Université Paris Diderot, Ecole Normale Supérieure, 75231 Paris Cedex 05, France; and
| | - Nick P. Proukakis
- Joint Quantum Centre (JQC) Durham–Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
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11
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White AC, Anderson BP, Bagnato VS. Vortices and turbulence in trapped atomic condensates. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4719-26. [PMID: 24704880 PMCID: PMC3970853 DOI: 10.1073/pnas.1312737110] [Citation(s) in RCA: 63] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
After more than a decade of experiments generating and studying the physics of quantized vortices in atomic gas Bose-Einstein condensates, research is beginning to focus on the roles of vortices in quantum turbulence, as well as other measures of quantum turbulence in atomic condensates. Such research directions have the potential to uncover new insights into quantum turbulence, vortices, and superfluidity and also explore the similarities and differences between quantum and classical turbulence in entirely new settings. Here we present a critical assessment of theoretical and experimental studies in this emerging field of quantum turbulence in atomic condensates.
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Affiliation(s)
- Angela C. White
- Joint Quantum Centre (JQC), Durham-Newcastle, School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Brian P. Anderson
- College of Optical Sciences, University of Arizona, Tucson, AZ 85721; and
| | - Vanderlei S. Bagnato
- Instituto de Física de São Carlos, Universidade de São Paulo 13560-970 São Carlos, Sao Paulo, Brazil
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12
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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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13
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Barenghi CF, Skrbek L, Sreenivasan KR. Introduction to quantum turbulence. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4647-52. [PMID: 24704870 PMCID: PMC3970860 DOI: 10.1073/pnas.1400033111] [Citation(s) in RCA: 194] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.
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Affiliation(s)
- Carlo F. Barenghi
- Joint Quantum Centre Durham-Newcastle and School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom
| | - Ladislav Skrbek
- Faculty of Mathematics and Physics, Charles University, 12116 Prague, Czech Republic; and
| | - Katepalli R. Sreenivasan
- Department of Physics and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
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14
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Vortex filament method as a tool for computational visualization of quantum turbulence. Proc Natl Acad Sci U S A 2014; 111 Suppl 1:4667-74. [PMID: 24704873 DOI: 10.1073/pnas.1312535111] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The vortex filament model has become a standard and powerful tool to visualize the motion of quantized vortices in helium superfluids. In this article, we present an overview of the method and highlight its impact in aiding our understanding of quantum turbulence, particularly superfluid helium. We present an analysis of the structure and arrangement of quantized vortices. Our results are in agreement with previous studies showing that under certain conditions, vortices form coherent bundles, which allows for classical vortex stretching, giving quantum turbulence a classical nature. We also offer an explanation for the differences between the observed properties of counterflow and pure superflow turbulence in a pipe. Finally, we suggest a mechanism for the generation of coherent structures in the presence of normal fluid shear.
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15
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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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16
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Energy and angular momentum balance in wall-bounded quantum turbulence at very low temperatures. Nat Commun 2013; 4:1614. [DOI: 10.1038/ncomms2618] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2012] [Accepted: 02/19/2013] [Indexed: 11/08/2022] Open
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17
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Silaev MA. Universal mechanism of dissipation in Fermi superfluids at ultralow temperatures. PHYSICAL REVIEW LETTERS 2012; 108:045303. [PMID: 22400854 DOI: 10.1103/physrevlett.108.045303] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2011] [Indexed: 05/31/2023]
Abstract
We show that the vortex dynamics in Fermi superfluids at ultralow temperatures is governed by the local heating of the vortex cores creating the heat flux carried by nonequilibrium quasiparticles emitted by moving vortices. This mechanism provides a universal zero temperature limit of dissipation in Fermi superfluids. For the typical experimental conditions realized by the turbulent motion of ^{3}He-B, the temperature of the vortex cores is estimated to be of the order 0.2 T(c). The dispersion of Kelvin waves is derived, and the heat flow generated by Kelvin cascade is shown to have a value close to that experimentally observed.
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Affiliation(s)
- Mihail A Silaev
- Institute for Physics of Microstructures RAS, 603950 Nizhny Novgorod, Russia
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18
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19
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Kerr RM. Vortex stretching as a mechanism for quantum kinetic energy decay. PHYSICAL REVIEW LETTERS 2011; 106:224501. [PMID: 21702604 DOI: 10.1103/physrevlett.106.224501] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2010] [Indexed: 05/31/2023]
Abstract
A pair of perturbed antiparallel quantum vortices, simulated using the three-dimensional Gross-Pitaevskii equations, is shown to be unstable to vortex stretching. This results in kinetic energy K(∇ψ) being converted into interaction energy E(I) and eventually local kinetic energy depletion that is similar to energy decay in a classical fluid, even though the governing equations are Hamiltonian and energy conserving. The intermediate stages include the generation of vortex waves, their deepening, multiple reconnections, the emission of vortex rings and phonons, and the creation of an approximately -5/3 kinetic energy spectrum at high wave numbers. All of the wave generation and reconnection steps follow from interactions between the two original vortices. A four vortex example is given to demonstrate that some of these steps might be general.
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Affiliation(s)
- Robert M Kerr
- Department of Mathematics, University of Warwick, Coventry, United Kingdom
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20
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Eltsov VB, de Graaf R, Heikkinen PJ, Hosio JJ, Hänninen R, Krusius M, L'vov VS. Stability and dissipation of laminar vortex flow in superfluid 3He-B. PHYSICAL REVIEW LETTERS 2010; 105:125301. [PMID: 20867649 DOI: 10.1103/physrevlett.105.125301] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2010] [Revised: 08/09/2010] [Indexed: 05/29/2023]
Abstract
A central question in the dynamics of vortex lines in superfluids is dissipation on approaching the zero temperature limit T→0. From both NMR measurements and vortex filament calculations, we find that vortex flow remains laminar up to large Reynolds numbers Re{α}∼10(3) in a cylinder filled with 3He-B. This is different from viscous fluids and superfluid 4He, where the corresponding responses are turbulent. In 3He-B, laminar vortex flow is possible in the bulk volume even in the presence of sizable perturbations from axial symmetry to below 0.2Tc. The laminar flow displays no excess dissipation beyond mutual friction, which vanishes in the T→0 limit, in contrast with turbulent vortex motion where dissipation has been earlier measured to approach a large T-independent value at T≲0.2Tc.
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Affiliation(s)
- V B Eltsov
- Low Temperature Laboratory, School of Science and Technology, Aalto University, Finland
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21
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Alamri SZ, Youd AJ, Barenghi CF. Reconnection of superfluid vortex bundles. PHYSICAL REVIEW LETTERS 2008; 101:215302. [PMID: 19113421 DOI: 10.1103/physrevlett.101.215302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2008] [Revised: 09/27/2008] [Indexed: 05/27/2023]
Abstract
Using the vortex filament model and the Gross-Pitaevskii nonlinear Schroedinger equation, we show that bundles of quantized vortex lines in He II are structurally robust and can reconnect with each other maintaining their identity. We discuss vortex stretching in superfluid turbulence and show that, during the bundle reconnection process, kelvin waves of large amplitude are generated, in agreement with the finding that helicity is produced by nearly singular vortex interactions in classical Euler flows.
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Affiliation(s)
- Sultan Z Alamri
- School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
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22
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Vinen WF. An introduction to quantum turbulence. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2008; 366:2925-2933. [PMID: 18534939 DOI: 10.1098/rsta.2008.0084] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
This paper provides a brief introduction to quantum turbulence in simple superfluids, in which the required rotational motion in the superfluid component is due entirely to the topological defects that are identified as quantized vortices. Particular emphasis is placed on the basic dynamical behaviour of the quantized vortices and on turbulent decay mechanisms at a very low temperature. There are possible analogies with the behaviour of cosmic strings.
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Affiliation(s)
- W F Vinen
- School of Physics and Astronomy, University of Birmingham, Birmingham, UK.
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23
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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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24
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Walmsley PM, Golov AI. Quantum and quasiclassical types of superfluid turbulence. PHYSICAL REVIEW LETTERS 2008; 100:245301. [PMID: 18643594 DOI: 10.1103/physrevlett.100.245301] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2008] [Indexed: 05/26/2023]
Abstract
By injecting negative ions in superfluid 4He in the zero-temperature limit (T<or=0.5 K), we have generated tangles of quantized vortex line with negligible large-scale flow. For this quantum regime of superfluid turbulence, the vortex line length L was found to decay at late time t as L proportional to t{-1}, the prefactor being independent of the initial value of L. The corresponding effective kinematic viscosity is 0.1 kappa, where kappa is the circulation quantum. At T>0.7 K, a jet of ions generates quasiclassical tangles identical to those produced by mechanical means.
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Affiliation(s)
- P M Walmsley
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
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25
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Kozik E, Svistunov B. Scanning superfluid-turbulence cascade by its low-temperature cutoff. PHYSICAL REVIEW LETTERS 2008; 100:195302. [PMID: 18518456 DOI: 10.1103/physrevlett.100.195302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2007] [Revised: 03/02/2008] [Indexed: 05/26/2023]
Abstract
On the basis of a recently proposed scenario of the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, we develop a theory of low-temperature cutoff. The theory predicts a specific behavior of the quantized vortex line density, L, controlled by the frictional coefficient, alpha(T)<<1, responsible for the cutoff. The curve ln L(lnalpha) is found to directly reflect the structure of the cascade, revealing four qualitatively distinct wave number regions. Excellent agreement with a recent experiment by Walmsley et al. [Phys. Rev. Lett. 99, 265302 (2007)] -- in which L(T) has been measured down to T ~ 0.08 K -- implies that the scenario of low-temperature superfluid turbulence is now experimentally validated and allows to quantify the Kelvin-wave cascade spectrum.
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Affiliation(s)
- Evgeny Kozik
- Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland
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26
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Eltsov VB, Golov AI, de Graaf R, Hänninen R, Krusius M, L'vov VS, Solntsev RE. Quantum turbulence in a propagating superfluid vortex front. PHYSICAL REVIEW LETTERS 2007; 99:265301. [PMID: 18233586 DOI: 10.1103/physrevlett.99.265301] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2007] [Indexed: 05/25/2023]
Abstract
We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.
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Affiliation(s)
- V B Eltsov
- Low Temperature Laboratory, Helsinki University of Technology, P.O. Box 5100, 02015 HUT, Finland
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27
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Walmsley PM, Golov AI, Hall HE, Levchenko AA, Vinen WF. Dissipation of quantum turbulence in the zero temperature limit. PHYSICAL REVIEW LETTERS 2007; 99:265302. [PMID: 18233587 DOI: 10.1103/physrevlett.99.265302] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2007] [Revised: 10/30/2007] [Indexed: 05/25/2023]
Abstract
Turbulence, produced by an impulsive spin down from angular velocity Omega to rest of a cube-shaped container, is investigated in superfluid 4He at temperatures 0.08 K-1.6 K. The density of quantized vortex lines L is measured by scattering negative ions. Homogeneous turbulence develops after time t approximately 20/Omega and decays as L proportional, t-3/2. The corresponding energy flux =nu'(kappaL)2 proportional, t-3 is characteristic of quasiclassical turbulence at high Re with a saturated energy-containing length. The effective kinematic viscosity in T=0 limit is nu'=0.003kappa, where kappa=10(-3) cm2 s(-1) is the circulation quantum.
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Affiliation(s)
- P M Walmsley
- School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
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28
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Kobayashi M, Tsubota M. Thermal dissipation in quantum turbulence. PHYSICAL REVIEW LETTERS 2006; 97:145301. [PMID: 17155265 DOI: 10.1103/physrevlett.97.145301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2006] [Indexed: 05/12/2023]
Abstract
The microscopic mechanism of thermal dissipation in quantum turbulence is numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtain the mutual friction coefficients of the vortex in dilute Bose-Einstein condensates dynamics as functions of temperature.
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Affiliation(s)
- Michikazu Kobayashi
- Department of Physics, Osaka City University, Sumiyoshi-Ku, Osaka 558-8585, Japan
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29
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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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30
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Barenghi CF, Gordeev AV, Skrbek L. Depolarization of decaying counterflow turbulence in He II. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:026309. [PMID: 17025541 DOI: 10.1103/physreve.74.026309] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2006] [Indexed: 05/12/2023]
Abstract
We present experimental evidence backed up by numerical simulations that the steady-state vortex tangle created in He II by heat-transfer counterflow is strongly polarized. When the heater that generates the counterflow turbulence is switched off, the vortex tangle decays, the vortex lines randomize their spatial orientation and the tangle's polarization decreases. The process of depolarization slows down the recovery of the transverse second sound signal which measures the vortex line density; at some values of parameters it even leads to a net decrease of the amplitude of the transverse second sound prior to reaching the universal -32 power temporal law decay typical of classical homogeneous isotropic turbulence in a finite-sized channel.
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Affiliation(s)
- C F Barenghi
- School of Mathematics, University of Newcastle, Newcastle upon Tyne NE1 7RU, United Kingdom
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