Energy cascade and the four-fifths law in superfluid turbulence

¹ 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

Received: 2 August 2011
Accepted: 14 December 2011

Abstract

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 R_λ≈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 R_λ≈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.