Volume 106, Number 2, April 2014
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||05 May 2014|
Effective viscosity in quantum turbulence: A steady-state approach
1 Institute of Physics ASCR - Na Slovance 2, 182 21 Prague, Czech Republic
2 Faculty of Mathematics and Physics, Charles University in Prague - Ke Karlovu 3, 121 16 Prague, Czech Republic
3 Laboratoire de Physique, Ecole Normale Supérieure de Lyon & CNRS, Université de Lyon 46 allée d'Italie, F-69364 Lyon cedex 7, France
4 Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon & CNRS, Université de Lyon 36 avenue Guy de Collonge F-69134, Ecully, France
5 Univ. Grenoble Alpes, Inst NEEL - F-38042 Grenoble, France
6 CNRS, Inst NEEL - F-38042 Grenoble, France
Received: 13 January 2014
Accepted: 7 April 2014
The concept of “effective viscosity” of superfluid helium, widely used to interpret decaying turbulence, is tested in the steady-state case. We deduce from measurements of the vortex line density, , in a grid flow. The scaling of with velocity confirms the validity of the heuristic relation defining , , where ϵ is the energy dissipation rate and κ the circulation quantum. Within , is consistent with that from decays, allowing for uncertainties in flow parameters. Numerical simulations of the two-fluid equations yield a second estimation of 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.
PACS: 47.37.+q – Hydrodynamic aspects of superfluidity; quantum fluids / 67.25.dg – Transport, hydrodynamics, and superflow / 67.25.dk – Vortices and turbulence
© EPLA, 2014
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