Energy cascade and the four-fifths law in superfluid turbulence
Institut Néel, CNRS/UJF - BP 166, F-38042 Grenoble cedex 9, France, EU
2 Laboratoire de Physique de l'ENS de Lyon, CNRS/Université Lyon - F-69364 Lyon cedex 7, France, EU
Accepted: 14 December 2011
The 4/5-law of turbulence, which characterizes the energy cascade from large to small-sized eddies at high Reynolds numbers in classical fluids, is verified experimentally in a superfluid 4He wind tunnel, operated down to 1.56 K and up to Rλ≈1640. The result is corroborated by high-resolution simulations of Landau-Tisza's two-fluid model down to 1.15 K, corresponding to a residual normal fluid concentration below 3% but with a lower Reynolds number of order Rλ≈100. Although the Kármán-Howarth equation (including a viscous term) is not valid a priori in a superfluid, it is found that it provides an empirical description of the deviation from the ideal 4/5-law at small scales and allows us to identify an effective viscosity for the superfluid, whose value matches the kinematic viscosity of the normal fluid regardless of its concentration.
PACS: 47.37.+q – Hydrodynamic aspects of superfluidity; quantum fluids / 67.30.hb – Transport, hydrodynamics, and superflow / 67.25.dk – Vortices and turbulence
© EPLA, 2012