Opposite Vorticity Research Articles

Ambient-gas forced convection dictated evaporation kinetics of generic sessile droplets

We probe the temporal evolution of internal thermo-hydrodynamic features of evaporating sessile droplets under external forced convection. A transient numerical model based on Arbitrary Lagrangian-Eulerian (ALE) framework is adopted. The governing equations corresponding to the transport phenomena (mass, momentum and energy) are solved in a fully coupled manner in both the droplet (liquid) and ambient (gaseous) domains while accurately tracing the droplet interface evolution. The role of initial wetting state, external convection velocity and convective heating/cooling effects due to the air-flow are explored in details, and good agreements are noted with previous reports from literature. Results show that although the evaporation rate is augmented significantly in forced convection conditions, the same does not increase in proportion at higher Reynolds numbers. This is primarily due to the enhanced cooling effects that reduce saturated vapor concentration at droplet surface, and thereby supress the diffusion mechanism. Also, depending upon the contact angle, the evaporative cooling effects are compensated partially or completely due to convective heating. This altered thermal profile substantially influences internal hydrodynamic features (Marangoni flow and heat advection) during the transient and stable regimes of droplet evaporation. At higher degrees of convective heating, the droplet interface temperature becomes higher than its base temperature. This condition results in a completely opposite internal Marangoni vortex at stable state compared to that induced due to evaporative cooling effects. We also provide a regime map to show the role of the gas-phase Stefan number on the droplet-phase hydrodynamic regimes.

Spontaneous convective pattern formation in a dusty plasma

We report on experimental observations of self-sustaining convective patterns in a dusty plasma system. The experiments are carried out in a capacitively coupled radio frequency (RF) argon plasma discharge in which a dusty plasma is produced by introducing micrometer-sized melamine formaldehyde particles. A self-sustained pair of convective cells with opposite vorticities is seen to appear in a lateral view of the system, beyond some threshold values of the background gas pressure and RF power. Particle tracking velocimetry measurements reveal the existence of a dust temperature gradient that is responsible for the convective counter-rotating patterns. The origin of the kinetic temperature gradient in the absence of any external heat source is attributed to the larger ion flux induced heating of the bottom layer of the dust cloud. The velocity and vorticity of the particles in the convective cell increase with an increase in the vertical kinetic temperature gradient. The experimental results compare reasonably well with the findings of molecular dynamics simulations of the laboratory system.

Effects of rough elements in fractures on seepage law based on lattice Boltzmann method

The rough structure in natural fractures will have impact on the fluid flow performance. It is difficult to understand its mechanism through direct research because of complex and disordered structure. In this context, a digital roughness crack model and introducing artificial roughness elements are constructed. And a crack simulation program based on the Lattice Boltzmann Method was written and verified to study the mechanism of the effect of crack roughness on seepage. The results show that: (1) Artificial elements with different shapes have different effects on fluid flow in the fracture, which are reflected in the local flow pattern. The rectangular element has the greatest obstruction effect on the fluid, and has the most developed vortex structure locally. The semicircular element and the triangular element have a decreasing effect on the fluid flow, and the degree of development of the local vortex is also reduced. (2) It is found that the interaction effect between height and distance disappears when the height is the same and the ratio of the distance and height between adjacent roughness elements is greater than 5 and two opposite vortices between adjacent rough elements merge into one. (3) The existence of roughness elements in rough fractures will have a strong viscous effect on the fluid. And with the change of the shape of the roughness element, the resistance strength of the viscous effect to the fluid is also different. The research results help to understand the seepage law of fluid flowing in rough fractures, and have certain reference significance for industrial applications such as oil production.

Characterization and low-order representation of the vortex meandering motion in upswept afterbody wakes

Vortex meandering is often characterized by seemingly stochastic motions of the vortex core. An elucidation of the underlying mechanisms of core movement aids not only in characterizing the meandering phenomenon but also forms a starting point to guide flow control techniques. This paper investigates the complex motion of longitudinal vortices behind an abstracted cargo aircraft fuselage. In contrast to wingtip vortices that arise in relative isolation, in this case the large aft region upsweep generates a meandering counter-rotating vortex pair that retains its coherence for long distances downstream. High-resolution spatio-temporal datasets obtained from large-eddy simulation of a cylindrical fuselage with longitudinally aligned axis and a sharp-edged base are used for this purpose. The circulation of each vortex in the pair initially increases immediately after formation and asymptotes to a near constant value downstream. Although the time-mean form of the vortices becomes nearly axisymmetric, the transient disorganized motions include time-local regions of opposite vorticity. The complicated meandering motion is decomposed using proper-orthogonal decomposition (POD) modes as primary building blocks. The first two modes constitute a mutually orthogonal |m|=1 elliptic pair, accounting for about 35% of the total energy; individually these modes account for the displacement of vortex cores along straight lines whose slopes coincide with their respective dipole axes. The wake outside of the immediate vicinity of the base displays low-rank behavior, in that the number of modes required to reproduce the flow to a given degree of accuracy diminishes rapidly. Beyond two fuselage (cylinder) diameters downstream, the two leading POD modes can reconstruct the dominant meandering motion and spatial structure in the LES data with less than 15% error using a suitable loss measure.

Cylinder flow and noise control by active base blowing

An extensive experimental investigation was undertaken to control the flow and noise characteristics influenced by vortex shedding from a circular cylinder by implementing air blowing at the base of the cylinder. The study synchronised near-field pressure and far-field noise measurements with the wake velocity field to understand the noise reduction mechanism of base blowing. Surface pressure fluctuations were measured using pressure taps distributed around the cylinder's circumference through a remote-sensing method, while velocity measurements were obtained using planar particle image velocimetry at the midspan to examine the flow dynamics. The study unveiled the crucial role of near-field pressure, particularly induced at the shoulders of the cylinder, in generating far-field noise. The rapid vertical flow movement, arising from the interaction between shear layers, was identified as a mechanism responsible for inducing surface pressure fluctuations. This phenomenon occurred as high-momentum fluid moved from the free stream into the interior of the vortex-formation region. By applying base blowing, a remarkable reduction in both near-field pressure and far-field noise was achieved at the fundamental vortex-shedding frequency, with reductions of approximately 20 and 25 dB, respectively, compared with the baseline. Additionally, base blowing caused the shear layers to roll up farther downstream than in the baseline by decreasing the entrainment of fluid-bearing opposite vorticity by the shear layer upstream of the growing vortex. Consequently, there was a substantial decrease in turbulent kinetic energy and Reynolds stress near the cylinder, resulting in slower vertical flow movement and weaker near-field pressure.

Arbitrary multi-directional acoustic beam emission from a cylindrical metasurface with grafted topological charge

Directional sound beam emission from compact devices is highly desirable in many practical acoustic applications. Here, we present an approach for the efficient control of arbitrary multi-directional emission through a grafted metasurface that is designed by cutting and stitching two cylindrical phase-gradient metasurfaces carrying two opposite topological charges. The grafted metasurface provides a compact and robust platform for diverse multi-directional beam emission, whose beam number and azimuthal angles are precisely controlled by the topological charge. The underlying mechanism contributes to the wave interference of two opposite partial vortex waves. This scheme was verified by simulation and experimental results. Our work provides a design methodology for directional sound beam emission devices and may be useful for applications such as acoustic imaging, beam steering, and vortex detection.

"Polymerization" of Bimerons in Quasi-Two-Dimensional Chiral Magnets with Easy-Plane Anisotropy.

We re-examine the internal structure of bimerons, which are stabilized in easy-plane chiral magnets and represent coupled states of two merons with the same topological charge |1/2| but with opposite vorticity and the polarity. We find that, in addition to the vortices and antivortices, bimerons feature circular regions which are located behind the anti-vortices and bear the rotational sense opposite to the rotational sense chosen by the Dzyaloshinskii-Moriya interaction. In an attempt to eliminate these wrong-twist regions with an excess of positive energy density, bimerons assemble into chains, and as such exhibit an attracting interaction potential. As an alternative to chains, we demonstrate the existence of ring-shaped bimeron clusters of several varieties. In some rings, bimeron dipoles are oriented along the circle and swirl clockwise and/or counterclockwise (dubbed "roundabouts"). Moreover, a central meron encircled by the outer bimerons may possess either positive or negative polarity. In other rings, the bimeron dipoles point towards the center of a ring and consequently couple to the central meron (dubbed "crossings"). We point out that the ringlike solutions for baryons obtained within the Skyrme model of pions, although driven by the same tendency of the energy reduction, yield only one type of bimeron rings. The conditions of stability applied to the described bimeron rings are additionally extended to bimeron networks when bimerons fill the whole space of two-dimensional samples and exhibit combinations of rings and chains dispersed with different spatial density (dubbed bimeron "polymers"). In particular, bimeron crystals with hexagonal and the square bimeron orderings are possible when the sides of the unit cells represent chains of bimerons joined in intersections with three or four bimerons, respectively; otherwise, bimeron networks represent disordered bimeron structures. Moreover, we scrutinize the inter-transformations between hexagonal Skyrmion lattices and disordered bimeron polymers occuring via nucleation and mutual annihilation of merons within the cell boundaries. Our theory provides clear directions for experimental studies of bimeron orderings in different condensed-matter systems with quasi-two-dimensional geometries.

Effect of SCWSP-VGs and thermal performance investigation of pillow-plate type heat exchanger (PPHX)

Vortex Generators (VGs) are an innovative heat transfer enhancement in traditional heat exchangers. With this technique, the study investigates the combined impact of upper-lower Staggered Circular Welding Spot Patterns (SCWSP) and VGs, termed SCWSP-VGs, in a periodic enhanced Pillow-plate type heat exchanger (PPHX) using ANSYS Fluent 18.1. Numerical results reveal SCWSP-VGs induce a periodic velocity profile and opposite elliptical recirculation vortex (OERV) turbulence, significantly improving thermo-hydrodynamics compared to smooth enclosures. In addition, the performance of the PPHX is described or presented in the graphical form in terms of Colburn j-factor, Nu/Nu0, f/f01/3, Reynolds analogy factor, normalized drag coefficient ratio (Cx/Cx0)0.33, and (Nu/Nu0)/(f/f0)1/3. The maximum Nu and performance evaluation criterion (PEC) are improved by 41.34% and 1.68 in the dh/XL = 0.076 and 0.043 at Re = 1000, respectively.

Divide and structure: generating and interswitching orthogonal eigenstates of complementary petal beams using a π-shifted Sagnac interferometer.

One of the many facets of structured light are Ferris wheel/petal beams that can be generated by the addition/superposition of two beams with opposite vorticity/orbital angular momentum (OAM). We demonstrate a simple scheme employing a π-shifted Sagnac interferometer (SI) containing a spiral phase plate (SPP) that divides and structures an incoming beam into two azimuthally complementary petal beams representing orthogonal eigenstates. The half-wave plate in the SI can interswitch/route these intensity patterns between the two outputs of the interferometer. The results are interpreted as a double symmetry breaking--that of helicity due to SPP and handedness due to HWP--experienced by counterpropagating beams in the π-shifted SI. In general, for a Laguerre-Gaussian (LG) incoming mode, the SI produces two orthogonal output states, each consisting of a sum or difference of distinct SPP-modified LG modes and resulting in complementary petal beams convoluted with the incoming mode. We also introduce a three-mirror π-shifted SI that can switch on and switch off opposite sign vortices into different SI arms. The scheme can find applications in particle trapping, information transmission/development of communications protocols, and signal processing (i.e.,multiplexing/demultiplexing when using beams with high vorticity/OAM).

Comparative study on stator corner separation vortex characteristics in axial-flow pump and tubular pump: To understand the effects of guide-vane cone diffusion on horn-like vortices

The guide-vane cone diffusion is a typical structural difference between an axial-flow pump and a tubular pump, which is shown as low diffusivity and high diffusivity respectively, but it is still unclear how this structural difference affects the vortex characteristics in stator corner separation flows. In this paper, a comparative study of stator corner separation flows in an axial-flow pump and a tubular pump was conducted, and the effects of guide-vane cone diffusion on vortical structures were clarified. Firstly, for the apparent vortical features, compared with the guide-vane of axial-flow pump with low diffusivity, the horn-like vortex in the guide-vane of tubular pump with high diffusivity has the features of smaller scale, weaker swirling strength, shorter evolution cycle and lower pressure fluctuations. Secondly, for the vortex dynamics mechanism, the guide-vane cone diffusion of tubular pump can cause additional pressure energy recovery, which leads to higher adverse pressure gradients, so it is easier to induce additional shroud backflow near the suction surface. In this coupled flow field of main flow, namely hub corner separation flow and shroud backflow, the streamwise periodic oscillation of the pressure function gradient ωS ·▽(▽p/ρ) is found, and it induces the unique vortex-street-like distributions of the deformational vorticity ωS and the rigid vorticity ωR . This physical effect causes a mutual competition between the horn-like vortex near the hub corner and the opposite backflow vortex near the shroud side. It is this competition effect originating from the guide-vane cone diffusion that greatly suppresses the development of the horn-like vortex in a tubular pump.

Regional Abyssal Vorticity Balance in the Northeast South China Sea: External and Internal Dynamics of Abyssal Circulation

Abstract Abyssal vorticity balance in the northeast South China Sea was assessed for over a year based on observations from 28 current- and pressure-recording inverted echo sounders distributed west of the Luzon Strait. The regional first-order balance was dominated by the planetary vorticity flux and bottom pressure torque, which reflect the external and internal dynamics of abyssal circulation. Vertical motion considerably contributed to the planetary vorticity flux, whereas the contribution of horizontal motion was negligible. Positive and negative planetary vorticity fluxes dominate the areas along the eastern and western boundaries, indicating upward and downward vertical transport, respectively. The opposite planetary vorticity fluxes in the different areas were accompanied by different current patterns; regional anticyclonic and cyclonic characteristics appeared near the western and eastern boundaries, respectively, owing to the deep topography as the abyssal current followed the boundary. The planetary vorticity flux near the eastern boundary was substantial in spring and autumn; in contrast, along the western boundary it was enhanced only in spring. Deep eddies played important roles in planetary vorticity flux and regional vorticity balance. The results of this study reveal the formation dynamics of abyssal circulation in the South China Sea as well as its spatiotemporal distributions, providing a more detailed description of abyssal circulation. Significance Statement The deep South China Sea (SCS) is a nearly enclosed basin characterized by cyclonic abyssal circulation. Based on the observations from 28 current- and pressure-recording inverted echo sounders distributed west of the Luzon Strait, the vorticity balance in the deep SCS was clarified. The planetary vorticity flux and bottom pressure torque maintain a first-order balance of vorticity, which acts as the external and internal dynamics of the abyssal circulation. The study describes the temporal variability and spatial distribution of vorticity terms in the deep ocean west of the Luzon Strait, which may contribute to a more detailed understanding of abyssal circulation formation and its evolution.

Melting Process of Frozen Sessile Droplets on Superhydrophobic Surfaces.

Superhydrophobic surfaces can exhibit icephobicity in many ways due to their large contact angles and small rolling angles. The melting process of frozen droplets on superhydrophobic surfaces is still unclear, hindering the understanding of surface icephobicity. In this experimental study of the melting process of frozen sessile droplets on superhydrophobic surfaces, we find two types of melting morphologies with opposite vortex directions on a single-scale nanostructured (SN) superhydrophobic substrate and a hierarchical-scale micronanostructured (HMN) superhydrophobic substrate. Melting pattern visualizations and flow field measurements showed Marangoni convection and natural convection occurring in the melting sessile droplets. For the HMN superhydrophobic substrate, the internal flow was found to be dominated by Marangoni convection due to the temperature gradient along the surface of the droplet. For the SN superhydrophobic substrate, Marangoni convection was inhibited by the superhydrophobic particles at the surface of the droplet, which were shed from the fragile superhydrophobic substrate during the freezing-melting process, as confirmed by surface characterizations of the substrate and flow measurements of a water pool. These results will help researchers better understand the melting process of frozen droplets and in designing novel icephobic surfaces for numerous applications.

Hydrodynamics of Supersonic Steam Jets Injected into Cross-Flowing Water

High-speed gas/vapour jets injected into a cross-moving sonic liquid signifies a vital phenomenon which bears useful applications in environmental and energy processes. In the present experimental study, a pulsating jet of supersonic steam was injected into cross-flowing water. Circulation zones of opposite vorticity owing to the interaction between the steam jet and cross-water flow were found. However, a large circulation appeared in front of the nozzle exit. Also, most small circulation regions were observed at higher water-flow rates (>2 m3/s). Among the prime mixing variables (i.e., turbulence kinetic energy (TKE) and Reynolds shear stress (RSS)), the RSS estimations backed a small diffusive phenomenon within a region far from the nozzle exit. Further information extracted from the PIV images indicated the existence of Kelvin–Helmholtz (KH) instabilities. The counter-rotating vortex pairs (CVPs) appeared to be significant in the region close to the nozzle exit, and they exhibited leeward side folds. Moreover, the effects of the operating conditions on the pressure recovery and mixing efficiency as well as the penetration and the separation height were evaluated to determine the optimisation of the phenomenon. By applying extreme difference analysis, the mixing efficiency was found as the most influential parameter.

Polariton vortex Chern insulator [Invited

We propose a vortex Chern insulator, motivated by recent experimental demonstrations on programmable arrangements of cavity polariton vortices by [S. Alyatkin et al., arXiv, ArXiv:2207.01850 (2022)10.48550/arXiv.2207.01850 ] and [J. Wang et al, Natl. Sci. Rev. 10, Nwac096 (2022)10.1093/nsr/nwac096]. In the absence of any external fields, time-reversal symmetry is spontaneously broken through polariton condensation into structured arrangements of localized co-rotating vortices. We characterize the response of the rotating condensate lattice by calculating the spectrum of Bogoliubov elementary excitations and observe the crossing of edge-states, of opposite vorticity, connecting bands with opposite Chern numbers. The emergent topologically nontrivial energy gap stems from inherent vortex anisotropic polariton-polariton interactions and does not require any spin-orbit coupling, external magnetic fields, or elliptically polarized pump fields.

Numerical simulation of lateral jet interaction with rarefied hypersonic flow over a two-dimensional blunt body

Reaction Control System (RCS) is a direct force control system that successfully adjusts a craft's attitude or orbit using the reaction force created by jet flow. RCS is frequently employed in the management of near-space vehicles due to its properties of fast response time and effective control efficiency. When the near-space vehicle is navigating at high altitude in a low density atmosphere, the Navier–Stokes equation is no longer applicable. The numerical approach utilized in this study is known as the Conserved Discrete Unified Gas Kinetic Scheme, and the governing equation is the Boltzmann equation, which is not constrained by the continuum hypothesis. In velocity space, an unstructured mesh is utilized, which minimizes the amount of discrete velocity points and considerably increases computation efficiency. The numerical results are in good agreement with the direct simulation Monte Carlo code DS2V when modeling large Knudsen number lateral jet flow. The interaction flow field between hypersonic free stream and lateral jet is then simulated at altitudes of 60–90 km using argon as the working gas and a two-dimensional blunt cone with lateral jet as the study object. Under a fixed jet pressure ratio, preliminary research was conducted on the variation of the lateral jet interference flow field characteristics with the freestream Knudsen number and angle of attack. The differences in surface pressure and heat flux caused by jet opening and shutting are compared. Under rarefied atmospheric conditions, the variation of the force/moment amplification coefficient is given. The numerical results show that when the angle of attack is 0°, the separation area in front of the nozzle and a pair of opposite vortices, which are common in the jet interference flow field, gradually disappear with increasing altitude, but the separation vortex reappears when the angle of attack of the freestream is increased. The high-pressure region generated upstream of the nozzle is the primary cause of the extra force/moment. The density of the main flow decreases as altitude increases, various shock wave patterns of the interference flow field gradually dissipate and the force/moment amplification factor changes considerably. The rarefied gas effect has a significant effect on the lateral jet interference flow.

Transfer of passive particles in the velocity field of vortex tripole moving on a plane

Purpose of this article is to study the transport of passive particles in the velocity field of a vortex tripole with a change in the parameter that determines the speed of the configuration movement. A structure consisting of a central vortex and satellite vortices rotating around it with the opposite vorticity is understood as a tripole. We employ a system of three point vortices, the most simple mathematical representation of a vortex tripole, which may be expressed as a system of nonlinear ordinary differential equations with a parameter. Consideration is limited to a particular case of a tripole with zero total vorticity. The influence of the speed values of vortex configuration movement on the processes of passive particle transport has been studied. Methods. The study was carried out numerically using algorithms based on the dynamical systems approaches including the construction of the Poincare map and the analysis of the dynamics of marker particles. Were carried out long ´ times calculations, corresponding to hundreds and thousands of turns around the tripole center. Integrators of high orders of accuracy were used to solve the Cauchy problems, which made it possible to adequacy of the calculation result control. Results. We found that transferring passive particles is fundamentally different depending on the speed of the tripole. A vast zone of chaotic dynamics forms in the neighborhood of the vortices when the velocity is low. This zone slowly shifts along with the tripole. There are subregions of active and slow mixing inside the chaos region. The possible stages of particle dynamics are: transfer from the region to the right of the tripole to the area to the left, vigorous mixing near the vortices, and slowly drifting to the region to the left of the tripole. At a high speed of vortex configuration in the entire chaotic region, the particles are strongly mixed. The vortex tripole removes particles from the vicinity of its initial position over long distances and practically does not capture new particles along its path. In intermediate situations, both processes can be realized at varying degrees. Conclusion. Non-trivial scenarios for the transport of passive particles by a vortex tripole, which can also occur in real vortex configurations of fluids, have been discovered and described.

Two-dimensional Airy waves and three-wave solitons in quadratic media

We address the dynamics of two-dimensional (2D) truncated Airy waves (TAWs) and three-component solitons in the system of two fundamental-frequency (FF) and second-harmonic (SH) fields, coupled by quadratic () terms. The system models second–harmonic-generating optical media and atomic-molecular mixtures in Bose–Einstein condensates. In addition to stable solitons, the system maintains truncated-Airy-waves states in either one of the FF components, represented by exact solutions, which are stable, unlike the Airy waves in the degenerate (two-component) system. It is also possible to imprint vorticity onto the 2D Airy modes. By means of systematic simulations, we examine interactions between TAWs originally carried by different FF components, which are bending in opposite directions, through the SH field. The interaction leads to fusion of the input into a pair of narrow solitons. This is opposed to what happens in the 1D system, where the interacting Aity waves split into a large number of solitons. The interaction of truncated Aity waves carrying identical imprinted vorticities creates an additional pair of solitons, while opposite vorticities create a set of small-amplitude ‘debris’ in the output. Slowly moving solitons colliding with a heavy TAW bounce back, faster ones are absorbed by it, and collisions are quasi-elastic for fast solitons. Soliton-soliton collisions lead to merger into a single mode, or elastic passage, for lower and higher velocities, respectively.

Analysis of Tip Clearance Effect on the Transportation Characteristics of a Multiphase Rotodynamic Pump Based on the Non-Uniform Bubble Model

The multiphase rotodynamic pump is widely used in petroleum and gas exploitation, and blade tip clearance may cause flow instability and performance deterioration. In the present work, the influence of tip clearance on the transportation characteristic in a multiphase rotodynamic pump is investigated based on the non-uniform bubble model, in which the bubbles’ coalescence and break-up are considered. The influence mechanism of tip clearance on the energy performance is revealed. The results show that the leakage flow rate increases linearly with the increase in tip clearance, but variation in pump energy performance shows the opposite trend. In addition, a larger tip clearance results in a sharply decreased pressure increment in the impeller, while in the guide vane, the increment is raised slightly. For the 0 mm tip clearance condition, a positive vortex (relative to the impeller rotation direction) is observed in the impeller passage. However, the opposite leakage vortex is also found in the region near the tip clearance when the tip clearance is considered, and the vortex strength increases for a larger tip clearance.

Abruptly autofocusing property of circular Pearcey vortex beams with different initial launch angles in harmonic potentials

We have studied and explored the influence of different launch angles on the circular Pearcey beams (CPBs) without vortex or with vortex for the first time. Although launch angles can manipulate the focal length and the contrast of peak intensity of the CPBs, the shape and propagation trajectory of the CPBs maintain invariant. When the vortex is considered, the focal pattern and the contrast of peak intensity of the circular Pearcey vortex beams (CPVBs) can be changed by adjusting the magnitude of topological charges and the position of vortex. In addition, we have deliberated the propagation of the CPVBs under the action of double opposite optical vortices.

Azimuthal and radial modulation of double-four-wave mixing in a coherently driven graphene ensemble.

We investigate in detail the azimuthal and radial modulation (i.e., the azimuthal order lj and radial order pj with j = 1, 2) of double-four-wave mixing (double-FWM) by use of two higher-order Laguerre-Gaussian (LG) beams in a Landau quantized graphene ensemble. A pair of weak probe pulses in the graphene ensemble interacts with two LG beams and thus two vortex FWM fields with the opposite vorticity are subsequently generated. In combination with numerical simulations, we reveal that (i) there appear l1 + l2 periods of phase jumps in the phase profiles under any conditions; (ii) p + 1 concentric rings emerge in the intensity profile and the strength is mainly concentrated on the inner ring when the two LG beams have the same radial orders (i.e., p1 = p2 = p); (iii) there are p raised narrow rings occurring in the phase profile in the case of p1 = p2 = p and l1 ≠ l2, and the raised narrow rings would disappear when p1 = p2 and l1 = l2; (iv) pmax + 1 concentric rings appear in the intensity profile, meanwhile, |p1 - p2| convex discs and pmin raised narrow rings emerge in the phase diagram in the case of p1 ≠ p2, here pmax = max(p1, p2) and pmin = min(p1, p2). Moreover, the two generated FWM fields have the same results, and the difference is that the phase jumps are completely opposite. These findings may have potential application in graphene-based nonlinear optical device by using LG beams with adjustable mode orders.