Grid superfluid turbulence and intermittency at very low temperature

Theory of anisotropic superfluid 4He counterflow turbulence

We develop a theory of strong anisotropy of the energy spectra in the thermally driven turbulent counterflow of superfluid ⁴He. The key ingredients of the theory are the three-dimensional differential closure for the vector of the energy flux and the anisotropy of the mutual friction force. We suggest an approximate analytic solution of the resulting energy-rate equation, which is fully supported by our numerical solution. The two-dimensional energy spectrum is strongly confined in the direction of the counterflow velocity. In agreement with the experiments, the energy spectra in the direction orthogonal to the counterflow exhibit two scaling ranges: a near-classical non-universal cascade dominated range and a universal critical regime at large wavenumbers. The theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Reply to "Comment on 'Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory' "

We refute the criticism expressed in a Comment by Krstulovic, L'vov, and Nazarenko [Phys. Rev. E 105, 027101 (2022)10.1103/PhysRevE.105.027101] on our paper [Phys. Rev. E 103, 023106 (2021)2470-004510.1103/PhysRevE.103.023106]. We first show that quantization of circulation is not ignored in our analysis. Then, we propose a more sophisticated analysis to avoid a subtle problem with the regularity of the velocity field. We thus defend the main results of our paper, which predicts the double-cascade scenario where the quantum stress cascade follows the Richardson cascade. We also provide a conjecture on the relation between the Kelvin-wave cascade and the quantum stress cascade.