赫姆霍兹对流体涡旋运动的开创性研究

着重讨论赫姆霍兹在特定的历史背景下,最先对流体涡旋运动进行研究并创建了流体涡旋理论,他所给出的涡线、涡丝等概念至今仍在流体力学中沿用,以他的名字命名的赫姆霍兹定理和赫姆霍兹速度分解定理更是流体涡旋理论中重要的基本定理,现代流体涡旋理论正是在他的研究基础上发展起来的,并进一步指出：赫姆霍兹的理论无论在物理上还是数学上都具有重要意义,而且对开尔等人后来的研究工作产生了重要影响。     

Topological Structure of Knotted Vortex Lines in Liquid Crystals

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 b-mapping topological current theory, we investigate the topological structure of the vortex lines in LCs in detail. A topological invariant, i.e., the Chern-Simons （CS） action for the knotted vortex lines is presented, and the CS action is shown to be the total sum of all the self-linking and linking numbers of the knot family. Moreover, it is pointed out that the CS action is preserved in the branch processes of the knotted vortex lines.     

圆柱尾迹涡的三维演化及结构特征

应用无粘涡丝运动学理论和局部诱导近似(LIA)方法,以Lagrange观点跟踪涡丝在背景流场中运动,用数值方法研究了中等Re数(≈10~3)下圆柱分离尾迹中Kármán涡和涡辫区涡丝的三维演化的机制和动力学过程,及其结构特征。背景流场考虑为尾迹时间平均速度流场和Kármán涡街流场。初始展向小扰动为指数形式和谐波形式。结果指出:Kármán涡和涡辫区中的涡丝具有展向不稳定性,形成流向涡量。在尾迹的初期输运过程中,表现出有序的大、小尺度涡结构。并进一步分析了其产生的机理。     

收缩螺旋涡线诱导速度的快速收敛法

给出了一种计算收缩涡线(桨尖涡和内部涡线)诱导速度所有组元的快速收敛方法,该方法是由Rand和Chiu的方法(计算螺旋涡线诱导速度快速收敛法)发展而来的,它以寻求上下界截断积分解析表达式为基础。其优点是能计算尾迹中任意一点的诱导速度,并且考虑了尾迹收缩。该方法不仅避免了离散涡线引起的截断误差。而且减小了沿有限方位角所产生的误差。     

Vortex Lines and Monopoles in Electrically Conducting Plasmas

Based on the φ-mapping topological current theory and the decomposition of gauge potential theory, the vortex lines and the monopoles in electrically conducting plasmas are studied. It is pointed out that these two topological structures respectively inhere in two-dimensional and three-dimensional topological currents, which can be derived from the same topological term n^→·（Эin^→×Эjn^→）, and both these topological structures axe characterized by the φ-mapping topological numbers-Hopf indices and Brouwer degrees. Furthermore, the spatial bifurcation of vortex lines and the generation and annihilation of monopoles are also discussed. At last, we point out that the Hopf invaxiant is a proper topological invaxiant to describe the knotted solitons.