Vortical Structure of Turbulent Shear Flows Studied by Vortex Dynamics Simulation

1. 采用旋涡blob方法模拟具有圆角的方形旋涡环的演化过程，在此过程中旋涡丝的连连性不被明确保持，从而获得三维无粘旋涡运动的变形模式和动力学不变量真正守恒的程度。模拟结果表明，这些不变量在发生灾难性的增加之前是守恒的。发现动能是讨论不变量守恒的最严格的判据。灾变行为发生的时间随着涡团核心半径的增大和角曲率半径的增大而增大。得到了涡旋环拓扑结构的演化规律，并对其进行了讨论。对由两个半径相同的半圆连接的平行线段组成的伪椭圆涡环的变形进行了涡动力学模拟，其长、短轴比在2 ~ 20之间。变形随纵横比的变化有四种基本模式：周期性轴向切换；轴向切换后分裂成两个旋涡环；分裂成两个旋涡环而不切换轴；在不切换轴的情况下分裂成三个漩涡环。后两种模式预计将导致进一步的轴转换，并最终在更长的时间内分裂成两个漩涡环。流动可视化实验证实了这一点。通过对几个环形涡环相互作用的无粘涡动力学模拟，得到了具有部分Kolmogorov -5/3幂律的功率谱。等效于均匀湍流耗散谱的熵能谱在相同波数范围内具有1/3幂律的一部分。这项研究是第一个显示-5/3功率谱的研究之一，这是几个（而不是很多）旋涡环无粘性相互作用的结果。-5/3幂律的波数范围与涡环的数量及其初始构型有轻微的关系，涡环核心半径越小，波数范围越宽。高涡度区域的均匀分布似乎对-5/3幂律至关重要。无粘涡旋运动的总能量、总动量、总角动量、总螺旋度、总涡度等5个不变量在相对初始值的可容忍偏差范围内保持恒定，直至涡度趋于发散。采用涡团法对斜圆盘周围非定常分离流动进行了数值模拟，从圆盘边缘分离形成的圆形涡环出发，得到了三维涡结构的演化过程。从垂直于气流方向的平面涡度轮廓来看，模拟结果证实了旋涡尾迹的螺旋结构。少

1. Evolution of square vortex rings with rounded corners was simulated by a vortex blob method, in which the connectivity of vortex filaments is not explicitly maintained, to obtain patterns of deformation and the exetnt to which dynamical invariants of the three-dimensional inviscid vortex motion are really conserved. The simulation showed that the invariants were conserved until their catastrophic increase took place. The kinetic energy was found to serve as the most stringent criterion to discuss the conservation of the invariants. The time when the catastrophic bahavior appeared increased with increasing radius of core of the vortex blobs and with increasing radius of curvature of the corners. Evolution of topology of the vortex rings was obtained and discussed.2. A vortex dynamics simulation was made on the deformation of pseudoelliptical vortex rings which consists of two parallel line segments connected by two semicircles of the same radius, the major-to-minor axis ratio being b … More etween 2 and 20. The deformation had four fundamental patterns depending on the aspect ratio : the periodic axis switching ; the splitting into two vortex rings after the axix switching ; the splitting into two vortex rings without the axis switching ; the splitting into three vortex rings without the axis switching. The last two patterns are expected to lead to further axis switching and eventual splitting into two vortex rings at larer times. This was confirmed by a flow visualization experiment.3. An inviscid vortex dynamics simulation of interaction of several circular vortex rings produced the power spectrum which had a part of the Kolmogorov -5/3 power law. The enstrophy spectrum, which is equivalent to the dissipation spectrum in homogeneous turbulence, had a part of the 1/3 power law in the same wavenumber range. This study is among the first to show the -5/3 power spectrum as a result of the inviscid interaction of several, not many, vortex rings. The wavenumber range of the -5/3 power law slightly depends on the number of the vortex rings and their initial configuration, being wider for smaller radius of core of the vortex rings. A uniform distribution of high-vorticity regions appears to be essential to have the -5/3 power law. Five invariants of the inviscid vortical motion, i. e. The total energy, total momentum, total angular momentum, total helicity and total vorticity were maintained constant within tolerable deviations from the corresponding initial valves until vorticity tends to diverge.4. The unsteady separated flow around an inclined circular disk was simulated by the vortex blob method to obtain the evolution of three-dimensional vortical structures from circular vortex rings formed by the separation from the edge of the disk. A spiral structure of the vortical wake was confirmed by the simulation in terms of the vorticity contour in planes normal to the direction of the approaching flow. Less