Jump to content

Two-dimensional quantum turbulence

Add links
From Wikipedia, the free encyclopedia
(Redirected from Two-dimensional turbulence)

Turbulent phenomena are observed universally in energetic fluid dynamics, associated with highly chaotic fluid motion, and typically involving excitations spreading 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, associated with the fluid supporting any local value of fluid rotation. Quantum fluids are distinguished by vorticity that is quantised, a restriction imposed by the quantum wavefunction that describes the fluid when it reaches a superfluid state; the ability of a fluid to form quantum vortices is the most widely used experimental signature of superfluidity. 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. When confined to move only in a plane, classical fluids exhibit a reversal in the direction of energy flow during turbulence. Instead of the three-dimensional process involving the formation of smaller rotating eddies, in two-dimensions small eddies tend to combine to make larger rotating structures.

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

[edit]

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

[edit]

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

[edit]

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

[edit]

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

[edit]
  1. ^ Simula, T P; Mizushima, T; Machida, K (2008). "Vortex waves in trapped Bose-Einstein condensates". Physical Review A. 78 (5): 053604. arXiv:0809.0993. Bibcode:2008PhRvA..78e3604S. doi:10.1103/PhysRevA.78.053604. S2CID 118441972.
  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. arXiv:1105.1189. Bibcode:2011PhRvA..84b3637R. doi:10.1103/PhysRevA.84.023637. S2CID 118641483.
  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. arXiv:1209.5824. Bibcode:2013PhRvL.110j4501R. doi:10.1103/PhysRevLett.110.104501. PMID 23521262. S2CID 9745274. 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. arXiv:1610.04382. Bibcode:2017PhRvE..95e2144S. doi:10.1103/PhysRevE.95.052144. hdl:10852/63199. PMID 28618591. S2CID 11934251.
  6. ^ Kraichnan, R H (1967). "Inertial Ranges in Two-Dimensional Turbulence". Physics of Fluids. 10 (7): 1417–1423. Bibcode:1967PhFl...10.1417K. doi:10.1063/1.1762301.
  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. Bibcode:1998PhRvL..81.2244R. doi:10.1103/PhysRevLett.81.2244.
  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. Retrieved 2019-11-17.
  9. ^ Kirchhoff, Gustav Robert (1876). Vorlesungenüber mathematische physik: mechanik. Vol. 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. Bibcode:1980PhRvB..21.1806A. 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. Bibcode:1949NCim....6S.279O. doi:10.1007/BF02780991. ISSN 1827-6121. S2CID 186224016. 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. Bibcode:2006RvMP...78...87E. 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. Bibcode:1990PhFlB...2.2961S. doi:10.1063/1.859362. ISSN 0899-8221. 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. arXiv:1405.3399. Bibcode:2014PhRvL.113p5302S. doi:10.1103/PhysRevLett.113.165302. PMID 25361262. S2CID 18868201.
  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. arXiv:1512.05517. Bibcode:2016PhRvA..94b3602Y. doi:10.1103/PhysRevA.94.023602. S2CID 119286552. 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. Bibcode:1992PhRvL..69.1644F. doi:10.1103/PhysRevLett.69.1644. PMID 10046277. 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. arXiv:0912.3773. Bibcode:2010PhRvL.104p0401N. doi:10.1103/PhysRevLett.104.160401. PMID 20482029. S2CID 10019882.
  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. arXiv:cond-mat/9912015. Bibcode:2000PhRvL..84..806M. doi:10.1103/PhysRevLett.84.806. PMID 11017378. S2CID 9128694. 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. arXiv:cond-mat/0505730. Bibcode:2005PhRvL..95n5301P. doi:10.1103/PhysRevLett.95.145301. PMID 16241664. S2CID 9035349. 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. arXiv:cond-mat/0610187. Bibcode:2007PhRvL..98k0402S. doi:10.1103/PhysRevLett.98.110402. PMID 17501028. S2CID 27780713.
  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. arXiv:0807.3323. Bibcode:2008Natur.455..948W. doi:10.1038/nature07334. S2CID 459795.
  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. arXiv:1002.2058. Bibcode:2010PhRvL.104o0404S. doi:10.1103/PhysRevLett.104.150404. PMID 20481976. S2CID 20206109. 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. arXiv:1608.02762. Bibcode:2016PhRvL.117x5301K. doi:10.1103/PhysRevLett.117.245301. PMID 28009203. S2CID 2946581.
  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; Davis, M J; Anderson, B P (2013). "Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid". Physical Review Letters. 111 (23): 235301. arXiv:1204.1102. Bibcode:2013PhRvL.111w5301N. doi:10.1103/PhysRevLett.111.235301. PMID 24476287. S2CID 13296892.
  25. ^ Sachkou, Yauhen P.; Baker, Christopher G.; Harris, Glen I.; Stockdale, Oliver R.; Forstner, Stefan; Reeves, Matthew T.; He, Xin; McAuslan, David L.; Bradley, Ashton S.; Davis, Matthew J.; Bowen, Warwick P. (2019). "Coherent vortex dynamics in a strongly interacting superfluid on a silicon chip". Science. 366 (6472): 1480–1485. arXiv:1902.04409. Bibcode:2019Sci...366.1480S. doi:10.1126/science.aaw9229. ISSN 0036-8075. PMID 31857478. S2CID 119330119. Retrieved 2020-02-27.
  26. ^ Carusotto, Iacopo; Ciuti, Cristiano (2013). "Quantum fluids of light". Reviews of Modern Physics. 85 (1): 299–366. arXiv:1205.6500. Bibcode:2013RvMP...85..299C. doi:10.1103/RevModPhys.85.299. S2CID 9675458.
  27. ^ Gauthier, G.; Reeves, M. T.; Yu, X.; Bradley, A. S.; Baker, M. A.; Bell, T. A.; Rubinsztein-Dunlop, H.; Davis, M. J.; Neely, T. W. (2019). "Giant vortex clusters in a two-dimensional quantum fluid". Science. 364 (6447): 1264–1267. arXiv:1801.06951. Bibcode:2019Sci...364.1264G. doi:10.1126/science.aat5718. ISSN 0036-8075. PMID 31249054. S2CID 195750381.
  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. arXiv:1801.06952. Bibcode:2019Sci...364.1267J. doi:10.1126/science.aat5793. ISSN 0036-8075. PMID 31249055. S2CID 4948239.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Two-dimensional_quantum_turbulence&oldid=1230801562"