## Energy cascade and the four-fifths law in superfluid turbulence    [PDF]

Julien Salort, Benoît Chabaud, Emmanuel Lévêque, Philippe-E. Roche
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_lambda ~ 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_lambda ~ 100. Although the K\'arm\'an-Howarth equation (including a viscous
term) is not valid \emph{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.
View original: http://arxiv.org/abs/1202.0710