Abstract
Low-temperature superfluid turbulence is studied experimentally in a Helium swirling flow and numerically with the Gross-Pitaevskii equation in the geometry of the Taylor-Green (TG) vortex flow. Numerically, it was found in Nore et al. (1997a, b) that the kinetic energy transfer in the superfluid TG vortex is comparable to that of the viscous TG vortex and that the energy spectrum of the superflow is compatible with Kolmogorov's scaling. The vorticity dynamics of the superflow are similar to that of the viscous flow. In both cases, many vortex reconnection events happen throughout the flow. Experimentally, power measurements and pressure fluctuation spectra show very little difference above and far below the superfluid transition temperature, where the normal-fluid component of Helium is negligible (less than 5% in mass at T = 1.2 K).
Highlights
Helium He4, below the,\ transition, behaves as a superposition of two fluids (Landau and Lifchitz, 1980): a superfluid and a normal fluid
The two fluids interact through mutual friction caused by the interaction of the normal fluid with the superfluid vortex filaments
It is currently admitted that, in ordinary turbulent situations, and at low fluctuation rates, Equation (3) is dominated by the dynamic term, so that by measuring the pressure fluctuations at the total head tube, one has a direct access to the velocity fluctuations u (t)
Summary
Helium He4 , below the ,\ transition, behaves as a superposition of two fluids (Landau and Lifchitz, 1980): a superfluid and a normal fluid. The second numerical tool uses the expression for the total energy density in physical space and Parseval's formula to define energy spectra; these make possible a separation of the various contributions to the total energy, One of the main quantitative results obtained by Nore et al (1997a, b) is the remarkable agreement of the energy dissipation rate with the corresponding data in the incompressible viscous TG flow. Both the moment tmax ,...., 10 of maximum energy dissipation and its value r::.
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