Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence.

Generic scaling laws, such as Kolmogorov's 5/3 law, are milestone achievements of turbulence research in classical fluids. For quantum fluids such as atomic Bose-Einstein condensates, superfluid helium, and superfluid neutron stars, turbulence can also exist in the presence of a chaotic tangle of evolving quantized vortex lines. However, due to the lack of suitable experimental tools to directly probe the vortex-tangle motion, so far little is known about possible scaling laws that characterize the velocity correlations and trajectory statistics of the vortices in quantum-fluid turbulence, i.e., quantum turbulence (QT). Acquiring such knowledge could greatly benefit the development of advanced statistical models of QT. Here we report an experiment where a tangle of vortices in superfluid 4He are decorated with solidified deuterium tracer particles. Under experimental conditions where these tracers follow the motion of the vortices, we observed an apparent superdiffusion of the vortices. Our analysis shows that this superdiffusion is not due to Lévy flights, i.e., long-distance hops that are known to be responsible for superdiffusion of random walkers. Instead, a previously unknown power-law scaling of the vortex-velocity temporal correlation is uncovered as the cause. This finding may motivate future research on hidden scaling laws in QT.

A cryogenic-helium pipe flow facility with unique double-line molecular tagging velocimetry capability.

Cryogenic helium-4 has extremely small kinetic viscosity, which makes it a promising material for high Reynolds (Re) number turbulence research in compact laboratory apparatus. In its superfluid phase (He II), helium has an extraordinary heat transfer capability and has been utilized in various scientific and engineering applications. In order to unlock the full potential of helium in turbulence research and to improve our understanding of the heat transfer mechanism in He II, a flow facility that allows quantitative study of helium heat-and-mass transfer processes is needed. Here, we report our work in assembling and testing a unique helium pipe-flow facility that incorporates a novel double-line molecular tagging velocimetry (DL-MTV) system. This flow facility allows us to generate turbulent pipe flows with Re above 107, and it can also be adapted to produce heat-induced counterflow in He II. The DL-MTV system, which is based on the generation and tracking of two parallel thin He2 * molecular tracer lines with an adjustable separation distance, allows us to measure not only the velocity profile but also both the transverse and longitudinal spatial velocity structure functions. We have also installed a differential pressure sensor on the flow pipe for pressure drop measurements. The testing results of the flow facility and the measuring instruments are presented. We discuss how this facility will allow us to solve some outstanding problems in the helium heat-and-mass transfer topic area.