A zero-temperature superfluid is arguably the simplest system in which to study complex fluid dynamics, such as turbulence. We describe computer simulations of such turbulence and compare the results directly with recent experiments in superfluid $^{3}\text{H}\text{e-B}$. We are able to follow the entire process of the production, evolution, and decay of quantum turbulence. We find striking agreement between simulation and experiment and gain insights into the mechanisms involved.
A zero-temperature superfluid is arguably the simplest system in which to study complex fluid dynamics, such as turbulence. We describe computer simulations of such turbulence and compare the results directly with recent experiments in superfluid 3He-B. We are able to follow the entire process of the production, evolution, and decay of quantum turbulence. We find striking agreement between simulation and experiment and gain insights into the mechanisms involved.
Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.
Abstract Chapter 5 delves into quantum turbulence in superfluid helium and atomic Bose-Einstein condensates (BECs). The foundation of quantum turbulence research lies in classical fluid dynamics and turbulence, which is why we begin by covering essential concepts like the Reynolds number and Kolmogorov’s -5/3 power law in the energy spectrum. These principles are crucial for understanding quantum turbulence. We then explore the shared aspects of quantum turbulence in superfluid helium and atomic BECs, such as the differences in vortex configurations compared to classical turbulence, energy spectra, cascades, and the distinction between quasiclassical (Kolmogorov) and ultraquantum (Vinen) turbulence, focusing on their decay behaviors. In superfluid helium, we emphasize experimental studies in thermal counterflow and numerical simulations using the Vortex Filament Model (VFM). The advent of visualization experiments in the mid-2000s was transformative, allowing the observation of normal fluid velocity profiles and accelerations via tracer particles, which led to more accurate simulations coupling the VFM with normal fluid dynamics. Another significant topic is the energy spectrum of quantum turbulence, and whether it mirrors classical turbulence remains a key question. In addition to thermal counterflow, localized quantum turbulence generated by oscillating objects has been a major area of study. We present research showing how quantized vortices grow and evolve into turbulence. Superfluid 3He-B also provides a platform for quantum turbulence, with advancements in microfabrication bringing MEMS and NEMS into focus for studying quantum hydrodynamics at micro- and nanoscale, influenced by boundary conditions. In atomic BECs, confined by potentials, turbulence is induced through techniques like shaking or moving potentials. A unique aspect of BECs is two-dimensional quantum turbulence, featuring inverse energy cascades, Onsager vortices, and negative temperature states. Finally, atomic BECs, being compressible, serve as a platform for both vortex and wave turbulence. Multicomponent BECs, such as spinor BECs, introduce spin turbulence, further diversifying the field.
The theory of how turbulent energy decays via a Richardson cascade is well‐established for classical fluids, and it also seems to apply to the case of so‐called co‐flowing He II turbulence in the range from the superfluid transition temperature Tλ down to ∼1 K, where its behaviour is similar to that of a classical fluid. For pure superfluids, e.g. He II in the mK range or 3He‐B in the μK range, where the normal fluid density ρn is near zero, the mode(s) through which quantum turbulence (QT) might decay have been much less clear because of the absence of viscosity to dissipate the turbulent energy on small length scales. Recent advances made in the theory of QT in this T → 0 limit are consistent with such experimental evidence as is available, but new experiments supported by new techniques for the production and detection of QT are urgently required. The experimental situation is reviewed and prospects for further advances are considered.
Motivated by the various indications that holographic superfluid is BCS like at the standard quantization but BEC like at the alternative quantization, we have implemented the alternative quantization in the dynamical holographic superfluid for the first time. With this accomplishment, we further initiate the detailed investigation of quantum turbulence in finite temperature BEC by a long time stable numerical simulation of bulk dynamics, which includes the two body decay of vortex number caused by vortex pair annihilation, the onset of superfluid turbulence signaled by Kolmogorov scaling law, and a direct energy cascade demonstrated by injecting energy to the turbulent superfluid. All of these results share the same patterns as the holographic superfluid at the standard quantization, thus suggest that these should be universal features for quantum turbulence at temperatures order of the critical temperature.
This article reviews recent developments in quantum fluid dynamics and quantum turbulence (QT) for superfluid helium and atomic Bose–Einstein condensates. Quantum turbulence was discovered in superfluid 4He in the 1950s, but the field moved in a new direction starting around the mid-1990s. Quantum turbulence is comprised of quantised vortices that are definite topological defects arising from the order parameter appearing in Bose–Einstein condensation. Hence, QT is expected to yield a simpler model of turbulence than does conventional turbulence. A general introduction to this issue and a brief review of the basic concepts are followed by a description of vortex lattice formation in a rotating atomic Bose–Einstein condensate, typical of quantum fluid dynamics. Then we discuss recent developments in QT of superfluid helium such as the energy spectra and dissipative mechanisms at low temperatures, QT created by vibrating structures, and the visualisation of QT. As an application of these ideas, we end with a discussion of QT in atomic Bose–Einstein condensates.