3D Vortex Research Articles

Spontaneous symmetry breaking of fundamental states, vortices, and dipoles in two- and one-dimensional linearly coupled traps with cubic self-attraction

We introduce two- and one-dimensional (2D and 1D) systems of two linearly-coupled Gross-Pitaevskii equations (GPEs) with the cubic self-attraction and harmonic-oscillator (HO) trapping potential in each GPE. The system models a Bose-Einstein condensate with a negative scattering length, loaded in a double-pancake trap, combined with the in-plane HO potential. In addition to that, the 1D version applies to the light transmission in a dual-core waveguide with the Kerr nonlinearity and in-core confinement represented by the HO potential. The subject of the analysis is spontaneous symmetry breaking in 2D and 1D ground-state (GS, alias fundamental) modes, as well as in 2D vortices and 1D dipole modes (the latter ones do not exist without the HO potential). By means of the variational approximation and numerical analysis, it is found that both the 2D and 1D systems give rise to a symmetry-breaking bifurcation (SBB) of the supercrtical type. Stability of symmetric states and asymmetric ones, produced by the SBB, is analyzed through the computation of eigenvalues for perturbation modes, and verified by direct simulations. The asymmetric GSs are always stable, while the stability region for vortices shrinks and eventually disappears with the increase of the linear-coupling constant, $ \kappa $. The SBB in the 2D system does not occur if $\kappa $ is too large (at $\kappa >\kappa_{\max }$); in that case, the two-component system behaves, essentially, as its single-component counterpart. In the 1D system, both asymmetric and symmetric dipole modes feature an additional oscillatory instability, unrelated to the symmetry breaking. This instability occurs in several regions, which expand with the increase of $\kappa $.

Multi-dimensional stable fundamental solitons and excitations in [formula omitted]-symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions

We demonstrate the parity-time- (PT-) symmetric harmonic-Gaussian potential with unbounded gain-and-loss distribution can support entirely-real linear spectra, stable spatial and spatio-temporal solitons in an inhomogeneous nonlinear medium (e.g., cubic nonlinear Schrödinger equation with the self-focusing and defocusing cases). Exact analytical solitons are derived in both one-dimensional (1D) and higher-dimensional (e.g., 2D, 3D) geometries such that they are verified to be stable in the given parameters regions. Particularly, several families of numerical fundamental solitons (especially the 1D double-peaked solitons, 2D vortex solitons, and 3D double bullets) can be found to be stable around the propagation parameters for exact solitons. Other significant properties of solitons are also explored including the interactions of solitons, stable soliton excitations, and transverse power flows. The results may excite the corresponding theoretical analysis and experiment designs.

Thermal activation energy of 3D vortex matter in NaFe1\u2212xCoxAs (x\u2009=\u20090.01, 0.03 and 0.07) single crystals

We report on the thermally activated flux flow dependency on the doping dependent mixed state in NaFe1−xCoxAs (x = 0.01, 0.03, and 0.07) crystals using the magnetoresistivity in the case of B//c-axis and B//ab-plane. It was found clearly that irrespective of the doping ratio, magnetoresistivity showed a distinct tail just above the Tc,offset associated with the thermally activated flux flow (TAFF) in our crystals. Furthermore, in TAFF region the temperature dependence of the activation energy follows the relation U(T,B)={U}_{0}(B){(1-T/{T}_{c})}^{q} with q = 1.5 in all studied crystals. The magnetic field dependence of the activation energy follows a power law of {U}_{0}(B)sim {B}^{-alpha } where the exponent α is changed from a low value to a high value at a crossover field of B = ∼2 T, indicating the transition from collective to plastic pinning in the crystals. Finally, it is suggested that the 3D vortex phase is the dominant phase in the low temperature region as compared to the TAFF region in our series samples.

Coupled dynamics of vortex-induced vibration and stationary wall at low Reynolds number

The flow past an elastically mounted circular cylinder placed in proximity to a plane wall is numerically studied in both two dimensions (2D) and three dimensions (3D). This paper aims to explain the mechanism of the cylinder bottom shear layer roll-up suppression in the context of laminar vortex-induced vibration (VIV) of a cylinder placed in the vicinity of a plane stationary wall. In 2D simulations, VIV of a near-wall cylinder with structure-to-displaced fluid mass ratios of m* = 2 and 10 is investigated at the Reynolds number of Re = 100 at a representative gap ratio of e/D = 0.90, where e denotes the gap distance between the cylinder surface and the plane wall. First, the cylinder is placed at five different upstream distances, LU, to study the effects of the normalized wall boundary layer thickness, δ/D, on the hydrodynamic quantities involved in the VIV of a near-wall cylinder. It is found that the lock-in range shifts towards the direction of the higher reduced velocity Ur as δ/D increases and that the lock-in range widens as m* reduces. Second, via visualization of the vortex shedding patterns, four different modes are classified and the regime maps are provided for both m* = 2 and 10. Third, the proper orthogonal decomposition analysis is employed to assess the cylinder bottom shear layer roll-up suppression mechanism. For 3D simulations at Re = 200, the circular cylinder of a mass ratio of m* = 10 with a spanwise length of 4D is placed at a gap ratio of e/D = 0.90 and an upstream distance of LU = 10D. The 3D vortex patterns are investigated to re-affirm the vortex shedding suppression mechanism. The pressure distributions around the cylinder are identified within one oscillation cycle of VIV. The pressure and the shear stress distributions on the bottom wall are examined to demonstrate the effects of near-wall VIV on the force distributions along the plane wall. It is found that both the suction pressure and the shear stress right below the cylinder peak when the cylinder is located at its negative maximum transverse displacement. This study represents a step towards an improved understanding of the hydrodynamics involved in the subsea pipelines subject to ocean currents with different boundary layer flows.

Experimental study of mixed convection heat transfer in a vertical channel with a one-sided semicylindrical constriction with prescribed heat flux

An experimental study of mixed convection heat transfer is carried out in a vertical channel with a one-sided semicylindrical constriction with prescribed heat flux while the other bounding walls are insulated and adiabatic. The semicylinder is placed horizontally at the mid-plane with a blockage ratio (BR, ratio between the semicylinder diameter and the thickness of the rectangular section) of 0.3 and a semicylinder aspect ratio (AR, ratio between the length and diameter of the semicylinder) of 6. The effect of opposing buoyancy on the flow and thermal behavior is analyzed for fixed Prandtl number of Pr = 7, Reynolds number based on semicylinder diameter of 20 ≤ Re ≤ 350 and buoyancy strength or modified Richardson number, Ri* = Gr*/Re2, from 20 to 350. For relatively large values of Ri*, flow visualization images and thermal analysis confirm the presence of a complex three-dimensional (3D) two-vortex structure with two recirculation bubbles present at the forebody and rear of the semicylinder. Surface temperature distributions and averaged Nusselt number at different Reynolds and modified Richardson numbers have been obtained. The results show that variation of the local temperature distributions with angular position and spanwise location become evident, and their relation to the presence of a complex 3D vortex structure that develops close to the semicylindrical constriction has been studied and discussed in detail. Moreover, empirical correlations for the overall Nusselt number are obtained using both Re and Gr* and Re and Ri* as the controlling parameters.

Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices

The nonlinear lattice---a new and nonlinear class of periodic potentials---was recently introduced to generate various nonlinear localized modes. Several attempts failed to stabilize two-dimensional (2D) solitons against their intrinsic critical collapse in Kerr media. Here, we provide a possibility for supporting 2D matter-wave solitons and vortices in an extended setting---the cubic and quintic model---by introducing another nonlinear lattice whose period is controllable and can be different from its cubic counterpart, to its quintic nonlinearity, therefore making a fully `nonlinear quasi-crystal'. A variational approximation based on Gaussian ansatz is developed for the fundamental solitons and in particular, their stability exactly follows the inverted \textit{Vakhitov-Kolokolov} stability criterion, whereas the vortex solitons are only studied by means of numerical methods. Stability regions for two types of localized mode---the fundamental and vortex solitons---are provided. A noteworthy feature of the localized solutions is that the vortex solitons are stable only when the period of the quintic nonlinear lattice is the same as the cubic one or when the quintic nonlinearity is constant, while the stable fundamental solitons can be created under looser conditions. Our physical setting (cubic-quintic model) is in the framework of the Gross-Pitaevskii equation (GPE) or nonlinear Schr\"{o}dinger equation, the predicted localized modes thus may be implemented in Bose-Einstein condensates and nonlinear optical media with tunable cubic and quintic nonlinearities.

Localized dark solitons and vortices in defocusing media with spatially inhomogeneous nonlinearity.

Recent studies have demonstrated that defocusing cubic nonlinearity with local strength growing from the center to the periphery faster than r^{D}, in space of dimension D with radial coordinate r, supports a vast variety of robust bright solitons. In the framework of the same model, but with a weaker spatial-growth rate ∼r^{α} with α≤D, we test here the possibility to create stable localized continuous waves (LCWs) in one-dimensional (1D) and 2D geometries, localized dark solitons (LDSs) in one dimension, and localized dark vortices (LDVs) in two dimensions, which are all realized as loosely confined states with a divergent norm. Asymptotic tails of the solutions, which determine the divergence of the norm, are constructed in a universal analytical form by means of the Thomas-Fermi approximation (TFA). Global approximations for the LCWs, LDSs, and LDVs are constructed on the basis of interpolations between analytical approximations available far from (TFA) and close to the center. In particular, the interpolations for the 1D LDS, as well as for the 2D LDVs, are based on a deformed-tanh expression, which is suggested by the usual 1D dark-soliton solution. The analytical interpolations produce very accurate results, in comparison with numerical findings, for the 1D and 2D LCWs, 1D LDSs, and 2D LDVs with vorticity S=1. In addition to the 1D fundamental LDSs with the single notch and 2D vortices with S=1, higher-order LDSs with multiple notches are found too, as well as double LDVs, with S=2. Stability regions for the modes under consideration are identified by means of systematic simulations, the LCWs being completely stable in one and two dimensions, as they are ground states in the corresponding settings. Basic evolution scenarios are identified for those vortices that are unstable. The settings considered in this work may be implemented in nonlinear optics and in Bose-Einstein condensates.

Experimental and numerical studies of beetle-inspired flapping wing in hovering flight

In this paper, we measure unsteady forces and visualize 3D vortices around a beetle-like flapping wing model in hovering flight by experiment and numerical simulation. The measurement of unsteady forces and flow patterns around the wing were conducted using a dynamically scaled wing model in the mineral-oil tank. The wing kinematics were directly derived from the experiment of a real beetle. The 3D flow structures of the flapping wing were captured by using air bubble visualization while forces were measured by a sensor attached at the wing base. In comparison, the size and topology of spiral leading edge vortex, trailing edge vortex and tip vortex are well matched from experimental and numerical studies. In addition, the time history of forces calculated from numerical simulation is also similar to that from theforce measurement. A difference of average force is in order of 10 percent. The results indicate that the leading edge vortex due to rotational acceleration at the end of the stroke during flapping wing causes significant reduction of lift. The present study provides useful information on hover flight to develop a beetle-like flapping wing Micro Air Vehicle.

Direct Observation of Current-Induced Motion of a 3D Vortex Domain Wall in Cylindrical Nanowires

The current-induced dynamics of 3D magnetic vortex domain walls in cylindrical Co/Ni nanowires are revealed experimentally using Lorentz microscopy and theoretically using micromagnetic simulations. We demonstrate that a spin-polarized electric current can control the reversible motion of 3D vortex domain walls, which travel with a velocity of a few hundred meters per second. This finding is a key step in establishing fast, high-density memory devices based on vertical arrays of cylindrical magnetic nanowires.

Elastic collision and breather formation of spatiotemporal vortex light bullets in a cubic-quintic nonlinear medium

The statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal vortex light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic nonlinearity are considered. The present study is based on an analytic variational approximation and a full numerical solution of the 3D nonlinear Schrödinger equation. The 3D vortex bullet can propagate with constant velocity. Stability of the vortex bullet is established numerically and variationally. Collision between two vortex bullets moving along the angular momentum axis is considered. At large velocities the collision is quasi-elastic, with the bullets emerging after collision with practically no distortion. At small velocities two bullets coalesce to form a single entity called a breather.

Numerical simulation of cryogen spray cooling by a three-dimensional hybrid vortex method

Cryogen spray cooling (CSC) can protect the epidermis from unwanted thermal damage during laser dermatological procedures. Numerical simulation of CSC can provide significant guidance for clinical implementation, but relevant research is sparse. Thus, a 3D two-way coupling hybrid vortex method is developed to simulate CSC. The two-way coupling and compressibility effects are implemented by introducing a vorticity source term into the grid. The validity of this algorithm has been confirmed in a previous simulation of the evaporating acetone spray. Comparisons between the simulation results and the R134a spray cooling experimental results demonstrate the accuracy of the present method in analyzing the complex atomization and evaporation. The simulated cooling capacity achieves the maximum experimental value at a spray distance of 26mm, which is close to the optimal spray distance of 30mm in clinical practice. Particulate count reveals that the central area with a radius of 2mm in R134a spray accounts for 74% of the total cooling capacity, which is beneficial for the precise control of the therapy area in laser surgery.

Iterative Brinkman penalization for simulation of impulsively started flow past a sphere and a circular disc

We present a Brinkman penalization method for three-dimensional (3D) flows using particle vortex methods, improving the existing technique by means of an iterative process. We perform simulations to study the impulsively started flow past a sphere at Re=1000 and normal to a circular disc at Re=500. The simulation results obtained for the flow past a sphere are found in qualitative good agreement with previously published results obtained using respectively a 3D vortex penalization method and a 3D vortex method combined with an accurate boundary element method. From the results obtained for the flow normal to a circular disc it is found that the iterative method enables the use of a time step that is one order of magnitude larger than required by the standard non-iterative Brinkman penalization method.

Insights into the growth rate of spatially evolving plane turbulent free-shear layers from 2D vortex-gas simulations

Although the free-shear or mixing layer has been a subject of extensive research over nearly a century, there are certain fundamental issues that remain controversial. These include the influence of initial and downstream conditions on the flow, the effect of velocity ratio across the layer, and the nature of any possible coupling between small scale dynamics and the large scale evolution of layer thickness. In the spirit of the temporal vortex-gas simulations of Suryanarayanan et al. [“Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics,” Phys. Rev. E 89, 013009 (2014)], we revisit the simple 2D inviscid vortex-gas model with extensive computations and detailed analysis, in order to gain insights into some of the above issues. Simulations of the spatially evolving vortex-gas shear layer are carried out at different velocity ratios using a computational model based on the work of Basu et al. [“Vortex sheet simulation of a plane canonical mixing layer,” Comput. Fluids 21, 1–30 (1992) and “Modelling plane mixing layers using vortex points and sheets,” Appl. Math. Modell. 19, 66–75 (1995)], but with a crucial improvement that ensures conservation of global circulation. The simulations show that the conditions imposed at the origin of the free shear layer and at the exit to the computational domain can affect flow evolution in their respective downstream and upstream neighbourhoods, the latter being particularly strong in the single stream limit. In between these neighbourhoods at the ends is a regime of universal self-preserving growth rate given by a universal function of velocity ratio. The computed growth rates are generally located within the scatter of experimental data on plane mixing layers and closely agree with recent high Reynolds number experiments and 3D large eddy simulation studies. These findings support the view that observed free-shear layer growth can be largely explained by the 2D vortex dynamics of the quasi-2D large-scale structures known to be a characteristic of plane mixing layers.

Volumetric Generation of Optical Vortices with Metasurfaces

Recent advances in metasurfaces, i.e., two-dimensional arrays of engineered nanoscale inclusions that are assembled onto a surface, have revolutionized the way to control electromagnetic waves with ultrathin, compact components. The generation of optical vortex beams, which carry orbital angular momentum, has emerged as a vital approach to applications ranging from high-capacity optical communication to parallel laser fabrication. However, the typically bulky elements used for the generation of optical vortices impose a fundamental limit toward on-chip integration with subwavelength footprints. Here, we investigate and experimentally demonstrate a three-dimensional volumetric optical vortices generation based on light–matter interaction with a high-efficiency dielectric metasurface. By employing the concepts of Dammann vortex gratings and spiral Dammann zone plates, a 3D optical vortex array with micrometer spatial separation is achieved from visible to near-infrared wavelengths. Importantly, we show that...

Propagation dynamics of deformed 2D vortex Airy beams

We numerically and experimentally investigate the propagation of deformed 2D vortex Airy beams. Our results show that, for different topological charges, two parabolic trajectories that can be controlled by changing the initial wing angle always dominate the beam propagations. In this case, the main lobes take different propagation distances to restore to the peak intensity. The profiles tend to evolve into 1D or 2D Airy-like patterns to various degrees in the same propagation distance. Furthermore, the whole profiles yield a small change in their acceleration direction, depending on the topological charge and the initial wing angle.

同軸２円板間の回転円柱により誘起される旋回流の不安定性に関する研究

The present study investigates a swirl flow instability induced by a rotating cylinder between coaxial two disks as a model of a vaneless diffuser at zero flow rate. To begin with, the experiment and three-dimensional finite volume simulation were performed. The rotating cylinder was used to produce the swirl flow. Small vortices were generated from the cylinder surface. They were combing and forming one croissant-shaped toroidal vortex (CTV), which was rotating around the cylinder. Small vortices were separating from the CTV and flowing away from the cylinder. In order to investigate the cause of the swirl flow instability, a 2D stability analysis for an annular vortex street was performed. The annular vortex street became less unstable for the larger radial location and the fewer number of vortices. This implies that the vortices could be forming into one vortex as their radial locations increased. In order to validate the stability analysis, the vortex simulations were carried out. The vortices generated from the cylinder surface were forming into one cell as their radial locations increased. In order to validate the stability analysis and vortex simulation, the 2D finite volume simulation was performed. The vortices were generated from the cylinder surface. They were combining and forming one cell, which was rotating around the cylinder. The vortices were separating from one cell and flowing away from the cylinder. The frequencies of vortex rotation agreed in the experiment, the two and three-dimensional simulations. Therefore, it is considered that the 2D vortex transforms to the 3D CTV, similarly the Tayler vortex. Furthermore, all the results indicate that the 2D swirl flow instability causes the CTV, and the vortices combining to and separating from the CTV.

Monte Carlo simulation of the crossover from Bose glass to Bragg glass phase in layered BSCCO with columnar defects

Monte Carlo simulations of layered BSCCO samples are used to investigate the behavior of vortex matter at low fields, particularly in connection with the possible occurrence of a Bragg glass (BrG) phase at low density of columnar defects, a phenomenon characterized by the prevalence of short-range over long-range order. In this dislocation-free topological phase the translational order correlation function displays a power law decay. For magnetic induction B = 0.1 kG the analysis of the data for the first Bragg peak of the planar structure factor, the hexatic order parameter, and the Delaunay triangulation shows that, as the density of columnar defects is lowered, a crossover (or transition) from Bose glass to BrG phase takes place in this highly anisotropic high-T superconductor. Most importantly, an analysis of the low-temperature 3D vortex–vortex correlation function in terms of the structure factor, calculated via a saddle point approach and the use of the numerical data as input, provides clear-cut evidence of the power law decay of the divergent Bragg peaks in the BrG phase, a fundamental feature that was inequivocally verified only in isotropic compounds.

Numerical Investigation of Fluid Flow and Performance Prediction in a Fluid Coupling Using Large Eddy Simulation

Large eddy simulation (LES) with various subgrid-scale (SGS) models was introduced to numerically calculate the transient flow of the hydraulic coupling. By using LES, the study aimed to advance description ability of internal flow and performance prediction. The CFD results were verified by experimental data. For the purpose of the description of the flow field, six subgrid-scale models for LES were employed to depict the flow field; the distribution structure of flow field was legible. Moreover, the flow mechanism was analyzed using 3D vortex structures, and those showed that DSL and KET captured abundant vortex structures and provided a relatively moderate eddy viscosity in the chamber. The predicted values of the braking torque for hydraulic coupling were compared with experimental data. The comparison results were compared with several simulation models, such as SAS and RKE, and SSTKW models. Those comparison results showed that the SGS models, especially DSL and KET, were applicable to obtain the more accurate predicted results than SAS and RKE, and SSTKW models. Clearly, the predicted results of LES with DSL and KET were far more accurate than the previous studies. The performance prediction was significantly improved.

A study on temporal accuracy of OpenFOAM

Crank–Nicolson scheme in native OpenFOAM source libraries was not able to provide 2nd order temporal accuracy of velocity and pressure since the volume flux of convective nonlinear terms was 1st accurate in time. In the present study the simplest way of getting the volume flux with 2nd order accuracy was proposed by using old fluxes. A possible numerical instability originated from an explicit estimation of volume fluxes could be handled by introducing a weighting factor which was determined by observing the ratio of the finally corrected volume flux to the intermediate volume flux at the previous step. The new calculation of volume fluxes was able to provide temporally accurate velocity and pressure with 2nd order. The improvement of temporal accuracy was validated by performing numerical simulations of 2D Taylor–Green vortex of which an exact solution was known and 2D vortex shedding from a circular cylinder.

Regularized characteristic boundary conditions for the Lattice-Boltzmann methods at high Reynolds number flows

This paper reports the investigations done to adapt the Characteristic Boundary Conditions (CBC) to the Lattice-Boltzmann formalism for high Reynolds number applications. Three CBC formalisms are implemented and tested in an open source LBM code: the baseline local one-dimension inviscid (BL-LODI) approach, its extension including the effects of the transverse terms (CBC-2D) and a local streamline approach in which the problem is reformulated in the incident wave framework (LS-LODI). Then all implementations of the CBC methods are tested for a variety of test cases, ranging from canonical problems (such as 2D plane and spherical waves and 2D vortices) to a 2D NACA profile at high Reynolds number (Re=105), representative of aeronautic applications. The LS-LODI approach provides the best results for pure acoustics waves (plane and spherical waves). However, it is not well suited to the outflow of a convected vortex for which the CBC-2D associated with a relaxation on density and transverse waves provides the best results. As regards numerical stability, a regularized adaptation is necessary to simulate high Reynolds number flows. The so-called regularized FD (Finite Difference) adaptation, a modified regularized approach where the off-equilibrium part of the stress tensor is computed thanks to a finite difference scheme, is the only tested adaptation that can handle the high Reynolds computation.