Vortex Modes Research Articles

Nonlinear evolution of vortical disturbances entrained in the entrance region of a circular pipe

The nonlinear evolution of free-stream vortical disturbances entrained in the entrance region of a circular pipe is investigated using asymptotic and numerical methods. Attention is focused on the low-frequency disturbances that induce streamwise elongated structures. A pair of vortical modes with opposite azimuthal wavenumbers is used to model the free-stream disturbances. Their amplitude is assumed to be intense enough for nonlinear interactions to occur inside the pipe. The formation and evolution of the perturbation flow are described by the nonlinear unsteady boundary-region equations in the cylindrical coordinate system, derived and solved herein for the first time. Matched asymptotic expansions are employed to construct appropriate initial conditions and the initial–boundary value problem is solved numerically by a marching procedure in the streamwise direction. Numerical results show the stabilising effect of nonlinearity on the intense algebraic growth of the disturbances and an increase of the wall-shear stress due to the nonlinear interactions. A parametric study is carried out to evince the effect of the Reynolds number, the streamwise and azimuthal wavelengths, and the radial length scale of the inlet disturbance on the nonlinear flow evolution. Elongated pipe-entrance nonlinear structures (EPENS) occupying the whole pipe cross-section are discovered. EPENS with $h$ -fold rotational symmetry comprise $h$ high-speed streaks positioned near the wall, and $h$ low-speed streaks centred around the pipe core. These distinct structures display a striking resemblance to nonlinear travelling waves found numerically and observed experimentally in fully developed pipe flow. Good agreement of our mean-flow and root mean square data with experimental measurements is obtained.

Orbital angular momentum superimposed mode recognition based on multi-label image classification

Orbital angular momentum (OAM) multiplexing technology has great potential in high capacity optical communication. OAM superimposed mode can extend communication channels and thus enhance the capacity, and accurate recognition of multi-OAM superimposed mode at the receiver is very crucial. However, traditional methods are inefficient and complex for the recognition task. Machine learning and deep learning can offer fast, accurate and adaptable recognition, but they also face challenges. At present, the OAM mode recognition mainly focus on single OAM mode and ±l superimposed dual-OAM mode, while few researches on multi-OAM superimposed mode, due to the limitations of single-object image classification techniques and the diversity of features to recognize. To this end, we develop a recognition method combined with multi-label image classification to accurately recognize multi-OAM superimposed mode vortex beams. Firstly, we create datasets of intensity distribution map of three-OAM and four-OAM superimposed mode vortex beams based on numerical simulations and experimental acqusitions. Then we design a progressive channel-spatial attention (PCSA) model, which incorporates a progressive training strategy and two weighted attention modules. For the numerical simulation datasets, our model achieves the highest average recognition accuracy of 94.9% and 91.2% for three-OAM and four-OAM superimposed mode vortex beams with different transmission distances and noise strengths respectively. The highest experimental average recognition accuracy for three-OAM superimposed mode achieves 92.7%, which agrees with the numerical result very well. Furthermore, our model significantly outperforms in most metrics compared with ConvNeXt, and all experiments are within the affordable range of computational cost.

Single- and dual-tube He-Ne lasers for high-power excitation of LG01-mode vortex beam

Abstract In this study, aiming to extend the power of LG01-mode vortex light at 632.8nm, the commercial He-Ne laser was upgraded to dual-tube gain geometry with the assistance of an intracavity spot defect for spatial filtering. We investigated the impact of using single and double He-Ne gas gain tubes on the powers of vortex laser output , and achieved a maximum 4.7-mW power of LG01-mode vortex light, correspionding to an optical-optical conversion efficiency of 39.2% and making it the highest power of vortex light obtained in He-Ne laser.

Generating optical vortex beams using cylindrical waveguides

As an initial step toward exciting optical vortices using high-power millimeter waves, this study developed a method for inducing vortex modes within a cylindrical waveguide using Gaussian beams. By examining the coupling between tilted and offset Gaussian beams and specific waveguide modes, appropriate tilt angles and offsets were obtained. Numerical simulations demonstrated that the vortex modes could be efficiently excited using four Gaussian beams. Furthermore, the results revealed that increasing the number of Gaussian beams improves the excitation efficiency of vortex modes.

Exotic spin-Hall effect in non-Hermitian optical systems

Abstract We systematically explore the origin and evolution of the exceptional points (EP) when a light beam is scattered by a parity-time (PT)-symmetric system using a scattering matrix approach and a full-wave theory. It is demonstrated that the PT-symmetric system switches between symmetry and symmetry-breaking phases at the EPs, giving rise to singular features in the Fresnel coefficients and causing the spin-Hall effect (SHE) near the EPs to exhibit anomalous features such as significantly enhanced transverse spin-Hall shifts and additional in-plane spin-Hall shifts. This exotic SHE can be explained by the significant beam intensity distortion caused by the destructive interference between the spin-maintained normal modes and the spin-reversed abnormal modes in the scattered light. This phenomenon can further be understood in terms of vortex mode decomposition, wherein it can be interpreted as the competition and superposition of three vortex modes with topological charges of −1, 0, and 1, respectively. These findings elucidate the mechanism of the unusual SHE around the EPs and offer potential avenues for EP-based sensing and structured light manipulation.

Spontaneous symmetry breaking and vortices in a tri-core nonlinear fractional waveguide

We introduce a waveguiding system composed of three linearly-coupled fractional waveguides, with a triangular (prismatic) transverse structure. It may be realized as a tri-core nonlinear optical fiber with fractional group-velocity dispersion (GVD), or, possibly, as a system of coupled Gross–Pitaevskii equations for a set of three tunnel-coupled cigar-shaped traps filled by a Bose–Einstein condensate of particles moving by Lévy flights. The analysis is focused on the phenomenon of spontaneous symmetry breaking (SSB) between components of triple solitons, and the formation and stability of vortex modes. In the self-focusing regime, we identify symmetric and asymmetric soliton states, whose structure and stability are determined by the Lévy index of the fractional GVD, the inter-core coupling strength, and the total energy, which determines the system’s nonlinearity. Bifurcation diagrams (of the supercritical type) reveal regions where SSB occurs, identifying the respective symmetric and asymmetric ground-state soliton modes. In agreement with the general principle of the SSB theory, the solitons with broken inter-component symmetry prevail with the increase of the energy in the weakly-coupled system. Three-components vortex solitons (which do not feature SSB) are studied too. Because the fractional GVD breaks the system’s Galilean invariance, we also address mobility of the vortex solitons, by applying a boost to them.

Optical orbital angular momentum analogy to the Stern-Gerlach experiment.

Symmetry breaking has been shown to reveal interesting phenomena in physical systems. A notable example is the fundamental work of Otto Stern and Walther Gerlach [Stern and Zerlach, Z. Physik9, 349 (1922)10.1007/BF01326983] nearly 100 years ago demonstrating a spin angular momentum (SAM) deflection that differed from classical theory. Here we use non-separable states of SAM and orbital angular momentum (OAM), known as vector vortex modes, to demonstrate how a classical optics analogy can be used to reveal this non-separability, reminiscent of the work carried out by Stern and Gerlach. We show that by implementing a polarization insensitive device to measure the OAM, the SAM states can be deflected to spatially resolved positions.

Generating optical vortex needle beams with a flat diffractive lens

We present a novel method for generating optical vortex needle beams (focused optical vortices with extended depth-of-focus) using a compact flat multilevel diffractive lens (MDL). Our experiments demonstrate that the MDL can produce focused optical vortices (FOVs) with topological charges l=1−4 (extendable to other l values), maintaining focus over distances significantly longer than conventional optical vortices. Specifically, FOVs exhibit non-diffracting behavior with a depth-of-focus (DOF) extended beyond 5 cm, compared to conventional optical vortices, which show continuous size increase due to diffraction. When the MDL is illuminated by an optical vortex of 3 mm diameter, it achieves a transmission efficiency of approximately 90% and extends the DOF several times beyond that of traditional lenses. Increasing the size of the input optical vortex further extends the DOF but introduces additional rings, with their number increasing proportionally to the value of l. Our approach, validated by both experimental results and numerical simulations, proves effective for beams such as optical vortex and Hermite-Gaussian modes and holds potential applications in high-resolution imaging, material processing, optical coherence tomography, and three-dimensional optical tweezers, offering a simple and efficient solution for generating non-diffracting beams.

Vortex light bullets in rotating Quasi-Phase-Matched photonic crystals

We present a methodology for the generation of stable vortex light bullets (LBs) in rotating Quasi-Phase-Matched (QPM) photonic crystals with quadratic nonlinearity. The photonic crystal is designed with a checkerboard structure, which is feasible to realize by using contemporary technological advancements. Within this framework, square- and rhombus-shaped LBs are observed, both of which are constructed as four-peak vortex mode. The control parameters include the effective phase mismatch, power, rotating frequency, and the size of checkerboard cells. These parameters play key roles in determining the distribution and stability domains of vortex LBs. In contrast to the stable vortex solitons observed in two-dimensional (2D) quadratic systems, the LBs investigated in the 3D rotating system exhibit narrower stability domains within the system’s parameter space. The rotating frequency results in the transition of LBs from quadrupole to traditional vortex modes. Potential applications of this research lie in the field of optical communications and information processing.

The study of propagation characteristics of the millimeter-wave vortex in magnetized plasma by using the FDTD method

It is pointed out that the millimeter-wave vortex may contribute to an efficient method of plasma heating since it was found that the millimeter-wave vortex can propagate in magnetized plasma even in which the normal plane wave is in cut-off condition. Then, it was assumed that the vortex field was the Laguerre–Gaussian (L–G) mode which is a free-space solution, but the generation and stable propagation of the L–G mode vortex are not easy in the millimeter frequency range. On the other hand, it is known that the millimeter-wave hybrid mode of the cylindrical corrugated waveguide also has vortex properties. In this paper, we investigate the propagation characteristics of a millimeter-wave vortex of a hybrid mode of a cylindrical corrugated waveguide in the magnetized plasma by using three-dimensional numerical simulations with the finite-difference time-domain (FDTD) method. It is found that the millimeter-wave vortex of hybrid mode also can propagate in the magnetized plasma even in a condition in which the normal plane wave is in cut-off condition, and the propagation power in the plasma is highly dependent on the topological charge l.

Impact of Polar Vortex Modes on Winter Weather Patterns in the Northern Hemisphere

This study is an additional investigation of stratosphere–troposphere coupling based on the recent stratospheric winter descriptions in five distinct modes: January, February, Double, Dynamical, and Dadiative. These modes, established in a previous study, categorize the main stratospheric winter typologies modulated by the timing of important sudden stratospheric warmings (SSWs) and final stratospheric warmings (FSWs). The novelty of this research is to investigate the Northern Annular Mode, mean sea level pressure (MSLP) anomalies in the Ural and Aleutian regions, and the decomposition of Eliassen–Palm flux into wavenumbers 1 and 2 within each mode. The results show that the January and Double modes exhibit similar pre-warming surface signals, characterized by Ural blocking and Aleutian trough events preceding weak polar vortex events. The January mode displays a positive MSLP anomaly of +395 hPa (−191 hPa) in the Ural (Aleutian) region in December, while the Double mode shows +311 hPa (−89 hPa) in November. These modes are primarily wave-1 driven, generating tropospheric responses via negative Arctic Oscillation patterns. Conversely, the February and Dynamical modes show opposite signals, with Aleutian blocking and Ural trough events preceding strong polar vortex events. In December, the February mode exhibits MSLP anomalies of +119 hPa (Aleutian) and −180 hPa (Ural), while the Dynamical mode shows +77 hPa and −184 hPa, respectively. These modes, along with important SSWs in February and dynamical FSWs, are driven by both wave-1 and wave-2 and do not significantly impact the troposphere. The Radiative mode’s occurrence is strongly related to the Aleutian blocking presence. These findings confirm that SSW timing is influenced by specific dynamical forcing related to surface precursors and underscore its importance in subsequent tropospheric responses. This study establishes a connection between early winter tropospheric conditions and upcoming stratospheric states, potentially improving seasonal forecasts in the northern hemisphere.

Direct numerical simulation of fully-developed supersonic turbulent channel flows with dense vapors

This work aims to investigate the impact of the molecule-complexity effect and the non-ideal effect on wall-bounded turbulent flows by applying direct numerical simulation (DNS) to fully-developed channel flows of two typical organic vapors: R1233zd(E) and octamethyltrisiloxane (MDM). For each vapor, three thermodynamic states are analyzed: one in the dilute-gas region, one near the saturation line, and one in the supercritical region. For mean flow fields, it is found that, due to smaller Prandtl and Eckert numbers, both the molecule-complexity effect and the non-ideal effect reduce the mean temperature rise from the cold wall to the channel center. Meanwhile, the molecule-complexity effect weakens the mean density drop, while the non-ideal effect strengthens the drop. Furthermore, once the density and viscosity variations are considered, the mean streamwise velocity profiles of dense vapors are practically the same as the ideal gas. For turbulent fluctuations, it is found that the correlations between T′, p′, and ρ′ in dense vapors are more complicated than the ideal gas: for the ideal gas, fluctuations are dominated by “vorticity mode”; hence, ρ′ and T′ are strongly related to u′ but independent of p′; however, for dense vapors, “acoustic mode” can also play an important role. A newly derived equation illustrates that, through the “acoustic mode,” the molecule-complexity effect obviously enhances the positive correlation between ρ′ and p′, while the non-ideal effect can enhance the positive correlation between T′ and p′. Further analysis of instantaneous flow fields shows that p′ is isotropic. The isotropic character affects fluctuation magnitudes but has limited effect on the specified wall-direction turbulent transport. Consequently, Walz's equation and Reynolds analogy in terms of enthalpy are still valid. Finally, a comparison between the DNS energy budget and k equation of Reynolds-averaged Navier–Stokes (RANS) model has been carried out. Results show that obvious deviation happens on the production term in spite of the careful selection of eddy viscosity model.

New insights on cavitating flows over a microscale backward-facing step

This study introduces the first experimental analysis of shear cavitation in a microscale backward-facing step (BFS) configuration. It explores shear layer cavitation under various flow conditions in a microfluidic device with a depth of 60 μm and a step height of 400 μm. The BFS configuration, with its unique characteristics of upstream turbulence and post-reattachment pressure recovery, provides a controlled environment for studying shear-induced cavitation without the complexities of other microfluidic geometries. Experiments were conducted across four flow patterns: inception, developing, shedding, and intense shedding, by varying upstream pressure and the Reynolds number. The study highlights key differences between microscale and macroscale shear cavitation, such as the dominant role of surface forces on nuclei distribution, vapor formation, and distinct timescales for phenomena like shedding and shockwave propagation. It is hypothesized that vortex strength in the shear layer plays a significant role in cavity shedding during upstream shockwave propagation. Results indicate that increased pressure notably elevates the mean thickness, length, and intensity within the shear layer. Instantaneous data analysis identified two vortex modes (shedding and wake modes) at the reattachment zone, which significantly affect cavitation shedding frequency and downstream penetration. The wake mode, characterized by stronger and lower-frequency vortices, transports cavities deeper into the channel compared to the shedding mode. Additionally, vortex strength, proportional to the Reynolds number, affects condensation caused by shockwaves. The study confirms that nuclei concentration peaks in the latter half of the shear layer during cavitation inception, aligning with the peak void fraction region.

Single degree of freedom vortex induced vibration of undulatory seal whiskers at low Reynolds number and various angles of attack: A computational fluid dynamics study

The cross-flow vortex-induced vibration (VIV) response of an elastically mounted idealized undulatory seal whisker (USW) shape is investigated in a wide range of reduced velocity at angles of attack (AOAs) from 0° to 90° and a low Reynolds number of 300. The mass ratio is set to 1.0 to represent the real seal whisker. Dynamic mode decomposition is used to investigate the vortex shedding mode in various cases. In agreement with past studies, the VIV response of the USW is highly AOA-dependent because of the change in the underlying vortex dynamics. At zero AOA, the undulatory shape leads to a hairpin vortex mode that results in extremely low lift force oscillation with a lowered frequency. The frequency remains unaffected by VIV throughout the tested range of reduced velocity. As the AOA deviates from zero, alternating shedding of spanwise vortices becomes dominant. A mixed vortex shedding mode is observed at AOA = 15° in the transition. As the AOA deviated from zero, the VIV amplitude increases rapidly by two orders, reaching the maximum of about 3 times diameter at 90°. An infinite lock-in branch is present for AOA from 60° to 90°, where the VIV amplitude remains high regardless of the increase in reduced velocity.

Superposition and interference of Gaussian wave packets for laser transverse modes

We interpret the intrinsic mechanism of the transition from geometric modes to eigenmodes in the Gaussian wave-packet representation based on numerical simulation. We then construct multiaxial super-geometric modes and polygonal vortex modes based on Gaussian wave packets. We highlight that the superposition of Gaussian wave packets can build the geometric modes described by Hermite polynomials and that the eigenmodes are the result of the interference of Gaussian wave packets. We conclude that Gaussian wave packets might serve as a complete basis for constructing structured light generated in solid-state laser cavities. Our study may provide meaningful insight into Gaussian wave packets for laser transverse modes.

Numerical investigation on the suppression of vortex-induced vibration system by assembling different rotors based on quasi-active control method

Combining the innovative concept of quasi-active control method, a numerical simulation is conducted to investigate the vortex-induced vibration (VIV) responses. The objects of this study include a main cylinder (MC) and a cylindrical system outfitted with a pair of rotors of different types (with Banki rotors, Darrieus rotors, and Savonius rotors, denoted as WBR, WDR, and WSR), and the VIV responses are analyzed within the Reynolds number range of 0.8 × 103≤Re ≤ 5.6 × 103. The findings indicate that all three kinds of rotors show excellent vibration suppression effect in downstream and cross-flow directions by adjusting the VIV response (amplitude, frequency, hydrodynamic coefficient) and vortex pattern (vortex mode, wake shape). The maximum amplitude suppression rate can reach 99% for the Banki and Savonius cases at high reduced velocity. Within the whole velocity range, the maximum amplitudes of WBR, WDR, and WSR cases in the downstream and cross-flow directions were 0.32 and 0.45 times, 0.73 and 0.65 times, and 0.28 and 0.33 times, respectively, compared to the maximum amplitude of MC. The time-averaged drag coefficient of the controlled cylinder in the WBR case was minimized to about 0.015. The Banki rotor and Savonius rotor significantly reduced the vibration frequency of the VIV system compared to the Darrieus rotor. Especially, the Banki rotor could keep the VIV system vibration frequency within a narrow range at different reduced velocity. Moreover, the vorticity contour of the VIV system with assembled rotors was significantly improved, with a narrower flow wake width and more regular vortex shedding at high reduced velocity. Considering both amplitude suppression and drag coefficient, Banki rotors were recommended.

Global Stability and Forced Response Analysis of Swirling Flows In Aviation Combustors

Abstract Swirling jets are canonical flow fields used to stabilize flames in many gas turbine combustion systems. These flows amplify background acoustic disturbances and perturb the flame, producing combustion noise and potentially combustion instabilities. Hydrodynamic flow response to acoustic excitations in reacting flows is an important modeling task for understanding combustion noise and combustion instabilities. This study utilizes a global hydrodynamic stability analysis in a Bi-Global and Tri-Global framework to model the vortical hydrodynamic modes of a reacting, swirling LES mean flow based on a commercial nozzle. After conducting an unforced, natural Bi-Global stability analysis to study the unstable eigenmodes of the flow, linearized equations of motion are used to study flow response of the flow to forcing. An empirical velocity transfer function is constructed by determining the flow response to a harmonically varying 150-1500 Hz u' velocity disturbance at the inflow boundary. These disturbances are strongly amplified, with amplification factors ranging from about 20 to 50 and peaking at about 1050 Hz, or st = 0.375. A comparison study with a cartesian, three-dimensional reacting base flow is also performed where the base-flow varies spatially in three-dimensions. The study utilizes a stable, high accuracy, but computationally effective centered finite difference scheme based on a three-dimensional structured mesh. Illustrative results present the qualitative modes and quantitative transfer functions for Bi-Global and Tri-Global stability analyses.

Analysis of coupling supersonic turbine stage with rotating detonation combustor under different turbine parameters

The rotating detonation gas turbine boasts several advantageous characteristics, including self-pressurization, minimal entropy increase, high thermal efficiency, and a high thrust-to-weight ratio. These features make it a promising candidate for the next generation of aerospace power devices. This study investigates the flow characteristics and performance attributes of the supersonic turbine stage coupled with a rotating detonation chamber based on different rotational speeds, blade ratio of rotor and stator, and hub radius, and uses DMD (Dynamic Mode Decomposition) to analyze the main modes of the supersonic turbine. The research identifies distinct wave modes in both the stator and rotor blades of the supersonic turbine. In the stator blades, the modes include waveless contact modes, opposite side λ-wave oblique shock wave modes, and derived modes from opposite side λ-wave oblique shock waves. In the rotor blades, the modes encompass non-separation modes (waveless modes, asymmetric dual λ-wave modes, oblique cut wave modes, and single-side λ-wave modes on the pressure surface), leading-edge stator excitation single separation bubble modes, saddle-type separation modes, and dual separation bubble modes. The efficiency and power of the supersonic turbine stage increase with the rotational speed. The turbine efficiency is highest when the blade ratio is 10:7. Under multi-wave mode conditions, detonation waves demonstrate adaptive self-regulation abilities, ultimately achieving equilibrium in speed, detonation wave height, and spacing. The dominant modes in the stator blades and combustion chamber are governed by detonation waves and slip lines, while in rotor blades, the primary mode is the flow-directional vortex mode governed by detonation waves and slip lines at a frequency lower than their propagation frequency. This research holds certain reference significance for understanding the internal flow characteristics of rotating detonation gas turbines, as well as discussing the patterns of efficiency, power, and load characteristics, thereby offering valuable insights for the practical application of rotating detonation gas turbines.

Optical edge-to-screw singularity state conversions

Optical singularity states, which significantly affect propagation properties of light in free space or optical medium, can be geometrically classified into screw and edge types. These different types of singularity states do not exhibit direct connection, being decoupled from each other in the absence of external perturbations. Here we demonstrate a novel optical process in which a higher-order edge singularity state initially nested in the propagating Gaussian light field gradually involves into a screw singularity with a new-born topological charge determined by order of the edge state. The considered edge state comprises an equal superposition of oppositely charged vortex and antivortex modes. We theoretically and experimentally realize this edge-to-screw conversion process by introducing intrinsic vortex–antivortex interaction. We also present a geometrical representation for mapping this dynamical process, based on the higher-order orbital Poincaré sphere. Within this framework, the edge-to-screw conversion is explained by a mapping of state evolution from the equator to the north or south pole of the Poincaré sphere. Our demonstration provides a novel approach for manipulating singularity state by the intrinsic vortex–antivortex interactions. The presented phenomenon can be also generalized to other wave systems such as matter wave, water wave, and acoustic wave.

Interactions between polymer molecules and hydrodynamic responses in multi-ion induced charge electroosmosis

Induced charge electroosmosis (ICEO) can assist lab-on-a-chip devices and macromolecular separation involving interface, multi-ion species, and solution properties. To supplement the mechanistic insights into the ICEO phenomenon in complex electrochemical scenarios, we numerically address electrokinetic ion transport–fluid flow coupling regulated by multi-ion species and polymer macromolecular rheology around a polarized cylinder. The physics of the ICEO are analysed from multiple perspectives, including the azimuthal velocity, flow type, energy distribution, interfacial ion transport, and electroelastic instability. The main findings are as follows: (1) Deviations under neutral pH conditions (multi-ion species) cause flow field asymmetry and alter the input energy distribution (PE) in the tight double layer. Polymers greatly modify the interfacial force features in ion-enriched regions, as identified by the first stress difference (N1). (2) The kinetic energy vs. viscosity ratio (β) represents the nonlinear enhancement curve Ek=0.011*exp(β/0.64)-0.0138 due to the weakened effective viscosity Rvis. In addition, shear thinning notably lifts the charge density and salt concentration at the cylinder surface, which boosts the PE. (3) Quadrupolar vortex modes impact the positive correlation between β and the ion current (Jtotal) at different pH levels, resulting in less ion current dependence for small β. A low enhancement efficiency occurs at 10-4 ≤ α (molecular anisotropy) ≤ 0.1, whereas a high efficiency exists at α > 0.1. Electroelastic instabilities are confirmed by the spatiotemporal evolution of the velocity fluctuation, with a broadband structural power-law decline in the power spectral density. These results allow microdevice mixing manipulation and disclose non-Newtonian barrier of electrokinetic dynamics.