Abstract
Velocity measurements in turbulent superfluid helium between co-rotating propellers are reported. The parameters are chosen such that the flow is fully turbulent, and its dissipative scales are partly resolved by the velocity sensors. This allows for the first experimental comparison of spectra in quantum versus classical turbulence where dissipative scales are resolved. In some specific conditions, differences are observed, with an excess of energy at small scales in the quantum case compared to the classical one. This difference is consistent with the prediction of a pileup of superfluid kinetic energy at the bottom of the inertial cascade of turbulence due to a specific dissipation mechanism.
Highlights
Tλ ≈ 2.18 K, liquid helium-4 is a classical “Navier-Stokes” fluid called He I
The dynamics of turbulent He II is greatly influenced by singularities in the superfluid component called quantum vortices, which form a complex tangle at high Reynolds number
Fitting the experimental data with Eq (7) leads to σnoise = 4.1 mm/s, and τ = 5.2 %. This level of turbulence intensity is consistent with the Laser Doppler Velocimetry (LDV) measurements in the SPHYNX cell in water, and to similar measurements obtained at even lower Reynolds number in air [45], suggesting that the turbulence intensity in this geometry does not depend much on the Reynolds number, over a large range of Reg
Summary
Tλ ≈ 2.18 K, liquid helium-4 is a classical “Navier-Stokes” fluid called He I. In the category (i), all turbulence quantities with a classical analogue were found to be identical in classical and quantum turbulence experiments when conducted at sufficiently high Reynolds number This category includes drag force [3, 4, 5, 6], pressure drop [7, 8], mean-torque [9], statistics of intense vorticity coherent structures [10] and velocity statistics including histograms [11], spectra [12, 13], energy cascade from large to small scales [11] and intermittency [12, 14]. From a classical turbulence standpoint, the reason for a lack of change above and below the superfluid transition is that the dynamics of turbulent flows at high Reynolds number is fully determined by the large scales [39] In principle this is expected to hold only at scales much larger than the typical inter-vortex distance, where He II behaves as a single fluid. The paper is organized as follows: in the first section, the flow properties are determined in He I using a reference hot-wire anemometer; in the second section a cantilever anemometer and a miniature Pitot-like sensor, which works in both He I and He II are validated against the hot-wire; in the third section, velocity spectra obtained in He II with the cantilever anemometer and the miniature Pitot sensor are discussed
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