Editing Quantum turbulence (section)

== Generation and detection of quantum turbulence ==

=== Physical generation of quantum turbulence ===
[[File:Vortextangle.png|thumb|375x375px|Fig 11. A simulated vortex tangle representing quantum turbulence in a cubic volume and showing the quantized vortices]]
There are a plethora of methods that can be used to generate a vortex tangle (visualised in fig 11) in the laboratory. Here they are listed by the quantum fluid that they can be generated in.

==== QT in helium II ====

* Suddenly towing a grid in the sample of fluid at rest <ref name=":0">{{Cite journal|last1=Smith|first1=M. R.|last2=Donnelly|first2=R. J.|last3=Goldenfeld|first3=N.|last4=Vinen|first4=W. F.|date=1993-10-18|title=Decay of vorticity in homogeneous turbulence|url=https://link.aps.org/doi/10.1103/PhysRevLett.71.2583|journal=Physical Review Letters|language=en|volume=71|issue=16|pages=2583–2586|doi=10.1103/PhysRevLett.71.2583|pmid=10054718|bibcode=1993PhRvL..71.2583S |issn=0031-9007}}</ref><ref>{{Cite journal|last1=Stalp|first1=S. R.|last2=Skrbek|first2=L.|last3=Donnelly|first3=R. J.|date=1999-06-14|title=Decay of Grid Turbulence in a Finite Channel|url=https://link.aps.org/doi/10.1103/PhysRevLett.82.4831|journal=Physical Review Letters|volume=82|issue=24|pages=4831–4834|doi=10.1103/PhysRevLett.82.4831|bibcode=1999PhRvL..82.4831S }}</ref>
* Moving the fluid along pipes or channels using bellows or pumps, creating a superfluid wind tunnel (the TOUPIE experiment in Grenoble <ref>{{Cite journal|last1=Salort|first1=J.|last2=Baudet|first2=C.|last3=Castaing|first3=B.|last4=Chabaud|first4=B.|last5=Daviaud|first5=F.|last6=Didelot|first6=T.|last7=Diribarne|first7=P.|last8=Dubrulle|first8=B.|author8-link= Bérengère Dubrulle |last9=Gagne|first9=Y.|last10=Gauthier|first10=F.|last11=Girard|first11=A.|date=2010-12-01|title=Turbulent velocity spectra in superfluid flows|url=https://aip.scitation.org/doi/10.1063/1.3504375|journal=Physics of Fluids|volume=22|issue=12|pages=125102–125102–9|doi=10.1063/1.3504375|arxiv=1202.0643 |bibcode=2010PhFl...22l5102S |s2cid=118453462|issn=1070-6631}}</ref>)
* Rotating one or two propellers inside a container; the configuration of two counter-rotating propellers is called the ''"von Karman flow"'' (e.g. the SHREK experiment in Grenoble)<ref name=":0" />
* Creating shockwaves and cavitation by locally focusing ultrasound (this allows for the generation of quantum turbulence away from the boundaries)<ref>{{Cite journal|last1=Finch|first1=R. D.|last2=Kagiwada|first2=R.|last3=Barmatz|first3=M.|last4=Rudnick|first4=I.|date=1964-06-15|title=Cavitation in Liquid Helium|url=https://link.aps.org/doi/10.1103/PhysRev.134.A1425|journal=Physical Review|volume=134|issue=6A|pages=A1425–A1428|doi=10.1103/PhysRev.134.A1425|bibcode=1964PhRv..134.1425F |osti=4881344}}</ref><ref name=":1">{{Cite journal|last1=Schwarz|first1=K. W.|last2=Smith|first2=C. W.|date=1981-03-30|title=Pulsed-ion study of ultrasonically generated turbulence in superfluid 4He|url=https://www.sciencedirect.com/science/article/abs/pii/0375960181902000|journal=Physics Letters A|language=en|volume=82|issue=5|pages=251–254|doi=10.1016/0375-9601(81)90200-0|bibcode=1981PhLA...82..251S |issn=0375-9601}}</ref>
* Oscillating/vibrating forks or wires <ref>{{Cite journal|last1=Schmoranzer|first1=D.|last2=Král’ová|first2=M.|last3=Pilcová|first3=V.|last4=Vinen|first4=W. F.|last5=Skrbek|first5=L.|date=2010-06-28|title=Experiments relating to the flow induced by a vibrating quartz tuning fork and similar structures in a classical fluid|url=https://link.aps.org/doi/10.1103/PhysRevE.81.066316|journal=Physical Review E|language=en|volume=81|issue=6|pages=066316|doi=10.1103/PhysRevE.81.066316|pmid=20866531|bibcode=2010PhRvE..81f6316S |issn=1539-3755}}</ref>
* Applying a [[heat flux]] (also termed the ''"thermal counterflow''" <ref>{{Cite journal|last1=Vinen|first1=W. F.|last2=Shoenberg|first2=D.|date=1957-04-24|title=Mutual friction in a heat current in liquid helium II I. Experiments on steady heat currents|url=https://royalsocietypublishing.org/doi/10.1098/rspa.1957.0071|journal=Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences|volume=240|issue=1220|pages=114–127|doi=10.1098/rspa.1957.0071|bibcode=1957RSPSA.240..114V |s2cid=94773152}}</ref>): the prototype experiment is a channel which is open to a helium bath at one end and the opposite is closed and has a [[resistor]]. An [[electric current]] is passed through the resistor and generates [[Ohmic heating (food processing)|ohmic heat]]; the heat is carried away from the heater towards the bath by the normal fluid component, while the superfluid moves towards the heater so that the net mass flux is zero as the channel is closed. A relative velocity <math>v_{ns} = |v_n - v_s|</math> (counterflow) of the two fluid components is set up in this way which is proportional to the applied heat. Above a small critical value of the counterflow velocity, a turbulent vortex tangle is generated.
* Injecting vortex rings (rings are generated by injecting electrons which form a small bubble of about 16 [[Angstrom]]s in size that are accelerated by an electric field, until, upon exceeding the critical velocity, the vortex ring is nucleated)<ref>{{Cite journal|last1=Walmsley|first1=P. M.|last2=Golov|first2=A. I.|date=2008-06-17|title=Quantum and Quasiclassical Types of Superfluid Turbulence|url=https://link.aps.org/doi/10.1103/PhysRevLett.100.245301|journal=Physical Review Letters|volume=100|issue=24|pages=245301|doi=10.1103/PhysRevLett.100.245301|pmid=18643594|arxiv=0802.2444 |bibcode=2008PhRvL.100x5301W |s2cid=30411193}}</ref>

==== QT in <sup>3</sup>He-B and atomic condensates ====
In <sup>3</sup>He-B, quantum turbulence can be generated by the vibration of wires.<ref>{{Cite journal|last1=Bradley|first1=D. I.|last2=Clubb|first2=D. O.|last3=Fisher|first3=S. N.|last4=Guénault|first4=A. M.|last5=Haley|first5=R. P.|last6=Matthews|first6=C. J.|last7=Pickett|first7=G. R.|last8=Tsepelin|first8=V.|last9=Zaki|first9=K.|date=2006-01-23|title=<nowiki>Decay of Pure Quantum Turbulence in Superfluid $^{3}\mathrm{He}\mathrm{\text{\ensuremath{-}}}\mathrm{B}$</nowiki>|url=https://link.aps.org/doi/10.1103/PhysRevLett.96.035301|journal=Physical Review Letters|volume=96|issue=3|pages=035301|doi=10.1103/PhysRevLett.96.035301|pmid=16486721|arxiv=0706.0621|s2cid=9778797}}</ref> For atomic condensates, quantum turbulence can be generated by shaking or oscillating the trap which confines the BEC <ref name=":9" /><ref name="Navon 72–75"/> and by phase imprinting the quantum vortices.

=== Detection of quantum turbulence ===
In classical turbulence, one usually measures the velocity, either at a fixed position against time (typical of physical experiments) or at the same time at many positions (typical of numerical simulations). Quantum turbulence is characterised by a disordered tangle of discrete (individual) vortex lines.

In helium II techniques exists to measure the vortex line density <math>L</math> (the length of vortex lines per unit volume based on detecting the  second sound attenuation. The average distance between vortex lines, <math>\ell</math>, can be found in terms of the vortex line density as <math>\ell = 1/\sqrt{L}</math> .

==== Detection in helium II ====

* Measuring the attenuation of second sound waves
* Measuring temperature or pressure gradients <ref>{{Cite journal|last1=Walstrom|first1=P. L.|last2=Weisend II|first2=J. G.|last3=Maddocks|first3=J. R.|last4=Van Sciver|first4=S. W.|date=1988-02-01|title=Turbulent flow pressure drop in various He II transfer system components|url=https://www.sciencedirect.com/science/article/abs/pii/0011227588900549|journal=Cryogenics|language=en|volume=28|issue=2|pages=101–109|doi=10.1016/0011-2275(88)90054-9|bibcode=1988Cryo...28..101W |issn=0011-2275}}</ref>
* Measuring ions trapped in the vortices<ref>{{Cite journal|last1=Milliken|first1=F. P.|last2=Schwarz|first2=K. W.|last3=Smith|first3=C. W.|date=1982-04-26|title=Free Decay of Superfluid Turbulence|url=https://link.aps.org/doi/10.1103/PhysRevLett.48.1204|journal=Physical Review Letters|volume=48|issue=17|pages=1204–1207|doi=10.1103/PhysRevLett.48.1204|bibcode=1982PhRvL..48.1204M }}</ref>
* Using tracer particles (small glass or plastic spheres/solid hydrogen snowballs) of size of the order of a micron, and then imaging them using lasers. Techniques that can be used are PIV (particle image velocimetry) or PTV (particle tracking velocimetry). Most recently, excimer helium molecules have been used <ref>{{Cite journal|last1=Bewley|first1=G. P.|last2=Lathrop|first2=D. P.|last3=Sreenivasan|first3=K. R.|date=June 2006|title=Visualization of quantized vortices|journal=Nature|language=en|volume=441|issue=7093|pages=588|doi=10.1038/441588a|pmid=16738652|bibcode=2006Natur.441..588B |issn=1476-4687|doi-access=free}}</ref><ref>{{Cite journal|last1=Chagovets|first1=T. V.|last2=Van Sciver|first2=S. W.|date=2011-10-01|title=A study of thermal counterflow using particle tracking velocimetry|url=https://aip.scitation.org/doi/10.1063/1.3657084|journal=Physics of Fluids|volume=23|issue=10|pages=107102–107102–5|doi=10.1063/1.3657084|bibcode=2011PhFl...23j7102C |issn=1070-6631}}</ref><ref>{{Cite journal|last1=Mantia|first1=M. La|last2=Duda|first2=D.|last3=Rotter|first3=M.|last4=Skrbek|first4=L.|date=February 2013|title=Lagrangian accelerations of particles in superfluid turbulence|url=https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/lagrangian-accelerations-of-particles-in-superfluid-turbulence/DC096198052DFC55296AE510CB074C50|journal=Journal of Fluid Mechanics|language=en|volume=717|doi=10.1017/jfm.2013.31|bibcode=2013JFM...717R...9L |s2cid=123402428|issn=0022-1120}}</ref>
* Using oscillating forks <ref name=":1" />
* Using cantilevers <ref>{{Cite journal|last1=Salort|first1=J.|last2=Monfardini|first2=A.|last3=Roche|first3=P.-E.|date=2012-12-01|title=Cantilever anemometer based on a superconducting micro-resonator: Application to superfluid turbulence|url=https://aip.scitation.org/doi/10.1063/1.4770119|journal=Review of Scientific Instruments|volume=83|issue=12|pages=125002–125002–6|doi=10.1063/1.4770119|pmid=23278018|bibcode=2012RScI...83l5002S |issn=0034-6748}}</ref>
* Using cryogenic hot wires <ref>{{Cite journal|last1=Diribarne|first1=P.|last2=Thibault|first2=P.|last3=Roche|first3=P.|date=2019-10-01|title=Nano-shaped hot-wire for ultra-high resolution anemometry in cryogenic helium|url=https://aip.scitation.org/doi/10.1063/1.5116852|journal=Review of Scientific Instruments|volume=90|issue=10|pages=105004|doi=10.1063/1.5116852|bibcode=2019RScI...90j5004D |s2cid=209972973 |issn=0034-6748}}</ref>

==== Detection in <sup>3</sup>He-B and atomic condensates ====
Quantum turbulence can be detected in <sup>3</sup>He-B in two ways: nuclear magnetic resonance (NMR) <ref>{{Cite journal|last1=Finne|first1=A. P.|last2=Araki|first2=T.|last3=Blaauwgeers|first3=R.|last4=Eltsov|first4=V. B.|last5=Kopnin|first5=N. B.|last6=Krusius|first6=M.|last7=Skrbek|first7=L.|last8=Tsubota|first8=M.|last9=Volovik|first9=G. E.|date=August 2003|title=An intrinsic velocity-independent criterion for superfluid turbulence|url=https://www.nature.com/articles/nature01880|journal=Nature|language=en|volume=424|issue=6952|pages=1022–1025|doi=10.1038/nature01880|pmid=12944960|issn=1476-4687|arxiv=cond-mat/0304586|bibcode=2003Natur.424.1022F |s2cid=11251284}}</ref> and by Andreev scattering of thermal quasiparticles.<ref>{{Cite journal|last1=Fisher|first1=S. N.|last2=Jackson|first2=M. J.|last3=Sergeev|first3=Y. A.|last4=Tsepelin|first4=V.|date=2014-03-25|title=Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in 3He-B|journal=Proceedings of the National Academy of Sciences|volume=111|issue=Supplement 1|pages=4659–4666|doi=10.1073/pnas.1312543110|pmc=3970857|pmid=24704872|doi-access=free}}</ref> For atomic condensates, it is typical that the condensate must be expanded (by switching off the trapping potential) so that is sufficiently large for an image to be taken. This procedure has a disadvantage as it leads to the condensate being destroyed. The outcome leads to a 2-dimensional image which allows for the study of 2-dimensional quantum turbulence, but imposes a constraint studying 3-dimensional quantum turbulence using this method. Individual quantum vortices have been observed in 3-dimensions, moving and reconnecting using a technique which extracts small fractions of the condensate at a time, allowing for the observation of a time sequence of the same vortex configuration.