Abstract
We investigate three-dimensional quantum turbulence as described by the Gross-Pitaevskii model using the analytical method exploited in the Onsager “ideal turbulence” theory. We derive the scale independence of the scale-to-scale kinetic energy flux and establish a double-cascade scenario: At scales much larger than the mean intervortex , the Richardson cascade becomes dominant, whereas at scales much smaller than , another type of cascade is induced by quantum stress. We then evaluate the corresponding velocity power spectrum using a phenomenological argument. The relation between this cascade, which we call quantum stress cascade, and the Kelvin-wave cascade is also discussed.
- Received 23 October 2020
- Accepted 27 January 2021
DOI:https://doi.org/10.1103/PhysRevE.103.023106
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