Quantum Turbulence Research Articles

Origin of the inverse energy cascade in two-dimensional quantum turbulence.

We establish a statistical relationship between the inverse energy cascade and the spatial correlations of clustered vortices in two-dimensional quantum turbulence. The Kolmogorov spectrum k^{-5/3} on inertial scales r corresponds to a pair correlation function between the vortices with different signs that decays as a power law with the pair distance given as r^{-4/3}. To test these scaling relations, we propose a forced and dissipative point vortex model that captures the turbulent dynamics of quantized vortices by the emergent clustering of same-sign vortices. The inverse energy cascade developing in a statistically neutral system originates from this vortex clustering that evolves with time.

Dual cascade and dissipation mechanisms in helical quantum turbulence

While in classical turbulence helicity depletes nonlinearity and can alter the evolution of turbulent flows, in quantum turbulence its role is not fully understood. We present numerical simulations of the free decay of a helical quantum turbulent flow using the Gross-Pitaevskii equation at high spatial resolution. The evolution has remarkable similarities with classical flows, which go as far as displaying a dual transfer of incompressible kinetic energy and helicity to small scales. Spatio-temporal analysis indicates that both quantities are dissipated at small scales through non-linear excitation of Kelvin waves and the subsequent emission of phonons. At the onset of the decay, the resulting turbulent flow displays polarized large scale structures and unpolarized patches of quiescense reminiscent of those observed in simulations of classical turbulence at very large Reynolds numbers.

Local and nonlocal energy spectra of superfluidHe3turbulence

Below the phase transition temperature $Tc \simeq 10^{-3}$K He-3B has a mixture of normal and superfluid components. Turbulence in this material is carried predominantly by the superfluid component. We explore the statistical properties of this quantum turbulence, stressing the differences from the better known classical counterpart. To this aim we study the time-honored Hall-Vinen-Bekarevich-Khalatnikov coarse-grained equations of superfluid turbulence. We combine pseudo-spectral direct numerical simulations with analytic considerations based on an integral closure for the energy flux. We avoid the assumption of locality of the energy transfer which was used previously in both analytic and numerical studies of the superfluid He-3B turbulence. For T<0.37 Tc, with relatively weak mutual friction, we confirm the previously found "subcritical" energy spectrum E(k), given by a superposition of two power laws that can be approximated as $E(k)~ k^{-x}$ with an apparent scaling exponent 5/3 <x(k)< 3. For T>0.37 Tc and with strong mutual friction, we observed numerically and confirmed analytically the scale-invariant spectrum $E(k)~ k^{-x}$ with a (k-independent) exponent x > 3 that gradually increases with the temperature and reaches a value $x\simeq 9$ for $T\approx 0.72 Tc$. In the near-critical regimes we discover a strong enhancement of intermittency which exceeds by an order of magnitude the corresponding level in classical hydrodynamic turbulence.

Detection of vortex coherent structures in superfluid turbulence

Filamentary regions of high vorticity irregularly form and disappear in the turbulent flows of classical fluids. We report an experimental comparative study of these so-called “coherent structures” in a classical vs. quantum fluid, using liquid helium with a superfluid fraction varied from 0% up to 83%. The low-pressure core of the vorticity filaments is detected by pressure probes located on the sidewall of a 78-cm-diameter von Kármán cell driven up to record turbulent intensity . The statistics of occurrence, magnitude and relative distribution of the filaments in a classical fluid are found indistinguishable from their superfluid counterpart, namely the bundles of quantized vortex lines. This suggests that the internal structure of vortex filaments, as well as their dissipative properties have a negligible impact on their macroscopic dynamics, such as lifetime and intermittent properties.

Andreev Reflection in Superfluid 3He: A Probe for Quantum Turbulence

Andreev reflection, familiar in superconducting systems, shows a much more extensive set of behaviors in the p-wave condensate of superfluid 3He. We discuss the basic ideas of Andreev reflection in the superfluid and its various manifestations. The fact that the process displays almost perfect retroreflection allows us to exploit the remarkable properties of the phenomenon for characterizing the pure quantum turbulence that can exist in these condensates. Finally, we discuss Andreev-reflection “optics” as a means of visualizing this turbulence in real time through the vortex video camera.

Observation of quantum turbulence in superfluid He3 -B using reflection and transmission of ballistic thermal excitations

We report measurements of quantum turbulence generated by a vibrating grid in superfluid $^3$He-B at zero pressure in the zero temperature limit. Superfluid flow around individual vortex lines Andreev-reflects incoming thermal ballistic quasiparticle excitations, and allows non-invasive detection of quantum vortices in $^3$He-B. We have compared two Andreev reflection-based techniques traditionally used to detect quantum turbulence in the ballistic regime: quasiparticle transmission through and reflection from ballistic vortex rings and a turbulent tangle. We have shown that the two methods are in very good agreement and thus complement each other. Our measurements reveal that vortex rings and a tangle generated by a vibrating grid have a much larger spatial extent than previously realised. Furthermore, we find that a vortex tangle can either pass through an obstacle made from a mesh or diffuse around it. The measured dependence of vortex signal as a function of the distance from the vibrating grid is consistent with a power-law behaviour in contrast to turbulence generated by a vibrating wire which is described by an exponential function.

Erratum to: Statistical Measurement of Counterflow Turbulence in Superfluid Helium-4 Using $$\hbox {He}^{{*}}_{2}$$ He 2 ∗ Tracer-Line Tracking Technique

We report preliminary results of a systematic study of the flow of normal fluid component in steady-state quantum turbulence in thermal counterflow of superfluid \(^{4}\hbox {He}\) using a high-precision flow visualisation technique based on the tracking of thin lines of \(\hbox {He}_2^{*}\) molecular tracers. Non-trivial profiles of mean velocity and turbulent fluctuation across the channel are observed with complicated temperature- and heat flux-dependencies. Mean turbulence intensity, however, depends on velocity only very weakly and is controlled primarily by the temperature.

Energy spectra of counterflow quantum turbulence at different temperatures

The spectrum of the energy generated by a vortex tangle in the counterflow of normal and superfluid components at different temperatures was obtained. The counterflow magnitude was varied from 0.3 cm/s to 1.2 cm/s and the temperature was varied from 1.3 K to 1.9 K. It was shown that at the distances of the order of intervortex separation, E(k) ∼ k−α, where 1.3 &amp;lt; α &amp;lt; 1.4 depending on the temperature. At larger distances, E(k) ∼ k−1. It was established that under the heat flux corresponding to the Gorter–Mellink regime, the density of energy dissipation is proportional to the cube of the counterflow of normal and superfluid components, i.e., the energy dissipation is due to the friction between the normal component of helium and the vortex tangle.

Large Eddy Simulations Analysis of the Energy Spectrum Without Mutual Friction in Superfluid $$ ^{4} $$ 4 He: HVBK Model

The reliability of the filtered on the Hall–Vinen–Bekarevich–Khalatnikov (HVBK) model without mutual friction force is now investigated via some large eddy simulations of freely decaying isotropic superfluid turbulence. The filtered HVBK model is solved using a fully pseudo-spectral method, which is an extension of the classical Rogallo’s method to the two-fluid model. Furthermore, in this paper, we analyze the evolution of various terms constituting the HVBK momentum equations using the balance equation for the energy-spectrum function. Our results are presented in both cases with and without mutual friction force. LES predictions have shown that this mutual friction decreases the energy dissipation of the normal part and the energy transfer is more significant when this force is taken into account.

Phantom vortices: hidden angular momentum in ultracold dilute Bose-Einstein condensates

Vortices are essential to angular momentum in quantum systems such as ultracold atomic gases. The existence of quantized vorticity in bosonic systems stimulated the development of the Gross-Pitaevskii mean-field approximation. However, the true dynamics of angular momentum in finite, interacting many-body systems like trapped Bose-Einstein condensates is enriched by the emergence of quantum correlations whose description demands more elaborate methods. Herein we theoretically investigate the full many-body dynamics of the acquisition of angular momentum by a gas of ultracold bosons in two dimensions using a standard rotation procedure. We demonstrate the existence of a novel mode of quantized vorticity, which we term the phantom vortex. Contrary to the conventional mean-field vortex, can be detected as a topological defect of spatial coherence, but not of the density. We describe previously unknown many-body mechanisms of vortex nucleation and show that angular momentum is hidden in phantom vortices modes which so far seem to have evaded experimental detection. This phenomenon is likely important in the formation of the Abrikosov lattice and the onset of turbulence in superfluids.

Influence of Quantum Turbulence on the Processes of Heat Transfer and Boiling in Superfluid Helium

We demonstrate that in a wide range of heat fluxes the dynamics of heat transfer in superfluid helium is determined by the existence of remanent quantized vortices. The vortex density dynamics determines the rise of temperature near the heater and the boiling-up of superfluid helium. It permits to understand the results of the experiments of several groups.

Collapsing vortex filaments and the spectrum of quantum turbulence

The method of correlation functions and the method of quantum vortex configurations are used to calculate the energy spectrum of a three-dimensional velocity field that is induced by collapsing (immediately before reconnection) vortex filaments. The formulation of this problem is motivated by the idea of modeling classical turbulence by a set of chaotic quantized vortex filaments. Among the various arguments that support the idea of quasi-classical behavior for quantum turbulence, the most persuasive is probably the resulting Kolmogorov energy spectrum resembling E(k)∝k−5/3 that was obtained in a number of numerical studies. Another goal is associated with an important and intensely studied theme that relates to the role of hydrodynamic collapse in the formation of turbulence spectra. Calculations have demonstrated that vortex filaments create a velocity field at the moment of contact, which has a singularity. This configuration of vortex filaments generates the spectrum E(k), which bears the resemblance to the Kolmogorov law. A possible cause for this observation is discussed, as well as the likely reasons behind any deviations. The obtained results are discussed from the perspective of both classical and quantum turbulence.

Hydrodynamics of vortices in Bose-Einstein condensates: A defect-gauge field approach

This work rectifies the hydrodynamic equations commonly used to describe the superfluid velocity field in such a way that vortex dynamics are also taken into account. In the field of quantum turbulence, it is of fundamental importance to know the correct form of the equations which play similar roles to the Navier-Stokes equation in classical turbulence. Here, such equations are obtained by carefully taking into account the frequently overlooked multivalued nature of the $U(1)$ phase field. Such an approach provides exact analytical explanations to some numerically observed features involving the dynamics of quantum vortices in Bose-Einstein condensates, such as the universal $t^{1/2}$ behavior of reconnecting vortex lines. It also expands these results beyond the Gross-Pitaevskii theory so that some features can be generalized to other systems such as superfluid $^{4}$He, dipolar condensates, and mixtures of different superfluid systems.

Anisotropic Formation of Quantum Turbulence Generated by a Vibrating Wire in Superfluid $${}^{4}\hbox {He}$$

To investigate the formation of quantum turbulence in superfluid \({}^{4}\hbox {He}\), we have studied the emission of vortex rings with a ring size of larger than 38 \(\upmu \hbox {m}\) in diameter from turbulence generated by a vibrating wire. The emission rate of vortex rings from a turbulent region remains low until the beginning of high-rate emissions, suggesting that some of the vortex lines produced by the wire combine to form a vortex tangle, until an equilibrium is established between the rate of vortex line combination with the tangle and dissociation. The formation times of equilibrium turbulence are proportional to \(\varepsilon ^{-1.2}\) and \(\varepsilon ^{-0.6}\) in the directions perpendicular and parallel to the vibrating direction of the generator, respectively, indicating the anisotropic formation of turbulence. Here, \(\varepsilon \) is the generation power of the turbulence. This power dependence may be associated with the characteristics of quantum turbulence with a constant energy flux.

Towards quantum turbulence in cold atomic fermionic superfluids

Fermionic superfluids provide a new realization of quantum turbulence, accessible to both experiment and theory, yet relevant to phenomena from both cold atoms to nuclear astrophysics. In particular, the strongly interacting Fermi gas realized in cold-atom experiments is closely related to dilute neutron matter in neutron star crusts. Unlike the liquid superfluids 4He (bosons) and 3He (fermions), where quantum turbulence has been studied in laboratory for decades, superfluid Fermi gases stand apart for a number of reasons. They admit a rather reliable theoretical description based on density functional theory called the time-dependent superfluid local density approximation that describes both static and dynamic phenomena. Cold atom experiments demonstrate exquisite control over particle number, spin polarization, density, temperature, and interaction strength. Topological defects such as domain walls and quantized vortices, which lie at the heart of quantum turbulence, can be created and manipulated with time-dependent external potentials, and agree with the time-dependent theoretical techniques. While similar experimental and theoretical control exists for weakly interacting Bose gases, the unitary Fermi gas is strongly interacting. The resulting vortex line density is extremely high, and quantum turbulence may thus be realized in small systems where classical turbulence is suppressed. Fermi gases also permit the study of exotic superfluid phenomena such as the Larkin–Ovchinnikov–Fulde–Ferrell pairing mechanism for polarized superfluids which may give rise to 3D supersolids, and a pseudo-gap at finite temperatures that might affect the regime of classical turbulence. The dynamics associated with these phenomena has only started to be explored. Finally, superfluid mixtures have recently been realized, providing experimental access to phenomena like Andreev–Bashkin entrainment predicted decades ago. Superfluid Fermi gases thus provide a rich forum for addressing phenomena related to quantum turbulence with applications ranging from terrestrial superfluidity to astrophysical dynamics in neutron stars.

Refrigeration of an Array of Cylindrical Nanosystems by Flowing Superfluid Helium

We consider the refrigeration of an array of heat-dissipating cylindrical nanosystems as a simplified model of computer refrigeration. We explore the use of He II as cooling fluid, taking into account forced convection and heat conduction. The main conceptual and practical difficulties arise in the calculation of the effective thermal conductivity. Since He II does not follow Fourier’s law, the effective geometry-dependent conductivity must be extracted from a more general equation for heat transfer. Furthermore, we impose the restrictions that the maximum temperature along the array should be less than T_{lambda } transition temperature and that quantum turbulence is avoided, in order not to have too high heat resistance.

Double-Paddle Oscillators as Probes of Quantum Turbulence in the Zero Temperature Limit

We present a technical report on our tests of a double-paddle oscillator as a detector of quantum turbulence in superfluid \(^{4}\)He at low temperatures ranging from 20 to 1100 mK. The device, known to operate well in the two-fluid regime (Zemma and Luzuriaga in J Low Temp Phys 166:171–181, 2012), is also capable of detecting quantum turbulence in the zero temperature limit. The oscillator demonstrated Lorentzian responses with quality factors of order \(10^5\) in vacuum, and displayed negative-Duffing resonances in liquid, even at moderate drives. In superfluid He-II at low temperatures, its sensitivity was adversely affected by acoustic damping at higher harmonics. While it successfully created and detected the quantum turbulence, its overall performance does not compare favourably with other oscillators such as tuning forks.

Small-scale universality of particle dynamics in quantum turbulence

We show that, in turbulent two-fluid flows of superfluid $^{4}\mathrm{He}$, the statistically described dynamics of small particles suspended in the liquid does not depend on the type of imposed flow, at scales smaller than the average distance between quantized vortices, the quantum length scale of the flow. More precisely, regardless of the mechanically or thermally driven nature of the large-scale flow, the tails of the observed particle velocity statistical distributions, indicating the occurrence of large-magnitude events in the proximity of quantized vortices, display the same power-law shape, characteristic of the quantum description of superfluid $^{4}\mathrm{He}$. This property of quantum turbulence can be linked to the small-scale universality observed in classical turbulent flows of viscous fluids.

Coexistence and interplay of quantum and classical turbulence in superfluidHe4: Decay, velocity decoupling, and counterflow energy spectra

We report complementary experimental, numerical and theoretical study of turbulent coflow, counterflow and pure superflow of superfluid He-4 in a channel, resulting in a physically transparent and relatively simple model of decaying quantum turbulence that accounts for interactions of coexisting quantum and classical components of turbulent superfluid He-. We further offer an analytical theory of the energy spectra of steady-state quantum turbulence in the counterflow and pure superflow, based on algebraic approximation for the energy fluxes over scales. The resulting spectra are not of the classic Kolmogorov form, but strongly suppressed by the mutual friction, leading to the energy dissipation at all scales, enhanced by the counterflow-induced decoupling of the normal- and superfluid velocity fluctuations.

Fluid dynamics: Turbulence in a quantum gas.

The discovery of a cascade of sound waves across many wavelengths in an ultracold atomic gas advances our understanding of turbulence in fluids governed by quantum mechanics. See Letter p.72 An important signature of turbulence is the emergence of a cascade of excitations involving all length scales. While turbulence has been observed in quantum fluids—typically liquid helium—it is difficult to control such systems and to observe the properties of turbulence on demand, because the particles therein strongly interact. Here Nir Navon et al. trap a weakly interacting homogeneous Bose–Einstein condensate consisting of rubidium-87 atoms in a cylindrical optical box and shake the gas to produce turbulence. This methodology lets them observe the full turbulent cascade. This work demonstrates that ultracold atomic gases could serve as models for quantum turbulence.