Vortex Lines Research Articles

Kinetic of the development of a quantum vortex tangle in superfluids under the influence of thermal activation

The study explores the development of a thermally equilibrated quantum vortex tangle in superfluid liquids under the influence of thermal activation. This problem is of interest to both applied and fundamental research and has been investigated by many authors in various aspects. Despite the important and impressive results obtained, a significant part of the process, namely, the kinetics of processes leading to equilibrium state, remained unexplored. In this article, we conduct a study of kinetic phenomena and focus our attention on the evolution of the vortex line density (VLD) L(t), the total length of the filament per unit volume. The initial development of VLD is due to random thermal fluctuations. The increase in the vortex line length L(t) can be obtained based on the famous Novikov–Furutsu theorem, which shows that the growth rate of L(t) is proportional to a random force correlator. As the length of the vortex filaments increases, the interaction between the vortices becomes significant and affects the dynamics process. At this point, we turn to the phenomenological Feynman–Vinen theory, which offers various models for the evolution of the quantity L(t). Next, we examine the evolution of a vortex tangle as a combination of growth due to random thermal excitations and decay in the Feynman–Vinen theory. Several applications leading to significant and remarkable results are considered.

Quantum turbulence in superfluid helium: Decay and energy spectrum

The paper presents a comprehensive numerical study of the free decay of vortex tangle in superfluid helium. The initial vortex tangle represents one of the stationary configurations of loops in a counterflow with a laminar normal fluid component. The calculations are carried out in the framework of the vortex line method using the full Biot–Savart law over a wide range of temperatures. The aim of the study is to identify the role of various factors introduced into the numerical procedures (removal of small loops and segments during reconnections, the addition of and exclusion of vortex points on loops) and to determine the evolution of energy spectrum during the decay of quantum turbulence. A statistical approach is used to calculate the kinetic energy distribution on length scales. The calculations are carried out using periodic boundary conditions in a cube. The results show that, in agreement with the Feynman–Vinen theory, initially the rates of reduction in vortex line density at different temperatures are the same. However, when the vortex structure becomes rarefied, the influence of the mutual friction force becomes apparent, in agreement with Schwarz's theory. Statistical method for determining the energy spectrum is used. The Kolmogorov spectrum is not observed during decays at any temperature.

An experimental and numerical study on the behavior of finite-length column vortex

This paper explores experimental and numerical investigation of the spatiotemporal dynamics of a finite-length vortex column in three dimensions using particle image velocimetry and large eddy simulation. The research examines the combined impact of bending, buckling, and core-splitting on a finite-length vortex column. More precisely, the work centers on the fundamental motions, evolutions in flow along the axis, how the shape of the vortex core changes over time, the instability caused by the long waves on the vortex column, and the division of the vortex core. A novel prototype is developed that utilizes piston-driven inflow and produces a vortex column through the principles of flow separation and Biot–Savart induction, which is studied for predicting an ex situ cyclonic line vortex. The present study discusses the complete three-dimensional overview of the same columnar vortex. The meridional swirl and the axial transport of vorticity deform the shape of the core cross sections in different lengths of the column. The jump in the axial velocity at the core boundary allows for the occurrence of bending instabilities with a left-handed helical structure. These instabilities have a long wavelength, similar to the length of the vortex column, and belong to the m = +1 mode. The vortex column experiences a non-uniform curvature and torsion caused by the intricate shape of the laboratory model and varying flow speeds at different heights of the vortex column. The results offer valuable insights into the role of inertia, Coriolis, and viscous forces on the dynamics of the vortex column.

Precise and accurate speed measurements in rapidly flowing dense suspensions

We introduce a method for precise and accurate measurements of particle speeds in dense suspensions flowing at high rates and demonstrate the utility of the approach for revealing complex flow fluctuations during shearing in a setup that combines imaging with a confocal microscope and shearing with a rheometer. We scan the focal point in one dimension, aligned with direction of flow, producing absolute measurements of speed that are independent of suspension structure and particle shape. We compare this flow-direction line scanning approach with a complementary method we introduced previously, measuring speed using line scanning in the vorticity direction. By comparing results in various flow conditions, including shear-thinning and thickening regimes, we demonstrate the efficacy of our new approach. We find that both approaches exhibit qualitatively similar flow profiles, but a comparative analysis reveals a 15%–25% overestimation in speed measurement using vorticity line scanning, with discrepancies generated by anisotropic suspension microstructure under flow. Moreover, in the thickening regime where complex flow fields are present, both approaches capture local speed fluctuations. However, line scanning in the flow direction reveals and precisely captures stagnation and backflows, a capability not achievable with vorticity line scanning. The approach introduced here not only provides a refined technique for speed measurement in fast-flowing suspensions but also emphasizes the significance of accurate measurement techniques in advancing our understanding of flow behavior in dense suspensions, particularly in contexts where strong non-affine flows are prevalent.

Shear lines trigger heavy rainfalls in the Philippines during the winter monsoon

Heavy rainfall events (HREs) occur almost throughout the year in the Philippines, with relatively limited research during the winter monsoon. This study analyzes the 20-year (2003–2022) daily precipitation from 55 rain gauges and Integrated Multi-satellitE Retrievals for GPM (IMERG) from November to February. HREs are classified into three clusters by employing a cluster analysis on the most pertinent principal modes extracted from the principal component analysis. Each cluster exhibits a distinct heavy rainfall spatial pattern, mostly showing more than 50 mm/day of rainfall in the eastern part of the country. We noted that heavy rainfall in the Philippines during the winter monsoon occurs during a strong East Asian Winter Monsoon and caused by the interaction of shear line and low-level cyclonic vortex. The different location of rainfall maxima in each HRE cluster is a result of the variation of locations of the shear line and cyclonic vortex.

Observation of Zero-Energy Modes with Possible Time-Reversal Symmetry Breaking on Step Edge of CaKFe4As4

Abstract Topologically nontrivial Fe-based superconductors attract extensive attentions due to their ability of hosting Majorana zero modes (MZMs) which could be used for topological quantum computation. Topological defects such as vortex lines are required to generate MZMs. Here, we observe the robust edge states along the surface steps of CaKFe4As4. Remarkably, the tunneling spectra show a sharp zero-bias peak (ZBP) with multiple integer-quantized states at the step edge under zero magnetic field. We propose that the increasing hole doping around step edges may drive the local superconductivity into a state with possible spontaneous time-reversal symmetry breaking. Consequently, the ZBP can be interpreted as an MZM in an effective vortex in the superconducting topological surface state by proximity to the center of a tri-junction with different superconducting order parameters. Our results provide new insights into the interplay between topology and unconventional superconductivity, and pave a new path to generate MZMs without magnetic field.

Twisting vortex lines regularize Navier-Stokes turbulence.

Fluid flows are intrinsically characterized via the topology and dynamics of underlying vortex lines. Turbulence in common fluids like water and air, mathematically described by the incompressible Navier-Stokes equations (INSE), engenders spontaneous self-stretching and twisting of vortex lines, generating a complex hierarchy of structures. While the INSE are routinely used to describe turbulence, their regularity remains unproven; the implicit assumption being that the self-stretching is ultimately regularized by viscosity, preventing any singularities. Here, we uncover an inviscid regularizing mechanism stemming from self-stretching itself, by analyzing the flow topology as perceived by an observer aligned with the vorticity vector undergoing amplification. While, initially, vorticity amplification occurs via increasing twisting of vortex lines, a regularizing anti-twist spontaneously emerges to prevent unbounded growth. By isolating a vortex, we additionally demonstrate the genericity of this self-regularizing anti-twist. Our work, directly linking dynamics of vortices to turbulence statistics, reveals how the Navier-Stokes dynamics avoids the development of singularities even without the aid of viscosity.

Effects of axisymmetric confinement on vortical structures emanating from round turbulent jets

Confined jets occur in many engineering applications including combustion chambers, jet pumps, and chemical reactors. The effects of axisymmetric confinement on the vortical structures identified in a turbulent jet are investigated using large eddy simulation at a Reynolds number of 30 000 (based on nozzle exit conditions) and expansion ratio (chamber-to-nozzle diameter ratio) of five. The results obtained from the confined jet are compared with those of a free jet under the same nozzle exit flow conditions. A prominent recirculation zone forms between the expanding jet and the confining wall, resulting in early shear layer distortion and a shorter interaction length in the confined jet (0.85 jet diameters) compared to the free jet (1.15 jet diameters). Using the λ2 criterion for vortex identification, two dominant structural modes are identified in the near-exit region of the free jet: ring and helical modes. However, in the confined jet, the helical mode is absent, and the turbulent confined fluid accelerates the breakup of the ring vortices. The interaction of the secondary line vortices with the breaking structures leads to the formation of new hairpin-like vortices, which also contribute to further vortex breakup. These results explain the enhanced mixing performance of confined jets as the mixing is directly tied to the breakup of large vortical structures. Proper orthogonal decomposition modes are also presented to identify the structures/events with the highest contribution to the total turbulent kinetic energy in both flow fields.

Curved vortex surfaces in four-dimensional superfluids. I. Unequal-frequency double rotations

The study of superfluid quantum vortices has long been an important area of research, with previous work naturally focusing on two-dimensional and three-dimensional systems, where rotation stabilizes point vortices and line vortices respectively. Interestingly, this physics generalizes for a hypothetical four-dimensional (4D) superfluid to include vortex planes, which can have a much richer phenomenology. In this paper we study the possibility of skewed and curved vortex planes, which have no direct analog in lower dimensions. By analytically and numerically studying the 4D Gross-Pitaevskii equation, we show that such vortex surfaces can be stabilized and favored by double rotation with unequal rotation frequencies. Our work raises open questions for further research into the physics of these vortex surfaces and suggests interesting future extensions to tilted vortex surfaces under equal-frequency double rotation and to more realistic 4D models. Published by the American Physical Society 2024

Curved vortex surfaces in four-dimensional superfluids. II. Equal-frequency double rotations

As is well known, two-dimensional and three-dimensional superfluids under rotation can support topological excitations such as quantized point vortices and line vortices, respectively. Recently, we have studied how, in a hypothetical four-dimensional (4D) superfluid, such excitations can be generalized to vortex planes and surfaces. In this paper we continue our analysis of skewed and curved vortex surfaces based on the 4D Gross-Pitaevskii equation and show that certain types of such states can be stabilized by equal-frequency double rotations for suitable parameters. This work extends the rich phenomenology of vortex surfaces in four dimensions and raises interesting questions about vortex reconnections and the competition between various vortex structures which have no direct analog in lower dimensions. Published by the American Physical Society 2024

Physical quantity characteristics of severe aircraft turbulence near convective clouds over Australia

Using FY–2G satellite data, Aircraft Meteorological Data Relay (AMDAR) downlink data, and the fifth generation European Centre for Medium–Range Weather Forecasts (ECMWF) atmospheric reanalysis of the global climate (ERA5) dataset, we analyzed the circulation, thermal, and dynamic characteristics of the convective aircraft turbulence over Australia in the Southern Hemisphere. The results show that the near-convective clouds turbulence (NCCT) in the Southern Hemisphere mostly occurred in front of deep warm high–pressure ridges in mid–latitude regions and on the left side of the axis of the subtropical westerly jet stream. The isotherms in this area were relatively dense (i.e., large gradients), and the wind speed was high, with strong horizontal and/or vertical cyclonic wind shear. In addition, the NCCT usually occurred near the zero–divergence or zero–vorticity line and in areas with large vertical wind speed gradients. There were also strong vertical and horizontal wind shears in this area, which could easily trigger severe turbulence. Furthermore, the NCCT in the Southern Hemisphere mostly occurred at the intersection of cold and warm temperature advections (i.e., near the zero–temperature advection line), and the turbulence point was located near the high–altitude frontal zone where there was a strong gradient of cold and warm advections. There was temperature inversion with pseudo–equivalent potential temperatures in the middle and lower troposphere on the warmer side of the turbulence point. The unstable stratification of cold air at the top and warm air at the bottom was conducive to triggering convection from the ground, forming strong convective clouds, and causing severe turbulence.

Line operators, vortex statistics, and Higgs versus confinement dynamics

We study a 2+1D lattice gauge theory with fundamental representation scalar fields which has both Higgs and confining regimes with a spontaneously-broken U(1) 0-form symmetry. We show that the Higgs and confining regimes may be distinguished by a natural gauge invariant observable: the phase Ω of a correlation function of a vortex line operator linking with an electric Wilson line. We employ dualities and strong coupling expansions to analytically explore parameter regimes which were inaccessible in previous continuum calculations, and discuss possible implications for the phase diagram.

Entanglement of Vortices in the Ginzburg–Landau Equations for Superconductors

In 1988, Nelson proposed that neighboring vortex lines in high-temperature superconductors may become entangled with each other. In this article we construct solutions to the Ginzburg–Landau equations which indeed have this property, as they exhibit entangled vortex lines of arbitrary topological complexity.

Reynolds number effect on the Lagrangian evolution of hairpin vortices in turbulent channel flow

The evolution and generation of hairpins are studied in a Lagrangian perspective in turbulent channel flows. Direct numerical simulation database of turbulent channel flow at friction Reynolds numbers R e τ = 590, 390, and 180 is employed to perform tracking and interpolation algorithms of fluid particles on hairpins. These particles are carefully selected using a vortex line identification technique developed to extract the hairpin's core line. Interesting results are observed regarding the Reynolds number impact on the evolution and regeneration of hairpins. As the Reynolds number increases, the head and the vortical tongues are compressed and aligned in the main flow direction and the hairpin structures tend to orient more horizontally. The deformation shape of hairpins using the strain state parameter, which is correlated with the dissipation rate, is analysed using the probability density function. Most phenomena related to the generation of secondary hairpins, including the existence of vortical tongues, occur in the range 35 ≲ y + ≲ 50 . The results reveal that the Lagrangian perspective is a proper technique to address the extension of vortical tongues, generation of the secondary hairpin, and stretch of hairpin legs.

Vortex-pair dynamics in three-dimensional homogeneous dipolar superfluids

The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole-interaction dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices. Published by the American Physical Society 2024

A new fast simulation method of wind turbine wake based on annular vortex element

A fast simulation method of wind turbine wake field based on the combination of lifting line and annular vortex elements is proposed to simulate the bound circulation on the blade by means of lifting line, and to simulate the evolution of the wake field by releasing the annular vortex elements through the blade. The method can be iterated until convergence is sufficient by distributing the vortex elements basin-wide through periodicity in the initialization stage. The accuracy and applicability conditions of the method are verified by comparing the above method with wind tunnel tests and software simulation results using different methods. The method is clear and simple, with low computational cost and high computational accuracy.

About gravitational radiation of semi local strings with non compact internal modes

The present work studies the gravitational radiation of a non abelian vortex with a non compact internal moduli describing its excitations. This situation may be realised by semi-local supersymmetric vortices [1]–[8], although supersymmetry is not necessary for this to happen. In the situation considered along this work, the internal space has infinite volume, and a largely energetic perturbation propagates along the object, even though the vortex line may not be moving. A specific configuration is presented, in which the internal space is the resolved conifold with its Ricci flat metric. The curious feature about it is that it corresponds to a static vortex, that is, the perturbation is only due to the internal modes. Even being static, the emission of gravitational radiation is in the present case of considerable order. This suggest that the presence of slowly moving objects that can emit a large amount of gravitational radiation is a hint of non abelianity.

Transition induced by a bursting vortex ring in channel flow

We investigate the influence of vortices remote from the boundary on the near-wall flow dynamics in wall-bounded flows. A vortex ring with precisely controlled local twist is introduced into the outer layer of a channel flow at a moderate Reynolds number. We find that the minimum vorticity flux for triggering the transition to turbulence is significantly reduced from the initial disturbance of an untwisted vortex ring to that of a twisted ring. In particular, the latter disturbance can cause vortex bursting in the early transitional stage. The impact of vortex bursting on the transition process is characterised by the near-wall, wall-normal velocity with the rapid distortion theory. The wall-normal velocity grows during vortex bursting, and leads to streak formation and then the transition to turbulence. The notable wall-normal velocity is induced by the large di-vorticity generated in vortex bursting. We model the growing radial component of the di-vorticity in terms of the local twist, and demonstrate that its surge is due to the generation of highly twisted vortex lines in vortex bursting. Then, we derive that the generation of the di-vorticity in the outer layer enhances the wall-normal velocity in the inner layer via the Poisson equation with the image method and the multipole expansion. Thus, we elucidate that the vortex bursting can have an effect on the transition process.

Lagrangian dynamics and regularity of the spin Euler equation

We derive the spin Euler equation for ideal flows by applying the spherical Clebsch mapping. This equation is based on the spin vector, a unit vector field encoding vortex lines, instead of the velocity. The spin Euler equation enables a feasible Lagrangian study of fluid dynamics, as the isosurface of a spin-vector component is a vortex surface and material surface in ideal flows. We establish a non-blowup criterion for the spin Euler equation, suggesting that the Laplacian of the spin vector must diverge if the solution forms a singularity at some finite time. The direct numerical simulations (DNS) of three ideal flows – the vortex knot, the vortex link and the modified Taylor–Green flow – are conducted by solving the spin Euler equation. The evolution of the Lagrangian vortex surface illustrates that the regions with large vorticity are rapidly stretched into spiral sheets. The DNS result exhibits a pronounced double-exponential growth of the maximum norm of Laplacian of the spin vector, showing no evidence of the finite-time singularity formation if the double-exponential growth holds at later times. Moreover, the present criterion with Lagrangian nature appears to be more sensitive than the Beale–Kato–Majda criterion in detecting the flows that are incapable of producing finite-time singularities.

Mathematical modeling of velocity field induced by the vortex

In new technological applications, it is important to use vortex distributions in the area for obtaining large velocity fields. This paper, it was calculated the distribution of the velocity field and distribution of stream function for ideal incompressible fluid, induced by a different system of the finite number of vortex threads: 1) circular vortex lines in a finite cylinder, positioned on its inner, 2) spiral vortex threads, positioned on the inner surface of the finite cylinder or cone, and 3) linear vortex lines in the plane channel, positioned on its boundary. An original method was used to calculate the components of the velocity vectors. Such kind of procedure allows calculating the velocity fields inside the domain depending on the arrangement, the intensity, and the radii of vortex lines. In this paper, we have developed a mathematical model for the process in the element of Hurricane Energy Transformer. This element is a central figure in the so-called RKA (ReaktionsKraftAnlage) used on the cars’ roofs.