We report complementary experimental, numerical, and theoretical study of turbulent coflow, counterflow, and pure superflow of superfluid ${}^4\mathrm{He}$ in a channel, resulting in a physically transparent and relatively simple model of decaying quantum turbulence that accounts for interactions of coexisting quantum and classical components of turbulent superfluid ${}^4\mathrm{He}$. We further offer an analytical theory of the energy spectra of steady-state quantum turbulence in the counterflow and pure superflow, based on algebraic approximation for the energy fluxes over scales. The resulting spectra are not of the classic Kolmogorov form, but strongly suppressed by the mutual friction, leading to the energy dissipation at all scales, enhanced by the counterflow-induced decoupling of the normal and superfluid velocity fluctuations.

• Received 15 June 2016
• Revised 25 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.174504