An intrinsic velocity-independent criterion for superfluid turbulence

Abstract

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60T(c) (where T(c) is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

Quantum turbulence in a trapped Bose-Einstein condensate

“…One of the main motivations of recent studies is to investigate the relationship between QT and CT. Some similarities between the two types of turbulence have been experimentally observed in superfluid 4 He [8, 9] and 3 He [10,11], and have been theoretically confirmed by numerical simulations of the quantized vortex-filament model [12] and a model using the Gross-Pitaevskii (GP) equation [13,14,15,16]. In particular, we have successfully obtained the Kolmogorov law for QT, which is one of the most important statistical laws in CT [17] by a numerical simulation of the GP equation [14,15].…”

Andreev reflection, a tool to investigate vortex dynamics and quantum turbulence in 3 He-B

“…There has been a great deal of renewed interest in quantum turbulence in recent years owing to several factors: quantum turbulence was discovered in superfluid 3 He (6)(7)(8), techniques were developed to extend the study of quantum turbulence in superfluid 4 He to very low temperatures (9,10), imaging techniques were developed to visualize superfluid turbulence at higher temperatures (11)(12)(13)) (see the review in ref. 14), mechanical resonator techniques were developed for quantum turbulence (15)(16)(17)(18), and quantum turbulence was studied in dilute gases (19,20); there were many important theoretical developments, for example refs.…”

Applications of the quartz tuning fork in classical and superfluid hydrodynamics

“…This process is, however, associated with temperature-dependent rather than velocity-dependent critical conditions [24]. As was already mentioned above, the transition to turbulence can be detected in 4 He by measuring the F (U ) dependence of a calibrated tuning fork.…”