The present article reviews the recent developments in the physics of quantum turbulence. Quantum turbulence (QT) was discovered in superfluid $^4$He in the 1950s, and the research has tended toward a new direction since the mid 90s. The similarities and differences between quantum and classical turbulence have become an important area of research. QT is comprised of quantized vortices that are definite topological defects, being expected to yield a model of turbulence that is much simpler than the classical model. The general introduction of the issue and a brief review on classical turbulence are followed by a description of the dynamics of quantized vortices. Then, we discuss the energy spectrum of QT at very low temperatures. At low wavenumbers, the energy is transferred through the Richardson cascade of quantized vortices, and the spectrum obeys the Kolmogorov law, which is the most important statistical law in turbulence; this classical region shows the similarity to conventional turbulence. At higher wavenumbers, the energy is transferred by the Kelvin-wave cascade on each vortex. This quantum regime depends strongly on the nature of each quantized vortex. The possible dissipation mechanism is discussed. Finally, important new experimental studies, which include investigations into temperature-dependent transition to QT, dissipation at very low temperatures, QT created by vibrating structures, and visualization of QT, are reviewed. The present article concludes with a brief look at QT in atomic Bose-Einstein condensates.
Generic scaling laws, such as the 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 …
We perform a numerical simulation of the dynamics of quantized vortices produced by coflow in a square channel using the vortex filament model. Unlike the situation in thermal counterflow, where the superfluid velocity $v_{\rm s}$ and normal-fluid velocity $v_{\rm n}$ flow in opposite directions, in coflow, $v_{\rm s}$ and $v_{\rm n}$ flow in the same direction. Quantum turbulence in thermal counterflow has been long studied theoretically and experimentally, and its various features have been revealed.In recent years, an experiment on quantum turbulence in coflow has been performed to observe …
Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.
Quantum mechanics places significant restrictions on the hydrodynamics of superfluid flows. Despite this it has been observed that turbulence in superfluids can, in a statistical sense, share many of the properties of its classical brethren; coherent bundles of superfluid vortices are often invoked as an important feature leading to this quasi-classical behavior. A recent experimental study [E. Rusaouen, B. Rousset, and P.-E. Roche, EPL, {\bf 118}, 1, 14005, (2017)] inferred the presence of these bundles through intermittency in the pressure field, however direct visualization of the quantized…
We have studied the interaction of metastable $^4$He$_2^*$ excimer molecules with quantized vortices in superfluid $^4$He in the zero temperature limit. The vortices were generated by either rotation or ion injection. The trapping diameter of the molecules on quantized vortices was found to be $96\pm6$\,nm at a pressure of 0.1\,bar and $27\pm5$\,nm at 5.0 bar. We have also demonstrated that a moving tangle of vortices can carry the molecules through the superfluid helium.
We performed the numerical simulation of quantum turbulence produced by thermal counterflow in superfluid $^{4}${\rm He} by using the vortex filament model. The pioneering work was made by Schwarz, which has two defects. One is neglecting non-local terms of the Biot-Savart integral (localized induction approximation, LIA), and the other is the unphysical mixing procedure in order to sustain the statistically steady state of turbulence. We succeeded in making the statistically steady state without the LIA and the mixing. This state shows the characteristic relation $L=γ^2 v_{ns}^2$ between the …
The understanding of turbulent flows is one of the biggest current challenges in physics, as no first-principles theory exists to explain their observed spatio-temporal intermittency. Turbulent flows may be regarded as an intricate collection of mutually-interacting vortices. This picture becomes accurate in quantum turbulence, which is built on tangles of discrete vortex filaments. Here, we study the statistics of velocity circulation in quantum and classical turbulence. We show that, in quantum flows, Kolmogorov turbulence emerges from the correlation of vortex orientations, while deviations…
Vortex filament model has become a standard and powerful tool to visualize the motion of quantized vortices in helium superfluids. In this article, we present an overview of the method and highlight its impact in aiding our understanding of quantum turbulence, particularly superfluid helium. We present an analysis of the structure and arrangement of quantized vortices. Our results are in agreement with previous studies showing that under certain conditions, vortices form coherent bundles, which allows for classical vortex stretching, giving quantum turbulence a classical nature. We also offer …
In my research career in the field of quantum turbulence, I have been encouraged by Vinen. In this article, I review my works motivated by him and my joint collaborations with him. Vinen encouraged me in studies on quantum turbulence at zero temperature, Kolmogorov spectrum of a vortex tangle without mutual friction, and fully coupled dynamics of quantized vortices and normal fluid. Joint works include studies on diffusion of a vortex tangle, Kelvin wave cascade, quantum turbulence created by an oscillating object, and coupled dynamics of tracer particles and quantized vortices.
We perform numerical simulation of quantum turbulence at zero temperature generated by an oscillating sphere. In this simulation, we injected vortices on the sphere to generate turbulence. Although we prepare injected vortex loops of identical length, they are extended by the oscillating sphere to form a tangle through numerous reconnections. The resulting tangle around the sphere is anisotropic and affected by the oscillation. The vortex tangle continues to emit vortex loops, which leave the sphere. The statistics of emitted loops differ significantly from those of the original injected vorti…
We report a comprehensive investigation of the effects of quantum turbulence and quantized vorticity in superfluid $^4$He on the motion of a micro-electromechanical systems (MEMS) resonator. We find that the MEMS is uniquely sensitive to quantum turbulence present in the fluid. To generate turbulence in the fluid, a quartz tuning fork (TF) is placed in proximity to the MEMS and driven at large amplitude. We observe that at low velocity, the MEMS is damped by the turbulence, and that above a critical velocity, $v_c \simeq 5\,$mm\,s$^{-1}$, the turbulent damping is greatly reduced. We find that …
Nonequilibrium condensate systems such as exciton-polariton condensates are capable of supporting a spontaneous vortex nucleation. The spatial inhomogeneity of pumping field or/and disordered potential creates velocity flow fields that may become unstable to vortex formation. This letter considers ways in which turbulent states of interacting vortices can be created. It is shown that by combining just two pumping intensities it is possible to create a superfluid turbulence state of well-separated vortices, a strong turbulence state of de-structured vortices, or a weak turbulence state in which…
The energy spectrum of quantum turbulence obeys Kolmogorov's law. The vortex length distribution (VLD), meaning the size distribution of the vortices, in Kolmogorov quantum turbulence also obeys a power law. We propose here an innovative idea to study the origin of the power law of the VLD. The nature of quantized vortices allows one to describe the decay of quantum turbulence with a simple model that is similar to the Barabasi-Albert model of large networks. We show here that such a model can reproduce the power law of the VLD well.
We review numerical studies of quantum turbulence. Quantum turbulence is currently one of the most important problems in low temperature physics and is actively studied for superfluid helium and atomic Bose--Einstein condensates. A key aspect of quantum turbulence is the dynamics of condensates and quantized vortices. The dynamics of quantized vortices in superfluid helium are described by the vortex filament model, while the dynamics of condensates are described by the Gross--Pitaevskii model. Both of these models are nonlinear, and the quantum turbulent states of interest are far from equili…
Turbulence is one of the most prototypical phenomena of systems driven out of equilibrium. While turbulence has been studied mainly with classical fluids like water, considerable attention is now drawn to quantum turbulence (QT), observed in quantum fluids such as superfluid helium and Bose-Einstein condensates. A distinct feature of QT is that it consists of quantum vortices, by which turbulent circulation is quantized. Yet, under strong forcing, characteristic properties of developed classical turbulence such as Kolmogorov's law have also been identified in QT. Here, we study the opposite li…
There is a growing interest in the relation between classical turbulence and quantum turbulence. Classical turbulence arises from complicated dynamics of eddies in a classical fluid. In contrast, quantum turbulence consists of a tangle of stable topological defects called quantized vortices, and thus quantum turbulence provides a simpler prototype of turbulence than classical turbulence. In this paper, we investigate the dynamics and statistics of quantized vortices in quantum turbulence by numerically solving a modified Gross-Pitaevskii equation. First, to make decaying turbulence, we introdu…
We study numerically nonuniform quantum turbulence of coflow in a square channel by the vortex filament model. Coflow means that superfluid velocity $\bm{v}_s$ and normal fluid velocity $\bm{v}_n$ flow in the same direction. Quantum turbulence for thermal counterflow has been long studied theoretically and experimentally. In recent years, experiments of coflow are performed to observe different features from thermal counterflow. By supposing that $\bm{v}_s$ is uniform and $\bm{v}_n$ takes the Hagen-Poiseiulle profile, our simulation finds that quantized vortices are distributed inhomogeneously…
We theoretically study the development of quantum turbulence from two counter-propagating superfluids of miscible Bose-Einstein condensates by numerically solving the coupled Gross-Pitaevskii equations. When the relative velocity exceeds a critical value, the counter-superflow becomes unstable and quantized vortices are nucleated, which leads to isotropic quantum turbulence consisting of two superflows. It is shown that the binary turbulence can be realized experimentally in a trapped system.
We study theoretically the dynamics of charged quantized vortices (CQVs). CQVs (ion-vortex complexes) have been used as an important probe in the field of quantum hydrodynamics. Recent experimental studies of quantum turbulence at very low temperatures utilize CQVs. In this work we propose the equation of motion of CQVs based on the vortex filament model. An analytical solution for a charged vortex ring shows how it expands under an electric field. Numerical simulation reveals the characteristic behavior of CQVs under an electric field.
We propose a different type of Landau instability in trapped Bose-Einstein condensates by a helically moving environment. In the presence of quantized vortices, the instability can cause spontaneous radiation and amplification of Kelvin waves. This study gives a microscopic understanding of the Donnelly-Glaberson instability which was known as a hydrodynamic instability in superfluid helium. The Donnelly-Glaberson instability can be a powerful tool for observing the dispersion relation of Kelvin waves, vortex reconnections, and quantum turbulence in atomic Bose-Einstein condensates.
The energy spectrum of superfluid turbulence is studied numerically by solving the Gross-Pitaevskii equation. We introduce the dissipation term which works only in the scale smaller than the healing length, to remove short wavelength excitations which may hinder the cascade process of quantized vortices in the inertial range. The obtained energy spectrum is consistent with the Kolmogorov law.
