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Home > Teams > Turbulence & Instabilities > Publications T&I > Publications T&I 2014

Article in Europhys. Lett. (2014)

Effective viscosity in quantum turbulence: A steady-state approach

Simone Babuin, Emil Varga, Ladislav Skrbek, Emmanuel Lévêque & Philippe-E. Roche

Effective viscosity in quantum turbulence: A steady-state approach

The concept of "effective viscosity" $\nu_\mathrm{{eff}}$ of superfluid helium, widely used to interpret decaying turbulence, is tested in the steady-state case. We deduce $\nu_{\mathrm{eff}}$ from measurements of the vortex line density, $\mathcal{L}$ , in a grid flow. The scaling of $\mathcal{L}$ with velocity confirms the validity of the heuristic relation defining $\nu_{\mathrm{eff}}$, $\epsilon = \nu_{\mathrm{eff}}\left(\kappa\mathcal{L}\right)^2$, where epsilon is the energy dissipation rate and κ the circulation quantum. Within $1.17\text{-}2.16\ \text{K}$, $\nu_{\mathrm{eff}}$ is consistent with that from decays, allowing for uncertainties in flow parameters. Numerical simulations of the two-fluid equations yield a second estimation of $\nu_{\mathrm{eff}}$ within an order of magnitude with all experiments. Its temperature dependence, more pronounced in numerics than experiments, shows a crossover 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.
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