Acceleration and ejection of interacting ring vortices by radial flow

Exact solution of two-dimensional hydrodynamic equations for symmetrical configuration of four point vortices in the presence of radial flow is found. This solution describes the dynamics of a dipole toroidal vortex (consisting of two counter-rotating vortex rings) in such a flow. It is shown that in a convergent flow the ring vortices are compressed and ejected with acceleration along the symmetry axes of the system. Possible application to the problem of jets formation in active galaxy nuclei is considered.     

Spectrum of the non-abelian phase in Kitaev’s honeycomb lattice model

The spectral properties of Kitaev’s honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the 2ⁿ-fold ground state degeneracy in the presence of 2n well separated vortices and the lifting of the degeneracy due to their short-range interactions. The calculations are performed on an infinite lattice. In addition to the analytic treatment, a numerical study of finite size systems is performed which is in exact agreement with the theoretical considerations. The general spectral properties of the non-abelian phase are considered for various finite toroidal systems.     

Exotic vortex structures of the dipolar Bose–Einstein condensates trapped in harmonic-like and toroidal potential

Based on the tunable intensity and waist of Gaussian laser, harmonic-like and toroidal potentials can be achieved and the ground-state properties of the dipolar Bose–Einstein condensate (BEC) trapped in such potentials are investigated. It is found that, in the harmonic-like potential, the singly and doubly quantized vortices can exist in the scale condensate and translate respectively into vortex pairs and triangular vortex lattice with increasing dipole–dipole interaction (DDI). Especially, the sandwich-like structure can be observed in the ground-state density profiles by tuning the direction and strength of DDI for some rotating frequency. In the toroidal potential, the competition between the inter-component interaction and DDI can induce the transition between immiscible and miscible states, and results in the structures of a doubly quantized vortex surrounded by a vortex ring. It is worth emphasizing that, with the increasing of DDI, the doubly quantized vortex in the harmonic-like potential becomes two singly quantized vortices, while in the toroidal potential it is no happen due to the presence of Gaussian barrier.     

Computer simulation of vortex self-maintenance and amplification

We consider a mechanism of the self-maintenance and amplification of vortices (tropical cyclones and toroidal vortices of various nature) on the basis of their common relationships. The results of numerical simulations show that the heat energy in these vortices is partially transformed into vortex rotational energy due to buoyancy and Coriolis forces.     

基于三角波瓣混合器的超声速流场精细结构和掺混特性

在超声速吸气式混合层风洞中,采用基于纳米粒子的平面激光散射(NPLS)技术对平板混合层和三角波瓣混合器诱导的混合层流场精细结构进行了对比实验研究.上下两层来流的实测马赫数分别为1.98和2.84,对流马赫数为0.2.NPLS图像清晰地展示了Kelvin-Helmholtz涡、流向涡、波系结构以及大尺度涡结构的配对合并过程.通过对比分析时间相关的NPLS流场图像,发现了大尺度拟序结构随时间发展演化的非定常特性.基于流动显示结果,采用分形维数和间歇因子指标对流场结构和混合特性进行了定量分析.实验研究表明,三角波瓣混合器诱导的流向涡结构显著提高了上下两层来流的掺混效率,其流动远场的分形维数突破了平板混合层中完全湍流区的分形维数值,达到了1.88,流场结构表现出明显的破碎性,有利于流动在标量层面的扩散和掺混.流动间歇性分析表明,流向涡与展向涡的相互剪切作用主导着混合层的掺混特性,同时由于流向涡的卷吸作用,三角波瓣混合器诱导的混合层混合区域更大,更多的流质被卷入混合区完成混合.     

Matched solutions of nonlinear forced equations and Rossby vortices

An analytical method for solving nonlinear equations with local forcing is proposed. It is shown in an example that a nonlinear forced equation may have many solutions, which generally do not turn to the solution of a linear equation in the limit of the nonlinear term becoming small. The solution of the Korteweg-de Vries (KdV) equation with forcing is applied to the problem of topographic Rossby vortices in shear flow. Solutions of other nonlinear equations with forcing are also obtained.     

谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的巨涡旋态

研究谐振子势与高斯势联合势阱中玻色爱因斯坦凝聚体的基态。发现凝聚体形成巨涡旋时,其涡旋个数等于平均角动量,且凝聚体密度分布和角动量密度分布相同,进而得到凝聚体形成巨涡旋时所处基态是角动量的本征态。发现势阱从各向同性的环形势阱逐渐变为各向异性的环形势阱的过程中,凝聚体的平均角动量与涡旋个数之比先由1平缓下降,然后迅速下降,最后保持在0.5附近。同时给出凝聚体密度分布和角动量分布的特征,并作出相应解释。     

激波冲击V形界面重气体导致的壁面与旋涡作用及其对湍流混合的影响

基于多组分混合物质量分数模型,采用色散最小耗散可控的高分辨率有限体积方法,数值模拟了弱激波冲击V形空气/SF_6界面后,界面不稳定性生成的旋涡与固体壁面作用问题.激波冲击V形界面之后,因斜压效应诱导涡量沉积在界面附近,形成沿界面规则排列的多个涡对结构.旋涡的诱导作用使界面不断变形和卷起,同时旋涡之间不断发生相互并对,诱导更多更小尺度的旋涡产生.旋涡诱导作用的叠加效应,使界面尖端处的初始涡对向上下壁面发展.随后,涡结构开始与壁面发生复杂的相互作用.旋涡与壁面作用后沿壁面加速,使得物质界面沿壁面伸展,随后,旋涡从壁面回弹,并诱导二次旋涡产生.旋涡与壁面相互作用的过程,能够明显加剧物质混合.本文从物质混合的角度研究了该过程的机理,分析了旋涡与壁面作用对物质混合的影响.     

Relativity of the metric

Although the form of the metric is invariant for arbitrary coordinate transformations, the magnitudes of the elements of the metric are not invariant. For Cartesian coordinates these elements are equal to one and are on the diagonal. Such a unitary metric can also apply to arbitrary coordinates, but only for a coordinate system inhabitant (CSI), to whom these coordinates would appear to be Cartesian. The meaning for a non-Euclidean metric consequently appears to be a simple coordinate system transformation for the appropriate CSI. The conversion of arbitrary coordinates to the flat Cartesian ones can be accomplished by a sequence of isomorphic mappings linking the arbitrary coordinates to the flat Cartesian ones. This is shown for two, three, and four-dimensional spaces. It is also applied to toroidal metrics and fluidfilled spaces for toroidal vortices that are discontinuous, half-wavelength, electromagnetic dipole field distributions. A number of other applications are discussed.     

Active control of coaxial jet mixing with manipulation of primary vortical structures by arrayed micro flap actuators

Active mixing control of a methane/air isothermal coaxial jet was achieved using micro magnetic flap actuators arranged on the inner surface of the outer annular nozzle. The spatio-temporal evolution of vortical structures and the scalar mixing were studied through the particle image velocimetry and planar laser-induced fluorescence methods. In contrast to studies on jet control using acoustic forcing, the mechanical movement of the flap directly generated large-scale intense vortices. The mixing was enhanced significantly by the vortices formed in the inner shear layer, although the control input was given to the outer shear layer. It was found that the primary vortex rings dominated the near-field mixing, while streamwise vortices were responsible for the downstream mixing. It was also demonstrated that the radial range of the inner fuel transportation could be manipulated flexibly by adjusting the shedding interval of the vortices. Especially, the mixing was enhanced most significantly when the primary vortices were most densely populated near the nozzle exit at the control Strouhal number of unity.     

脉冲激励下超音速混合层涡结构的演化机理

采用大涡模拟方法对脉冲激励作用下的超音速混合层流场进行数值模拟,所得结果清晰展示了流场中涡结构的独特生长机理.基于涡核位置提取方法,对超音速混合层流场中涡结构的空间尺寸和瞬时对流速度等动态特性进行了定量计算.通过分析流场中涡结构的动态特性在不同频率脉冲激励下的变化,揭示出受脉冲激励超音速混合层流场中涡结构的演化机理:涡结构的生长不再是依靠相邻涡-涡结构之间的配对与融合,而是通过涡核外围的一串小涡旋结构被依次吸进涡核来实现,且受激励流场中各个涡结构的空间尺寸变化较小;流场中的涡结构数量与脉冲频率成正比例关系,而涡结构的空间尺寸与脉冲频率成反比例关系;涡结构的平均对流速度随脉冲频率的增大而减小.针对受脉冲激励超音速混合层,给出了能够表征涡结构特性与脉冲激励参数之间关系的方程式,即受激励流场中涡结构的平均对流速度与脉冲周期的乘积近似等于流场中涡结构的空间尺寸(涡结构平均直径).     

Vortex ring energy variation in a homogeneous medium

The equation of energy variation of vortex rings (free toroidal vortices) in a homogeneous medium (air and water at atmospheric pressure and temperature ～293 K) depending on their initial parameters and medium was derived. It was shown that the solution to this equation is in agreement with experimental data.     

Vortex rings and plasma toroidal vortices in a homogeneous infinite medium. I. Maximum vortex path

The maximum path L _MAX of vortex rings (toroidal vortices) in air and water before the beginning of their decay was experimentally determined in a wide variation range of their initial integral characteristics. A formula for L _MAX was derived as a function of primary characteristics of such vortices from the laws of their motion and energy variation. It was shown that this formula is in satisfactory agreement with experimental data.     

Multipolar Structure of Equilibrium Shear Flow Field in Toroidal Plasmas

The multipolar velocity field structures are investigated by 2D momentum conservation equation with 3D equilibrium sheared flows in the full toroidal system. Numerical results show that the non-existence of radial velocity field in equilibrium surfaces is suitable only for the zero-order term of our 2D simulation. The non-zero-order radial velocity field is still preserved, even when converted to conventional magnetic surface coordinates. The distribution of velocity field vectors of the order of 1, 2, and 3 are presented respectively in 2, 4, and 6 polar fields with the local vortex structure. The excitation mechanisms of these velocity vortices are the coupling effects of the magneto-fluid structure patterns and the toroidal effects. These results can help us understand the complexity of core physics, the transverse transport across magnetic field by the radial plasma flow and the formation of velocity vortices.     

Structure of optical vortices

Helical modes of light can be focused into toroidal optical traps known as optical vortices, which are capable of localizing and applying torques to small volumes of matter. Measurements of optical vortices created with the dynamic holographic optical tweezer technique reveal an unsuspected dependence of their structure and angular momentum flux on their helicity. These measurements also provide evidence for a novel optical ratchet potential in practical optical vortices.     

Vortex rings and plasma toroidal vortices in homogeneous unbounded media. II. The study of vortex formation process

The conditions of the formation of toroidal vortices (TVs), i.e., the plasma TV and air vortex ring at atmospheric pressure, are experimentally determined. The TV formation process is numerically simulated. Local characteristics of the pulsed jet, induced flow of ambient medium (air), and forming TV at various time points are obtained. It is shown that the results of the preliminary numerical calculation are in agreement with experimental data.     

宽波段高分辨率小型紫外成像光谱仪光学系统研究

结合小型紫外光谱仪器设计原理对紫外成像光谱仪进行了研究。以离轴抛物镜为望远镜,超环面光栅为成像光谱系统设计了系统方案;该光学系统的优化设计就是对超环面光栅的参数设计。分析了光栅的光程函数和像差方程,总结了单超环面光栅结构的完善聚焦条件和完善成像条件;这两种条件无法在代数计算下得到完善代数解,限制了光谱仪的工作波段和视场,引入遗传算法解决了这个问题。以一工作波段为200~280 nm的日盲紫外成像光谱仪为例对设计理论进行验证,根据优化理论计算了初始结构最优解并进行光线追迹模拟,成功得到了F数为5.7,焦距为102 mm,全视场全波段调制传递函数值在奈奎斯特频率(20 lp·mm-1)下大于0.65的高分辨率成像光谱仪光学系统。设计结果表明这种光学系统设计理论适用于小型宽波段高分辨率紫外成像光谱仪。     

Stepwise coupled mode scattering of ambient noise by a cylindrically symmetric seamount

The question of how underwater ambient noise, at low frequencies, interacts with seamounts is addressed. The vertical directivity of the ambient noise, with and without the seamount interaction, is of particular interest. The problem of ambient noise scattering by seamounts motivates the development of a numerical modeling procedure, based on stepwise coupled modes. The procedure is designed to analyze scattering from a cylindrically symmetric seamount. The stepwise coupled mode procedure is extended to more general boundary conditions and brought up to date in the process. An example, using the geometry of the Dickins seamount, suggests that the seamount removes energy from the steeply traveling ambient noise, for this case. The energy is not converted into angles near the horizontal; the energy is lost through bottom interaction and attenuation.     

Pulsed axisymmetric ejection of a dense plasma into a gas. 2. Conditions for the formation and stability of a plasma toroidal vortex

This work continues our previous investigations on pulsed ejection of a dense plasma into a gas. The conditions for the formation of high-temperature (plasma) and low-temperature gaseous toroidal vortices during pulsed axisymmetric ejection of a dense plasma/gas into air are investigated experimentally at different parameters of the ambient medium and jet generator. Quantitative criteria for the formation and stable propagation of such vortices are established using experimental data.     

A Rotating Bose-Einstein Condensation in a Toroidal Trap

We have studied the ground state configurations of a rotating Bose-Einstein condensation in a toroidal trap as the radius of the central Gaussian potential expands adiabatically. Firstly, we observe that the vortices are devoured successively into the central hole of the condensate to form a giant vortex as the radius of the trap expands. When all the pre-existing vortices are absorbed, the angular momentum of the system still increase as the radius of the
gaussian potential enlarges. When increasing the interaction strength, we find that more singly quantized vortices are squeezed into the condensate, but the giant vortex does not change.