Energy cascade and the four-fifths law in superfluid turbulence

• Published in: Europhysics letters Vol. 97; no. 3; p. 34006
• Main Authors: Salort, J., Chabaud, B., Lévêque, E., Roche, P.-E.
• Format: Journal Article
• Language: English
• Published: EPS, SIF, EDP Sciences and IOP Publishing 01-02-2012; European Physical Society / EDP Sciences / Società Italiana di Fisica / IOP Publishing
• Subjects: 47.37.+q; 67.25.dk; 67.30.hb; Condensed Matter; Engineering Sciences; Fluid mechanics; Fluids mechanics; Mechanics; Other; Physics
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/97/34006

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.