Theory of energy spectra in superfluid He-4 counterflow turbulence

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