Physics:Two-dimensional quantum turbulence

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Turbulent phenomena are observed universally in energetic fluid dynamics, associated with highly chaotic fluid motion involving excitations spread over a wide range of length scales. The particular features of turbulence are dependent on the fluid and geometry, and specifics of forcing and dissipation.

In classical fluids the fluid vorticity is a continuous field able to acquire any value at each point in the fluid. Quantum fluids are distinguished by vorticity that is quantised, a restriction imposed by the quantum wavefunction that describes the fluid. While quantum fluids can also support classical turbulence, quantum turbulence involves the chaotic dynamics of many interacting quantum vortices. In highly excited bulk superfluid, many vortex lines interact with each other forming quantum turbulent states.

By introducing tight confinement along one direction the Kelvin wave excitations involving bending of otherwise straight vortex lines[1] can be strongly suppressed, favouring vortex alignment with the axis of tight confinement. Vortex dynamics can then enter a regime of effective 2D motion, equivalent to point vortices moving on a plane.[2] In general, 2D quantum turbulence (2DQT) can exhibit complex phenomenology involving coupled vortices and sound in compressible superfluids. The quantum vortex dynamics can exhibit signatures of turbulence including a Kolmogorov −5/3 power law,[3][4][5] a quantum manifestation of the inertial transport of energy to large scales observed in classical fluids, known as an inverse energy cascade.[6][7]

Point vortices

The point vortex model, introduced by Helmholtz[8] and Kirchhoff,[9] describes the motion of ideal point vortices confined to a plane, with direct mapping to planar electrodynamics.[10] The model plays a central role in the study of planar Navier-Stokes flows, and can be realized in compressible superfluids such as those in ultracold gas Bose-Einstein condensates, when the healing length setting the vortex core size is very small compared to the system size.

Negative temperature

Point vortices confined to finite area were predicted by Onsager to exhibit states of negative temperature.[11][12] This possibility of negative absolute temperature can be traced to the finite phase space of the point vortex system: in contrast to a massive particle moving on a plane, each point vortex only has two degrees of freedom. Specifying the spatial coordinates of the vortex also completely determines the superfluid velocity. At leading order a quantum vortex is massless, with each filament moving with the net background flow and obeying a form of the Biot–Savart law. Guiding-centre plasmas exhibit a symmetry breaking transition at high energy per vortex associated with negative temperature.[13] In Bose-Einstein condensates the annihilation of low-energy vortex dipoles can raise the energy per vortex[14] until the system undergoes spontaneous ordering into macroscopic same-sign vortex clusters associated with negative temperature.[15] Clustered equilibrium states have high energy per vortex, with clusters forming as a consequence of the limited phase space of confined point vortices.

Forced turbulence

Vortices can be injected into a planar superfluid through various forcing mechanisms such as obstacle dragging[16][17] or elliptical stirring[18][19] that induce a localized breakdown of superfluidity, or through mechanisms that exploit abrupt phase evolution at the merging of multiple condensates[20] or the condensate phase transition itself.[21]

Small-scale forcing from appropriately dragging an obstacle can inject small vortex clusters into a planar superfluid.[22][23] In strongly non-equilibrium quantum fluid dynamics, clustered states can develop as a result of steady inverse energy cascade from small scale forcing, leading to an accumulation of energy at the system scale in the form of macroscopic flow due to vortex charge ordering.

Superfluid experiments

Advances in quantum fluids experiments have provided access to the point vortex regime in compressible superfluids. 2DQT regime has been established in ultracold gases,[24] superfluid helium,[25] and in exciton-polariton condensates comprising quantum fluids of light.[26] Negative temperature states predicted by Onsager have recently been observed in systems with hard-wall boundary conditions.[27][28]

References

  1. ↑ Simula, T P; Mizushima, T; Machida, K (2008). "Vortex waves in trapped Bose-Einstein condensates". Physical Review A 78 (5): 053604. doi:10.1103/PhysRevA.78.053604. Bibcode: 2008PhRvA..78e3604S. 
  2. ↑ Rooney, S J; Blakie, P Blair; Anderson, B P; Bradley, A S (2011). "Suppression of Kelvon-induced decay of quantized vortices in oblate Bose-Einstein condensates". Physical Review A 84 (2): 023637. doi:10.1103/PhysRevA.84.023637. Bibcode: 2011PhRvA..84b3637R. 
  3. ↑ Novikov, E. A. (1975). "Dynamics and statistics of a system of vortices". Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki 68: 1868–1882. 
  4. ↑ Reeves, Matthew T.; Billam, Thomas P.; Anderson, Brian P.; Bradley, Ashton S. (2013-03-04). "Inverse Energy Cascade in Forced Two-Dimensional Quantum Turbulence". Physical Review Letters 110 (10): 104501. doi:10.1103/PhysRevLett.110.104501. PMID 23521262. Bibcode: 2013PhRvL.110j4501R. https://link.aps.org/doi/10.1103/PhysRevLett.110.104501. Retrieved 2021-12-17. 
  5. ↑ Skaugen, Audun; Angheluta, Luiza (2017). "Origin of the inverse energy cascade in two-dimensional quantum turbulence". Physical Review E 95 (5): 1868. doi:10.1103/PhysRevE.95.052144. PMID 28618591. Bibcode: 2017PhRvE..95e2144S. 
  6. ↑ Kraichnan, R H (1967). "Inertial Ranges in Two-Dimensional Turbulence". Physics of Fluids 10 (7): 1417–1423. doi:10.1063/1.1762301. Bibcode: 1967PhFl...10.1417K. 
  7. ↑ Rutgers, M A (1998). "Forced 2D turbulence: Experimental evidence of simultaneous inverse energy and forward enstrophy cascades". Physical Review Letters 81 (11): 2244–2247. doi:10.1103/PhysRevLett.81.2244. Bibcode: 1998PhRvL..81.2244R. 
  8. ↑ Helmholtz, H. (1867-01-01). "LXIII. On Integrals of the hydrodynamical equations, which express vortex-motion". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 33 (226): 485–512. doi:10.1080/14786446708639824. ISSN 1941-5982. https://doi.org/10.1080/14786446708639824. Retrieved 2019-11-17. 
  9. ↑ Kirchhoff, Gustav Robert (1876). Vorlesungenüber mathematische physik: mechanik. 1. Teubner. 
  10. ↑ Ambegaokar, Vinay; Halperin, B. I.; Nelson, David R.; Siggia, Eric D. (1980-03-01). "Dynamics of superfluid films". Physical Review B 21 (5): 1806–1826. doi:10.1103/PhysRevB.21.1806. Bibcode: 1980PhRvB..21.1806A. https://link.aps.org/doi/10.1103/PhysRevB.21.1806. Retrieved 2022-03-24. 
  11. ↑ Onsager, L. (1949-03-01). "Statistical hydrodynamics". Il Nuovo Cimento 6 (2): 279–287. doi:10.1007/BF02780991. ISSN 1827-6121. Bibcode: 1949NCim....6S.279O. https://doi.org/10.1007/BF02780991. Retrieved 2019-11-17. 
  12. ↑ Eyink, Gregory L.; Sreenivasan, Katepalli R. (2006-01-17). "Onsager and the theory of hydrodynamic turbulence". Reviews of Modern Physics 78 (1): 87–135. doi:10.1103/RevModPhys.78.87. Bibcode: 2006RvMP...78...87E. https://link.aps.org/doi/10.1103/RevModPhys.78.87. Retrieved 2022-03-07. 
  13. ↑ Smith, Ralph A.; O’Neil, Thomas M. (1990-12-01). "Nonaxisymmetric thermal equilibria of a cylindrically bounded guiding‐center plasma or discrete vortex system". Physics of Fluids B: Plasma Physics 2 (12): 2961–2975. doi:10.1063/1.859362. ISSN 0899-8221. Bibcode: 1990PhFlB...2.2961S. https://aip.scitation.org/doi/10.1063/1.859362. Retrieved 2020-09-09. 
  14. ↑ Simula, T P; Davis, M J; Helmerson, K (2014). "Emergence of Order from Turbulence in an Isolated Planar Superfluid". Physical Review Letters 113 (16): 165302. doi:10.1103/PhysRevLett.113.165302. PMID 25361262. Bibcode: 2014PhRvL.113p5302S. 
  15. ↑ Yu, Xiaoquan; Billam, Thomas P.; Nian, Jun; Reeves, Matthew T.; Bradley, Ashton S. (2016-08-01). "Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid". Physical Review A 94 (2): 023602. doi:10.1103/PhysRevA.94.023602. Bibcode: 2016PhRvA..94b3602Y. https://link.aps.org/doi/10.1103/PhysRevA.94.023602. Retrieved 2021-10-28. 
  16. ↑ Frisch, T.; Pomeau, Y.; Rica, S. (1992-09-14). "Transition to dissipation in a model of superflow". Physical Review Letters 69 (11): 1644–1647. doi:10.1103/PhysRevLett.69.1644. PMID 10046277. Bibcode: 1992PhRvL..69.1644F. https://link.aps.org/doi/10.1103/PhysRevLett.69.1644. Retrieved 2021-07-27. 
  17. ↑ Neely, T W; Samson, E C; Bradley, A S; Davis, M J; Anderson, B P (2010). "Observation of Vortex Dipoles in an Oblate Bose-Einstein Condensate". Physical Review Letters 104 (16): 160401. doi:10.1103/PhysRevLett.104.160401. PMID 20482029. Bibcode: 2010PhRvL.104p0401N. 
  18. ↑ Madison, K. W.; Chevy, F.; Wohlleben, W.; Dalibard, J. (2000-01-31). "Vortex Formation in a Stirred Bose-Einstein Condensate". Physical Review Letters 84 (5): 806–809. doi:10.1103/PhysRevLett.84.806. PMID 11017378. Bibcode: 2000PhRvL..84..806M. https://link.aps.org/doi/10.1103/PhysRevLett.84.806. Retrieved 2021-10-20. 
  19. ↑ Parker, N. G.; Adams, C. S. (2005-09-29). "Emergence and Decay of Turbulence in Stirred Atomic Bose-Einstein Condensates". Physical Review Letters 95 (14): 145301. doi:10.1103/PhysRevLett.95.145301. PMID 16241664. Bibcode: 2005PhRvL..95n5301P. https://link.aps.org/doi/10.1103/PhysRevLett.95.145301. Retrieved 2020-12-07. 
  20. ↑ Scherer, David; Weiler, Chad; Neely, Tyler; Anderson, B P (2007). "Vortex Formation by Merging of Multiple Trapped Bose-Einstein Condensates". Physical Review Letters 98 (11): 110402. doi:10.1103/PhysRevLett.98.110402. PMID 17501028. Bibcode: 2007PhRvL..98k0402S. 
  21. ↑ Weiler, Chad N; Neely, Tyler W; Scherer, David R; Bradley, A S; Davis, M J; Anderson, B P (2008). "Spontaneous vortices in the formation of Bose–Einstein condensates". Nature 455 (7215): 948–951. doi:10.1038/nature07334. Bibcode: 2008Natur.455..948W. 
  22. ↑ Sasaki, Kazuki; Suzuki, Naoya; Saito, Hiroki (2010-04-16). "Bénard--von Kármán Vortex Street in a Bose-Einstein Condensate". Physical Review Letters 104 (15): 150404. doi:10.1103/PhysRevLett.104.150404. PMID 20481976. Bibcode: 2010PhRvL.104o0404S. https://link.aps.org/doi/10.1103/PhysRevLett.104.150404. Retrieved 2022-09-19. 
  23. ↑ Kwon, Woo Jin; Kim, Joon Hyun; Seo, Sang Won; Shin, Y (2016). "Observation of von Kármán Vortex Street in an Atomic Superfluid Gas". Physical Review Letters 117 (24): 245301. doi:10.1103/PhysRevLett.117.245301. PMID 28009203. Bibcode: 2016PhRvL.117x5301K. 
  24. ↑ Neely, T W; Bradley, A S; Samson, E C; Rooney, S J; Wright, E M; Law, K J H; Carretero-González, R; Kevrekidis, P G et al. (2013). "Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid". Physical Review Letters 111 (23): 235301. doi:10.1103/PhysRevLett.111.235301. PMID 24476287. Bibcode: 2013PhRvL.111w5301N. 
  25. ↑ Sachkou, Yauhen P.; Baker, Christopher G.; Harris, Glen I.; Stockdale, Oliver R.; Forstner, Stefan; Reeves, Matthew T.; He, Xin; McAuslan, David L. et al. (2019). "Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip". Science 366 (6472): 1480–1485. doi:10.1126/science.aaw9229. ISSN 0036-8075. PMID 31857478. Bibcode: 2019Sci...366.1480S. https://science.sciencemag.org/content/366/6472/1480. Retrieved 2020-02-27. 
  26. ↑ Carusotto, Iacopo; Ciuti, Cristiano (2013). "Quantum fluids of light". Reviews of Modern Physics 85 (1): 299–366. doi:10.1103/RevModPhys.85.299. Bibcode: 2013RvMP...85..299C. 
  27. ↑ Gauthier, G.; Reeves, M. T.; Yu, X.; Bradley, A. S.; Baker, M. A.; Bell, T. A.; Rubinsztein-Dunlop, H.; Davis, M. J. et al. (2019). "Giant vortex clusters in a two-dimensional quantum fluid". Science 364 (6447): 1264–1267. doi:10.1126/science.aat5718. ISSN 0036-8075. PMID 31249054. Bibcode: 2019Sci...364.1264G. 
  28. ↑ Johnstone, S. P.; Groszek, A. J.; Starkey, P. T.; Billington, C. J.; Simula, T. P.; Helmerson, K. (2019). "Evolution of large-scale flow from turbulence in a two-dimensional superfluid". Science 364 (6447): 1267–1271. doi:10.1126/science.aat5793. ISSN 0036-8075. PMID 31249055. Bibcode: 2019Sci...364.1267J. 



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