Energy cascade and the four-fifths law in superfluid turbulence

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_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 Kármán-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.
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Julien Salort, Benoît Chabaud, Emmanuel Lévêque, Philippe-Emmanuel Roche. Energy cascade and the four-fifths law in superfluid turbulence. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2012, 97, pp.34006. ⟨10.1209/0295-5075/97/34006⟩. ⟨hal-00635578v2⟩

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