# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

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Article dans Europhys. Lett. (2014)

## Effective viscosity in quantum turbulence : A steady-state approach

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

The concept of "effective viscosity" $\nu_{eff}$ of superfluid helium, widely used to interpret decaying turbulence, is tested in the steady-state case. We deduce $\nu_{{eff}}$ 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 $\nu_\mathit{eff}$, $\epsilon = \nu_\mathit{eff}\left(\kappa\mathcal{L}\right)^2$, where epsilon is the energy dissipation rate and κ the circulation quantum. Within $1.17\text{-}2.16\ \text{K}$, $\nu_\mathit{eff}$ is consistent with that from decays, allowing for uncertainties in flow parameters. Numerical simulations of the two-fluid equations yield a second estimation of $\nu_\mathit{eff}$ 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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