Editing Quantum turbulence (section)

=== 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.