Editing Quantum turbulence (section)

=== Vinen turbulence ===
[[File:Vortex-tangle-vinen.png|alt=Quantum turbulence-vinen regime|thumb|373x373px|Fig 9b. Numerically simulated vortex tangle representing vinen quantum turbulence. The thin lines represent vortex lines inside of a cubic container. The colorbar<ref name=":3" /><ref name=":4" /> represents the amount of non-local interaction, i.e. the amount by how much a section of the vortex line is affected by the other vortex lines surrounding it. (Credit AW Baggaley)]]
[[File:Vinen-in-qf.png|thumb|373x373px|Fig 10. Schematic diagram of the energy spectrum for vinen turbulence. A <math>k^{-1}</math> regime can be observed for very large wavenumbers, with the peak of the energy spectrum occurring at the wavenumber <math>k_{\ell}</math> associated to the quantum length scale <math>\ell</math>. The green line represents a <math>k^{-5/3}</math> regime for comparison.]]
Vinen turbulence can be generated in a quantum fluid by the injection of vortex rings into the system, which has been observed both numerically and experimentally. It has been observed also in numerical simulations of turbulent Helium II driven by a small heat flux and in numerical simulations of trapped atomic Bose-Einstein condensates; it has been found even in numerical studies of superfluid models of the early universe.<ref name=":3" /> Unlike the Kolmogorov regime which appears to have a classical counterpart, Vinen turbulence has not been identified in classical turbulence..

Vinen turbulence occurs for very low energy inputs into the system, which prevents the formation of the large scale partially polarised structures that are prevalent in Kolmogorov turbulence, as is shown in Fig 9a. The partial polarization contributes strongly to the amount of non-local interactions between the vortex lines, which can be seen in the figure. In stark contrast, Fig 9b displays the Vinen turbulence regime, where there is very little non-local interaction. The energy spectrum of Vinen turbulence peaks at the intermediate scales around <math>k_{\ell}</math>, rather than at large length scales <math>k_{D}</math>. From Fig 10, it can be seen that for small length scales the turbulence follows the typical <math>k^{-1}</math> behaviour of an isolated vortex. As a result of these properties Vinen turbulence appears as an almost completely random flow with a very weak or negligible energy cascade.