Theory of energy spectra in superfluid 4 He counterflow turbulence

In the thermally driven superfluid He-4 turbulence, the counterflow velocity U_ns partially decouples 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 n_exp of the second-order normal-fluid velocity structure function S₂(r) ∝ r^nexp in the counterflow turbulence [J. Gao et al., Phys. Rev. B 96, 094511 (2017)] confirmed our scenario of gradual dependence of the turbulence statistics on 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 mutual friction and the Uns-induced turbulent velocity decoupling and (ii) the turbulent energy dissipation by 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 m₁₀, found without fitting parameters, qualitatively agree with the observed n_exp+ 1 for T 1.85 K.