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

被引:0
作者
Jou, David [1 ,2 ]
Sciacca, Michele [3 ]
机构
[1] Univ Autonoma Barcelona, Dept Fis, Bellaterra 08193, Catalonia, Spain
[2] Inst Estudis Catalans, Carme 47, Barcelona 08001, Catalonia, Spain
[3] Univ Palermo, Dipartimento Ingn, Viale Sci, I-90128 Palermo, Italy
关键词
Superfluid helium; Heat transfer; Quantum turbulence; Energy spectrum; Kolmogorov cascade; Quantized vortices;
D O I
10.1007/s10440-023-00568-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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) regime (equipartition regime) in the transition region between the hydrodynamic regime and the Kelvin wave regime (namely, between the k(-5/3) and k(-1) regions in coflow situations and between the k(-3) and 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 between -5/3 and -1 (or between -3 and -1), instead of the positive 2 exponent of the equipartition regime.
引用
收藏
页数:13
相关论文
共 43 条
  • [1] Coexistence and interplay of quantum and classical turbulence in superfluid 4He: Decay, velocity decoupling, and counterflow energy spectra
    Babuin, S.
    L'vov, V. S.
    Pomyalov, A.
    Skrbek, L.
    Varga, E.
    [J]. PHYSICAL REVIEW B, 2016, 94 (17)
  • [2] Thermally and mechanically driven quantum turbulence in helium II
    Baggaley, A. W.
    Sherwin, L. K.
    Barenghi, C. F.
    Sergeev, Y. A.
    [J]. PHYSICAL REVIEW B, 2012, 86 (10):
  • [3] Vortex-Density Fluctuations, Energy Spectra, and Vortical Regions in Superfluid Turbulence
    Baggaley, Andrew W.
    Laurie, Jason
    Barenghi, Carlo F.
    [J]. PHYSICAL REVIEW LETTERS, 2012, 109 (20)
  • [4] Regimes of turbulence without an energy cascade
    Barenghi, C. F.
    Sergeev, Y. A.
    Baggaley, A. W.
    [J]. SCIENTIFIC REPORTS, 2016, 6
  • [5] Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid
    Barenghi, Carlo F.
    L'vov, Victor S.
    Roche, Philippe-E.
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2014, 111 : 4683 - 4690
  • [6] Barenghi CF., 2001, Quantized Vortex Dynamics and Superfluid Turbulence, V1, DOI [10.1007/3-540-45542-6, DOI 10.1007/3-540-45542-6]
  • [7] Superfluid Helium in Three-Dimensional Counterflow Differs Strongly from Classical Flows: Anisotropy on Small Scales
    Biferale, L.
    Khomenko, D.
    L'vov, V
    Pomyalov, A.
    Procaccia, I
    Sahoo, G.
    [J]. PHYSICAL REVIEW LETTERS, 2019, 122 (14)
  • [8] Energy and vorticity spectra in turbulent superfluid 4He from T=0 to Tℷ
    Boue, Laurent
    L'vov, Victor S.
    Nagar, Yotam
    Nazarenko, Sergey V.
    Pomyalov, Anna
    Procaccia, Itamar
    [J]. PHYSICAL REVIEW B, 2015, 91 (14)
  • [9] Donnelly R. J., 1991, QUANTIZED VORTICES H
  • [10] Frisch U., 1995, Turbulence: The Legacy of A.N. Kolmogorov