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 He-4. 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)'.

Automated summary

We develop a theory to explain the strong anisotropy of energy spectra in the thermally driven turbulent counterflow of superfluid He-4. The theory involves the differential closure of the energy flux vector and the anisotropy of the mutual friction force. We propose an approximate analytic solution and validate it with numerical solutions. The energy spectrum is strongly confined in the direction of the counterflow velocity, and in the direction orthogonal to the counterflow it exhibits two scaling ranges. This theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters.