No abstract

Recent preliminary experiments (Marakov et al Phys. Rev. B 91, 094503 (2015)), using tripletstate He2 excimer molecules as tracers of the motion of the normal fluid, have shown that, in thermal counterflow turbulence in superfluid 4 He, small scale turbulence in the superfluid component is accompanied, above a critical heat flux, by partially-coupled large-scale turbulence in both fluids, with an energy spectrum proportional to k −m , where m is greater than the Kolmogorov value of 5/3. Here we report the results of a more detailed study of this spectrum, over a range of temperatures and heat fluxes, using the same experimental technique. We show that the exponent m varies systematically with heat flux, but is always greater than 5/3. We interpret this as arising from the steady counterflow, which causes large-scale eddies in the two fluids to be pulled in opposite directions, giving rise to dissipation by mutual friction at all wave numbers, mutual friction tending also to oppose the effect of the counterflow. Comparison of the experimental results with a simple theory suggests that this process may be more complicated than we might have hoped, but experiments covering a wider range of heat fluxes, which are technically very difficult, will probably be required before we can arrive at a convincing theory.

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.