Abstract
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)’.
Highlights
Most universal properties of turbulence are only revealed in flows with very high Reynolds number
Similar to our previous studies of superfluid turbulence [14,23,24,36,37], we describe the largescale turbulence in superfluid 4He by the coarse-grained Navier–Stokes equation (2.1) coupled by the mutual friction force
We developed a theory of energy spectra in the thermally driven turbulent counterflow of superfluid 4He, which generalizes the L’vov–Pomyalov theory of counterflow turbulence [24] to the strongly anisotropic case
Summary
Most universal properties of turbulence are only revealed in flows with very high Reynolds number. The two-fluid nature of the superfluid 4He allows generation of turbulence by thermal gradient [2,5,8,19,20,21,22] In such a flow that has no classical analogy, the two fluid components flow in opposite directions: the normal fluid carries the heat flux away from the heat source with the mean velocity Un, while the superfluid flows towards the heater with the mean velocity Us. The mutual friction force that couples the components leads to both the energy exchange and additional dissipation by mutual friction that are scale-dependent [23,24].
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