Vortex Clusters Research Articles

Abrikosov clusters in chiral liquid crystal droplets.

Self-organizing triangular lattices of topological vortices have been observed in type-II superconductors, Bose-Einstein condensates, and chiral magnets under external forcing. Liquid crystals exhibit vortex self-organization in dissipative media. In this study, we experimentally investigate the formation of vortex clusters, analogous to Abrikosov lattices, in temperature-driven chiral liquid crystal droplets. Based on a Ginzburg-Landau-like equation, we derive the interaction laws underlying the formation of these Abrikosov clusters of chiral domains. The origin of these is elucidated due to the competition between the repulsive interaction and the spatial effect of the confinement within the droplet. Our results advance the theoretical understanding of localized vortex self-organization in liquid crystals and open up possibilities for controlling the clustering of these topological defects.

Vortex clusters and their active control in a cold Rydberg atomic system with $\mathcal{PT}$-symmetric Bessel potential

Vortex clusters and their active control in a cold Rydberg atomic system with $\mathcal{PT}$-symmetric Bessel potential

Author Correction: Onset of vortex clustering and inverse energy cascade in dissipative quantum fluids

Author Correction: Onset of vortex clustering and inverse energy cascade in dissipative quantum fluids

Microstructure evolution and mechanical properties of a lamellar AlCoCrFeNi2.1 eutectic high-entropy alloy processed by high-pressure torsion

High-pressure torsion (HPT) was applied to a lamellar eutectic high-entropy alloy (EHEA) to study the effect of severe plastic deformation (SPD) on the composite structure and mechanical properties. We found that the existence of multiple phases affects defect distribution and the fragmentation process during HPT. Structural evolution shows orientation dependence with respect to the shear plane, which finally leads to a refined multiphase structure with nanograins and vortex clusters after a shear strain γ of 24. In nanograins, dislocation-mediated deformation prevails. The high density of grain boundaries, forest dislocations, and the generation of deformation twins restrict dislocation movement. As a result, an EHEA with a yield strength of 1.75 GPa, an excellent tensile strength of 2.20 GPa, and an appreciable failure strain of 5 % is realized. Our results demonstrate that the HPT deformation process of the lamellar EHEA is significantly affected by the structure. SPD on the multiphase structure is a suitable route for designing high-strength yet ductile alloys.

Microscopic solutions for vortex clustering in two-band type-1.5 superconductors

Two-band superconductors exhibit a distinct phase characterized by two correlation lengths, one smaller and the other larger than the magnetic field penetration length. This regime was coined type-1.5 superconductivity, with several unconventional properties, such as vortex clustering. However, a fully microscopic solution for vortex clusters has remained challenging due to computational complexities beyond quasiclassical models. This work presents numerical solutions obtained in a fully self-consistent two-band Bogoliubov–de Gennes model. We show the presence of discrepant correlation lengths leading to vortex clustering in two-band superconductors. Published by the American Physical Society 2024

Quantum vortex stability in draining fluid flows

Quantum vortices with more than a single circulation quantum are usually unstable and decay into clusters of smaller vortices. One way to prevent the decay is to place the vortex at the center of a convergent (draining) fluid flow, which tends to force vortices together. It is found that while the primary splitting instability is suppressed in this way (and completely quenched for strong enough flows) a secondary instability can emerge in circular trapping geometries. This behavior is related to an instability of rotating black holes when superradiantly amplified waves are confined inside a reflective cavity. The end state of the secondary instability is dramatic, manifesting as a shock wave that propagates round the circular wall and nucleates many more vortices. Published by the American Physical Society 2024

Statistics and evolution of Reynolds shear stress structure in cylinder-wake/boundary-layer interaction

The three-dimensional structures based on the quadrant classification of the tangential Reynolds stress (Qs), are studied in direct numerical simulations of cylinder-wake/boundary-layer interaction with a moderate gap ratio (G/D=1.0) and low or middle Reynolds numbers. In this paper, direct numerical simulations are performed using the immersed boundary lattice Boltzmann method (LBM). We utilize a three-dimensional clustering method to identify Reynolds shear stress structures (Qs-structures) associated with intense events. The kinematic characteristics of coherent structures are discussed through the statistical properties of Qs-structures. The spatial relationship of between vortex clusters and Qs-structures (mainly Q2-structures as well as Q4-structures) is explained by their evolution characteristics. The spatial distribution of Qs-structures, determined by the volume distribution of the minimum and maximum wall distances (ymin and ymax), are found to be similar to that of vortex clusters in the cylinder/wall interaction. In the near-wall statistical region, the secondary vortex clusters are surrounded by the parallel Q2 and Q4 pairs, and mostly lodged within the Q2. During the evolution process of coherent structures, the Q2-structures and the secondary vortex clusters developed into hairpin-like structures, respectively. The conditional average results demonstrated that the generated hairpin vortex structures are attributed to the momentum transfers.

Control of the oscillation frequency of a vortex cluster in the trapped polariton condensate

An optically trapped exciton–polariton condensate forms states corresponding to excited energy levels of the confining potential. Recently, it was shown that non-uniformity of the ring-shaped trapping potential leads to the simultaneous occupation of two split energy levels. This results in the formation of an oscillating vortex cluster with periodically changing signs of topological charges. Here, we experimentally demonstrate the control of the topological charge oscillation frequency by tuning the ellipticity of the excitation profile. Our observations are corroborated using the linear Schrödinger equation for a two-dimensional quantum harmonic oscillator. Our findings open a promising avenue for the investigation of optical vorticity properties and their applications in controllable settings.

Impact of harmonic inflow variations on the size and dynamics of the separated flow over a bump

The separated flow over a wall-mounted bump geometry under harmonic oscillations of the inflow stream is investigated with direct numerical simulations. The bump geometry gives rise to streamwise pressure gradients similar to those encountered on the suction side of low-pressure turbine (LPT) blades. Under steady inflow conditions, the separated-flow laminar-to-turbulent transition is initiated by self-sustained vortex shedding due to Kelvin-Helmholtz (KH) instability. In LPTs the dynamics are further complicated by the passage of the wakes shed by the previous stage of blades. The wake-passing effect is modeled here by introducing a harmonic variation of the inflow conditions. Three inflow oscillation frequencies and three amplitudes are considered. The frequencies are comparable to the wake-passing frequencies in practical LPTs. The amplitudes range from 1% to 10% of the inflow total pressure. The dynamics of the separated flow are studied by isolating the flow components that are respectively coherent with and uncorrelated to the inflow oscillation. Three scenarios are identified. The first one is analogous to the steady inflow case. In the second one, the KH vortex shedding is replaced during a part of the inflow period by the formation and release of a large vortex cluster. The third scenario consists solely of the periodic formation and release of the vortex cluster; it leads to a consistent reduction of the separated flow length over the entire period compared to the steady inflow case and would be the most desirable flow condition in a practical application. Published by the American Physical Society 2024

Three-dimensional particle image velocimetry experimental study of transient motion characteristics of different scale vortices in gasoline engine

The paper adopted three-dimensional (3D) Particle Image Velocimetry (PIV) combined with high-speed measurement technology to study the transient motion characteristics of tumble flow induced by small and medium-sized vortices on an optical gasoline engine. Meanwhile, the Proper Orthogonal Decomposition (POD) method was introduced to analyze the evolution of transient vortices, revealing the three-dimensional motion principle of vortices with different spatial scales within the cylinder. The results showed that increasing the engine speed can cause boosted in-plane and out-of-plane velocity, especially for the in-plane velocity. However, the average velocity in the plane was higher than that out of the plane with the difference generally within an order of magnitude. The strong intake jet was the main reason for bringing turbulent kinetic energy in the cylinder. The average kinetic energy and turbulent kinetic energy in the cylinder are both significantly improved at high engine speed. From the results of this experiment, it was revealed that there exists isotropic turbulent pulsation characteristics. Overall, the corresponding flow characteristics of different decomposed modes were different. The first mode section had the lowest average velocity ratio, while the other two had the highest. Due to the dissipation of large vortices into small vortices or the shear action between flow layers, new vortices were generated, leading to the intermittent phenomenon of the motion path of the vortex cluster in the target plane. The average vortex size and velocity circularity corresponding to two varied engine speeds presented a downward trend. The average vortex size was smaller at high engine speed, while the vortex intensity was higher. In addition, increasing the engine speed would decrease the vortex scale but increase the vortex strength. This work provided new fundamental insights into analyzing the characteristics of micro-scaled vortices in turbulent flow, as well as the organization of intake in the gasoline engine.

A CFD Study of Particulate Deposition on Dimple-Type Flue Walls of Coal-Fired Power Plants

The study of particle deposition in bends is always a continuous challenge in various engineering and industrial applications. New types of channels with special microstructures on the surfaces can be effective in modifying the flow field structure as well as particle deposition in channels. In this study, a 90° circular bend with a convex dimple structure was used, and the flow field and the deposition of particles in the channel were analyzed; the Stokes numbers (St) used were 0.016, 0.355 and 1.397. The reliability of the model was ensured by mesh-independence validation as well as speed validation. In a 90° bend channel with convex dimples, the temperature distribution, particle deposition distribution, flow structure and secondary flow were examined. The effects of the number of convex dimples and St in the bend on the flow field structure and particle deposition characteristics were analyzed. The results show that the main factors affecting the deposition characteristics of particles in bends are St, gravitational deposition, thermophoretic force, turbulent vortex clusters and secondary flow distribution. The effect of St is more pronounced, with the deposition rate increasing as the St increases, and the deposition location of the particles is mainly clustered on the outside of the bend structure of the elbow.

Vortex polarization and circulation statistics in isotropic turbulence.

We carry out an in-depth analysis of a recently introduced vortex gas model of homogeneous and isotropic turbulence. Direct numerical simulations are used to provide a concrete physical interpretation of one of the model's constituent fields: the degree of vortex polarization. Our investigations shed light on the complexity underlying vortex interactions and reveal, furthermore, that despite some striking similarities, classical and quantum turbulence exhibit distinct structural characteristics, even at inertial range scales. Crucially, these differences arise due to correlations between the polarization and circulation intensity within vortex clusters.

On the generation of near-wall dilatational motions in hypersonic turbulent boundary layers

Dilatational motions in the shape of travelling wave packets have been identified recently to be dynamically significant in hypersonic turbulent boundary layers. The present study investigates the mechanisms of their generation and their association with the solenoidal motions, especially the well-recognized near-wall self-sustaining process of the regeneration cycle between the velocity streaks and quasi-streamwise vortices. By exploiting the direct numerical simulation databases and orchestrating numerical experiments, we explore systematically the near-wall flow dynamics in the processes of the formation and transient growth of low-speed streaks. We conclude via theoretical ansatz that the nonlinearity related to the parallel density and pressure gradients close to the wall due to the restriction of the isothermal boundary condition is the primary cause of the generation of the dilatational structures at small scales. In fully developed turbulence, the formation and the existence of healthy dilatational travelling wave packets require the participation of the turbulence at scales larger than those of the near-wall regeneration cycles, especially the occurrence of the bursting events that generate vortex clusters. This is proven by the less intensified dilatational motions in the numerical experiments in which the Orr mechanism is alleviated and the vortical structures and turbulent bursts are weakened.

An investigation of flow regimes and mixing in a novel arrow-shaped jet reactor

Fluid mixing plays a vital role in the industry of chemical engineering. In this work, a novel arrow-shaped jet reactor by varying the angle of fluid impingement in the inlet channel was investigated. Flow field visualization experiments using Planar Laser-Induced Fluorescence (PLIF) technique were carried out to study various flow regimes and mixing performance. Results show that differentiated flow patterns of engulfment flow regimes appear within the arrow-shaped jet reactor. Particularly, vortex ring shedding was found in the unsteady engulfing flow regime, which promoted the mixing significantly. Besides, the mechanism of the variation of fluid impinging angle on mixing in an arrow-shaped jet reactor was investigated by numerical simulation. The results indicate that the transformation from double-leg vortex to single-leg vortex and the increase of the volume of vortex clusters caused by vortex ring shedding are the main reasons for the improvement of the mixing of engulfment flow regime.

Vortex-antivortex lattices in a holographic superconductor

We employ the Einstein-Abelian-Higgs theory to investigate the structure of vortex-antivortex lattices within a superconductor driven by spatial periodic magnetic fields. By adjusting the parameters of the external magnetic field, including the period (T) and the amplitude (B0), various distinct vortex states emerge. These states encompass the Wigner crystallization state, the vortex cluster state, and the suppressed state. Additionally, we present a comprehensive phase diagram to demarcate the specific regions where these structures emerge, contributing to our understanding of superconductivity in complex magnetic environments. Published by the American Physical Society 2024

Machine learning and parametrisation of multi-cell structures of secondary circulation in a tight open channel bend using LES

Large eddy simulations of an open channel bend are performed at a variety of water depths and flow rates. The results at several cross sections are decomposed into sub-cells of secondary circulation using clusters of instantaneous vortices. The strength and position of the sub-cells are then modelled using decision trees, multiple linear regression, multi-layer perceptrons, and adaptive neuro-fuzzy inference systems to obtain parametric models of secondary circulation development in a channel bend. The development of individual cells and total circulation is shown for an arbitrary flow condition using the model, as well as the dependence of all the circulation output variables on the input parameters of aspect ratio and Froude number. The positions of the sub-cells (but not their circulations) are largely independent of the Froude number, and the cross-stream position of the centre cell is found to behave linearly. The model with the best performance across all predicted variables is the ANFIS model without classification.

Conformal invariance of 2D quantum turbulence in an exciton–polariton fluid of light

The similarities of quantum turbulence with classical hydrodynamics allow quantum fluids to provide essential models of their classical analog, paving the way for fundamental advances in physics and technology. Recently, experiments on 2D quantum turbulence observed the clustering of same-sign vortices in strong analogy with the inverse energy cascade of classical fluids. However, self-similarity of the turbulent flow, a fundamental concept in the study of classical turbulence, has so far remained largely unexplored in quantum systems. Here, thanks to the unique features of exciton–polaritons, we measure the scale invariance of velocity circulations and show that the cascade process follows the universal scaling of critical phenomena in 2D. We demonstrate this behavior from the statistical analysis of the experimentally measured incompressible velocity field and the microscopic imaging of the quantum fluid. These results can find wide application in both quantum and classical 2D turbulence.

Vortex clustering in trapped Bose-Einstein condensates

We numerically study the formation of vortex clusters in trapped Bose-Einstein condensates where vortices are initially imprinted in a line. We show that such a system exhibits a rich phenomenology depending on the distance at which the vortices are imprinted and their number. In particular we observe that it is possible to obtain systems of twin vortex clusters, twin vortex clusters with orbiting satellite vortices, and triplets of clusters. By using a clustering algorithm we are able to quantitatively describe the formation and dynamics of the clusters. We finally utilise an analytical model to determine the range of parameters for which the clustering occurs. Our work sets the stage for possible experimental implementations where the formation of vortex clusters and more exotic bound states of vortices could be observed.

Vortex dynamics in rotating Rayleigh–Bénard convection

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh–Bénard convection in a reduced Rayleigh number range $1.3\le Ra/Ra_{c}\le 83.1$ . Under slow rotations ( $Ra\approx 80\,Ra_{c}$ ), the vortices are distributed randomly, which is manifested by the size distribution of the Voronoi cells of the vortex centres being a standard $\varGamma$ distribution. The vortices exhibit Brownian-type horizontal motion in the parameter range $Ra\gtrsim 10\,Ra_{c}$ . The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ( $4\,Ra_{c}\le Ra\lesssim 10\,Ra_{c}$ ), the centrifugal force leads to radial vortex motions, i.e. warm cyclones (cold anticyclones) moving towards (outwards from) the rotation axis. The horizontal scale of the vortices decreases with decreasing $Ra/Ra_c$ , and the size distribution of their Voronoi cells deviates from the $\varGamma$ distribution. In the rapidly rotating regime ( $1.6\,Ra_{c}\le Ra\le 4\,Ra_{c}$ ), the vortices are densely distributed. The hydrodynamic interaction of neighbouring vortices results in the formation of vortex clusters. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the outward motion of the strong anticyclones, and the radial velocity of the anticyclones is enhanced. The radial mobility of isolated vortices, scaled by their vorticity strength, is shown to be a simple power function of the Froude number. For all flow regimes studied, we show that the number of vortices with a lifespan greater than $t$ decreases exponentially as $\exp ({-t/{\tau }})$ for large time, where $\tau$ represents the characteristic lifetime of long-lived vortices.

Large-Eddy simulations on interaction flow structures of pulsed jets in a crossflow

Numerical investigations of pulsed jets in a crossflow are carried out using large-eddy simulation. The flow mechanism and coherent structure evolution of pulsed jets with different frequencies (f = 20 Hz, 50 Hz, and 100 Hz) are analyzed and compared with the steady-state jet. The proper orthogonal decomposition (POD) method is used to analyze the effect of different vortex structures in the flow field, which further elaborates the influence mechanism of frequency on pulse jets in the crossflow. The results show that under the same velocity ratio, the normal penetration depth of pulsed jets to the crossflow are greater than that of the steady-state jet. Due to the pulsating effect, the pulsed jets will form a large-scale shear layer vortex, which strengthens the turbulence pulsation and promotes the mixing between jets and the crossflow. As the pulse frequency increases, the scale of the vortex rings in the downstream shear layer will become smaller but the number will increase, and fine vortex clusters will be formed around them. At f = 50 Hz, the counter-rotating vortex pair (CVP) and the jet front shear layer vortex have a greater influence in the flow field, followed by the downstream shear layer vortex, and the wake vortex has the least influence in the flow field. At f = 20 Hz and 100 Hz, the wake vortex has a greater influence in the flow field than that at f = 50 Hz.