Effective viscosity in quantum turbulence: A steady-state approach

Abstract

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.

Diffusion of quantum vortices

“…Our values of ν ′ /κ are slightly larger but in fair agreement with ν ′ /κ ≈ 0.1 reported by Tsubota et al [54], and in the related (but not the same as spatial spreading) problem of the decay of superfluid turbulence [56][57][58]. The difference is probably due to the fact that our calculation is two-dimensional and lacks three-dimensional effects such as vortex reconnections and Kelvin waves.…”

Quantum turbulence of bellows-driven4He superflow: Steady state

“…The effective viscosity measured from decays starting from different vortex line density L 0 is found to slightly vary, but in a manner uncorrelated with L 0 . In any case, we do not expect ν ′ to be dependent on L 0 because we understand ν ′ to be a robust property of the flow independent of flow details, as it is shown by consistent values coming from different decay experiments [20] and also from steady-flows, hence from an entirely independent approach [53]. For these reasons, we think it justified to average ν ′ originating from different L 0 -which is reflected in the error bars in Fig.…”

“…We notice that, despite the data from the three experiments at the same temperature being roughly consistent within error bars, the superflow data for D10 lie systematically lower than those for D7, which puts pressure on the understanding that ν ′ should not depend on flow details. At any rate, as we have discussed in our works which include determination of effective viscosity [53,54], the absolute value of ν ′ obtained from decay measurements can have uncertainties up to a factor of 4, depending on how strictly the assumption on saturation of the large eddies size attains. Accurate experimental determination of ν ′ to better than a factor of 4 remains therefore still a challenge.…”

Hot-wire anemometry for superfluid turbulent coflows

“…• The mean vortex spacing δ = L −1/2 was found to behave similarly with the Kolmogorov dissipative scale in classical turbulence, 32,33 i.e., L increases with the Reynolds number as Re 3/2 and thus with velocity. This leads to the conclusion that a higher mean velocity would lead to a degraded heat transfer, which is obviously opposite to the observation of Fig.…”