Theory of energy spectra in superfluid He-4 counterflow turbulence

TL;DR

This paper develops an analytical theory explaining how counterflow velocity in superfluid He-4 turbulence affects energy spectra and dissipation, aligning well with experimental observations of turbulence scaling.

Contribution

The paper introduces a new analytical model that captures the scale-dependent decoupling and mutual friction effects in superfluid He-4 counterflow turbulence.

Findings

The theory predicts energy spectra across various flow parameters.

Predicted mean exponents of energy spectra agree with experimental data.

The model explains the dependence of turbulence statistics on flow conditions.

Abstract

In the thermally driven superfluid He-4 turbulence, the counterflow velocity $U_{\rm ns}$ partially decouples the normal and superfluid turbulent velocities. Recently we suggested [J. Low Temp. Phys. 187, 497 (2017)] that this decoupling should tremendously increase the turbulent energy dissipation by mutual friction and significantly suppress the energy spectra. Comprehensive measurements of the apparent scaling exponent nexp of the 2nd-order normal fluid velocity structure function $S_2(r)\propto r^{n_{\rm exp}}$ in the counterflow turbulence [Phys.Rev.B 96, 094511 (2017)] confirmed our scenario of gradual dependence of the turbulence statistics on the flow parameters. We develop an analytical theory of the counterflow turbulence, accounting for a twofold mechanism of this phenomenon: i) a scale-dependent competition between the turbulent velocity coupling by the mutual friction and the $U_{\rm ns}$-induced turbulent velocity decoupling and ii) the turbulent energy dissipation by the mutual friction enhanced by the velocity decoupling. The suggested theory predicts the energy spectra for a wide range of flow parameters. The mean exponents of the normal fluid energy spectra $\langle m_n\rangle_{10}$, found without fitting parameters, qualitatively agree with the observed $n_{\rm exp} + 1$ for $T\gtrsim 1.85$K