We report on studies of quantum turbulence with second-sound in superfluid 4 He in which the turbulence is generated by the flow of the superfluid component through a wide square channel, the ends of which are plugged with sintered silver superleaks, the flow being generated by compression of a bellows. The superleaks ensure that there is no net flow of the normal fluid. In an earlier paper [Phys. Rev. B, 86, 134515 (2012)] we have shown that steady flow of this kind generates a density of vortex lines that is essentially identical with that generated by thermal counterflow, when the average relative velocity between the two fluids is the same. In this paper we report on studies of the temporal decay of the vortex-line density, observed when the bellows is stopped, and we compare the results with those obtained from the temporal decay of thermal counterflow re-measured in the same channel and under the same conditions. In both cases there is an initial fast decay which, for low enough initial line density approaches for a short time the form t −1 characteristic of the decay of a random vortex tangle. This is followed at late times by a slower t −3/2 decay, characteristic of the decay of large "quasi-classical" eddies. However, in the range of investigated parameters, we observe always in the case of thermal counterflow, and only in a few cases of high steady-state velocity in superflow, an intermediate regime in which the decay either does not proceed monotonically with time or passes through a point of inflexion. This difference, established firmly by our experiments, might represent one essential ingredient for the full theoretical understanding of counterflow turbulence.

The concept of "effective viscosity" ν eff of superfluid helium, widely used to interpret decaying turbulence, is tested in the steady-state case. We deduce ν eff from measurements of vortex line density, L, in a grid flow. The scaling of L with velocity confirms the validity of the heuristic relation defining ν eff , = ν eff (κL) 2 , where is the energy dissipation rate and κ the circulation quantum. Within 1.17 − 2.16 K, ν eff is consistent with that from decays, allowing for uncertainties in flow parameters. Numerical simulations of the two-fluid equations yield a second estimation of ν eff within an order of magnitude with all experiments. Its temperature dependence, more pronounced in numerics than experiments, shows a cross-over from a viscous-dominated to a mutual-friction-based dissipation as temperature decreases, supporting the idea that the effective viscosity of a quantum turbulent flow is an indicator of the dissipative mechanisms at play.

We report heat transport measurements in a cylindrical convection apparatus rotating about the vertical axis. The aspect ratio was 1/2. The working fluid was cryogenic helium gas and the following parameter ranges applied: the Rayleigh number, Ra, varied in the range 1011 < Ra < 4.3 × 1015, the Taylor number, Ta, varied in the range 1011 < Ta < 3 × 1015, the convective Rossby number, Ro, varied in the range 0.4 < Ro < 1.6 and the Prandtl number, Pr, varied in the range 0.7 < Pr < 5.9. Boussinesq conditions applied quite closely. The heat transport for steady rotation, under all conditions of the present experiments, was smaller than that for the non-rotating case. When the rotation rate varied periodically in time, a sharp transition to a state of significantly enhanced heat transport was observed for modulation Taylor numbers Ta* ≳ 1014, where Ta* is based on the peak value of the modulation angular velocity.

We report complementary experimental, numerical and theoretical study of turbulent coflow, counterflow and pure superflow of superfluid 4 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 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. PACS numbers: 67.25.dg, 67.25.dk, 67.25.dm I. arXiv:1509.03765v2 [cond-mat.other]