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Dissipation anomaly in a turbulent quantum fluid

Luca Galantucci1,2,*, Em Rickinson2, Andrew W. Baggaley2, Nick G. Parker2, and Carlo F. Barenghi2

  • 1Istituto per le Applicazioni del Calcolo M. Picone, IAC-CNR, Via dei Taurini 19, 00185 Roma, Italy
  • 2Joint Quantum Centre (JQC) Durham–Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, United Kingdom

  • *l.galantucci@iac.cnr.it
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Phys. Rev. Fluids 8, 034605 – Published 23 March, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.034605

Abstract

When the intensity of turbulence is increased (by increasing the Reynolds number, e.g., by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off to a nonzero constant as smaller and smaller vortical flow structures are generated. This fundamental property, called the dissipation anomaly, is sometimes referred to as the zeroth law of turbulence. The question of what happens in the limit of vanishing viscosity (purely hypothetical in classical fluids) acquires a particular physical significance in the context of liquid helium, a quantum fluid which becomes effectively inviscid at low temperatures achievable in the laboratory. By performing numerical simulations and identifying the superfluid Reynolds number, here we show evidence for a superfluid analog to the classical dissipation anomaly. Our numerics indeed show that as the superfluid Reynolds number increases, smaller and smaller structures are generated on the quantized vortex lines on which the superfluid vorticity is confined, balancing the effect of weaker and weaker dissipation.

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References (41)

  1. K. R. Sreenivasan, On the scaling of the turbulence energy dissipation rate, Phys. Fluids 27, 1048 (1984).
  2. Y. Kaneda, T. Ishihara, M. Yokokawa, K. Itakura, and A. Uno, Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box, Phys. Fluids 15, L21 (2003).
  3. L. Onsager, Statistical hydrodynamics, Nuovo Cimento 6, 279 (1949).
  4. G. L. Eyink and K. R. Sreenivasan, Onsager and the theory of hydrodynamic turbulence, Rev. Mod. Phys. 78, 87 (2006).
  5. C. F. Barenghi, V. L'vov, and P.-E. Roche, Experimental, numerical and analytical velocity spectra in turbulent quantum fluid, Proc. Natl. Acad. Sci. USA 111, 4683 (2014).
  6. S. R. Stalp, L. Skrbek and R. J. Donnelly, Decay of Grid Turbulence in a Finite Channel, Phys. Rev. Lett. 82, 4831 (1999).
  7. J. Maurer and P. Tabeling, Local investigation of superfluid turbulence, Europhys. Lett. 43, 29 (1998).
  8. J. Salort, C. Baudet, B. Castaing, B. Chabaud, F. Daviaud, T. Didelot, P. Diribarne, B. Dubrulle, Y. Gagne, F. Gauthier, A. Girard, B Henbral, B. Rousset, P. Thibault, and P. E. Roche, Turbulent velocity spectra in superfluid flows, Phys. Fluids 22, 125102 (2010).
  9. A. N. Kolmogorov, The local structure of turbulence in an incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk. SSSR 30, 301 (1941).
  10. C. F. Barenghi, W. F. Vinen, and R. J. Donnelly, Friction on quantized vortices in helium II: A review, J. Low Temp. Phys. 52, 189 (1983).
  11. C. Nore, M. Abid, and M. E. Brachet, Kolmogorov Turbulence in Low-Temperature Superflows, Phys. Rev. Lett. 78, 3896 (1997).
  12. R. N. Hills and P. H. Roberts, Superfluid mechanics for a high density of vortex lines, Arch. Ration. Mech. Anal. 66, 43 (1977).
  13. A. P. Finne, T. Araki, R. Blaauwgeers, V. B. Eltsov, N. B. Kopnin, M. Krusius, L. Skrbek, M. Tsubota, and G. E. Volovik, An intrinsic velocity-independent criterion for superfluid turbulence, Nature (London) 424, 1022 (2003).
  14. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid He4: Homogeneous superfluid turbulence, Phys. Rev. B 38, 2398 (1988).
  15. R. Hänninen and A. W. Baggaley, Vortex filament method as a tool for computational visualization of quantum turbulence, Proc. Natl. Acad. Sci. USA 111, 4667 (2014).
  16. K. W. Schwarz, Three-dimensional vortex dynamics in superfluid He4: Line-line and line-boundary interactions, Phys. Rev. B 31, 5782 (1985).
  17. D. Kivotides, C. F. Barenghi, and D. C. Samuels, Triple vortex ring structure in superfluid helium II, Science 290, 777 (2000).
  18. L. Galantucci, A. W. Baggaley, C. F. Barenghi, and G. Krstulovic, A new self-consistent approach of quantum turbulence in superfluid helium, Eur. Phys. J. Plus 135, 547 (2020).
  19. L. Galantucci, G. Krstulovic, and C. F. Barenghi, Friction-enhanced lifetime of bundled quantum vortices, Phys. Rev. Fluids 8, 014702 (2023).
  20. D. Kivotides, Relaxation of superfluid vortex bundles via energy transfer to the normal fluid, Phys. Rev. B 76, 054503 (2007).
  21. K. Morris, J. Koplik, and D. W. L. Rousen, Vortex Locking in Direct Numerical Simulations of Quantum Turbulence, Phys. Rev. Lett. 101, 015301 (2008).
  22. P. M. Walmsley and A. I. Golov, Quantum and Quasiclassical Types of Superfluid Turbulence, Phys. Rev. Lett. 100, 245301 (2008).
  23. A. Leonard, Computing three dimensional incompressible flows with votrex elements, Annu. Rev. Fluid Mech. 17, 523 (1985).
  24. O. Yurkina and S. K. Nemirovskii, On the energy spectrum of the 3D velocity field, generated by an ensemble of vortex loops, Low Temp. Phys. 47, 652 (2021).
  25. P. M. Walmsley, D. E. Zmeev, F. Pakpour, and A. I. Golov, Dynamics of quantum turbulence of different spectra, Proc. Natl. Acad. Sci. USA 111, 4691 (2014).
  26. L. Skrbek and K. R. Sreenivasan, Developed quantum turbulence and its decay, Phys. Fluids 24, 011301 (2012).
  27. W. F. Vinen, Theory of quantum grid turbulence in superfluid He3-B, Phys. Rev. B 71, 024513 (2005).
  28. V. S. L'vov, S. V. Nazarenko, and G. E. Volovik, Energy spectra of developed superfluid turbulence, JETP Lett. 80, 479 (2004).
  29. L. Skrbek, Phenomenology of quantum turbulence in superfluid helium, Proc. Natl. Acad. Sci. USA 118, e2018406118 (2021).
  30. E. V. Kozik and B. V. Svistunov, Kelvin-Wave Cascade and Decay of Superfluid Turbulence, Phys. Rev. Lett. 92, 035301 (2004).
  31. V. S. L'vov and S. V. Nazarenko, Spectrum of Kelvin-wave turbulence in superfluids, JETP Lett. 91, 428 (2010).
  32. G. Krstulovic, Kelvin-wave cascade and dissipation in low-temperature superfluid vortices, Phys. Rev. E 86, 055301(R) (2012).
  33. W. F. Vinen and J. J. Niemela, Quantum turbulence, J. Low Temp. Phys. 128, 167 (2002).
  34. W. F. Vinen, Mutual Friction in a heat current in liquid helium II. III. Theory of mutual friction, Proc. R. Soc. London A 242, 493 (1957).
  35. J. Gao, W. Guo, S. Yui, M. Tsubota, and W. F. Vinen, Dissipation in quantum turbulence in superfluid He4 above 1 K, Phys. Rev. B 97, 184518 (2018).
  36. A. W. Baggaley, C. F. Barenghi, and Y. A. Sergeev, Quasiclassical and ultraquantum decay of superfluid turbulence, Phys. Rev. B 85, 060501(R) (2012)
  37. T. Araki, M. Tsubota, and S. K. Nemirovskii, Energy Spectrum of Superfluid Turbulence with No Normal-Fluid Component, Phys. Rev. Lett. 89, 145301 (2002).
  38. J. T. Mäkinen, S. Autti, P. J. Heikkinen, J. J. Hosio, R. Hänninen, V. S. L'vov, P. M. Walmsley, V. V. Zavjalov, and V. B. Eltsov, Rotating quantum wave turbulence, Nat. Phys. (2023), doi:10.1038/s41567-023-01966-z.
  39. J. Panickacheril John, D. A. Donzis, and K. R. Sreenivasan, Does dissipative anomaly hold for compressible turbulence? J. Fluid Mech. 920, A20 (2021).
  40. R. J. Donnelly and C. F. Barenghi, The observed properties of liquid helium at saturated vapour pressure J. Phys. Chem. Ref. Data 27, 1217 (1998).
  41. W. J. Kwon, G. Del Pace, K. Xhani, L. Galantucci, A. Muzi Falconi, M. Inguscio, F. Scazza, and G. Roati, Sound emission and annihilations in a programmable quantum vortex collider, Nature (London) 600, 64 (2021).

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Phys. Rev. Fluids 8, 034605– Published 23 March, 2023
  • Received 2 August 2020
  • Accepted 3 March 2023
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