Topological aspect of vortex lines in two-dimensional Gross-Pitaevskii theory

Using the C-mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross Pitaevskii theory in （3＋l）-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the function indicates that the vortices can only be generated from the zero points of Ф and are quantized in terms of the Hopf indices and Brouwer degrees. The C-mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.

Vortex lines in a ferromagnetic spin-triplet superconductor

Based on Duan＇s topological current theory,we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines.Such defects are different from the Abrikosov vortices in one-component condensate systems.We investigate the inner topological structure of the vortex lines.The topological charge density,velocity,and topological current of the vortex lines can all be expressed in terms of 未 function,which indicates that the vortices can only arise from the zero points of an order parameter field.The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of-mapping.The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a 未-like function.Finally,based on the implicit function theorem and the Taylor expansion,we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.

Vortex Lines and Monopoles in Electrically Conducting Plasmas

基于印射拓扑的当前的理论和在电子上进行血浆的计量器潜力理论，旋涡线和单极的分解被学习。这二拓扑的结构分别地在二维、三维的拓扑的水流生来即存在于，这被指出，它能从一样的拓扑的术语· 被导出(∂ i × ∂ j ),和两这些拓扑的结构被印射描绘拓扑的数字 Hopf 索引和 Brouwer 度。而且，单极的旋涡线的空间分叉和产生和歼灭也被讨论。最后，我们指出 Hopf 不变一合适拓扑对不变描述系的 solitons。

Topological Structure of Knotted Vortex Lines in Liquid Crystals

<正> In this paper,a novel decomposition expression for the U(1)gauge field in liquid crystals(LCs)is derived.Using this decomposition expression and the φ-mapping topological current theory,we investigate the topological struc-ture of the vortex lines in LCs in detail.A topological invariant,i.e.,the Chern-Simons(CS)action for the knottedvortex lines is presented,and the CS action is shown to be the total sum of all the self-linking and linking numbers ofthe knot family.Moreover,it is pointed out that the CS action is preserved in the branch processes of the knotted vortexlines.

The prediction on in-line vortex-induced vibration of slender marine structures

The in-line （IL） vortex-induced vibration （VIV） that occurs frequently in ocean engineering may cause severe fatigue damage in slender marine structures. To the best knowledge of the authors, in existing literatures, there is no efficient analytical model for predicting pure IL VIV. In this paper, a wake oscillator model capable of analyzing the IL VIV of slender marine structures has been developed. Two different kinds of van der Pol equations are used to describe the near wake dynamics related to the fluctuating nature of symmetric vortex shedding in the first excitation region and alternate vortex shedding in the second one. Some comparisons are carried out between the present model results and experimental data. It is found that many phenomena observed in experiments could be reproduced by the present wake oscillator model.

The Instability of the Vortex Sheet along the Shear Line

The traditional Kelvin-Helmholtz notion of studying the shear instability is not suitable for the case associated with shear line with the strong wind shear in the vortex sheet. Since then, the shear instability becomes theinstability of the vortex sheet. If the velocity is induced by the vortex sheet, the inequalities (1? R r + Ri d)> 0 and U(v,t)> U(A(t)) become the criterion of the vortex sheet instability. This criterion indicates that 1) the disposition of environment field restrains the disturbance developing along the shear line. 2) There exist multi—scale interactions in the unstable process of the shear line. The calculation of the necessary condition for the instability is also presented in this paper. Key words Shear line - Induced velocity - Instability of the vortex sheet This work was supported by the project on the study of the formative mechanism and predictive theory of the significant climate and weather disaster in China under Grant G 1998040907 and by the key project on the Dynamic Study of Severe Mesoscale Covective Systems sponsored by the National Natural Science Foundation of China under Grant No.49735180.

Experimental Study on Coupled Cross-Flow and in-Line Vortex-Induced Vibration of Flexible Risers

In this work, we study the coupled cross-flow and in-line vortex-induced vibration （VIV） of a fixedly mounted flexible pipe, which is free to move in cross-flow （ Y- ） and in-line （ X- ） direction in a fluid flow where the mass and natural frequencies are precisely the same in both X- and Y-direction. The fluid speed varies from low to high with the corresponding vortex shedding frequency varying from below the first natural frequency to above the second natural frequency of the flexible pipe. Particular emphasis was placed on the investigation of the relationship between in-line and cross-flow vibration. The experimental results analyzed by using these measurements exhibits several valuable features.

Nonlinear Coupled in-Line and Cross-Flow Vortex-Induced Vibration Analysis of Top Tensioned Riser

The fluctuating furces of the fluid exerted on the top terrsioned riser （＇FIR） in the in-line and cross-flow directions are both modeled by van del Pol wake oscillator model and the nonlinear coupled dynamics of the in-line and cross-flow vortex-induced vibrations （VIV） of the riser are analyzed in time domain in this papar. The numencal shnulation results of the riser＇s in-line and cross-flow displacements and curvatures are compared with experimental measurements and the comparison shows the validity of this method in modeling some main features of the riser＇s VIV. Finally, the effects of the riser＇s top tensions and internal flow velocities on the coupled vibrations of the riser are investigated.

基于铁水搅拌的漩涡图像信息增强方法

现有的铁水漩涡图像识别系统的性能很大程度上取决于图像的质量。然而由于钢渣、光线变化和脱硫剂雾气的干扰,摄像头系统在获取漩涡图像中的特征信息时面临一定的困难,导致图像存在大面积的低质量区域。基于此,提出了一种基于铁水特性和漩涡特性的二维图像漩涡信息识别及增强方法,并采用Gabor小波算法来改进提取漩涡图像的特征以及连接断裂纹线信息,通过特征处理单元对图像进行处理以减少伪特征的存在并通过涡径识别方法得出漩涡的量化参数。以生产现场采集的视频数据为对象进行试验,试验结果表明,该方法对比现有方法降低漩涡图像信息伪特征率43.4%,提升涡径识别准确率3.6百分点,实现对自由表面漩涡特征信息的增强并准确识别。

华北局地大暴雨过程中多个β中尺度对流系统发生发展对比分析

利用常规地面高空观测、多普勒雷达、风廓线、VDRAS(Variational Doppler Radar Analysis System)和NCEP再分析资料,对2018年8月5—6日副热带高压(以下简称副高)控制下华北一次局地大暴雨过程中多个β中尺度对流系统触发和发展机制进行了分析。结果表明:这次大暴雨发生在副高控制下,处于高温、高湿气团中,大气层结极不稳定。暴雨由多个相继发展的中尺度对流系统造成,分别是太行山迎风坡上西南—东北向、华北平原地区保定一带南北向、保定至霸州附近西南—东北向和以雄安新区为中心东西向原地生消的准静止MCS-Ⅰ、MCS-Ⅱ、MCS-Ⅲ和MCS-Ⅳ,均属于β中尺度。在相似的环境中,不同中尺度对流系统触发机制有较大差异,太行山迎风坡上的MCS-Ⅰ是由近地层偏东暖湿气流在迎风坡与山风形成的辐合抬升触发;由辐射差异和前期强降水形成的局地冷池受MCS-Ⅰ影响再次加强后,其出流与环境风形成的两条地面辐合线分别触发了MCS-Ⅱ和MCS-Ⅲ,并组织对流沿辐合线呈带状发展;而超低空偏东风增强叠加冷池出流在地形抬升作用下促使沿山暖湿气团进一步抬升,使得原本消亡的MCS-Ⅰ再次重建。MCS-Ⅳ发展最旺盛、持续时间最长,是大暴雨中心的直接制造者,一方面MCS-Ⅱ与MCS-Ⅲ、MCS-Ⅰ与MCS-Ⅳ的两次合并过程,是MCS-Ⅳ增强、持久的重要原因;另一方面边界层偏东风急流为MCS-Ⅳ的发展提供了水汽和不稳定能量等有利条件,同时推动其左前方中尺度涡旋的发展,导致MCS-Ⅳ所在地的气旋性涡度大大增加,加强了以急流轴为中心的垂直次级环流发展,造成MCS-Ⅳ的发展维持,形成华北平原地区以雄安新区为中心的东西向大暴雨带。

Track of Grain in Forced Vortex with Horizontal Axis

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NUMERICAL INVESTIGATION OF THE MECHANISM OF ASYMMETRIC VORTEX FLOWS

A robust iterative method suitable for the numerical simulation of high angle-of-attack vortex flows is established based upon the multiple line-vortex model(MLVM).With symmetric or asymmetric positions of sep- aration lines given,the first converged solution at an angle of attack as high as 60 degree is obtained by means of the present method.Numerical experiments for a tangent-ogive forebody indicate the viscous onset mechanism of asymmetric vortex flows over a body of revolution at high angles of attack and zero sideslip.

Mechanisms governing the evolution of a long-lived northwest vortex that caused a series of disasters in Northwest China

西北涡是我国西北地区一类发生频率较高的中尺度涡旋,其所引发灾害的强度与西南低涡,高原涡相当,但相关研究却远远少于前两种涡旋.为了深化对西北涡的认识,本文利用水汽与环流收支对一次长生命史西北涡(其在西北地区引发了一系列暴雨过程,导致了严重的输电线路故障与城市内涝)进行了研究,发现,东海与渤海是此西北涡引发暴雨的主要水汽来源,东风与东南风则是主要的输送气流.辐合所引起的垂直伸展是西北涡发展的主导因子,而涡旋由较强背景涡度区向较弱背景涡度区的移动则一定程度上延缓了涡旋的发展.

Dynamics of vortex–antivortex pair in a superconducting thin strip with narrow slits

In the framework of phenomenological time-dependent Ginzburg-Landau（TDGL） formalism,the dynamical properties of vortex-antivortex（V-Av） pair in a superconductor film with a narrow slit was studied.The slit position and length can have a great impact not only on the vortex dynamical behavior but also the current-voltage（Ⅰ-Ⅴ） characteristics of the sample.Kinematic vortex lines can be predominated by the location of the slit.In the range of relatively low applied currents for a constant weak magnetic field,kinematic vortex line appears at right or left side of the slit by turns periodically.We found such single-side kinematic vortex line cannot lead to a jump in the Ⅰ-Ⅴ curve.At higher applied currents the phase-slip lines can be observed at left and right sides of the slit simultaneously.The competition between the vortex created at the lateral edge of the sample and the V-Av pair in the slit will result in three distinctly different scenarios of vortex dynamics depending on slit length：the lateral vortex penetrates the sample to annihilate the antivortex in the slit;the V-Av pair in the slit are driven off and expelled laterally;both the lateral vortex and the slit antivortex are depinned and driven together to annihilation in the halfway.

2021年吉林中部一次极端雷暴大风的中尺度成因分析

基于常规观测资料、地面加密自动气象观测站、多普勒天气雷达和ERA5再分析资料等,对2021年9月9日上午发生在吉林省中部一次罕见的极端雷暴大风的中尺度成因进行了详细分析。结果表明:产生雷暴大风的飑线系统是在深厚的东北冷涡配合大尺度锋生作用在冷锋尾部激发形成的。中层较强干空气和逆温层以下接近干绝热的温度递减率有利于极端雷暴大风产生。干暖盖的存在导致低层暖湿空气迅速增强,临近时刻CAPE值超过1600 J·kg~(-1),层结在短时间内变为极不稳定结构,夹卷层平均风达到20 m·s~(-1)以上,动量下传有利于地面风速增强,极端雷暴大风发生在断裂后飑线尾部前沿γ中尺度涡旋附近,但涡旋附近2个站点极端雷暴大风形成原因明显不同,其中农大站极端雷暴大风发生时气压陡降,气温陡升且分钟降水量弱,是由飑线前侧强下沉辐散气流(冷池出流)在较强的偏南风气流作用下加速流入涡旋内部、辐合上升气流迅速增强导致,与其附近农博园站和长春站由降水粒子拖曳作用形成的强下沉辐散气流导致的极端雷暴大风明显不同。

螺旋线对斜拉索涡激振动特性影响的试验研究

为研究不同参数的螺旋线对斜拉索涡激振动特性和气动力的影响规律,进行了针对表面无螺旋线斜拉索和缠绕不同参数螺旋线斜拉索的节段模型风洞试验,螺旋线参数包括根数、直径和缠绕间距.结果表明:斜拉索表面缠绕1根螺旋线的涡激振动振幅远大于2根或3根螺旋线;在亚临界雷诺数区,缠绕螺旋线斜拉索的平均气动阻力系数均小于无螺旋线斜拉索,最多可减小10.9%;缠绕2根螺旋线的斜拉索平均阻力系数整体比3根螺旋线小.斜拉索表面缠绕间距s=8D(D为斜拉索直径)的2根螺旋线时,缠绕直径d<15 mm螺旋线的斜拉索涡激振动现象明显;d≥15 mm的螺旋线可显著降低斜拉索涡激振动响应幅值,其脉动升力系数相较于无螺旋线斜拉索有明显降低,证明缠绕大直径螺旋线对涡激振动响应控制的有效性.螺旋线的缠绕间距对斜拉索涡激振动的影响与螺旋线直径有关,当螺旋线直径较小时,缠绕间距对涡激振动的影响并不明显;当螺旋线直径较大时,间距的大小直接影响涡激振动的抑制效果.

Large Eddy Simulation on Interaction Between in-Line and Cross-Flow Oscillation of A Circular Cylinder

This paper discusses numerical results from three-dimensional large eddy simulations of an oscillating cylinder under prescribed movements in uniform flow. Six cases, namely pure in-line, pure cross-flow and two groups of ＇Figure of Eight＇ oscillation patterns are under investigation at Reynolds number Re = 24000. The ＇ Figure of Eight＇ pattern in each group is with identical shape but oppusite orbital directions. The numerical results on hydrodynamic forces, higher order force components, and vortex shedding modes are extensively studied and compared with the measured experimental data. It is found that the fluid force in phase with the velocity, which represents the energy transfer between the fluid and the cylinder, has opposite sign and different magnitude due to the opposite orbital direction. Higher order force components in cross-flow direction are found to occur at odd nmnber times of the oscillating frequency, while even nmbers dominate the higher order force components in in-llne direction. The 2C and 2T vortex shedding modes are well reproduced due to the opposite orbital direction effect. Comparisons between numerical and experimental results indicate that the present numerical model could be a rational tool for the identification of hydrodynamic coefficients which are normally applied in empirical models to predict the vortex-induced vibrations of slender marine structures.

Exploration of the mechanism of cavitation vortex rope and vortex development in the draft tube of tubular turbine units

Draft tube vortex rope is considered a special cavitation flow phenomenon in tubular turbine units.Cavitation vortex rope is one of the most detrimental factors affecting the safety of hydraulic turbines.In this study,ANSYS CFX software was utilized to numerically simulate the internal cavitation flow of a hydraulic turbine draft tube.The evolution of the cavitation vortex core was characterized by vortex line distribution and vorticity transport equation.The shape and number of blades influenced the revolving direction and distribution characteristics of the vortex close to the runner cone,which formed a counterclockwise-clockwise-counterclockwise distribution pattern.Simultaneously,there were many secondary flows in the draft tube.Mutual cancellation and dissipation between the flows was one of the reasons for reduction in vorticity.When the cross-sectional shape of the draft tube was changed,the vorticity was distributed from the center of the vortex rope to all parts of the cross-sectional draft tube,with extreme values at the center and at the walls.The vortex stretching and dilatation terms played a major role in the change in vorticity,with the baroclinic torque having an effect at the center of the vortex rope,this study is helpful to understand the flow of water in the draft tube and guide the design and optimization of the draft tube in engineering application.

A modified-Liutex-based vortex-core-line extractor and its application

Vortices,which appear as swirling behaviour of a flow field,are an important phenomenon in fluid dynamics,and the extraction of vortex cores is necessary for the research of vortex evolution in many areas of fluid mechanics.The Liutex method is a milestone in vortex identification and provides a reasonable mathematical definition for a vortex core.Based on this definition,a novel integration-based method is presented,which can reduce the numerical error in the integration process through location optimization.Two typical test cases,the wake vortices of an A320 in the near-ground stage and a helicopter rotor,are examined to show that the proposed method can extract continuous vortex core lines with accuracy and efficiency for vortex parameter study.

水平轴风力机偏航与俯仰尾流特性

风力机的尾流干扰效应是影响风场下游风力机性能和风场出力的主要因素,通过调整风轮姿态可有效改善尾流干扰效应,但同时也引入了更为复杂的非定常气动特性和尾流场分布。为了研究风轮姿态控制的尾流特性,基于升力线和自由涡尾迹模型建立了水平轴风力机气动和尾流仿真模型,以NREL 5MW风力机为研究对象,在额定风速条件下,研究了叶轮偏航和俯仰工况下的尾流结构特性。在此基础上,对存在风切变和塔架影响时的风力机偏航和俯仰工况产生的尾流干扰进行了分析。研究结果表明:风轮的偏航和俯仰会引起尾流涡结构失稳提前、远尾流区湍流度增大,同时会导致尾流中心发生偏转和尾流作用区域减小,并加快速度亏损恢复,降低尾流效应对下游的干扰。风切变会产生类似风力机俯仰的效果,使得尾流抬升,作用区域减小。塔架对近尾流区的干扰较为显著,而俯仰控制会降低塔架对尾流的干扰。