We address a question which, after a decade-long discussion, still remains open: what is the nature of the ultraquantum regime of decay of quantum turbulence? The model developed in this work reproduces both the ultraquantum and the quasiclassical decay regimes and explains their hydrodynamical natures. In the case where turbulence is generated by forcing at some intermediate length scale, e.g., by the beam of vortex rings in the experiment of Walmsley and Golov [Phys. Rev. Lett. 100, 245301 (2008)], we explain the mechanisms of generation of both ultraquantum and quasiclassical regimes. We also find that the anisotropy of the beam is important for generating the large-scale motion associated with the quasiclassical regime.
We address a question which, after a decade-long discussion, still remains open: what is the nature of the ultraquantum regime of decay of quantum turbulence? The model developed in this work reproduces both the ultraquantum and the quasiclassical decay regimes and explains their hydrodynamical natures. In the case where turbulence is generated by forcing at some intermediate length scale, e.g., by the beam of vortex rings in the experiment of Walmsley and Golov [Phys. Rev. Lett. 100, 245301 (2008)], we explain the mechanisms of generation of both ultraquantum and quasiclassical regimes. We also find that the anisotropy of the beam is important for generating the large-scale motion associated with the quasiclassical regime.
Single-body diffusion and two-body dispersion are fundamental processes in classical turbulence, governing particle mixing and transport. However, their behaviors in superfluid turbulence remain largely unexplored. In this study, we numerically investigate the diffusion and relative dispersion of both quantized vortices and superfluid parcels in the 0 K limit in two distinct turbulence regimes: ultraquantum turbulence, characterized by a randomized vortex tangle, and quasiclassical turbulence, in which locally polarized vortices create large-scale flows resembling classical turbulence. Our results reveal that while vortex segments exhibit similar superdiffusion behavior at short times in both regimes, superfluid parcels behave differently—following the same superdiffusion scaling in ultraquantum turbulence but deviating significantly in quasiclassical turbulence. This contrast provides a key clue to the origin of short-time superdiffusion, a puzzle since its recent discovery. Additionally, we show that two-body dispersion of both vortex segments and superfluid parcels exhibits distinct scaling behaviors in ultraquantum and quasiclassical turbulence, highlighting fundamental differences in these two turbulence regimes. Our findings bridge a critical gap in superfluid turbulence research, offering useful insights into turbulent transport in inviscid quantum fluids.
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.
In this thesis, we numerically investigate quantum turbulence in trapped atomic Bose-Einstein condensates (BECs). We first discuss the appropriate qualitative characterization of turbulence in these systems, showing the limitation of analogies with classical hydrodynamics and turbulence in large superfluid Helium experiments. Due to their lack of available length scales, our investigated systems can only fit the ultraquantum (or Vinen) type of quantum turbulence. Secondly, we propose experimentally feasible schemes for more controlled investigations of turbulence making use of dynamical instability of multicharged vortices as an onset for complex vortex dynamics. In two dimensions, our suggested scheme allows control over vortex polarization in the harmonically trapped system. This setup is then used to study how turbulence decays in such a scenario, through the phenomenological modeling of a vortex-number rate equation. As a consequence, we were able to identify that vortex annihilation in these trapped systems happens through a four-vortex process. For three dimensions, we have first provided a study on the decay of a quadruply-charged vortex, also in a harmonically trapped BEC. Having this setting as a comparison point, we propose a quasi-isotropic turbulent system, starting from a phase-imprinted initial state of two doubly-charged, anti-parallel vortices. The vortex turbulence arisen from such configuration was shown to agree with the Vinen turbulent regime, after we characterized specific features of its decay, such as the energy spectrum [E(k) ∼ k1] and the time evolution of the vortex-line density [L(t) ∼ t1]. Although these features have been frequently verified in the context of superfluid Helium turbulence, here this identification was for the first time done for realistic, trapped atomic BECs.
Using the classical field method, we study numerically the characteristics and decay of the turbulent tangle of superfluid vortices which is created in the evolution of a Bose gas from highly nonequilibrium initial conditions. By analyzing the vortex line density, the energy spectrum, and the velocity correlation function, we determine that the turbulence resulting from this effective thermal quench lacks the coherent structures and the Kolmogorov scaling; these properties are typical of both ordinary classical fluids and of superfluid helium when driven by grids or propellers. Instead, thermal quench turbulence has properties akin to a random flow, more similar to another turbulent regime called ultraquantum turbulence, which has been observed in superfluid helium.
We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with q −1 playing the same role as the Reynolds number Re= UR/ν in classical hydrodynamics. It marks the transition between the “laminar” and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re≫1 in classical hydrodynamics, and q ≪1 in superfluid hydrodynamics. Another parameter of superfluid turbulence is the superfluid Reynolds number Re s = UR/κ , which contains the circulation quantum κ characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. A phase diagram of the dynamical vortex states is suggested.
The decay of quantum turbulence in superfluid (_^4)He in the zero temperature limit wasinvestigated. Quantum turbulence was created by impulsive spin-down from a specific angular velocity to rest. A measurement of the vortex line density was performed using the scattering of charged vortex rings. The vortex line density decayed as L ? t^(-3/2) which is the characteristic of quasiclassical turbulence forced at large length scales. The interaction of metastable spin-triplet ?He?_2^* molecules with quantized vortex lines in superfluid (_^4)He at temperatures below 200 mK was studied too. The molecules were generated during an injection of electrons from a sharp metal tip at high voltage. They were detected as a current into a metal collector after ionization upon colliding with the collector surface. The detected current was suppressed by even a small rotation indicating the trapping of the molecules on quantized vortices. The presence of (_^3)He impurities at the level of 0.3 ppb strongly suppressed the detected signal. The temperature dependence of the detected signal showed a sharp peak, most probably associated with the condensation of (_^3)He atoms on vortex cores. The time of flight of the molecules as a function of temperature was measured. It was observed that there are three regimes for ?He?_2^* molecules transportation in superfluid (_^4)He : ballistic regime for T 200 mK, and an intermediate regime between them. The vortex lines were created by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be 96 � 6 nm at pressure of 0.1 bar and 27 � 5 nm at 5.0 bar. It was also demonstrated that a tangle of vortices moving in superfluid (_^4)He are capable of conveying the ?He?_2^* molecules through the drift region.