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

Abstract : The concept of ''effective viscosity'' $\nueff$ of superfluid helium, widely used to interpret decaying turbulence, is tested in the steady-state case. We deduce $\nueff$ from measurements of vortex line density, $\LL$, in a grid flow. The scaling of $\LL$ with velocity confirms the validity of the heuristic relation defining $\nueff$, $\epsilon = \nueff \left(\kappa \LL\right)^2$, where $\epsilon$ is the energy dissipation rate and $\kappa$ the circulation quantum. Within $1.17\, - 2.16\,{\rm K}$, $\nueff$ is consistent with that from decays, allowing for uncertainties in flow parameters. Numerical simulations of the two-fluid equations yield a second estimation of $\nueff$ 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.
Document type :
Journal articles
Domain :

Cited literature [7 references]

https://hal.archives-ouvertes.fr/hal-00984313
Contributor : Philippe-Emmanuel Roche <>
Submitted on : Tuesday, February 24, 2015 - 5:04:27 PM
Last modification on : Wednesday, November 20, 2019 - 2:35:18 AM
Long-term archiving on: Friday, May 29, 2015 - 9:45:29 AM

### File

Files produced by the author(s)

### Citation

Simone Babuin, Emil Varga, Ladislav Skrbek, Emmanuel Lévêque, Philippe-Emmanuel Roche. Effective viscosity in quantum turbulence: a steady-state approach. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2014, 106 (2), pp.24006. ⟨10.1209/0295-5075/106/24006⟩. ⟨hal-00984313v2⟩

Record views