Thesis presented October 21, 2024
Abstract:
At atmospheric pressure, helium-4 is a liquid at temperatures below 4.2 K. Up to 2.17 K at saturation, it behaves as a Newtonian liquid (He I), characterized by an extremely low viscosity of about 2 × 10?? m²/s. Below 2.17 K at saturation, helium enters a second liquid phase (He II) which exhibits remarkable properties: complete absence of viscosity in certain types of flow, extremely high apparent thermal conductivity, fountain effect...
Currently, no model can fully describe the dynamics of this "superfluid." To enhance our understanding, this thesis presents a comparative experimental study of turbulence in He II (or quantum turbulence) along with in He I (or classical turbulence). Within the temperature range explored (down to 1.6 K), He II is generally described as a superposition of two components: a normal, Newtonian component, and a superfluid component with no viscosity, where vorticity is concentrated in quantized filaments. These two components are coupled by a force known as mutual friction. Despite their intrinsically different natures, it has been reported that classical and quantum turbulence exhibit similar behavior at large scales.
In our experiment, the flow is generated by the oscillation of a double-grid (three-dimensional inertial forcing), with its frequency and amplitude adjustable to modulate the intensity of velocity fluctuations. Two complementary approaches are used to characterize turbulence properties. The first involves analyzing the 2D and 3D trajectories of particles, reconstructed from flow images captured by high-speed cameras through the cryostat windows. The second approach examines the attenuation of a stationary second sound wave due to its interaction with the quantum vortex lines in the flow.
The trajectory analysis allowed us to establish the scaling law relating turbulent velocity fluctuations to agitation parameters, which agrees with those reported in the literature. Characterization of the third-order structure function of longitudinal velocity increments, calculated from 3D measurements, confirmed the four-fifths law. We were thus able to estimate the dissipation rate and deduce the integral scale of the flow. Our measurements of the average vortex line density as a function of the forcing intensity confirm the scaling law reported in the literature: δ/L = ß Re-3/4. Thanks to the cross-diagnostics implemented, we determine ß = 0.48 ± 0.01 with good precision, whereas only an order of magnitude of this constant was previously known. It is then shown that the intensity of the vorticity associated with this scale is in very good agreement with that predicted by the Kolmogorov cascade mechanisms.
The interpretation of these measurements leads us to propose a scenario for the mechanisms of energy transfer and dissipation in He II. In this paradigm, the energy injected at large scales is distributed between the normal and superfluid components up to the mean inter-vortex scale. At this scale, the mutual friction force becomes significant and dissipates a portion of the energy. Depending on the remaining proportion, it also allows the transfer of energy from the superfluid component to the normal component. A new cascade then carries this residual energy and dissipates it at scales where viscosity becomes significant.
Keywords:
Turbulence, 4D-PTV, Superfluid Helium, Oscillating Grids, 2nd Sound Attenuation